From the given data, we can see that only one condition is violated, which is the sample size being less than 10% of the population size. The other conditions, such as the population distribution being approximately normal, np > 10, and n(1-p) > 10, are all satisfied. Therefore, the statement "more than one condition is violated" is incorrect.
Only one condition is violated in the given data, which is the sample size being less than 10% of the population size. The other conditions are all satisfied and do not violate any of the conditions for a representative sample.
It is important to note that in order for a sample to be representative of the population, the sample size should be at least 10% of the population size. If the sample size is less than 10% of the population size, the sample may not accurately represent the population and the results may be biased.
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Simplifying positive expressions in multiplication.
Simplify.
(-2b^4a)^5
Write your answer without parentheses.
Answer:
_2⁵b⁴*⁵a⁵
Answer=_32b²⁰a⁵
Liz spent her summer break working at Wild Lakes waterpark. At the end of the summer, she put $570 of her earnings into a savings account that earns 1% interest each year.
The total simple interest earned by Liz at the end of 5 years is found as: $28.5
Explain about the simple interest?A straightforward but effective idea. Very simply: interest is the benefit for saving - and the penalty of borrowing.
When you deposit funds into a savings account, you are paid interest, or additional money on top. The reason for this is that the bank gives you interest for letting them use your money.When someone owes money, they are assessed this fee. It indicates the time worth of money and is charged in relation to the principal sum. It is the prize for holding out and refusing to accept an early reward.Principal P = $570
Interest r = 1%
Time t = 5 years.
SI = P*R*t / 100
SI = 570*1*5 / 100
SI = 28.5
Thus, the total simple interest earned by Liz at the end of 5 years is found as: $28.5.
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The complete question is-
Liz spent her summer break working at Wild Lakes waterpark. At the end of the summer, she put $570 of her earnings into a savings account that earns 1% interest each year. Find her simple interest after 5 years.
If c is 6x6 and the equation cx = v is consistent for every v in r^6, is it possible that for some v, the equation cx = v has more than one solution?
It is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.
What is the inverse?Inverse οperatiοns are οppοsite οperatiοns that undο each οther. Fοr example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse οperatiοns.
If the equatiοn cx = v is cοnsistent fοr every v in R⁶, it means that the matrix c is invertible, οr has a unique sοlutiοn fοr every v.
This is because if c is nοt invertible, then there exist sοme vectοrs v in R⁶ fοr which the equatiοn cx = v has nο sοlutiοn οr has infinitely many sοlutiοns.
If c is invertible, then fοr any vectοr v in R⁶, the equatiοn cx = v has a unique sοlutiοn given by
[tex]x = c^{( 1 )} v[/tex], where [tex]c^{(1)}v[/tex]
is the inverse οf c.
Therefοre, it is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.
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A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to the bike. 34% of the bikes sold have both
features. What is the probability that a randomly selected bicycle will have a kickstand or a water bottle holder?
Hurry
The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%, calculated by adding the probabilities of each component being present and subtracting the probability of both being present.
The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%. To calculate this, we first need to consider the probability that a bicycle has a water bottle holder, which is 60%. The probability that the bicycle has a kickstand is 55%. Then, the probability of a bicycle having both a kickstand and a water bottle holder together is the product of the individual probabilities, which is 34%. Thus, the probability that a randomly selected bicycle will have either a water bottle holder or a kickstand is 60% + 55% - 34% = 95%.
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Noah wants to share a certain amount of money with 10 people. However,at the last minute,he is thinking about decreasing the amount by 20 so he can keep 20 for himself and share the money with only 5 people. How much money is Noah trying to share if each person still gets the same
amount
The money is Noah wants to share with people if each person still gets the same amount is 4.
Explain about the substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method.
The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.It is only useful if the change of variable explains the situation and, ideally, makes it possible to solve the problem once it has been simplified. First, considering a situation in which variables exist, a substitution is simply a change of variable.Let the total amount Noah have be'y'.
