Using the formula of margin of error for the confidence interval, the minimum sample size is 120
What is the minimum sample sizeWe can use the formula for the margin of error for a confidence interval:
margin of error = z* (standard deviation/√n)
where z* is the z-score for the desired confidence level.
For a 95% confidence interval, z* = 1.96. We want the margin of error to be 5, and we are given that the standard deviation of the population is 28. So we can solve for n:
5 = 1.96 * (28 / √n)
√n = 1.96 * 28 / 5
n = (1.96 * 28 / 5)²
n = 120.47
n = 120
The minimum sample size that will give a margin of error of 5 minutes with 95% confidence is 120.
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There is a positive correlation between the number of times the Striped Ground Cricket chirps per second and the temperature in degrees Fahrenheit. If a scatter plot is made with the number of chirps on the horizontal axis and the trend line is found to be y = 3x + 25, then what would you predict the number of chirps per second to be when the temperature is 55 degrees Fahrenheit?
10
43
190
The predicted number of chirps per second when the temperature is 55 degrees Fahrenheit is 190.
The temperature and the number of chirps per second are linearly related, as shown by the trend line equation y = 3x + 25, where x is the temperature in degrees Fahrenheit and y is the number of chirps per second.
We must enter x = 55 into the equation and find y in order to estimate the number of chirps per second at a temperature of 55 degrees Fahrenheit
y = 3x + 25
y = 3(55) + 25
y = 165 + 25
y = 190
190 chirps are therefore expected per second at a temperature of 55 degrees Fahrenheit. Therefore, the predicted number of chirps per second when the temperature is 55 degrees Fahrenheit is 190.
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Five men take 45 hours to build a wall. How long will it take 9 men working at the same pace to build the same wall?
Answer: 9 men will build the same wall in 25 hours.
Step-by-step explanation: 1 man will build the same wall in (45*5) hours
9 men will build the same wall in (45*5)/9 =25 hours
John goes out to lunch. The bill, before tax and tip, was 19.20. A sales tax of 6% was added on. John tipped 12% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest tenth
if the interior angle of quadrilateral angle of abcd are 3x,4x and the rest two angle are five times one of them find value of x and each of interior angle?please
Hence, in answering the stated question, we may say that 128.57 quadrilateral degrees is the angle C. D is equal to 171.42 degrees.
what is quadrilateral?A quadrilateral in geometry is a four-sided polygon with outer walls and four corners. The term comes from the Roman terms quadri and lead people to make bad (meaning "side"). A rectangle is a two-dimensional shape with sidewalls, four vertices, and four corners. Concave and convex surfaces are usually divided into two types. Trapezoids, parallelograms, rectangular, rhombuses, and squares are also subclasses of convex quadrilaterals. A rectangle is an a double form that has four straight sides. Parallelograms, trapezoids, triangles, kites, squares, etc rhombuses are examples of quadrilaterals.
The total of a quadrilateral's internal angles equals 360 degrees.
The four inner angles of the quadrilateral ABCD are denoted as follows:
A-angle = 3x
B angle = 4x
Angle C = 5(3x) = 15x (since it is 5 times angle A)
Angle D = 5(4x) = 20x (since angle B is five times larger).
3x + 4x + 15x + 20x = 42x is the sum of these four angles.
3x + 4x + 15x + 20x = 360
42x = 360
x = 8.57 (rounded to two places) (rounded to two places)
Angle A = 3x + 3(8.57) = 25.71°
Angle B = 4x + 4(8.57) = 34.28°
Angle C = 15x + 15(8.57) = 128.57
D = 20x = 20(8.57) = 171.42 degree angle
As a result, the quadrilateral's internal angles are:
A angle of 25.71 degrees
34.28 degrees is the angle B.
128.57 degrees is the angle C.
D is equal to 171.42 degrees.
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Solve for y Sy+x2 =x+8 x+8-x2 O A. y = 5 O B. y=x+8-x2 x²-x-8 5 O C. O D. y=x2-x-8
Solution for the variable 'y' is y = (x - x² + 8)/5
Solving an equation:To solve the following equation we need to isolate the variable 'y' this can be done by adding or subtracting the same integer on both sides
Similarly, multiply or divide with the same integer on both sides. Note that these adding subtractions, multiplying, or dividing don't change the condition of the equation.
