The side length, s, of the resulting polyhedron is (20√3)/3 cm.
To find the value of s, the side length of the resulting polyhedron, we can analyze the original cube's corners and the pyramids that Donatello slices off. Each corner of the cube contributes one-eighth of a pyramid to the polyhedron. These pyramids are similar, and their base is an equilateral triangle with side length s/2, and the height is s/2.
Considering one of these pyramids, we can use the Pythagorean theorem to find its slant height (the side length of the original cube):
(s/2)^2 + (s/2)^2 + (s/2)^2 = 10^2
Simplifying:
3/4 * s^2 = 100
Now, solve for s:
s^2 = (4/3) * 100
s^2 = 400/3
s = √(400/3)
s = 20/√3
To rationalize the denominator, multiply by (√3/√3):
s = (20/√3) * (√3/√3)
s = (20√3)/3
So, the side length s of the resulting polyhedron is (20√3)/3 cm.
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The side length of the resulting polyhedron after slicing off corner pyramids is [tex]\( \frac{10}{3} \).[/tex]
Of course, here's the solution in LaTeX:
To find the side length ( s ), we can break down the process step by step:
1. Start with a cube of side length ( 10 ).
2. Slice off a pyramid from each corner.
Since all the edges of the resulting polyhedron have the same length, let's find the side length of the pyramid. Consider one of the corner pyramids:
- It has a square base, with side length ( x , which is also equal to the side length of the cube.
- It has four congruent triangular faces.
If we draw a cross-section through the pyramid and the cube, we'll see that the cross-section of the pyramid is an isosceles right triangle with legs of length ( x ).
Given this, we can use Pythagoras' theorem to find the height of the pyramid. The hypotenuse of the right triangle is ( x ), and the legs are each x ). So, we have:
[tex]\[ x^2 = x^2 + x^2 + h^2 \][/tex]
Solving for \( h \), the height of the pyramid, we get:
[tex]\[ h = \sqrt{x^2 - x^2} = \sqrt{x^2 - \left(\frac{x}{\sqrt{2}}\right)^2} \]\[ h = \sqrt{x^2 - \frac{x^2}{2}} = \sqrt{\frac{x^2}{2}} = \frac{x}{\sqrt{2}} \][/tex]
Now, we know that the height of the pyramid is [tex]\( \frac{x}{\sqrt{2}} \).[/tex]
When we remove the corner pyramid, the remaining shape is a pentagonal pyramid with a square base. This means the side length of the square base of the remaining polyhedron is [tex]\( 10 - 2x \).[/tex]
The height of this pentagonal pyramid is the same as the height of the corner pyramid, which is [tex]\( \frac{x}{\sqrt{2}} \).[/tex]
So, we can set up an equation for the height of the remaining pyramid:
[tex]\[ 10 - 2x = \sqrt{2} \cdot \frac{x}{\sqrt{2}} \]\[ 10 - 2x = x \][/tex]
Solving for \( x \):
[tex]\[ 10 = 3x \]\[ x = \frac{10}{3} \][/tex]
So, the side length [tex]\( s \) of the polyhedron after slicing off the corner pyramids is \( \boxed{\frac{10}{3}} \).[/tex]
Rachel received $650 for her birthday. She purchased a surfboard for $477 and some additional accessories without spending more than the money she received.
She wrote the inequality 477 + x < 650.
Is the inequality correct?
Yes, because 477 and an unknown amount is less than 650.
No, because 477 and an unknown amount is greater than 650.
No, because the inequality symbol should be less than or equal to 650.
No, because x should be subtracted from 477.
Answer:
No, because the inequality symbol should be less than or equal to 650.
Step-by-step explanation:
it should be "No, because the inequality symbol should be less than or equal to 650." because the statement says she gets the accessories without spending MORE than the amount she received, it says nothing about spending the exact amount.
Answer:
No, because the inequality symbol should be less than or equal to 650.
Which of the following is a correct equation for the linear graph shown below?
(1) 2y+3x=-6
(2) 3y-2x=-6
(3) 2y+3x-2
(4) 3y-2x=-2
Given:
Given that the graph of the line.
