On a standardized exam, the scores are normally distributed with a mean of 400 and a standard deviation of 50. Find the z-score of a person who scored 390 on the exam.

The height of the triangular pyramid is 9 cm. A triangular pyramid has the volume of 270 cm , base edge 15 cm , and heigh of base 4 cm ,

To find the height of a triangular pyramid, we can use the formula for the volume of a pyramid and the given information about the volume, base edge, and height of the base. By rearranging the formula, we can solve for the height of the pyramid.

The formula for the volume of a pyramid is given by:

Volume = (1/3) * base area * height

In this case, we are given the volume as 270 cm³, the base edge as 15 cm, and the height of the base as 4 cm. We need to find the height of the pyramid.

First, let's calculate the base area of the pyramid. Since the base of the pyramid is a triangle, we can use the formula for the area of a triangle:

Base area = (1/2) * base edge * height of base

Plugging in the given values, we have:

Base area = (1/2) * 15 cm * 4 cm

Base area = 30 cm²

Now, we can substitute the known values (volume and base area) into the volume formula and solve for the height:

270 cm³ = (1/3) * 30 cm² * height

To isolate the height, we can multiply both sides by 3/30:

270 cm³ * (3/30) = height

Simplifying, we have:

height = 27 cm

Therefore, the height of the triangular pyramid is 9 cm.

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According to the given situation in question, The height of the 7th bounce of the ball is 0.85 feet as each successive bounce is 70 percent of previous bounce.

Given that he successive bounce is 70% of the previous bounce's height, the;

Height of the first bounce height = 7.25 feet

Height of the 2nd bounce height = 7.25 x 0.7

                                      = 5.075 feet

Height of the 3rd bounce = 5.075 x 0.7

                       = 3.5525 feet

Height of the 4th bounce = 3.5525 x 0.7

                         = 2.48675 feet

Height of the 5th bounce = 2.48675 x 0.7

                         = 1.740725 feet

Height of the 6th bounce = 1.740725 x 0.7

                          = 1.2185075 feet

Height of the 7th bounce = 1.2185075 x 0.7

                        = 0.85295525 feet

Thus, the height of the 7th bounce of the ball is 0.85 feet.

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—----------- CORRECT QUESTION FORMAT IS GIVEN BELOW - - - - - - -

(Q). A bouncy ball is dropped such that the height of its first bounce is 7.25 feet and each successive bounce is 70% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).

Answer:

6. 12cm

7. 11.2 cm

8. 92 degrees

9. 53 degrees

10. 37.5 cm

11. $ 693.12

Step-by-step explanation:

For questions 6-9 the triangle is congurent which means both their angles will be equal.

For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5

So for Q. 6 we can multiply side PQ by 1.5.

For Q.7 divide CA by 1.5.

For Q. 10 we can do cross multiplication:

5/4 = x/30

= 150= 4x

= 37.5=x

For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)

So the shorter side is 30.4 cm.

Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.

Then to figure out the money we multiply again and we get $693.12.

Step-by-step explanation:

it is the vertical of 5 and 6 aww you can do that

Answer:

the answer is B D and E

Step-by-step explanation:

as you can see the enlargement is by 3

Answer:

D and E :)

Step-by-step explanation:

Answer:

Is - 4

Step-by-step explanation:

29/29  cancel it out

so it will leave -4 out

Answer:

domain: (–∞,∞)    or  all real numbers

range: (–∞,∞)       or  all real numbers

Step-by-step explanation:

domain is left to right (x-axis). looking at the graph, as you go from left to right, the x-values are infinitely getting more negative and positive.

range is bottom to top (y-axis). as you go from bottom to top, the y-values are infinitely getting more negative and positive.

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\(slope = \frac{ - 8 - ( - 11)}{7 - 4} \\ \)

\(slope = \frac{ - 8 + 11}{7 - 4} \\ \)

\(slope = \frac{3}{3} \\ \)

\(slope = 1\)

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Answer:

R=70.20-$0.80(12)

Step-by-step explanation:

Answer:

Slope is 2.