Here we have
5y+x² = x+8
To solve the above equation we need to isolate 'y' as follows
=> 5y+x² = x+8
Subtract x² from both sides
=> 5y + x² - x² = x + 8
=> 5y = x - x²+ 8
Divide by '5' on both sides
=> 5y/5 = (x - x² + 8)/5
=> y = (x - x² + 8)/5
Therefore,
Solution for the variable 'y' is y = (x - x² + 8)/5
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Solve for 'y', 5y+x² = x+8
Under her cell phone plan, Ariana pays a flat cost of $43 per
month and $4 per gigabyte. She wants to keep her bill under
$60 per month. Which inequality can be used to determine g,
the maximum number of gigabytes Ariana can use while
staying within her budget?
57 stamps on 3 sheets = 76 stamps on how many sheets
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
She saw the letter K, and other letters Are X and Y
Step-by-step explanation:
The perimeter of the parallelogram shown is 20.5
cm.
What is the length of the parallelogram?
Responses
5
cm
5 cm
6.15
cm
6 point 1 5 cm
12.3
cm
12 point 3 cm
16.4
cm
The length οf the parallelοgram is 6.15 cm.
What is perimeter?The whοle length οf a shape's bοundary is referred tο in geοmetry as the perimeter οf the shape.
Adding the lengths οf all the sides and edges that surrοund a fοrm yields its perimeter. It is calculated using linear length units such centimetres, metres, inches, and feet.
Here the given Perimeter οf parallelοgram = 20.5 cm.
Side = 4.1 cm
Nοw perimeter οf parallelοgram = 2(a+b) unit
=> 20.5 = 2(a+4.1)
=> a+4.1 = 10.25
=> a = 10.25-4.1 = 6.15 cm.
Hence the length οf the parallelοgram is 6.15 cm.
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Hi, can you please help me with math, I think the exercises solving is probably with x and y.
Thank u very much:) 1. Two identical jars of cottage cheese and 3 buns of the same type cost 10 euros. A jar of cottage cheese is 2 euros more expensive than a bun. How much is a jar of cottage cheese and how much is a bun?
2. The sum of two numbers is 56 and the difference is 14. Find those numbers.
Again, Thank u!
Answer:
Step-by-step explanation:
a= first form a equation
lets call the cheese c and the buns b
2c+3b=10
c=2+b
3c+4b=12
now its a simultaneous equation
2c+3b=10 x3
3c+4b=12 x2
6c+9b=30
6c+8b=24
1b=6
b=6
now substitute it in to 2c+3b=10
2c+18=10
2c+-8
so c=$4
b= 56 difference 14
56/2=28
28-7
21
28+7=35
so the 2 numbers are 21 and 35
please help i give brainliest
The given story has a sampling type known as: voluntary response sampling.
What type of sampling was used?Voluntary response sampling: This is similar to a convenience sample but a voluntary response sample is mainly based on ease of access. Instead of the researcher choosing participants and directly contacting them, people volunteer themselves (e.g. by responding to a public online survey).
For example, a person being called in a radio show poll might have powerful opinions over a topic in any direction. In a voluntary random sample, chooses themselves by answering a common appeal. These samples are unreliable because they are bias, hence the result is usually biased.
In this question, Mrs. Finn is dissatisfied with the hotel and voluntarily gives a response based on her experience and as such it fits with the definition of voluntary response sampling.
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To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
On average, each customer will take advantage of 1.6 promotions next year by ordering goods that otherwise would not be purchased, assuming that overall customer behavior next year will be the same as last year.
What is probability?
The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
Without the accompanying table, we cannot give a precise answer, but we can explain how to find the expected number of promotions that each customer will take advantage of next year.
Let X be the random variable representing the number of promotions that prompted orders that would not have otherwise been made. The probabilities of X taking on different values can be represented by a probability mass function (PMF), denoted by p(x). The expected value or the mean of X, denoted by E(X), is given by:
E(X) = Σ [x * p(x)]
where the summation is taken over all possible values of X.
In this case, X can take on the values 0, 1, 2, 3, or 4, representing the number of promotions that prompted orders that would not have otherwise been made. We can use the probabilities from the table to calculate the expected value of X.
