Find the exact coordinates of point E.

Answer:

1. Yes, the sample data provides convincing evidence to support the claim that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37

2. The correct hypotheses are;

The null hypothesis is H₀: p ≥ p₀

The alternative hypothesis is Hₐ: p < p₀

Step-by-step explanation:

given

The null hypothesis is H₀: p ≥ p₀ where p₀ = 0.37

The alternative hypothesis is Hₐ: p < p₀

The formula for the z test is presented as follows;

[tex]z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0 (1 - p_0)}{n}}}[/tex]

Where:

[tex]\hat p[/tex] = Sample proportion = 206/780 = 0.264

p₀ = Population proportion = 0.37

n = Sample size = 780

α = Significance level = 10% = 0.01

Plugging in the values, we have;

[tex]z=\dfrac{0.264-0.37}{\sqrt{\dfrac{0.37 (1 - 0.37)}{780}}} = -6.13[/tex]

From the the z relation/computation, we have the p value = 0.000000000451

Since the p value which is 0.000000000451 is less than α, which is 0.01 we reject the null hypothesis and we fail to reject the alternative hypothesis, that is there is sufficient statistical evidence to suggest that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37.

Answer:

(56 - x) * 3/4

Step-by-step explanation:

x + y = 56

y = 56 - x

y' = (56 - x) * 3/4

Complete Question

The complete question is shown on the first uploaded image

Answer:

  Value  x of X     -3    -7     -15

          [tex]P_X (x)[/tex]          [tex]\frac{1}{2}[/tex]      [tex]\frac{3}{8}[/tex]       [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

From the question we are told that  

     The values of X are  [tex]X = -3 , -7 , -15[/tex]

     The total number of outcomes is  n =  8

The probability distribution function of X is evaluated as follow

   [tex]p(X = -3 ) = \frac{N_{-3}}{n}[/tex]

Where  [tex]N{-3}[/tex] is the number of time  X = -3  occurred and from the table the value is  [tex]N _{-3} = 4[/tex]

     Therefore

       [tex]p(X = -3 ) = \frac{4}{8}[/tex]

        [tex]p(X = -3 ) = \frac{1}{2}[/tex]

Now  

    [tex]p(X = -7 ) = \frac{N_{-7}}{n}[/tex]

Where [tex]N_{-7} = 3[/tex] from table  

So  

     [tex]p(X = -7 ) = \frac{3}{8}[/tex]

Also  

    [tex]p(X = -15 ) = \frac{N_{-15}}{n}[/tex]

    [tex]p(X = -15 ) = \frac{1}{8}[/tex]

Answer:

5, 1, 7, 0, 9, -1, 11, -2, 13

Step-by-step explanation:

5, 1, 7, 0, 9, -1, 11

Two series in one:

Answer:

17 weeks

Step-by-step explanation:

Please refer to the picture attached.

At the end of each week, she will be able to save 13 dollars. I'm the 17th week, whe will save more than 218 dollars and will be able to afford to buy the computer.

However, in 16th week, she will only save 208 dollars which is insufficient to buy the laptop.

Hence, u round up the value of x in order to get the answer.

Using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.

Cosine ratio is: cos ∅ = adjacent side/hypotenuse

Given the right triangle in the diagram above, thus:

Thus:

cos 35 = BC/6

BC = cos 35 × 6

BC = 4.91

Thus, using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.

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Answer:

(1)19°

Step-by-step explanation:

The diagram is drawn and attached below.

Let x=mAC = 72°; and

y=mBD = 34°

By the Angle-Arc relationship, the external angle is half the difference.

[tex]\angle P=\frac{1}{2}(x^\circ-y ^\circ)\\$Therefore:\\m\angle P=\frac{1}{2}(72^\circ-34 ^\circ)\\m\angle P=19^\circ[/tex]

Answer:

5

Step-by-step explanation:

Take the number of markers and divide by the number in each package

70/15

4.6666repeating

Round to the nearest whole number to determine the number of packages

5

They will need to buy 5 packages

Answer:

Let's solve for m.

3m + 4n = 625

Step 1: Add -4n to both sides.

3m + 4n + −4n = 625 + −4n

3m = −4n + 625

Step 2: Divide both sides by 3.

3m/3 = 4n + 625/3

m = -4/3 n + 625/3

C) The variable m in the equation represents the number of hours Amy traveled on the

first train.

D) The variable n in the equation represents the number of hours Amy traveled on the

second train.