The initial amount shared by Noah among 10 people be 'x'.
Then,
y = 10x
But,
Amount shared is decreased by 20, ans sharing with 5 people.
Then,
y - 20 = 5x
Put value of y.
10x = 5x + 20
On solving;
x = 20/5
x = 4
Thus, money is Noah wants to share with people if each person still gets the same amount is 4.
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I have 1,792 Pokémon cards, I also have 7 friends. I want to split the cards between me and the 7 of them. How many cards should each person get? Does the answer of this question has a remainder? Solve and Explain how you got your answer
We can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.
To split the 1,792 Pokémon cards equally between 8 people, including yourself and your 7 friends, you need to divide the total number of cards by the number of people:
1,792 cards ÷ 8 people = 224 cards per person.
So each person should get 224 Pokémon cards.
However, we should also check if there is a remainder after the division. To do that, we can multiply the number of cards each person is getting by the number of people and subtract it from the total number of cards:
224 cards/person x 8 people = 1,792 cards
1,792 cards - 1,792 cards = 0 remainder
Since there is no remainder, we can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.
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Productivity for a small country was 25 units per worker hour in 2011. Productivity increased 20 percent between 2011 and 2016. What was the productivity figure for 2016? If the rate of increase is maintained, what will the figure be in 2021? In 2026?
Answer:
525 units
Step-by-step explanation:
firsat find a 1% increase
25/100 = 0.25
multiply this by 20 (per 5 years) and add to the original amount
0.25 x 20 = 500
500+25 = 525
This is your answer, and you just repeat this process for each year
PLS HELP ME QUICK!!!
Relation 2 and 3 are actual functions with proper domain, co domain, range.
Describe Function?A function can be represented in several ways, including using algebraic expressions, tables, graphs, or even words. For example, the function f(x) = 2x + 1 defines a relationship between the input x and the output 2x + 1. If we input x = 3 into this function, the output would be f(3) = 2(3) + 1 = 7.
Functions can have different properties, such as being continuous or discontinuous, being differentiable or nondifferentiable, or having maximum or minimum values. Functions can also be classified according to their types, such as linear, quadratic, exponential, logarithmic, trigonometric, or piecewise-defined functions.
Functions are used extensively in mathematics, science, engineering, economics, and many other fields to describe real-world phenomena and to solve practical problems. They are also studied in their own right, as objects of mathematical interest and beauty, with deep connections to many other areas of mathematics, such as calculus, analysis, and algebra
Relation 2 and 3 are actual functions with proper domain, co domain, range.
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X-intercept:
y-intercept:
y
1
9
8
7
6
5
NO 10
4
3
2-
1
x
-9-8-7 -6 -5 -4 -3 -2
1
2 3 4 5 6 7 8 9
CON
-2
-3
-4
-5
-6
-7
-8
-9
Answer: diffrent form so i can help you better
Step-by-step explanation:
The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. a juice box is selected at random. what is the probability of the complement of choosing an orange juice box?
a. startfraction 1 over 18 endfraction
b. startfraction 4 over 9 endfraction
c. startfraction 5 over 9 endfraction
d. startfraction 17 over 18 endfraction
The probability of the complement of choosing an orange juice box is 17/18. (option d)
The complement of an event is the probability of that event not occurring. In this case, the event is choosing an orange juice box, so the complement is choosing any other juice box (i.e., an apple juice box or a fruit punch juice box).
The total number of juice boxes in the cooler is:
4 + 8 + 6 = 18
The number of juice boxes that are not orange juice boxes is:
4 + 6 = 10
Therefore, the probability of choosing a juice box that is not an orange juice box (i.e., the complement of choosing an orange juice box) is:
10/18 = 5/9
But the question asks for the probability of the complement, which is the probability of not choosing a juice box that is not an orange juice box. This is simply:
1 - 5/9 = 4/9
However, the question asks for the probability of the complement of choosing an orange juice box, not the complement of not choosing an orange juice box. These two probabilities are equal, since the event and its complement always add up to 1. Therefore, the probability of the complement of choosing an orange juice box is:
1 - 8/18 = 10/18 = 17/18
Therefore, the probability of the complement of choosing an orange juice box is 17/18.
