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3 years ago

Given a circle with measures of (C, d, and r) and a circle with measures of (C', d', and r'), what is r if C C' = 5 and d' = 20?

Mathematics

1 answer:

Irina-Kira [14]3 years ago

7 0

Answer:

Step-by-step explanation:

We know that:

$\frac{C}{C'}=5$
$d'=20$

So, the ratio between the circumferences is 4 and the diameter of the second circle is 20. In this case, we have to use the ratio between those two circumferences, because that's what is our given data.

$\frac{C}{C'}=\frac{d}{d'}\\5=\frac{d}{20}\\ 100=d$

From this proportion, we deduct that the diameter of the initial circle is 100. Now, we know that the radius in a circumference is have the diameter. Therefore, the radius is:

$r=\frac{d}{2}=\frac{100}{2}=50$

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What does this mean exactly?

bekas [8.4K]

Answer: Choice B $y \le 0$

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

Explanation:

They want to know what are all the possible y values here. The range is the set of all possible outputs of a function.

The largest y value is y = 0 which occurs at the vertex, in this case the highest point. There is no smallest y value as those arrows point downward forever.

So y is between negative infinity and 0, which means we write $-\infty < y \le 0$

Converting that to interval notation leads to $(-\infty, 0]$ . Note the square bracket to include the endpoint.

The compound inequality $-\infty < y \le 0$ simplifies to $y \le 0$

One way to describe this particular relation's range is to say "The set of negative real numbers with 0 included".

Side note: The domain is the set of all possible x inputs. In this case, the domain is the set of all real numbers.

6 0

3 years ago

An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholde

n200080 [17]

Answer:

(a)

$\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}$

(b)

$P(3 \le x \le 6) = 0.30$

$P(4 \le x)=0.60$

Step-by-step explanation:

Given

$F(x) = \left[\begin{array}{ccc}0& x$

Solving (a): The pmf

This means that we list out the probability of each value of x.

To do this, we simply subtract the current probability value from the next.

So, we have:

$\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}$

The calculation is as follows:

$0.30 - 0 = 0.30$

$0.40 - 0.30 = 0.10$

$0.45 - 0.40 = 0.05$

$0.60 - 0.45 = 0.15$

$1 - 0.60 = 0.40$

The x values are gotten by considering where the equality sign is in each range.

$1 \le x < 3$ means $x = 1$

$3 \le x < 4$ means $x = 3$

$4 \le x < 6$ means $x=4$

$6 \le x < 12$ means $x = 6$

$12 \le x$ means $x = 12$

Solving (b):

$(i)\ P(3 \le x \le 6)$

This is calculated as:

$P(3 \le x \le 6) = F(6) - F(3-)$

From the given function

$F(6)= 0.60$

$F(3-) = F(1) = 0.30$

So:

$P(3 \le x \le 6) = 0.60 - 0.30$

$P(3 \le x \le 6) = 0.30$

$(ii)\ P(4 \le x)$

This is calculated as:

$P(4 \le x)=1 - F(4-)$

$P(4 \le x)=1 - F(3)$

$P(4 \le x)=1 - 0.40$

$P(4 \le x)=0.60$

8 0

3 years ago

$15,000 is invested for 15 years with an APR of 4.2% and monthly compounding.

Phoenix [80]

Answer:

51-54: Simple Interest. Calculate the amount of money you will have in the following accounts after 5 years, assuming that you eam simple interest 51. You deposit $ 700 in an account with an annual interest rate of 4% 52. You deposit $1200 in an account with an annual interest rate of 3% 53. You deposit $3200 in an account with an annual interest rate of 3.5% 54. You deposit $1800 in an account with an annual interest rate of 3.8% 55-56: Simple versus Compound Interest. Complete the following tables, which show the performance of two investments over a 5-year period. Round all figures to the nearest dollar. 55 Suzanne deposits $3000 in an account that earns simple interest at an annual rate of 2.5%. Derek deposits $3000 in an account that earns compound interest at an annual rate of 2.5%. Suzanne's Suzanne's Derek's Annual | Derek's Year Annual Interest Balance Interest Balance rest formula to the stated pe 57-62: Compound Interest. Use the compound interest form compute the balance in the following accounts after the state riod of time, assuming interest is compounded annually. 57. $10,000 is invested at an APR of 4% for 10 years. 58. $10,000 is invested at an APR of 2.5% for 20 years. 59. $15,000 is invested at an APR of 3.2% for 25 years. 60. $3000 is invested at an APR of 1.8% for 12 years. 61. 55000 is invested at an APR of 3.1% for 12 years. 62. $ 40,000 is invested at an APR of 2.8% for 30 years. 63-70: Compounding More Than Once a Year. Use the appropriate compound interest formula to compute the balance in the following accounts after the stated period of time. 63. $10,000 is invested for 10 years with an APR of 2% and quarterly compounding. 64. $2000 is invested for 5 years with an APR of 3% and daily compounding 65. $25,000 is invested for 5 years with an APR of 3% and daily compounding 66. $10,000 is invested for 5 years with an APR of 2.75% and monthly compounding. 67. $2000 is invested for 15 years with an APR of 5% and monthly compounding 68. $30,000 is invested for 15 years with an APR of 4.5% ana daily compounding. 69. $25,000 is invested for 30 years with an APR of 3.7% quarterly compounding. 70. $15,000 is invested for 15 years with an APR of 4.2% monthly compounding. 71-74. Annual.

Hope this helps

7 0

2 years ago

PLEASE HELP AND SHOW WORK i'm very confused

noname [10]

Answer:

a. about 15.51 miles, rounded to 15.5 miles

b. about 31.02 miles, rounded to 31 miles

Step-by-step explanation:

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

10 20 40 80 160 320 640

1280 2560 5120 10240 20480 40960 81920

81920/5280 = 15.51515151, rounded to the nearest tenth of a mile, 15.5 miles

Question b asks for how many miles in total has he ran. That means we have to add each of the values shown above and that equals to 163830 feet.

Divide that by 5280 and that equals 31.02 miles, rounded to the nearest tenth, 31 miles.

4 0

3 years ago

1. Which point on the axis satisfies the inequality y

grigory [225]

Answer:

1) Point $(1,0)$ -----> see the attached figure N $1$

2) The value of x is $4$

3) I quadrant

4) $(1,1)$

5) $y>-5x+3$

Step-by-step explanation:

Part 1)

we know that

If the point satisfy the inequality

then

the point must be included in the shaded area

The point $(1,0)$ is included in the shaded area

Part 2)

we have

$x-2y\geq 4$

see the attached figure N $2$

we know that

The value for x on the boundary line and the x axis is equal to the x-intercept of the line $x-2y= 4$

For $y=0$

Find the value of x

$x-2(0)= 4$

$x=4$

The solution is $x=4$

Part 3)

we have

$x\geq 0$ -----> inequality A

The solution of the inequality A is in the first and fourth quadrant

$y\geq 0$ -----> inequality B

The solution of the inequality B is in the first and second quadrant

the solution of the inequality A and the inequality B is the first quadrant

Part 4) Which ordered pair is a solution of the inequality?

we have

$y\geq 4x-5$

we know that

If a ordered pair is a solution of the inequality

then

the ordered pair must be satisfy the inequality

we're going to verify all the cases

<u>case A)</u> point $(3,4)$

Substitute the value of x and y in the inequality

$x=3,y=4$

$4\geq 4(3)-5$

$4\geq 7$ ------> is not true

therefore

the point $(3,4)$ is not a solution of the inequality

<u>case B)</u> point $(2,1)$

Substitute the value of x and y in the inequality

$x=2,y=1$

$1\geq 4(2)-5$

$1\geq 3$ ------> is not true

therefore

the point $(2,1)$ is not a solution of the inequality

<u>case C)</u> point $(3,0)$

Substitute the value of x and y in the inequality

$x=3,y=0$

$0\geq 4(3)-5$

$0\geq 7$ ------> is not true

therefore

the point $(3,0)$ is not a solution of the inequality

<u>case D)</u> point $(1,1)$

Substitute the value of x and y in the inequality

$x=1,y=1$

$1\geq 4(1)-5$

$1\geq -1$ ------> is true

therefore

the point $(1,1)$ is a solution of the inequality

Part 5) Write an inequality to match the graph

we know that

The equation of the line has a negative slope

The y-intercept is the point $(3,0)$

The x-intercept is a positive number

The solution is the shaded area above the dashed line

the equation of the line is $y=-5x+3$

The inequality is $y>-5x+3$

3 0

4 years ago

Read 2 more answers