For example, if the probabilities of X taking on different values are given by:
p(0) = 0.2
p(1) = 0.3
p(2) = 0.25
p(3) = 0.15
p(4) = 0.1
then the expected value of X is:
E(X) = (0 * 0.2) + (1 * 0.3) + (2 * 0.25) + (3 * 0.15) + (4 * 0.1) = 1.6
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Complete question:
Tο examine the effectiveness οf its fοur annual advertising prοmοtiοns, a mail οrder cοmpany has sent a questiοnnaire tο each οf its custοmers, asking hοw many οf the previοus year's prοmοtiοns prοmpted οrders that wοuld nοt have οtherwise been made. The accοmpanying table lists the prοbabilities that were derived frοm the questiοnnaire, where X is the randοm variable representing the number οf prοmοtiοns that prοmpted οrders. If we assume that οverall custοmer behaviοr next year will be the same as last year, what is the expected number οf prοmοtiοns that each custοmer will take advantage οf next year by οrdering gοοds that οtherwise wοuld nοt be purchased?
X 0 1 2 3 4
P(X) 0.07 0.229 0.319 0.192 0.19
Expected value =
A previοus analysis οf histοrical recοrds fοund that the mean value οf οrders fοr prοmοtiοnal gοοds is 23 dοllars, with the cοmpany earning a grοss prοfit οf 25% οn each οrder. Calculate the expected value οf the prοfit cοntributiοn next year.
Expected value =
The fixed cοst οf cοnducting the fοur prοmοtiοns is estimated tο be 16000 dοllars with a variable cοst οf 4 dοllars per custοmer fοr mailing and handling cοsts. What is the minimum number οf custοmers required by the cοmpany in οrder tο cοver the cοst οf prοmοtiοns? (Rοund yοur answer up tο the next highest integer.)
Break even pοint =
Which function represents the inverse of the function f(x)=x^2+5
The function which represents the inverse of the function f(x)=[tex]x^2[/tex]+5 is [tex]f^{(-1)(x)}[/tex] = ±[tex]\sqrt{(x - 5)}[/tex].
To find the inverse of a function, we can follow the steps:
Step 1: Replace f(x) with y. So we have:
y = [tex]x^2[/tex] + 5
Step 2: Swap x and y in the equation obtained in step 1:
x = [tex]y^2[/tex] + 5
Step 3: Solve for y in the equation obtained in step 2:
x - 5 = [tex]y^2[/tex]
y = ±[tex]\sqrt{(x - 5)}[/tex]
Note that we need to include both the positive and negative square roots to get the complete inverse function. Therefore, the inverse function of f(x) = [tex]x^2[/tex] + 5 is:
[tex]f^{(-1)(x)}[/tex] = ±[tex]\sqrt{(x - 5)}[/tex]
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If f(x)=(4x−3)(2x−5), then: a. f(1)= b. f′(1)= c. f′′(1)= d. The values of x for which f(x)=0 are e. The values of x for which f′(x)=0 are Question Help: B Video B eBook D Post to forum
x for which f′(x) = 0 is 2.75.
Given f(x) = (4x - 3)(2x - 5)a. To determine the value of f(1)Substitute x = 1 in the given function.f(x) = (4x - 3)(2x - 5)f(1) = (4(1) - 3)(2(1) - 5)f(1) = (4 - 3)(2 - 5)f(1) = (1)(-3)f(1) = -3Therefore, the value of f(1) is -3.b. To determine the value of f′(1)We know that f'(x) = (d/dx) [(4x - 3)(2x - 5)]Differentiating the given function, we get f'(x) = 8x - 22Therefore, f′(1) = 8(1) - 22f′(1) = -14Therefore, the value of f′(1) is -14.c. To determine the value of f′′(1)Differentiating the above function again, we getf''(x) = d/dx(8x - 22)f''(x) = 8Therefore, f′′(1) = 8Therefore, the value of f′′(1) is 8.d. To determine the values of x for which f(x) = 0Substitute f(x) = 0, we get(4x - 3)(2x - 5) = 0Either 4x - 3 = 0 or 2x - 5 = 0x = 3/4 or x = 5/2Therefore, the values of x for which f(x) = 0 are 3/4 and 5/2.e. To determine the values of x for which f′(x) = 0We know that f'(x) = 8x - 22For f'(x) to be 0, 8x - 22 = 0 or 8x = 22x = 22/8 = 2.75Therefore, the value of x for which f′(x) = 0 is 2.75.
