5 . 3n

A. 15,30,45,60
B.5,15,45,135
C.0,15,45,135
D.15,45,135,405

In one hour Nina runs 51 ¹/₅ miles.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

In 1/4 hours, Number of laps run by Nina = 12 ⁴/₅.

To find the number of laps Nina could run in one hour,

Use ratio property,

Since,

In 1/4 hours = 12 ⁴/₅ laps = 64 / 5 laps

In 1 hour = (64 / 5) x 4

               = 256 / 5

                = 51 ¹/₅

Nina runs 51 ¹/₅ laps in one hour.

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Answer:

-8x^2 + 6x - 14

Step-by-step explanation:

(3x^2 + 4x - 5) - (7x^2 + x + 9) = -4x^2 + 3x - 14

(-4x^2 + 3x - 14) - (4x^2 - 3x) = -8x^2 + 6x - 14

Answer:

the difference is 14

Step-by-step explanation:

Hello

I think  I can help you with this

step 1

Subtracting 3x2 + 4x – 5 from 7x2 + x + 9

[tex]7x^{2} +x+9-(3x^{2} +4x-5)\\=7x^{2} +x+9-3x^{2} -4x+5\\=4x^{2} -3x+14\\[/tex]

Step2

After subtracting 4x2 – 3x from this polynomial

[tex]4x^{2} -3x+14-(4x^{2} -3x)\\4x^{2} -3x+14-4x^{2} +3x\\14[/tex]

the difference is 14

Have a fantastic day,I hope it helps

Answer:

It's the first choice.

Step-by-step explanation:

cos θ  = √(1 - sin^2 θ ) and cos θ  will be positive because  sin θ > 0  tan θ > 0. The angle  θ  will be in the first quadrant.

cos  θ  = √( 1 - (2/7)^2)

cos  θ = √(1 - 4/49) = √(45/49)

cos  θ  = √9√5 / 7

cos  θ  = 3√5 / 7.

Answer:

3 square root of 5 over 7. it's positive answer because both sin and tan are positive meaning they are sitting in the first quadrant were all ∅'s are positive

Step-by-step explanation:

Answer:

Claire should place the mirror 6 and 1/4 (6.25) inches from each corner of the wall in order for the mirror to be centered.  

Step-by-step explanation:

In order to find out how far the mirror would need to be set from each corner of the wall, you need to first take the total length of the wall and subtract the total width of the mirror:  31 - 18.5 = 12.5.  12.5 inches is the amount of wall space that would be left when the mirror is hanging.  In order for the mirror to be centered, we need to take the amount of wall space left and divide by two (2) to find the measurement from each corner:  12.5 ÷ 2 = 6.25 or 6 1/4.  By placing the mirror 6.25 inches from each corner of the wall, the mirror will be centered on the wall.

Answer: your answer should be 0.51

Some people are saying it's 0.04 but that is the wrong answer.

You can analyze it in this way:

1)(2) in y2-2y can show that was (y-1)^2 so we add -1 to -8 => -9

2)(8) in x2-8x show us that was (x-4)^2 so we add -16 to -9 => -25

and finally we have:(x-4)^2 + (y-1)^2 =25

it means C is true!

Answer:(x−4)2+(y−1)2=25 is the answer

Answer:

Final answer in simplified form is [tex]-7x^2+10x-18[/tex]

Step-by-step explanation:

Given expression is [tex](-7x^2+4x-3)+(6x-15)[/tex]

Now we need to find an equivalent expression for [tex](-7x^2+4x-3)+(6x-15)[/tex]

First we can distribute the positive sign and remove the parenthesis the combine like terms

[tex](-7x^2+4x-3)+(6x-15)[/tex]

[tex]=-7x^2+4x-3+6x-15[/tex]

[tex]=-7x^2+4x+6x-3-15[/tex]

[tex]=-7x^2+10x-18[/tex]

Hence final answer in simplified form is [tex]-7x^2+10x-18[/tex]

Answer:

[tex]\boxed{\text{3. }\dfrac{7\pi}{30} \text{; 4. } -20^{\circ}\text{; 5. } -\dfrac{720^{\circ}}{\pi}}[/tex]

Step-by-step explanation:

