Answer:
She needs a sample size of 25.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.68}{2} = 0.16[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.16 = 0.84[/tex], so Z = 0.995.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population SD is 2 grams.
This means that [tex]\sigma = 2[/tex]
What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?
She needs a sample size of n.
n is found when M = 0.4. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.4 = 0.995\frac{2}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = \frac{0.995*2}{0.4}[/tex]
[tex](\sqrt{n})^2 = (\frac{0.995*2}{0.4})^2[/tex]
[tex]n = 24.8[/tex]
Rounding up:
She needs a sample size of 25.
PLEASE HELP!!
1. devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid. each side of the base of the pyramid is 6 cm and the height of the pyramid is 9 cm. to get the wax for the candle, devin melts cubes of wax that are each 4 cm by 4 cm by 4 cm. how many of the wax cubes will devin need in order to make the candle? show your work.
Answer:
1.69
approximately 2 wax cubes
Step-by-step explanation:
number of wax cubes needed = volume of square pyramid / volume of cube
Volume of a pyramid = 1/3 x ( base area x height)
base area = length²
6² = 36
volume = 1/3 x (36 x 9) = 108
volume of a cube = length³
4³ = 64cm³
108/64 = 1.69
A car dealership pays a wholesale price of $20,000 to purchase a vehicle. The car dealership wants to make a 32% profit. By how much will the mark up to the price of the vehicle?
If the probability of s1 = .6 and the probability of F = .40 what is the value at node 4.
Group of answer choices
320
280
310
260
200
If the probability of s1 = .6 the value above node degree 4 will be 320, as determined by the solution.
What does a node's degree mean?The area of mathematics known as probability deals with numerical descriptions about how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
According to the given information:S1 probability = 0.6
F's likelihood is 0.40.
If the probability of S1 is given a value of 0.6, then
Probability of S2 then equals 0.4.
Using the table equation's payoff values as an exception.
EV=Σ
Each decision's expected value is calculated.
EV(Node 8) = 0.6 * 100 + 0.4 * 300
= 180
EV(Node 9) = 0.6 * 400 + 0.4 * 200= 320
We chose the best value for node 4 from nodes 8 and 9.
The ideal option for node 9 is the line complicated branch with EV(node 8) = 180.
The ideal anticipated value is determined to be 320.
Node 4's EV is 320.
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Solve the inequality,
x + 6.56 > 25.2
Answer: x>18.64
Step-by-step explanation:
x+6.56-6.56>25.2-6.56
x>18.64
name all the terms realted to subtraction
Answer:
Other words for subtraction:
taking away
withdrawal
abstraction
removal
discounting
Step-by-step explanation:
12 divided by four
plus 2 x 6+4
Answer:
19
Step-by-step explanation:
12 divided by four plus 2 x 6+4
assuming that the question is:
12 : 4 + 2 x 6 + 4 =
3 + 12 + 4 = (remember PEMDAS)
19
What is 2 plus 2 minus 4 plus 2
Answer:
2
Step-by-step explanation:
2 + 2 - 4 + 2 = 2
Answer:
2
Step-by-step explanation:
2 + 2 = 4
4 - 4 = 0
0 + 2 = 2
Round 0.21545977 to the nearest hundredth
Answer:
0.22
Step-by-step explanation:
Since 5 rounds up, it would be 0.22
Answer:
0.22 Is the answer.
I wish you luck on your assignments.
what would be themissing side length
The missing side length is 5.7.
What would be themissing side length?The missing side length AB, can be calculated using the Pythagorean Theorem.The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two sides adjacent to the right angle (A and B) is equal to the square of the length of the hypotenuse (C).In other words, AB^2 + BC^2 = AC^2.In this case, AB^2 = AC^2 - BC^2, or AB^2 = 6.7^2 - 3^2, which simplifies to AB^2 = 44.89.Taking the square root of both sides yields AB = 6.7.Therefore, the missing side length, AB, is 6.7.The missing side length of a triangle with sides of lengths a, b, and c is calculated by using the Pythagorean theorem, which states that a^2 + b^2 = c^2. In this case, we are given that side c is 3, and side a is 6.7.Using the Pythagorean theorem, we can solve for side b by rearranging the equation to read b^2 = c^2 - a^2. Plugging in our known values, we get b^2 = 9 - 44.89, or b^2 = -35.89.Since the square root of a negative number is not a real number, this implies that there is no real number solution for b, and therefore the missing side length of the triangle is not possible.
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Which graph below is a tree graph?
I think that it is the last one
Hope this helps
Answer: D
Step-by-step explanation:
The function h(t) = -4.9t2 + h0 gives the height (h), in meters, of an object t seconds after it falls from an initial height (h0). The table shows data for a pebble that fell from a cliff. Image description Choose the quadratic equation that models the situation.