We need to determine the equation of the line.
Slope:
The slope of the line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us substitute any two points that the line passes through.
Substituting the point (3,0) and (0,-2) in the formula, we get;
[tex]m=\frac{-2-0}{0-3}[/tex]
[tex]m=\frac{-2}{-3}[/tex]
[tex]m=\frac{2}{3}[/tex]
Thus, the slope of the equation is [tex]m=\frac{2}{3}[/tex]
y - intercept:
The y - intercept of the equation is the point at which the line passes through the y - axis.
Thus, from the graph, the value of y - intercept is b = -2.
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y = mx+b[/tex]
Substituting the values, we have;
[tex]y=\frac{2}{3}x-2[/tex]
Taking LCM, we have;
[tex]y=\frac{2x-6}{3}[/tex]
Multiplying both sides by 3, we get;
[tex]3y=2x-6[/tex]
Subtracting both sides by 2x, we get;
[tex]3y-2x=-6[/tex]
Thus, the equation of the line is [tex]3y-2x=-6[/tex]
Hence, Option 2 is the correct answer.
Fifteen hundred students attend Biship Ryan High School. 120 students were asked "Do you think that Library hours should be extended?" 40 students agreed that hours should be extended, 10 said they were against extended hours, and 70 students had no opinion. The school newspaper reported: "80% of students who had an opinion agree that school library hours should be extended". Is this a valid inference? Justify your reasoning.
Answer:
The inference is valid.
Step-by-step explanation:
In this case we need to test whether, 80% of students who had an opinion agree that school library hours should be extended.
A sample of 120 students were selected.
Of these 120, 50 students had an opinion and 70 did not.
Since we need to test for the students having an opinion, the sample size is, n = 50.
The sample proportion of students who had an opinion and agreed is:
[tex]\hat p=\frac{40}{50}=0.80[/tex]
The hypothesis can be defined as follows:
H₀: The proportion of students who had an opinion agree that school library hours should be extended is 80%, i.e. p = 0.80.
Hₐ: The proportion of students who had an opinion agree that school library hours should be extended is different from 80%, i.e. p ≠ 0.80.
The z-test for single proportion will be used.
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.80-0.80}{\sqrt{\frac{0.80(1-0.80}{50}}}=0[/tex]
The test statistic value is 0.
Compute the p-value of the test:
[tex]p-value=2\times P (Z < 0)\\=2\times 0.50\\=1[/tex]
The p-value of the test is 1.
The p-value is very large, so the null hypothesis will not be rejected at any significance level.
Thus, it can be concluded that the proportion of students who had an opinion agree that school library hours should be extended is 80%.
Hence, the inference is valid.
At Robin's Snow Cones, the shaved ice portion of the cone is shaped like a perfect sphere with a diameter of 8 cm. Exactly half of the shaved ice sphere extends above the paper cup holder. What is the volume of ice that extends above the cup to the nearest cubic centimeter? In your calculations, use LaTeX: \pi\:=\:3.14
Answer:
The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3
Step-by-step explanation:
Solution:-
- The shaved ice is modeled as a sphere.
- The half of the shaved ice sphere extends above the cup holder.
- The volume of sphere with radius r = diameter d / 2 :
[tex]V = \frac{4}{3}*\pi *r^3[/tex]
- We are to calculate the volume of the extended part of the sphere with diameter d = 8 cm or radius r = 4 cm.
- The volume of hemisphere is:
[tex]V = \frac{1}{2} *\frac{4}{3}*3.14 *r^3= \frac{2}{3}*3.14 *r^3\\\\V = \frac{2}{3}*3.14 *4^3 \\\\V =134.04128 cm^3[/tex]
- The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3
if you roll a six-sided die, what is the probability of rolling a number greater than 2?
Answer:1/6
Step-by-step explanation:
Plzz help!
