In circle O two secants,
ABP and CDP, are drawn to external point P. If mAC = 72°, and mBD = 34°, what is the measure of ∠P?
(1) 19° (3) 53°
(2) 38° (4) 106°

Answer:

27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 211, \sigma = \sqrt{2.89} = 1.7, n = 86, s = \frac{1.7}{\sqrt{86}} = 0.1833[/tex]

What is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches.

Either greater than 211 + 0.2 = 211.2 or smaller than 211 - 0.2 = 210.8. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability of being less than 210.8:

This is the pvalue of Z when X = 210.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{210.8 - 211}{0.1833}[/tex]

[tex]Z = -1.09[/tex]

[tex]Z = -1.09[/tex] has a pvalue of 0.1379

Probability of differing from the population mean by greater than 0.2 inches :

2*0.1379 = 0.2758

27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches

Answer:

Probability is 86.24%

Step-by-step explanation:

We can solve this by using the Z-score formula.

Z = (X - μ)/σ

Where;

μ is mean = 211 inches

σ is standard deviation

Now, we are given variance as 2.89

Formula for standard deviation using variance is;

SD = √variance

SD = √2.89

SD = 1.7

To find the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches, we will find the p-value of z and subtract 1 from it.

Since we are told that the sample shafts would differ by 0.2 inches, thus;

X = 211 + 0.2 = 211.2

Since we are working with sample mean of 86, then we have;

Z = (X - μ)/s

s = σ/√86

s = 1.7/√86

s = 0.1833

So,

Z = (211.2 - 211)/0.1833

Z = 1.0911

From z-score calculator, the p-value is gotten to be 0.1376

Thus, probability that mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches is;

Probability = 1 - 0.1376 = 0.8624 = 86.24%

Answer:

a) Check the bar graph in the picture attached

b) The two categorical variables are:

1) Type of owners

2) Likelihood to give CPR

c) Information on the population( in number or percentage) of the dog/cat owners.

Step-by-step explanation:

a) the bar chart is drawn with % of owners likely to give CPR to their pets on the y-axis and the owner types on the x - axis.

b) The two categorical variables are:

1) Type of owners

2) Likelihood to give CPR

c) To construct a 2 x 2 table, the percentage (or number) of either dog owners or cat owners.

Since we know that the total number of pet owners that were sampled = 1166.

If the number of dog owners is known, it can be subtracted from the total number of pet owners to know the number of cat owners and vice versa. If this information is gotten, then the 2 x 2 table can be constructed.

Answer:

3. Vertical is the same as horizontal for linear equations because when moving the function up, it moves the whole line left along the x-axis too. When moving it down, it moves the equation right on the x-axis.

4. Alex is correct

5. g(x)=(2x-8)^2+5

6. This accomplishes these transformations because I made a graph about it

Step-by-step explanation:

Answer:

0-9(n-1)

Step-by-step explanation:

We can tell the first term of the sequence is 0 and the common difference is -9. So the explicit formula would be h(n)=0-9(n-1)

The explicit formula for h(n) comes to be h(n)=9-9n.

An arithmetic progression is a list of numbers where the difference between consecutive terms is always constant.

[tex]h(n)=h(n-1)-9[/tex]

[tex]h(n)-h(n-1)=-9[/tex]

So the common difference of the arithmetic progression will be -9.

[tex]h(1)=0[/tex] means the first term of the AP is 0.

We know that [tex]n^{th}[/tex] term of an AP is given by:

[tex]h(n)=a+(n-1)d[/tex]

Where a is the first term and d is a common difference.

Fo the given series [tex]a=0[/tex] and [tex]d=-9[/tex]

So, [tex]h(n)=0+(n-1)(-9)[/tex]

[tex]h(n)=9-9n[/tex]

So, the explicit formula for h(n) is [tex]h(n)=9-9n[/tex]

Hence, the explicit formula for h(n) comes to be [tex]h(n)=9-9n[/tex].