The quadratic equation that models the situation is
h(t) = - 4.9t² + 60.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c
Given is that the function h(t) = - 4.9t² + h₀ gives the height (h), in meters, of an object (t) secs after it falls from an initial height h₀. The table shows data for a pebble that fell from a cliff as -
TIME (t) HEIGHT (h)
1 55.1
2 40.4
3 15.9
The given function is -
h(t) = - 4.9t² + h₀
For the point (1, 55.1), we can write as follows -
55.1 = - 4.9 x 1 x 1 + h₀
h₀ = 55.1 + 4.9
h₀ = 60
So, we can write the function as -
h(t) = - 4.9t² + 60
Therefore, the quadratic equation that models the situation is
h(t) = - 4.9t² + 60.
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Answer:
c on edge
3.5
Step-by-step explanation:
The law firm of Dewey, Cheetham, and Howe handled 18 personal injury cases this past year. This was 9/7 of the cases handled by the rival firm of Gypsum-Goode. How many personal injury cases were handled by Gypsum-Goode this year?
Answer:
14 cases
Step-by-step explanation:
Let x be the number of personal injury cases this year by Gypsum Goode
x* 9/7 = 18
Multiply each side by 7/9
x * 9/7 *7/9 = 18 * 7/9
x = 14
Find the quotient: 3 3/4 ÷ 2
Answer:
[tex]1\frac{7}{8}[/tex]
Step-by-step explanation:
Answer:
1.875
Step-by-step explanation:
Convert the whole number 3, and you get 15/4
complete the process, and you get 1.875 aka 1 7/8
Use the graphs of f and g to graph h(x)=(f+g)(x). (Graph segments with closed endpoints).
The required graph of the function of h(x) is shown, where h(x) = |x| + |x + 2|.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the graph, functions f and g are absolute functions,
f = |x|
g = |x + 2|
So,
h(x) = f + g
Now substitue the functions,
h(x) = |x| + |x + 2|
Thus, the required graph of the function of h(x) is shown.
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Can someone solve 18?
The piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function. Piecewise functions are implemented in the Wolfram Language as PiecewiseAdditional piecewise functions include the Heaviside step function, rectangle function, and triangle function.Given is the absolute value function -
f(x) = 1/2 |x|
We can write it as a piecewise function as follows. The given function is as follows :
f(x) = 1/2 |x|
The absolute value function is given as -
|x| = - x {x < 0}
|x| = x {x ≥ 0}
So, we can write the piecewise function as -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
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The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form?
The net of a rectangular prism. The length is 4 units, width is 2 units, and height is 1 unit.
8 square units
20 square units
24 square units
28 square units
I NEED HELP NOWWW!!!
Answer:
I think it's 28 square units
need help!!!!!!!!!!!!
HELPP NO LINKS OR ELSE ILL BE SCREENSHOTTING AND REPORTING RAT
Answer:
I think it's TWO
Step-by-step explanation:
I NEED HELP IM CONFUSED
Answer:
x=-2 or x=8Step-by-step explanation:
Isolate by the x from one side of the equation.
|x-3|=5
x-3=-5 and x-3=5
1. x-3=-5
Add 3 from both sides.
x-3+3=-5+3
Solve.
-5+3=(-2)
x=-2
2. x-3=5
Add 3 from both sides.
x-3+3=5+3
Solve.
5+3=8
x=8
Therefore, the correct answer is x=-2 or x=8.
can anyone help me with this. Click to see
Answer: mean = 6
median = 7
mode = 8
Step-by-step explanation:
A manufacturer produces soda cans and a quality control worker randomly selects two cans from the assembly line for testing. Past statistics show that 10% of the cans are defective. What is the probability that the two selected cans are defective if the quality control worker selects the two cans from a batch of 60 cans?
Answer:
It would be 1%
Step-by-step explanation:
First of all, note that any of the cans with the batch have the same chance at being defective, so ingore that. However, note the chance that each one is defective:
10%
So if you picked up any can, it would have a 10% chance of being defective. With this, by picking up two cans, you would do:
0.1 * 0.1 = 0.01
To find the chance of both cans being defective, being 1% for both of the selected cans being defective.
A restaurant records the number of tables served each night, and the results have the values: minimum = 3, lower
quartile = 14, median = 23, upper quartile = 29, and maximum = 40.
Answer: A. The first one
Step-by-step explanation:
The first data can be represented in the box plot if the restaurant records the number of tables served each night, and option (A) is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have data:
Minimum = 3
Lower = quartile = 14
Median = 23
Upper quartile = 29
Maximum = 40
From the above data, we can plot the data in the box plot.
Thus, the first data can be represented in the box plot if the restaurant records the number of tables served each night, and option (A) is correct.
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What is the expected value of the following game?
Pay $8. Win $100 if we draw a King from a standard deck. Win nothing if we draw something else.
Answer: Expected Value = -0.31
We expect to lose about 31 cents each time we play the game.
============================================================
Explanation:
A = event of selecting a king
B = event of not selecting a king
P(A) = 4/52 since there are 4 kings out of 52 total. This fraction reduces to 1/13.