4^2 × 5^2 + 30
[tex] {4}^{2} \times {5}^{2} + 30 = 16 \times 2 5+ 30 = \\ = 400 + 30 = 430[/tex]
or
[tex] {4}^{2} \times {5}^{2} + 30 = (4 \times 5)^{2} + 30 = \\ = 20^{2} + 30 = 400 + 30 = 430 [/tex]
Solve for n:
3⁄5 · n = 6
Answer:
n = 10
Step-by-step explanation:
Solve for n:
(3 n)/5 = 6
Multiply both sides of (3 n)/5 = 6 by 5/3:
(5×3 n)/(3×5) = 5/3×6
5/3×3/5 = (5×3)/(3×5):
(5×3)/(3×5) n = 5/3×6
5/3×6 = (5×6)/3:
(5×3 n)/(3×5) = (5×6)/3
(5×3 n)/(3×5) = (3×5)/(3×5)×n = n:
n = (5×6)/3
6/3 = (3×2)/3 = 2:
n = 5×2
5×2 = 10:
Answer: n = 10
To solve for n in 3⁄5 · n = 6, divide both sides of the equation by 3⁄5. The solution is n = 10.
Explanation:To solve for n in the equation 3⁄5 · n = 6, we need to isolate n on one side of the equation. To do this, we can divide both sides of the equation by 3⁄5, which is the same as multiplying both sides by its reciprocal, 5⁄3. This cancels out the fraction on the left side, leaving us with n = 6 × 5⁄3. Multiplying 6 by 5 gives us 30, and dividing that by 3 gives us a final answer of n = 10.
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Is (x +1) a factor of f(x) = x^3 + x^2 −4x − 4?
Select the appropriate response:
Yes
or
No
Answer:
Yes
Step-by-step explanation:
( x^3 + x^2) (-4x - 4)
x^2 ( x+1) -4 (x+1)
(x^2 - 4) (x+1)
(x-2) (x+2) (x+1)
X= 2 x=-2 x=-1
Answer:
Yes
Step-by-step explanation:
f(x) = x^3 + x^2 −4x − 4
Factor by grouping taking x^2 out of the first group and -4 out of the second
0 = x^3 + x^2 −4x − 4
x^2(x+1) -4(x+1)
Factor out (x+1)
0=(x+1)(x^2-4)
Now we have the difference of squares
0=(x+1) (x-2)(x+2)
x+1 is a factor
Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3jb+2c+3jb, plus, 2, c, plus, 3, j where bbb is the number of hours Ben spends chopping, ccc is the number of hours Cam spends chopping, and jjj is the number of hours Justin spends chopping. How many trees do they chop down after Ben spends 888 hours chopping, Cam spends 333 hours chopping, and Justin spends 444 hours chopping?
Answer:
26 trees.
Step-by-step explanation:
The number of trees Ben, Cam, and Justin can chop down is given by:
b+2c+3j
Where:
b is the number of hours Ben spends chopping.
c is the number of hours Cam spends chopping.
j is the number of hours Justin spends chopping.
We want to determine the number of trees they chop down after Ben spends 8 hours chopping, Cam spends 3 hours chopping, and Justin spends 4 hours chopping.
b=8, c=3, j=4
Substituting these in the given equation
b+2c+3j=8+2(3)+3(4)=8+6+12 = 26
They chop down a total of 26 trees.
Answer:
26 trees chopped altogether
Step-by-step explanation:
We are given that;
-Ben, Cam, and Justin are lumberjacks.
-The number of trees they chop down is given by b+2c+3j
where;
b is the number of hours Ben spends chopping
c is the number of hours Cam spends chopping
j is the number of hours Justin spends chopping.
We are told that;
Ben spends 8 hours to chop
Cam spends 3 hours to chop
Justin spends 4 hours to chop
Thus, Substituting in the given equation we get
Total nmber of trees chopped = b + 2 c + 3 j = 8 + 2(3) + 3(4) = 8 + 6 + 12
= 26
They have chopped 26 trees altogether
a number, truncated to 1 dp, is equal to 11.9, what are the upper and lower bounds
At the beginning of a snowstorm, Tristan had 3 inches of snow on his lawn. The snow then began to fall at a constant rate of 1.5 inches per hour. Assuming no snow was melting, how much snow would Tristan have on his lawn 4 hours after the snow began to fall? How much snow would Tristan have on his lawn after
tt
t hours of snow falling?
