The mean score for a math test taken by Class A is 84, with the scores ranging from 78 to 94. The mean score for the same math test taken by Class B is 76, with the scores ranging from 68 to 88. Which BEST compares the scores of the two classes?
A) The highest score for the test was in Class B.
B) On average, the scores of Class A are lower than Class B.
C) On average, the scores of Class B are lower than Class A.
D) The scores of Class A vary more than the scores of Class B.
D) 22

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Work Shown:

Straight lines DF and EC intersect at point A. Because of this, angle DAF is a 180 degree angle.

Angles DAB, BAC, and CAF all combine to form a straight 180 degree angle.

Add up the angles mentioned, set the sum equal to 180, and solve for x

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(angle DAB) + (angle BAC) + (angle CAF) = 180

x + 80 + 60 = 180

x + 140 = 180

x + 140-140 = 180-140 ... subtract 140 from both sides

x = 40

Answer:

[tex]\Huge \boxed{x=40\°}[/tex]

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

We can create an equation and solve for x.

x + 80 + 60 = 180

Add the numbers on the left side.

x + 140 = 180

Subtract 140 from both sides.

x + 140 - 140 = 180 - 140

x = 40

Answer:

------->

Step-by-step explanation:

corresponding parts - angles or sides in the same position on similar figures

congruent - having the same exact size and shape

similar figures - figures that have the same shape but not necessarily the same size

congruent figures - figures that have the same size and shape

scale factor - the ratio between the lengths of corresponding sides in similar figures

Answer:

"statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = [tex]4x[/tex]

Let, Number of girls = [tex]5x[/tex]

Total number of students = Number of boys + Number of girls = 270

[tex]\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}[/tex]

Therefore, number of boys = 4 [tex]\times[/tex] 30 = 120

And, number of girls = 5 [tex]\times[/tex] 30 = 150

As per Statement 1:

Finding [tex]\frac{4}5[/tex] of the number of girls:

[tex]\dfrac{4}{5}\times 150 = 4 \times 30 = 120[/tex] = Number of boys.

Finding [tex]\frac{4}9[/tex] of the total number of students:

[tex]\frac{4}{9}\times 270= 4 \times 30 = 120[/tex] = Number of boys.

Number of boys is equal to [tex]\frac{4}9[/tex] of total number of students.

So, "statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.

Answer:

2x/3 - 5 = 21

2x/3 = 26

2x = 78

x = 39

Step-by-step explanation:

Answer:

x = 39

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

To make m the subject send n to the left side of the equation

That's

Divide both sides by 5

We have

Find the square root of both sides to make m stand alone

That's

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

r = 5m² - n

Add n to both sides

r + n = 5m² - n +n

r + n = 5m²

Divide both sides by 5

(r+n)/5 = 5m²/5

(r + n)/5 = m²

Take square root ,

[tex]\sqrt{\frac{r + n}{5}} =\sqrt{m^{2}} \\\\\sqrt{\frac{r + n}{5}}=m\\\\\\m=\sqrt{\frac{r + n}{5}}[/tex]

Answer:

4

Step-by-step explanation:

- and - become +

so, -12 + 8 = -4

but we remove the minus and make it a positive 4

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{10 {x}^{2} - 8x + 8}}}}}[/tex]

Option A is the correct option

Step-by-step explanation:

[tex] \sf{8 {x}^{2} + x - 5 + (2 {x}^{2} - 9x + 13)}[/tex]

When there is a ( + ) in front of an expression in parentheses , there is no need to change the sign of each term.

That means, the expression remains the same.

Also, Remove the unnecessary bracket

⇒[tex] \sf{8 {x}^{2} + x - 5 + 2 {x}^{2} - 9x + 13}[/tex]

Collect like terms

⇒[tex] \sf{8 {x}^{2} + 2 {x}^{2} + x - 9x - 5 + 13}[/tex]

⇒[tex] \sf{10 {x}^{2} - 8x - 5 + 13}[/tex]

Calculate

⇒[tex] \sf{10 {x}^{2} - 8x + 8}[/tex]

Hope I helped!

Best regards!!

The answer to the question is 46

Answer:

2+2y

Step-by-step explanation:

20=2(y-6)+10

20= (2×y-2×6)+10

20= (2y-12)+10

Open the bracket

20=2y-12+10

Collect liked terms

20=12+10+2y

20=22+2y

=22-20+2y

2+2y

Hope this helps

Comment for more explanation

Answer:

In the problem, the sum of the two functions is 2x + 2

Step-by-step explanation:

For this problem, we have to add together f(x) and g(x).

f(x) = 9 - 3x

g(x) = 5x - 7

(f + g)(x) = (9 - 3x) + (5x - 7)

Combine like terms.

