Use the information to write the vertex form of the parabola

Vertex (1, 3) passes through (-1, 11)

Help plsss, if u could explain how to do this in general that would be very helpful

The value of quadratic equation is,

⇒ y = x² + 10x + 22

Let the value of quadratic equation is,

⇒ y = ax² + bx + c

Now, Let the points from tables as;

⇒ (- 6, 2) (- 5, - 1) (- 4, - 2)

Substitute all the values in equation as;

⇒ y = ax² + bx + c

⇒ 2 = a(- 6)² + b(-6) + c

⇒ 2 = 36a - 6b + c

⇒ - 1 = a (- 5)² + b (- 5) + c

⇒ - 1 = 25a - 5b + c

⇒ - 2 = a (- 4)² + b (- 4) + c

⇒ - 2 = 16a - 4b + c

Solve expression for the values of a, b and c as;

a = 1

b = 10

c = 22

Thus, the value of quadratic equation is,

⇒ y = x² + 10x + 22

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X is a continuous uniform random variable with a mean of 9.5 am and a variance of 1/12.

Since X denotes a random delivery time anywhere between 9 am and 10 am, X is a continuous random variable that follows a uniform distribution.

The uniform distribution is a probability distribution where all values between a lower bound (a) and an upper bound (b) have equal probability.

In this case, a = 9 am and b = 10 am, so the probability density function of X can be expressed as:

f(x) = 1/(b-a) = 1/(10-9) = 1

for 9 ≤ x ≤ 10, and f(x) = 0 otherwise.

The expected value or mean of X can be calculated as the average of the lower and upper bounds:

E[X] = (a + b)/2 = (9 + 10)/2 = 9.5 am

The variance of X is given by:

[tex]Var[X] = (b - a)^2/12 = (10 - 9)^2/12 = 1/12[/tex]

Therefore, X is a continuous uniform random variable with a mean of 9.5 am and a variance of 1/12.

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Answer:

30 lbs

Step-by-step explanation:

40/4=10

10 lbs per leg

10x3=30

Answer:

30

Step-by-step explanation:

The volume of the hemisphere is 301.44mm²

Any circle drawn around the Earth that divides it into two equal halves is called a hemisphere. Examples is a ball cut into two part. Each part will be an hemisphere.

The volume of an hemisphere is expressed as;

V = 2/3πr³

where v is the volume and r is the radius

Here, r = 12mm

Therefore;

V = 2/3 × ×3.14 × 12²

V = 904.32/3

V = 301.44mm²

therefore the volume of the hemisphere is 301.44mm²

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To say that d divides n means the same as saying that n is divisible by d.

The notation d | n means that d is a divisor of n, or in other words, n is a multiple of d. So, we can say that d divides n if and only if n is divisible by d.

For example, if d = 2 and n = 10, we know that 2 | 10 since 10 is a multiple of 2. In this case, we can also say that 10 is divisible by 2.

This property is important in number theory and is often used in proofs involving divisibility and prime numbers. By understanding the relationship between d and n and the idea of divisibility, we can gain insight into the properties of numbers and their factors.

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Answer:

Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.

Step-by-step explanation:

pls mark brainlest

It is explained how to obtain the four measures in this problem.

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Answer:

35%

Step-by-step explanation:

1. Add all the participants that attended

20 - 0-19yrs

40 - 20-39yrs

60 - 40-59yrs

50 - 60-79yrs

170 total

2. Divide the age group 40 - 59 by the total amount of participants to get the answer.

60/170 = about .35 = 35%

Answer:

Step-by-step explanation:

Going top row first:

V=180

SA=216

V=64

SA=96

V=1539.4

SA=747.7

V=600

SA=520

Bottom Row:

SA = 96

V=80

V=72

SA=132

V=628.3

SA=408.4

Answer: The LCD is x(x-3)(x+1) the answer is c

Step-by-step explanation:

The correct answer is d  is used to test the effect of the IV on the variability of the DV.

The correct answer is d. The "stand alone F test" is used to test the effect of the independent variable (IV) on the variability of the dependent variable (DV). It is an inferential test commonly used in analysis of variance (ANOVA) to determine if there is a significant difference among the means of three or more groups.

Option a is incorrect because the "stand alone F test" is an inferential test that involves making a conclusion about a population based on sample data.

Option b is incorrect because the "stand alone F test" is used to test the assumption of equal variances, not homogeneity of variance.

Option c is incorrect because the "stand alone F test" can be directional or non-directional, depending on the research question and hypothesis being tested.

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The ellipse in a scatterplot becomes thinner, the correlation coefficient (r) between the variables x and y will increase.

The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables.

It ranges from -1 to 1, where values close to -1 or 1 indicate a strong linear relationship, and values close to 0 indicate a weak or no linear relationship.

When the scatterplot forms an ellipse, it indicates that there is some degree of correlation between the variables x and y.

If the ellipse is elongated, it suggests that the correlation is weak, while if the ellipse is more circular, it suggests that the correlation is stronger.

As the ellipse becomes thinner, it means that the spread of the data along one of the variables is becoming smaller, while the spread along the other variable is remaining the same.

