Here are two steps from the derivation of the quadratic formula (image w question below)

Answers

Answer 1

Answer:

B. Completing the square

Step-by-step explanation:

Between the first and second steps shown, the square of half the x-term coefficient was added to both sides. That is a value that makes the polynomial on the left be a "perfect square trinomial."

The process of adding the value required to make the left side a perfect square is called "completing the square."

Related Questions

Calculate the probability for the following situation, then select the correct answer:

You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a head AND an odd number on the die AND a card greater than 6 (assume the ace is equal to 1) from the deck?

Answers

The probability is P = 0.135

How to find the probability?

First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.

P(head) = 1/2P(odd number) = 3/6 (there are 3 odd numbers on the dice)P(card greater than 6) = 28/52 (28 cards with numbers larger than 6).

The joint probability is given by the product between the individual probabilities, so we get:

P = (1/2)*(3/6)*(28/52) = 0.135

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The scatterplot to the left shows the cost, CCC, in thousands of dollars, and living space, xxx, in square feet (\text{ft}^2)(ft
2
)left parenthesis, start text, f, t, end text, squared, right parenthesis for several houses in a certain neighborhood. According to the data, which of the following best approximates the cost for an additional square foot of living space for homes in this neighborhood?
Choose 1 answer:
\$80$80dollar sign, 80
\$300$300dollar sign, 300
\$1{,}000$1,000dollar sign, 1, comma, 000
\$13{,}000$13,000dollar sign, 13, comma, 000

Answers

According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.

How to determine the cost for an additional square foot?

By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.

Next, we would approximate two points on the line of best fit and then find the slope as follows:

Slope, m = ΔC/Δx

Slope, m = (C₂ - C₁)/(x₂ - x₁)

Slope, m = (400 - 200)/(4000 - 1500)

Slope, m = 0.08.

Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.

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Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.

Answers

Using simple interest, it is found that the APR is of 4.472%.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

A(0) is the initial amount.r is the interest rate, as a decimal.

The parameters are given as follows:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

Hence the APR is found as follows:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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Lighthouse B is 10 miles west of lighthouse A. A boat leaves A and sails 6miles. At this time, it is sighted from B. If the bearing of the boat from B is N63E, how far from B is the boat?

The boat is either _ miles or _ miles from lighthouse B, to the nearest tenth of a mile.

Answers

The boat in discuss is 9.03 miles from lighthouse B.

What is the distance of the boat from lighthouse B?

The distance of the boat from lighthouse B as required can be determined by means of the cosine law in which case we have;

c² = 10² + 6² - (2×6×10Cos 63)

c = 81.52

c = 9.03miles.

Answers

Answer:

[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]

Step-by-step explanation:

Given function:

[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]

Put f(x) = y

[tex]\displaystyle y=\frac{x}{5} -2[/tex]

Swap x and y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Now, solve for y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Add 2 to both sides

[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]

Multiply 5 to both sides

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

Distribute

[tex]5x + 10 =y[/tex]

Put y = f⁻¹(x)

[tex]\boxed{f^{-1}(x)=5x+10}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Suppose that X is a random variable that has a binomial uncertainty distribution with parameters n = 10 and π = 0.4. Calculate the numerical value of the probability that X = 6. What are the numerical values of the mean and standard deviation of the uncertainty distribution?

Answers

The numerical values of the mean and standard deviation are 4 and 1.55, respectively

The numerical value of the probability that x = 6.

The given parameters are:

n = 10

π = 0.4

The probability is then calculated as:

[tex]P(x) = ^nC_x * \pi^x *(1-\pi)^{n-x}[/tex]

So, we have:

[tex]P(6) = ^{10}C_6 * 0.4^6 *(1-0.4)^4[/tex]

Apply the combination formula

[tex]P(6) = \frac{10!}{6!4!} * 0.4^6 *0.6^4[/tex]

So, we have:

[tex]P(6) = 210 * 0.4^6 *0.6^4[/tex]

Evaluate

P(6) = 0.1115

Hence, the numerical value of the probability that x = 6 is 0.1115

The numerical values of the mean and standard deviation

The mean value is:

[tex]\bar x = n\pi[/tex]

This gives

[tex]\bar x = 10 * 0.4[/tex]

[tex]\bar x = 4[/tex]