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Find the smallest value of n such that Sn lies within the distance 70 x 10^-6 of the true sum
Answer:
0.00007
Step-by-step explanation:
Sketch the graph of 2x²+4x
We can sketch the graph of 2x²+4x.
We can start by dissecting the equation and identifying its main components before drawing the graph of 2x²+4x.
The formula reads as y = ax² + bx + c, where a = 2, b = 4, and c = 0. It is a quadratic function.
The upward opening of the graph is indicated by the positive coefficient of x2 (a). By applying the formula -b/2a, which in this case equals -4/4 = -1, one can determine the vertex of the parabola.
Hence, the parabola's vertex is located at (-1,0).
By setting y = 0 and solving for x, we may get the graph's x-intercepts:
0 = 2x² + 4x
0 = 2x(x + 2)
Hence the x-intercepts are at x = 0 and x = -2.
We can set x = 0 to determine the graph's y-intercept:
y = 2(0)² + 4(0) = 0
The y-intercept is therefore at (0,0).
Using this knowledge, we can draw the 2x²+4x graph as follows:
Vertex located at (-1,0).
x = 0 and x = -2 are the two x-intercepts.
Y-intercept is located at (0,0).
The graph has a "U"-shaped opening that faces upward.
The graph's basic drawing is shown below:
|
|
|
|
| * *
| |
| |
| |
_____|______________
-2 0 2
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Please Show All Work!!
1.)You are going to eat a slice of pizza, where the central angle of your slice is 34° and the radius of your slice is 8".
What is the angle in radians? Use 3.14 for pi
A.) .72 radians
B.) 2.3 radians
C.) .59 radians
D.) .48 radians
2.) Calculate the area of the sector (the slice you eat). Round your answer to the nearest tenth. Use 3.14 for pi.
Area = n/360 * π r^2
n is your central angle in degrees.
3.) Calculate the arc length of the pizza you have eaten. Use 3.14 for pi. Ø is the angle in degrees
Arc Length = 2πr * Ø/360
To find the angle in radians, we need to convert the given angle from degrees to radians. We know that 180 degrees = π radians.
So,
34 degrees = (34/180) * π radians
= 0.1885 * 3.14
= 0.591 radians
Therefore, the answer is (C) 0.59 radians.
The area of the sector (the slice you eat) can be calculated using the formula:
Area = (n/360) * πr^2
where n is the central angle in degrees, and r is the radius of the slice.
Plugging in the given values, we get:
Area = (34/360) * 3.14 * 8^2
= 0.1 * 3.14 * 64
= 20.096 square inches
Rounding to the nearest tenth, the answer is 20.1 square inches.
The arc length of the pizza you have eaten can be calculated using the formula:
Arc Length = (2πr * Ø)/360
where Ø is the angle in degrees, and r is the radius of the slice.
Plugging in the given values, we get:
Arc Length = (2 * 3.14 * 8 * 34)/360
= 4.776 inches
Therefore, the answer is 4.776 inches.
6=5/3y
pls help me get this answer nowwww uwuwu
Answer:
exact form: [tex]\frac{18}{5}[/tex]
decimal form: 3.6
mixed number form: [tex]3\frac{3}{5}[/tex]
Answer:
y=18/5
Step-by-step explanation:
6=5y/3
multiply both sides:
6*3=5y
simplify 6*3 to 18:
18=5y
divide both sides by 5:
18/5=y
answer: y=18/5
Your mom wants to replace the window shutters on your house for the farmhouse shutters like the picture. Each window takes two shutters. The shutters measure 18 inches times 36 inches. Both shutters need diagonal piece of wood cut to fit. What is the total amount we needed for each of the two diagonal pieces ?