This indicates that there is a stronger linear relationship between the variables, and as a result, the correlation coefficient (r) will increase.

Therefore, we can conclude that as the ellipse becomes thinner, the correlation coefficient (r) between the variables x and y will increase.

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The game awards 2.5 points for 10 minutes of play.

Part A:

Let's use the given information to find the constant of proportionality. For every 2 minutes of play, the game awards one-half point. Therefore,

1 min of play  = 0.5/2 = 0.25 points

6 min of play = 0.25 x 6 = 1.5 points

The constant of proportionality is 0.25

Part B:

We can use the formula for a proportional relationship,

y = kx

where

y = number of points awarded,

x = amount of time played (in minutes), and

k = constant of proportionality.

Substituting k = 0.25, we get:

y = 0.25x

Part C:

To graph this relationship, let x be the independent variable (amount of time played) and y be the dependent variable (number of points awarded). Then, we can choose several values for x, compute the corresponding values of y using the equation above, and plot the ordered pairs (x, y).

Part D: To find the number of points awarded for 10 minutes of play, we can simply substitute x = 10 into the equation we found in Part B:

y = 0.25x = 0.25(10) = 2.5

Therefore, 2.5 points are awarded for 10 minutes of play.

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Answer: To find the approximate number of voters who are undecided about the candidates for mayor, we can first add up the percentages of voters who have already made their decision:

14 + 31 + 39 = 84%

This means that 84% of the voters have made up their minds about the candidates. To find the percentage of voters who are undecided, we can subtract this percentage from 100:

100 - 84 = 16%

So approximately 16% of the 2,500 voters in Newtville would be undecided about the candidates for mayor. To find the number of voters who are undecided, we can multiply the total number of voters by the percentage that is undecided:

2,500 x 0.16 = 400

Therefore, approximately 400 voters in Newtville would be undecided about the candidates for mayor.

The soccer ball reaches a maximum height of approximately 34.8 feet.

The parametric equations for the motion of the soccer ball are:

x(t) = 39*cos(44°)t ≈ 26.9t

y(t) = [tex]39\sin(44)*t - 16t^2[/tex] ≈ [tex]22.7t - 16t^2[/tex]

where t is the time elapsed since the ball was kicked.

To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).

The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).

So, t = -b/2a ≈ 1.1 seconds.

Substituting this value of t into the equation for y(t), we get the maximum height:

y(max) = [tex]39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.[/tex]

Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.

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The minimum amount monthly credit card payment be in order to pay off his debt in 14 months is $244.15, the correct option is C.

We are given that;

Out of savings=  $2,300

Credit card debt = $5,390

Rate=16.5%

Now,

We need to know the percentage rate that Alex’s issuer uses to calculate the minimum payment, and the interest charge and fees for each month. Assuming that Alex’s issuer uses a 2% rate, and that there are no fees or past-due amounts, we can use this formula:

Credit Card Minimum Payment = (A * P) + I

Where A is the statement balance, P is the percentage rate, and I is the interest charge.

The interest charge can be calculated by multiplying the balance by the APR and dividing by 123. For example, the interest charge for the first month is:

I = ($5,390 - $2,300) * 0.165 / 12 I = $42.74

The minimum payment for the first month is:

Credit Card Minimum Payment = ($5,390 - $2,300) * 0.02 + $42.74 Credit Card Minimum Payment = $104.54

To pay off the debt in 14 months, Alex needs to pay more than the minimum payment every month. We can use an online calculator4 to find out how much he needs to pay monthly to achieve this goal.

Therefore, by percentage the answer will be $244.15.

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True.  Under appropriate circumstances, many discrete random variables can be described by the normal distribution.

Under appropriate circumstances, many discrete random variables can be approximated by the normal distribution using the Central Limit Theorem. This theorem states that the sum of a large number of independent and identically distributed random variables, regardless of their individual distributions, tends to follow a normal distribution.

This is often the case in practice, making the normal distribution a useful tool for modeling and analyzing data. However, it's important to note that not all discrete random variables can be accurately described by the normal distribution, and it's important to assess the appropriateness of the normal approximation on a case-by-case basis.

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The sample in this example is a small group of local college students selected for observation.

In this example, the researcher is working with a specific group of interest, which is college students.

She narrows down her focus to local college students and selects a small group to be observed.

The sample in this case would be the small group of local college students chosen for observation.

This sample is a subset of the larger population (all college students) that the researcher is interested in studying to test her hypothesis.

The sample in this example is the small group of local college students who were selected to be observed.

A sample is a subset of the population that is being studied in order to make inferences about the entire population.

In this case, the population of interest is college students, and the researcher is observing a sample of that population. It is important that the sample is representative of the population in order for the findings to be generalizable to the population as a whole.

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Answer:

Step-by-step explanation:

338.33 ft

The scale of the blueprint is 1.5 inches : 4.5 feet, which means that every 1.5 inches on the blueprint represents 4.5 feet in the actual house. To find the length and width of the room on the blueprint, we need to convert the actual dimensions from feet to inches using the scale. The length of the room on the blueprint is (45 ft / 4.5 ft) * 1.5 in = 15 in. The width of the room on the blueprint is (60 ft / 4.5 ft) * 1.5 in = 20 in. The perimeter of the room on the blueprint is 2 * (15 in + 20 in) = 70 in.