Answer:
Step-by-step explanation:
3+1.5*4
3+6
9 inches in total 4 hours from now
Answer:
3 + 1.5(4) = 9
then the second one will be: 3 + 1.5t
Step-by-step explanation:
1.5t is increasing do therefore that is the answer.
When records were first kept (t=0), the population of a rural town was 260 people. During the following years, the population grew at a rate of P'(t) = 45(1+sqrt(t)).
a) what is the population after 15 years?
b) find the popuation P(t) at any time t > 0.
Answer:
(a) The population after 15 years is 2678.
(b)Therefore the population P(t) at any time t>0 is
[tex]P(t)= 45t+30 {t^{\frac32}}+260[/tex]
Step-by-step explanation:
Given that,
The population grew at a rate of
[tex]P'(t)=45(1+\sqrt t)[/tex]
Integrating both sides
[tex]\int P'(t) dt=\int 45(1+\sqrt t)dt[/tex]
[tex]\Rightarrow \int P'(t) dt=\int (45+45\sqrt t)dt[/tex]
[tex]\Rightarrow \int P'(t) dt=\int 45\ dt+\int 45\sqrt t\ dt[/tex]
[tex]\Rightarrow P(t)= 45t+45\ \frac{t^{\frac12+1}}{\frac12+1}+c[/tex] [ c is integration constant]
[tex]\Rightarrow P(t)= 45t+45\ \frac{t^{\frac32}}{\frac32}+c[/tex]
[tex]\Rightarrow P(t)= 45t+45\times\frac 23 \times {t^{\frac32}}+c[/tex]
[tex]\Rightarrow P(t)= 45t+30 {t^{\frac32}}+c[/tex]
When t=0 , P(0)= 260
[tex]\therefore 260= 45\times0+30\times {0^{\frac32}}+c[/tex]
[tex]\Rightarrow c=260[/tex]
[tex]\therefore P(t)= 45t+30 {t^{\frac32}}+260[/tex]
Therefore the population P(t) at any time t>0 is
[tex]P(t)= 45t+30 {t^{\frac32}}+260[/tex]
To find the population after 15 years, we need to plug t=15 in the above expression.
[tex]P(15)=( 45\times 15)+30( {15^{\frac32}})+260[/tex]
≈2678
The population after 15 years is 2678.
The regular octagon in the ceiling has a radius of 10.5 feet and a perimeter of 64 feet. What is the length of the apothem of the octagon?
Answer:
Nearest tenth of a foot
9.7
Nearest tenth of a square foot
310.4
Step-by-step explanation:
y = x^2 - 2x; domain {-3, 0, 5}
Answer:
range:{0,15}
Step-by-step explanation:
y=x²-2x
domain:{-3,0,5}
for range
when x=-3
y=(-3)²-2×(-3)=9+6=15
when x=0
y=0-0=0
when x=5
y=5²-2×5=25-10=15
range:{0,15}
or
y=x²-2x+1-1=(x-1)²-1
when x=-3
y=(-3-1)²-1=16-1=15
when x=0
y=(0-1)²-1=1-1=0
when x=5
y=(5-1)²-1=16-1=15
The student's question involves calculating the output values of a quadratic function for a given domain. The specific output values for the domain {-3, 0, 5} of the function y = x^2 - 2x are 15, 0, and 15, respectively.
Explanation:The student is dealing with a question that involves the evaluation of a quadratic function y = x^2 - 2x at different values within its domain. Here, the domain is specified as the set {-3, 0, 5}. To answer the student's question, we calculate the value of y for each x in the domain:
For x = -3: y = (-3)^2 - 2(-3) = 9 + 6 = 15For x = 0: y = (0)^2 - 2(0) = 0For x = 5: y = (5)^2 - 2(5) = 25 - 10 = 15Therefore, the corresponding output values for the function at the points in the domain are 15, 0, and 15, respectively.
Simplify each equation. Tell whether the equation has one, no, or infinite
solutions.
