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Carlton and Leon are expert bowlers. Seventy percent of Carlton's rolls are strikes, while 67% of Leon's rolls are strikes. Suppose that Carlton and Leon each bowl 25 games. What is the probability that Leon's proportion of strikes is greater than Carlton's for these games?
Answer:
The probability that Leon strikes is greater than Carlton strike is 0.40905
Step-by-step explanation:
From the question, we have;
The percentage of Carlton's rolls are strikes, [tex]\hat p_1[/tex] = 70%
The number of games Carlton played, n₁ = 25
The percentage of Leon's rolls that are strikes, [tex]\hat p_2[/tex] = 67%
The number of games Leon played, n₂ = 25
Therefore, we have;
[tex]\hat p=\dfrac{k_1 + k_2}{n_1 + n_2}[/tex]
Where;
k₁ = 0.7 × 25 = 17.5
k₂ = 0.67 × 25 = 16.75
[tex]\therefore \hat p=\dfrac{17.5 + 16.75}{25 + 25} = 0.685[/tex]
The test statistic is given as follows;
[tex]Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p} \cdot (1-\hat{p})\cdot \left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}[/tex]
[tex]Z=\dfrac{0.7-0.67}{\sqrt{0.685 \cdot (1-0.685)\cdot \left (\dfrac{1}{25}+\dfrac{1}{25} \right )}} \approx 0.2283[/tex]
From the z-table, we have;
The p-value for Carlton strikes is greater than Leon's strike = 0.59095
∴ The p-value for Leon strikes is greater than Carlton strike = 1 - 0.59095 = 0.40905
The probability that Leon strikes is greater than Carlton strike = 0.40905
Reduce this algebraic fraction.
27c^4d^5
--------------
9c^7d^4
Answer:
Step-by-step explanation:
[tex]\frac{a^{m}}{a^{n}}=a^{m-n}\\\\a^{-m}= \frac{1}{a^{m}}[/tex]
[tex]\frac{27c^{4}*d^{5}}{9c^{7}d^{4}}= 3*c^{4-7}*d^{5-4}\\\\ = 3c^{-3}d^{1}\\\\= \frac{3d}{c^{3}}[/tex]
You bought a $1750 worth of stocks in
2012. The value of the stocks has been
decreasing by 12% each year. Let y = the
value of the stocks and let x = the
number of years since 2012. Write and exponential function to represent this situation.
What will your stock be worth in 2020? Round your answer to the nearest cent.
Answer:
f(x) = 1750 x 0.88^x
It will be worth $629.36 in 2020.
Step-by-step explanation:
Find the surface area of rectangular prism
Solve for k 9k^3=1125
9k³ = 1125
k³ = 1125 : 9
k³ = 125
k = 5 (because 5³ = 5 * 5 * 5 = 125)
The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph of the function.
(Enter the xxx-intercepts from least to greatest.)
This is the graph of a
function.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
The xxx-intercepts of the graph (in order from least to greatest) are located at x=\:x=x, equals
and x=\:x=x, equals
.
The greatest value of yyy is y=\:y=y, equals
, and it occurs when x=\:x=x, equals
.
For xxx between x=2x=2x, equals, 2 and x=6x=6x, equals, 6, the function value y\:yy
\:000.
Answer:
This is the graph of a {\text{nonlinear function}}nonlinear functionstart text, n, o, n, l, i, n, e, a, r, space, f, u, n, c, t, i, o, n, end text.
The yyy-intercept of the graph is the function value y={{-6}}y=−6y, equals, minus, 6.
The xxx-intercepts of the graph are located at x={2}x=2x, equals, 2 and x={6}x=6x, equals, 6.
The greatest value of yyy is y={2}y=2y, equals, 2, and it occurs when x={4}x=4x, equals, 4.
For xxx between x=2x=2x, equals, 2 and x=6x=6x, equals, 6, the function value {y \, {\geq } 0}y≥0y, is greater than or equal to, 0.
Step-by-step explanation:
1 / 7
Let's use the graph to complete the sentences one by one.
Hint #22 / 7
A function with a constant rate of change produces a graph that is a line, and we say the function is linear. If the rate of change of the function is not constant, the graph will not be a line, and we say the function is nonlinear.
The graph shown is not a line. Therefore, we are looking at the graph of a nonlinear function.
Hint #33 / 7
The yyy-intercept of a graph is the value of the function when \red{x=0}x=0start color #df0030, x, equals, 0, end color #df0030. The yyy-intercept of this graph is the function value \blue{y=-6}y=−6start color #6495ed, y, equals, minus, 6, end color #6495ed.
Hint #44 / 7
The xxx-intercepts of a graph are the values of \red{x}xstart color #df0030, x, end color #df0030 for which \blue{y=0}y=0start color #6495ed, y, equals, 0, end color #6495ed. The xxx-intercepts of this graph are located at \red{x=2}x=2start color #df0030, x, equals, 2, end color #df0030 and \red{x=6}x=6start color #df0030, x, equals, 6, end color #df0030.
Hint #55 / 7
The maximum value of \blue{y}ystart color #6495ed, y, end color #6495ed occurs at the top of the bump in the graph. The coordinates of the top of the bump are (\red{4},\blue{2})(4,2)left parenthesis, start color #df0030, 4, end color #df0030, comma, start color #6495ed, 2, end color #6495ed, right parenthesis. Therefore, the maximum value is \blue{y=2}y=2start color #6495ed, y, equals, 2, end color #6495ed, and it occurs when \red{x=4}x=4start color #df0030, x, equals, 4, end color #df0030.
Hint #66 / 7
The graph of the function is above the xxx-axis for values of \red{x}xstart color #df0030, x, end color #df0030 between \red{x=2}x=2start color #df0030, x, equals, 2, end color #df0030 and \red{x=6}x=6start color #df0030, x, equals, 6, end color #df0030. For these values of \red{x}xstart color #df0030, x, end color #df0030, the function value y\geq 0y≥0y, is greater than or equal to, 0.
Hint #77 / 7
We can now complete the sentences:
This is the graph of a {\text{nonlinear function}}nonlinear functionstart text, n, o, n, l, i, n, e, a, r, space, f, u, n, c, t, i, o, n, end text.
The yyy-intercept of the graph is the function value y={{-6}}y=−6y, equals, minus, 6.
The xxx-intercepts of the graph are located at x={2}x=2x, equals, 2 and x={6}x=6x, equals, 6.
The greatest value of yyy is y={2}y=2y, equals, 2, and it occurs when x={4}x=4x, equals, 4.
For xxx between x=2x=2x, equals, 2 and x=6x=6x, equals, 6, the function value {y \, {\geq } 0}y≥0y, is greater than or equal to, 0.
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