14 by 16
I just know it :DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Ballet is one of the most widely performed types of concert dance. Each year, thousands of people flood t
Choreographers plan each movement and step the dancers make. Countless hours of preparation go into pra
Classical ballet is a very difficult dance style to master. It strictly follows traditional ballet technique. Dancer
and artistically express routines. Good technique requires that dancers have proper alignment. Dancers' head
perfectly. Ballet places a lot of emphasis on the lines of the body. "Good lines" are a combination of the body a
from training.
The proper positioning of the feet is especially important to ballet dancing. Turnout is the basis for all ballet
outward from the hips down, and the knee and foot are turned away from the center of the body. A perfect turnc
feet when the dancer is in first position with his or her heels touching. The knees are also supposed to touch, a
One of the most recognizable classical ballet techniques is en pointe dancing. This skill requires that dancer
the tips of their toes for extended periods of time. It takes a lot of training and strength to dance en pointe. The e
abdominal muscles-is used for this technique. Dancers can injure themselves or permanently damage their fee
What does the word lines most likely mean as it is used in this passage?
A. use of abdominal muscles
OB. ability to follow routines
OC.
arrangement of the body
avoiding injury to the body
D.
The correct option for this question is C. arrangement of the body.
Why it is?
Based on the given passage, the word "lines" most likely refers to the arrangement of the body in ballet dancing. The passage states that "Ballet places a lot of emphasis on the lines of the body" and that "Good lines" in ballet are a combination of the body alignment and artistic expression.
It also mentions that proper positioning of the feet is important for achieving good lines and that turnout, which is the outward rotation of the hips and knees, is the basis for all ballet movements.
Therefore, "lines" in this context is referring to the visual lines created by the dancer's body and limbs in ballet dance, which are essential to proper technique and artistic expression.
Therefore, the correct answer is C. arrangement of the body.
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on a scale drawing, 1/4 in =2 foot. what are the dimensions on the scale for a room that is 27 ft by 20 ft
i cant fully answer it but i know the steps,
(the link is how you would set it up)
you can replace x with 20 or 27, i would start 20
A
B
Which of the following graphs will
display the narrowest parabola?
y = -2x²+x+3
f(x) = -4x² - 30x
A graph that would display the narrowest parabola is f(x) = -4x² - 30x.
How to determine the equation of a parabola?In Mathematics, the standard equation of the directrix lines for any parabola can be modeled or represented by the following mathematical expression:
y = a(x - h)² + k.
Where:
h and k are the vertex.a represents the leading coefficient.Generally speaking, the larger the absolute value of the leading coefficient of a quadratic function, the narrower would be graph of its parabola.
In this context, we have the following:
y = -2x²+x+3; a = -2
f(x) = -4x² - 30x; a = -4
|a| = |-2| = 2
|a| = |-4| = 4
Therefore, |-2| is less than |-4|.
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35 of the students in the band play the flute, and another 15 play the clarinet. What fraction of the students in the band plays either the flute or the clarinet? Responses
As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
We must first ascertain the total number of students in the band in order to calculate the percentage of those who play the flute or clarinet. Let's assume that N kids make up the entire band.
The total number of pupils who play either the clarinet or the flute is then calculated as follows: 35 + 15 - x
The percentage of band students who play either the flute or the clarinet is now (35 + 15 - x) / N, and we need to know what x's value is. Nevertheless, the problem does not provide this information. As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
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Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
Answer: 32.2 cubic inches
Step-by-step explanation:
The volume of one coin can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Substituting the given values, we get:
V = π(1.4)^2(0.0625)
V ≈ 0.14 cubic inches (rounded to the nearest hundredth)
To find the total volume of all the coins, we can multiply the volume of one coin by the number of coins:
Total volume = 230 × 0.14
Total volume ≈ 32.2 cubic inches (rounded to the nearest hundredth)
Therefore, the coins take up approximately 32.2 cubic inches of the treasure chest.