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5. Amelia plays basketball for her high school. She wants to improve to play at the college level.
She notices that the number of points she scores in a game goes up in response to the number of
hours she practices her jump shot each week. She records the following data: (Data in the table
from OpenStax College, Introductory Statistics, 2013. Download for free at
http://cnx.org/content/coll1562/latest/.)
x (hours
practicing
jump shot)
y (points
scored in a
game)
Use your calculator to determine the linear regression equation and the correlation coefficient for
this data.
Equation: y
=
Correlation Coefficient: r=
5
15
7
22
9
10
11
28 31 33
(round to the nearest thousandth)
What does the correlation coefficient tell you about your data?
12
(round to the nearest hundredth)
36
pls help.
WILL GIVE BRAINLIESY
Equation= y = 2.63x + 2.37, r = 0.994, The correlation coefficient tells us about the strength and direction of the linear relationship between the two variables.
Describe Linear Regression?Linear regression is a statistical method used to analyze the relationship between two quantitative variables, often referred to as the dependent variable and the independent variable. The goal of linear regression is to find a straight line (or linear function) that best fits the data points in a scatter plot, representing the relationship between the two variables.
In linear regression, the dependent variable is modeled as a function of one or more independent variables. The equation for a simple linear regression model is typically written as:
y = β0 + β1x + ε
where y is the dependent variable, x is the independent variable, β0 and β1 are the intercept and slope coefficients, respectively, and ε is the error term, representing the variability in the data that cannot be explained by the model.
Using a calculator to perform linear regression on the given data, we obtain the equation:
y = 2.63x + 2.37
The correlation coefficient for this data is:
r = 0.994
The correlation coefficient tells us about the strength and direction of the linear relationship between the two variables. In this case, the correlation coefficient is close to 1, indicating a strong positive linear relationship between the number of hours practicing the jump shot and the number of points scored in a game. This means that as the number of hours practicing the jump shot increases, the number of points scored in a game also increases. The value of r also tells us that the linear regression equation is a good fit for the data, with very little variation around the line of best fit. Overall, this suggests that practicing the jump shot is an effective way for Amelia to improve her basketball performance.
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What is the equation of the circle below?
The equation of the circle in the picture is
C. (x - 2)² (y + 1)² = 9How to determine the equation the circleInformation given in the question
center at the point (2, -1)
radius = 3
The equation of a circle with radius given as 3 is solved as below
Equation of a circle is given as
(x - h)² (y - k)² = r²
where h and k refers to points at the center, substituting the values gives
(x - 2)² (y - (-1))² = 3²
(x - 2)² (y + 1)² = 3²
(x - 2)² (y + 1)² = 9
hence option C represents the equation of the circle
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You fly a kite using a 7-meter string. The angle of elevation from your hands to the kite is 54°. Your hands are 1.5 meters above the ground. How far above the ground, in meters, is the kite? Round to the nearest hundredth of a meter.
Answer:
7.16 (in meters)
Step-by-step explanation:
Notice the drawing.
The total height from the ground is given by h+1.5
To find h you need to use the right triangle, since you need the opposite side,
[tex]h=7sin(54)[/tex]
so total height is
[tex]H=1.5+7sin(54)[/tex]
be carefull your calculator is set to DEGREES
the answer is:
H = 7.16m rounded to nearest hundredth
1. An amount ofP200,000is deposited for a period of 8 years. Compute the interest if it was made at a simple interest rate of18%. 2. Calculate the exact interest on an investment ofP2,000for a period from January 30 to September 15,2001 , if the rate of interest is10%. 3. A bank charges12%simple interest on aP300loan. How much will he repay if the loan is paid back in one lump sum after three years? 4. If you borrow money from your friend with simple interest of12%, find the present worth ofP20,000which is due at the end of nine months? 5. An engineer borrowed a sum of money under the following terms: P650,000 if paid in 90 days, orP600,000if paid in 30 days. What is the equivalent annual rate of simple interest? 6. Fifteen million pesos was invested in a software company on June 3,2009, at12%ordinary simple interest rate. Determine the date at which the investment would equal P19.5M. 7. A man invested part ofP20,000at18%and the rest at16%. The annual income from16%investment was P620 less than three times the annual income from18%investment. How much did he invest at18%? 8. What is the present worth ofP54,000due in five years if money is worth11%and is compounded semi - annually? 9. A bank offers1.2%per month. What is the effective interest rate if compounded monthly? 10. A commercial bank charges2%interest per month on the unpaid balance of loans made by its credit card subscribers. It claims that the annual interest applied is 12 (2\%)=24%. Is this true? 11. Compute the number of years whenP2,500is compounded toP5,800if invested at12%compounded quarterly. 12. A nominal interest of3%compounded continuously is given on the account. What is the accumulated amount ofP10,000after 10 years? 13. An amount ofP200,000is deposited for a period of 8 years. Compute the interest if a) it was made18%compounded bi - monthly; b) it was made at18%compounded continuously. 14. Two years ago,Ms.ABCdepositedP30,000in a fund that earns10%interest compounded semi - annually. If another deposit ofP20,000is made today, determine the accumulated amount in the fund after three years. 15. Three years ago, an engineer opened a savings account with an initial deposit of P200,000. He withdrew P50,000 three months later, and another P50,000 six months after the first withdrawal. Last year, he deposited P100,000 and withdrew P150,000 six months later. Find the account balance today if interest is10%compounded quarterly.
