Sarah only knows the diameter of a circle. What should she do to find the radius?
Multiply the diameter by 2.
Divide the diameter by 2.
Multiply the diameter by pi
Divide the diameter by pi

Answer:

The correct option is A.

Step-by-step explanation:

A geometric sequence is defined as

[tex]A(n)=ar^{n-1}[/tex]

Where, a is the first term of the sequence, r is the common ratio and n is number of term. So, n can not be negative or zero.

In option A, the given sequence is

[tex]A(n)=P(1+i)^{n-1}[/tex]

Where, n is positive integers.

Here the first term is P and (1+i) is the common ratio. So, this sequence is geometric sequence.

Therefore the correct option is A.

Answer:

A is correct just took the test

Step-by-step explanation:

The graph demonstrates a uniform relationship between speed and height, indicating that as speed increases, height also increases. Therefore, the correct answer is:

D. As speed increases, height increases.

The Graph indicates a uniform relationship between speed and height. To interpret this in the context of the answer choices:

D. As speed increases, height increases.

This is the most appropriate choice based on the information provided. In a uniform relationship, as speed increases, the corresponding height also increases. Therefore, Option D accurately captures the relationship depicted on the graph.

Final answer:

The equation 100 cm = 1 m is used to create a conversion factor that allows for conversion between centimeters and meters. This conversion factor is essential when measuring lengths and is part of the metric system, which also includes units like kilometers, millimeters, micrometers, and nanometers.

Explanation:

Understanding Conversion Factors

When considering the statement that 100 cm is equivalent to 1 m, we can create a conversion factor to help us switch from one unit of measurement to another. A conversion factor is a ratio of equivalent measurements used to convert a quantity from one unit to another. In this case, 100 cm/1 m is our conversion factor, and it is equal to 1 because both numerator and denominator represent the same length but in different units.

If we were to divide both sides of the equation by 1 meter, we would get 1 m/1 m on one side and 100 cm/1 m on the other, simplifying to just 1 because any fraction with the same number in the numerator and denominator equals 1. Hence, utilizing this conversion factor allows any given number in meters to be converted into centimeters, and vice versa, without changing the measure's value.

Furthermore, knowing other unit conversions like 1 meter equals 0.001 kilometers, 1.094 yards, or 39.37 inches can be very useful in different contexts. Similarly, we can break down meters into smaller units such as centimeters, millimeters, micrometers, and nanometers, with each having its place in the metric system.

Answer:

18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down.  That means 18.14 rounds down to 18

9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up.  That means 9.88 rounds up to 10.

Now it's just simple math.  18-10 = 8

Step-by-step explanation:

Answer:

18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down.  That means 18.14 rounds down to 18

9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up.  That means 9.88 rounds up to 10.

18-10=8.

Answer:

The correct option is 2.

Step-by-step explanation:

The equations that are true for any value of the variable, no matter what value is plugged in for the variable, then they are called Identity equations.

The first equation is

[tex]7m-5=8m+7-m[/tex]

[tex]7m-5=7m+7[/tex]

Subtract 7m from both the sides.

[tex]-5=7[/tex]

This statement is false for any value of m. Therefore this is not an Identity equation.

The second equation is

[tex]3w+8-w=4w-2(w-4)[/tex]

Using distributive property,

[tex]2w+8=4w-2w+8[/tex]

[tex]2w+8=2w+8[/tex]

[tex]0=0[/tex]

This statement is true for any value of w. Therefore this is an Identity equation.

The third equation is

[tex]9-(2v+3)=-2v-6[/tex]

[tex]9-2v-3=-2v-6[/tex]

[tex]-2v+6=-2v-6[/tex]

[tex]6=-6[/tex]

This statement is false for any value of v. Therefore this is not an Identity equation.

The fourth equation is

[tex]-3y+3=-3y-6[/tex]

Add 3y on both the sides.

[tex]3=-6[/tex]

This statement is false for any value of y. Therefore this is not an Identity equation.

Hence the correct option is 2.

A student is calculating how many additional boxes can be added to an elevator that already has 10 boxes of a certain weight. By using the weight capacity of the elevator and the weights of the boxes, the student determines the number of extra boxes that can be accommodated in the elevator's load.