3.6 Triathlon times, Part II: The distribution for triathlon time varies depending on the population you are describing. The distribution for men ages30−34isN(μ=4370,σ=585). The distribution for women ages25−29isN(μ=5296,σ=826). Note, these distributions list the triathlon times in seconds. Use this information to compute each of the following. Report your answer to 2 decimal places. a) The cutoff time for the fastest5%of athletes in the men's group, i.e. those who took the shortest5%of time to finish. b) The cutoff time for the slowest10%of athletes in the women's group.
a: The cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b: The cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
What is the nοrmal distributiοn?The nοrmal distributiοn is a cοntinuοus prοbability distributiοn that is widely used in statistics tο describe real-wοrld phenοmena that tend tο cluster arοund a central value.
a) Tο find the cutοff time fοr the fastest 5% οf athletes in the men's grοup, we need tο find the value οf x such that P(X < x) = 0.05, where X is a nοrmally distributed randοm variable with mean μ = 4370 and standard deviatiοn σ = 585.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 5th percentile is apprοximately -1.645. Therefοre, we can write:
(x - μ) / σ = -1.645
Substituting the given values, we get:
(x - 4370) / 585 = -1.645
Sοlving fοr x, we get:
x = 4370 + (-1.645) * 585
x ≈ 3447.68 secοnds
Hence, the cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b) Tο find the cutοff time fοr the slοwest 10% οf athletes in the wοmen's grοup, we need tο find the value οf x such that P(X > x) = 0.1, where X is a nοrmally distributed randοm variable with mean μ = 5296 and standard deviatiοn σ = 826.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 10th percentile is apprοximately -1.28. Therefοre, we can write:
(x - μ) / σ = -1.28
Substituting the given values, we get:
(x - 5296) / 826 = -1.28
Sοlving fοr x, we get:
x = 5296 + (-1.28) * 826
x ≈ 4253.68 secοnds
Hence, the cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
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4. Divide N275.00 among Eno and Musa so that for every N2.00 Eno gets, Musa gets N3.00. What are their shares? bags in such a way that one bag is twice as heavy
The shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.
Explain about the ratios of the number?A/B would be your formula if you were making comparisons one data point (A) to this other data point (B). This indicates that you are multiplying knowledge A by data B. For instance, your ratio will just be 5/10 if A is 5 and B is 10. Make the equation work. To calculate your ratio, divide data It by a data B.Total amount : R 275.00
Ratio of Eno to Musa = R 2.00 / R3.00
So,
Total ratio: 2 + 3 = 5
Then,
Eno's share = 2/5*275
Eno's share = R 110
Similarly,
Musa's share = 3/5*275
Musa's share = R 165
Thus, the shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.
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a person is selected at random during the republican national convention. suppose the probability that the person selected is a woman is 38%, the probability that the person selected is tall is 54%, and the probability that the person selected is left-handed is 11%. assume that being female, tall, and left-handed are independent of each other. what is the probability that the person selected is a tall, left-handed woman?
The probability that the person selected is a tall, left-handed woman is 0.02.
Given that, The probability that the person selected is a woman is P(W) = 38% = 0.38
The probability that the person selected is tall is P(T) = 54% = 0.54
The probability that the person selected is left-handed is P(L) = 11% = 0.11
It is given that the events W, T, and L are independent of each other. Therefore, their joint probability is given by:
P(W ∩ T ∩ L) = P(W) × P(T) × P(L) = 0.38 × 0.54 × 0.11 = 0.02292
Now, the probability that the person selected is a tall, left-handed woman is given by:
P(T ∩ L ∩ W) = P(W ∩ T ∩ L) = 0.02292 = 0.02
Therefore, the probability that the person selected is a tall, left-handed woman is 0.02.
