In the diagram, m 23 = 120° and mZ12 = 80°. Which
angle measures are correct? Check all that apply.
1
2
mZ1 = 60°
V
9 10
11 12
4
e
m2 13 = 80
56
13 14
m26 = 80
7
8 15 16
f
m25 = 60°
Om Z10 = 120°
'c
d
m2 14 = 100
Intro
Done
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Answer:

t times 5 is t * 5 or 5t.

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.

Learn more about cosine ratio on:

https://brainly.com/question/15793827

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:

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:

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:

[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:

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:

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.

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]

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.

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: 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:

(56 - x) * 3/4

Step-by-step explanation:

x + y = 56

y = 56 - x

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

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:

X=96

Step-by-step explanation:

180-134=46

180-130=50

SUM OF TWO INTERIOR ANGLES = EXTERIOR ANGLE

50 + 46=96

Answer:

Height = 47.77 inches

Step-by-step explanation:

We are given;

Mean = 49.9 in

Standard deviation;SD = 3.15 in

The first quartile is the 25th percentile, which means it's where 25% of the data falls.

Now from the normal distribution table attached, we can see that the z-value for 25% or 0.25 is approximately

-0.675.

To find the height that represents the first quartile of these students, we will use the formula;

z = (height - mean)/(SD)

Making height the subject ;

height = (z × SD) + mean

Plugging in the relevant values to obtain;

Height = (-0.675 × 3.15) + 49.9

Height ≈ 47.77 inches

Answer:

Hypotenuse = 5√2 units

Step-by-step explanation:

Triangle ABC:

The legs are 5 units each

Opposite = 5unit

Adjacent = 5unit

Triangle ACB:

lengths of sides A C and C B are 5

The legs are 5 units each

Leg =AC = Opposite = 5unit

Leg = CB = Adjacent = 5unit

The hypotenuse for both ∆ACB is unknown. Since ∆ACB is a right angled triangle, we would apply Pythagoras theorem to find the hypotenuse.

Using Pythagoras theorem:

Hypotenuse ² = opposite ² + adjacent ²

Hypotenuse ² = leg² + leg²

AB = hypotenuse in ∆ACB

AB² = 5² + 5²

AB² = 25+25 = 50

AB = √50 = √(25×2)

AB = 5√2

Hypotenuse = 5√2 units

Answer:

The answer is B! Person above me is right!

Step-by-step explanation:

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

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:

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:

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:

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:

The integers are 11 and 12

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

Y: number of new leaves of Bromeliads grown under different types of fertilization.

Factor: Type of fertilizer

Treatments: 1. Nitrogen, 2. Phosphorus, 3. Both, 4. Neither (control group)

To compare these four groups you have to conduct an ANOVA

The hypotheses are:

H₀: μ₁= μ₂= μ₃= μ₄

H₁: At least one population mean is different from the others.

α: 0.05

a)

The degrees of freedom of the F-statistic are:

[tex]F_{I-1;N-I}= F_{4-1;31-4}= F_{3;27}[/tex]

I= number of treatments

N= total number of experimental units (in all groups)

b)

SSTreatments= 39.37

SSError= 72.18

MSTreatments= SStreatments/DfTreatments= 39.37/3= 13.12

MSError=SSError/DfError= 72.18/27= 2.67

[tex]F= \frac{MS_{Treatments}}{MS_{Error}} = \frac{13.12}{2.67} = 4.91[/tex]

c)

This test is one-tailed to the right and so is the p-value:

P(F₃;₂₇≥4.91)= 1 - P(F₃;₂₇<4.91)= 1 - 0.9925= 0.0075

d)

The decision rule using the p-value is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value is less than α, the test is significant at 5% significance level.

"We have significant evidence at the 5% level that the means are not all the same."

I hope this helps!

Answer:

As angel WVU = angel WVF + angel FVU

Therefore angel WVF =152 - 70

so, angel WVF = 82

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:

30.7

Step-by-step explanation:

add  the 15,3.7 ,and the 12

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]

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..