A university record search of 250 incoming freshmen
at a state university shows that 26 had received college
credit for science courses but not math courses,
and 12 had received college credit for math but not
science. There were 202 that had not received college
credit for either.
a. How many of the students had received college credit for math?
b. How many had received credit for science courses?

Answer:

x = 24, x = -16

Step-by-step explanation:

Given the function f(x) = 0.5|x – 4| – 3, we are to find the values of x for f(x) = 7

Substitute f(x) = 7 into the expression;

7 = 0.5|x – 4| – 3

For the positive function

7 = 0.5(x – 4) – 3

7 = 0.5x - 2 - 3

7 = 0.5x - 5

7+5 = 0.5x

12 = 0.5x

12 = x/2

Swap

x/2 = 12

x = 12 * 2

x = 24

For the negative function

7 = 0.5-(x – 4) – 3

7 = 0.5(-x +4) - 3

7 = -0.5x +2 - 3

7 = -0.5x - 1

7+1 = -0.5x

8 = -x/2

Swap

-x/2 = 8

-x = 8 * 2

-x = 16

x = -16

Hence the required values of x are -16 and 24

Answer:

[tex]50 \pi \: sq \: ft.[/tex]

Explanation:

as we can see that the sector bounded by the 180° arc is a semi- circle

area of a circle =

[tex]\pi {r}^{2} [/tex]

area of semi circle =

[tex] \\ \frac{\pi {r}^{2} }{2} [/tex]

[tex] = \frac{\pi {10}^{2} }{2} \\ = 50\pi[/tex]

Answer:

[tex](a)\ y = -0.75x + 26[/tex]

[tex](b)\ y = 14.75[/tex]

Step-by-step explanation:

Given

See attachment for scatter plot

Required

Equation of the line of best fit

Pick any two points on the line

[tex](x_1,y_1) = (24,8)[/tex]

[tex](x_2,y_2) = (8,20)[/tex]

Calculate the slope (m)

[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]

[tex]m =\frac{20-8}{8-24}[/tex]

[tex]m =\frac{12}{-16}[/tex]

[tex]m =-0.75[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = -0.75(x - 24) + 8[/tex]

[tex]y = -0.75x + 18 + 8[/tex]

[tex]y = -0.75x + 26[/tex]

Solving (b): y, when [tex]x = 15[/tex]

[tex]y = -0.75x + 26[/tex] becomes

[tex]y = -0.75*15 + 26[/tex]

[tex]y = -11.25 + 26[/tex]

[tex]y = 14.75[/tex]

Answer:

The answer is "The decimal could be five-tenths".

Step-by-step explanation:

Given value:

[tex]\to 67.5 \times 4. \_= \_ .50[/tex]

Let the decimal value is: (2)

[tex]\to 67.5 \times 4. 2= 283 .50[/tex]

Step-by-step explanation:

The area of a square is given by :

A = a²

Where

a is the side of the square

For square A, Area = 64 sq units

64 = a²

a = 8 units

For square B, Area = 30 sq units

30 = a²

a = [tex]\sqrt{30}[/tex] units

For square C, Side length = 14 units

A = 14²

A = 196 sq units

For square D, Side length =  [tex]\sqrt{30}[/tex] units

A = [tex](\sqrt{30})^2[/tex]²

A = 30 sq units

Hence, this is the required solution.

Answer:

MP = RS 7,800

Step-by-step explanation:

Let

Marked price = MP

MP x (100 – 15) / 100 = Rs 6,630

MP × (85)/100 = Rs 6,630

MP = Rs 6,630 ÷ 85/100

MP = 6,630 × 100/85

MP = 663,000/85

MP = 7,800

MP = RS 7,800

Answer:

The tower is approximately 57.34 meters long

Step-by-step explanation:

The given parameters are;

The type of triangle formed by ΔABC = Non-right triangle

The measure of ∠ACB = 55°

The horizontal displacement of the tower, BX = 5 m

The length of BC = 45 m

Therefore, we have;

Triangle ΔABC type = Right triangle

By the tangent to an acute angle, θ, in a right triangle, we have;

[tex]Tan(\theta) = \dfrac{Opposite \, side \ length}{Adjacent\, side \ length}[/tex]

Where θ is the 55°, we have angle, we have;

[tex]Tan(55^{\circ}) = \dfrac{XA}{XC}[/tex]

BC = BX + XC

∴ XC = BC - BX

XC = 45 m - 5 m = 40 m

[tex]\therefore Tan(55^{\circ}) = \dfrac{XA}{40}[/tex]

XA = 40 × tan(55°) ≈ 57.126

The type of triangle formed by ΔABX = Right triangle

According to Pythagoras theorem, AB² = XA² + BX²

∴ AB = √((40 × tan(55°))² + 5²) ≈ 57.34

The length of the tower, AB ≈ 57.34 m

Answer:

x ≈ 52.6°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{17}{28}[/tex] , then

x = [tex]cos^{-1}[/tex] ([tex]\frac{17}{28}[/tex] ) ≈ 52.6° ( to the nearest tenth )

Answer:

16. 8/x

17. 8x

18. 4x⁴/y³ (not clear)

19. 16x^8

20. 256 R⁴

21. 64x^6

22. 81x^8

23. 1/ 3x

24. 5x

25. 1

Answers:

=====================================================

Explanation:

The diagrams for problems 7 and 8 are shown below.

