suppose the z-score of your grade in this statistics course turns out to be .97. interpret this z-score.

Answer:

Y-a=x

Step-by-step explanation:

Y=a-x

Subtract a from both sides to get x on its own.

Answer:

N=11/5

Step-by-step explanation:

Answer:

n = 2.2

Step-by-step explanation:

Given

- 6.5(n - 5) = 18.2 ( divide both sides by - 6.5 )

n - 5 = - 2.8 ( add 5 to both sides )

n = 2.2

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Answer:

67

Step-by-step explanation:

She can drive 2 hours before she runs out of fuel and needs 5 liters of more fuel to complete her journey. The price for the amount of fuel that Roselyn will use for the entire drive is $25

Calculation:

Total distance = 150km

Average speed = 60km/h

Total fuel = 20 L

Fuel efficiency = 6km/l

The car's tank has 20 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 kilometers per liter.

Total distance she can drive with 20L fuel in her car's tank = 6*20 = 120km

Time taken to cover 120 km = 120/60

Time taken = 2 hours

Therefore, She can drive 2 hours before she runs out of fuel.

Distance left to travel = 150 - 120

= 30km

To travel 30 km, extra fuel needed = Distance/Fuel efficiency = 30/6

= 5 liters

The cost of the fuel is $0.60/L

For 5km, extra fuel would cost her 0.60*5 = $3

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Answer:

Cal can buy seven tickets for $57.75

Answer:

FE

Step-by-step explanation:

FE- radius

AC- diameter

ED- arc

DC- arc

» Which line segment is a radius of circle F?

_______________∞_______________

Answer:

B.

Step-by-step explanation:

Unit rate is $4.04 per oz

Answer:

4

Step-by-step explanation:

3*4 is 12 and if you divide 12 by 3(the divisor) you will get 4

The dividend of the given divisor and quotient is 36.

The dividend is the number that is being divided in a division problem. In this case, we can use the formula:

Dividend = divisor × quotient

Here is the step-by-step explanation:

Therefore, if the divisor is 3 and the quotient is 12, the dividend is 36.

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Answer:

(17^1/7)^7 SIMPLIFIED is 498.26016735

The equation of a hyperbola satisfying the given conditions, Vertices at (0,9) and (0,−9); foci at (0,41) and (0,−41) is x^2/324 - y^2/1045 = 1.

To get the equation of the hyperbola in standard form, we require the center of the hyperbola. From the vertex, we obtain the center of the hyperbola by taking the midpoint. Thus, the center of the hyperbola is (0,0).

We can now determine the transverse axis length and the conjugate axis length. The distance between the center of the hyperbola and each vertex is the transverse axis length.

Thus, the length of the transverse axis is 2a = 18.

Since the foci are on the transverse axis, the distance between the center and each focus is c = 41.

We can use the equation c^2 = a^2 + b^2 to find the length of the conjugate axis.

b^2 = c^2 - a^2 = 41^2 - 18^2b^2 = 1369 - 324b^2 = 1045b = √1045

The equation of the hyperbola is (x^2)/a^2 - (y^2)/b^2 = 1 .

Substituting the values we have just calculated, we obtain (x^2)/(18^2) - (y^2)/(√1045)^2 = 1``x^2/324 - y^2/1045 = 1/

Therefore, the equation of the hyperbola is x^2/324 - y^2/1045 = 1

The equation of a parabola satisfying the given information, Focus (8,0), directrix x=−8 is y = (x^2 + 8x + 16)/4.

Given that the focus of the parabola is (8,0) and the directrix is `x = -8`, the vertex is halfway between the focus and the directrix.The vertex is `(0 + (-8))/2 = -4`.

Thus, the equation of the parabola is of the form y = a(x - h)^2 + k

where `(h, k)` is the vertex.

The focus of the parabola is to the right of the vertex, so it is a horizontal parabola.

The distance between the vertex and the focus is the same as the distance between the vertex and the directrix. The distance between the vertex and the directrix is 4, so the equation of the parabola is y = 1/4(x + 4)^2

Simplifying, we obtain y = (x^2 + 8x + 16)/4.

Therefore, an equation for a parabola satisfying these conditions is y = (x^2 + 8x + 16)/4.

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Answer:

Step-by-step explanation:

first one A and second one C

Answer:

              The correct scale faction the first pentagon dilated by to create the second pentagon is 1.25.

Step-by-step explanation:

              Since the second pentagon is a dilation of the first pentagon, we can conclude these pentagons are similar, meaning the shape retained all of its previous angles, and all the corresponding sides are dilated by a common scale factor. Since we know the values of a pair of corresponding sides, we can use those to find the scale factor of dilation.