(f + g)(x) = 2x + 2

So, when you combine the two functions together, you will get 2x + 2.

The value of f(x)+g(x) according to the question given is; 2x + 2.

To evaluate the sum of functions f(x) and g(x); we have;

Therefore;

Read more on addition:

https://brainly.com/question/1397278

Answer:

B. Sen α = BC/b

Step-by-step explanation:

Para un ángulo recto, el lado opuesto es el lado opuesto al ángulo, el lado adyacente es el lado entre el ángulo y el ángulo recto y la hipotenusa es el lado más largo (el lado opuesto al ángulo recto).

De identidades trigonométricas:

[tex]sen\ \alpha=\frac{opuesto}{hipotenusa}[/tex]

De la figura, el lado opuesto = altura = BC y la hipotenusa = b. Por lo tanto:

[tex]sen\ \alpha=\frac{opuesto}{hipotenusa}\\\\sen\ \alpha=\frac{BC}{b}[/tex]

Answer:ok

Step-by-step explanation:wow

Answer:

y = ½x + ¾

slope (m) = ½

y-intercept(b) = ¾

Step-by-step explanation:

4y - 2x = 3

4y = 2x + 3

y = (2x + 3) ÷ 4

y = 2/4x + 3/4

y = ½x + ¾

slope (m) = ½

y-intercept(b) = ¾

Answer:

7√2

Step-by-step explanation:

Knowing that the angle is 45° (or π/4 radians) and the opposite leg has a length of 7,  you can find the length of b with:

7 / b = sin(π / 4)

7 / (sin(π / 4)) = b

b = 7 / (1 / √2)

b =7√2

A simpler way to get the answer is to note that a right triangle with one 45° angle must be an isoceles right triangle, so both legs are the same length. Using the Pythagorean Theorem:

a² + 7² = b²

Since we know a = 7,

7² + 7² = b²

b = √(2 * 49)

b = 7√2

Answer:

24

Step-by-step explanation:

Answer:

they are equivalent

Step-by-step explanation:

[tex]\frac{3}{6} = \frac{1}{2} (both \: can \: be \: divide \: by \: 3)[/tex]

[tex] \frac{4}{8} = \frac{1}{2} (both \: can \: be \: divide \: by \: 4)[/tex]

The two (2) fractions are equivalent.

In this exercise, you're required to determine whether or not given fractions are equivalent (equal). In order to do this, we would reduce the fractions to the lowest term.

Given the following fractions;

For Fraction A, we would divide both the numerator and the denominator by 3 because it's common to both them.

Fraction A = [tex]\frac{3}{6} = \frac{1}{2}[/tex]

Simplifying Fraction B, we have;

Fraction B = [tex]\frac{4}{8} = \frac{1}{2}[/tex]

Also, for two (2) fractions to be equivalent, their sums must be equal to one (1).

[tex]Fraction \;A + Fraction \;B = 1[/tex]

[tex]\frac{1}{2} + \frac{1}{2} = 1[/tex]

Therefore, we can deduce from the calculations that the two (2) fractions are equivalent.

Find more information: https://brainly.com/question/14748058

Answer:

√ is 10

Step-by-step explanation:

it is a number less then zero

Answer:

a negative number is when a number exceeds below zero

for example 7 --8 would be -1

Answer:

DIVISION PROPERTY OF EQUALITY

Step-by-step explanation:

Given the equation r4 = 16,wm we can rewrite the equation as 4r = 16

The coefficient at the left hand side of the equation that we are to move to rge right is 4 (the number attached to the r variable). To do this we are going to apply the Division property of equality. This property is a property where both sides of an equation is divided through by the same constant without affecting the equality sign or by still keeping the equation.

To move the coefficient of r to the other side, we will divide both sides of the equation by 4 as shown;

4r/4 = 16/4

r = 4×4/4

r = 4

Hence the property that is used to move the coefficient (4) to the other side of the equation is the DIVISION PROPERTY OF EQUALITY.