Step-by-step explanation:

We can use the points in either order and you will still get the same slope. I usually solve in order that is given. So the first coordinates I label (x1,y1) and the second is (x2,y2).

Slope=m=(y2-y1)/(x2-x1)

m=(9-5)/(3-1)=4/2=2

Answer:

slope = 2

Step-by-step explanation:

use y2-y1 over x2-x1

For the total expenditures to be similar, each car must travel  165.79 x 10^3 miles or 1.6579 x 10^5  miles during its lifetime.

The cost of the first automobile is $3.25 x 10^4, and its fuel efficiency is 25.0 miles/gallon of fuel.

The cost of the second automobile is $4.71 x 10^4, and its fuel efficiency is 17.0 km/liter of fuel.

The cost of fuel is $3.50/gallon.

The lifetime of each vehicle requires calculating the number of miles that each automobile must travel for the total cost (purchase cost + fuel cost) to be equivalent.

The total fuel cost of the first vehicle is:

Total Fuel Cost 1 = Fuel Efficiency 1 / Fuel Cost Per Gallon

= 25.0 / 3.50

= 7.1429

The total fuel cost of the second vehicle is:

Total Fuel Cost 2 = Fuel Efficiency 2 * Fuel Cost Per Gallon / Km Per Mile

= 17.0 * 3.50 / 0.621371

= 95.2449

The total cost of the first vehicle for a lifetime of x miles driven is:

Total Cost 1 = Purchase Cost 1 + Fuel Cost 1x

= $3.25 x 10^4 + 7.1429x

The total cost of the second vehicle for a lifetime of x miles driven is:

Total Cost 2 = Purchase Cost 2 + Fuel Cost 2x

= $4.71 x 10^4 + 95.2449x

To find the number of miles each vehicle must travel in its lifetime for the total costs to be equivalent, we need to solve these simultaneous equations by setting them equal to each other:

$3.25 x 10^4 + 7.1429x = $4.71 x 10^4 + 95.2449x

Simplifying the equation:

-$1.46 x 10^4 = 88.102 x - $1.46 x 10^4

Solving for x:

x = 165.79

Therefore, the number of miles that each vehicle must travel in its lifetime for the total costs to be equivalent is 165.79 x 10^3 miles or 1.6579 x 10^5 miles.

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Answer:

0.5

Step-by-step explanation:

delta math

If q is positive and increasing, for what value of q is the rate of increase of q3 twelve times that of the rate of increase of q is option a. 2.

Let's differentiate the equation q^3 with respect to q to find the rate of increase of q^3:

d/dq (q^3) = 3q^2

Now, we can set up the equation to find the value of q:

12 * d/dq (q) = d/dq (q^3)

12 * 1 = 3q^2

12 = 3q^2

4 = q^2

Taking the square root of both sides, we get:

2 = q

Therefore, the value of q for which the rate of increase of q^3 is twelve times that of the rate of increase of q is q = 2.

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Explanation:

2 freshmen + 3 sophomores + 2 juniors + 2 seniors = 9 students total.

Let's consider the cases where we have the same number of juniors and seniors. We'll then take the complement of this to get the final answer.

-----------

Case A: There is 1 junior and 1 senior

There are 2 ways to pick a junior and 2 ways to pick a senior. That's 2*2 = 4 ways so far.

Then we have 9-4 = 5 students left to pick from (i.e. 2 freshmen+3 sophomores = 5 students left) and we have 5-2 = 3 seats to fill. Order doesn't matter on the committee since each person has equal rank.

We use the nCr combination formula.

n = 5 students

r = 3 seats to fill

n C r = (n!)/(r!(n-r)!)

5 C 3 = (5!)/(3!*(5-3)!)

5 C 3 = (5!)/(3!*2!)

5 C 3 = (5*4*3!)/(3!*2!)

5 C 3 = (5*4)/(2!)

5 C 3 = (5*4)/(2*1)

5 C 3 = (20)/(2)

5 C 3 = 10

There are 10 ways to fill the remaining 3 seats when we pick from the freshmen and sophomores only.

To recap everything so far:

Therefore, we have 4*10 = 40 different combinations possible for case A. We'll refer to this value later.

