Answer:
The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Step-by-step explanation:
For a circulus with radius r, we have that:
The area of the circulus is:
[tex]A = \pi r^{2}[/tex]
That is, the radius is squared, not multiplied by 2, so the first statement is incorrect.
The circumference of the circulus is:
The derivative of the area, so
[tex]C = 2\pi r[/tex]
However
The radius if half the diameter. So
[tex]C = 2\pi \frac{d}{2}[/tex]
[tex]C = \pi d[/tex]
So the correct statement is:
The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Both statements are correct. The formula for the area of a circle is A = πr², where r is the radius, and the formula for the circumference of a circle is C = πd, where d is the diameter.
The formula for the area of a circle is given by A = πr², where A represents the area and r represents the radius of the circle. In this formula, the radius is squared and then multiplied by the mathematical constant π (pi) to calculate the area enclosed by the circle.
On the other hand, the formula for the circumference of a circle is given by C = πd, where C represents the circumference and d represents the diameter of the circle. In this formula, the diameter is multiplied by the mathematical constant π to calculate the total distance around the circle.
These formulas are derived from the properties of circles. The radius is the distance from the center of the circle to any point on its edge, while the diameter is the distance across the circle passing through its center. The circumference represents the boundary or perimeter of the circle, while the area represents the space enclosed by the circle.
It's important to note that the relationship between the radius and diameter is given by the equation d = 2r, where d represents the diameter and r represents the radius. This relationship allows us to interchangeably use the radius or diameter in the formulas for the area and circumference of a circle.
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Complete Question:
1. The formula for the area, A, of a circle is A = [tex]\pi r^2[/tex] , where r is the circle’s radius.
2. The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Which of the above statements is correct?
Recently in a large random sample of teens a proportion of 0.76 teens said they send text messages to friends. the margin of error for a 98% confidence interval was 0.030. (a) what is the sample statistic for the proportion of teens who send text messages to friends
The sample statistic for the proportion of teens who send text messages to friends is 0.76 or 76%. This result was obtained with a 98% confidence interval and a margin of error of 0.03.
Explanation:The sample statistic in this scenario is the proportion of teens who said they send text messages to friends. In statistics, a sample proportion (also known as a sample percentage) is a way to express the count of observations in a category as a ratio or a fraction of the total sample size.
In your case, the sample statistic is 0.76, meaning that 76% of the teens in your sample said they send text messages to friends. This result was accompanied by a margin of error of 0.030 for your 98% confidence interval.
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
The margin of error represents the range in which we are confident that the true population proportion lies given our sample statistic. With a confidence level of 98%, we are sure that if we repeated our sample many times, 98% of those samples would produce a proportion between 76%- 3% and 76% + 3%.
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Suppose that g(x) = f(x – 8). Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 8 units to the left.
B. The graph of g(x) is the graph of f(x) shifted 8 units down.
C. The graph of g(x) is the graph of f(x) shifted 8 units up.
D. The graph of g(x) is the graph of f(x) shifted 8 units to the right.
The graph of g(x) is the graph of f(x) shifted 8 units to the right.
Option D is correct.
What is shifting of a function?A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.
According to the question
g(x) = f(x – 8)
If the function is shifted to the left it is going to plus(+).
If the function is shifted to the right it is going to minus(-).
Hence, The graph of g(x) is the graph of f(x) shifted 8 units to the right.
Option D is correct.
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Can you please help me out ?
Desiree made 100 cookies this week, she baked 4 more than three times the total she made last week. How many cookies did she bake last week?
Desiree made 100 cookies this week. She baked 4 more than three times the total she made last week. How many cookies did she bake last week.
3x + 4 = 100 x = 32 cookies
at the local baseball diamond,the distance from home base to second base is 100 feet. Determine the distance from home base to first base.
Answer:
70.7 ft
Step-by-step explanation:
The triangle formed by home plate, first base, and second base is an isosceles right triangle with hypotenuse 100 ft. Then the side length (base-line distance between bases) is (100 ft)/√2 ≈ 70.7 ft.
___
For an isosceles right triangle with side lengths 1, the hypotenuse can be found from the Pythagorean theorem to be ...
hypotenuse = √(side² + side²) = √(1²+1²) = √2
Then the diamond distances satisfy the proportion ...
hypotenuse/side = 100 ft/(base distance) = √2/1
or ...
base distance = (100 ft)/√2 ≈ 70.71068 ft
Samatha has 24 cards. Chelsea saw 15 more cards than Samatha. How many cards does Chelsea have?
What fraction of the circle does the shaded angle represent??
How many quarter inches long is 7 3/4
The number of quarters in 7 is 28 and the number of quarters in 3/4 is 3. Then the total number of quarters is 33.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The quarter is written as one-fourth.