To get more about arithmetic progressions visit:

https://brainly.com/question/6561461

Answer:

A: f(x) = (3/4 x)^2 - 1

Step-by-step explanation:

As you can see in the first image i attached, option A is the function that matches the one in your image. the "- 1" in the function is the y-intercept, and the 3/4 is what stretches your parabola which made it larger. You could also use process of elimination to get rid of option B and D since the y-intercepts do not match. Then you are left with A and C. the 4 in "(4x)^2" would make the parabola shrink, as you can see in the second image.

Answer:

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] s= 0.286[/tex]

And then the estimator for the standard error is given by:

[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

20.05, 20.56, 20.72, and 20.43

We can assume that the distribution for the sample mean is given by:

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

And the standard error for this case would be:

[tex] SE= \frac{\sigma}{\sqrt{n}}[/tex]

And we can estimate the deviation with the sample deviation:

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] s= 0.286[/tex]

And then the estimator for the standard error is given by:

[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]

Answer:

Answers are below

Step-by-step explanation:

10a) Find how many multiples of 3 there are       4/12 = 1/3

10b) Find how many factors of 12 there are         6/12 = 1/2

10c) Find how many prime numbers there are    5/12

10d)                                                                         3/12 = 1/4

10e) Find how many numbers are less than 12   11/12

Answer:

X=8

Step-by-step explanation:

3x+ 6 = 5x -10

6+10=5X-3X

16=2X

X=8

Answer:

Step-by-step explanation:

ported that 22% of adults in France admitted to texting or e-mailing while driving. A random sample of 110 French adults was randomly selected. What is the probability that 26

Using a binomial distribution with mean = n*p = 110*0.22 = 24.2 and variance = n*p*(1-p) = 24.2*(1-0.22) = 18.876

Approximating it to a normal distribution,

[tex]P(x\geq 26)\\\\=P(Z\geq \frac{26-24.2}{\sqrt{18.876} } )\\\\=P(Z\geq 0.41)\\\\=0.3481[/tex]

Answer:

Step-by-step explanation:

Volume of a triangular based prism = [tex]Base\ area * height[/tex]

Base area = Area of the triangle = 1/2 * base of the triangle * height of the triangle

Since the  triangular base has dimensions of 3" by 4" by 5", then it is a right angled triangle with base of 4in and height of 3in

Base Area = 1/2 * 3 * 4

Base Area = 6in²

Substituting the volume and the base area value in the formula to get the height of the prism we have;

210 = 6H

H = 210/6

H = 35in

Surface area of the triangular prism = bh + pH

b= base of the triangle  = 4in

h- height of the triangle  = 3in

p= perimeter of the triangle  = 3+4+5 = 12in

H= height of the prism = 35in

Surface area of the triangular prism = 4(3)+12(35)

Surface area of the triangular prism = 12+420in

Surface area of the triangular prism = 432in²

Answer:

The maximum possible error of in measurement of the angle is  [tex]d\theta_1 =(14.36p)^o[/tex]

Step-by-step explanation:

From the question we are told that

    The angle of elevation  is  [tex]\theta_1 = 15 ^o = \frac{\pi}{12}[/tex]

     The height of the tree is  h

      The distance from the base is  D

h is mathematically represented as

            [tex]h = D tan \theta[/tex]       Note : this evaluated using SOHCAHTOA i,e

                                               [tex]tan\theta = \frac{h}{D}[/tex]

Generally for small angles the series approximation of  [tex]tan \theta \ is[/tex]

          [tex]tan \theta = \theta + \frac{\theta ^3 }{3}[/tex]

So given that [tex]\theta = 15 \ which \ is \ small[/tex]

       [tex]h = D (\theta + \frac{\theta^3}{3} )[/tex]

       [tex]dh = D (1 + \theta^2) d\theta[/tex]

=>        [tex]\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta[/tex]

Now from the question the relative error of height should be at  most

        [tex]\pm p[/tex]%

=>    [tex]\frac{dh}{h} = \pm p[/tex]

=>    [tex]\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p[/tex]

=>      [tex]d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p[/tex]

 So  for   [tex]\theta_1[/tex]

            [tex]d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p[/tex]

substituting values  

          [tex]d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p[/tex]

 =>       [tex]d\theta_1 = 0.25 p[/tex]

Converting to degree

           [tex]d\theta_1 = (0.25* 57.29) p[/tex]

            [tex]d\theta_1 =(14.36p)^o[/tex]

Answer:

Center is [tex](-12,9)[/tex]

Step-by-step explanation:

Given: Equation of a circle is [tex](x+12)^2+(y-9)^2=35[/tex]

To find: center of the circle

Solution:

A circle is a locus of all points which are at equidistant from the fixed point (center).

