Which of the following is an example of theoretical probability?
O A. Lisa attempted 25 basketball free throws and made 14 of them.
The probability Lisa will make a free throw is
14
25
O B. Mike invited 10 friends to a party, and 7 of them said yes. The
probability that a friend will say yes is
7
10
O C. Kelli put 6 red marbles and 5 blue marbles in a bag. The probability
of selecting a red marble is
6
11
O D. Tony listened to 40 songs on the radio and liked 29 of them. The
probability he will like a song is
29
40

Answer:

14 ft × 14 ft × 8.75 ft

Step-by-step explanation:

A garbage company is designing an open rectangular container that should have a volume of 1,715 cubic feet.

So we have the length of the container = "x" ft, the width of the container = "y" ft and the height of the container = "z" ft

Therefore the volume of the rectangular container would be:

x * y * z = 1715 ft³

z = 1715 / x * y

The cost of making the bottom of the container is $ 5 per square foot, that is:

5 * (x * y)

Now, area of ​​all sides of the container would be:

2 * (x * z + y * z) = 2 * z * (x + y)

We know that it has been given that the cost of making all the sides of the container is = $ 4 per square foot, so:

4 * (2 * z * (x + y)) = 8 * z * (x + y)

In total the costs would be:

5 * (x * y) + 8 * z * (x + y)

If we replace z, in the previous equation we have:

5 * (x * y) + 8 * (1715 / x * y) * (x + y)

solving, and we would have that the total cost would be:

C = 5 * (x * y) + 13720 / x + 13720 / y

Now we will find the derivative of C and make it equal to zero:

dC / dx = 0; dC / dy = 0

For dC / dx = 0:

dC / dx = 5 * y + 13720 * -1 / (y ^ 2) + 13720 * 0

0 = 5 * y - 13720 / y ^ 2

5 * y = 13720 / y ^ 2

y ^ 3 = 13720/5 = 2744

y = 14

For dC / dy = 0:

dC / dy = 5 * x + 13720 * 0 + 13720 * -1 / (x ^ 2)

0 = 5 * x - 13720 / x ^ 2

5 * x = 13720 / x ^ 2

x ^ 3 = 13720/5 = 2744

x = 14

now for z:

z = 1715 / (14 * 14)

z = 8.75

Therefore, the dimensions of the container should be 14 ft × 14 ft × 8.75 ft to minimize manufacturing cost.

Answer:

The resultant polynomial is: [tex]6x^2-6x+5[/tex]

Step-by-step explanation:

We need to subtract [tex](x+1)^{2}[/tex] from [tex]7x^2-4x+6[/tex]

so, we start by performing the multiplication involved in the perfect square of the binomial [tex](x+1)[/tex], and obtain its expression in separate terms that can be combined:

[tex](x+1)^{2}=(x+1)\,(x+1)=x^2+x+x+1=x^2+2x+1[/tex]

Now we can subtract this trinomial from  [tex]7x^2-4x+6[/tex], and  combining like terms to get the resultant polynomial expression:

[tex]7x^2-4x+6-(x^2+2x+1)=7x^2-4x+6-x^2-2x-1=7x^2-x^2-4x-2x+6-1=6x^2-6x+5[/tex]

Then the resultant polynomial is: [tex]6x^2-6x+5[/tex]

Answer:

Step-by-step explanation:

(x + k) is a factor of f(x)

x+k=0 => x= -k;    -k is a root of f(x)

=> f(-k)=0

[tex](x + k) is a factor of f(x)x+k=0 = > x= -k; -k is a root of f(x)= > f(-k)=0[/tex]

So the correct option is B.fl-k)=0.

The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression. The following are examples of rational functions: f(x)=√2x4−5 f ( x ) = 2 x 4 − 5 ; g(x)=3√4x−7 g ( x ) = 4 x − 7 3 ; h(x)=7√−8x2+4 h ( x ) = − 8 x 2 + 4 7 .

The root function is used to find a single solution to a single function with a single unknown. In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns. For now, we will focus on using the root function.

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Answer:

Rectangle C is 14 cm longer than B

Step-by-step explanation:

Let  x be the length of Rectangle A. Rectangle B is ¹/₅ longer than A Block B,

Therefore the length of rectangle B is:

[tex]x+\frac{1}{5}x[/tex]

Rectangle C is ¹/₃ longer than B, therefore the length of rectangle c is:

[tex]x+\frac{1}{5}x+\frac{1}{3}(x+\frac{1}{5}x) =x+ \frac{1}{5}x+\frac{1}{3}x+\frac{1}{15}x=x+\frac{9}{15}x[/tex]

The total length of all three rectangles is 133 cm.