5x + 6 = 2 + 3x
no solutions
one
infinite solutions
10pts will mark brainliest if right
Answer:
one solution
Step-by-step explanation:
5x + 6 = 2 + 3x
Subtract 3x from each side
5x-3x + 6 = 2 + 3x-3x
2x +6 = 2
Subtract 6 from each side
2x+6-6 = 2-6
2x = -4
Divide each side by 2
2x/2 = -4/2
x = -2
There is one solution
Answer:
One solution
Step-by-step explanation:
To solve, we need to isolate the variable, x
5x+6=2+3x
Subtract 2 from both sides
5x+4=3x
Subtract 5x from both sides
4= -2x
Divide both sides by -2
x= -2
There is one solution to this equation, -2
work out the next term of this quadratic sequence
6 9 15 24
Answer:
36
Step-by-step explanation:
6 9 15 24 ...
The sequence goes like this:
+3, +6, +9, +12, +15 (Adding 3 each time)
For example:
6 + 3 = 9 (First +3)
9 + 6 = 15 (Then +6)
15 + 9 = 24 (Then +9)
24 + 12 = 36
The next term of this quadratic sequence will be 36.
What is Quadratic equation?
An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The quadratic sequence is,
⇒ 6, 9, 15, 24
Now,
The first term = 6
The second term = 6 + 3 = 9
The third term = 9 + 6 = 15
The fourth term = 15 + 9 = 24
Thus, The pattern of adding are;
3 , 6 , 9, ..
So, For next term we add 12 in fourth term, we get;
The next term = 24 + 12
= 36
Thus, The next term of this quadratic sequence will be 36.
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What is the factored form of this expression? x2 + 9x + 16
Answer:
this problem is not factorable.
Step-by-step explanation:
Final answer:
The factored form of the quadratic expression x^2 + 9x + 16 is (x + 7)(x + 2), found by identifying two numbers that multiply to 16 and add up to 9.
Explanation:
To find the factored form of the expression x2 + 9x + 16, we are looking for two binomials that when multiplied together will yield the original quadratic expression. Since the coefficient of x2 is 1, we only need to find two numbers that add up to the coefficient of x (which is 9) and multiply together to get the constant term (which is 16).
To factor the quadratic expression, we look for two numbers that multiply to 16 and add to 9. These numbers are 7 and 2. Therefore, the factored form of the expression is (x + 7)(x + 2).
In ΔKLM, the measure of ∠M=90°, the measure of ∠L=48°, and KL = 28 feet. Find the length of LM to the nearest tenth of a foot
Answer: x= 18.7357 or 18.7 feet
What is the measure of Au?
889
44°
50°
64°
92°
Answer:
50
Step-by-step explanation:
The measure of AU is 50.
What is an arc?An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
Given:
arc QU = 88 and <QUA = 111
QDA = 2 <QUA
= 2 X 111
= 222
Now, QUA = 360- 222 = 138
arc AU = QUA - arc QU
= 138- 58
= 50
Hence, the measure of AU is 50.
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Find a value for m and n to make a true statement.
a) mx^2 - 36 = (3x + 6)(3x - 6)
b) (mx + ny)^2 = 4x^2 + 12xy + 9y^2
Answer:
Correct answer: a) m = 9 ; b) m = 2 and n = 3
Step-by-step explanation:
Given:
a) m x² - 36 = (3 x + 6) (3 x - 6) ⇒ m = ?
b) (m x + n y)² = 4 x² + 12 x y + 9 y² ⇒ m, n = ?
a) m x² - 36 (3 x + 6) (3 x - 6)
The right side of the equation is the difference of the square, so we will present the left side in the same way:
(√m x)² - 6² = (3 x + 6) (3 x - 6)
(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)
√m = 3 /² when we square both sides of the equation we get:
m = 9
b)
(m x + n y)² = 4 x² + 12 x y + 9 y²
The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:
(m x + n y)² = (2 x)² + 2 · 2 x · 3 y + (3 y)² = (2 x + 3 y)²
(m x + n y)² = (2 x + 3 y)² ⇒
m = 2 and n = 3
God is with you!!!
For part (a), m must be 9 to make the equation true. For part (b), m can be 2 or -2, and n can be 3 or -3 to satisfy the equation.
Explanation:To find values for m and n to make the statements true, we must compare coefficients or recognize patterns in the given equations.