-----------

Case B: We pick 2 juniors and 2 seniors

Since there 2 juniors to pick from, and 2 junior seats to fill, there's only 1 way to do this. Likewise, there's only 1 way to pick the 2 seniors to fill the 2 seats.

In total so far there is 1*1 = 1 way to pick the 2 juniors and 2 seniors in any order you like.

Then we have 9-4 = 5 students left that are freshmen or sophomores. This is the number of choices we have for the final 5th seat.

We have 1*5 = 5 ways to have case B happen.

----------

Summary so far:

There are 45 ways to have the same number of juniors as seniors (either 1 of each or 2 of each).

Now we must calculate the number of total combinations possible on this committee. We'll turn to the nCr formula again.

n = 9 students

r = 5 seats

n C r = (n!)/(r!(n-r)!)

9 C 5 = (9!)/(5!*(9-5)!)

9 C 5 = (9!)/(5!*4!)

9 C 5 = (9*8*7*6*5!)/(5!*4!)

9 C 5 = (9*8*7*6)/(4!)

9 C 5 = (9*8*7*6)/(4*3*2*1)

9 C 5 = (3024)/(24)

9 C 5 = 126

There are 126 different five-person committees possible.

Of those 126 committees, 45 of them consist of cases where we have the same number of juniors and seniors.

That must mean there are 126-45 = 81 combinations where we do not have the same number of juniors and seniors. This is where the concept of "complement" comes in.

The equation that visualizes the full linear model of the data in a randomized block design with each treatment replicated once per block is: RESPONSE = CONSTANT + BLOCK + TREATMENT

In a randomized block design, the goal is to control the variability associated with the blocks while examining the effect of different treatments.

The equation RESPONSE = CONSTANT + BLOCK + TREATMENT represents the full linear model, where RESPONSE is the dependent variable, CONSTANT is the intercept term, BLOCK is the categorical variable representing the blocks, and TREATMENT is the categorical variable representing the treatments.

Including the BLOCK term in the model allows us to account for the variation associated with different blocks, while the TREATMENT term represents the effect of the treatments.

The model assumes that the effect of the treatments is the same across all blocks.

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Answer:

a. 2(^3 sqrt 3) - ^3 sqrt 18

Step-by-step explanation:

got it right on edge

\(\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}\)\(\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}\)\(2(\sqrt[3]{3})-\sqrt[3]{18}\) option (A)  is Correct.

The problem can be solved by following steps.

The expression given is \(\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}\)

So , The first step we will do is Rationalize the figure

= \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }}{\sqrt[3]{9}*\sqrt[3]{9} }\)

The product of radicals with the same index equals the radical of the product:\(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9*9^2} }\)

Simplify using exponent with same base

\(a^{n}*a^{m} = a^{a+m}\)

= \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^1+^2} }\)

Calculate the sum or difference: \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^3} }\)

Simplify the radical expression: \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {{9} }\)

Calculate the power : \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{9} }\)

Cross out the common factor: \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{3} }\)

Factor Greatest Common Factors : \(\frac{3*2\sqrt[3]{3}-\sqrt[3]{18} }{3}\)\(3*2\sqrt[3]{3}-\sqrt[3]{18}}\)

Reduce the fraction : \(2\sqrt[3]{3}-\sqrt[3]{18}}\)

Hence the First option is correct

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The main answer to the given question is:

y = xln|x| + 4x or y = -√(x^2 ln|x|) + 4x

y = xln|x|

y = x - 2

y = -2

No specific solution provided

In the given set of differential equations, we can solve four out of the five equations with their respective initial value problems (IVPs). For each equation, the solution is provided in terms of the variable x and y, along with the initial conditions.

In the first equation, the solution is given as y = xln|x| + 4x or y = -√(x^2 ln|x|) + 4x, with the initial condition y(1) = -2.

The second equation has a simple solution of y = xln|x|, with the initial condition y(1) = 0.

The third equation yields y = x - 2, with the initial condition y(1) = 1.

The fourth equation has a constant solution of y = -2, which does not depend on the initial condition.

However, for the fifth equation, no specific solution is provided.

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The length of DC found using Pythagorean theorem given AD = 10.6 and DB = 5.6 and AD and AB are tangent of circle O, is DC = 1.6

The given parameters are;

The tangents of circle O = AD and AB

The segment passing through O = DB

AD = 10.6

DB = 5.6

Required; The length of DC

Solution;

According to Pythagorean theorem, we have;

AB = √(10.6² - 5.6²) = 9

AB = AC = 9

AD = DC + AC

Which gives;

10.6 = DC + 9

DC = 10.6 - 9 = 1.6

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The question is not complete, so i have attached it.

Answer:

Options A, B & E are correct

Step-by-step explanation:

In the synthetic division attached, we see that:

: 2 , -2 & -12 are the coefficient of the dividend of the function 2x² - 2x - 12

: The divisor is 3

Thus;

x = 3 is a root of f(x) = 2x² - 2x - 12

Thus, (x - 3) is a factor of the dividend which is the function f(x) = 2x² - 2x - 12

- Now, from the attached image, the coefficients of the quotient are 2 , 4

- The quotient will be 1 degree less than the dividend since it was divided by the factor (x - 3)

The degree of the dividend will be 2 since it contains x²

Thus, the degree of the quotient will be 1

Therefore, the quotient in factor form is (2x + 4)

Looking at the given statements in the options;

- Option A is true, because we have established earlier that 3 is a root of f(x) = 2x² - 2x - 12

- Option B is true because we have established that (x - 3) is a factor of 2x² - 2x - 12

- Option C is not true because the factor is (x + 3) and not (x - 3)

-Option D is not true because the root is 3 and not -3

- Option E is true because we have established that quotient as a factor is: (2x + 4)

Thus, the correct options are A , B , E

Answer:

Step-by-step explanation:

your mom played with dad and then there was you

.Therefore, the probability that a randomly chosen vehicle is traveling at a legal speed is 0.0475 or 0.00024 rounded to two decimal places.

(a) The probability that a randomly chosen vehicle is traveling at a legal speed is 0.00024.A highway has a speed limit of 100 km/h, and the speeds of vehicles are usually distributed, with a mean of 115 km/h and a standard deviation of 9 km/h.

In other words, the distribution is as follows:X ∼ N(115, 9).P(X ≤ 100) is the probability that a randomly selected vehicle is traveling at a legal speed, where X represents the speed of a randomly selected vehicle.Let Z = (X - µ)/σ be the standardized value of X.Then,  Z =\((100 - 115)/9 = - 1.67\).The probability of Z is - 1.67 is given by P(Z ≤ - 1.67).Using the standard normal distribution table,\(P(Z ≤ - 1.67) = 0.0475\). The probability that a randomly chosen vehicle is traveling at a legal speed is 0.0475

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Answer: Real, equal, rational.

Step-by-step explanation:

\(-x^2-8x-16=0\\-(x^2+8x+16)=0\\Multiply \ the\ left \ and\ right \ sides\ of\ the\ equation\ by \ -1:\\x^2+8x+16=0\\x^2+2*x*4+4^2=0\\(x+4)^2=0\\x+4=0\\x=-4.\)

Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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The rate of conversion between pounds and ounces is shown as;

16 ounces = 1 pound

Then you have a digital scale that measures weight in ounces. If you put an object that weighs "exactly 1 pound" on the digital scale, its supposed to display 16 ounces.

However the scale has been described as "not accurate," which implies that the calibration (fine tuning) has been altered either accidentally or on purpose. This also implies that the result would not be 100 percent correct, but it might be a little over or below 16 ounces. Hence the scale might display what in mathematics is termed as "plus or minus" and is denoted by the sign ±

The scale therefore might display 15 ounces or 17 ounces (that is ± 16)

±

The location of the values square root of 10, square root of 13, and twenty two ninths on the number line will be A. Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.

The square root of 10 will be 3.16

The square root of 13 will be 3.6

Twenty two ninths will be 22/9 = 2.44

Therefore, the location of the values square root of 10, square root of 13, and twenty two ninths on the number line will be Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.

In conclusion, the correct option is A.

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Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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