The diameter of a small gear is 16cm. This is 2.5 cm more than 1/4 of the diameter of a larger gear. What is the diameter of the larger g!ear
Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now?
Let the age of the Jane be [tex] x [/tex]
So age of Helen = [tex] x [/tex] + 8
Twenty years ago,
Age of Jane = [tex] x [/tex] - 20
And age of Helen = [tex] x [/tex] + 8 - 20 = [tex] x [/tex] - 12
Helen was three times as old as Jane
[tex] x [/tex] - 12 = 3 ([tex] x [/tex] - 20)
[tex] x [/tex] - 12 = 3 [tex] x [/tex] - 60
Add - 3[tex] x [/tex] on both sides,
[tex] x [/tex] - 3 [tex] x [/tex] - 12 = 3 [tex] x [/tex] - 3 [tex] x [/tex] - 60
-2[tex] x [/tex] - 12 = - 60
Add 12 on both sides
-2[tex] x [/tex] - 12 + 12 = - 60 + 12
-2[tex] x [/tex] = - 48
Divide both side by -2
[tex] \frac{-2x}{-2}=\frac{-48}{-2} [/tex]
[tex] x [/tex] = 24
Age of Jane = 24 yrs
Age of Helen = 32 yrs
Find the pair of numbers whose sum is 46 and whose product is a maximum.
what is the slope of the line
When paying off debts ,you should ___ .
A. pay the minimum
B.pay as much as possible
C.pay slightly more than the minimum
D.pay exactly half of what you owe
B.pay as much as possible
Step-by-step explanation:
Debts are unpaid money that a person owes to its lenders. The lender can be any bank or any other financial institution or any person.
Long accumulated debts on banks, if not paid, can result in a person filing for bankruptcy. So, it is always good if you pay your debts on time.
Paying minimum or slightly more than minimum amount will result in paying more in the near future. It is possible that if you always pay minimum amount, you will not be able to clear debts anytime soon.
So, its best that if you have money, always pay as much as possible to get rid of your debt.
what does 1/2x+30=55 equals?
given the function, f(x)=(x^3)-(3x^2)+(64x)-192 find the zeros
can someone help me!!!
A ____________ is a graph that uses adjacent rectangles to display frequencies, or relative frequencies, of quantitative data values. box-and-whisker plot histogram convenience sample mean absolute deviation
dose any one know these 4 answer i am raly struggling and i need the help asap
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Use the drop-down menus to identify the method used to collect data for each scenario. Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years. Mia asked 20 random students at her school how many hours they spend on the computer each day. Beatriz recorded the number of customers entering a store for each hour interval.
Answer:
Step-by-step explanation:
Given:
1) Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years.
Published data - Already recorded data used
2) Mia asked 20 random students at her school how many hours they spend on the computer each day.
Survey by Random sampling -- since a small size of whole population selected at random
3) Beatriz recorded the number of customers entering a store for each hour interval.
This is observational data because data was collected after really observing and recording the number of customers entering a store for each hour interval.
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Solve for y in terms of x.
2/3y - 4 = x
Please help . Time is critical for me in school rn
Answer:
[tex]y=\frac{3}{2}(x+4)[/tex]
Step-by-step explanation:
We are given
[tex]\frac{2}{3}y-4=x[/tex]
Since, we have to solve for y
so, we will isolate y on anyone side
Firstly, we add both sides by 4
[tex]\frac{2}{3}y-4+4=x+4[/tex]
[tex]\frac{2}{3}y=x+4[/tex]
Multiply both sides by 3
[tex]3\times \frac{2}{3}y=3\times(x+4)[/tex]
[tex]2y=3\times(x+4)[/tex]
now, we can divide both sides by 2
and we get
[tex]y=\frac{3}{2}(x+4)[/tex]
What is the complete factorization of r2 - 6r - 9s2 + 9? A) (r - 3 + 3s)(r - 3 - 3s) B) (r + 3 + 3s)(r - 3 - 3s) C) (r - 3 + 3s)(r - 3 + 3s)
We have factorized the expression 'r2 - 6r - 9s2 + 9' into (r - 3)^2 - (3s)^2 and then used the difference of squares formula to find the factorization as (r - 3 + 3s)(r - 3 - 3s). So the correct answer is option A)
Explanation:The question asked for the complete factorization of the expression r2 - 6r - 9s2 + 9. To factorize this, we can rewrite it into the formula form of a perfect square, which is a^2 - 2ab + b^2 = (a - b)^2.
Our expression fits this form when a = r and b = 3s. Following this, we can rewrite the expression as (r - 3)^2 - (3s)^2 = (r - 3 + 3s)(r - 3 - 3s). Therefore, the correct answer is option A) (r - 3 + 3s)(r - 3 - 3s)
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What is the quotient? x-1/7x2-3x-9
The quotient of the expression (x - 1)/(7x² - 3x - 9) cannot be determined
How to determine the quotient of the expression
From the question, we have the following parameters that can be used in our computation:
(x - 1)/(7x² - 3x - 9)
From the above, we have
degree of the numerator = 1
degree of the denominator = 2
The degree of the numerator is less than the degree of the denominator
This implies that the quotient of the expression cannot be determined
A plane left Chicago at 8 A.M. At 12 P.M., the plane landed in Los Angeles, which is 1,700 miles away.
If the plane travels at a constant rate, how many miles did it travel per hour?