Part (a)
We have the equation mx^2 - 36 = (3x + 6)(3x - 6). We can expand the right side to get 9x^2 - 36. To make this equation true, we need the coefficient of x^2 on the left to be equal to the coefficient on the right, which is 9. Therefore, m must be 9 for the equation to be true.
Part (b)
We have (mx + ny)^2 = 4x^2 + 12xy + 9y^2. Expanding the left side, we get m^2x^2 + 2mnxy + n^2y^2. To equate it to the right side, we need m^2 = 4 and n^2 = 9. This gives us two possibilities each for m and n: m can be 2 or -2 and n can be 3 or -3.
In this diagram, like segment AD is tangent and line segment AC is secant. If AB = 6 and BC = 18, what is the length of line segment AD?
9514 1404 393
Answer:
12
Step-by-step explanation:
The applicable relationship here is ...
AD² = AB·AC
AD = √(AB·(AB +BC)) = √(6·(6+18)) = √144
AD = 12
1. Lake Turkana is in the Great Rift Valley in northwest Kenya. As part of a study of water quality, the water temperature in the lake was measured at different depths. The data are shown in this scatter plot.
Answer:
a. 26° C
b. 40m
c. Yes
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
a. What was the approximate temperature at a depth of 70 m? At the surface?
26° C
b. At what depth was the temperature a little more than 27°C?
40 m
c. Do the points in the scatter plot show a relationship? Explain your thinking.
Yes, the scatter plot show a relationship between the depth and the temperature of Lake Turkana. It shows a negative correlation between the two variables. The deeper the lake is, the cooler the temperature .
Hope it will find you well.
Judy spent 1 hour and 15 minutes less than Sandy exercising last week Sandy Sprint 50 minutes less than Mary who's been 3 hours at the gym how long did Judy spend exercising
Answer:
Judy spent 55 min at the gym.
Step-by-step explanation:
From the three people that are listed in the problem Mary is the only one we know the actual time she was at the gym which is 3 h. Sandy on the other hand spent 50 minutes less sprinting than Mary, so we have:
Sandy = Mary - 50 minutes
Sandy = 3h - 50 minutes
Sandy = 3*60 - 50
Sandy = 180 - 50 = 130 minutes
Judy spent 1h and 15 min less than Sandy exercising so we have:
Judy = Sandy - 1h 15min
Judy = 130 min - (60 min + 15 min)
Judy = 130 min - 75 min = 55 min
Judy spent 55 min at the gym.
2) There are 45 dogs and 30 cats at the animal recovery center. Of these animals, there are 16 colored dogs and 8 solid cats. What percentage of the animals are solid colored?
Answer:
32%
Step-by-step explanation:
Total animals: 45 + 30 = 75
Coloured: 16 + 8 = 24
24/75 × 100
32%
In the United States, 36 percent of the people have a blood type that is A positive. From a random sample of 150 people from Norway, 66 had a blood type that was A positive. Consider a hypothesis test to investigate whether the proportion of people in Norway with a blood type of A positive is different from that in the United States. Which of the following is the standard deviation used to calculate the test statistic for the one-sample z-test? (0.24) (0.76) 150 (0.44) (0.56) 150 (0.36)(0.64) 150 (0.44)(0.56) 150 (0.36 (0.64) 150
Answer:
The standard deviation used to calculate the test statistic for the one-sample z-test is 0.04.
Step-by-step explanation:
A single proportion z-test can be performed to determine whether the proportion of people in Norway with a blood type of A positive is different from that in the United States.
It is provided that the percentage of people in the US with blood type A positive is, p = 36%.
A random sample of n = 150 people from Norway are selected to check the above claim.
The hypothesis can be defined as:
H₀: The proportion of people in Norway with a blood type of A positive is same as that in the United States, i.e. p = 0.36.
Hₐ: The proportion of people in Norway with a blood type of A positive is different from that in the United States, i.e. p ≠ 0.36.
The test statistic for the the hypothesis testing is:
[tex]z=\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
The mean of the sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
Compute the standard deviation value as follows:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]=\sqrt{\frac{0.36(1-0.36)}{150}}[/tex]
[tex]=0.03919184\\\approx0.04[/tex]
Thus, the standard deviation used to calculate the test statistic for the one-sample z-test is 0.04.