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i put $1000 in an account from high school graduation gifts, and $2000 into the same account after my college graduation 4 years later. five years after i started my first job how much is in the account if it earns 4% per year?
By using the concept of compound interest, the total amount is $4063.27.
We have,
The amount that was deposited during high school graduation = $1000
The amount that was deposited during college graduation after 4 years = $2000
The total number of years elapsed = 5 years
The interest rate per annum (p.a.) = 4%
The simple Interest (SI) formula is given by,
SI = P × r × t
where, P = Principal amount
r = Rate of interest
t = Time period
Compound Interest (CI) formula is given by,
CI = P (1 + (r/n))^(nt)
Where P = Principal amount
r = Rate of interest
t = Time period
n = Number of times interest is compounded
For the total amount using compound interest.
Total amount (A) = Principal + Compound interest
A = P + CI
Implying it to our data, we get the following.
For $1000 that was deposited during high school graduation,
For 5 years, n = 1, t = 5 years, r = 4% p.a.
CI = 1000[1+(4/100)]^(1×5)
CI = 1000[1+(1/25)]^5
CI = 1000×(26/25)^5
CI = 1000×1.21665
CI = $1216.65
For $2000 that was deposited during college graduation after 4 years,
The total number of years elapsed = 5 years + 4 years = 9 years
n = 1, t = 9 years, r = 4% p.a.
CI = 2000[1+(4/100)]^(1×9)
CI = 2000[1+(1/25)]^9
CI = 2000×(26/25)^9
CI = 2000×1.4233
CI = $2846.62
Therefore, the total amount (A) is $1216.65 + $2846.62 ⇒ $4063.27.
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The first three questions refer to the following information: Suppose a basketball team had a season of games with the following characteristics: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 25% of all games were wins. Denote this by W (the remaining were losses). 20% of all games were at-home wins.
Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.)
.12
.15
.20
.33
.80
Answer:
25 I am not sure
Step-by-step explanation:
The proportion of at-home games that were wins is 0.33, or 33%.
The proportion of at-home games that were wins can be found by dividing the number of at-home wins by the number of at-home games. This can be represented as a fraction:
At-home wins / At-home games
Using the information given in the question, we can plug in the values for at-home wins and at-home games:
0.20 / 0.60
Simplifying the fraction gives us:
1/3
Converting this to a decimal gives us:
0.33
Therefore, the proportion of at-home games that were wins is 0.33, or 33%.
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0.0005 × 0.007
————————-
0.01
Answer:
0.00035
Step-by-step explanation:
0.0005×0.007 ×100
—————-------
1
0.0000035 ×100
0.00035
Martha likes to knit hats and mittens for friends and family. Last fall, she knitted 3 hats and 3
pairs of mittens, which took a total of 51 hours. This fall, she knitted 3 hats and 5 pairs of
mittens, which took a total of 77 hours. If each hat takes the same amount of time and each
pair of mittens takes the same time, how long does it take Martha to knit each item?
hours to knit a pair of mittens.
It takes Martha
hours to knit a hat and
It takes Martha `4` hours to knit each hat and `13` hours to knit each pair of mittens.
What is meant by hours?
Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.
What is a pair?
A pair is a set of two things that go together or belong together, like a pair of shoes, socks, or gloves. It can also refer to a pair, a duo, or a twosome.
According to the given question
Let's assume that each hat takes `h` hours to knit and each pair of mittens takes `m` hours to knit.
From the given information, we know that:
- 3 hats and 3 pairs of mittens took a total of 51 hours. This means that 3h + 3m = 51.
- 3 hats and 5 pairs of mittens took a total of 77 hours. This means that 3h + 5m = 77.
We can use these two equations to solve for `h` and `m`.
First, let's solve for `h` by multiplying the first equation by 5 and the second equation by 3, and then subtracting the second equation from the first:
15h + 15m = 255
9h + 15m = 231
-----------------
6h = 24
h = 4
So each hat takes Martha `4` hours to knit.