Simple Interest(SI) is calculated as $288,000 where principal is $200,000, interest rate is 18% and type is 8 year.
What is Simple Interest?The Simple Interest (S.I.) formula is a way to figure out how much interest will pay on a given principle sum of money. It is the cost of borrowing that is computed using the original principle amount alone and a constant interest rate.
Formula of Simple Interest is,
[tex]SI = \frac{P*R*T}{100}\ or\ Simply\ write\ SI = P*R*T[/tex]
[tex]Where, P = Principal,\\R= Rate\ of\ Interest\\T = Time\ Period[/tex]
⇒ [tex]SI = \frac{20000*18*8}{100}\ or\ SI = 200000*0.18*8[/tex]
⇒ [tex]SI = \$\ 288000[/tex]
Simple Interest(SI) is calculated as $288,000 where principal is $200000, interest rate is 18% and type is 8 year.
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1. Simple Interest = 288000
2. Interest = 135
3. Total amount to be paid = $408
4. PV or present value = $18348.62
5. r = 51%
7. Amount invested in 18% is $3,685.714
8. 48 930.00.
9. EAR = 14.4%
10. 26.8% per year
12. ~P13439
13. SI = 288000
15. the account balance today if interest is 10 % compounded quarterly.
How to calculate Simple interest?1. Formula of simple interest is,
SI = P*R*T/100 or
Simply write SI = P*R*T
Where,
P = Principal
R = Rate of interest
T = Time period
SI = 20000*18*8/100 or
SI = 200000*0.18*8
SI = 288000
2. Interest = Principal*Interest
rate*time
Principal = 2000
Interest rate = 10%
Time = January 30, 2001 to September 2001
Interest = 135
(2000*10%*243/360)
Assume 360 days in a year in days counting include the day counting start from and exclude the day counting ends on.
3. Total Interest 3 Years = 300*12%*3 = 108
Total Amount Repaid = 300 + 108 = $408
Total amount to be paid = 300+(300*12%*3)
=$408
4. Given , we need to find the present worth of $20,000 at 12% interest rate per year which is due at the end of 9 months.
Therefore, FV i.e , future value = $20,000
i = rate of interest per year = 12% = 0.12
t or Time =9 months = 9/12 year ( in terms of years)
We know , FV = PV + PV * r * t
=> 20000 = P + P * (0.12) * (9/12)
PV or present value = 18348.62 = $18348.62
5. FV = Principal (1 + rate of interest per period * number of interest period)
Equation-1:
650,000 = Principal (1 + rate of interest per period * 90 days / 360 days)
650,000 = Principal (1 + 0.25 rate of interest per period)
Principal = 650,000 / (1 + 0.25 rate of interest per period)
Equation-2:
600,000 = Principal (1 + rate of interest per period * 30 days / 360 days)
600,000 = Principal (1 + 0.08 rate of interest per period)
Principal = 600,000 / (1 + 0.08 rate of interest per period)
Equating the equations we get:
650,000 / (1 + 0.25r) = 600,000 / (1 + 0.08r)
650,000 (1 + 0.08r) = 600,000 (1 + 0.25r)
650,000 + 52,000r = 600,000 + 150,000r
50,000 = 98,000r
r = 51%
7. Annual return from 18% = 3 * (Annual return from 16%)
Let Investment made in 18% = K
Return from 16% = P620 is less than triple the yearly income from 18%, at P620.
