Which point gives the vertex of f(x) = x2 - 4x + 21?

Answer:

You have found 24 nickels.

Step-by-step explanation:

Let N be the number of nickles, D be the number of dimes and Q be the number of quarters. The number of coins and their face values are given by the following expressions, respectively:

[tex]N+D+Q=72\\0.05N+0.10D+0.25Q=10.20[/tex]

As of now we have three variables and two expressions, the final expression needed to solve the linear system is given by the amount offered by the coin dealer:

[tex]10N+20D+15Q=1,060[/tex]

Solving the linear system:

[tex]N+D+Q=72\\5N+10D+25Q=1,020\\10N+20D+15Q=1,060\\\\10N-10N+20D-20D+15Q-50Q=1,060-(2*1,020)\\-35Q=-980\\Q=28\\\\5N-10N+10D-10D+25Q-10Q=1,020-720\\-5N+15Q=300\\-5N=300-(15*28)\\N=24[/tex]

You have found 24 nickels.

Answer:

  see below for a graph

Step-by-step explanation:

A graphing calculator makes this short work.

__

You can find the x- and y-intercepts by setting the opposite variable to zero.

First equation x-intercept is the solution to 2x +0 = 1: x = 1/2. The y-intercept of that equation is the solution to 2·0 +y = 1: y = 1. The graph is the line through these points.

Second equation x-intercept is the solution to 2x +4·0 = 12: x = 6. The y-intercept is the solution to 2·0 +4y = 12: y = 3. The graph is the line through these points.

Answer:

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)

Step-by-step explanation:

Step(i):-

Given sample size 'n' =41

Mean of the sample(x⁻)  = 3.55

The estimated standard error

                                             [tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]

Given  estimated standard error ( S.E) = 3.478

Level of significance ∝=0.05

Step(ii):-

95% for the true average increase in total cholesterol under these circumstances

[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]

Degrees of freedom

ν= n-1 = 41-1 =40

t₀.₀₅ = 1.6839

95% for the true average increase in total cholesterol under these circumstances

[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]

( 3.55 - 1.6839 ×3.478 ,3.55 + 1.6839 ×3.478 )

(3.55 - 5.856 , 3.55 + 5.856)

(-2.306 , 9.406)

Conclusion:-

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)

Answer:

2h x (l+b)

2x10 X (12+10)

20 X 22

44 cm cube is your answer...

Answer: 3.9

Step-by-step explanation: Khan Academy

The length of BD if The angle ∠ DAC is equal to the angle ∠ BAD is 3.92.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The angle ∠ DAC = angle ∠ BAD

As we can see that the triangle BAD and triangle DAC are similar By SAS similarity,

AC / AB = CD / BD  (By the proportional theorem of similarity)

5.6 / 5.1 = 4.3 / BD

1.09 = 4.3 / BD

BD = 4.3 / 1.09

BD = 3.92

Thus, the length of BD is 3.92.

To know more about Triangles:

https://brainly.com/question/16886469

#SPJ2

Answer:

Step-by-step explanation:

In order to convert 0.0004578, which is in decimal, to scientific notation, all we need to do in this case is to move our decimal point to the right till we arrive at the first number that is not a zero, and then eliminate all the zero.

In this case, we will have to move the decimal point 4 spaces to our right, which would mean our exponent would be negative. The number of decimal spaces we moved to our right would be the value of our exponent, which is -4 in this case.

Thus, we have:

[tex] 4.578 * 10^{-4} [/tex]

Answer:

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.

Step-by-step explanation:

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].

Population:

[tex]\mu = 14.5, \sigma = 2.5[/tex]

Sample:

55 students, so [tex]n = 55[/tex]

Then

[tex]\mu = 55, s = \frac{2.5}{\sqrt{55}} = 0.34[/tex]

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.

Answer:

d. 10 minutes and 1.33 minutes.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

[tex]M = \frac{a + b}{2}[/tex]

The variance of the uniform distribution is given by:

[tex]V = \frac{(b-a)^{2}}{12}[/tex]

The assembly time for a product is uniformly distributed between 8 and 12 minutes.

This means that [tex]a = 8, b = 12[/tex].

Mean:

[tex]M = \frac{8 + 12}{2} = 10[/tex]

Variance:

[tex]V = \frac{(12-8)^{2}}{12} = 1.33[/tex]

So the correct answer is:

d. 10 minutes and 1.33 minutes.

