If mACD = 100°, then mACE = [?]

Answer:

third one

Step-by-step explanation:

when

x=0,      y=0

x=1,       y=8

x=2      y=0

and so on.

Answer:

C. f(x)= -2x^3 -2x^2 +12x

Step-by-step explanation:

edge 2020

Answer:

1. 0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.

2. 0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]

In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day.

This means that [tex]\lambda = 320n[/tex], in which n is the number of days.

1. Find the probability that an average American adult watches more than 309 minutes of television per day.

One day, so [tex]\mu = 320, \sigma = \sqrt{320} = 17.89[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 309. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{309 - 320}{17.89}[/tex]

[tex]Z = 0.61[/tex]

[tex]Z = 0.61[/tex] has a pvalue of 0.729

1 - 0.729 = 0.271

0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.

2. Find the probability that an average American adult watches more than 2,250 minutes of television per week.

[tex]\mu = 320*7 = 2240, \sigma = \sqrt{2240} = 47.33[/tex]

This is 1 subtracted by the pvalue of Z when X = 2250. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2250 - 2240}{47.33}[/tex]

[tex]Z = 0.21[/tex]

[tex]Z = 0.21[/tex] has a pvalue of 0.583

1 - 0.583 = 0.417

0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.

Answer:

The answer is 100.

Step-by-step explanation:

The original figure has 3 significant figures

Rounded to 1 significant figure is 100

Answer: m=6, m=-4

Step-by-step explanation:

To solve this proportion, we have to cross multiply.

[tex]\frac{m-3}{7} =\frac{m}{m+8}[/tex]

[tex](m-3)(m+8)=7m[/tex]

Now that we have cross multiplied, we actually need to FOIL the left side to expand the equation.

[tex]m^2+8m-3m-24=7m[/tex]

Combine like terms.

[tex]m^2+5m-24=7m[/tex]

We can move all terms to one side and then solve for m.

[tex]m^2-2m-24=0[/tex]

We can actually factor this to:

[tex](m-6)(m+4)=0[/tex]

We set each factor equal to 0 to find m.

m-6=0

m=6

m+4=0

m=-4

Answer:

V = 51.3 in.³

Step-by-step explanation:

Volume of Sphere = [tex]\frac{4}{3} \pi r^3[/tex]

Where r = 3.5

So,

V = [tex]\frac{4}{3} (3.14)(3.5)^3[/tex]

V = [tex]\frac{4}{3} (3.14)(12.25)[/tex]

V = [tex]\frac{153.9}{3}[/tex]

V = 51.3 in.³

Answer:

The answer would be 3.14

Step-by-step explanation:

6.28

2 π

≈ 6.28

  2 ⋅ 3.14 = 1

π r 2 ≈ 3.14 ⋅ 1 2 =

3.14

Hope that was helpful.Thank you!!!

Answer:

Step-by-step explanation:

Circumference = 6.28 units

2πr = 6.28

2*3.14 *r = 6.28

           [tex]r=\frac{6.28}{2*3.14}\\\\[/tex]

           r = 1 unit

Area =πr²

        = 3.14 * 1 * 1

       = 3.14 square units

Answer:

It is a probability sample because it utilizes some form of random selection. It is not a simple random sample because there is not an equal possibility of A, B, or C.

Step-by-step explanation:

Answer:

The food would last 51 days

Step-by-step explanation:

After 15 days are over, you could say that the 16th day would be as follows -

80 soldiers, food finished in 60 - 15 = 45 days.

If 20 more soldiers arrive, there would be a total of 100 soldiers, so if  80 soldiers can finish their food in 45 days  - 1 soldier can finish = 45 * 80. Respectively,  100 soldiers can consume their food in ( 45 * 80 ) / 100  = 36 days.

As 15 days are already over, adding 36 more days = 51 days

The food would last 51 days if 20 more soldiers join after 15 days

There are several possible ways to answer this question, but I hope that explanation helps!

Answer:

A total of 51 days, or 36 days after the extra soldiers join in.

Step-by-step explanation:

Let's say a soldier eats 1 portion of food in 1 days. That portion may be divided into breakfast, lunch , and dinner, but it is still accounted as 1 portion per soldier per day.