------------------------------------

Problem 7

Apply the tangent ratio to find that...

tan(angle) = opposite/adjacent

tan(42) = x/28

28*tan(42) = x

x = 28*tan(42)

x = 25.2113132403396

x = 25.2

Make sure your calculator is in degree mode. One way to check is to type in tan(45) and you should get 1 as a result.

------------------------------------

Problem 8, part 1

To find the angle y, we must use the sine ratio

sin(angle) = opposite/hypotenuse

sin(y) = 18/23

y = arcsin(18/23)

y = 51.5000495907521

y = 52 degrees approximately

------------------------------------

Problem 8, part 2

We can use the pythagorean theorem to find the missing side x

a^2+b^2 = c^2

18^2+x^2 = 23^2

324+x^2 = 529

x^2 = 529-324

x^2 = 205

x = sqrt(205)

x = 14.3178210632763

x = 14.3

Or alternatively, we can apply the tangent ratio on the angle y we found earlier to help find x

tan(angle) = opposite/adjacent

tan(y) = 18/x

tan(51.50004959) = 18/x

x*tan(51.50004959) = 18

x = 18/tan(51.50004959)

x = 14.3178210636621

x = 14.3

------------------------------------

Problem 9

The double tickmarks show that BE = EC = 10. That means BC = BE+EC = 10+10 = 20.

Since we have similar triangles, we can solve for x like so

DE/AC = BE/BC

x/44 = 10/20

20x = 44*10

20x = 440

x = 440/20

x = 22

So DE is 22 units long. Note how this is half as long as the side AC = 44.

Answer:

Step-by-step explanation:

Hope this helps u !!

a³ + b³ + c³ + 3abc = ( a + b + c)(a² + b² + c² + ab + bc + ca)

if a + b + c = 0. then a³ + b³ + c³ = 3abc

here a + b + c = 15 + (-9) + (-6)

a + b + c = 15 - 15

a + b + c = 0

so a³ + b³ + c³ = 3abc

15³ + (-9)³ + (-6)³ = 3(15)(-9)(-6)

= 2430

so the answer is 2430

Answer: 1.28 cups of water per cup of milk

Step-by-step explanation:

0.8 divided by 5/8 equals 1.28

verified by my teacher :)

Answer:

6.4 meters per second

Step-by-step explanation:

Sarah the cheetah ran 100 meters at a speed of 16.8 meters per second. An olympian ran the 100-meter dash in 9.6 seconds. How much faster was Sarah the cheetah’s speed, to the nearest tenth of a meter per second?

0.9 meters per second

1.6 meters per second

6.4 meters per second

10.4 meters per second

Speed = distance / time

Olympian's speed = 100 / 9.6 = 10.4 meters per second

Sarah's speed = 16.8 meters per second.

Difference in speed = 16.8 - 10.4 = 6.4

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Answer:

Starting from

2(-x) = 3x - 5

Distribute

-2x = 3x - 5

add 2x to both sides

0 = 5x - 5

Add 5 to both side

5 = 5x

Flip

5x = 5

Answer:

x = 37 y = 27

Step-by-step explanation:

x = y + 10

x + y = 64

y + 10 + y = 64

y = 27

64 - 27 = 37

Answer:

What coatside dad said

Step-by-step explanation:

Answer:

5x-20=3x(alternate angle)

5x-3x=20

2x=20

x=20/2

x=10

now ,

2y +4y+5x-20=180(sum of angles of a triangle)

6y+50-20=180

6y+30=180

6y=180-30=150

y=150/6

y=25

hope this will help

Answer:

40%

Step-by-step explanation:

Amount of money discounted

= $40 - $24

= $16

Percentage of discounted money

= 16/40 x 100%

= 40%

Answer:

Step-by-step explanation:

it has a 50/50 chance if it lands on tailes it is 50/50

Answer:

C. It is shifted 4 units down.

Step-by-step explanation:

Shifted four units down. When a number is at the end of the equation, it means that that number shifts up or down depending on its sign.  

Answer:

It is shifted 4 units down

Step-by-step explanation:

When we have a function the constant number that is not multiplied by a variable, in this case, 4 in the first function, indicates where the function will intercept the y-axis, or when x is equal to 0.