             The corresponding side of the original pentagon is 4 units, and the corresponding side of the dilated pentagon is 5 units. Since the first pentagon dilated to become the second, in order to solve the scale factor the pentagon dilated by, we'd have to divide the side given on the second pentagon by the corresponding side of the first, which will be 5 ÷ 4 = 1.25. Therefore, that will be the scale factor the pentagon dilated by.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

268.08 cm^3

Step-by-step explanation:

the formula for the volume of a sphere is 4/3*pi*r^3 where r is the radius.

so put in the value 4/3*pi*4^3

4/3*pi*64

=268.08 cm^3

Answer:

268 cm^3

Step-by-step explanation:

Volume of sphere is \(\frac{4}{3} \pi r^3\)

so(assuming pi is 3.14) \(\frac{4}{3}*3.14(\pi )*4^3\)

4/3*3.14=4.187

\(4^3=64\)

4.187*64=267.968

So volume would round up to 268 cm.

Hope this helps :)

1 - According to the conjugate zeros theorem if a complex number is the root of a polynomial its conjugate is a root as well.

2 - So the conjugates of i, -7i would be

-i, 7i, so

-i , 7i would ALSO be roots of the polynomial according to the conjugates zeros theorem and those are the two roots we were missing.

The total number of possibilities in this case is 24 + 25 = 49. Hence, the probability of selecting two consecutive whole numbers where one of them is a multiple of 4 is: P = (25 + 49) / (100 × 99) = 0.74.

Probability is defined as the measure of the likelihood of an event occurring. It can be determined by dividing the number of ways an event can occur by the total number of possible outcomes. The probability of randomly selecting two consecutive whole numbers where one of them is a multiple of 4 can be found

There are two scenarios to consider:Either the first number is a multiple of 4 or the second number is a multiple of 4.Case 1: The first number is a multiple of 4There are 25 such multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, and 100. Therefore, the number of possibilities in this case is 25.Case 2: The second number is a multiple of 4If the first number is a multiple of 4.

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The number of people attending affects how much food is prepared for a catered event. The number of people attending is the explanatory variable in this scenario.

One kind of independent variable is an explanatory variable. Both words are frequently used interchangeably. This is the variable that changes as we change it or watch it change. In other words, it is a factor that a researcher has changed in an experiment.

In the given situation, the number of people attending is an explanatory variable and the amount of food prepared is a dependent variable. As the number of people attending increases, the amount of food prepared also increases. This means the effect of one variable alters the effect of another variable. The change of one variable is called an independent variable while the change that occurs because of the independent variable is a dependent variable.

Therefore, the required answer is the number of people attending.

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Answer:Math is important

Step-by-step explanation:

It could help you get into collage and get a good job and with that you could start your life.

Answer:

1.)

I love working with numbers

I love math because of what a challenge it is

I love math because I can become a engineer

I love math because I can also become a doctor with it

I love math because it is useful

2.)

I don't like math because of the word problems

I don't like math because it sometimes gets too easy

I don't like math because I usually have to help others

I don't like math because people call me a nerd

I don't like math because it makes me explain in words

3.)

when your in the store and it helps you with knowing how much your spending

lets you know about if the discount in the store is really good or bad

helps you with becoming certain things when you grow up

it will help you with most of your jobs

Will help others if you know it, you can share your knowledge

Step-by-step explanation:

brainlist pls :>

The open sentence has integers that are true: (a) |n - 2| = 3, (b) 2n² – 5n + 2 = 0, (c) n² > 0, (e) |Inl + In - 1| + In - 2| = 3 and (d) n³ = 2n is false.

To determine the true value of open sentences involving integers, we can use the concept of substitution. We substitute each possible integer value into the open sentence and determine whether the resulting statement is true or false.

(a) For the first function substitute -1 and 5 into the expression |n-2|=3 and find that both result in a true statement.

The open sentence P(n): |n-2| = 3 is true for n = -1 and n = 5.

(b) For the second function substitute 1/2 and 2 into the expression 2n² - 5n + 2 = 0 and find that both result in a true statement.

The open sentence P2(n): 2n² - 5n + 2 = 0 is true for n = 1/2 and n = 2.

(c) Third function is a universally true statement, as n² is always positive for any integer except n = 0.

The open sentence P3(n): n² > 0 is true for all integers n except for n = 0.

(d) For the fourth function substitute 2 into the expression n³ = 2n and find that it results in a true statement.

The open sentence P4(n): n³ = 2n is true for n = 2 and false for all other integers.