There are 80 soldiers and enough food for 60 days.

The number of portions is

60 * 80 = 4800

The fort started with 4800 portions.

80 soldiers ate their portions for 15 days.

80 * 15 = 1200

After 15 days, they have

4800 - 1200 = 3600 portions left.

After 15 days, 20 more soldiers joined in.

Now there are 80 + 20 = 100 soldiers.

There are 3600 portions left for 100 soldiers.

3600/100 = 36

The food would last 36 days after the 15 days, or a total of 51 days.

Answer:

D. Both distributions are skewed left, so the interquartile range is the best measure to compare variability.

Step-by-step explanation:

Plotting the data roughly shows that the data is skewed to the left. In other words, data is skewed negatively and that the long tail will be on the negative side of the peak.

In such a scenario, interquartile range is normally the best measure to compare variations of data.

Therefore, the last option is the best for the data provided.

please mark me brainliest :)

Answer: B. false

Step-by-step explanation:

An equilateral triangle has 3 equal sides

Isosceles triangle has two equal sides.

Which means that equilateral triangles cannot become isosceles.

Answer:

False

Step-by-step explanation:

An equilateral triangle has all three sides equal

An isosceles triangle has at least 2 sides equal

An equilateral triangle is a special isosceles triangle

Answer

option D

Step-by-step explanation:

The population of interest to the research is the set of all gun ownership status (yes/no) values for all adults in the country. Or all total adults in a country including those that own a gym or not. This is the population of interest. The sample is the 2550 individuals adults surveyed in the household telephone survey.

Answer:

36=2×3×3×3

Answer

[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]

Step-by-step explanation:

First write the prime factors of 36 that you can see here

[tex]2 \: \: \: 2 \: \: \: 3 \: \: \: 3[/tex]

Now write 36 as a product of its prime factors.

[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]

Answer:

(a) 3, 5 and 6

Step-by-step explanation:

In the experiment, 43 are to be given a gel that contains the tooth-whitening chemicals while the remaining 42 are to be given a placebo. Therefore, a placebo is used.

The 43 that will receive the gel are to be selected randomly.

After the experiment, the whiteness of the two groups will be compared to see the effect of the gel.

Therefore for the experiment to be completely random,  3, 5, and 6 apply.

(b)

For the experiment to be double-blind, the researchers who will evaluate the whiteness and interact with the subjects, and the subjects would not know which subjects received either the whitening gel or the placebo.

Answer:

The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 110, \sigma = 0.15[/tex]

The proportion of infants with birth weights between 125 oz and 140 oz is

This is the pvalue of Z when X = 140 subtracted by the pvalue of Z when X = 125. So

X = 140

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140 - 110}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 125

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{125 - 110}{15}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.9772 - 0.8413 = 0.1359

The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.

Answer:

Step-by-step explanation:

Let x represent the numerator and y represent the denominator.

The numerator of a rational number is greater than its denominator by 3. It means that

x = y + 3

If the new number becomes 13/4 when the numerator is tripled and the denominator is decreased by 23, it means that

3x/(y - 23) = 13/4

Cross multiplying, it becomes

3x × 4 = 13(y - 23)

12x = 13y - 299- - - - - - - - - - -1

Substituting x = y + 3 into equation 1, it becomes

12(y + 3) = 13y - 299

12y + 36 = 13y - 299

13y - 12y = 36 + 299

y = 335

x = y + 3 = 335 + 3

x = 338

The original number is 338/335

Answer:

7/15

Step-by-step explanation:

There are 15 marbles total. -->

3 of them are yellow => 4 of them are green

3 + 4 = 7

7/15

Hope This Helps!

Answer: 7/15=46%

Step-by-step explanation:

There is in total of 15 marbles

but 3 of them are yellow and 4 are green.

4+3=7

7/15=0.466...

7/15≈0.46

0.46=46%

Answer:

x= -3 +√2 ≈ -0.1716,  and x = - 3 -2√2 ≈ -5.8284

Step-by-step explanation:

y= -1/2(x+3)² +4

For x -intercept, y = 0.