The lengths of infants at birth in a certain hospital are normally distributed with a mean of 18 inches and a standard deviation of 2.2 inches. find the probability that an infant selected at random from this hospital measures between 16 and 21 inches.
how will the volume of the pyramid change if each side is multiplied by a factor of 1/2
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To prepare for the party, the host made a large batch of punch. The recipe makes 8 gallons of punch. How many cups of punch can be served from this batch?
A. 24
B. 128
C. 64
Apply the commutative property to 13 × 7 × 21 to rearrange the terms and still get the same solution
The commutative property in mathematics says that the order in which numbers are multiplied doesn't change the product. For example, using the commutative property, the product of 13 x 7 x 21 will be the same as 7 x 21 x 13, which is 1911.
Explanation:The commutative property is a fundamental concept in Mathematics which states that for multiplication and addition, numbers can be moved around (or commuted) without changing the result. For example, if you have the multiplication problem 13 * 7 * 21, thanks to the commutative property, you can rearrange this problem to: 7 * 21 * 13 or 21 * 13 * 7 or any other arrangement of these three numbers, and the result will remain the same.
Let’s see this in action:
Original arrangement: 13 * 7 * 21 = 1911
Changed arrangement: 7 * 21 * 13 = 1911
As you can see, regardless of how the terms were rearranged, the answer remained the same, thus demonstrating the commutative property.
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what does life expectancy measure
determine 7th term in the geometric sequence whose first term is 5 and whose common ratio is 2.
The 7th term of the geometric sequence with the first term being 5 and a common ratio of 2 is calculated using the formula Tn = [tex]a * r^{n-1}[/tex]. The 7th term is found to be 320.
The question asks us to determine the 7th term in a geometric sequence where the first term is 5 and the common ratio is 2. The formula for the nth term of a geometric sequence is given by
Tn = [tex]a * r^{n-1}[/tex], where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number. Substituting the given values into the formula, we can find the 7th term as follows:
T7 = [tex]5 * 2^{(7-1)}[/tex] = 5 * 2⁶ = 5 * 64 = 320. Hence, the 7th term of the geometric sequence is 320.
Form a sequence that has two arithmetic means between -13 and 89. a. -13, 33, 43, 89 c. -13, 21, 55, 89 b. -18, -36, -72, -144 d. -18, -81, -144
The trash can is in the shape of a cylinder that has a radius of 2 ft and a height of 5 feet what is the volume of the trash can round to the nearest tenth
Volume is a three-dimensional scalar quantity. The volume of the trash can is 62.8318 ft³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the trash can = π×r²h = π×(2ft)²×(5ft) = 62.8318 ft³
Hence, the volume of the trash can is 62.8318 ft³.
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Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let P(t), left parenthesis, t, right parenthesis denote the number of pages to read P as a function of time t (measured in hours). Write the function's formula
The function's formula that represents the number of pages Naoya has left to read at time t would be P(t) = 570 - 55t.
Explanation:From the information given we know that Naoya reads at a rate of 55 pages per hour. After 4 hours of reading, he still has 350 pages left to read. This means that before he started reading, he had (55 pages/hour * 4 hours + 350 pages) = 570 pages in total. Since he reads at constant rate, the function that describes the remaining pages to read would be P(t) = 570 - 55t, where t represents the time in hours and P(t) is the number of pages left to read.
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A woman is looking for a bigger square office. She finds an office twice the area of her current office. if the perimeter of her current office is 88feet, how many square feet is the new office?
The woman's new office has twice the area of her current office. By calculating the side length of the current square office from the perimeter and then finding the area, we determine the new office's area to be 968 square feet.
The question asks about calculating the area of a larger office which is twice the area of the woman's current office. Knowing the current office perimeter allows us to find the side length of the current square office and use it to calculate the area of both the current and the new office.
Calculate the side length of the current office from the given perimeter. The formula for the perimeter of a square is 4 × side length. Given that the perimeter is 88 feet, we divide by 4 to find that the side length of the current office is 22 feet. (88 ÷ 4 = 22)To find the area of the current office we square the side length (side length × side length). Thus, the area is 22 feet × 22 feet = 484 square feet.The new office has twice the area of the current one, so its area is 2 × 484 square feet = 968 ft².The area of the new, larger office is 968 ft².
If the diameter of a penny is 19.05 millimeters and the width of each penny is 1.52 millimeters, what is the approximate volume of the roll of pennies? Use 3.14 for π and round your answer to the nearest tenth.
Answer:
Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).
Step-by-step explanation:
Given : diameter of a penny is 19.05 millimeters and the width of each penny is 1.52 millimeters.
To find : volume of the roll of pennies.
Solution : We have given that
Diameter of a penny = 19.05 millimeters.
Width of each penny = 1.52 millimeters.
Volume of cylindrical roll of penny = pi * r² * h
Where, r = radius , h =height
Radius = [tex]\frac{Diameter}{2}[/tex]
Radius= [tex]\frac{19.05}{2}[/tex].
Radius = 9.525 mm
Plugging the values of r , h and pi = 1.14.
Volume of cylindrical roll of penny = pi * r² * h
Volume of cylindrical roll of penny =3.14 * (9.525)² * 1.52
Volume of cylindrical roll of penny = 433.02 mm³
Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).
Therefore, Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).
On the 4th of July, the probability of a person having a car accident is 0.08. What is the probability of a person driving while intoxicated or having a car accident if the probability of a person driving while intoxicated is 0.25 and the probability of a person having a car accident while intoxicated is 0.13?