To start a board game,the player who rolls two sixes gets to go first. What is the probability that a player will roll two
number cubes and get two sixes?
) Intro
Done
There is a 1/36 or a ~2.8% chance that a player will roll two sixes. Because the dice is cubed, the player will have a 1/6 probability of rolling a six one time. Because the player needs to get six 2 times in a row, you would simply need to multiply 1/6 by itself twice(1/6•1/6 or 1/6^2) which equals 1/36.
Suppose AC = 5 cm, BC = 12 cm, and mAC = 45.2°.
To the nearest tenth of a unit, the radius of the circumscribed circle
is __?__ cm and m∠OAC = __?__°.
Help pls
9514 1404 393
Answer:
6.5 cm67.4°Step-by-step explanation:
AB is shown as a diameter, which means that inscribed angle C is a right angle. The length of the diameter can be found from the Pythagorean theorem to be ...
AB^2 = AC^2 + BC^2
AB = √(5^2 +12^2) = 13
The radius is half the length of the diameter, so is ...
OA = 13 cm/2 = 6.5 cm . . . . radius
__
The measure of inscribed angle B is half the measure of arc AC, so is ...
∠B = 45.2°/2 = 22.6°
The measure of angle OAC is the complement of this, so is ...
∠OAC = 90° -22.6°
∠OAC = 67.4°
Answer:
Step-by-step explanation:
For the study described below, identify the population parameter. A bank manager wants to know the average amount of time customers of his bank have to wait in line. 300 customers were polled and asked their average wait time at the bank. 27 of the 300 people were extremely dissatisfied with the amount of time they had had to wait in line in recent months.A) The 300 customers poll
B) The 27 people who were dissatisfied
C) The customers who were waiting in line at the bank the day of the poll
D) All customers of the bank
Answer:
The population parameter is the average wait time for all the bank's customers.
Step-by-step explanation:
The population parameter is a numerical value that defines a specific characteristic of the population. For example, the population mean describes the average value of the population, the population variance describes the variance of the population and the population proportion describes the proportion of a certain variable in the population.
The sample statistic is a numerical value that defines a specific characteristic of the sample that is selected from the population. The examples of sample statistic are, sample mean, sample variance and sample proportion.
In this case it is provided that the bank manager wants to know the average amount of time customers of his bank have to wait in line.
The experiment involved, asking 300 customers about their average wait time at the bank.
So, the parameter under study is the mean time the customers have to wait at the bank.
Hence, the population parameter is the average wait time for all the bank's customers.
Final answer:
The population parameter the bank manager wants to know is the average wait time for all customers of the bank, which is represented by option D) All customers of the bank.
Explanation:
The population parameter the bank manager is interested in determining is the average wait time for all customers of the bank, not just the 300 polled customers or the subset of dissatisfied customers. Therefore, the correct answer to the student's question is D) All customers of the bank.
This average wait time is a parameter that describes some aspect of the entire population of the bank's customers. In terms of statistics, a population parameter is a value that represents a characteristic of the entire population, which in this case, includes all the customers of the bank, whether they were part of the survey or not.
whats the area of a circle if the diameter is 24.26 mm
Answer:
approximately 462.24
Step-by-step explanation:
A research team conducted a critical study, and constructed a 95% confidence interval from their data. The team was not happy with the result because they felt the margin of error was much too large. All other things being equal, if they were to repeat the study, what could they do to reduce the margin of error?
A) They could construct the confidence interval with a lower confidence level than they previouslyused.B) They could include a greater number of subjects in the experiment.C) They could reduce the population standard deviation ?.D) All of the above are possible things for them to try.E) None of the above will work because of the randomness in the experiment.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample mean ± margin of error
Margin of error = z × population standard deviation/sample size
A higher confidence level gives a higher z score. Reducing z and increasing number of samples could reduce the margin of error.
To reduce the margin of error, the correct options are
A) They could construct the confidence interval with a lower confidence level than they previously used.
B) They could include a greater number of subjects in the experiment.