P(B) = 48/52 = 12/13
Note: P(A) + P(B) = 1.
V(A) = net value of selecting a king
V(A) = 100-8 = 92, so you net $92 if event A occurs.
V(B) = -8, meaning you lose 8 dollars if you select anything but a king
We multiply the probability values with their corresponding net values
P(A)*V(A) = (1/13)*(92) = 7.07692 approximately
P(B)*V(B) = (12/13)*(-8) = -7.38462 approximately
Add up the results:
7.07692 + (-7.38462) = -0.3077
The expected value is approximately -0.3077 which rounds to -0.31
We expect to lose on average 31 cents each time we play the game. The nonzero expected value means this is not a mathematically fair game.
At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is
$19 and the price for 2 cheeseburgers and 4 cups of lemonade is $18. How much
does it cost for 1 cheeseburger and 1 cups of lemonade?
*
By solving system of linear equation we get Cost for 1 cheeseburger $5 and 1 cups of lemonade $2
What is a system of linear equations?A system of linear equations is a collection of two or more linear equations that have the same variables. A linear equation is an equation in which the highest power of the variable is 1. In other words, the equation is a straight line when graphed.
Here is an example of a system of linear equations:
3x + 2y = 19
2x + 4y = 18
This is a system of equations problem, where we can use the information provided to set up two equations and then solve for the unknown variables. Let x be the cost of one cheeseburger and y be the cost of one cup of lemonade.
From the information provided, we know that:
3x + 2y = 19 (the cost of 3 cheeseburgers and 2 cups of lemonade is $19)
2x + 4y = 18 (the cost of 2 cheeseburgers and 4 cups of lemonade is $18)
To find the cost of one cheeseburger and one cup of lemonade, we can solve this system of equations. One way to do this is by substitution.
3x + 2y = 19
we get
[tex]x=\frac{19-2y}{3}[/tex]
substituting x in equation 2x+4y=18
we get
[tex]2(\frac{19-2y}{3})+4y=18[/tex]
[tex]38 - 4y + 12y = 54\\8y = 16\\y = 2[/tex]
substituting y in equation 3x+2y=19
[tex]3x+2(2)=19\\3x=19-4\\3x=15\\x=5[/tex]
The cost of one cup of lemonade is $2
The cost of one cheeseburger is $5
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A recipe calls for 3/4 cup of sugar.
How many cups of sugar are
needed to make the recipe 8 times?
Which of the following choices is an equivalent expression for (12r + 2t) - (4r + 10t)
Which of the following choices is an equivalent expression for (12r + 2t) - (4r + 10t)
A
8(r - t)
B
8(r + t)
C
8r + 7t
Answer: 8(r-t)
Step-by-step explanation:
[tex](12r+2t)-(4r+10t)=12r+2t-4r-10t=8r-8t=8(r-t)[/tex]
Miss Morgan is a science teacher she found that 30% of her 120 students are athletes and Mr. Gregory is a math teacher he found that 27 or 15% of his students are athletes
3 coins are tossed
probability that:
a. no heads are tossed:
b. at least 1 head is tossed:
c. exactly 1 head is tossed:
d. 3 heads are tossed
Answer:
a. 12.50%
b. 87.50%
c. 37.50%
d. 12.50%
Step-by-step explanation:
Find the measure of line segment TU. Assume that lines which appear to be tangent to the circle are tangent.
A)
7
B)
8
0
9
D)
10
Answer:
d 10
Step-by-step explanation:
Answer:
Answer is D I’ve done it and got it right before
Step-by-step explanation:
The volume of a cylinder is 542pi in?. The height of the cylinder is 16 in. What is the radius of the cylinder to the nearest hundredth?
The volume of a sphere is 5,055pi m. What is the surface area of the sphere to the nearest square meter?
Answer:
I. Radius, r = 5.82 in
II. S.A of a sphere = 19.61 meters
Step-by-step explanation:
Given the following data;
I. Volume of cylinder = 542π in³
Height = 16 in
To find the radius of the cylinder;
Volume of cylinder = πr²h
542π = πr²*16
Dividing both sides by π, we have;
542 = 16r²
r² = 542/16
r² = 33.875
Radius, r = 5.82 in
II. Volume of sphere = 5.055π m³
To find the surface area of the sphere;
First of all, we would find the radius of the sphere.
[tex] Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} [/tex]
Substituting into the formula, we have;
[tex] 5.055 \pi = \frac {4}{3} \pi r^{3} [/tex]
Cross-multiplying, we have;
[tex] 5.055 \pi * 3 = 4 \pi r^{3} [/tex]
[tex] 15.165 \pi = 4 \pi r^{3} [/tex]
Dividing both sides by 4π, we have;
[tex] 3.79 = r^{3} [/tex]
Taking the cube root of both sides, we have;
r = 1.56 m
Next, we find the surface area (S.A) of the sphere;
S.A of a sphere = 4πr
S.A of a sphere = 4*3.142*1.56
S.A of a sphere = 19.61 meters