[tex]\rm quarter = \dfrac{1}{4}[/tex]
We have 7 + 3/4
We know that one has 4 quarters then 7 has
→ 7 × 4 = 28
And 3/4 has three quarters.
Then the total quarter will be
[tex]\rm Number\ of \ quarter = 7 \dfrac{3}{4} \times 4 = \dfrac{33}{4} \times 4 = 33[/tex]
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There are 31 quarter inches in 7 3/4 inches. This is determined by converting the mixed number into an improper fraction and then dividing by ¼, which gives us 31/4 or 31 quarter inches.
Explanation:The question asks how many quarter inches there are in 7 3/4 inches. To find this, we can convert the mixed number into an improper fraction and then divide by the fraction representing a quarter inch (¼ inch).
First, convert 7 ¾ to an improper fraction by multiplying the whole number 7 by the denominator 4 and then adding the numerator 3. This gives us 28 + 3 = 31, so 7 ¾ inches is equivalent to ⅔31/4 or 31 quarter inches. Therefore, 7 3/4 inches is 31 quarter inches long.
the figure shown is made up of a square and a triangle. Express the area of the figure in terms of y.
A protractor is used to measure an angle. Which of the following could be the measure of the angle if we know it is an acute angle?
125°
75°
0°
it can't be determined
Final answer:
To find an acute angle using a protractor, choose the angle less than 90°. The acute angle could be 75°.
Explanation:
To determine an acute angle using a protractor, we look for an angle that is less than 90 degrees, as acute angles are those that measure less than 90 degrees.
75° could be the measure of the angle as it falls within the range of acute angles.
Hence, in this case, the angle that could be the measure of the acute angle is 75°.
Which of the following best describes the algebraic expression 5(x+2)-3? A. Three less than five times a number plus two B. Three less than five times the quantity of a number plus two
Answer:
Option B is correct.
Three less than five times of a quantity of a number plus two.
Step-by-step explanation:
Given the expression: [tex]5(x+2)-3[/tex]
To describe the given algebraic expression.
Here, x be the number.
x+ 2 means "a number plus 2"
5(x+2) means "five times the quantity of a number plus two".
and
5(x+2)-3 means "Three less than five times of a quantity of a number plus two".
Therefore, the following which best describe the algebraic expression [tex]5(x+2)-3[/tex] is, Three less than five times of a quantity of a number plus two.
The legs of a right triangle are 12 cm and 16 cm. What is the length of the hypotenuse? 15 cm 17 cm 20 cm 28 cm
Answer:
20cm
Step-by-step explanation:
Write three equations whose graphs are the same line as the equation 3x+2y=7.
If a stadium has 15,000 seats sold at $10.00, $12.50, and $15.00 equally distributed in three sections, how much can be made if the stadium sells out?
Answer:
$187,500
Step-by-step explanation:
There must be 15,000/3 = 5,000 seats in each section. Then the total revenue can be ...
5000·$10.00 + 5000·12.50 + 5000·15.00 = 5000·($10 + 12.50 +15.00)
= 5000·$37.50 = $187,500
Stadium revenue can be $187,500 if all seats are sold.
The total earnings from selling out the stadium with tickets priced at $10.00, $12.50, and $15.00, equally distributed, would amount to $637,500.
The total earnings from selling out the stadium would be $15 x 15,000 = $225,000 for tickets priced at $10.00.
For tickets priced at $12.50, the earnings would be $12.50 x 15,000 = $187,500.
Lastly, for tickets priced at $15.00, the earnings would be $15 x 15,000 = $225,000.
To find the total earnings, add the earnings from each section: $225,000 + $187,500 + $225,000 = $637,500.
There is an ice cream and candy shop next-door that is the same size as your bakery. How many 30th of the space does it take up
A graphic designer is planning the layout for a magazine advertisement of three pictures, shown below. The ratio of the sum of the widths of the three pictures to the total width of the advertisement is 4:5. If each picture is 4 inches wide, what is the length of each of the four empty spaces between the pictures (t)?