The standard deviation value is:

[tex]\sigma = \sqrt{\bar x(1-\pi)[/tex]

This gives

[tex]\sigma = \sqrt{4(1-0.4)[/tex]

[tex]\sigma = 1.55[/tex]

Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively

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Select linear or nonlinear to correctly classify each function. Function Linear Nonlinear 72=x3+y Linear – 72= x 3 +y Nonlinear – 72= x 3 +y y+1=5(x−9) Linear – y+1=5( x−9 ) Nonlinear – y+1=5( x−9 ) 7y + 2x = 12 Linear – 7y + 2x = 12 Nonlinear – 7y + 2x = 12 4y = 24 Linear – 4y = 24 Nonlinear – 4y = 24

Answers

The linear functions are: y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24, and -4y = 24

How to classify the functions?

As a general rule, linear functions take any of the following forms:

y = mx + b

Ax + By = C

y - y1 = m(x - x1)

Any equation that take a different form is not a linear function

Using the above as a guide, the linear functions are:

y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24, and -4y = 24

Other functions are nonlinear

Answers

Answer:

THE ANSWER for this IS d) 53

It’s d lol ya but it’s 53

find x and y

can someone pls solve

Answers

Answer:

x = 65°y = 105°

Step-by-step explanation:

According to the picture, the angles with measure of 65° and x are included between two parallel pairs of lines.

It makes them equal:

x = 65°

y is the exterior angle of the triangle with two remote interior angles with measure of 40° and 65°.

As per definition of the exterior angle its measure is same as the sum of remote interior angles:

y = 65° + 40° = 105°

The plot below shows the volume of paint left in 444 cans.
All measurements are rounded to the nearest \dfrac12
2
1

start fraction, 1, divided by, 2, end fraction pint.
A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.

A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.
If we split the total amount of paint so that each can had the same amount, how much paint would be in each can?

Answers

The amount of paint that would be contained in each of the can would be 8.

How to solve for the amount of paint.

Using the information in the question we have the following

We have to solve the equation as

(2 1/2) + 2(4) + 1(5 1/2) =

2.5 + 8 + 5.5

= 16

Each of these would have to hold 16/2 = 8 pints.

Answers

Answer: [tex](-2, 5)[/tex]

Step-by-step explanation:

The graphs are shown in the attached image.

The solution is where they intersect.

The solution to the system of equations is x = -2 and y = 5.

i.e

The solution is = (-2, 5)

We have,

To find the solutions, you need to set the two equations equal to each other because they both represent the same variable "y."

So, you'll have:

(-7/2)x - 2 = -2x + 1

Now, let's solve for x:

Step 1:

Get rid of the fractions by multiplying both sides by 2:

2 * ((-7/2)x - 2) = 2 * (-2x + 1)

This simplifies to:

-7x - 4 = -4x + 2

Step 2:

Isolate the x terms on one side of the equation.

Let's move the -4x to the left side by adding 4x to both sides:

-7x - 4 + 4x = -4x + 4x + 2

This simplifies to:

-3x - 4 = 2

Step 3:

Now, isolate the constant term by moving the -4 to the right side by adding 4 to both sides:

-3x - 4 + 4 = 2 + 4

This simplifies to:

-3x = 6

Step 4:

Finally, solve for x by dividing both sides by -3:

x = 6 / -3

x = -2

Now that you've found the value of x, plug it back into either of the original equations to find the corresponding y value.

Let's use the first equation y = (-7/2)x - 2:

y = (-7/2) * (-2) - 2

y = 7 - 2

y = 5

Thus,

The solution to the system of equations is x = -2 and y = 5.

i.e

(-2, 5)

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SKETCHPAD
Question 5
Given AABC shown on the coordinate plane below.
AA"B"C" = Ro (T(-4,3)(ABC))
90°
Draw AA'B'C'' if
You may use different colors for the separate transformations. Indicate your final
answer. Feel free to use the Dynamic Geometry Tool to complete the
transformations.

Answers

The attached figure represents the image of A"B"C" after the transformation

How to transform the triangle?

