A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the following grouped frequency distribution. What is
the class width?
The class width is

Figure 1 is representing a right-angle triangle and figure 2 is representing the isosceles triangle.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given diagram in the question,

For figure 1.

It is a right-angle triangle because it contains an angle of 90°.

For figure 2.

It is an isosceles triangle because according to the figure its two sides are the same which indicates that it is an isosceles triangle.

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Answer: The answer is y=10.

Step-by-step explanation:

4y + 10 = -10 + 6y First subtract 4y from both sides.

10 = -10 + 2y Then, add 10 to both sides.

20 = 2y Finally, divide both sides by 2.

y = 10.

The amount of carbon dioxide will you prevent from entering the atmosphere in one year is 280028 lb

We are given 1.37 pounds of carbon dioxide per kWh

Using a 100-watt light bulb daily for 8 hours, for a year, the amount of carbon dioxide produced will be:

100 × 1.37 × 8 ×365 = 400040 lb

Using a 30-watt CFL bulb for 8hrs/ day for a year, the amount of carbon dioxide produced will be:

30× 1.37 × 8 × 365 = 120012 lb

Therefore, carbon dioxide prevented:

= 400040-120012

= 280028 lb

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Supplementary angles are angles that have a sum of 180 degrees. They are formed on a straight line.

Looking at the given diagram, we can notice how angle SUV and SUT are supplementary angles. We know this because they form the straight line, VT.

We are given angle SUT, which is 58 degrees.

Because angles SUV and SUT have a sum of 180 degrees, we can solve for angle SUV by subtracting 58 from 180:

180 - 58 = 122

Therefore, angle SUV is 122 degrees.

122 degrees

Answer:

Angle SUV = 180 - 58

= 122° (adjacent angles on a straight line)

Answer:

= -0.4

Step-by-step explanation:

3d-4 when d=1.2

3(1.2) - 4

3.6 - 4

= -0.4

Answer: 0.4

Step-by-step explanation:

Equation: 3d - 4

1. Substitute the variable with the given number (d = 1.2)

3(1.2) - 4

2. Solve 3 × 1.2

3.6 - 4

3. Solve

3.6 - 4 = -0.4

The value of x is 15 if the expression is  1/2x−5=10−3/4x after applying the arithmetic operation.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

1/2x−5=10−3/4x

After solving:

5x/4 = 15

5x = 60

x = 60/5

x = 12

Thus, the value of x is 15 if the expression is  1/2x−5=10−3/4x after applying the arithmetic operation.

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The wire used for the triangular pendant can have a cost more than 664.65 USD and less than 791.25 USD.

In this problem we find the case of a triangle, in which the length of two sides are known and we need to determine the range of costs associated to the set of all possible triangles. This can be derived by the geometric system described in the image attached below. The minimum and the maximum costs of the pendant:

θ = 0°

l = 10.5 cm - 2.5 cm

l = 8 cm

s = 10.5 cm + 8 cm + 2.5 cm

s = 21 cm

C = (31.65 USD / cm) · (21 cm)

C = 664.65 USD

θ = 180°

l = 10.5 cm + 2.5 cm

l = 13 cm

s = 10.5 cm + 2.5 cm + 12.5 cm

s = 25 cm

C = (31.65 USD / cm) · (25 cm)

C = 791.25 USD

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If the population grows 3% every year, then each year's population is 103% of the previous year's population.  This gives us the exponential function:    

        [tex]f(x) = 17000 (1.03)^x[/tex]

17000 for the current population, 1.03 growth factor for the 103%, raised to the x power because we'll need 103% of 103% of 103% and so on until we multiply by 103% for the correct number of years.

[tex]f(10) = 17000(1.03)^{10} \approx 22846.578448850072648[/tex]

Following standard math rounding this would round to 22,847 people.  

If you argue that last 0.57844 of a person really round up, you could argue that this is really 22,846 people.

The solution to the inequality r - 6 > −11 will be r > -5.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information, the solution to the inequality r - 6 > −11 will be solved thus:

r - 6 > −11

Collect the like terms

r > - 11 + 6

r > -5

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Answer:

Negative slope of 3 so -3x and -9y

Step-by-step explanation:

-3x=-9y

Answer:

slope = -3 ; y- intercept = (0,-9)

Step-by-step explanation:

A (-3,0)

B(0,-9)

slope = (-9-0)/(0-(-3)

-9/3

-3

The evaluated expression of 24 / b + 8 when b = 9 is [tex]10\frac{2}{3}[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) .