Length of rectangle A + Length of rectangle B + Length of rectangle C = 133 cm

[tex]x+x+\frac{1}{5}x +x+\frac{9}{15}x=133\\x+x+x+\frac{1}{5}x +\frac{9}{15}x=133\\3x+\frac{12}{15}x=133\\ 45x+12x=1995\\57x=1995\\x=35cm[/tex]

Therefore the length of rectangle A is 35 cm, the length of rectangle B is [tex]35+\frac{1}{5}*35=42\ cm[/tex] and the length of rectangle C is [tex]35+\frac{9}{15}*35=56\ cm[/tex]

Rectangle C is ¹/₃ longer than B, which is 14 cm (42\3) longer than B

Answer:

y= 1/5x + 12/5

Step-by-step explanation:

Parallel line to this has same slope and passes through the point (-2, 2)

The required equation in slope- intercept form is:

Answer:

17.3 Inches

Step-by-step explanation:

Given that the diagonal of a cube = 30 inches

For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]

Therefore:

[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]

Side Length of the cube is 17.3 Inches.

Answer:

17.3

Step-by-step explanation:

Edge 2020

The answer is graph A 7/9/20 edge

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

AOB = 73

BOC = 107

Step-by-step explanation:

So make an equation.

9x + 27 = 180

9x = 153

x = 17

AOB = 73

BOC = 107

Answer:

  ∠F ≈ 43.9°

Step-by-step explanation:

The Law of Cosines is used to find an angle when all triangle sides are known.

  f² = d² +e² -2de·cos(F)

  cos(F) = (d² +e² -f²)/(2de) = (25² +28² -20²)/(2·25·28) = 1009/1400

  F = arccos(1009/1400)

  F ≈ 43.9°

Answer:

D

Step-by-step explanation:

Length × Width = Area

So we'll substitute the Area of the circle having formula, πr²

Answer:

  2 + h = 14 and k - 25 = 2

Step-by-step explanation:

An equation has an equal sign.

Apparently, your answer choices are of the form ...

  (math expression) and (math expression)

In order for this to be "only equations", each "math expression" must contain an equal sign. That is, you must have ...

  ( ... = ... ) and ( ... = ... )

Something like ...

  c -14  and  d +134

contains no equal signs, so has no equations.

It looks like your appropriate choice is ...

  2 + h = 14 and k - 25 = 2

Answer:

the answer is a

Step-by-step explanation:

i took the test

:)

note: have a wonderful day!

Answer:

  (x, y) = (-3, -6)

Step-by-step explanation:

The (x, y) distance from R to T is ...

  (Δx, Δy) = T - R = (3, -3) -(-5, -7) = (3 -(-5), -3 -(-7)) = (8, 4)

Then 1/4 of the distance is ...

  (Δx, Δy)/4 = (8, 4)/4 = (2, 1)

This is added to the R coordinates to find the desired point:

  point = R +(2, 1) = (-5, -7) +(2, 1) = (-5+2, -7+1) = (-3, -6)

The coordinates are ...

  x-coordinate: -3

  y-coordinate: -6

Answer:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Step-by-step explanation:

For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Answer:

see explanation

Step-by-step explanation:

Given

y = x² - 2x - 8

To find the x- intercepts let y = 0 , that is

x² - 2x - 8 = 0 ← in standard form

(x - 4)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 2 = 0 ⇒ x = - 2

x- intercepts : x = - 2, x = 4

The x- coordinate of the vertex is mid way between the x- intercepts, that is

[tex]x_{vertex}[/tex] = [tex]\frac{-2+4}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1

Substitute x = 1 into the equation for corresponding y- coordinate

y = 1² - 2(1) - 8 = 1 - 2 - 8 = - 9

vertex = (1, - 9 )

Answer:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Step-by-step explanation:

For this problem we have the following parameters:

[tex] \mu = 520, \sigma = 90[/tex]

We select a sample size of n =100 and we want to find this probability:

[tex] P(\bar X <510) [/tex]

The distribution for the sample mean using the central limit theorem would be given by:

[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]

And we can solve this problem with the z score formula given by:

[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score formula we got:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Answer:

(a) P(CBM) = 0.07

(b) P(not CBW) = 0.996

(c ) P(neither is color-blind) = 0.926

(d) P=(at least one is color-blind) = 0.074

Step-by-step explanation:

The correct data is  that Approximately 7% of American men and 0.4% of American women are red-green color-blind.

(a) Probability that he is red-green color-blind:

[tex]P(CBM) = 0.07[/tex]

(b) Probability that she is NOT red-green color-blind:

[tex]P(not\ CBW) =1- P(CBW)\\P(not\ CBW) = 1 -0.004\\P(not\ CBW) =0.996[/tex]

(c) Probability that neither are red-green color-blind

[tex]P(neither) = P(not\ CBW)*P(not\ CBM) \\P(neither) = 0.996 *(1-0.07)\\P(neither)=0.926[/tex]

(d) Probability that at least one of them is red-green color-blind

[tex]P(at\ least\ one) = 1- P(neither) \\P(at\ least\ one) = 1-0.926\\P(at\ least\ one) = 0.074[/tex]

Answer:

118 cm

Step-by-step explanation:

1 m = 100 cm

1 m = 1000 mm

1.18 m = 118 cm = 1180 mm

11.8 mm   ----> too small

118 cm   ----> just right

1.8 m    ----> too big

11.18 mm    ----> too small

Where the above dimensions are given, the suitable guitar case for Liam would be the one that is 1.8 m long.