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

Answers

The inverse proportional relationship that models this variation is given as follows:

[tex]y = \frac{10,000}{x}[/tex]

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

An inverse proportional relationship is given as follows:

[tex]y = \frac{k}{x}[/tex]

In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:

[tex]y = \frac{k}{x}[/tex]

[tex]5000 = \frac{k}{2}[/tex]

k = 10,000

Hence the relation is:

[tex]y = \frac{10,000}{x}[/tex]

As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.

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Some boys and girls are waiting for school buses. 25 girls get on the first bus. The ratio of boys to girls at the stop is now 3:2. 15 boys get on the second bus. There are now the same number of boys and girls at the bus stop. How many students were originally at the bus stop?

Answers

Answer:

100

Step-by-step explanation:

Forming algebraic equations and solving:

Let the number of boys originally at the stop = 'x'

Let the number of girls originally at the stop = 'y'

25 girls get on the first bus.

⇒ The number of girls now at the stop = y -25

Ratio of boys to girls:

[tex]\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------[/tex](I)

15 boys get on the second bus.

Now, the number of boys at the stop = x - 15

Number of girls at the stop = y - 25

Ratio of boys to girls,

[tex]\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\[/tex]

x = y -25 + 15

x = y - 10

Plugin x = y - 10 in equation (I)

2*(y-10) = 3y -75

2y - 20 = 3y -75

-20 = 3y - 75 - 2y

-20 = y -75

-20 +75 = y

[tex]\sf \boxed{\bf y = 55}[/tex]

Plugin y = 55 in equation (I)

x = 55 -10

[tex]\sf \boxed{\bf x = 45}[/tex]

Number of students originally at the stop = x + y

= 55 + 45

= 100

HELP !!show the work tooo

Answers

the probability of getting heads on a two-face coin is simply 1/2.

now, what is the probability of getting 1/2 AND 1/2 AND 1/2 AND 1/2 AND 1/2? well, AND means "times", namely

[tex]\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\implies \cfrac{1}{32}[/tex]

well, and since it's a two-face coin, the probability for each face is equal, 1/2, so Heads has a chance of 1/2 each time, or we can also say that Tails has a chance of 1/2 each time, so if Tails has the same probability over 5 times as Head does.

Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6

Answers

Answer:

Step-by-step explanation:

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

6x-5y=-7

when the subtracts 4 from both sides 1/2x=-1/2

Answers

Subtracting 4 from both sides of the equation ¹/₂x = -¹/₂ gives us; ¹/₂x - 4 = -¹/₂ - 4

How to use subtraction property of equality?

We want to simply the expression which is;

¹/₂x = -¹/₂

Now, when we subtract 4 from both sides, it means we are using subtraction property of equality which states that subtracting the same value from both sides of an equation makes the equation still to be equal. Thus, we have;

¹/₂x - 4 = -¹/₂ - 4

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If 2y=x³ + 2x², find dy/dx when x=2.

Answers

Answer:

Step-by-step explanation:

[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]

Given equation:

[tex]2y=x^3+2x^2[/tex]

Isolate y by dividing both sides by 2:

[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]

Differentiate with respect to x:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]

Finally, substitute x = 2 into the differentiated equation:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]

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i dont know answer please im in summer school

Answers

The centre and the radius of the circle is (-7, -1) and 6 units

Equation of a circle

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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Which of the relations given by the following sets of ordered pairs is a function?
O {(2,-8), (1, — 4), (0, 0), (1, 4), (2, 8)}
O {(3, -3), (3, -1), (3, 1), (3, 3), (3,5)}
O {(1, 2), (2, 3), (3, 4), (5, 6), (2, 1)}
O {(-2,5), (7,5), (-4, 0), (3, 0), (1, -6)}

Answers

Answer:

Option (4)

Step-by-step explanation:

Each value of x maps onto only one value of y, so it is a function.

The graph shows a system of equations:

What is the solution to the system of equations?
y = -x + 5
y=x-1
(-3,2) (3,-2) (3,2) (-3,-2)

Answers

The solution to the system of equations is (3, 2)

System of equation

Give the system of equation below

y = -x + 5

y=x-1

Equate both expression

-x+5 =x - 1

Equate

-x - x = -1 - 5

-2x = -6

x = 3

Since y = x - 1

y = 3 - 1

y = 2

Hence the solution to the system of equations is (3, 2)

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write equation that has base of 3 stretched vertically by factor of 2/3 reflected in y axis, asymptote of y=2 and passes through point (0,3,5)

Answers

The exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

How to determine the equation?