In other words, an expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

Therefore, let's evaluate 24 / b + 8 when b = 9

Hence,

[tex]\frac{24}{9}+8 = \frac{24+ 72}{9}=\frac{96}{9} = 10\frac{6}{9}=10\frac{2}{3}[/tex]

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Hence, the solution is [tex]-11[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

[tex]5(2x - 1) - 11x[/tex]

When [tex]x=6[/tex]

[tex]5(2x-1)-11x=5(2(6)-1)-11(6)\\=5(12-1)-66\\=5(11)-66\\=55-66\\=-11[/tex]

Hence, the solution is [tex]-11[/tex].

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The equation of the line with y - intercept (0, 6) is [tex]y = -\frac{3}{2}x + 6[/tex].

What is tangent?

The straight line that "just touches" the curve at a given point is referred to as the tangent line to a plane curve in geometry. It was defined by Leibniz as the path connecting two points on a curve that are infinitely close together.

Given:

Graph is a parabola tangent to the x-axis at (4,0) with y-intercept 6.

That is there are two points (4, 0) and (0, 6).

From these two points we have to find the slope of the line.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{0-6}{4-0} = -\frac{6}{4} = -\frac{3}{2}[/tex]

Now to use point slope form of the line.

[tex]y-y_1 = m(x-x_1)\\ y - 6 = -\frac{3}{2}(x-0)\\ y - 6 = -\frac{3}{2}x\\ y = -\frac{3}{2}x + 6[/tex]

Hence, the equation of line is, [tex]y = -\frac{3}{2}x + 6[/tex].

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The age of the paint is 14,290.0 years old

For any particular drug, understanding the concept of half-life is helpful in calculating steady-state concentrations and excretion rates. Although different drugs have different half-lives, they all adhere to the same principle: 50% of the initial drug dose is eliminated from the body after one half-life.

Since radiocarbon (14C) has a half-life of 5700 30 years, it is especially helpful for dating in archaeology. However, the so-called Gamow-Teller ß-decay, an exceptional hindrance to the beta decay from 14C to 14N, is what causes this half-life to be so long.

According to the given question :-

0.18 = e^(-0.00012t)

ln(0.18) = -0.00012t

t = - ln(0.18) / 0.00012 ≈ 14289.98690076605833 ≈ 14,290.0 years old

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[tex]\begin{array}{ccll} books&\$\\ \cline{1-2} 12 & 8\\ 3& x \end{array} \implies \cfrac{12}{3}~~=~~\cfrac{8}{x} \\\\\\ 4 ~~=~~ \cfrac{ 8 }{ x }\implies 4x=8\implies x=\cfrac{8}{4}\implies x=2[/tex]

Answer:

2$

Step-by-step explanation:

If 12 paperback books could be purchased for 8$,

We need to divide by 4 on each side to find the answer.

Therefore, 3 paperback books costs 2$.

I would appreciate it if you mark my answer as brainliest.

a) If the sum of the square of the larger side is smaller than the squares of          the shorter sides, then the triangle is an acute triangle.

b) To determine if a triangle is a right triangle.

c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Given,Pictures

According to the  converse of the Pythagorean Theorem.

a) If the sum of the square of the larger side is smaller than the squares of          the shorter sides, then the triangle is an acute triangle.

b) To determine if a triangle is a right triangle.

c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.

Therefore,

a) If the sum of the square of the larger side is smaller than the squares of          the shorter sides, then the triangle is an acute triangle.

b) To determine if a triangle is a right triangle.

c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.

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The amount will be $6660 after 3 years. It can be solved by the cocept of the compound interest.

What is compound interest?

In compound interest, the interest is added in the principal amount after the end of each term. The value after addition the interest is considered as the principal amount for the next term.

The annual interest is 5.2% hence, monthaly interest will be 5.2\12%

Apply the formula of conpound interest.

[tex]A=P(1+\frac{r}{100})^t[/tex]

Here, A is the total amount after the end of time period t, P is the initial amount, and r is the rate of intrest at which the amount is compounded.

Substitute $5700 for P, 5.2/12% for r and 36 for t. Here t is 36 becasue the amount compounded monthly and there are 36 months in a year.

 [tex]A=\$ 5700(1+\frac{5.2/12}{100})^{36}\\= \$ 6660[/tex]

Hence, the amount will be $6660 after 3 years. It can be solved by the cocept of the compound interest.