Equation of a circle is of form [tex](x-a)^2+(y-b)^2=r^2[/tex] where [tex](a,b)[/tex] represents center of the circle and r denotes radius of the circle.

Given equation is [tex](x+12)^2+(y-9)^2=35[/tex]

[tex]\left [ x-(-12) \right ]^2+(y-9)^2=35[/tex]

Compare this equation with [tex](x-a)^2+(y-b)^2=r^2[/tex]

Center is [tex](a,b)=(-12,9)[/tex]

Answer:

The raidus is 5.92

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a hypothesis testing involving population proportion. The null hypothesis would be that fewer than or 50% of the people would favor spending money for a sewer system. Since she will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure, then the alternative hypothesis which she should test is that more than 50% of the people would favor spending money for a sewer system.

Answer:

Check the answer. 1. ... 5 times a number plus 8 is equal to 3 times the number minus 4. 7 times a ... Twice a number is equal to 5 times the sum of the number and 6. The product ... If the equation is an identity, write the answer as “All real numbers.

Step-by-step explanation:

Answer:

(y-6)(y-6)

Step-by-step explanation:

y^2 - 12y + 36= y^2-2*6y+6^2= (y-6)^2= (y-6)(y-6)

Answer:

[tex](y-6)(y-6)[/tex]

Step-by-step explanation:

[tex]y^2 - 12y + 36[/tex]

[tex]y^2-6y-6y+36[/tex]

[tex]y(y-6)-6(y-6)[/tex]

[tex](y-6)(y-6)[/tex]

Answer:

Option C.

Step-by-step explanation:

Solid in the given picture is a rectangular prism and a rectangular prism has 6 faces. Each face is formed by joining 4 vertices of the prism.

All the faces joining four vertices are: AFGB, BGHC, ADEF, DCHE, FEHG, ADCB.

From the given options,

Option (C). ADEF will be one of the face of the solid.

Answer:

it should be 40.5 i believe

Step-by-step explanation:

Answer:

The probability that both are red is [tex]P(red\:and \:red)=\frac{45}{946}\approx0.04756\approx4.756\%[/tex].

Step-by-step explanation:

Probability is simply how likely something is to happen and its given by

Probability of an event = (# of ways it can happen) / (total number of outcomes)

Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.

                                     [tex]P(A\:and\: B)=P(A)\cdot P(A|B)[/tex]

At our first pull, there is an [tex]P(red)=\frac{10}{10+34}[/tex] chance that a red will be pulled.

At the second pull there is a [tex]P(red)=\frac{9}{9+34}[/tex] chance that the second marble will be red.

Therefore, the probability that both are red is

[tex]P(red\:and \:red)=\frac{10}{10+34}\cdot \frac{9}{9+34}=\frac{45}{946}\approx0.04756\approx4.756\%[/tex]

Answer:

YG, YT, YU, BG, BT, BU, WG, WT and WU

Step-by-step explanation:

The sample space are all the posibles options that you can take, so the sample space in these case is:

YG, YT, YU, BG, BT, BU, WG, WT and WU

Where, for example, YG means that you choose Yellow for your game room and Green for your entertainment center and BU means that you chosse Yellow for your game room and Unfinished for your entertainment center.

Answer:

37044 different combinations of 4 movies can he rent if he wants at least one comedy

Step-by-step explanation:

The order in which the movies are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

How many different combinations of 4 movies can he rent if he wants at least one comedy

The easier way to solve this is subtract the total from the number of combinations with no comedies.

Total:

4 movies from a set of 14 + 19 = 33. So

[tex]C_{33,4} = \frac{33!}{4!(33-4)!} = 40920[/tex]

No comedies:

4 movies from a set of 19.

