A recent CBS News survey reported that 64% of adults felt the U.S. Treasury should continue making pennies. Suppose we select a sample of 18 adults. a-1. How many of the 18 would we expect to indicate that the Treasury should continue making pennies
Answers
Complete Question
A recent CBS News survey reported that 64% of adults felt the U.S. Treasury should continue making pennies. Suppose we select a sample of 18 adults.
a-1. How many of the 18 would we expect to indicate that the Treasury should continue making pennies
a-2) What is the standard deviation?
a-3) What is the likelihood that exactly 3 adults would indicate the Treasury should continue making pennies?
Answer:
a-1 \(\= x = 11 .52\)
a-2 \(\sigma = 2.036\)
a-3 \(P(3) = 4.7*10^{-5}\)
Step-by-step explanation:
From the question we are told that
The sample size is \(n = 18\)
The proportion of adult that felt the U.S. Treasury should continue making pennies is p = 0.64
The proportion of adult that feel otherwise is
\(q = 1- p = 1-0.64 = 0.36\)
The mean is mathematically evaluated as
\(\= x = n * p\)
substituting values
\(\= x = 18 * 0.64\)
\(\= x = 11 .52\)
The standard deviation is mathematically represented as
\(\sigma = \sqrt{ npq}\)
substituting values
\(\sigma = \sqrt{18 * 0.64 * 0.36}\)
\(\sigma = 2.036\)
The likelihood that 3 adult would indicate the Treasury should continue making pennies is mathematically evaluated as
\(P(3) = \left n} \atop \right. C_3 (p)^{3} * (q)^{n-3}\)
Now
\(\left n} \atop \right. C_3 = \frac{n! }{[n-3] ! 3!}\)
substituting values
\(\left n} \atop \right. C_3 = \frac{18! }{[15] ! 3!}\)
\(\left n} \atop \right. C_3 = \frac{18 * 17 * 16 * 15! }{[15] ! (3 *2 *1 )}\)
\(\left n} \atop \right. C_3 = \frac{18 * 17 * 16 }{ (3 *2 *1 )}\)
\(\left n} \atop \right. C_3 = 816\)
So
\(P(3) = 816 * (0.64 )^3 * (0.36 )^{18-3}\)
\(P(3) = 4.7*10^{-5}\)
Related Questions
Determine whether the equation defines y as function of x.
a)
\(3x + 2y = 5\)
b)
\(y = - \sqrt{x + 1} \)
Answers
Answer:
The answer is A I just took the test
Step-by-step explanation:
write the slope intercept form of the equation of each line just need help with 1 to undersand the subject. i will do the rest :)
EXPLAIN YOUR ANSWER OR I WILL NOT MARK BRAINLIEST AND I WILL REPORT
Answers
3x-2y=-16
slope intercept form is y=mx+b
move 3x to the other side
sign changes from +3x to -3x
3x-3x-2y=-3x-16
-2y=-3x-16
divide both sides by -2 to get y by itself
-2y/-2=-3x/-2-16/-2
y=3x/2+8
answer:
y=3x/2+8
which equation has x=8 for a solution
2x + 3 = 13
4x + 6 = 38
3x - 5 = 29
5x - 8 = 48
Answers
Answer:
4x + 6 = 38
Step-by-step explanation:
Substitute x in for x and see which equation is true
2x + 3 = 13
2*8+3 = 16+3 = 19 this is not 13 so it is false
4x + 6 = 38
4*8+6 = 32+6 = 38
This is true
3x - 5 = 29
3*8 -5 = 24-5 = 19
False
5x - 8 = 48
5*8-8 = 40-8 = 32
False
4(8) + 6=38
32 + 6=38
38=38
Which number line correctly shows look at pic
Answers
Answer:
A - The first one
Step-by-step explanation:
Answer:
The first line.
Step-by-step explanation:
The line starts off at 0,
then it goes to the left of the line -3 times.
Then it goes to the left -1.5 times.
this means it goes one and a half.
so it would land on the line after -4.
If a fair coin is tossed 8 times, what is the probability, rounded to the nearest
thousandth,of getting at least 6 heads?
Answers
The probability of getting at least 6 heads is3/256 or 0.0117
What is probability ?Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.
Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.
Given that,
A fair coin is tossed = 8 time.
We have to find the probability of getting at least 6 heads.
Since, the probability of getting head, when one coin is tossed = 1/2
And the probability of getting tale = 1/2
The probability of getting head at least 6 times when coin is tossed 8 times can be given as,
The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) = (1/2)⁸
The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸
The head can come 8 times, then probability = (1/2)⁸
The probability of getting head at least 6 times
= (1/2)⁸ + (1/2)⁸ + (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117
The probability of getting at least 6 heads is3/256 or 0.0117
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6 + 4 x 3 +7}
Pls helpppp
Answers
Answer:
25
Step-by-step explanation:
none
Answer:
6+4×3+7=37
Step-by-step explanation:
6+4= 10
3x10=30
30+7=37
3. MODELING REAL LIFE An apple growing on a tree
has a circumference of 6 inches. (See Example 2.)
a. The apple has a density of 0.46 gram per cubic
centimeter. Find the mass of the apple.
b. The radius of the apple increases inch per week
for the next five weeks. How does the volume
change during the five-week period? Explain
Answers
a. The mass of the apple is approximately 33.879 grams.
b. The volume of the apple increases by approximately 1.454 cubic inches during the five-week period.
a. To find the mass of the apple, we need to calculate its volume first. The circumference of the apple can be used to determine its radius.
The formula for the circumference of a circle is C = 2πr,
where C is the circumference and r is the radius.
Rearranging the formula, we have r = C / (2π).
Plugging in the given circumference of 6 inches.
we get r = 6 / (2π) ≈ 0.955 inches.
Now, we need to convert the radius from inches to centimeters since the density is given in grams per cubic centimeter.
Since 1 inch is approximately 2.54 centimeters, the radius in centimeters is \(0.955 \times 2.54\) ≈ 2.427 cm.
Next, we can calculate the volume of the apple using the formula for the volume of a sphere: V = (4/3)πr³.
Plugging in the radius in centimeters, we get
V ≈ (4/3)π(2.427)³ ≈ 73.682 cm³.
Finally, we can find the mass of the apple by multiplying the volume by the density:
mass = volume \(\times\) density
= 73.682 cm³ \(\times\) 0.46 g/cm³
≈ 33.879 grams.
Therefore, the mass of the apple is approximately 33.879 grams.
b. The volume of a sphere increases with the cube of its radius.
Since the radius increases by 1/8 inch per week for five weeks, the change in radius would be\((1/8) \times 5 = 5/8 inch.\)
Now, let's calculate the change in volume during the five-week period. The formula for the volume of a sphere is V = (4/3)πr³.
Initially, the radius was 0.955 inches.
After five weeks, the radius would be 0.955 + 5/8 inches.
To compare the change in volume, we can calculate the new volume and find the difference:
Change in Volume = New Volume - Initial Volume
Initial Volume = (4/3)π(0.955)³
New Volume = (4/3)π(0.955 + 5/8)³
By subtracting the initial volume from the new volume, we can determine how the volume changes during the five-week period.
Please note that the exact calculation will depend on the precise values used for π and the measurements provided.
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Like the land bridge people, what factors might have pulled the Solutreans into North America?
overpopulation
job opportunities
better schools
grasses and animals
Answers
Answer:
mayne because of grasses and animals
Answer:
D
Step-by-step explanation:
Write a polynomial function in standard form with zeros at 0, 1, and 2.
f(x) = x(x - 1)(x - 2)
f(x) = x(x + 1)(x + 2)
f(x) = x3 – 3x2 + 2x
f(x) = x3 + 3x2 + 2x
Answers
Answer:
the first one is correct
Answer:
b
Step-by-step explanation:
Find the slope of the line that passes through the pair of points.
(2, -3). (-5, 1)
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Help ksjsjsjs
Answers
1+1? i dont now what the answer is.
Answers
Answer:
its 2
Step-by-step explanation:
4. The physician's order states: Add 60mEq of potassium chloride to 1000ml D5W and infuse at a rate of 42 ml per hour. Available are ampoules labeled potassium chloride 40 mEq = 20 ml. The infusion set has a drop factor of 60 gtt/ml. (a) How much potassium chloride should be added to the IV?
Answers
Using concentration-volume relationship, 30 ml of potassium chloride should be added to the IV solution.
How much potassium chloride should be added to the IV?To calculate the amount of potassium chloride to be added to the IV, we need to consider the concentration of the potassium chloride ampoules and the desired final concentration in the IV solution.