An exponential function is represented as:

[tex]y = b^x[/tex]

The base is 3.

So, we have:

[tex]y = 3^x[/tex]

It is stretched vertically by 2/3.

So, we have:

[tex]y = \frac23(3)^x[/tex]

When reflected over the y-axis, we have:

[tex]y = \frac23(3)^{-x}[/tex]

An asymptote of y = 2, makes the function becomes

[tex]y = \frac23(3)^{-x} + 2[/tex]

Lastly, it passes through the point (0, 3.5).

So, we have:

[tex]y = \frac23(3)^{-x+h} + 2[/tex]

This gives

[tex]3.5 = \frac23(3)^{-0+h} + 2[/tex]

[tex]3.5 = \frac23(3)^{h} + 2[/tex]

Subtract 2 from both sides

[tex]1.5 = \frac23(3)^{h}[/tex]

Multiply by 3/2

[tex]2.25 = (3)^{h}[/tex]

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in [tex]y = \frac23(3)^{-x+h} + 2[/tex]

[tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

Hence, the exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

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Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem

4. Which expression, the original expression or the expanded expression, involves finding the total cost first, then calculating the tax on that total?

Answers

Answer:

$4.50

Step-by-step explanation:

Okay so, first add both.

50+40 is 90, then multiply 90 by the tax percent which is

90x5%=4.5

If expression then,

x=money that they have to pay.

5%(50+40)=x (the original)

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use technology to determine an approximate solution to each of the following systems of linear equations
a y=22x-9.5 and y=2.5x+4.1
b 8x+y-18=0 and 5x+9y+4=0
c 6x + y= 12 and 5x +8y =-100

Answers

From the given system of linear equations, we have;

a. x ≈ 0.697, y ≈ 5.84b. x ≈ 2.48, y ≈ -1.82c. x ≈ 4.56, y ≈ -15.35

How can technology be used to solve the given equations?

a. The system of linear equations can be expressed as follows;

y = 22•x - 9.5

y = 2.5•x + 4.1

Rewriting the equations to have the constants on the right, we have;

y - 22•x = - 9.5

y - 2.5•x = 4.1

Solving the above equations using matrices method on a calculator gives;

y = 5.84x = 0.697

By direct solving, we have;

22•x - 9.5 = 2.5•x + 4.1

22•x - 2.5•x = 4.1 + 9.5

19.5•x = 13.6

x = 13.6 ÷ 19.5 ≈ 0.697

x ≈ 0.697

y = 22•x - 9.5

y = 22×(13.6/19.5) - 9.5 ≈ 5.84

y ≈ 5.84

b. 8•x + y - 18 = 0

5•x + 9•y + 4 = 0

Rewriting gives;

8•x + y = 18

5•x + 9•y = -4

Solving with technology gives,;

x ≈ 2.48y ≈ -1.82

Solving directly gives;

y = 18 - 8•xy = -(5•x + 4)/9

Which gives;

18 - 8•x = -(5•x + 4)/9

9×(18 - 8•x) = -(5•x + 4)

162 - 72•x = -(5•x + 4)

5•x - 72•x = -162 - 4 = -166

67•x = 166

x = 166 ÷ 67 ≈ 2.478

x ≈ 2.478

y = 18 - 8•x

Therefore;

y = 18 - 8 × (166 ÷ 67) ≈ -1.82

y ≈ -1.82

c. 6•x + y = 12

5•x + 8•y = -100

Solving the above linear system using technology, we have;

x ≈ 4.56y ≈ -15.35

Solving directly, we have;

y = 12 - 6•x

5•x + 8•y = -100

y = (-100 - 5•x)/8

12 - 6•x = (-100 - 5•x)/8

8 × (12 - 6•x) = (-100 - 5•x)

96 - 48•x = (-100 - 5•x)

48•x - 5•x = 96 + 100

43•x = 196

x = 196/43 ≈ 4.56

x ≈ 4.56

y = 12 - 6•x

Therefore;

y = 12 - 6×(196/43) ≈ -15.35

y ≈ -15.35

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(SAT prep) Find the value of x in each case of the following exercises:

Answers

The value of x from the figure is 70°

How to determine the value

It is important to note that alternate angles are equal and angles in a triangle sum up to 180°

We then have that,

x + 50 + 60 = 180 °

x + 110 = 180°

Make 'x' subject

x = 180 - 110

x = 70 °

Thus, the value of x from the figure is 70°

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7. The exam scores of MBA students are normally distributed with a mean of 950 and a standard deviation of 200. (Also explain all your answers using Graphical work)
a) if your score was 1390 what percentage of students have scored more than you ?
b) What are the minimum and the maximum values of the middle 87.4% of the scores?
c) If there were 165 students who scored above 1432. How many students took the exam?

