Answers
Answer:
A. V = 81π(7.25) = 1,844.90 cubic inches
V = 81(3.14)(7.25) = 1,843.97 cubic inches
B. Let p be the number of cans of paint.
1,843.97p = 10,000, so p = 5.42
Jessie will need 6 cans of paint.
C. Area of each storage area = π(9.5^2) = 283.53 square inches. Using 3.14 for π, this area is (3.14)(9.5^2) = 283.385 square inches. The base area of each paint can is 81π = 254.46 square inches (254.34 square inches if we use 3.14 for π). Jessie can't use the carrier because the area of each storage area exceeds the base area of each paint can.
Related Questions
Given the unit circle what is the value of y PLEASE HELP
Answers
Answer: √35/6
Step-by-step explanation:
see image for explanation
Solve the following for θ, in radians, where 0≤θ<2π.
2cos2(θ)−8cos(θ)−1=0
Select all that apply:
1.07
1.69
4.59
2.49
2
2.33
Answers
Answer:correct answers 1.69
4.59
Step-by-step explanation:
We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
2u^2 - 8u - 1 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = -8, and c = -1. Substituting these values, we get:
u = (8 ± sqrt(8^2 - 4(2)(-1))) / 2(2)
u = (8 ± sqrt(72)) / 4
u = 2 ± sqrt(18)
Therefore, either:
What types of polynomials do you think could factor using the relationship made
in the previous question?
If a is replaced with an x, and b is replaced with a 2, how would the equation
look, and what does it mean?
Create your own replacement of a and b and explain how your equations would
look and what would it mean?
Answers
The relationship in the previous question involves the difference of squares pattern, which applies to polynomials of the form:
a^2 - b^2
where a and b are any real numbers.
If we replace a with x and b with 2, the equation would look like:
x^2 - 2^2 = (x + 2)(x - 2)
This means that any polynomial of the form x^2 - 4 can be factored using the difference of squares pattern.
As for creating our own replacement of a and b, let's say we replace a with y and b with 3. Then the equation would look like:
y^2 - 3^2 = (y + 3)(y - 3)
This means that any polynomial of the form y^2 - 9 can be factored using the difference of squares pattern.
Line ac and df are parallel they are cut by transversal Hj with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E
Answers
The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,
m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
Two lines AC and DF are parallel to each other in the attached figure
Transversal HJ cut lines AC and DF at point B and E respectively.
Measure of ∠ABE = 63°.
Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,
Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)
⇒Measure of ∠DEH = 63°
Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)
⇒Measure of ∠BEF = 63°
Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)
⇒Measure of ∠CBJ = 63°
Using the result of linear pair angles,
Measure of ∠ABE + Measure of ∠CBE = 180°
⇒ Measure of ∠CBE = 180° -63°
⇒ Measure of ∠CBE = 117°
Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)
⇒Measure of ∠FEH = 117°
Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)
⇒Measure of ∠BED = 117°
Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)
⇒Measure of ∠ABJ = 117°
Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
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The above question is incomplete, the complete question is:
Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.
In the attached figure.
HELP FASTER WILL GIVE BRAINLIEST!!!!!!!!! NOTICE ITS + AND THEN - IN EQUATION NOT TWO +, SO D ISNT CORRECT!!!!!!
Identify the correct graph of the system of equations.
3x + y = 12
x − 4y = 4
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
Answers
The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:
The graph shows a line with an x-intercept at (4, 0) and a y-intercept at
(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).
We have,
To graph the system of equations 3x + y = 12 and x − 4y = 4, we first need to rearrange them in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept:
3x + y = 12 => y = -3x + 12
x - 4y = 4 => y = (1/4)x - 1
Now we can see that the first equation has a slope of -3 and a y-intercept of 12, while the second equation has a slope of 1/4 and a y-intercept of -1.
Now,
The x-intercept is when y = 0.
So,
3x + y = 12
3x = 12
x = 4
And,
x - 4y = 4
x = 4
Thus,
The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:
The graph shows a line with an x-intercept at (4, 0) and a y-intercept at
(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).
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If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where t is the
number of years from today.
p(t)=1200 (1.026)
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.
Current price ?$
Price 8 years from today?$
Answers
a) Based on the exponential function, p(t)=1200 (1.026)^t, the item's current price with a rate of inflation of 2.6% per year is $1,200.
b) In 8 years, the future price of the item would be $1,473.53.
What is an exponential function?An exponential function is a mathematical equation depicting the relationship between one variable and another with a periodic constant rate of growth or decline.
Exponential functions are classified into two:
Exponential growth functionExponential decay function.Let the number of years from today = t
Annual inflation rate = 2.6%
Current price = $1,200
Time in years = 8 years
Exponential function:p(t)=1200 (1.026)^t
p(8) = 1,200(1.026)^8
= $1,473.53
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What is the value of c in the equation?
15.3 = StartFraction c Over 2.1 EndFraction
13.2
17.4
32.13
321.3
Answers
Answer:
32.13
Step-by-step explanation:
The value of c in the equation 15.3 = c/2.1 is 32.13. To solve for c, you can cross-multiply and simplify the equation to c = 15.3 x 2.1 = 32.13.
The solution to the equation "the quotient of a number and 8 is 16" is 128. To solve for the number, you can multiply both sides by 8 to get "the number is 16 x 8 = 128."
To translate the sentence "the quotient of a number and 8 is 16" into an equation, you can use "x" to represent the number and write x/8 = 16.
Answer:
c or a
Step-by-step explanation:
i thing a
Each triangle in the quilting square pattern shows has a base and height of 2 inches how much fabric is needed to create one quilting square
Answers
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Step-by-step explanation:
Question 20 of 42
Which of the following is a type of data that is likely to be normally
distributed?
A. The weights of all the 5-year-olds in the United States
B. The outcomes of a fair die rolled 100 times
C. The number of students in a class who get a perfect score on a
test
D. The number of students in a class who get a B on a test
Answers
Answer: Option B, the outcomes of a fair die rolled 100 times, is likely to be normally distributed.
Step-by-step explanation:
Answer: Option B, The outcomes of a fair die rolled 100 times
Step-by-step explanation:
that would most likely be normally distributed.
hope it helped! Good luck!!! :)
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
Answers
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.
Which of the following is not an exponential function?To determine which option is not an exponential function, we will apply general equation of an exponential function.
f(x) = aⁿ
where;
a is the base of the functionn is the exponentSo from the given options;
(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.
4ˣ is an exponential function, because 4 is the base while x is the exponent.
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.
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Triangle ABC and triangle DEF are similar. What is the measure
of side DF?
B
E
9 cm
15 cm
D
с
? cm
25 cm
F
Answers
The measure of side DF is 15cm
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. For two traingles to be similar, the corresponding angles of the triangles must be equal.
And also, the ratio of corresponding sides of Similar triangles are equal
This means;
15 /25 = 9/DF
representing DF by x
15/25 = 9/x
15x = 25×9
15x = 225
divide both sides by 15
x = 225/15
x = 15cm
Therefore the measure of DF is 15cm
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URGENT! Can someone please help?
Answers
a. The missing values of the logarithm expression is log₃(40).
b. The missing values of the logarithm expression is log₅(8).
c. The missing values of the logarithm expression is log₂(1/25).
What is the missing of the logarithm expression?The missing values of the logarithm expression is calculated as follows;
(a). log₃5 + log₃8, the expression is simplified as follows;
log₃5 + log₃8 = log₃(5 x 8) = log₃(40)
(b). The log expression is simplified as;
log₅3 - log₅X = log₅3/8
log₅X = log₅8
X = 8
(c). The log expression is simplified as;
-2log₂5 = log₂Y
log₂5⁻² = log₂Y
5⁻² = Y
1/25 = Y
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Name 2 other categories of data you could use to better understand the physical fitness levels of these students.