Given:
Physician's order: Add 60mEq of potassium chloride to 1000ml D5W
Potassium chloride concentration in ampoules: 40 mEq per 20 ml
Desired final concentration: Not specified
To determine the amount of potassium chloride to be added, we can set up a proportion based on the mEq (milliequivalents) of potassium chloride:
This is done using concentration-volume relationship
40 mEq / 20 ml = 60 mEq / x ml
Cross-multiplying, we have:
40 mEq * x ml = 60 mEq * 20 ml
Simplifying:
40x = 1200
Dividing both sides by 40:
x = 30 ml
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Your town has a park at points (-9,-9), (-3,-9) and (-6,-5). What is the area of the park?
Answers
The area of the park is 12 square units.
To find the area of the park, we can use the Shoelace Formula (also known as Gauss's area formula). This formula allows us to calculate the area of any polygon given the coordinates of its vertices.
The Shoelace Formula states that if we have the coordinates of the vertices of a polygon in counterclockwise order (x₁, y₁), (x₂, y₂), ..., (xn, yn), then the area (A) of the polygon is given by:
A = 1/2 × |(x₁y₂ + x₂y₃ + ... + xn-1yn + xny₁) - (y₁x₂ + y₂x₃ + ... + yn-1xn + ynx₁)|
In our case, the coordinates of the park's vertices are (-9, -9), (-3, -9), and (-6, -5). Let's calculate the area using the Shoelace Formula:
A = 1/2 × |(-9 × -9 + -3 × -5 + -6 * -9) - (-9 × -3 + -9 × -6 + -5 × -9)|
Simplifying further:
A = 1/2 × |(81 + 15 + 54) - (27 + 54 + 45)|
A = 1/2 × |150 - 126|
A = 1/2 × |24|
A = 12
Therefore, the area of the park is 12 square units.
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Answer:
12 square units---------------------
Plot the given vertices and connect.
See attached.
Then add the height CD.
The base is AB, with the length:
AB = - 3 - (- 9) = -3 + 9 = 6The height is CD, with length:
CD = -5 - (- 9) = - 5 + 9 = 4Find the area using equation:
A = bh/2A = 6*4/2A = 12
What is the rate of change for the interval between 0 and
2 for the quadratic equation as f(x) = 2x² + x - 3
represented in the table?
O
23/1/2
04
05
O 10
Answers
\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)
The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The function is given below.
f(x) = 2x² + x - 3
The rate of change of the function for the interval between 0 to 2 is calculated as,
Average rate = [f(2) - f(0)] / [2 - 0]
Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2
Average rate = 10 / 2
Average rate = 5
The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.
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pls helppppppppppppppp
Answers
Answer:
4 seems to be it
Step-by-step explanation:
2.952 + 39.24 =
A: 42.192
B: 68.76
C: 6.876
D: 687.6
E: 36.288
F: 42.76
Answers
Answer:
The answer to this question is A
Answer:A:42.192
Step-by-step explanation:
line them up by the decimals and place value
39.24
+2.952
add a zero onto 39.24 to line them up correctly
39.240
+2.952
then add to get an answer of
A:42.192
6a-11=13 What does a equal?
Answers
Answer:
a=4
Step-by-step explanation:
13+11=24
24÷6=4 ima just say hi so that there is 20 characters in this
Solve x^2 + 6x + 15 = 0 using the Quadratic Formula
Answers
PLEASE HELP ASAP!! (NO LINKS)
Tell whether the ordered pair
(-5, -4) is a solution of the system.
Answers
Everyone at Ethan's school wore either brown or yellow for school spirit day. 74 out of the 100 students at the school wore brown. What percentage of the students wore brown?
Answers
Answer:
It would be 74% out of 100%
Step-by-step explanation:
A towns population grew from 7500 people to 8210 over the span of 10 years. What is the rate of growth in people per year for those 10 years?
Answers
Answer: 71 people per year
Step-by-step explanation:
8210 - 7500 = 710
710 ÷ 10 = 71.
Rate of growth in people per year for those 10 years = 71 people per year.
The equation is y = 7500 × (1.00908)ˣ. Then the rate of growth in people per year for those 10 years is 1.00908.
What is an exponent?Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
A town's population grew from 7500 people to 8210 over the span of 10 years.
