1. The radius, r, of a circle is one-half of the length of its diameter, d.
r = d
2r = d
+ r = d
r=d
r=

The solution of (−213+515)+113 is 415

Add -213 and 515:

-213 + 515

= 302

Add 113 to the result:

302 + 113

= 415

So, the final answer is 415.

Question:

Solve: (−213+515)+113

The measure of ∠JHG is 70 degree.

An angle is formed by two rays called the arms of the angle meeting at a common endpoint called the vertex of the angle.

There are three types of angles, acute angle, right angle and obtuse angle.

Protractor is used to measure angles, it is of semicircular shape with degrees of angles engraved upon it.

Acute Angle : The angle whose measure is less than 90 degree is called the acute angle.

Right Angle : The angle whose measure is equal to 90 degree is called right angle.

Obtuse Angle: The angle whose measure is greater than 90 degree is called obtuse angle.

The ∠JHG has JH and HG are the arms of the angle.

The measure of ∠JHG = 70 degree, it is less than 90 degree, it is an acute angled triangle.

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180-b

180-b

c

Step-by-step explanation:

Final answer:

To calculate the likelihood of both Sue and Jim getting red gumballs, we multiply the probability of each event occurring sequentially. After Sue gets a red gumball, the chances are 1/4, and then 99/399 for Jim. The final probability of both getting red gumballs is 99/1596 or about 6.203%.

Explanation:

The likelihood that both Sue and Jim will get red gumballs from the gumball machine can be calculated using basic probability principles. First, we need to determine the total number of gumballs in the machine. This is the sum of black, white, red, and yellow gumballs, which are 50, 150, 100, and 100 respectively, making a total of 400 gumballs.

The probability that Sue gets a red gumball is the number of red gumballs divided by the total number of gumballs in the machine, which is 100/400, simplifying to 1/4. When Sue takes a gumball, assuming she gets a red one, there are now 399 gumballs left with 99 being red. Therefore, the probability that Jim also gets a red gumball is 99/399. To find the likelihood of both events occurring, we multiply these probabilities:

P(Both Sue and Jim get red gumballs) = P(Sue gets a red gumball) × P(Jim gets a red gumball after Sue) = (1/4) × (99/399).

Now we simplify and multiply these fractions to get the final probability. After simplifying, the final probability is 99/1596, which is approximately 0.06203 or 6.203% chance that both Sue and Jim will get red gumballs.

Gemma gets 6 biscuits, and Zak gets 24 biscuits when Mrs. Perry shares out 30 biscuits between them in the ratio 1:4.

To solve this problem, we need to divide the 30 biscuits according to the ratio 1:4 between Gemma and Zak.

Calculate the total parts in the ratio.

Total parts = 1 (from Gemma) + 4 (from Zak) = 5 parts

Find out how many parts each child gets.

For Gemma:

Gemma's share = (1 part ÷ 5 parts) × 30 biscuits

= (1/5) × 30

= 6 biscuits

For Zak:

Zak's share = (4 parts ÷ 5 parts) × 30 biscuits

= (4/5) × 30

= 24 biscuits

Verify the result.

Gemma gets 6 biscuits, and Zak gets 24 biscuits.

6 + 24 = 30 biscuits (which is the total), so the division is correct.

Thus, Gemma gets 6 biscuits, and Zak gets 24 biscuits when Mrs. Perry shares out 30 biscuits between them in the ratio 1:4.

13/16 - 3/8

 convert 3/8 to 16ths

3/8 = 6/16

13/16 - 6/16 =

13/6 =7

7/16 is the answer

Answer:

The correct option is 1.

Step-by-step explanation:

The given expression is

[tex]\frac{13}{16}-\frac{3}{8}[/tex]

We need to perform the indicated operation.

Make denominator common.

[tex]\frac{13}{16}-\frac{3\times 2}{8\times 2}[/tex]

[tex]\frac{13}{16}-\frac{6}{16}[/tex]

It can be written as

[tex]\frac{13-6}{16}[/tex]

[tex]\frac{7}{16}[/tex]

The value of given expression is [tex]\frac{7}{16}[/tex].