0 = - 1/2(x+3)² + 4 /*(-2)

0 = (x+3)² - 8

(x+3)² = 8

√(x+3)² = +/-√8

x+3 = +/-√8

x = - 3+/- 2√2

x= -3 +√2 ≈ -0.1716,  and x = - 3-2√2 ≈ -5.8284

Answer:

Center: (1, 5)

Radius: r = 5

Step-by-step explanation:

Step 1: Rewrite equation

x² - 2x + y² - 10y = -1

Step 2: Complete the Square (x2)

x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25

(x - 1)² + (y - 5)² = 25

Step 3: Find answers

Center = (h, k)

(1, 5) as Center

Radius = r

r² = 25

r = 5

Answer: Center = (1, 5)

               Radius = 5

Step-by-step explanation:

The standard form for a circle is: (x - h)² + (y - k)² = r²     where

First, group the x's and group the y's in order to complete the square.

x² - 2x        + y² - 10y         = -1

     ↓                    ↓

   (-2/2)²=1         (-10/2)²=25

Add those values to BOTH sides:

x² - 2x + 1      +  y² - 10y + 25    = -1 + 1 + 25

Rewrite the left side as perfect squares and simplify the right side.

  (x - 1)²       +     (y - 5)²         = 25

We end up with (h, k) = (1, 5)   this is the center

        and r² = 25 --> r = 5         this is the radius

To graph the circle, place an x at the center (1, 5).  Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.

Answer:

[tex]t=\frac{370.69-360}{\frac{24.36}{\sqrt{26}}}=2.238[/tex]  

The degrees of freedom are given by:

[tex] df = n-1= 26-1=25[/tex]

And the p value would be:

[tex]p_v =P(t_{25}>2.238)=0.0172[/tex]  

If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change

Step-by-step explanation:

Information given

[tex]\bar X=370.69[/tex] represent the sample mean

[tex]s=24.36[/tex] represent the sample standard deviation

[tex]n=26[/tex] sample size  

[tex]\mu_o =6*60 =360 s[/tex] represent the value to verify

z would represent the statistic

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

Hypothesis to test

We want to check if the true mean is at most 360 seconds, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 360[/tex]  

Alternative hypothesis:[tex]\mu > 360[/tex]  

The statistic for this case would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

We can replace in formula (1) the info given like this:  

[tex]t=\frac{370.69-360}{\frac{24.36}{\sqrt{26}}}=2.238[/tex]  

The degrees of freedom are given by:

[tex] df = n-1= 26-1=25[/tex]

And the p value would be:

[tex]p_v =P(t_{25}>2.238)=0.0172[/tex]  

If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change

Answer:

The probability that none of the households are tuned to 50 Minutes is 0.04398.

Step-by-step explanation:

We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.

A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.

The above situation can be represented through binomial distribution;

[tex]P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........[/tex]

where, n = number of samples (trials) taken = 14 households

r = number of success = none of the households are tuned to 50 min

p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%

Let X = Number of households that are tuned to 50 Minutes

So, X ~ Binom(n = 14, p = 0.20)

Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)

               P(X = 0)  =  [tex]\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}[/tex]

                              =  [tex]1 \times 1 \times 0.80^{14}[/tex]

                              =  0.04398

Answer:

The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.

Step-by-step explanation:

Let the random variable X denote the amount of coffee dispensed by the machine.

It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.

It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.

And 10% of the cups contain less than the amount stated on the sign.

To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,

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

This implies that:

P (X < 100) = 0.10

⇒ P (Z < z) = 0.10

The value of z for the above probability is, z = -1.28.

*Use a z-table

Compute the value of standard deviation as follows:

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

[tex]-1.28=\frac{100-105}{\sigma}[/tex]

     [tex]\sigma=\frac{-5}{-1.28}[/tex]

        [tex]=3.90625\\\\\approx 3.91[/tex]

Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.

Answer:

C and B

Step-by-step explanation:

31. Thrice means 3 times as much. Let's call Rahul and Shivam's present ages r and s respectively. We can write:

r = 3s

r + 8 = 1 + (s + 8) * 2

Simplifying the second equation gives us r + 8 = 2s + 17. When we substitute r = 3s into the second equation we get 3s + 8 = 2s + 17 which gives us s = 9. This means r = 9 * 3 = 27 so Rahul's age 8 years before the present is 27 - 8 = 19.