Answers
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
Cardiovascular fitness data:
We have,
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
This data can include measurements such as body mass index (BMI), body fat percentage, and waist circumference.
By collecting body composition data for students, we can better understand their overall physical health and identify potential risk factors for chronic diseases related to physical fitness.
Cardiovascular fitness data:
This data can include measurements such as resting heart rate, maximal oxygen uptake (VO2 max), and cardiovascular endurance test results.
By collecting cardiovascular fitness data for students, we can better understand their cardiovascular health and fitness levels, as well as identify potential risk factors for heart disease and other related conditions.
Thus,
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
Cardiovascular fitness data:
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Subtract t⁴-3t²+7 from 5t³-9.
Answers
Answer:
t⁴+5t³-3t²-2
Step-by-step explanation:
You can't subtract a variable with a different exponent:
Example:
CAN'T BE SUBTRACTED - 3x²-3x⁴
CAN BE SUBTRACTED - 4x²-2x²=2x²
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf (5t^{3} -9)-(t^{4}-3t^{2} +7 )[/tex]
2. Remove the parenthesis.Beware of the terms of the right hand side parenthesis, as we'll have to change the symbol of all of them because of the minus (-) symbol infront of the parenthesis.
[tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
3. Work with like terms.Like terms are terms that contain the same variables and can be added and subtracted simply. For example, 7x and 2x are like terms, because they are both expressed in terms of x. However, 7x and x² are not like terms, because one os expressed in terms of x and the ither in terms of x².
• Note: All natural numbers not being multiplied by any variables are like terms.
So now let's identify those like terms:
From this expression: [tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
Only -9 and -7 are like terms. And, since -9-7= -16, the resulting expression should be the following:
[tex]\sf 5t^{3} -t^{4}+3t^{2} -16[/tex]
4. Order the terms correctly.So even though the last expression is the answer to this problem, we can polish it a little bit by ordering the terms. In math and other exact sciences, terms are normally ordered alphabetically and from greatest to least of it's the same variable with different exponents. Therefore, the final answer is:
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
what type of number is 15/10
Answers
Answer:
The number 15/10 is a fraction, specifically a rational number. It can be expressed as the quotient of two integers, where 15 is the numerator and 10 is the denominator. In this case, the fraction is equivalent to 1.5, which is a decimal representation of the rational number.
Step-by-step explanation:
Answer:
Fraction, 15/10 is written out as 15 Over 10
prove the identity tan3x-tanx =2sinxsec3x
Answers
(Problem #1) 2sin(x)/cos(3x) = tan(3x) - tan(x)
Let's try to prove that 2sin(x) = sin(3x) - tan(x)cos(3x).
Using the identities sin(3x) ? 3sin(x) - 4sin³(x) and cos(3x) ? 4cos³(x) - 3cos(x),
sin(3x) - tan(x)cos(3x) = 3sin(x) - 4sin³(x) - tan(x)(4cos³(x) - 3cos(x))
= sin(x)(3 - 4sin²(x) - (4cos²(x) - 3))
= sin(x)(6 - 4(sin²(x) + cos²(x)))
= 2sin(x).
(The above is simpler than using the standard identity that gives tan(3x) in terms of tan(x).)
(Problem #2) (1 - tan²((?/4)-x))/(1 + tan²((?/4)-x)) = sin(2x)
Multiplying the numerator and denominator of the left-hand side by cos²((?/4)-x)) gives
(cos²((?/4)-x)) - sin²((?/4)-x)))/(cos²((?/4)-x)) + sin²((?/4)-x))),
which equals cos(2(?/4 - x))/1, i.e., cos(?/2 - 2x), i.e., sin(2x).
(Problem #3) (1 + sin(2x) - cos(2x))/(1 + sin(2x) + cos(2x)) = tan(x)
Hint: use the identities cos(2x) = 1 - 2sin²(x) = 2cos²(x) - 1 and sin(2x) = 2sin(x)cos(x) to express the left-hand side in terms of sin(x) and cos(x), then factorize the numerator and denominator.