Question 3

[tex]42^{\circ} \times \dfrac{\pi}{180^{\circ}} = \boxed{\dfrac{7\pi}{30}}[/tex]

Question 4

[tex]-\dfrac{\pi}{9} \times \dfrac{180^{\circ}}{\pi}= \boxed{-20^{\circ}}[/tex]

Question 5

[tex]-4\times \dfrac{180^{\circ}}{\pi}= \boxed{-\dfrac{720^{\circ}}{\pi}}[/tex]

Answer:

Step-by-step explanation:

This is a right triangle problem.  The reference angle is x, the side opposite the reference angle is 32, and the hypotenuse is 58.  The trig ratio that relates the side opposite a reference angle to the hypotenuse is the sin.  Filling in accordingly:

[tex]sin(x)=\frac{32}{58}[/tex]

Because you are looking for a missing angle, you will use your 2nd button and then the sin button to see on your display:

[tex]sin^{-1}([/tex]

Within the parenthesis enter the 32/58 and you'll get your angle measure.  Make sure your calculator is in degree mode, not radian mode!!!

Answer:

b. sin or csc

Step-by-step explanation:

Remember that sine trigonometric function is the ratio of the opposite side of a right triangle to its hypotenuse; in other words:

[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]

Also, the cosecant is the inverse of sine, so:

[tex]csc(\alpha )=\frac{1}{sin(\alpha) } =\frac{hypotenuse}{opposite-side}[/tex]

Now, for our triangle, our angle is 27°, the longest side of it is TS, and the opposite side of our angle (27°) is TR; therefore, [tex]\alpha =27[/tex], [tex]hypotenuse=TS[/tex], and [tex]opposite-side=TR[/tex].

Replacing values:

- Using the sine trigonometric function

[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]

[tex]sin(27)=\frac{TR}{TS}[/tex]

[tex]sin(27)=\frac{TR}{TS}[/tex]

[tex]sin(27)=\frac{7}{TS}[/tex]

[tex]TS=\frac{7}{sin(27)}[/tex]

[tex]TS=15.42[/tex]

- Using the cosecant trigonometric function

[tex]csc(\alpha )=\frac{hypotenuse}{opposite-side}[/tex]

[tex]csc(27)=\frac{TS}{TR}[/tex]

[tex]csc(27)=\frac{TS}{7}[/tex]

[tex]TS=7csc(27)[/tex]

[tex]TS=15.42[/tex]

We can conclude that we can use either the sine trigonometric function or the cosecant trigonometric function to solve the problem.

Answer:

The correct answer option is D. [tex] \frac { 3 n ^ { 3 } } { 5 m ^ { 2 } } [/tex].

Step-by-step explanation:

We are given the following expression and we are to simplify it:

[tex] \frac { 3 m ^ { - 2 } } { 5 n ^ { - 3 } }[/tex]

Here the variables [tex]m[/tex] and [tex]n[/tex] are having negative powers. So to change these powers from negative to positive, we will take their reciprocals to get:

[tex] \frac { 3 n ^ { 3 } } { 5 m ^ { 2 } } [/tex]

Answer:

The correct answer is option D

3n³/5m²

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

X⁻ᵃ = 1/Xᵃ

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

To find the correct answer

It is given that,

3m⁻²/5n⁻³

By using identities we can write,

m⁻² = 1/m²  and 1/n⁻³ = n³

3m⁻²/5n⁻³ = 3n³/5m²

Therefore the correct answer is option D.  3n³/5m²

The answer is:

The length of "x" is equal to 4 units.

To solve the problem and find the length of x, we need to remember the alternate angles rule. The alternate angles rule establish that alternate angles will be also equal.

So, for the triangles, we have:

The angle((α)) formed between the base (2.5) and the hypotenuse (5)  of the big triangle is equal to the angle(α) formed between the base (2) and the hypotenuse (x) of the small triangle. It also means that the triangles are similar since they have congruent angles(α) and proportional sides (SAS).

We are given:

First triangle,

[tex]AdjacentSide=2.5\\Hypotenuse=5\\[/tex]

Second triangle,

[tex]AdjacentSide=2\\Hypotenuse=x\\[/tex]

So, using the cosine identity, we have:

[tex]Cos(\alpha)=\frac{AdjacentSide}{Hypotenuse}[/tex]

[tex]Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}[/tex]

[tex]Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}\\\\\frac{2.5}{5}=\frac{2}{x}\\\\x=2*\frac{5}{2.5}=4[/tex]

Therefore, we have that the hypotenuse of the second triangle (x) is equal to 4 units.