32. Let's call Ravi and Kishan's ages r and k. We can write:

r + k = 69

r - 8 = 2(k - 8) - 4

Rewriting the first equation gives us r = -k + 69 and when we substitute this into the second equation we get -k + 69 - 8 = 2k - 16 - 4. Solving for k we get k = 27 which means r = 42. 42 - 27 = 15.

Answer:

10x² + 3xy + 6x + 3y - y²

Step-by-step explanation:

Step 1: Distribute

10x² - 2xy + 6x + 5xy - y² + 3y

Step 2: Combine like terms

10x² + 3xy + 6x + 3y - y²

And we have our final answer!

Answer:

9672 per year

Step-by-step explanation:

Take the amount he earns per week times the number of weeks he works

186* 52

9672 per year

Answer:

$9672

Step-by-step explanation:

Jack earns $186 in 1 week.

In 52 weeks,

186 × 52 = 9672

He earns $9672.

Answer:

Step-by-step explanation:

The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.

"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"

Area of a parallelogram = Base * Height.

Given the height of the parallelogram = (x-4)cm

Base = (2x² + 2x-6) cm

Area of the parallelogram =  (x-4)cm *  (2x² + 2x-6) cm

Area of the parallelogram = (x-4)(2x²+2x-6)

Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24

= 2x³+2x²-8x²-6x-8x+24

=  (2x³-6x²-14x+24)cm²

Answer:

C.

Step-by-step explanation:

Perpendicular ⇒ So the slope will be the negative reciprocal to this slope

Slope = m = 2

Point = (x,y) = (4,-8)

So, x = 4, y = -8

Putting in the slope-intercept form

[tex]y = mx+b[/tex]

-8 = (2)(4) + b

b = -8-8

b = -16

Now we'll put it in the slope-intercept form

y = 2x-16

=> y = 2x-8-8

=> y+8 = 2(x-4)

Answer:

140$

Step-by-step explanation:

4 hours = 20

28 hours divided by 4 is 7

7 x 20 = 140

Answer:

[tex] 167.47 \: {cm}^{3} [/tex]

Step-by-step explanation:

[tex]V_{cone} = \frac{1}{ 3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \pi \times {4}^{2} \times 10 \\ \\ = \frac{1}{ 3} \times 3.14 \times 16 \times 10 \\ \\ = \frac{1}{ 3} \times \: 502.4 \\ \\ = 167.466667 \\ \\ = 167.47 \: {cm}^{3} [/tex]

Answer:

Step-by-step explanation:

Check part

[tex]y= C_1y_1 + C_2y_2 = C_1cos(7x)+C_2sin(7x)[/tex]

[tex]y'= -7 C_1sin(7x)+7C_2cos(7x)[/tex]

[tex]y"= -49 C_1cos(7x) - 49 C_2sin(7x)[/tex]

Now, replace to the original one.

[tex]y"+49 y = -49C_1cos(7x)-49 C_2 sin(7x) + 49 C_1cos(7x) +49 C_2sin(7x) = 0\\[/tex]

Done!!

Particular solution

[tex]y(0) = C_1cos(0) + C_2 sin(0) = C_1= 10[/tex]

I believe that y'(0) = 4, not y(0) anymore. Since y(0) CANNOT have two different solution.

[tex]y(0)'= -7 C_1sin(0) + 7 C_2 cos (0) = 7 C_2= -4[/tex]

[tex]C_2 = -4/7[/tex]

The last step is to put C1, C2 into your solution. You finish it.

Answer:

See explanation below.

Step-by-step explanation:

Let's take P as the proportion of new candidates between 30 years and 50 years

A) The null and alternative hypotheses:

H0 : p = 0.5

H1: p < 0.5

b) Type I error, is an error whereby the null hypothesis, H0 is rejected although it is true. Here, the type I error will be to conclude that there was age discrimination in the hiring process, whereas it was fair and random.

ie, H0: p = 0.5, then H0 is rejected.