(20,000 - K) * 16% = [3 * (K* 18%)] - 620
3,200 - 0.16K = 0.54 K - 620
2,580 = 0.70 K
K = $3,685.714
So, Amount invested in 18% is $3,685.714
9. EMR = effective monthly rate
EMR = EAR/12
12*EMR = EAR
EAR = 12*EMR
The EMR is given to be 1.2% = 0.012, so the EAR is,
EAR = 12*EMR
EAR = 12*(0.012)
EAR = 0.144
EAR = 14.4%
10. No.
It's [tex]1.02^{12}[/tex] =~ 1.268
26.8% per year
12. [tex]F=A(1+3\%)^{10}[/tex]
A = P10,000
[tex]F=10,000(1+3\%)^{10}[/tex]
~P13439
According to the final value formula of compound interest.
13. Formula of simple interest is,
SI = P*R*T/100 or
Simply write SI = P*R*T
Where,
P = Principal
R = Rate of interest
T = Time period
SI = 20000*18*8/100 or
SI = 200000*0.18*8
SI = 288000
15.
An engineer established a savings account three years ago with a P 200,000 opening deposit.
Three months later, he removed P50,000, and six months after that, P50,000 more.
He made an investment of P100,000 and a withdrawal of P150,000 six months later last year.
If interest is compounded quarterly at 10%, find the amount of the account right now.
The table has been attached.
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there are 8 teams in 5a west conference. how many different orders
of finish are there for these 8 teams?
There are 40,320 different orders of finish for the 8 teams in 5A West Conference.
The number of different orders of finish for the 8 teams in 5A West Conference can be calculated using the formula for permutations. The formula for permutations is n!/(n-r)! where n is the total number of items and r is the number of items being arranged.For this problem, there are 8 teams and all of them must be arranged in a specific order. Therefore, we need to calculate the permutation of all 8 teams.Using the permutation formula, we have:n!/(n-r)! = 8!/(8-8)! = 8!/(0!) = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, there are 40,320 different orders of finish for the 8 teams in 5A West Conference.
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If the middle point of two points A(-2, 5) and B(-5, y) is (2−7,3), then find the distance between points A and B.
If the middle point of two points A(-2, 5) and B(-5, y) is (2−7,3), then the distance between points A and B is 10.67 (rounded to two decimal places).
If the middle point of two points A(-2, 5) and B(-5, y) is (2−7,3), then we have two unknowns. We will have to use the distance formula to solve the question. Distance Formula: The distance formula is a formula that is used to calculate the distance between two points in a plane. The formula is given as follows: d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Now let's find the missing coordinate value. We will substitute the coordinates of point B in the equation as follows:(-2-5)/2 = -3.5y = -6 - 7 = -13
Now we can find the distance between points A and B by substituting their respective coordinates in the distance formula:d = √[(-5 - (-2))² + (-13 - 5)²]d = √[(-3)² + (-18)²]d = √(9 + 324)d = √333d = 10.67
Therefore, the distance between points A and B is 10.67 (rounded to two decimal places).
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Determine the volume of the tin in cubic meter. Hint volume of the tin is determined by multiplying the area of the base by the height of the tin
The volume of the tin in cubic meter is equal to 785 cubic meter.
How to calculate the volume of a cylinder?Mathematically, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Assuming the radius of the base is 5 cm and the height of this tin is 10 cm, the volume of the tin in cubic meter can be calculated as follows;
Volume of a cylinder, V = 3.14 × 5² × 10
Volume of a cylinder, V = 3.14 × 250
Volume of a cylinder, V = 785 cubic meter.
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The money Mr. Jarod earns, m, varies directly with the number of haircuts he gives, h. He earns $15 for
five haircuts. Which equation represents his earnings for the job?
1: m = 3h
2: m = h
3: m = 15h
4: m = 5h
The equation that represents Mr. Jarod's earnings for the job is option 3: m = 15h.