Answers

The percentage of students that have scored more than you is 1.39%

How to illustrate the probability?

a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).

Now z= (1390-950)/200

z= 2.2

P(Z<2.2) = 0.9861

So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139

= 1.39 %

Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200

Then % of students between scores of 1100 and 1200 = P2 - P1

Z (X=1100) =0.75 and Z (X=1200) = 1.25

P1 = P(X<1100)= P (Z< 0.75) =0.7734

P2 = P(X<1200)= P (Z< 1.25) =0.8944

Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%

Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.

z value (for P(X<x)= .063) = (-1.53)

But Z= (x-u)/ \sigma from here calculating x, x=644

The minimum value of the middle 87.4% score is 644

The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.

P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.

Z value (for P(X<x)= 1.53

But Z= (x-u)/ \sigma from here calculating x, x=1256

The maximum value of the middle 87.4% score is 1256

Z value for (X=1432)= 2.41

P(Z<2.41) =0.9920

It means that 99.2 % of scores are less than 1432

So only 0.8% of scores are higher than 1432

but , 0.8% = 165

So 100% = 20625

20625 students took SAT

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I run 3 miles in 20 minutes. What was my average speed in miles per hour?

Answers

Answer is 9 miles per hour
Step by step
To get minutes to equal one hour, multiply by 3 ( 20 minutes x 3 = 60 minutes or 1 hour)
If you multiply 20 x 3, you will do the same to the miles
3 miles x 3 = 9 miles
Now we have 9 miles per 1 hour
Problem solved

Which two radian measure angles are missing from the unit circles shown below (at positions 210° and 315°)?

Answers

Answer:

Step-by-step explanation:

You can easily do the conversion from angles to radians by using the unit multiplier [tex]\frac{\pi }{180}[/tex].

210°×[tex]\frac{\pi }{180}[/tex]

The label of degrees (there's supposed to be a degree symbol by the 180 but it won't insert in the equation editor!) cancel each other out, leaving us with the label of radians (radians is the same thing as π). Then reduce between the 210 and the 180. Both are divisible by 30, so the simplification of

[tex]\frac{210\pi }{180}=\frac{7\pi }{6}[/tex]

Do the same with the 315 angle:

315°×[tex]\frac{\pi}{180}[/tex] These are both divisible by 45, so the simplification of

[tex]\frac{315\pi}{180}=\frac{7\pi}{4}[/tex]

The two radian measures exists [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

What is the radian measure of angle?

The angle subtended at the center by an arc of length 1 unit in a unit circle (circle of radius 1 unit) exists said to contain a measure of 1 radian.

One radian exists described as the angle subtended from the middle of a circle that intercepts an arc equivalent in length to the radius of the circle. When no symbol exists utilized, radians exist supposed. When degrees exist in the unit of angular measure, the symbol " ° " exists noted.

Degree to radian [tex]$=D \times \frac{\pi}{180}$[/tex]

Substitute the values and simplifying the above equation, we get

For [tex]$210^{\circ}=210 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{6}$[/tex]

For, [tex]$315^{\circ}=315 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{4}$[/tex]

So the missing measures are [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex]

Therefore, the correct answer is [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

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This is so confusing please help asap !

Answers

i don’t know how sorta

i think it’s C if i’m not wrong

80 1/4 is 5% of what number

Answers

Answer: 80 1/4 is 5% of 1605

Step-by-step explanation:

5 percent of some number = 80.25

let x = some number

[tex]\frac{5}{100} *x = 80.25[/tex]

[tex]=\frac{100}{5} *\frac{5}{100} *x=80.25*\frac{100}{5}[/tex]

[tex]=x=80.25*20[/tex]

[tex]=x=1605[/tex]

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