Answer:

Step-by-step explanation:

The directrix is a horizontal line (y=-2). The parabola will open in the direction the focus is from the directrix. Here, the y-coordinate of the focus is 10, so the focus is above the directrix and the parabola opens upward.

The vertex is halfway between the directrix and the focus, so has y-coordinate ...

   (-2 +10)/2 = 4

Since the parabola opens upward, the vertex is a minimum (the "low value"). Its x-coordinate is the same as that of the focus, so the vertex is (5, 4).

  The parabola has a vertex at (5, 4), has a low value of 4, and it opens upward.

Answer: C.

Step-by-step explanation:

To find the discounted value off of a full price, you can multiply the full price by the discount percentage to find the discount:

250 * 0.20 = 50

The discount is 50 dollars.

The laptop costs $250, but with the discount of $50, it is now for sale for $200.

The correct answer is C.

Answer:

As angel WVU = angel WVF + angel FVU

Therefore angel WVF =152 - 70

so, angel WVF = 82

Answer:

12 and -12

Step-by-step explanation:

12x-12y is the expansion using the distributive property, so the coefficient of x is 12 and the coefficient of y is -12

Step-by-step explanation:

Radius (R) =diameter /2 =8/2 =4

So area=

[tex]\pir {r}^{2} = \pi {4}^{2} = 50.27[/tex]

Hope this helps..

Answer:

(a) The probability that a randomly selected athlete uses a stairclimber for​  less than 19 ​minutes is 0.2388.

(b) The probability that a randomly selected athlete uses a stairclimber for​  between 24 and 33 ​minutes is 0.3997.

(c) The probability that a randomly selected athlete uses a stairclimber for​  more than 40 minutes is 0.0113.

Step-by-step explanation:

We are given that the amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 24 minutes and a standard deviation of 7 minutes.

Let X = amounts of time per workout an athlete uses a stairclimber

So, X ~ Normal([tex]\mu=24,\sigma^{2} =7^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                               Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean time = 24 minutes

            [tex]\sigma[/tex] = standard deviation = 7 minutes

(a) The probability that a randomly selected athlete uses a stairclimber for​  less than 19 ​minutes is given by  P(X < 19 minutes)

        P(X < 19 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{19-24}{7}[/tex] ) = P(Z < -0.71) = 1 - P(Z [tex]\leq[/tex] 0.71)

                                                           = 1 - 0.7612 = 0.2388

The above probability is calculated by looking at the value of x = 0.71 in the z table which has an area of 0.7612.

(b) The probability that a randomly selected athlete uses a stairclimber for​  between 24 and 33 ​minutes is given by = P(24 min < X < 33 min)

     P(24 min < X < 33 min) = P(X < 33 min) - P(X [tex]\leq[/tex] 24 min)

     P(X < 33 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{33-24}{7}[/tex] ) = P(Z < 1.28) = 0.8997

     P(X [tex]\leq[/tex] 24 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{24-24}{7}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50

The above probability is calculated by looking at the value of x = 1.28 and x = 0 in the z table which has an area of 0.8997 and 0.50 respectively.

Therefore, P(24 min < X < 33 min) = 0.8997 - 0.50 = 0.3997

(c) The probability that a randomly selected athlete uses a stairclimber for​  more than 40 minutes is given by  P(X > 40 minutes)

        P(X > 40 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{40-24}{7}[/tex] ) = P(Z > 2.28) = 1 - P(Z [tex]\leq[/tex] 2.28)

                                                           = 1 - 0.9887 = 0.0113

The above probability is calculated by looking at the value of x = 2.28 in the z table which has an area of 0.9887.

The event of probability that a randomly selected athlete uses a stairclimber for​  more than 40 minutes is unusual because this probability is less than 5% and any even whose probability is less than 5% is said to be unusual.

Answer:

G = 53 degrees

Step-by-step explanation:

Since this is  a right triangle, we can use trig functions

sin theta = opp/ hyp

sin G = 24/30

Take the inverse sin of each side

sin ^-1 sin G =  sin ^-1 (24/30)

G =53.13010235

To the nearest degree

G = 53 degrees

Answer:

X=96

Step-by-step explanation:

180-134=46

180-130=50

SUM OF TWO INTERIOR ANGLES = EXTERIOR ANGLE

50 + 46=96

Answer:

6.28 inches

Step-by-step explanation:

Given that the diameter of the pie=8 inch

Radius=Diameter/2

Therefore: Radius of the pie=8/2=4 Inch

Circumference of a circle [tex]=2\pi r[/tex]

Since the pie is sliced into 4 equal parts:

Length of the Pie crust of one slice[tex]=\dfrac{2\pi r}{4}[/tex]

Substituting the value of r, we obtain:

Length of the Pie crust of one slice[tex]=\dfrac{2*\pi *4}{4}\\=2\pi $ inches\\=6.28 inches (correct to 2 decimal places)[/tex]

Answer:

t times 5 is t * 5 or 5t.