[tex]C_{19,4} = \frac{19!}{4!(19-4)!} = 3876[/tex]

At least one comedy:

40920 - 3876 = 37044

37044 different combinations of 4 movies can he rent if he wants at least one comedy

Answer: choice B

Step-by-step explanation:

50C40

=50C10

=50!/40!*10!

Answer:

10.5 minutes

Step-by-step explanation:

Thinking about the problem

The modeling function is of the form P(t)=A⋅Bf(t), where B=4B=4B, equals, 4 and f(t)=\dfrac{t}{10.5}f(t)=

10.5

t

​

f, left parenthesis, t, right parenthesis, equals, start fraction, t, divided by, 10, point, 5, end fraction.

Note that each time f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111, the quantity is multiplied by B=4B=4B, equals, 4.

Therefore, we need to find the ttt-interval over which f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111.

Hint #22 / 3

Finding the appropriate unit interval

fff is a linear function whose slope is \dfrac{1}{10.5}

10.5

1

​

start fraction, 1, divided by, 10, point, 5, end fraction.

This means that whenever ttt increases by \Delta tΔtdelta, t, f(t)f(t)f, left parenthesis, t, right parenthesis increases by \dfrac{\Delta t}{10.5}

10.5

Δt

​

start fraction, delta, t, divided by, 10, point, 5, end fraction.

Therefore, for f(t)f(t)f, left parenthesis, t, right parenthesis to increase by 111, we need \Delta t=10.5Δt=10.5delta, t, equals, 10, point, 5. In other words, the ttt-interval we are looking for is 10.510.510, point, 5 minutes.

Hint #33 / 3

Summary

The number of people who yawned quadruples every 10.510.510, point, 5 minutes.

Answer & Step-by-step explanation:

(2/5 + 3/4) * [ 3 - (1/4 : 1/5)]

When you see this sign, : , it usually means to divide the numbers because they represent some form of a ratio. So, we will divide 1/4 by 1/5.

First, do all of the operations in the parentheses ().

(2/5 + 3/4)*[ 3 - (1/4 : 1/5)]

(23/20) * [ 3 - (5/4)]

(23/20) * (7/4)

Now, we multiply 23/20 by 7/4.

(23/20) * (7/4)

161/80

This number can not be simplified so we will keep it as it is.

So, the answer to this expression is 161/80

Answer:

OK so we can see that when x increases y does too. The answer is C

Answer:

The probability that a customer purchases a black SUV is 0.05.

Step-by-step explanation:

The question is incomplete:

At a certain car dealership, the probability that a customer purchases an SUV is 0.20. Given that a customer purchases an SUV, the probability that it is black is 0.25.

The probability that a customer purchases a black SUV can be calculated as the multiplication of this 2 factors:

We know then:

[tex]P(SUV)=0.25\\\\P(B | SUV)=0.20[/tex]

We can now calculate the probability as:

[tex]P(B\,\&\,SUV)=P(B|SUV)\cdot P(SUV)=0.25\cdot0.20=0.05[/tex]

Answer:

Step-by-step explanation:

Since we are dealing with binomial probability in this scenario, then the outcome is either a success or a failure. A success in this case means that a chosen adult has a bachelor's degree. The probability of success, p would be 20/100 = 0.2

The number of adults sampled, n is 100

The number of success, x is 60

The probability that more than 60 adults have a bachelor's degree P(x >60) would be represented as

d. P(x<60)=binomcdf (100.0.20.60)

binompdf is used when we want to determine P(x = 60)

Answer:

c) Population parameter or Population statistic

Step-by-step explanation:

Population:-

The totality of observation with which we are concerned , whether this number be finite or infinite is called population

Sample :

A sample is subset of a Population

Given data  the USA today internet poll is called Population

Given data 73 percent of readers are satisfied with their lives.

This is called Population parameter.

Answer:

6 sqrt(5)

Step-by-step explanation:

(3√2) ( √10)

We know that sqrt(a) * sqrt(b) = sqrt(ab)

3 sqrt(2*10)

3 sqrt(20)

3 sqrt(4*5)

We know that sqrt(a) * sqrt(b) = sqrt(ab)

3 sqrt(4) sqrt(5)

3 * 2 * sqrt(5)

6 sqrt(5)