(Problem #4) sin(2x) + (1/sin(2x)) = 5/2; for 0 ? x <2?
This is an equation you have to solve, not an identity. Start by treating it as a quadratic equation in sin(2x). The quadratic factorizes easily.
Please help with this simple question (Large reward)
Answers
Answer:
H
Step-by-step explanation:
Firstly, G and J cannot be the answers because the beginning numbers are too big. If you look at the fractions, you can see 2 and 7/8 because 2 is the smallest of all of them. Now the answer is between F and H.
In F, the second number is 3 and 1/2.
In H, the second number is 3 and 1/4.
If you want to make it an improper fraction to visualize better, it would be 7/2 and 12/4=6/2. Or you can just compare to see which is smaller, 1/2 or 1/4. In this case, 3 and 1/4 is smaller. Therefore the answer is H.
Amelia gathered data about the heights of students at her school. Based on the displays, what inferences can you make about each sample?
Answers
Amelia can make inferences by using
The range of heightsThe shape/mean of the distributionThe presence of outliers, etc.What is the inferences about?Inferences from data on student heights include range determination based on minimum and maximum values, indicating greater variability with a larger range.
The average height of students can be determined using measures like mean, median, and mode. The distribution's shape can be determined by the histogram or box plot, indicating how the heights are distributed. inferences can be made by the use of height samples to gain insight into school population.
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A man has 16 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.50, how many dimes and how many quarters does he have?
Let d = number of dimes, q = number of quarters.
Step one:
A man has 16 coins in his pocket, all of which are dimes and quarters.
Set up the first equation for the number of dimes and quarters. Help PLS
Answers
Answer: 10 dimes and 6 quarters, see below for the equations.
Step-by-step explanation:
We know how much a dime is worth and how much a quarter is worth, and they give us the total number of coins and the total number of change.
This equation shows the total number of coins:
d + q = 16
This equation shows the worth of these coins:
0.10d + 0.25q = 2.5
Now, we can graph these equations. See attached. The point of intersection, where the lines cross, is our solution. In the graph, d = x and q = y.
This point is (10, 6) meaning he has 10 dimes and 6 quarters in his pocket.
Which equation represents a direct variation?
Oy - 4x = 8
Oy + 2 = 7x
Oy - 3x = 0
O y = 5x - 2
Answers
Answer:
The equation that represents a direct variation is y = 5x - 2.
In a direct variation, one variable is proportional to the other variable, which means that as one variable increases or decreases, the other variable also increases or decreases in direct proportion. The general form of an equation that represents direct variation is y = kx, where k is a constant of proportionality.
In this case, the equation y = 5x - 2 is in the form of y = kx, where k = 5. This means that as x increases or decreases, y will also increase or decrease proportionally, with a constant rate of change of 5. Therefore, this equation represents a direct variation.
Claire got 17 out of 20 questions correct on her vocabulary quiz. What percent of the questions did she get wrong?
Answers
The percentage of the questions she got wrong is 15%
What is a Percentage?
Percentage is a number or ratio by dividing the value by the total value and then multiplying the result by 100.
How to determine this
Out of 20 questions, Claire got 17 questions
i.e the questions she got right = 17
The questions she got wrong = 20 - 17 = 3
To get the percentage she got wrong
= 3/20 *100%
= 300/20%
= 15%
Therefore, the percentage she got wrong is 15%
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geometry please help
Answers
A graph of triangle CAT is shown below.
A graph of triangle C'A'T, the image of ΔCAT after a reflection in the x-axis is shown below.
ΔC'A'T represents a rigid motion because the pre-image and the image are congruent.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (x, -y)
C (-1, 2) → (-1, -(2)) = C' (-1, -2)
A (-1, 4) → (-1, -(4)) = A' (-1, -4)
T (3, 2) → (3, -(2)) = T' (3, -2)
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Let p be the constant function p (z) = 1,000,000,000. Let q be the exponential function q (2) = 10
The product of the two functions is (pq) (z) = 10ª-2, where a is a constant. What is the value of a?
