Find each value and measure. Assume that segments that appear to be tangent are tangent.

Answer:

79.45

Step-by-step explanation:

Given:

It is given that the measurements of the triangle.

The measure of ∠2 is (3x + 3)°

The measure of ∠3 is (3x - 4)°

The measure of ∠4 is (5x + 8)°

We need to determine the measure of ∠1 and ∠4.

Value of x:

The value of x can be determined using the exterior angle theorem.

Applying the theorem, we have;

[tex]m \angle 4=m \angle 2+m \angle 3[/tex]

Substituting the values, we get;

[tex]5x+8=3x+3+3x-4[/tex]

[tex]5x+8=6x-1[/tex]

[tex]-x+8=-1[/tex]

     [tex]-x=-9[/tex]

        [tex]x=9[/tex]

Thus, the value of x is 9.

Measure of ∠4:

Substituting the value of x in the expression of ∠4, we get;

[tex]m\angle 4=5(9)+8[/tex]

       [tex]=45+8[/tex]

[tex]m\angle 4=53^{\circ}[/tex]

Thus, the measure of ∠4 is 53°

Measure of ∠1:

The angles 1 and 4 are linear pairs and hence these angles add up to 180°

Thus, we have;

[tex]\angle 1+ \angle 4=180^{\circ}[/tex]

Substituting the values, we get;

[tex]\angle 1+ 53^{\circ}=180^{\circ}[/tex]

         [tex]\angle 1=127^{\circ}[/tex]

Thus, the measure of ∠1 is 127°

The region represented by the shaded area has 25% and accounts for one-quarter of the overall circle.

The area is the space occupied by any two-dimensional figure in a plane. The area of the circle is the space occupied by the circle in a two-dimensional plane.

The formula for calculating circle area is r2, where r is the radius of the circle.

The entire area of the circle in the accompanying figure is r2. The shaded area accounts for one-fourth of the circle's overall area.

Total area =  πr²

Shaded area = ( 1 / 4 )πr²

The percentage of the shaded area will be calculated as

Shaded area = ( 1 / 4 )πr²

Shaded area = ( 0.25 )πr²

To convert it into a percentage multiply by 100.

Shaded area = ( 0.25 x 100 )πr²

Shaded area =25% πr²

Put πr² as the total area.

Shaded area =25% of Total area.

Therefore, the region represented by the shaded area has 25% and is 1/4th of the total circle.

Answer:

P(Fewer than 3) = 0.05.

Step-by-step explanation:

We are given that a student takes a true-false test that has 10 questions and guesses randomly at each answer.

The above situation can be represented through Binomial distribution;

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

where, n = number of trials (samples) taken = 10 questions

            r = number of success = fewer than 3

           p = probability of success which in our question is probability

                that question is answered correctly, i.e; 50%

LET X = Number of questions answered correctly

So, it means X ~ Binom(n = 10, p = 0.50)

Now, Probability that Fewer than 3 questions are answered correctly is given by = P(X < 3)

P(X < 3)  = P(X = 0) + P(X = 1) + P(X = 2)

=  [tex]\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0}+ \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1}+ \binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}[/tex]

=  [tex]1 \times 0.50^{10} + 10 \times 0.50^{10} +45 \times 0.50^{10}[/tex]

=  0.05

Hence, the P(Fewer than 3) is 0.05.

To find the probability of the student passing the test with at least a 70 percent, we can use the binomial probability formula. The probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).

To find the probability of the student passing the test with at least a 70 percent, we need to find the probability of the student answering 7, 8, 9, or 10 questions correctly out of the 10 questions. Since the student randomly guesses at each answer, the probability of guessing correctly is 0.5. Now we can calculate the probability using the binomial probability formula:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

P(X = k) = C(10, k) * (0.5)^k * (0.5)^(10-k), where C(n, r) is the binomial coefficient (n choose r).

Calculating each probability and summing them up, we get P(X ≥ 7) = 0.171875. Therefore, the probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).

Answer: The rate of change of the distance between the spider and the ant is 4.92 inches/sec

Step-by-step explanation: Please see the attachments below

Answer:

20

Step-by-step explanation:

Of means multiply and is means equals

80% * 25 = ?