Therefore the correct option is 1.

Answer:

y =  [tex](\frac{4}{5})[/tex]x + 20

Step-by-step explanation:

The equation of line q is 5y - 4x = 10

                                       5y = 4x + 10

                                       y = [tex]\frac{4}{5}x+2[/tex]

If a line is parallel to this line the slope of the line will be the same as the given line = [tex](\frac{4}{5})[/tex]

Let the parallel line is y = mx + c

where m = slope

and    c = y-intercept

equation will be y = [tex]\frac{4}{5}x+c[/tex]

This line passes through (-15, 8)

so   8 = (-15)  [tex](\frac{4}{5})[/tex] + c

8 = -12 + c

c = 12 + 8

c = 20

Now the equation of the parallel line will be y =  [tex](\frac{4}{5})[/tex]x + 20

Answer:

C. The balloon starts at a height of 500 ft  and rises at a rate of 150 ft.

Step-by-step explanation:

We have been given a graph which represents the height of the balloon over time.

We can see from our graph that y-intercept, which represents the height of the balloon (in thousand feet) at time equals zero, is 0.5. To find the correct y-intercept we will multiply 0.5 by 1000 as height of the balloon is given in thousand feet.

[tex]\text{y-intercept}=(0.5\times 1000)\text{ feet}=500\text{ feet}[/tex]

Therefore, y-intercept represents that the balloon starts at a height of 500 feet.  

Now let us find slope of our given line using slope formula.

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

[tex]y_2-y_1[/tex] is vertical change or rise.

[tex]x_2-x_1[/tex] is horizontal change or run.

Upon substituting given values in above formula we will get,

[tex]\text{Slope}=\frac{3.5-0.5}{20-0}[/tex]

[tex]\text{Slope}=\frac{3}{20}[/tex]

[tex]\text{Slope}=0.15[/tex]

Now let us multiply 0.15 by 1000 as height of balloon is given in thousand feet.

[tex]\text{Slope}=0.15\times 1000=150[/tex]

Therefore, slope of our line is 150 which means that height of balloon is increasing 150 feet per second or balloon is rising at a rate of 150 feet per second.

Upon looking at our given options we can see that option C is the correct choice.

Answer:



Step-by-step explanation:

60minutes per hour

25/60 = 5/12

1 2/3 / 5/12 =

5/3 / 5/12 =

5/3 * 12/5 = 60/15 = 4 miles

Answer:

2.8

Step-by-step explanation:

From the congruence statement, we see that AB corresponds with EF; this means they will be congruent.

To find the measure of FE, we will find the distance between points A and B using the distance formula:

[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Using our coordinates for A and B, we have

[tex]A(0,2)\text{and }B(2, 4)\\\\d=\sqrt{(4-2)^2+(2-0)^2}=\sqrt{2^2+2^2}\\\\=\sqrt{4+4}=\sqrt{8}=2.828427\approx 2.8[/tex]

Answer:

The time elapsed is greater than 7 seconds

Step-by-step explanation:

From definition

acceleration = change in speed/time elapsed

or:

a = Δv/t

Rearranging:

a*t = Δv

If your speed decreases by more than 10.5 miles per hour, then:

Δv > 10.5

Replacing with the previous equation and solving for t:

a*t > 10.5

t > 10.5/1.5

t > 7 s

The required simplified value fo x is 16 in the expression of the line segment.

Given that,
If EF =9x+17 , FG = 35 , and EG=196 , find the value of x is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here
EG = 196
EF + FG = 196
9x + 17 + 35 = 196
9x + 52 = 196
9x = 196 - 52
9x = 144
x = 144/ 9
x = 16

Thus, the required simplified value fo x is 16 in the expression of the line segment.

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To write a piecewise function, you need to define different equations for different intervals of the independent variable.

To write a piecewise function, you need to define different equations for different intervals of the independent variable. Each equation represents a different part or piece of the function. Here's an example:

f(x) =

In this function, the equation 2x + 1 is used for values of x that are less than or equal to 0, the equation x^2 is used for values of x between 0 and 5 (inclusive), and the equation 4 - x is used for values of x greater than 5.

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