Answer:

10

Step-by-step explanation:

Remove parentheses.

|9+1|

Simplify  9+1  to 10.

|10|

simplify

10

Answer:

89 , 91

Step-by-step explanation:

let one be x and the other be x+2

Supplementary angles are those angles that sum up to [tex]180^{o}[/tex]

equating both sides

x+x+2 = 180

2x+2 = 180

2x = 180-2

2x = 178

x = 89

x+2 = 89+2 = 91

Answer:

its a.

Step-by-step explanation:

Answer:

(-8)/27

Step-by-step explanation:

Simplify the following:

(-2)/(3 (2 + 1/4))

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

(-2)/(3 (4×2)/4 + 1/4)

4×2 = 8:

(-2)/(3 (8/4 + 1/4))

8/4 + 1/4 = (8 + 1)/4:

(-2)/(3 (8 + 1)/4)

8 + 1 = 9:

((-2)/3)/(9/4)

Multiply the numerator by the reciprocal of the denominator, ((-2)/3)/(9/4) = (-2)/3×4/9:

(-2×4)/(3×9)

3×9 = 27:

(-2×4)/27

-2×4 = -8:

Answer: (-8)/27

Answer:

-8/27

Step-by-step explanation:

-2/3 ÷ 2  1/4

Change to an improper fraction

-2/3 ÷ ( 4*2+1)/4

-2/3 ÷9/4

Copy dot flip

-2/3 * 4/9

-8/27

The U shape is called a parabola

If the "a" is positive, then the parabola opens upward as shown in the graph on the left.

If "a" is negative, then the parabola opens downward. This is the parabola on the right.

The way I remember is that "a" being positive means it puts a smile on, which is what the parabola on the left resembles. The parabola on the right is a frowny face so "a" is negative.

A parabola is vertically cut in half by the axis of symmetry. One half mirrors over this vertical line to get the other half. The axis of symmetry passes through the vertex. The vertex is either the highest point or the lowest point depending on whether 'a' is negative or positive.

Answer: 1/4

Step-by-step explanation: In algebra, we use the word slope to describe how steep a line is and slope can be found using the ratio rise/run between any two points that are on that line.

So for the line you see here, let's use these two points to find its slope.

Let's go from left to right.

To get from the point that has the coordinates (0,1) to (4,2),

we rise 1 unit and run 4 units to the right and we end up the other point.

So the slope of this line is 1/4.

Answer:

-2 + 9i

Step-by-step explanation:

( 3 + 2i ) + ( -5 + 7i )

→ Remove brackets

3 + 2i +- 5 + 7i

→ Remember that the negative cancels out the plus

3 + 2i - 5 + 7i

→ Add the whole numbers together

-2 + 2i + 7i

→ Add the i values together

-2 + 9i

Answer:

[tex]\huge\boxed{-2 + 9i}[/tex]

Step-by-step explanation:

[tex]\sf (3+2i)+(-5+7i)\\Expanding \ Parenthsis\\3+2i -5 +7i\\Combining \ like \ terms\\3-5 + 2i+7i\\-2 + 9i[/tex]

This is the required answer in the form a + b i

Answer:

Height of the cliff = 13.66 m

Step-by-step explanation:

Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.

From right triangle AOC,

tan 30° = [tex]\frac{\text{Opposite triangle}}{\text{Adjacent side}}[/tex]

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

y = [tex]x\sqrt{3}[/tex] ------(1)

From right angle triangle BOC,

tan 45° = [tex]\frac{x}{y-10}[/tex]

[tex]1=\frac{x}{y-10}[/tex]

x = y - 10

y = x + 10 -------(2)

From equations (1) and (2),

[tex]x\sqrt{3}=x+10[/tex]

[tex]x(\sqrt{3}-1)=10[/tex]

[tex]x=\frac{10}{\sqrt{3}-1 }[/tex]

x = 13.66 m

Therefore, height of the cliff is 13.66 m.

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Explanation:

To go from term to term, we are multiplying by 2

-7 * 2 = -14

-14 * 2 = -28

-28 * 2 = -56

This means the common ratio is 2 and this sequence is geometric.

---------

Alternatively, you can divide each term by its prior term

-56/(-28) = 2

-28/(-14) = 2

-14/(-7) = 2

Each time we get the same result showing the common ratio is 2.

Answer:

Geometric

Step-by-step explanation:

It multiplies by two each time

Answer:

6 ducks

Step-by-step explanation:

Monday, Brian counted 28 ducks and Cathy counted 15 ducks

                = 28+15 =43

Tuesday, they counted 37

Monday count - Tuesday count

43 - 37 =6