To solve this problem, we need to first calculate the total weight of the 10 boxes:

The next three terms in the geometric sequence are 25, 12.5 and 6.25.

The given geometric sequence is 400, 200, 100, and 50.

We need to find the next three terms in the geometric sequence.

A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term. i.e., To get the next term in the geometric sequence, we have to multiply with a fixed term (known as the common ratio), and to find the preceding term in the sequence, we just have to divide the term by the same common ratio.

In the given geometric sequence the common ratio is 1/2.

5th term=50/2=25

6th term=25/2=12.5

7th term=12.5/2=6.25

Therefore, the next three terms in the geometric sequence are 25, 12.5 and 6.25.

To learn more about the geometric sequence visit:

https://brainly.com/question/11266123.

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Using the least common factor of 15 and 12, it is found that the fewest number of packages that could be bought is of 5.

To find the lcm(least common multiple), we factor the numbers by prime factors, and then multiply these factors.

In this problem, packages of 12 candies will be used to give candies for 9 + 6 = 15 people, hence the least number of candies is lcm(12,15).

Then:

12 - 15|2

6 - 15|2

3 - 15|3

1 - 5|5

1 - 1

Hence lcm(12,15) = 2 x 2 x 3 x 5 = 60.

Since 60 candies are needed, and each package has 12 candies, the number of packages is given by:

n = 60/12 = 5.

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The weight of the bar of soap can be found by setting up the equation [tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex] and solving for 'w', which results in the soap weighing 3 pounds.

To find the weight of the bar of soap, we can set up an equation based on the given information. Let's define the weight of the soap as 'w'. According to the problem, the weight of the soap is equal to [tex]\frac{3}{4}[/tex] of itself plus [tex]\frac{3}{4}[/tex] of a pound, which can be written as:

[tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex]

Now, to solve for 'w', we need to isolate it on one side of the equation. We can do this by subtracting [tex]\(\frac{3}{4}w\)[/tex] from both sides:

[tex]w - \(\frac{3}{4}w\) = \(\frac{3}{4}\)[/tex]

This simplifies to [tex]\(\frac{1}{4}w\) = \(\frac{3}{4}\)[/tex], so when we multiply both sides by 4 to solve for 'w', we get:

w = 3 pounds

Therefore, the bar of soap weighs 3 pounds.

Answer:

Value of  [tex]P(Q \cap R)[/tex] is, 0.0081

Step-by-step explanation:

For an independent events A and B is given by:

[tex]P(A \cap B) =P(A) \cdot P(B)[/tex]

As per the statement:

Suppose Q and R are independent events.

P(Q) = 0.27 and P(R) = 0.03.

We have to find [tex]P(Q \cap R)[/tex]

By definition we have;

[tex]P(Q \cap R) =P(Q) \cdot P(R)[/tex]

Substitute the given values we have;

[tex]P(Q \cap R) =0.27 \cdot 0.03[/tex]

⇒[tex]P(Q \cap R)=0.0081[/tex]

therefore, the value of  [tex]P(Q \cap R)[/tex] is, 0.0081

Answer:

Question 1)

Option: B

( unpaid balance)

Question 2)

Option: D

( Minimum payment )

Step-by-step explanation:

Question 1)

UNPAID BALANCE:

unpaid balance is the remaining balance of a loan, cash advance or credit that has not been paid.

Hence, The amount left when you subtract last month's payment from last month's balance on a credit card statement is the:

unpaid balance.

Question 2)

Minimum payments are typically calculated as percentage of your outstanding balance plus any fees that have been added to your balance.

Hence, The percentage charged each month on purchases charged to the credit card account is called the:

Minimum payment.

The solution for the problem is:

Tan 33(degrees) = opposite/adjacent 

Starting off with the submarine, find how far it is from point R. 

Tan 21 = 19,000/x 

or 

19,000/Tan 21= x 

x = 49496.69 feet the submarine is from point R. 

Now, find how far the tanker is from point R. 

Tan 33= 19,000/x 

or 

19,000/Tan 33 = x 

x = 29257.43 feet the tanker is from point R. 

Now subtract and the difference would be the answer

= 49496.69 - 29257.43

The tanker and sub are 20239.26  feet away from each other. 