C2023 Illuminate Education, Inc.
P
C
Answers
[tex]\large \boxed{\mathrm{10}}[/tex]
The constant function p has a fixed output of one billion, while the exponential function q has a base of two and an output of 10. As the input increases by one, the output of q doubles. For example, q(3) = 20 and q(4) = 40. The rate of growth of q is much faster than p. In fact, q will eventually surpass p for large enough inputs. This demonstrates the power of exponential growth and highlights the importance of understanding the functions used in equations and models.
Answer:
10 or 1b
Step-by-step explanation:
Chantel is deciding which of two similar wallets she will buy. Both are rectangular, but she wants the one that will best fit in her purse. The larger wallet is 18 centimeters long and the smaller one is 10 centimeters long. What is the area of the larger wallet if the area of the smaller one is 60 square centimeters?
Answers
The requried area of the larger wallet is 194.4 square centimeters.
Since the two wallets are similar, their corresponding sides are proportional. Let x be the width of the smaller wallet, then the width of the larger wallet is 18/10 times x, or 9/5 times x. Therefore, the dimensions of the larger wallet are 9/5 times the dimensions of the smaller wallet.
The area of the smaller wallet is x times 10 (length times width), or 10x square centimeters. We are given that this area is 60 square centimeters, so:
10x = 60
x = 6
Therefore, the width of the smaller wallet is 6 centimeters. The width of the larger wallet is 9/5 times 6, or 10.8 centimeters. The length of the larger wallet is 18 centimeters.
The area of the larger wallet is 10.8 times 18, or 194.4 square centimeters. Therefore, the area of the larger wallet is 194.4 square centimeters.
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∠1 and ∠2 are vertical angles. ∠2 has a measure of 31°.
What is the measure of ∠1?
Enter your answer in the box.
Answers
The measure of <1 is 31°.
What are vertical angles?Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.
In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;
<2 = 31° (given)
So that;
<1 = <2 = 31°
Thus,
<1 = 31°
Therefore, it can be concluded that the measure of <1 is 31°.
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Select all of the figures that show axis symmetry.
Answers
Answer: All of them
Step-by-step explanation:
All of them can be divided into two equal halves.
The figures that show axis symmetry are 1, 2, and 3.
What is the axis of symmetry?The axis of symmetry is a line, plane, or other axis that divides a geometric figure into two mirror-image halves that are congruent to each other.
A figure has axis symmetry if it looks the same after being rotated around an axis.
Out of the given figures, the ones that have axis symmetry are:
Sphere (has infinite axis symmetry)Cone (has rotational symmetry around its central axis)Cylinder (has rotational symmetry around its central axis)The figures that do not have axis symmetry are:
Cube (has only point symmetry)Rectangular cone (has no rotational symmetry)So, the figures that show axis symmetry are 1, 2, and 3.
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The volume in a set of wine bottles is known to follow a normal distribution with mean μ ounces and standard deviation of σ = 0.5 ounces. You take a sample of the bottles and measure their volumes. How many bottles do you need to sample to construct a 90% confidence interval for μ with a margin of error at most 0.1 ounces?
Answers
We need to sample at least 18 wine bottles to construct a 90% confidence interval for the mean volume of the population, with a margin of error of at most 0.1 ounces.
To determine the sample size required for a given confidence interval and margin of error, we need to use the following formula:
[tex]n = (Z^2 * \sigma^2) / E^2[/tex]
Where:
n = sample size
Z = the z-score associated with the desired confidence interval (for 90% confidence, Z = 1.645)
σ = the standard deviation of the population (0.5 ounces in this case)
E = the desired margin of error (0.1 ounces in this case)
Plugging in the values, we get:
[tex]n = (1.645^2 * 0.5^2) / 0.1^2[/tex]
n = 17.1
Thus, we need to sample at least 18 wine bottles to create a 90% confidence interval for the population's mean volume, with a margin of error of no more than 0.1 ounces.