9/20 as a percent
320% as a fraction
2 3/8 as a decimal and percent
.1% as a decimal and fraction
1.2 as a percent and fraction
5 1/3 as a percent and decimal
Answer:
1) 45%
2) [tex]\frac{16}{5}[/tex]
3) 2.335
237.5%
4) 0.0001
[tex]\frac{1}{1000}[/tex]
5) 120%
[tex]\frac{6}{5}[/tex]
6) 533.3%
5.333
Step-by-step explanation:
1) Divide the numerator by the denominator and multiply by 100, then:
[tex]\frac{9}{20}=0.45*100=45\%[/tex]
2) Write 320 has the numerator and 100 has the denominator, then reduce the fraction:
[tex]\frac{320}{100}=\frac{32}{10}=\frac{16}{5}[/tex]
3) As a decimal:
Divide the numerator by the denominator and add it to the integer part:
[tex]2+0.375=2.375[/tex]
As a percent:
Multiply the decimal number obtained above by 100:
[tex]2.375*100=237.5\%[/tex]
4) As a decimal:
Divide it by 100:
[tex]\frac{0.1}{100}=0.0001[/tex]
As a fraction:
As you can see, the decimal point were moved three spaces to the left. Therefore, the integer 1 is divided by 1000. Write 1 as the numerator and 1000 has the denominator:
[tex]\frac{1}{1000}[/tex]
5) As a percent:
Multiply 1.2 by 100, then:
[tex]1.2*100=120\%[/tex]
As a fraction:
To make 1.2 an integer you must multiply by 10, therefore, 12 will be the numerator and 10 the denominator:
[tex]\frac{12}{10}[/tex]
Reduce it:
[tex]\frac{6}{5}[/tex]
6) As a decimal:
Divide the numerator by the denominator and add it to the integer part:
[tex]5+0.33=5.333[/tex]
Multiply the decimal number obtained above by 100:
[tex]5.33*100=533.3\%[/tex]
Answer:
9/20 as a percent- 45%
320% as a fraction- 16/5
2 3/8 as a decimal- 2.38
2 3/8 as a percent- 237.5%
.1% as a decimal- 0.001
.1% as a fraction- 1/100
1.2 as a percent- 120%
1.2 as a fraction- 6/5
5 1/3 as a percent- 533.3%
5 1/3 as a decimal- 5.33
A cab driver is paid $6 plus $0.45 per mile driven. Which expression shows the amount of money the cab driver earns in m miles?
Answer:
C/ 0.45m + 6
Step-by-step explanation:
i did the quiz
What is simplified form of the expression -(4)^-2
A large bottle of Dragon Breath mouthwash costs $5.00 before tax and $5.30 after tax. What is the percentage the tax?
you lease a car valued at 23,495 for 3 years at $429.95/month with a $500 down payment. If interest is 30% of the payment, how much interest is paid over the 3 years?
Solution:
Present Value of car= $ 23,495
Down Payment = $ 500
Total Amount paid monthly for 3 years that is 36 months, if you pay $ 429.95 per month=$ 15478.20
Total amount paid for the car as an agreement which includes Down payment of $ 500 as well as monthly Payment of $ 429.95 for 36 months= $ 15478.20+$ 500=$ 15978.20
As, given Interest is 30% of the payment.
So, total interest = 30% of $ 15978
[tex]=\frac{30}{100}\times 15978.20[/tex]
= $ 4793.40
But if you will calculate interest on payment of $ 429.95 at the rate of 30%, it gives
[tex]=\frac{30}{100}\times 429.95[/tex]
= $128.985
So, total interest for 3 years= $128.985 ×36=$ 4643.46
Also, if you will calculate interest on payment of ($500+$429.95=$929.95) at the rate of 30%
[tex]=\frac{30}{100}\times 929.95[/tex]
=$278.985
Total interest for 3 years= $278.985 ×36=$10,043.46
In the month of January, a certain restaurant claimed it sold 9,000 burgers and expects sales to grow at a rate of 4.8% per month over the next year. Which formula will determine the number of burgers the restaurant expects to sell this year?
Answer:
[tex]y=9000(1.048)^x[/tex]
Step-by-step explanation:
This will be an exponential growth problem. This is because the amount of burgers is expected to change at the same rate every month.
These equations are of the form
[tex]y=a(1+r)^x[/tex],
where a is the original amount, r is the growth rate and x is the amount of time.
In this problem, the original amount, a, is 9000.
The rate of growth is 4.8%; 4.8% = 4.8/1000 = 0.048
This gives us
[tex]y=9000(1+0.048)^x\\\\y=9000(1.048)^x[/tex]
Answer:
The answer is 9000(1.048)^t {limit from n = 1 to n = 12}.
Step-by-step explanation:
The value of Maggie's car decreased by 10% since last year, when she bought it. If the car is now worth $11,000.00, how much was the car worth when she bought it?
How many possible outcomes are there from choosing an outfit from a blue shirt, a red shirt, black shorts, tan shorts, a pair of sneakers, and a pair of sandals?
Alex lives eight tenth of a mile from Sarah. What is eight tenths written as a decimal
which of the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola is xy=4
which of the following functions gives the length of the base edge
Select the ratios that are equivalent to 3 boys and 5 girls
HELP SUPER FAST PLS A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of the cardboard in inches?
Rectangle with width labeled on the right, width equals 4 and 1 over 2 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says area equals 36 and 3 over 4 square inches
Answer:
8 1/6
Step-by-step explanation:
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which is more, 5,998 millimeters or 6 meters