Answer:

Let x be her initial distance from the building, then tan 37 = 130/x

x = 130/tan 37 = 130/0.7536 = 172.5 feet

Let y be her distance from the building after moving forward, then

tan 40 = 130/y

y = 130/tan 40 = 130/0.8391 = 154.9

After moving forward, she is 172.5 - 154.9 = 17.6 ft closer.

Answer: B. 17.6 ft.

Step-by-step explanation: I just did it on the edge 2023 assignment. Check attached image.

Answer:

B

Step-by-step explanation:

[tex]6.79 \times 0.7[/tex]

[tex]=4.753[/tex]

Answer:

The correct answer would be $4.75

Step-by-step explanation:

6.79 × 0.7

=$4.75

Hope that was helpful.Thank you!!!

Answer:

B

The highest point of the mountain defined by the function is 16 feet.

ED 2020

Step-by-step explanation:

The highest point of the mountain defined by the function is 16. Therefore, option B is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given information, we have;

The distance in feet from the edge of the mountain is given as the independent variable, x

The distance in feet from the ground (which is the height) is given the as the dependent variable f(x)

Therefore, given that the point (12, 16) are the values of x and f(x) such that x = 12 and f(x) = 16 and 16 is the largest value of f(x) in the data, therefore, 16 represents the highest defined point of the mountain.

Therefore, option B is the correct answer.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ2

"Your question is incomplete, probably the complete question/missing part is:"

The computer rendering of a mural in a town’s square uses the function represented in the table to define the outline of a mountain in the town’s logo, where x is the distance in feet from the edge of the mural and f(x) is the distance from the ground in feet. How can the point (12, 16) be explained?

A) The highest point of the mountain defined by the function is 12 feet.

B) The highest point of the mountain defined by the function is 16 feet.

C) The width of the base of the mountain defined by the function is 12 feet.

D) The width of the base of the mountain defined by the function is 16 feet.

Answer:

47

Step-by-step explanation:

The probability for tails to land is 1/2 when you flip 1 coin.

When you flip 94 times, 1/2 × 94

= 47

Answer:

The 95% confidence interval for the average hourly wage of all information system managers is (39.14,42.36)

Step-by-step explanation:

In order to calculate the 95% confidence interval for the average hourly wage we would have to calculate first the margin of error as follows:

ME=t0.05/2,n-1s/√n

for n=75, t0.025,74=1.993

Therefore, ME=1.993*7/√75

ME=1.61

Therefore, the 95% confidence interval for the average hourly income of all syatem manager would be as follows:

(X-ME,X+ME)=(40.75-1.61,40.75+1.61)

=(39.14,42.36)

Answer:

83.29% probability that at least 2 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives late, or it does not arrive late. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

80 % of its flights arriving on time.

So 100 - 80 = 20% arrive late, which means that [tex]p = 0.2[/tex]

15 Southwest flights

This means that [tex]n = 15[/tex]

Find the probability that at least 2 flights arrive late.

Either less than two arrive late, or at least 2 do. The sum of the probabilities of these outcomes is 1. So

[tex]P(X < 2) + P(X \geq 2) = 1[/tex]

We want [tex]P(X \geq 2)[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352[/tex]

[tex]P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1671 = 0.8329[/tex]

83.29% probability that at least 2 flights arrive late.

Answer:

c. [1.771;4.245] feet

Step-by-step explanation:

Hello!

The variable of interest is

X: height of a student at UH

X~N(μ;σ²)

You have to estimate the population standard deviation using a 95% confidence interval.

The statistic to use for the interval is a student Chi-Square with n-1 degrees of freedom. First you have to calculate the CI for the population variance:

[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]

[tex]X^2_{n-1;1-\alpha /2}= X^2_{11;0.975}= 21.920[/tex]

[tex]X^2_{n-1;\alpha /2}= X^2_{11;0.025}= 3.816[/tex]

n=12

S= 2.5

[tex][\frac{11*6.25}{21.920} ;\frac{11*6.25}{3.816}} ][/tex]

[3.136; 18.016] feet²

Then you calculate the square root of both limits to get the CI for the population standard deviation:

[√3.136; √18.016]

[1.771;4.245] feet

I hope this helps!

Answer:

x = ±2√2, ±i

Step-by-step explanation:

Step 1: Factor

(x² - 8)(x² + 1)

Step 2: Find roots

x² - 8 = 0

x² = 8

x = ±2√2

x² + 1 = 0

x² = -1

x = ±i

Answer:

The answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Pascal triangle is used to determine the coefficients of the terms when we expand the expression.