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We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.
We have,
To construct a confidence interval for the mean volume of the wine bottles, we need to use the formula:
Confidence interval = sample mean ± margin of error
Where,
Margin of error = z (σ/√(n))
Here, we want to construct a 90% confidence interval with a margin of error at most 0.1 ounces.
This means that the margin of error should be less than or equal to 0.1, and the confidence level is 90%, so the critical value of z is 1.645
(using a standard normal table or calculator).
We are given that the standard deviation is σ = 0.5 ounces.
We don't know the sample mean or the sample size (number of bottles), so we'll use the worst-case scenario to find the sample size that gives the largest margin of error.
The worst-case scenario is when the sample mean is equal to the population mean (μ) plus the margin of error (0.1 ounces), and the sample size is as small as possible (which gives the largest margin of error).
So, we have:
0.1 = 1.645 x (0.5/sqrt(n))
Solving for n, we get:
n = (1.645 x 0.5/0.1)²
n = 68.225
Rounding up to the nearest whole number, we get:
n = 69
Therefore,
We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.
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5a-3b=7b find the ratio of a:b
(i need answers quick)
Answers
The ratio of a:b in 5a-3b=7b is 4:5.
We know that,
A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are equal to each other. For example, if there are 2 boys and 6 girls, you can write the ratio as: 1 : 3 (for every boy there are 3 girls).
Ratios compare two numbers obtained by dividing. If one data point (A) is compared to another data point (B), it is expressed as A/B. It means that we are partitioning information A from information B. For example, if A is five and B is 10, your ratio would be 5/10, or 1/2.
For above information,
5a - 3b = 7b
5a = 7b- 3b
5a= 4b
So, a/b= 4/5
a:b is 4:5
Thus, the ratio of a:b in 5a-3b=7b is 4:5.
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A quantity shrinks at a continuous rate of
per year. Its effective growth rate is
per year.
Answers
Answer:
Based on the information provided, there seems to be a discrepancy between the given information about the quantity shrinking at a continuous rate and the requested information about its effective growth rate. If a quantity is shrinking continuously, it is not experiencing growth, and therefore there is no effective growth rate. Nonetheless, assuming that the requested information was about the effective shrinkage rate of the quantity per year, this information can be extracted from the given information that "A quantity shrinks at a continuous rate of 33% per year." The effective shrinkage rate of the quantity can be calculated as follows:
Let r be the continuous shrinkage rate of the quantity
The effective shrinkage rate of the quantity is given by the expression (1 - r).
From the given information , r = 33% = 0.33.
Therefore, the effective shrinkage rate of the quantity is (1 - r) = (1 - 0.33) = 0.67 or 67% per year.
Note that if the phrase "effective growth rate" was a mistake, and the original intent was to ask for the shrinkage rate, then the above calculation gives the answer. Otherwise, further clarification is needed.
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Step-by-step explanation:
The question refers to the concept of continuous growth or shrinkage, and the effective growth rate in a financial context. Despite missing figures, assuming a quantity shrinks at a continuous rate of 3% and its effective growth rate is 2%, it implies a net shrinkage is 1% annually.
Explanation:The question pertains to the subject of compound interest in finance, but it appears that some of the figures and percentages are missing. However, generally speaking, continuous growth or shrinkage refers to the rate at which a quantity increases or decreases for a specific period of time. The effective growth rate is a term in finance that is used to compare the annual interest rates between financial products that have different compounding terms. For instance, if a quantity shrinks at a continuous rate of 3% per year, and its effective growth rate is 2% per year, it means that net shrinkage is 1% per year.
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What is the equation of the line shown in this graph?
Answers
Answer:
The equation is y=-3
Step-by-step explanation:
The line is horizontal, cutting across the y-axis, which means it will be a y= line. The point it hits the y-axis is -3, so it is y=-3.