Final answer:

To determine how many integers between 100 and 999 have distinct digits, we calculate the possibilities for each position, giving us 9 options for the first digit, 9 for the second, and 8 for the third, resulting in a total of 648 integers.

Explanation:

The question is about finding the number of integers between 100 and 999 with distinct digits. To find this, we calculate the possibilities for each digit separately. The first digit can be anything from 1 to 9 (excluding 0 because the number cannot be less than 100), so there are 9 possibilities for the first digit. For the second digit, since it cannot be the same as the first, there are 9 possibilities (0 can now be included). Finally, for the third digit, we subtract the choices we've already used, so there are 8 possible digits left.

Calculating the total, we multiply the possibilities for each digit: 9 (first digit) × 9 (second digit) × 8 (third digit) = 648. Therefore, there are 648 integers between 100 and 999 that have all distinct digits.

The quotient of the expression [tex]\(\frac{a-3}{7} \div \frac{3-a}{21}\)[/tex] is -3.

To find the quotient of the expression [tex]\(\frac{a-3}{7} \div \frac{3-a}{21}\)[/tex], we follow the rules of division for fractions, which involves multiplying the first fraction by the reciprocal of the second fraction.

The expression can be rewritten as:

[tex]\[\frac{a-3}{7} \times \frac{21}{3-a}\][/tex]

Now, we can simplify the expression by canceling out common factors. Notice that [tex]\(a-3\)[/tex] and [tex]\(3-a\)[/tex] are negatives of each other, and [tex]\(7\)[/tex] is a factor of [tex]\(21\)[/tex].

First, we can cancel [tex]\(a-3\)[/tex] with [tex]\(3-a\)[/tex], keeping in mind that a negative sign will be introduced since [tex]\(a-3 = -(3-a)\)[/tex]:

[tex]\[\frac{-1}{7} \times \frac{21}{-1}\][/tex]

Next, we simplify [tex]\(21\)[/tex] divided by [tex]\(7\)[/tex], which is [tex]\(3\)[/tex]:

[tex]\[-1 \times 3\] = -3[/tex]

To solve for the sum of the lengths of the legs of the larger triangle, we need to know the sum of the legs of the smaller triangle and multiply it by the scaling factor, which is 5. However, we can't find this sum with the given information because we don't have individual leg lengths of the smaller triangle.

To find the sum of the lengths of the legs of the larger triangle, we first need to establish the scale factor between the two similar triangles based on their areas. The area of a triangle scales with the square of the length of its sides. Given that one triangle has an area of 6 square inches and the other has an area of 150 square inches, the scale factor in area is given by the square root of the ratio of the larger area to the smaller area, which is √(150/6), which simplifies to 5. Therefore, if the hypotenuse of the smaller triangle is 5 inches, the hypotenuse of the larger triangle will be 5 times larger, that is 5 * 5 = 25 inches.

Given that the triangles are similar, all corresponding lengths scale by the factor of 5. If we denote the length of the legs of the smaller triangle as a and b, and the legs of the larger triangle as A and B, then A = 5a and B = 5b. Although we don't know the exact lengths of a and b, we can use the Pythagorean Theorem which states that the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b). For the smaller triangle, we have c² = a² + b². But since we only know c (which is 5 inches for the smaller triangle), we cannot directly find the individual lengths of a and b.

Since the question asks for the sum of the legs of the larger triangle (A+B), we only need to find the sum of the legs of the smaller triangle (a+b) and scale it up by the same factor. If a and b were known, we would do (a+b)*5 to get the sum for the larger triangle. However, without those individual lengths, we cannot find the sum based on the given information. To solve this problem, additional information about the lengths of the legs of the smaller triangle would be needed.

24/2 = 12 pairs of students

 if he gave 9 pairs of students magnets there are 12-9 = 3 pairs left

3 magnets per pair

3*3 = 9 more magnets are needed

Answer:

the answer is d

Step-by-step explanation:

This problem can be solved directly by subtraction.

We are given that there are initially 78 emails in her inbox.

We take out or delete 47 emails therefore we subtract 47 from 78, hence:

                78 – 47 = 31

So there are 31 emails left in her inbox.