                                             1                                [tex](A + B) ^ 0[/tex] = 1

                                         1       1                            [tex](A +B ) ^ 1 = 1A + 1B[/tex]

                                   1          2        1          [tex](A+ B) ^ 2 = 1A^2 + 2 AB + 1B^2[/tex]

By extending the triangle, you will get the 9th row, which is your expression, of the coefficients. that is

1          9       36    84    126    126    84    36    9    1

Now, fill in AB in the gaps.

1AB + 9 AB + 36AB + 84AB + 126AB + 126AB +84AB + 36AB + 9AB + 1AB

Next, you need to go from the left to fill out the exponent of A and it will go down from 9 (the exponent of the whole thing) . That is

[tex]1A^9B+9A^8B+36A^7B+84A^6B+126A^5B+126A^4B+84A^3B+36A^2B+9A^1B+1A^0B[/tex]

Next will be the exponent of B. this time, you go from the right and do the same with A. You can go from the left also, but go up from 0 to 9 for the exponent of B

[tex]1A^9B^0+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+1A^0B^9[/tex]

The last step is just to simplify the A^0=1 and B^0 =1 at the first and the last terms.

[tex]A^9+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+B^9[/tex]

Hope you can learn the method

Answer:

81.64

Step-by-step explanation:

To find the circumference of this circle we take pi or 3.14 and multiply it by 2

3.14 * 2 = 6.28

Then we multiply 6.28 by 13

6.28 * 13 = 81.64

Answer:

Volume = 14.5 cm³

Step-by-step explanation:

Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]

Where r = 2 and h = 3.46

Volume = [tex](3.14)(2)^2\frac{3.46}{3}[/tex]

Volume = (3.14)(4)(1.15)

Volume = 14.5 cm³

Answer:

Question 1: 3 - 5 hours.

Question 2: 0 - 1 hour

Step-by-step explanation:

Question 1: As you can see in the diagram, the guy is moving really slowly and is almost stuck, therefore, it is 3 - 5  hours.

Question 2:  In hours 0 - 1, you can see that the graph is the closest to vertical as it gets.

Answer:

how many hours do you spend on your laptop

Answer:

the question is 17 hours - 2 hours

Answer:

[tex]\theta = \frac{4\pi}{3}[/tex]

Step-by-step explanation:

Given

Let A represent the Length of Arc CD and C, represents the circumference

[tex]A = \frac{2}{3} C[/tex]

Required

Find the central angle (in radians)

The length of arc CD in radians is as follows;

[tex]A = r\theta[/tex]

Where r is the radius and [tex]\theta[/tex] is the measure of central angle

The circumference of a circle is calculated as thus;

[tex]C = 2\pi r[/tex]

From the question, it was stated that the arc length is 2-3rd of the circumference;

This means that

[tex]A = \frac{2}{3} C[/tex]

Substitute [tex]2\pi r[/tex] for C and [tex]r\theta[/tex] for A

[tex]A = \frac{2}{3} C[/tex] becomes

[tex]r\theta = \frac{2}{3} * 2\pi r[/tex]

[tex]r\theta = \frac{4\pi r}{3}[/tex]

Divide both sides by r

[tex]\frac{r\theta}{r} = \frac{4\pi r}{3}/r[/tex]

[tex]\frac{r\theta}{r} = \frac{4\pi r}{3} * \frac{1}{r}[/tex]

[tex]\theta = \frac{4\pi r}{3} * \frac{1}{r}[/tex]

[tex]\theta = \frac{4\pi}{3}[/tex]

Hence, the measure of the central angle; [tex]\theta = \frac{4\pi}{3}[/tex]

Answer:

The answer is C on Edge 2020

Step-by-step explanation:

I did the assignment

Answer:

The answer is B

Step-by-step explanation:

Hope this helps.. if not im sorry :(

Answer:

I love Spanish food said Jim

I'm going to Singapore next month said Emily

Answer:

1) Jim said that he loves spanish food.

2) Emily said that she is going to SINGAPORE next month.

Step-by-step explanation:

I hope it helps.

Answer:

Bb

Step-by-step explanation:

Answer:

(a) The average number of passengers that will be on each flight is 28.8.

(b) Everyone will have a seat on about 84.4% of the flights.

Step-by-step explanation:

The correct question is:

Suppose that past experience shows  that about 10% of passengers who are schedule to take a particular flight fail to show up. For this  reason, airlines sometimes overbook flights, selling more tickets than they have seats, with the  expectation that they will have some no shows. Suppose an airline used a small jet with seating  for 30 passengers on a regional route and assume that passengers are independent of each other in  whether they show up for the flight. Suppose that the airline consistently sells 32 tickets for every  one of these flights.