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Answer: -4

Step-by-step explanation:

1. Add x on both sides

-8-x=x-4x → -8=2x-4x

2. Combine like terms

-8=2x-4x → -8=-2x

3. Divide negative 2 from both sides

-8=2x → -4=x

a. The monthly payment must be $193.53 in order to pay off the account at the end of 4 years.

b. The total interest paid will be $4372.02.

Answer: See the attachment

Step-by-step explanation: You would use the formula y=mx+b and since b is the y-intercept you would plug that into the equation and then plug in 3/4 as m resulting in

y=3/4x -1 then you just graph it!

Place a point on -1 in the y axis, (0,-1) then go up three units up and four units right, (4,2)

The absolute value inequality to find the percentages is given as follows:

|P - 44| ≤ 3.

Then the percentages are given as follows:

The estimate of the percentage is of:

44%.

The margin of error is of:

±3%.

Both the estimate and the margin of error are taken from the problem.

This means that the absolute difference between the percentage P and the estimate of 44% is of at most the margin of error of 3%, hence the inequality is given as follows:

|P - 44| ≤ 3.

The absolute difference means that the difference can be either positive or negative.

Then the lowest percentage is obtained when:

P - 44 = -3

P = -3 + 44

P = 41.

The highest percentage is obtained when:

P - 44 = 3

P = 3 + 44

P = 47.

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Answer:

[tex]B. \;\dfrac{24}{40}[/tex]

[tex]C. \;\dfrac{3}{5}[/tex]

Step-by-step explanation:

Answer: y = 4x

Step-by-step explanation: The number of devices a company can produce is a function of the number of hours spent making the devices. On average, 4 devices are produced each hour. If we let x represent the number of hours spent making the devices and y represent the number of devices produced, we can write an equation to describe this relationship as follows:

y = 4x

This equation states that the number of devices produced is equal to 4 times the number of hours spent making the devices. For example, if the company spends 10 hours making the devices, the number of devices produced will be 4 * 10 = 40.

Therefore, the equation y = 4x describes the number of devices produced by the company as a function of the number of hours spent making the devices.

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

Given function:

h(t) = -16t² + 72t + 7

By differentiating the function, we have

h'(t) = -32t + 72

Set the function to 0

-32t + 72 = 0

32t = 72

Divide both sides by 32

t = 2.25

Hence, the time is 2.25 seconds

To find the maximum height reached by the rocket,

Substitute t = 2.25 into

h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

= -16(5.0625) + 162 + 7

= -81 + 162 + 7

h(2.25) = 88

In conclusion, the maximum height the rocket reached is 88 feet

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Answer:

x = 4

Step-by-step explanation:

to find the zero equate f(x) to zero , that is

5x - 20 = 0 ( add 20 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

then the zero is x = 4

The value of y when x = -3 represents that the population of the lizard three years before the researcher measures the population size is 63

From the question, we have the following parameters that can be used in our computation:

y = 500 * 2 ^ x

The above equation is an exponential function

Such that

x is the number of years after a researcher measures the population size

When x = -3, we have the equation to be

y = 500 * 2^-3

Evaluate the product

y = 62.5

Approximate

y = 63

This means that the value of y at x = -3 is 63

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Answer:

6 hours I think

When we divide fractions, we multiply the first fraction by the second fraction's reciprocal.

[tex]5\div \dfrac{7}{10}[/tex]

⇒ Multiply by the reciprocal of 7/10:

[tex]= 5\times \dfrac{10}{7}[/tex]

[tex]= \dfrac{50}{7}[/tex]

⇒ If you would like, you can change this into a mixed number fraction. The whole number value from 50/7 is 7. 7 times 7 is 49, which is 1 less than 50. 1 is the numerator and 7 is the whole number:

[tex]= 7\dfrac{1}{7}[/tex]

[tex]\dfrac{50}{7}[/tex] or [tex]7\dfrac{1}{7}[/tex]

Answer:

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

Let's simplify left sides of each statement and compare with right sides:

The discount percentage offered on the new video game as of a sale is 75%.

For the stated question-

The listed price on the video game = $46.

price paid exclusive of tax = $34.50.

Let 'x' be the percentage discount of the listed price.

Then,

x% of 46 = 34.50

x = 34.50 x 100 / 46

x = 75%

Thus, the discount percentage offered on the new video game as of a sale is 75%.

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