(e) For the fifth function we need to consider several cases depending on the sign of Inl + In-1 and In-2. By systematically considering each case and the corresponding value of n, we find that the statement is true only for n = 2, 3, and 4.

The open sentence Ps(n): |Inl + In - 1| + |In - 2| = 3 is true for n = 2, 3 and 4.

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17. The point on the line 2x - 4y = 3 that is closest to the origin is (-3/10, 3/20).

To solve this problem using Lagrange multipliers, we can define the distance squared function as D² = x² + y², which represents the square of the distance from any point (x, y) to the origin. The constraint equation is given by 2x - 4y = 3.

We set up the Lagrange function L = D² - λ(2x - 4y - 3), where λ is the Lagrange multiplier. To find the minimum of L, we take partial derivatives with respect to x, y, and λ and set them equal to zero:

∂L/∂x = 2x - 2λ = 0

∂L/∂y = 2y + 4λ = 0

∂L/∂λ = 2x - 4y - 3 = 0

Solving this system of equations gives x = -3/10, y = 3/20, and λ = -1/20.

Thus, the point on the line closest to the origin is (-3/10, 3/20).

To find the point on the line closest to the origin, we need to minimize the distance between any point on the line and the origin. This can be done by minimizing the distance squared function D² = x² + y².

However, we have a constraint given by the equation of the line 2x - 4y = 3.

By introducing the Lagrange multiplier λ, we create a Lagrange function L = D² - λ(2x - 4y - 3). Taking the partial derivatives and setting them equal to zero, we find the critical point that minimizes the Lagrangian function.

Solving the resulting system of equations gives us the coordinates of the point on the line closest to the origin.

In this case, the point is (-3/10, 3/20).

18. The point on the line y = 2x + 3 that is closest to (4,2) is (2, 7).

To solve this problem using Lagrange multipliers, we can define the distance squared function as D² = (x - 4)² + (y - 2)², which represents the square of the distance from any point (x, y) to (4, 2). The equation of the line is y = 2x + 3.

We set up the Lagrange function L = D² - λ(y - 2 - 2x - 3), where λ is the Lagrange multiplier. To find the minimum of L, we take partial derivatives with respect to x, y, and λ and set them equal to zero:

∂L/∂x = 2(x - 4) - 2λ = 0

∂L/∂y = 2(y - 2) - λ = 0

∂L/∂λ = y - 2x - 3 = 0

Solving this system of equations gives x = 2, y = 7, and λ = -2. Thus, the point on the line closest to (4, 2) is (2, 7).

To find the point on the line closest to the given point (4, 2), we need to minimize the distance between any point on the line and (4, 2).

This can be done by minimizing the distance squared function D² = (x - 4)² + (y - 2)².

The equation of the line y = 2x + 3 serves as the constraint. By introducing the Lagrange multiplier λ, we create a Lagrange function L = D² - λ(y - 2 - 2x - 3).

Taking the partial derivatives and setting them equal to zero, we find the critical point that minimizes the Lagrange function.

Solving the resulting system of equations gives us the coordinates of the point on the line closest to (4, 2). In this case, the point is (2, 7).

20. The point on the plane 4x + 3y + z = 2 that is closest to (1,-1,1) is (2/7, -4/7, 2/7).

To solve this problem using Lagrange multipliers, we can define the distance squared function as D² = (x - 1)² + (y + 1)² + (z - 1)², which represents the square of the distance from any point (x, y, z) to (1,-1,1). The equation of the plane is 4x + 3y + z = 2.

We set up the Lagrange function L = D² - λ(4x + 3y + z - 2), where λ is the Lagrange multiplier. To find the minimum of L, we take partial derivatives with respect to x, y, z, and λ and set them equal to zero:

∂L/∂x = 2(x - 1) - 4λ = 0

∂L/∂y = 2(y + 1) - 3λ = 0

∂L/∂z = 2(z - 1) - λ = 0

∂L/∂λ = 4x + 3y + z - 2 = 0

Solving this system of equations gives x = 2/7, y = -4/7, z = 2/7, and λ = 1/7. Thus, the point on the plane closest to (1,-1,1) is (2/7, -4/7, 2/7).

To find the point on the plane closest to the given point (1,-1,1), we need to minimize the distance between any point on the plane and (1,-1,1).

This can be done by minimizing the distance squared function D² = (x - 1)² + (y + 1)² + (z - 1)².

The equation of the plane 4x + 3y + z = 2 serves as the constraint. By introducing the Lagrange multiplier λ, we create a Lagrange function L = D² - λ(4x + 3y + z - 2).