Change to decimal form

.80 *25 =

20

A deposit of at least $95.75 is needed to avoid the service fee, as this will bring the balance from $204.25 back to the required $300 minimum.

To avoid a service fee, we need to ensure that the checking account balance is at least $300 at the end of the month. Starting with a balance of $337.03 and after spending $132.78, the new balance is calculated as follows:

$337.03 - $132.78 = $204.25.

To avoid the service fee, the account balance must return to at least $300. Therefore, you need to deposit the difference between your current balance and the minimum balance required:

$300 - $204.25 = $95.75.

Any deposit amount greater than or equal to $95.75 will therefore avoid the service fee.

Answer:

Let's assume the following data:

Price in Dollars (X) 26 29 32 38 47

Number of Bids (Y) 12 13 15 16 18

For our case we have this:

n=10 [tex] \sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118[/tex]  

[tex]r=\frac{5(2623)-(172)(74)}{\sqrt{[5(6194) -(172)^2][5(1118) -(74)^2]}}=0.974[/tex]  

So then the correlation coefficient would be r =0.974

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

And in order to calculate the correlation coefficient we can use this formula:  

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]  

Let's assume the following data

Price in Dollars (X) 26 29 32 38 47

Number of Bids (Y) 12 13 15 16 18

For our case we have this:

n=10 [tex] \sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118[/tex]  

[tex]r=\frac{5(2623)-(172)(74)}{\sqrt{[5(6194) -(172)^2][5(1118) -(74)^2]}}=0.974[/tex]  

So then the correlation coefficient would be r =0.974

Answer:

Step-by-step explanation:

The first derivative is ...

  f'(x) = 30x^5 -40x^3 = 10x^3(3x^2 -4)

This will have zeros (critical points) at x=0 and x=±√(4/3).*

We don't need the second derivative to tell the nature of these critical points. Since the degree is even, the function is symmetrical about x=0. Since the leading coefficient is positive, it generally has a U-shape. This means the "outer" critical points will be minima, and the central one will be a local maximum.

__

However, since we're asked to use the 2nd derivative test first, we find the 2nd derivative to be ...

  f''(x) = 150x^4 -120x^2 = 30x^2(5x^2 -4)

For x=0, f''(0) = 0 -- as we expect for a function with a high multiplicity of the root at that point. For x either side of zero, both the function and the second derivative are negative, indicating downward concavity. That is, x = 0 is a local maximum.

For x² = 4/3, the second derivative is positive, indicating upward concavity. At x = ±√(4/3), we have local minima.

_____

* The "simplified" equivalent to √(4/3) is (2/3)√3.

The critical points of the function f(x) = 5x^6 − 10x^4 are x = 0, x = ±√(4/3). The point at x = 0 is a relative maximum while the points at x = ±√(4/3) are relative minima based on the second derivative test.

Given the function f(x) = 5x^6 − 10x^4, we first find the critical points. This is done by finding the derivative of the function and setting it equal to zero. For this function, the derivative, f'(x), is 30x^5 - 40x^3 = 0. Solving this equation for x, we get x = 0, and x = ±√(4/3).

Next, we apply the second derivative test by taking the second derivative of the original function, f''(x). This gives us f''(x) = 150x^4 - 120x^2. We substitute the obtained critical points into the second derivative. If f''(x) > 0, then the point is a relative minimum, if f''(x) < 0, it's a relative maximum. If neither, we need to consider higher order derivatives or other methods.

The second derivative is negative at x = 0, so that position is a relative maximum. The second derivative is positive at x = ±√(4/3), so these positions are relative minima.

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Given:

In the given triangle ΔABC,

AB = 9 unit

AC = 2 unit

To find the value of ∠ABC.

Formula

From trigonometric ratio we get,

[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]

Let us take, ∠ABC = [tex]\theta[/tex]

With respect [tex]\theta[/tex], AC is the opposite side and AB is the hypotenuse.

So,

[tex]sin \theta = \frac{AC}{AB}[/tex]

or, [tex]sin \theta[/tex] = [tex]\frac{2}{9}[/tex]

or, [tex]\theta = sin^{-1} (\frac{2}{9} )[/tex]

or, [tex]\theta= 12.84^\circ[/tex]

Hence,

The value of ∠ABC is 12.84°.

Answer:

-16x+4

Step-by-step explanation:

-6x+2/3(9-15x)-2

Distribute

-6x +2/3 *9 +2/3*(-15x) -2

-6x +6 -10x -2

Combine like terms

-6x-10x +6-2

-16x+4

Answer:

A prism that has a length of 2, height of 1 and one-half, and width of 2.

Step-by-step explanation:

The formula for calculating the area of a prism is base area × height

Volume = L×W×H

L is the length of the prism

W is the width

H is the height.

To determine the prism that has an area of 6 cubic units, we will substitute the values in the option in the formula.

Using option D i.e prism that has a length of 2, height of 1 and one-half, and width of 2.

L = 2units, H = 1 1/2 units , W = 2units

Substituting in the formula for finding the volume

V = 2×2×3/2

Volume of the prism = 6cubic units

Answer:

B

Step-by-step explanation:

Answer:

The p-value for the test of hypothesis is P(z<-3.617)=0.0002.

Step-by-step explanation:

Hypothesis test on the difference between proportions.

The claim is that the percent of males who are underclassmen stats students (π1) is less than the percent of females who are underclassmen stats students (π2).

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2<0[/tex]

The male sample has a size n1=156. The sample proportion is p1=81/156=0.52.

The female sample has a size n2=221. The sample proportion in this case is p2=221/320=0.69.

The weigthed average of proportions p, needed to calculate the standard error, is:

[tex]p=\dfrac{n_1p_1+n_2p_2}{n_1+n_2}=\dfrac{81+221}{156+320}=\dfrac{302}{476}= 0.63[/tex]

The standard error for the difference in proportions is:

[tex]\sigma_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.63*0.37}{156}+\dfrac{0.63*0.37}{320}}\\\\\\\sigma_{p1-p2}=\sqrt{\dfrac{0.2331}{156}+\dfrac{0.2331}{320}}=\sqrt{0.001503871+0.000728438}=\sqrt{0.002232308}\\\\\\\sigma_{p1-p2}=0.047[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_1-p_2}{\sigma_{p1-p2}}=\dfrac{0.52-0.69}{0.047}=\dfrac{-0.17}{0.047}=-3.617[/tex]

The P-value for this left tailed test is:

[tex]P-value = P(z<-3.617)=0.00015[/tex]

Answer:

[tex]z=\frac{0.519-0.691}{\sqrt{0.634(1-0.634)(\frac{1}{156}+\frac{1}{320})}}=-3.657[/tex]    

[tex]p_v =P(Z<-3.657)=0.0001[/tex]  

Step-by-step explanation:

Data given and notation  

[tex]X_{1}=81[/tex] represent the number of males underclassmen

[tex]X_{2}=221[/tex] represent the number of females underclassmen

[tex]n_{1}=156[/tex] sample of male

[tex]n_{2}=320[/tex] sample of female

[tex]p_{1}=\frac{81}{156}=0.519[/tex] represent the proportion of males underclassmen

[tex]p_{2}=\frac{221}{320}= 0.691[/tex] represent the proportion of females underclassmen

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the value for the test (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the percent of males who are underclassmen stats students is less than the percent of females who are underclassmen stats students   , the system of hypothesis would be:  

Null hypothesis:[tex]p_{1} \geq p_{2}[/tex]  

Alternative hypothesis:[tex]p_{1} < p_{2}[/tex]  

We need to apply a z test to compare proportions, and the statistic is given by:  

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)  

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{81+221}{156+320}=0.634[/tex]  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

[tex]z=\frac{0.519-0.691}{\sqrt{0.634(1-0.634)(\frac{1}{156}+\frac{1}{320})}}=-3.657[/tex]    

Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test.    