(a) On average, how many passengers will be on each flight?

(b) How often will they have enough seats for all of the passengers who show up for the flight?

Solution:

Let the random variable X measure the number of passengers (out of 32) who show up for a flight.

For each passenger  there is a 90% chance of showing up, so X is a binomial random variable with n = 32 and p = 0.90.

(a)

The average of a binomial random variable is:

[tex]\text{Average}=np[/tex]

Compute the average number of passengers that will be on each flight as follows:

[tex]\text{Average}=np[/tex]

             [tex]=32\times 0.90\\=28.8[/tex]

Thus, the average number of passengers that will be on each flight is 28.8.

(b)

To have enough seats for all of the passengers who show up for the flight, the value of X must be less than or equal to 30.

Compute the value of P (X ≤ 30) as follows:

P (X ≤ 30) = 1 - P (X > 30)

                = 1 - P (X = 31) - P (X = 32)

                [tex]=1-[{32\choose 31}\ (0.90)^{31}\ (1-0.90)^{32-31}]-[{32\choose 32}\ (0.90)^{32}\ (1-0.90)^{32-32}]\\\\=1-0.122087-0.034337\\\\=0.843576\\\\\approx 0.844[/tex]

Thus, everyone will have a seat on about 84.4% of the flights.

Answer:

HJ > PK

Step-by-step explanation:

Notice that the side PL in one triangle has the same length as side GJ in the other, and side GH has the same size as side LK of the other triangle. Now what is different is the angle subtended between these sides in the case of the triangle on the lower left, the subtended angle is [tex]90^o[/tex] , which is larger angle than that subtended between equal sides on the other triangle ([tex]85^o[/tex])

Therefore, if the angle subtended by the equivalent sides in the triangle on the left is larger than the angle subtended on the right hand side triangle, then the sides associated with such angle aperture must keep the inequality. That is:

Since [tex]\angle\,G\,\,\,>\,\,\,\angle \,L[/tex], then   HJ > PK

Answer:

The equation of regression is

[tex]y = 16.522 - 0.00279 \cdot x[/tex]

The predicted crash fatality rate is 15.057 for 525 metric tons of lemon import.

Step-by-step explanation:

We are given the following lemon/crash data,

Lemon Imports = 226 264 366 470 539

Crash Fatality Rate = 16 15.7 15.4 15.3 15

The regression​ equation is given by

[tex]y = a + b \cdot x[/tex]

where x is the lemon imports in metric tons and y is the fatality rate per​ 100,000 people.

The constants b is the slope and a is the y-intercept of the regression line and are given by

[tex]$ a = \frac{\sum Y \times \sum X^2 - \sum X \times \sum XY }{n \times \sum X^2 - (\sum X)^2} $[/tex]

[tex]$ b = \frac{n \times \sum XY - \sum X \times \sum Y }{n \times \sum X^2 - (\sum X)^2} $[/tex]

Using Excel to find [tex]\sum X, \sum Y, \sum XY, \sum X^2[/tex]

[tex]\sum X[/tex] = 1865

[tex]\sum Y[/tex] = 77.4

[tex]\sum XY[/tex] = 28673.2

[tex]\sum X^2[/tex] = 766149

So the constants a and b are

[tex]$ a = \frac{77.4 \times 766149 - 1865 \times 28673.2 }{5 \times 766149 - (1865)^2} $[/tex]

[tex]a = 16.522[/tex]

[tex]$ b = \frac{5 \times 28673.2 - 1865 \times 77.4 }{5 \times 766149 - (1865)^2} $[/tex]

[tex]b = -0.00279[/tex]

Therefore, the equation of regression is

[tex]y = a + b \cdot x \\\\y = 16.522 - 0.00279 \cdot x[/tex]

The best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports is given by

[tex]y = 16.522 - 0.00279 \cdot (525) \\\\y = 16.522 - 1.465 \\\\y = 15.057[/tex]

The predicted crash fatality rate of 15.057 for 525 metric tons of lemon import seems to be satisfactory since it lies between the crash fatality rate of 15 to 15.3 for lemon imports of 539 to 470.

Answer:

Step-by-step explanation:

From the information given, the population is divided into sub groups. Each group would consist of citizens picking a particular choice as the most important problem facing the country. The choices are the different categories. In this case, the null hypothesis would state that the distribution of proportions for all categories is the same in each population. The alternative hypothesis would state that the distributions is different. Therefore, the correct test to use to determine if the distribution of​ "problem facing this country ​today" is different between the two different​ years is

A) Use a​ chi-square test of homogeneity.