Since Liam's guitar case needs to be 1.18 m long, we need to select the option that is closest in length without exceeding it.

Among the given options, 11.8 mm and 11.18 mm are too small, and 118 cm is equal to 1.18 m, which exceeds the required length.

Hence , the only suitable option is 1.8 m, which matches Liam's requirement of a guitar case with a length of 1.18 m.

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Answer:

the value of x is 3

Step-by-step explanation:

Hope this helps!!!! :)

Answer:

one is a

two is c

three is b

Step-by-step explanation:

Answer:

The 85% confidence interval is ( 7.7 , 8.0 )

Step-by-step explanation:

In order to find the 85% confidence interval you use the following formula:

[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]       (1)

where

[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8

σ: standard deviation = 2.2

n: sample size = 967

α: 1 - 0.85 = 0.15

Zα/2: Z factor of the density distribution = 1.44

You replace the values of all parameters in the equation (1):

[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]

Then, the confidence interval is:

[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]

Answer:

Graph A

Step-by-step explanation:

The common ratio is less than 1, so the graph will be decreasing. The initial value is 2, so the y-intercept will be 2. Graph A fits this criteria.

I hope this helps :))

The graph A is correct.

A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

The equation is,

[tex]y=2(0.5)^{x}[/tex]

Plotting the graph, we get,

Option A

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Answer:

3x-5=2x+6

x-5=6

x=11

Answer:

Option (2).

Step-by-step explanation:

In the figure attached,

A, C and B are the points lying on a straight line.

2 lines EC and DC have been drawn by extending the lines from C to E and D respectively.

Ray CE is the angle bisector of ∠ACD.

That means CE divides ∠ACD in two equal parts.

m∠ACE = m∠DCE

Since m∠ACD = m∠ACE + m∠DCE

                        = 2(m∠ACE)

          m∠ACE = [tex]\frac{1}{2}(\angle ACD)[/tex]

Therefore, option (2) will be the answer.

Answer:

b

Step-by-step explanation:

took test

Answer:

[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.17)=0.00076[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

[tex]\hat p=\frac{59}{400}=0.1475[/tex] estimated proportion of defectives from the company B  

[tex]p_o=0.1[/tex] is the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.1[/tex]  

Alternative hypothesis:[tex]p > 0.1[/tex]  

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.17)=0.00076[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Answer:

So if 17/25 of the students like math, science, and art and 3/20 of the students like art only. We first need to find common demoninator. 68/100 and for the second one 15/100. Subtract them both

68-15 = 53/100 of the students factor math, and science or 53%

Answer:

hope this helps :)

Step-by-step explanation:

1/4 because 2/1 is 2 and 2 to the power of -2 is 1/4

Answer:

26/3 as an improper fraction in simplest form. :)

Step-by-step explanation:

Answer:

The sample proportion for the births that are girls is 0.505. It is slightly higher than the expected value of 0.5, but the right way to answer if it is an unusual proportion is by performing an hypothesis test.

The hypothesis test results in not enough evidence to claim that the outcome is unlikely. This sample result has a probability of 0.7627 of appearing by pure chance in a population with proportion p=0.5.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion of girls birth differs significantly from the expected proportion (50%).

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi\neq 0.5[/tex]

The significance level is 0.05.

The sample has a size n=1100.

The sample proportion is p=0.505.

p=X/n=556/1100=0.505

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1100}}\\\\\\ \sigma_p=\sqrt{0.000227}=0.015[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.505-0.5-0.5/1100}{0.015}=\dfrac{0.005}{0.015}=0.302[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z>0.302)=0.7627[/tex]

As the P-value (0.7627) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of girls birth differs significantly from the expected proportion (50%).

Answer:

about $3.84

Step-by-step explanation:

you do 69.20 divided by 18

Answer:

2 2/3

Step-by-step explanation:

Answer:

[tex]75.6\%[/tex]

Step-by-step explanation:

Let B be the event of buying a basic model.

Given that P(B) = 41%

Let D be the event of buying a basic model.

Given that P(D) = 1 - 41% = 59%

Let E be the event of extended warranty.

Given that:

P(E [tex]\cap[/tex] B) = 31% and

P(E [tex]\cap[/tex] D) = 48%

P(E) = P(E [tex]\cap[/tex] B) [tex]\times[/tex] P(B) + P(E [tex]\cap[/tex] D) [tex]\times[/tex] P(D)

P(E) = 31% [tex]\times[/tex] 41% + 48% [tex]\times[/tex] 59% = 0.4103

To find: P(B/E)

Formula:

[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]

[tex]\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%[/tex]

So, the correct answer is [tex]75.6\%[/tex].