The correct statement is:

B. If -2/5r = -20, then r = 50

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To solve the equation, we can isolate the variable by multiplying both sides of the equation by the reciprocal of -2/5, which is -5/2:

(-2/5r) * (-5/2) = (-20) * (-5/2)

r = 50

Therefore, if -2/5r = -20, then r = 50.

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Angelo bought 3 slices, Nick bought 6 slices, Sabrina bought 7 slices, Carmine bought 13 slices, and Siobhan bought 33 slices.

We should call the quantity of cuts Angelo purchased "A".

Scratch purchased two times as numerous as Angelo, so Scratch purchased 2A cuts.

Sabrina purchased four under three fold the number of as Angelo, so Sabrina purchased 3A - 4 cuts.

Carmine purchased two times the amount of what Angelo purchased and five more, so Carmine purchased 2(A + 5) cuts.

Siobhan purchased multiple times the amount of what Angelo and Sabrina purchased, so Siobhan purchased 3(A + (3A - 4)) cuts, which streamlines to 9A - 12 cuts.

We realize that the all out number of cuts sold was 57, so we can set up a situation:

A + 2A + (3A - 4) + 2(A + 5) + (9A - 12) = 57

Streamlining and settling for A:

A = 3

So Angelo purchased 3 cuts, Scratch purchased 2A = 6 cuts, Sabrina purchased 3A - 4 = 5 cuts, Carmine purchased 2(A + 5) = 16 cuts, and Siobhan purchased 9A - 12 = 15 cuts

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To find the P(Z>0.93) using Appendix C-2, we first need to find the row containing 0.9 in the far left column. Next, we find the column containing 0.03 in the top row. The intersection of the row and column is 1.546. Therefore, the probability of Z being greater than 0.93 is 1 - 0.8289 = 0.1711 (rounded to four decimal places).

The values in Appendix C-2 represent the area to the left of a standard normal distribution. Since the total area under the curve is equal to 1, we can find the area to the right of a certain value by subtracting the area to the left from 1.

In this case, we want to find the area to the right of 0.93, which is equivalent to finding the area to the left of -0.93 (since the standard normal distribution is symmetric). By finding the corresponding value in Appendix C-2 and subtracting from 1, we get the probability of Z being greater than 0.93.

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For strain 1 the average rate of change is 20, while for strain 2 it is 16.7, then Strain 1 has the larger one.

For a function y = f(x), we define the average rate of change on an interval [a, b] as:

R = (f(b) - f(a))/(b - a)

For the table, the average rate of change will be:

R = (85 - 25)/(4 - 1)

R = 60/3 = 20

For the graph, it will be:

R' = (70 - 20)/(4 - 1) = 50/3 = 16.7

Then we can see that the table (Strain 1) has a greater rate of change.

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From the given triangle, the statement that julie says "sinA/cosA = tan A and sinB/cosB = tan B" is true.

To prove whether Julie's statement is true or false, we need to use the triangle and the definitions of the trigonometric ratios.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. And, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Using the definitions of sine and cosine, we can write:

sin A = b/c

cos A = a/c

sin B = a/c

cos B = b/c

Dividing sin A by cos A, we get:

sin A / cos A = (b/c) / (a/c) = b/a

Similarly, dividing sin B by cos B, we get:

sin B / cos B = (a/c) / (b/c) = a/b

We can see that sin A/cos A and sin B/cos B equals to tan A or tan B respectively. Therefore, Julie's statement is true.

In conclusion, we can prove whether a trigonometric statement is true or false by using the definitions of the ratios and the triangle. In this case, Julie's statement was proved to be true.

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When the book on baseball states that your favorite player gets on base 41% of the time he goes to bat, this percentage indicates the player's on-base percentage (OBP), a measure of how often a batter reaches base through hits, walks, or being hit by a pitch.

The on-base percentage is an important statistic in baseball as it helps to evaluate a player's offensive contribution to their team. A higher OBP means the player is more successful at getting on base, creating more scoring opportunities for their team. In this case, a 41% OBP for your favorite player signifies that they are quite proficient in reaching base.
To calculate the OBP, you can use the formula:
OBP = (Hits + Walks + Hit by Pitch) / (At Bats + Walks + Hit by Pitch + Sacrifice Flies)

Having a 41% OBP means that, on average, your favorite player reaches base 41 times out of 100 plate appearances. This is considered an above-average performance for a batter, as the league average OBP typically hovers around 32%. Your favorite player's OBP demonstrates that they are an effective offensive player, contributing to their team's success by getting on base more frequently than the average player.

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Answer:

The first one and the third on are both right

Step-by-step explanation:

Remember that in order to find the volume, you need to multiply the length by the width by the height.

Answer:

V= 8×4×5

V= 32×5

Step-by-step explanation:

volume= base × height × width

V= 8×4×5