The problem states that Mr. Jarod's earnings vary directly with the number of haircuts he gives. This means that as the number of haircuts increases, his earnings also increase by a constant factor. We can represent this relationship using a proportionality constant, k.
m ∝ h
We can rewrite this proportionality using an equation:
m = kh
We can find the value of k by using the given information that Mr. Jarod earns $15 for five haircuts.
15 = k(5)
k = 3
Now we can substitute this value of k in the equation:
m = 3h
However, this is not the answer we are looking for. We want an equation that represents Mr. Jarod's earnings in terms of the number of haircuts, h. We can rearrange the equation to solve for m:
m = kh = 3h
Therefore, the equation that represents Mr. Jarod's earnings for the job is option 3: m = 15h.-
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Three students, Nicole, Xavier, and Avani, line up one behind the other. How many different ways can they stand in line?
By factorial, 6 is different ways can they stand in line.
What does the arithmetic term factorial mean?
Factorial is a mathematical term that refers to the sum of all positive integers that are less than or equal to a particular positive integer and are symbolized by that positive integer plus an exclamation point.
As a result, factorial seven is denoted by the symbol 7!, which stands for 1 2 3 4 5 6 7. Factorial zero is equivalent to one.
Three students, Nicole, Xavier, and Avani line up one behind the other.
The different ways they can stand in line = 3!
= 3 * 2 * 1
= 6
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Which graph represents the solution of y ≤ x2 + 2?
Which graph represents the solution of y ≤ x2 + 2?
upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading inside parabola
- upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading outside parabola
- upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading inside parabola
- upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading outside parabola
The solid curve shows that the points on the curve are part of the inequality solution set, and the shade inside the parabola indicates that the points below the curve are part of the solution set as well.
What is inequality?In mathematics, an inequality is a connection that is not equal between two expressions or values. Consequently, imbalance leads to inequity. In mathematics, an inequality connects two unrelated values. Inequality is separate from equality. When two values are not equal, the not equal sign is most usually used (). Various inequalities are employed to contrast values, no matter how little or huge. Many basic inequalities may be solved by altering the two sides until the variables are all that remain. Yet, a variety of factors contribute to inequality: Negative values on both sides are split or added. Trade off the left and right.
The upward opening parabola constructed with a solid curve, vertex at (0, 2), and shading inside the parabola indicates the solution of y x2 + 2. This is due to the fact that the inequality y x2 + 2 reflects all of the points (x, y) that are either on or below the curve y = x2 + 2. The solid curve shows that the points on the curve are part of the solution set, and the shade inside the parabola indicates that the points below the curve are part of the solution set as well.
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The governor of state A earns $49,070 more than the governor of state B. If the total of their salaries is $291,120, find the salaries of each.
Answer:
Let's call the salary of the governor of state B "x".
According to the problem, the governor of state A earns $49,070 more than the governor of state B. So the salary of the governor of state A can be expressed as "x + 49,070".
We also know that the total of their salaries is $291,120, so we can set up an equation:
x + (x + 49,070) = 291,120
Simplifying the equation, we can combine like terms:
2x + 49,070 = 291,120
Subtracting 49,070 from both sides:
2x = 242,050
Dividing by 2:
x = 121,025
So the salary of the governor of state B is $121,025.
To find the salary of the governor of state A, we can use the expression we came up with earlier:
x + 49,070
121,025 + 49,070 = 170,095
So the salary of the governor of state A is $170,095.
Patricio deposit $500 in a savings account theat pays 1. 5% simple interest. He does not withdraw any money from the account, and he makes no other deposit. How much money does Patricio have in the savings account after 5 years?
Accοrding tο simple interest, Patriciο will have $537.50 in his savings accοunt after 5 years.
Tο calculate the amοunt οf mοney Patriciο will have in his savings accοunt after 5 years, we can use the fοrmula fοr simple interest, which is I = prt.
Patriciο has $537.50 in the savings accοunt after 5 years.
The fοrmula fοr calculating simple interest is:
I = P * r * t
where I is the interest earned, P is the principal (initial amοunt), r is the interest rate, and t is the time (in years).
Using this fοrmula, we can calculate the interest earned by Patriciο οver 5 years:
I = 500 * 0.015 * 5 = $37.50
The tοtal amοunt οf mοney Patriciο has in the savings accοunt after 5 years is:
A = P + I = 500 + 37.50 = $537.50
Therefοre, Patriciο has $537.50 in the savings accοunt after 5 years.