Hence, the length of "x" is equal to 4 units.

Have a nice day!

Answer:

The length of x = 4

Step-by-step explanation:

From the figure we can see that two triangles are similar. (AAA similarity criteria)

Therefore the ratio of similar corresponding sides are equal.

Answer:

The length of x = 4

Step-by-step explanation:

From the figure we can see that two triangles are similar. All angles are equal(AAA similarity criteria)

Therefore the ratio of similar corresponding sides are equal.

To find the value of x

From the figure we can write,

x/5 = 2/2.5

x = (5 * 2)/2.5

x = 10/2.5 = 4

Therefore the length of x = 4

From the figure we can write,

x/5 = 2/2.5

x = (5 * 2)/2.5

x = 10/2.5 = 4

Therefore the length of x = 4

Answer:

[tex]t=5\ sec[/tex]

Step-by-step explanation:

we have

[tex]-t^{2} +4t+5=0[/tex]

Solve the quadratic equation to find the zero's or x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero ( water balloon reach the ground)

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]-t^{2} +4t+5=0[/tex]

so

[tex]a=-1\\b=4\\c=5[/tex]

substitute in the formula

[tex]t=\frac{-4(+/-)\sqrt{4^{2}-4(-1)(5)}} {2(-1)}[/tex]

[tex]t=\frac{-4(+/-)\sqrt{36}} {-2}[/tex]

[tex]t=\frac{-4(+/-)6} {-2}[/tex]

[tex]t=\frac{-4(+)6} {-2}=-1[/tex]

[tex]t=\frac{-4(-)6} {-2}=5[/tex]

therefore

the solution is [tex]t=5\ sec[/tex]

Answer:

5 seconds

Step-by-step explanation:

ttm/imagine math

Answer:

  (1/4, ln(1/2))

Step-by-step explanation:

The slope of the given line is -1/4, so the perpendicular line will have a slope of -1/(-1/4) = 4.

The slope of the given function is its derivative:

  y' = 2/(2x) = 1/x

That will have a value of 4 when x = 1/4.

The point on the graph where the slope is 4 is (x, y) = (1/4, ln(1/2)).

Answer:

[tex](\frac{1}{4},-\ln(2))[/tex]

Step-by-step explanation:

Let's first differentiate [tex]y=\ln(2x)[/tex].

This gives us [tex]y'=\frac{(2x)'}{2x}=\frac{2}{2x}=\frac{1}{x}[/tex].  This gives us the slope of any tangent line to any point on the curve of [tex]y=\ln(2x)[/tex].

Let [tex](a,b)[/tex] be a point on [tex]y=\ln(2x)[/tex] such that the tangent line at that point is perpendicular to [tex]x+4y=1[/tex].

Let's find the slope of this perpendicular line so we can determine the slope of the tangent line. Keep in mind, that perpendicular lines (if not horizontal to vertical lines or vice versa) have opposite reciprocal slopes.

Let's begin.

[tex]x+4y=1[/tex]

Subtract [tex]x[/tex] on both sides:

[tex]4y=-x+1[/tex]

Divide both sides by 4:

[tex]y=\frac{-x}{4}+\frac{1}{4}[/tex]

The slope is -1/4.

This means the line perpendicular to it, the slope of the line we wish to find, is 4.

So we want the following to be true:

[tex]\frac{1}{x} \text{ at } x=a[/tex] to be [tex]4[/tex].

So we are going to solve the following equation:

[tex]\frac{1}{a}=4[/tex]

Multiply both sides by [tex]a[/tex]:

[tex]1=4a[/tex]

Divide both sides by 4:

[tex]\frac{1}{4}=a[/tex]

So now let's find the corresponding [tex]y[/tex]-coordinate that I called [tex]b[/tex] earlier for our particular point that we wished to find.