In this case, we have two functions:

y = 5x^2 - 4, in which -4 is the constant that will determine where the function intercepts the y-axis. So if we say that we have x=0, then y=-4

In the second function we have:

y= 5x^2, this function is very similar but we don´t have another number after 5x^2, so we will have a similar graph but when x = 0 then y = 0.

So the first graph is shifted 4 units down. We can see this in the attachment.

It shifted 4 u it’s to the left

It is shifted 4 units to the left.

Answer:

[tex](180-73)=z+114/2[/tex]

[tex]107*2=z+114[/tex]

[tex]z=214-114[/tex]

[tex]z=100[/tex]

❄ B. 100

------------------------

hope it helps...

have a great day!!

In the given circle in which angles are 73°,96°,114° then the value of z is equal to 100 which is option b.

Circle is a shape consisting fall points in a plane thata are at a given distance from a given distance from a given point which is the centre of the circle.

In the circle we can see the following:

(180-73)=(z+114)/2

107*2=z+114

214=z+114

z=214-114

=100

Hence in the given circle in which angles are 73°,96°,114° then the value of z is equal to 100 which is option b.

Learn more about angles at https://brainly.com/question/25716982

#SPJ2

Answer:

[tex]\frac{x}{3} + \frac{1}{1} = \frac{x+3}{3}[/tex]

Step-by-step explanation:

[tex]\frac{x}{3} + \frac{1}{1} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ LCM \ of \ 1 , 3 = 3 \ ]\\\\= \frac{x}{3} + \frac{1 \times 3}{1 \times 3} \\\\= \frac{x}{3} + \frac{3}{3}\\\\=\frac{x+ 3}{3} \\\\[/tex]

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is :

To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation g = 748u, where g is the total number of gallons of water used and u is the number of units. Determine which statements about the relationship are true. Check all that apply.

g is the dependent variable.

u is the dependent variable.

g is the independent variable.

u is the independent variable.

The variables cannot be labeled without a table of values.

The variables cannot be labeled since any value can be selected for either

Solution :

Given equation :

g = 748 u

Here, g = total number of gallons of water used

         u = number of units

Customers uses the number of units of water.

The unit of water is independent of the total number of gallons of water used.

So the number of units u is an independent variable.

But the value of gallons of water depends on the number of units that is used.

Therefore, number of gallons of water g is a dependent variable.

Thus, we can say that :

Answer:

1/4

Step-by-step explanation:

Let a₁, a₂, a₃ and a₄ be the four numbers. Since the geometric mean of the first 3 positive numbers is 4, we have that

∛(a₁a₂a₃) = 4. (1)

Also the geometric mean of the four numbers is 2, we have that ⁴√(a₁a₂a₃a₄) = 2   (2).

So, taking the cube of (1), we have

[∛(a₁a₂a₃)]³ = 4³

a₁a₂a₃ = 64  (3)

Also, taking the fourth power of equation (2), we have

[⁴√(a₁a₂a₃a₄)]⁴ = 2⁴  

a₁a₂a₃a₄ = 16  (4)

Dividing (4) by (3), we have

a₁a₂a₃a₄/a₁a₂a₃ = 16/64

a₄ = 1/4

The fourth value is 1/4

Answer:

b=112°

Step-by-step explanation:

two complementary angles

b=180°-68°=112°

sum of 2 angles is

x= 35°+25°=60°

Answer:

3. b=112

4. x = 60

Step-by-step explanation:

3.

b is equal to 112 since 68+b will be equal to a supplementary angle; an angle that adds up to 180. 180-68 is equal to 112.

4.

35+25 = 60, therefore x = 60.

Answer:

All shapes except the cone with 5in radius and 8in height

Step-by-step explanation:

Volume of the cylinder with radius 5in and height 8in is expressed as;

V = πr²h

V = 3.14*5²*8

V = 3.14*25*8

V = 628 square inches

The volume of the cylinder is greater than 500in³

Volume of the cone with radius 5in and height 24in is expressed as;

V = 1/3πr²h

V = 1/3*3.14*5²*24

V = 3.14*25*8

V = 628 square inches

The volume of the cone is greater than 500in³

Volume of the spheree with radius 5in is expressed as;

V = 4/3πr³

V = 4/3π(5)³

V = 4/3 * 3.14 * 125

V = 523.33 square inches

The volume of the sphere is greater than 500in³

Answer:

What are the statements?

Step-by-step explanation:

You have to list the statements.

Answer:

You wrote the question wrong...

m is not -16 it is -1/6 (that is a big difference)

y=mx+b

y=-1/6x+b

3 = -1/6(12) + b

3 = -2 + b

b=5

Step-by-step explanation:

Answer:

DE = AE - AD

=> DE = 18.5 - 15.5 = 3

CD = CE - DE = 8 - 3 = 5