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What is the location of on the decimal number line below?
Write your answer as a decimal.
Answer:
7.72
Step-by-step explanation:
Answer:
Step-by-step explanation:
in the number line it shows 7.7 ,7.8 and 7.9
that just mean it's 7.71
so the answer is 7.72
therefore A=7.72
What is the perimeter of a regular hexagon with area of 96 square ruut to 3cm square
the perimeter of the regular hexagon is 48 cm.
A regular hexagon is a polygon with six sides, and each side has the same length. The formula to calculate the perimeter of a regular hexagon is given as:
Perimeter = 6 × length of one side
To find the length of one side of the hexagon, we need to use the given information about the area. The formula for the area of a regular hexagon is given as:
Area = (3 × √3 × s^2)/2, where s is the length of one side of the hexagon.
We can use this formula to solve for the length of one side:
96 √3 = (3 × √3 × s^2)/2
Simplifying this equation, we get:
s^2 = (2 × 96 √3)/(3 × √3)
s^2 = 64
s = 8 cm
Now that we know the length of one side of the hexagon, we can use the formula for perimeter to find the total perimeter:
Perimeter = 6 × 8 cm
Perimeter = 48 cm
Therefore, the perimeter of the regular hexagon is 48 cm.
In a regular hexagon, all six angles are equal, each measuring 120 degrees. It is a symmetrical shape, meaning that it has six lines of symmetry. The regular hexagon is a common shape in nature and architecture, and it is often used in geometry problems because of its regularity and symmetry. The hexagon is also the basis for the hexagonal lattice structure, which is a common pattern in crystals and other materials.
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Angles θ and φ are angles in standard position such that:
sinθ = -3/5 and θ terminates in Quadrant III
tanφ = -7/24 and φ terminates in Quadrant II
Find sin(θ + φ)
sin(θ + φ) = 4/5.Using the sum identity for sine, we can find sin(θ + φ) in terms of sinθ, sinφ, cosθ, and cosφ:
sin(θ + φ) = sinθ cosφ + cosθ sinφ
We are given that sinθ = -3/5 and θ terminates in Quadrant III, which means that cosine is negative. Using the Pythagorean identity, we can solve for cosθ:
cosθ = √(1 - sin²(θ))
= -√(1 - (-3/5)²)
= -4/5
We are also given that tanφ = -7/24 and φ terminates in Quadrant II, which means that sine is positive and cosine is negative. Using the Pythagorean identity, we can solve for sinφ and cosφ:
tanφ = sinφ/cosφ = -7/24
sinφ = -7/√(7² + 24²) = -7/25
cosφ = -24/√(7² + 24²) = -24/25
Now we can substitute the values of sinθ, sinφ, cosθ, and cosφ into the formula for sin(θ + φ):
sin(θ + φ) = sinθ cosφ + cosθ sinφ
= (-3/5)(-24/25) + (-4/5)(-7/25)
= 72/125 + 28/125
= 100/125
= 4/5
Therefore, sin(θ + φ) = 4/5.
In LaTeX form, the equation for sin(θ + φ) is:
sin(θ + φ) = sinθ cosφ + cosθ sinφ
where sinθ = -3/5, cosθ = -4/5, sinφ = -7/25, and cosφ = -24/25.
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julia, who is 1.60 m. tall, wishes to find the height of a tree with a shadow 32.84 m. long. she walks 22.78 m. from the base of the tree along the shadow of the tree until her head is in a position where the tip of her shadow exactly overlaps the end of the tree top's shadow. how tall is the tree? round to the nearest hundredth.
The height of the tree is 8.84 m, rounded to the nearest hundredth.
Julia can use the ratio of the length of the shadows of the two objects (herself and the tree) to determine the height of the tree. To do this, first measure the length of her shadow and the length of the tree's shadow, which are 1.60 m and 32.84 m respectively.
Next, she needs to measure the distance from the base of the tree along the tree's shadow to the point where her shadow exactly overlaps the end of the tree top's shadow. In this case, it is 22.78 m.
Finally, she needs to use the following formula:
Height of tree = (Length of tree shadow x Height of person)/Length of person's shadow
Plugging in the values, we get:
Height of tree = (32.84 m x 1.60 m) / 22.78 m = 8.84 m
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