[tex]y=\ln(2x)[/tex] for [tex]x=a=\frac{1}{4}[/tex]:

[tex]y=\ln(2\cdot \frac{1}{4})[/tex] (this is our [tex]b[/tex])

[tex]y=\ln(\frac{1}{2})[/tex]

[tex]y=\ln(1)-\ln(2)[/tex]

[tex]y=0-\ln(2)[/tex]

[tex]y=-\ln(2)[/tex]

So the point that we wished to find is [tex](\frac{1}{4},-\ln(2))[/tex].

---------------------Verify--------------------------------

What is the line perpendicular to the tangent line to the curve [tex]y=\ln(2x)[/tex] at [tex](\frac{1}{4},-\ln(2))[/tex]?

Let's find the slope formula for our tangent lines to this curve:

[tex]y'=\frac{1}{x}[/tex]

[tex]y'=\frac{1}{x}[/tex] evaluated at [tex]x=\frac{1}{4}[/tex]:

[tex]y'=\frac{1}{\frac{1}{4}}=4[/tex]

This says the slope of this tangent line is 4.

A line perpendicular this will have slope -1/4.

So we know our line will be of the form:

[tex]y=\frac{-1}{4}x+c[/tex]

Multiply both sides by 4:

[tex]4y=-1x+4c[/tex]

Add [tex]1x[/tex] on both sides:

[tex]4y+1x=4c[/tex]

Reorder using commutative property:

[tex]1x+4y=4c[/tex]

Use multiplicative identity property:

[tex]x+4y=4c[/tex]

As we see the line is in this form. We didn't need to know about the [tex]y[/tex]-intercept,[tex]c[/tex], of this equation.

Answer:

50 mph, 450 mi, 73.3 ft/sec

Step-by-step explanation:

Part 1:

Find the unit rate (which here is mph).

 175 mi

------------- = 50 mph

3.5 hrs

Part 2:

In 8.5 hrs, the Andersons can expect to cover (50 mph)(8.5 hr) = 425 mi

Part 3:

50 mph       88 ft/sec

------------ *  ----------------- = 73.33 ft/sec, or 73.3 ft/sec to the nearest tenth.

      1              60 mph

The temperature in degrees Celsius is 20°C.

To calculate the temperature in degrees Celsius, we can use the formula:

C = 5/9 (F – 32)

Given that the temperature outside Brayden's window is 68°F, we plug this value into the formula:

C = 5/9 (68 - 32)

Now, we perform the calculations:

C = 5/9 (36)

C = (5/9) * 36

C = 20

Therefore, the temperature outside Brayden's window is 20°C.

To explain further, the formula C = 5/9 (F – 32) is used to convert Fahrenheit to Celsius. First, we subtract 32 from the Fahrenheit temperature to get the difference in scale between Celsius and Fahrenheit. Then, we multiply by 5/9 to convert the difference into Celsius. Finally, we add the Celsius symbol to indicate the temperature scale. In this case, when we apply this formula to 68°F, we find that it equals 20°C.

Complete question:

Brayden read the thermometer outside his window. It said that it was 68°F. What is the temperature in degrees Celsius? Use the formula C = 5/9 (F – 32) where C represents the temperature in degrees Celsius and F represents the temperature in degrees Fahrenheit.

The temperature in degrees Celsius is 20°C.

To convert 68°F to degrees Celsius, use the formula [tex]\( C = \frac{5}{9} \times (F - 32) \).[/tex]

Substituting 68 for  F :

[tex]\[ C = \frac{5}{9} \times (68 - 32) \][/tex]

Simplifying inside the parentheses:

 [tex]\[ 68 - 32 = 36 \][/tex]

Applying the multiplication:

[tex]\[ C = \frac{5}{9} \times 36 \][/tex]

Divide 36 by 9:

[tex]\[ C = 5 \times 4 = 20 \][/tex]

Thus, the temperature in degrees Celsius is 20°C.

Answer:

Each sweater costs $35.

Step-by-step explanation:

First subtract the total price ($160) by the price of the shirt ($20).

160 - 20 = 140

Now were left with $140. Since Katie bought 4 sweaters, divide 140 by 4.

140/4 = 35

This means that each sweater was $35. If you want to make sure this is correct just multiply 35 by 4 and then add the $20. You should end up with $160.