Since is a one side test the p value would be:  

[tex]p_v =P(Z<-3.657)=0.0001[/tex]  

Answer:

[tex]P(X<64)=P(\frac{X-\mu}{\sigma}<\frac{64-\mu}{\sigma})=P(Z<\frac{64-50}{8})=P(z<1.75)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<1.75)=0.9599[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the number of rushing yards of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(50,8)[/tex]  

Where [tex]\mu=50[/tex] and [tex]\sigma=8[/tex]

We are interested on this probability

[tex]P(X<64)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

[tex]P(X<64)=P(\frac{X-\mu}{\sigma}<\frac{64-\mu}{\sigma})=P(Z<\frac{64-50}{8})=P(z<1.75)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<1.75)=0.9599[/tex]

Answer:

7.47

Step-by-step explanation:

6.5b - 12.03

Let b=3

6.5(3) - 12.03

Multiply first

19.5 - 12.03

7.47

Hi I think your answer is - 5.5

6.5b b=3. So you replace B with 3 and that makes it 6.53-12.03.

wich gives you - 5.5.

Answer:

3 nights

Step-by-step explanation:

because 1 flight there and one flight back =300 then add 3 nights =480

Answer:

5 nights or less

Step-by-step explanation:

You can do this by writing an inequality and solving it.

Let n = number of nights.

1 hotel night costs $60. n number of hotel nights cost 60n.

The flight costs $150.

The total cost is the price of the hotel plus the price of the flight.

60n + 150

The total price must be less than or equal to $500.

[tex] 60n + 150 \le 500 [/tex]

Now we solve the inequality.

Subtract 150 from both sides.

[tex] 60n \le 350 [/tex]

Divide both sides by 60.

[tex] n \le \dfrac{350}{60} [/tex]

350 divided by 60 is 5.8333...

[tex] n \le 5.8 [/tex]

The number of night is less than or equal to 5.8, and it must be a whole number, so the most number of nights she can afford is 5.

Answer:

11/17

Step-by-step explanation:

slope between two points: slope = (y2 - y1) / (x2 - x1)

(x1, y1) = (-19, -6), (x2, y2) = (15, 16)

m = (16 - ( - 6)) / (15 - ( - 19))

refine

m = 11/17

sorry it is hard to follow... i am on my phone rn :/

Final answer:

The slope between the points (-19, -6) and (15, 16) is 11/17.

Explanation:

To find the slope of the line connecting the points (-19,-6) and (15,16), we will use the slope formula which is the change in y-coordinates divided by the change in x-coordinates. Here is the process:

Therefore, the slope of the line connecting the two points is 11/17.

Answer:

No

Step-by-step explanation:

3x + 9 = 13

Subtract 9 from each side

3x + 9-9 = 13-9

3x = 4

Divide each side by 3

3x/3 = 4/3

x = 4/3

8 is not a solution

Answer:

(a)f(x)=0.8869x

(b)g(x)=143.1126x

(c)g(f(x))=126.9266x

(d)g(f(1000))=126926.6 Yen

Step-by-step explanation:

Given on a particular day

(a)If x represents the number of Dollars

Since one can purchase 0.8869 Euro with 1 USD, the function f(x) is a direct relationship where x is dollars and f(x) is in Euros.

(b)If x represents the number of Euros

Since one can purchase 143.1126 yen with 1 Euros, the function g(x) is a direct relationship where x is Euros and g(x) is in Yen.

(c)Given:

g(f(x))=143.1126(0.8869x)

(d)g(f(1000))

To decompose the fraction 2 3/4, convert it to an improper fraction by multiplying the whole number by the denominator of the fraction, add the numerator, and place over original denominator, resulting in 11/4.

The question asks to decompose the fraction 2 3/4 into its components. To decompose this mixed number, we need to convert it to an improper fraction. The process involves multiplying the whole number by the denominator of the fraction part, adding the numerator of the fraction part, and then placing the result over the original denominator.

Therefore, the mixed number 2 3/4 decomposed into an improper fraction is 11/4.

Answer:

a) 83%

b) 0.892

Step-by-step explanation:

percentage that attends class on friday = 74%

percentage that pass because they attend class on friday = 88%

percentage that pass but did not go to school on friday = 20%

a) percentage of students expected to pass the course

  = (74% x 88%) +(88% x 20%)

   = 0.6512 + 0.176

   = 0.8272

   = 83%

b) If a person passes the course, what is the probability that he/she attended classes on Fridays

        = 74% divided by 83%

        = 0.892

Answer: o Subtract 7 tens from 8 tens.