We know that the equation is given as
\(\rm y = ab^x\)
We have
y = 8210
a = 7500
x = 10
Then the value of b will be
\(\begin{aligned} \rm 8210 = \rm 7500\times b^{10}\\\\\rm b^{10} = 1.09467 \\\\\rm b = \sqrt[10]{1.09467}\\\\\rm b =1.00908\end{aligned}\)
Then the rate of growth in people per year for those 10 years is 1.00908.
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What is the correct numerical expression for "12 times the sum of 5 and 25 minus 2?"
(12 x 5) + 25 − 2
12 x (5 + 25) − 2
12 x (5 + 25 − 2)
12 x 5 + (25 − 2)
Answers
The correct numerical expression for "12 times the sum of 5 and 25 minus 2" by simplification is option (b) , i.e 12 x (5 + 25) − 2.
What is simplification in mathematics?Simplification means simplifying an expression by reducing it to a simpler form. Approximating means simplifying the formula to the nearest value, which is not exactly correct.
What is BODMAS?BODMAS stands for Bracket, Off, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction.
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Answer:
12 x (5 + 25) − 2
Step-by-step explanation:
hope this helps!
What is the perimeter of the shaded part of this??
Answers
Answer:
18.9cm ( I rounded of and used Π as 3.14)
Step-by-step explanation:
P=distance all round
=1\2ΠD +Πd
see you have to calculate the upper length of the circle , since its half u multiply by a half. And since its not fully shaded the two semi circles are now included as the lower part of the whole shape. so you add them too. (I hope I'm making sense)
Question 15 of 60
Choose the symbol that correctly compares the fractions below.
8 8
-?-
10 10
OA. None of these are correct.
OB. <
C. >
OD. =
SUBMIT
Answers
Answer:
D
Step-by-step explanation:
can anyone help with my math hw
Answers
The value of x in the inequality will be x ≥ 2
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
5x^2 +3 ≥ 23
5x^2 ≥ 23 - 3
5x^2 ≥ 20
x^2 ≥ 20/5
x^2 ≥ 4
\(x \geq \sqrt{4}\)
x ≥ 2
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. If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?
Answers
The answer is:
⇨ x = 39°Work/explanation:
Bear in mind that the sum of all the angles in a triangle is 180°.
Given two angles, we can easily find the third one.
Let's call it x.
Next, we set up an equation:
\(\sf{54+87+x=180}\)
\(\sf{141+x=180}\)
Subtract 141 on each side.
\(\sf{x=180-141}\)
\(\sf{x=39}\)
Hence, the other angle is 39°.Find the volume of this cylinder.
Round to the nearest tenth.
r = 3 cm
3cm
V = [?] cm³
![Find the volume of this cylinder.Round to the nearest tenth.r = 3 cm3cmV = [?] cm](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Vmgyk5cjo53BHPo7juVcmr5BMz8dcPuq.png)
Answers
The volume of the given cylinder is 84.8 cm³.
Given: Radius of cylinder, r = 3cm Height of cylinder, h = 3cm
Formula used: Volume of cylinder = πr²hπ is a constant and is approximately equal to 3.14.
Volume of cylinder = πr²h= 3.14 x 3² x 3= 84.78 cm³ (rounded to the nearest tenth)= 84.8 cm³
Therefore, the volume of the given cylinder is 84.8 cm³.
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can someone help me with this question?
Answers
Distance from Starting Point of Spring (inches) 6 2 1 7 Weight on Spring (kilograms) Part A According to the graph, what is the constant of proportionality in kilograms per inch? (Note: This is also called the spring constant. The spring constant is determined by the spring's material and design.)
Answers
Answer:
The constant of proportionality is the number of kilograms that will stretch the spring by 1 inch. When y = 1, x = 1/3, so the constant of proportionality in kilograms per inch is 1/3.
PLEASE HELP W THIS I WILL Give YOU THE BRAINLIEST PLEASE ! - What does it mean to have a skewed distribution? What causes a skew in statistical terms? And how does one deal with skewed data when conducting research? Are there specific types of
research questions and types of data where one would expect the data to be skewed?
Answers
Answer:
Explained below
Step-by-step explanation:
A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.
B) If in a data set, if there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.
Also, if the curve is inclined to the left, it means there are few extreme values to the left and it is negatively skewed.
Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.
C) Example of a research question is;
If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data is positively skewed.