35 x 4 = 140

140 + 20 = 160

ANSWER

f(5)=52

EXPLANATION

The given function is

[tex]f(x) = 2 {x}^{2} + 2[/tex]

We substitute x=5 to obtain;

[tex]f(5) = 2 {(5)}^{2} + 2[/tex]

We evaluate the exponent to obtain:

[tex]f(5) = 2 (25) + 2[/tex]

We multiply out to get:

[tex]f(5) = 50 + 2[/tex]

We now simplify to get:

[tex]f(5) = 52[/tex]

Answer:

a) The minimum y-value of f(x) is -3

d) The minimum y-value of g(x) is -3

Step-by-step explanation:

Given in the question that,

f(x) = 3[tex]^{x}[/tex]-3

g(x) = 7x² - 3

At large negative exponents, the value approaches to zero

y = [tex]3^{-100}-3=-3[/tex]

y = [tex]3^{-1000}-3=-3[/tex]

y = [tex]3^{-10000}-3=-3[/tex]

Minimum y-value of g(x) will be when x = 0

y = 7x² - 3

y = 7(0) - 3

y = -3

Answer :B and D

explanation: that’s correct

Answer:

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

The experimental probability of breakage is 5 out of 100, or 0.05.

Thus, if the shipment of bulbs numbers 10,000, the expected number of broken bulbs is 0.05(10,000), or 500.

Answer:

B

Step-by-step explanation:

The surface area of this solid is the sum of all the surfaces.

There are 4 rectangular surfaces all around, each measuring 4 by 5 m.

So area of 4 of these surfaces is: 4 * (4*5)= 4 * 20 = 80

The bottom is a rectangle with dimensions 4 and 4. So area is 4 * 4 = 16

There are 4 triangular faces in the top portion, each with base 4 and height 3. Area of triangle is 1/2 * base * height. Hence,

Area of 4 of these triangles is 4*[(1/2)*4*3] = 4 * 6 = 24

Thus, the surface area = 80 + 16 + 24 = 120 m^2

Answer choice B is right.

Answer:

Would this be science?

Step-by-step explanation:

Answer:

The vertex of a quadratic equation corresponds to the point where the maximum or minimum value is located.

If the function has a positive leading coefficient, the vertex corresponds to the minimum value.

If it has a negative leading coefficient,  the vertex corresponds to the maximum valuevalue

If the vertex is located at

(–2, 0)

The possibilities are

y =  (x-2)^2

or,

y = - (x-2)^2

Since the problem tells us the answer, we adopt the positive values

Answer:

y =  (x-2)^2

See attached picture

Answer:

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

Step-by-step explanation:

A graph that is a parabola with a vertex at (–2, 0)

Vertex form of parabola equation is

[tex]y=a(x-h)^2 + k[/tex]

where (h,k) is the vertex

WE are given with vertex (-2,0)

(-2,0) is (h,k)

h=-2 and k=0

Plug the value in vertex form of equation. Lets take a=1

[tex]y=a(x-h)^2 + k[/tex]

Equation becomes [tex]y=1(x-(-2))^2 + 0[/tex]

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

To find out the total time Mrs. Winter's students spent reading, add up all the fractional hour amounts on the line plot for each student.

In this question, we are dealing with the issue of determining the total time that Mrs. Winter's students spent on reading, using a line plot that displays fractional hours. Unfortunately, without the actual line plot, we can't provide a specific numerical answer. However, the process would involve adding up all the fractional hour amounts for each student. For instance, if one student read for 1/2 hour and another for 1/3 hour, the total would be 1/2 + 1/3 = 5/6 hour. Repeat this addition process for all the students in the class to find the overall total time spent reading.

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The total time which Mrs. Winter's students spend reading last night is: A. 10 3/4 hours.

In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the information provided about the fraction of an hour, a frequency table can be computed as follows;

Hour    Frequency

1/4                 10

1/2                  9

3/4                 5

In this context, we can calculate the total amount of time as follows;

Total amount of time = 1/4(10) + 1/2(9) + 3/4(5)

Total amount of time = 10/4 + 9/2 + 15/4

Total amount of time = 10 3/4 hours.

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Answer:

1) f

4 * ¼ = 1 (Multiplicative inverse property)

2) c

6 * 1 = 6 (Identity property of multiplication)

3) h

5 + 7 = 7 + 5 (Commutative property of addition)

4) j

If 5 + 1 = 6 and 4 + 2 = 6, then 5 + 1 = 4 + 2 (Transitive property)

5) a

4(x - 3) = 4x - 12 (Distributive property)

6) i

3(5) = 5(3) (Commutative property of multiplication)

7) k

Rules that allow us to take short cuts when solving algebraic problems.(Properties)

8) d

5 * (3 * 2) = (5 * 3) * 2 (Associative property of multiplication)

9) g

4 + (-4) = 0 (Additive inverse property)

10) e

2 + 0 = 2 (Identity property of addition)

11) b

A + (B + C) = (A + B) + C (Associative property of addition)

Answer: Option D

D. 880 = 45d + 70; 18 days

Step-by-step explanation:

We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.

We also know that a total of $ 880 was paid last month

To write an equation that represents this situation, let us call d the number of days that Barry attends school

So the cost was:

[tex]45d + 70 = 880[/tex]

Now we solve the equation for the variable d

[tex]45d= 880-70[/tex]

[tex]45d= 810[/tex]

[tex]d= \frac{810}{45}[/tex]

[tex]d= 18\ days[/tex]

The answer is the option D

Answer:

a difference of two squares

Step-by-step explanation:

Note that 36 − 16 is a difference of two squares:  6^2 - 4^2.

Answer:

a) [tex]S_n=(0.4+0.1n)n[/tex]

b) 15

Step-by-step explanation:

The first time Miguel trains, he runs 0.5 mile, so [tex]a_1=0.5[/tex]

Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time, so [tex]d=0.2[/tex]

Use the formula for nth term of arithmetic sequence

[tex]a_n=a_1+(n-1)d\\ \\a_n=0.5+0.2(n-1)=0.5+0.2n-0.2=0.3+0.2n[/tex]

a) The sum of n terms of the arithmetic sequence is

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_n=\dfrac{0.5+0.3+0.2n}{2}\cdot n=(0.4+0.1n)n[/tex]

b) A marathon is 26.2 miles, then

[tex](0.4+0.1n)n\ge 26.2\\ \\0.1n^2+0.4n-26.2\ge 0\\ \\n^2+4n-262\ge 0\\ \\D=4^2-4\cdot (-262)=16+1048=1064\\ \\n_{1,2}=\dfrac{-4\pm\sqrt{1064}}{2}=-2\pm \sqrt{266} \\ \\n\in (-\infty,-2-\sqrt{266}]\cup[-2+\sqrt{266},\infty)[/tex]

Since n is positive and [tex]\sqrt{266}\approx 16.31[/tex], the least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon is -2+17=15

Answer:

A) the bottom left is the correct answer (0.3+0.2k)

B) 15 times

Step-by-step explanation

Answer:

604

Step-by-step explanation:

"Top 15%" corresponds to the rightmost area under the standard normal curve to the right of the mean.  That means 85% of the area under this curve will be to the left.  Which z-score corresponds to the area 0.85 to the left?

Using a calculator (invNorm), find this z-score:  invNorm(0.85) = 1.0346.

Which raw score corresponds to this z-score?

Recall the formula for the z-score:

       x - mean

z = ------------------

         std. dev.

Here we have:

       x - 500

z = ------------------ - 1.0364, or x - 500 = 103.64.  Then the minimum score

          100                necessary to be in the top 15% of the scores is

                                  found by adding 500 to both sides:

                                   x = 603.64

Minimum score necessary to be in the top 15% of the SAT scores is 604.

The middle 80% of the distribution ranges from 372 to 628.

The SAT scores form a normal distribution with a mean (")") of 500 and a standard deviation (")") of 100. We need to find:

1. Minimum Score to be in the Top 15%

X = μ + zσ

Calculating the SAT Score:

So, X = 500 + 1.04 * 100 = 604. Therefore, the minimum score necessary to be in the top 15% is 604.

2. Range of Values for the Middle 80%

From a z-score table, the z-scores are approximately -1.28 and +1.28.

X_low = μ + (-1.28)σ  and X_high = μ + 1.28σ

Calculating the Range:

So, the range of scores that define the middle 80% is 372 to 628.

Answer:

y = 32.0°

Step-by-step explanation:

Using the sine ratio in the right triangle

siny° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{17}[/tex], hence

y = [tex]sin^{-1}[/tex] ([tex]\frac{9}{17}[/tex] ) ≈ 32.0°