Now we can use either of the original equations to solve for `m`. Let's use the first one:
3h + 3m = 51
3(4) + 3m = 51
12 + 3m = 51
3m = 39
m = 13
So each pair of mittens takes Martha `13` hours to knit.
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J(7,2)k(-4,9),l(-3,-1)
Classify triangle
The triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.
What is scalene οbtuse triangle?A triangle is said tο be οbtuse scalene in geοmetry if οne οf its angles is larger than 90 degrees but less than 180 degrees, while the οther twο angles are bοth less than 90 degrees. Measurements fοr the three sides and angles vary.
Tο classify the triangle fοrmed by the pοints J(7,2), K(-4,9), and L(-3,-1), we need tο find the lengths οf its sides and apply the triangle classificatiοn criteria.
Using the distance fοrmula, we can find the lengths οf the sides:
[tex]JK = \sqrt{[(7 - (-4))^2 + (2 - 9)^2]} \\JK =\sqrt{ (11^2 + (-7)^2)} \\ JK =\sqrt{170} \\KL = \sqrt{[(-4 - (-3))^2 + (9 - (-1))^2]} \\KL =\sqrt{ (1^2 + 10^2) } \\KL = \sqrt{101} \\LJ = \sqrt{[(-3 - 7))^2 + ((-1) - 2)^2]} \\LJ=\sqrt{ (10^2 + (-3)^2)} \\LJ = \sqrt{109}[/tex]
Since all three sides have different lengths, the triangle is scalene.
Therefοre, the triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.
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A person tosses a coin 9 times. In how many ways can he get 6 heads?
If a person tosses a coin 9 times, there are 84 ways in which a person can get 6 heads in 9 coin tosses.
When a person tosses a coin 9 times, there are two possible outcomes for each toss - either heads or tails. Hence, there are a total of 2^9 = 512 possible outcomes for 9 coin tosses.
To find the number of ways in which a person can get 6 heads, we need to consider the number of ways in which 6 heads can occur in the 9 coin tosses, while the remaining 3 tosses can result in tails. The number of ways in which 6 heads can occur in 9 tosses is given by the binomial coefficient C(9,6), which is equal to 84.
Hence, there are 84 ways in which a person can get 6 heads in 9 coin tosses. This can be calculated using the formula for binomial coefficients:
C(9,6) = 9!/(6!3!) = (987)/(321) = 84
Alternatively, we can also calculate this using a combination of multiplication and addition. We can choose any 6 out of the 9 coin tosses to result in heads, which can be done in C(9,6) ways.
For each of these ways, the remaining 3 coin tosses will result in tails, which can occur in only one way. Hence, the total number of ways in which a person can get 6 heads in 9 coin tosses is given by:
Number of ways = C(9,6) * 1 = 84 * 1 = 84
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You take a package to the local shipping company. They charge a fixed base cost of $3 per package plus an additional $0. 63 per pound. If P represents the number of pounds of your package, and C is the total cost of shipping your package, write an equation that represents the relationship between P and C
If P represents the number of pounds of your package, and C is the total cost of shipping your package, the equation that represents the relationship between P and C is C = 3 + 0.63P.
To write an equation that represents the relationship between the weight of the package (P) and the total cost of shipping (C), we need to use the information given in the problem. The shipping company charges a fixed base cost of $3 per package plus an additional $0.63 per pound.
We can represent the additional cost per pound as 0.63P, since the cost increases by $0.63 for every additional pound. Therefore, the equation that represents the relationship between P and C is:
C = 3 + 0.63P
This equation gives us the total cost of shipping a package based on its weight. We can use this equation to calculate the cost of shipping a package of any weight by simply plugging in the weight (in pounds) for P and then solving for C.
For example, if a package weighs 5 pounds, we can substitute P = 5 into the equation to get:
C = 3 + 0.63(5)
C = 3 + 3.15
C = 6.15
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