Answer:

3x^2 + 9x + 8

Step-by-step explanation:

2x+5+3x^2+7x+3

2x+5+3x^2+7x+3

(3x^2)+(2x+7x)+ (5+3)

3x^2+9x+8

Answer:

[tex] x^{12} w^{-10}[/tex]

And we can find this rewriting the expression in terms of the info given and we got:

[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]

And replacing we got:

[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]

And the best option would be:

C. 180

Step-by-step explanation:

For this case we know that:

[tex] x^6, w^{10} = 20[/tex]

And we want to find the value for:

[tex] x^{12} w^{-10}[/tex]

And we can find this rewriting the expression in terms of the info given and we got:

[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]

And replacing we got:

[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]

And the best option would be:

C. 180

Answer:

C. [tex](f+g)(x)=-5^x-3x-6[/tex]

Step-by-step explanation:

→Set it up, like so:

[tex](-5^x-4)+(-3x-2)[/tex]

[tex]-5^x-4-3x-2[/tex]

→Add like terms (-4 and -2):

[tex]-5^x-3x-6[/tex]

Answer:

In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

hope it helps :)

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In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention.

An experiment is designed to test the effect of an intervention or treatment on a particular outcome, by comparing the results from a group that receives the intervention to a control group that does not receive the intervention. In this way, the experiment can establish cause-and-effect relationships and determine if the treatment has a significant effect.

On the other hand, an observational study does not involve any manipulation of the independent variable. It simply observes and records the relationship between variables. Observational studies cannot establish cause-and-effect relationships and the results may be subject to confounding variables, which can make it difficult to interpret the findings.

Hence, the correct answer would be an option (C).

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Answer:

The integers are 11 and 12

Step-by-step explanation:

11 and 12 are consecutive positive integers, and 11 x 12 = 132.

Answer:

Sugar concentration of the mixed soft drink will be 32.5%.

Step-by-step explanation:

Sugar concentration of first drink = 20%

Volume of first soda = 250 ml

Sugar in first soda = 20% of 250 ...... (1)

Sugar concentration of second drink = 45%

Volume of second soda = 250 ml

Sugar in second soda = 45% of 250 ...... (2)

Let [tex]x\%[/tex] be the sugar concentration in resultant mixture.

Volume of mixture = 250 + 250 = 500 ml

Sugar in mixture = [tex]x\%[/tex] of 500 ml ...... (3)

Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):

20% of 250 + 45% of 250 = [tex]x\%[/tex] of 500

[tex]\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%[/tex]

Hence, Sugar concentration of the mixed soft drink will be 32.5%.

Answer:

30°

Step-by-step explanation:

supplementary angles are two sets of angles whose sum form 180°

According to the problem, one set equals 5 times the other.

Let the other be x,

It means it's compliment is 5x;

It means therefore that ;

x + 5x = 180°

6x = 180°;

x = 180°/ 6 = 30°;

Therefore the angle measures 30° and it's supplement 150°.

Answer:

36.87°  

Step-by-step explanation:

Assume the triangles are as in the diagram below.

∠BAC includes ∠DAE.

The measure of ∠BAE is 36.87°.

Answer:

36.87°

Step-by-step explanation:

i just had this question on edmentum and it was right.

Answer:

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test.

Event B: Having breast cancer.

3.65% of women in their 60s get breast cancer

This means that [tex]P(B) = 0.0365[/tex]

A mammogram can typically identify correctly 85% of cancer cases

This means that [tex]P(A|B) = 0.85[/tex]

Probability of a positive test.

85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So

[tex]P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792[/tex]

What is the probability that a woman in her 60s who has a positive test actually has breast cancer?

[tex]P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917[/tex]

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

If I'm understanding the problem correctly, the vendor sells water in exactly 8 oz increments, but only has glasses that can hold 6 oz or 10 oz.

Fill up the 10 oz glass, then (carefully) pour its contents into a 6 oz glass until it it is full. Then the 10 oz glass should contain 4 oz of water. Drink the 4 oz, repeat this process to get your 8 oz, and pay the man.