Taking the partial derivatives and setting them equal to zero, we find the critical point that minimizes the Lagrange function.

Solving the resulting system of equations gives us the coordinates of the point on the plane closest to (1,-1,1). In this case, the point is (2/7, -4/7, 2/7).

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Considering Justin's serve, it is found that:

a) The ball traveled 21.4 feet, which means that Justin's estimate is correct.

b) An assumption regarding the angle of Justin's serve was made.

c) The Pythagorean Theorem was used to solve this mathematical problem.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

\(h^2 = l_1^2 + l_2^2\)

Assuming that the ball was served at an angle of 90º, the situation can be summarized as follows:

Hence the Pythagorean Theorem is applied and the distance is calculated as follows:

d² = 7.5² + 20²

d = sqrt(7.5² + 20²)

d = 21.4 feet.

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The least number of trips that Ava must make in order to deliver 250 cartons of books is 10 trips.

The least number of trips that Ava must make in order to deliver 250 cartons of books can be found by dividing the total number of cartons by the number of cartons that her car can hold per trip.

This can be written as:
Least number of trips = Total number of cartons / Number of cartons per trip

Substituting the given values into the equation, we get:
Least number of trips = 250 cartons / 26 cartons
Least number of trips = 9.62

Since Ava cannot make a fraction of a trip, we need to round up to the nearest whole number. Therefore, the least number of trips that Ava must make in order to deliver 250 cartons of books is 10.

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Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them. So the monthly charge for Danielle's cable bill is $5.

Danielle pays a monthly charge of $69 for her cable bill.

She also pays a fee every time she watches a movie on demand.

Last month Danielle watched 7 movies on demand, and her total monthly bill was $104.

We have to find the monthly charge for Danielle's cable bill to choose.

Remove the monthly fee of 69 dollars for cable service from the total of 104 dollars, then check the statement to see that there is still a mystifying 35 dollars on it.

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them, giving you the result of $5 per on-demand movie.

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The equation of the translated function is:

g(x) = (x + 3)^2 - 2

We can see that the blue graph is a translation of the red one, where the equation for the red graph is:

f(x) = x^2

Remember that the translations are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.

If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

By analyzing the vertices, we can see that the vertex of the blue graph is at (-3, -2) so we have a translation of 3 units to the left and 2 units down, meaning that we have:

g(x) = f(x + 3) - 2 = (x + 3)^2 - 2

So the correct option is A.

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Answer:

60

Step-by-step explanation:

x and 2x are co - interior angles, sum of co - interior angles is 180,

x + 2x = 180

3x = 180

x = 180 / 3

x = 60

The case fatality rate is 400 * 100 / 1500 = 26.67 (option d).

For the first scenario, the data determine that there is a difference in average expenditure between the two countries (option c). The P-value of 0.063 suggests that there is a moderate level of statistical significance, indicating that the difference in average expenditure is likely not due to random chance.

In the second scenario, the fact that the 95% confidence interval for the average number of times participants saw their provider per year (3.3) ranges from 0.1 to 6.1 is of statistical use because it provides a range estimate within which the true population means is likely to fall. This interval helps account for the uncertainty associated with the sample estimate and provides a measure of the precision of the estimate (option a).

For the third scenario, the average operating margin is appropriate to use because it is a measure of central tendency that represents the typical financial performance of rural hospitals. The standard deviation provides information about the variability of the operating margins (option d).

In the fourth scenario, the consideration factor that will ultimately contribute to the spread of Ebola is the population density of the affected area (option b). While factors like the influence of non-indigenous people and climatic conditions may play a role, population density is a key determinant in the transmission and spread of infectious diseases.

For the fifth scenario, the case fatality rate is calculated by dividing the number of deaths from the disease (400) by the total reported cases (1500) and multiplying by 100. Therefore, the correct calculation is 400 * 100 / 1500 = 26.67 (option d). This indicates that the case fatality rate is approximately 26.67%.

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Using re-grouping to solve 21 x 43, the four products that would be calculated and then added is: 800 + 40 + 60 + 3.

Given data:

21 x 43

Now let make use of re-group to find the for product

21 x 43

So,

20 +1 = 21

40 + 3 =43

Hence,

(20+1) × (40+3)

Expand

(20 × 40) + (1 × 40) + (20 ×3) + (1 ×3)

800 + 40 + 60 + 3

= 903

Check:

21 x 43 = 903

800 + 40 + 60 + 3 =903

Therefore the correct option is C.

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Answer:

The expression for the area of the given triangle is 5x^4+4x^3units

Step-by-step explanation: