SAT scores are normally distributed, with a mean of 500 points and a
standard deviation of 100 points. Suppose you take the SAT. Several weeks
later, you receive your results, which show that you reached the 90th
percentile for the math portion.
Recalling that SAT scores are always expressed as multiples of 10, how many
points did you get on the test?
A.600
B.630
C.130
D.590
E.690

Based on the values in the table of values, the expected value of the data is -3.3

The dataset is given as

x −5 −4 −3 −2 −1

P(X=x) 0.1 0.3 0.1 0.2 0.3

The expected value of the dataset is calculated as

E(x) = ∑x * P(x)

Substitute the known values in the above equation

So, we have

E(x) = (-5 * 0.1) + (-4 * 0.3) + (-3 * 0.3) + (-2 * 0.2) +(-1 * 0.3)

Evaluate the products in the above equation

So, we have

E(x) = -0.5 - 1.2 - 0.9 - 0.4 - 0.3

Evaluate the difference in the above equation

So, we have

E(x) = -3.3

Hence, the expected value of the data is -3.3

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The value equal to the direct opposite of Samantha's hike from her camp = -18 yards.

As per the given question;

Samantha descends a mountain from her camp.

Samantha discovered that she was 18 yards below the camp on the path she was on.

To locate the value that is the inverse of the distance Samantha hiked from her camp.

Samantha was 18 yards away from the camp.

Samantha hiked for 18 yards underneath the camp (in downwards )

Therefore;

Samantha hiked the opposite distance of 18 yards from the camp.

Samantha hiked for -18 yards.

Thus, the value equal to the inverse of the distance Samantha hiked from her tent = -18 yards

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Answer: 18

Step-by-step explanation:

Answer:

[tex](x^2y^5)5 = 5x^2y^5[/tex]

Step-by-step explanation:

Remove the parentheses to factor.

[tex]= x^2y^5 \times 5[/tex]

Flip the expression, creating a leading term and simplifying the equation.

[tex]= 5x^2y^5[/tex]

Answer:

10

Step-by-step explanation:

50.75 = 50

0.18 = 0.2

50x 0.2 = 50/5

50/5 = 10

Step-by-step explanation:

number of hamburgers for x pounds of ground meat is

h(x) = x/0.5

x = 3.23

h(3.23) = 3.23/0.5 = 6.46

so, he could make 6 hamburgers and had some meat (0.23 pound) left.

The mathematical statement given as 0.09 is 1/10 as much as 0.90 is true

The mathematical statement is given as:

0.09 is 1/10 as much as 0.90

To determine if the above statement is true, we start by representing the statement as an equation

So, we have

0.09 = 1/10 * 0.90

Express 1/10 as decimal

So, we have

0.09 = 0.10 * 0.90

Evaluate the product

So, we have

0.09 = 0.09

The above equation is true

Hence, the mathematical statement given as 0.09 is 1/10 as much as 0.90 is true

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Possible question

Determine if the following statement is true or false

Answer:

D

Step-by-step explanation:

[tex]h(x)=2x^5+(a+s)x^4+(b+t)x^3[/tex]

For the polynomial to be divisible by x⁴, the coefficient od the x³ term must be 0, and thus the answer is D.

Answer:

you should cook it for 19 hours

The interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall and  and the function rate of changes are 55.236, 68.276, 110.473 and 289.221

The given parameter is the graph of the beam

From the graph, we can see that the beam does not shine on all parts of the wall.

It shines on some part and doesn't on other parts

This means that the function is undefined

Hence, the interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall

To do this, we use the following computations:

[d(0.1) - d(0)]/[0.1 - 0] = [5.5236 - 0]/[0.1 - 0] = 55.236

[d(0.2) - d(0.1)]/[0.2 - 0.1] = [12.3512 - 5.5236]/[0.2 - 0.1] = 68.276

[d(0.3) - d(0.2)]/[0.3 - 0.2] = [23.3985 - 12.3512]/[0.3 - 0.2] = 110.473

[d(0.4) - d(0.3)]/[0.4 - 0.3] = [52.3206 - 23.3985]/[0.4 - 0.3] = 289.221

Hence, the function rate of changes are 55.236, 68.276, 110.473 and 289.221

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Antonio will save $113.4 after calculating using mensuration and buying from Pets Galore instead of Healthy pets.

As per the question statement, Antonio needs to buy 150 pounds of dog food for the local dog shelter. Healthy Pets, sells dog food in 50-pound bags for $85.95 per bag and Pets Galore sells one bag for $48.15

We are supposed to calculate the amount of money saved by Antonio if he buys 150 pounds of dog food from Pets Galore instead of from Healthy Pets.

Using concept of mensuration,

Quantity of dog food in one bag = 50 pounds

Quantity required of dog food = 150 pounds

Therefore number of bags required = 150/50 = 3

Price of dog food at Pets Galore per bag = $48.15

Total money to be paid to Pets Galore for 3 bags = $48.15*3  = $144.45

Total money to be paid to Healthy Pets for 3 bags = $85.95*3 = $275.85

Therefore money saved = $275.85 - $144.45  = $113.4

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Answer: 22.5

Step-by-step explanation:

25% is [tex]\frac{1}{4}[/tex] of 100%

So, 90/4 = 22.5

Answer:

22.5

Step-by-step explanation:

10% of 90 is 9

Multiply that by 2 then you get 18.

Half of 10% will give you the remaining 5% which is 4.5

Then add 18 and 4.5 you 22.5

Compute the characteristic polynomial of [tex]A[/tex].

[tex]p(\lambda) = \det(A - \lambda I) \\\\ ~~~~~~~~ = \begin{vmatrix} \beta - \lambda & 0 & 1 \\ 2 & 1 - \lambda & -2 \\ 3 & 1 & -2-\lambda \end{vmatrix} \\\\ ~~~~~~~~ = (\beta-\lambda)\begin{vmatrix}1-\lambda&-2\\1&-2-\lambda\end{vmatrix} + \begin{vmatrix}2&1-\lambda \\ 3 & 1 \end{vmatrix} \\\\ ~~~~~~~~ = -\lambda^3 + (\beta-1) \lambda^2 + (\beta + 3) \lambda - 1[/tex]

By the Cayley-Hamilton theorem,

[tex]p(A) = -A^3 + (\beta - 1) A^2 + (\beta + 3) A - I = 0[/tex]

Note that

[tex]A^7 - (\beta - 1) A^6 - \beta A^5 \\\\ ~~~~~~~~ = -(-A^3 + (\beta - 1) A^2 + \beta A) A^4 \\\\ ~~~~~~~~ = -(\underbrace{-A^3 + (\beta - 1) A^2 + (\beta + 3) A - I}_{p(A)=0} - 3A + I) A^4 \\\\ ~~~~~~~~ = (3A - I) A^4[/tex]

Recall that [tex]\det(AB) = \det(A) \det(B)[/tex]. Note that [tex]A[/tex] is not singular, and hence [tex]A^n[/tex] is not singular for any natural [tex]n[/tex].

[tex]\det(A) = \begin{vmatrix} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{vmatrix} \\\\ ~~~~~~~~ = \beta \begin{vmatrix}1&-2\\1&-2\end{vmatrix} + \begin{vmatrix}2&1\\3&1\end{vmatrix} \\\\ ~~~~~~~~ = -1 \neq 0[/tex]

Then [tex]3A-I[/tex] must be singular. So

[tex]\det(3A-I) = \begin{vmatrix} 3\beta - 1 & 0 & 3 \\ 6 & 2 & -6 \\ 9 & 3 & -7 \end{vmatrix} \\\\ ~~~~~~~~ = (3\beta-1) \begin{vmatrix}2&-6\\3&-7\end{vmatrix} + 3 \begin{vmatrix}6&2\\9&3\end{vmatrix} \\\\ ~~~~~~~~ = 4 (3\beta-1)[/tex]

[tex]4(3\beta-1) = 0 \implies \beta = \dfrac13 \implies 9\beta = \boxed{3}[/tex]

Answer:

36 min

Step-by-step explanation:

rate b = 1 / 90

rate m = 1/60

now add the rates together for 1 lawn

1 lawn / (1/60 + 1/90) = 36 min

Answer:

x, y =8 -3

Step-by-step explanation:

System of Linear Equations entered :

  [1]    x - 4y = 20

  [2]    2x + 5y = 1

Graphic Representation of the Equations :

   -4y + x = 20        5y + 2x = 1  

Solve by Substitution :

// Solve equation [1] for the variable  x

 [1]    x = 4y + 20

// Plug this in for variable  x  in equation [2]

  [2]    2•(4y+20) + 5y = 1

  [2]    13y = -39

// Solve equation [2] for the variable  y

  [2]    13y = - 39

  [2]    y = - 3

// By now we know this much :

   x = 4y+20

   y = -3

// Use the  y  value to solve for  x

   x = 4(-3)+20 = 8

Solution :

{x,y} = {8,-3}

The measure of the angles 1,2 and 3 are 75, 42 and 138 respectively.

The value of ∠1 = 180- 105             [supplementary angles]

∠1 = 75°

∠1 + ∠2 + 63° = 180                          [angle - sum property]

75 + ∠2 + 63 = 180

∠2 = 180 - (75 + 63)

∠2 = 42°

∠2 + ∠3 = 180                                       [supplementary angles]

42 + ∠3 = 180

∠3 = 180 - 42

∠3 = 138°

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Simplifying the expression y to the negative seventh power over x to the negative third power using law of exponents gives; x³y⁷

Some of the Laws of Exponents are;

We want to simplify y to the negative seventh power over x to the negative third power. This is expressed as;

y⁷/x⁻³

Now, x⁻³ can also be expressed as 1/x³. Thus, our original equation is now; y⁷/(1/x³) = x³y⁷

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The probability of P(A and B) based on the information given will be E. None of the above.

It should be noted that probability is used to illustrate the likelihood that something will occur.

In this case, P(A) = 0.1 and P(B) = 0.4. Therefore, the probability of P(A and B) will be

= P(A) + P(B)

= 0.1 + 0.4

= 0.5

Sine the value of 0.5 isn't given, the correct option is E.

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Answer:

x(down 1)=-11/5, x(down 2) =3

Step-by-step explanation:

Solving a system of equations we can see that the two numbers are 727 and 4

Let's define x as the 3-digit number and y as the one-digit number.

Then we know that the sum is equal to 731:

x + y = 731

And the product is equal to 2,908, then:

x*y = 2,908

So we have a system of equations:

x + y = 731

x*y = 2,908

Isolating x on the first equation gives:

x = 731 - y

Now we can replace that in the other equation to get:

(731 - y)*y = 2,908

Now we can solve this quadratic equation to find the value of y.

731*y - y^2 = 2,908

-y^2 + 731*y - 2,908 = 0

The solutions are:

y = (-731 ± √( 731^2 - 4*(-2,908)*(-1))/(-2)

y = (-731 ± 723)/-2

Now, y is an one digit number, then:

y = (-731 + 723)/-2 = 4

And x will be the 3 digit number:

x = 731 - x = 731 - 4 = 727

So the two numbers are 727 and 4

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The distance between two points A (-10, -7) and B(-8,1) will be equal to 8.2 units.

What do you mean by the distance between points ?

Distance between two points is the length of the line segment that connects the two locations in a plane.

It is given that the distance between points A (-10, -7) and B(-8,1) is to be calculated.

We can find out the distance by using the distance formula which is given by :

AB = [tex]\sqrt({x_{2} - x_{1})^2 + (y_{2}- y_{1})^2}[/tex]

AB = √ [( -8 -(-10)]^2 + [ 1 - (-7)]^2}

AB = √ (2² + 8²)

AB = √68

AB = 8.24 units

If we round off it to the nearest tenth then , hundredth place is less than 5 that meant 2 will be at the tenths place.

or

AB = 8.2 units.

Therefore , the distance between two points A (-10, -7) and B(-8,1) will be equal to 8.2 units.

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Reason:

Subtract 3x from both sides. They cancel out and go away. The x term is fully eliminated and we're left with the equation 8 = 9, which is a false statement. Therefore, the original equation is always false regardless of what you pick for x. This is why there aren't any solutions.

Visually you can graph y = 3x+8 and y = 3x+9. You'll get parallel lines that never intersect. We need the lines to intersect if we wanted a solution point. Parallel lines have the same slope, but different y intercepts.

Because the system has no solutions, we consider the system inconsistent.

Answer:

-6 = 1

-4 = 2

0 = 4

2 = 5

8 = 8

Answer:

hey the answer is d(0,4)

Answer:

It is D

Step-by-step explanation:

I've done this problem before

The raw score x, corresponding to z = 2 is calculated as; 90

We are given;

Population Mean; μ = 78

Sample mean; x' = ?

Population standard deviation; σ = 6

z-score; z = 2

The formula for z-score is;

z = (x' - μ)/σ

Thus, making x' the sample mean the subject of the formula gives;

x' = zσ + μ

Plugging in the relevant values gives;

x' = (2 * 6) + 78

x' = 12 + 78

x' = 90

Thus, the raw score x, corresponding to z = 2 is 90

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The image of the translation is shape WYX is shown by option 2.

The process of substituting the axes inside a Cartesian coordinate system with such a new set of axes parallel to the first, which is used to write equations for curves that are not centered about the origin.

As, from the rule of translation along x axis;

The coordinates of the x axis are not changed and y are changed.

Thus, for the given figure XWY the image after translation about the x axis is shown by the option 2 graph.

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Answer: A. 5.19$

Step-by-step explanation: divide 25.95 by 5

Using the concept of absolute and relative change, it is found that:

a) The absolute change in the monthly cost of cable TV is of $4.15.

b) The relative change in the monthly cost of cable TV is of 5.53%.

c) The absolute change in the monthly cost of eggs is of $0.67.

d) The relative change in the monthly cost of eggs is of 39.41%.

e) Due to the higher relative change, the cost of the eggs increased the most.

Hence the absolute changes are given as follows:

The relative changes are given as follows:

Hence, for item e:

Due to the higher relative change, the cost of the eggs increased the most.

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The equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up.

The parent function is:

f(x) = ∛x

Horizontally stretched by a factor of 4:

g(x) = ∛[(1/4)x]

Translated 5 units right:

G(x) = ∛[(1/4)x - 5]

Translated 3 units up:

h(x) = ∛[(1/4)x - 5] + 3

Thus, the equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.

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