Step-by-step explanation: you subtract

Answer:

Step-by-step explanation:subtract 7 tens from 8 tens

Answer:

32 ounces

Step-by-step explanation:

She bought 1 cucumber. She bought twice as much lettuce.

1(2) = 2 lbs of lettuce.

There are 16 ounces to the lb.

2 (16 ounces) = 32 ounces

Answer:

She bought 32 oz of lettuce.

Step-by-step explanation:

There are 16 oz in 1 lb. twice as much means 2x. 2 x 16 = 32.

Answer:

36

Step-by-step explanation:

[tex] \frac{c}{4} - 5 = 4 \\ \\ \frac{c}{4} = 4 + 5\\ \\ \frac{c}{4} = 9 \\ \\ c = 9 \times 4 \\ \\ \huge \red{ \boxed{ c = 36}}[/tex]

Answer:

1, [tex]\frac{m}{n}[/tex], [tex]\frac{1-m}{n}[/tex].

Step-by-step explanation:

probability = [tex]\frac{Number of Possible Outcomes}{Total Outcomes}[/tex]

Total number of persons in the party = n

a) Pr ( every person gets their phone back) = Pr (each person picks his phone ) multiplied by number of person

   = [tex]\frac{1}{n}[/tex] × n = 1.

     No of first m persons to pick = m

     No of last m persons to pick = 1 - m

b) Pr (first m persons to pick each gets their phones back) = [tex]\frac{m}{n}[/tex]

c) Pr( first m persons get a phone belonging to last m persons) = [tex]\frac{1-m}{n}[/tex]

Answer:

2.47 times more likely.

Step-by-step explanation:

16 out of 178 cases were reported for exposure.

And 8 out of 220 control reported for exposure.

Chances that a case would be reported for exposure = (16/178) = 0.0898876404

Chances that one control would report for exposure = (8/220) = 0.0363636364

Comparing both, how likely were cases to report an exposure compared with controls

= (0.0898876404) ÷ (0.0363636364)

= 2.4719101085 = 2.47 times more likely.

Hope this Helps!!

To find the minimum score needed to receive a grade of A, we need to determine the cutoff point for the top 16.6% of students. We can use the Z-score formula to convert a raw score into a standardized score and then find the corresponding raw score. The minimum score needed to receive a grade of A is approximately 88.

To find the minimum score needed to receive a grade of A, we need to determine the cutoff point for the top 16.6% of students. In a normal distribution, we can use the Z-score formula to convert a raw score into a standardized score. We need to find the Z-score that corresponds to the 83.4th percentile, as 16.6 percent is the area to the left of this score. We can then use the Z-score formula to find the corresponding raw score.

Z = (X - μ) / σ

Where: Z is the Z-score, X is the raw score, μ is the mean, and σ is the standard deviation. Rearranging the formula, we have:

X = (Z * σ) + μ

Since the mean is 78 and the standard deviation is 10, we substitute the values into the formula:

X = (Z * 10) + 78

Next, we need to find the Z-score that corresponds to the 83.4th percentile using a Z-score table or a calculator. From the table, we find that the Z-score is approximately 0.9998. Substituting this value into the formula, we can solve for X:

X = (0.9998 * 10) + 78

X = 9.998 + 78

X ≈ 87.998

Therefore, the minimum score needed to receive a grade of A is approximately 88.

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Answer:

141 cookies

Step-by-step explanation:

amount of cookies

= 9(15) + 6

= 135 + 6

= 141

Answer:

temperature on the beach = T2 = 34.56 °C

Step-by-step explanation:

We are given;

P1 = 4.5 atm

T1 = 24 °C = 24 + 273 = 297 K

P2 = 4.66 atm

Thus, P1/T1 = P2 /T2

So, T2 = P2•T1/P1

Thus, T2 = (4.66x 297)/4.5

T2 = 307.56 K

Let's convert to °C to obtain ;

T2 = 307.56 - 273

T2 = 34.56 °C