Final answer:
To find percentages of numbers, convert the percent to a decimal and then multiply. To find the unknown quantity in an equation involving percentages, divide the given number by the percent expressed as a decimal.
Explanation:
To find 66 2/3 percent of 87, first convert the percent to a decimal by dividing it by 100: 66 2/3 ÷ 100 = 0.6667. Then multiply the decimal by 87: 0.6667 x 87 = 58.33. So, 66 2/3 percent of 87 is approximately 58.33.
To find 1 percent of 3,620, divide 3,620 by 100: 3,620 ÷ 100 = 36.2. So, 1 percent of 3,620 is 36.2.
To find x in the equation 62 1/2 percent of x is 5, first convert the percent to a decimal: 62 1/2 ÷ 100 = 0.625. Then divide 5 by the decimal: 5 ÷ 0.625 = 8. So, x is 8.
To find k in the equation 300 percent of k is 42, first divide 42 by 300: 42 ÷ 300 = 0.14. So, k is 0.14.
A stop sign that is 7 feet tall casts a shadow that is 8 feet long. Find the length of the shadow casted by a nearby 63-foot tall building.
Answer:
72 feet is the answer. The shadow of the 63 ft tower.
To find the shadow length of a 63-foot building given a 7-foot stop sign's 8-foot shadow, a proportion is used, resulting in a shadow length of 72 feet.
A student asked how to find the length of the shadow cast by a 63-foot tall building given that a 7-foot tall stop sign casts an 8-foot long shadow. This problem can be solved using simple proportions since the ratio of the height of an object to the length of its shadow is constant when the sun's angle is constant. The proportion is as follows: height of stop sign / length of stop sign's shadow = height of building / length of building's shadow. Plugging in the numbers: 7 / 8 = 63 / x, where x is the length of the building's shadow. Solving for x, we find that x = 8 * 63 / 7 = 72. Therefore, the length of the shadow cast by the 63-foot tall building is 72 feet.
Y=1/3x-4; y=7/3x+4 solve by substitution
Answer Problem 1: 3*(y+4)
Show Work:
1) y = (1/3)*x-4 // - (1/3)*x-4
2) y-((1/3)*x)+4 = 0
3) (-1/3)*x+y+4 = 0
4) y-1/3*x+4 = 0 // - y+4
5) -1/3*x = -(y+4) // : -1/3
6) x = (-(y+4))/(-1/3)
7) x = 3*(y+4)
8) x = 3*(y+4)
Answer Problem 2: Y=-7/12
Show Work:
Step 1: Flip the equation.
7/3 x+4=y
Step 2: Add -4 to both sides.
7/3x+4+−4=y+−4
7/3x=y−4
Step 3: Divide both sides by 7/3.
PLEASE ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
Given the equation y = 3x - 9
Check each of the given equations
A
y = 3(x - 9) ← distribute
= 3x - 27 ≠ 3x - 9 ← False
B
y = [tex]\frac{1}{3}[/tex](x - 3) ← distribute
= [tex]\frac{1}{3}[/tex] x - 1 ≠ 3x - 9 ← False
C
y = [tex]\frac{1}{3}[/tex](x - 27) ← distribute
= [tex]\frac{1}{3}[/tex] x - 9 ≠ 3x - 9 ← False
D
y = 3(x - 3) ← distribute
= 3x - 9 ← True
Jesus spent 1/4 of his money on a pizza and 1/4 of his money on salad. What fraction of his money did Jesus spend on dinner?
Answer:
2/4 of his money was spent on dinner
Step-by-step explanation:
Answer:
2/4 or 1/2 of his money of dinner
Step-by-step explanation:
When using your brain you come to the conclusion that the pizza and the salad is his dinner because it is food, so we add those two fractions together to get 2 out of 4 or 1 out of 2.
I need answer for this
The perimeter of the garden is 57.14 m and
the total area of the garden is 178.28 sq. m.
Solution:
Given length of the rectangle = 16 m
Width of the rectangle = 8 m
Radius of the semi-circle = half of the width of the rectangle
Radius = 4 cm
Perimeter of the garden is two lengths of the rectangle and 2 curve sides of the semi-circle.
Perimeter = [tex]2l+2(\frac{2\pi r}{2} )[/tex]
= [tex]2l+2\pi r[/tex]
= [tex]2(16)+2\times\frac{22}{7}\times4[/tex]
= 32 + 25.14
= 57.14 m
Total area of the garden is the area of the rectangle and area of the two semi-circles.
Area of the garden = [tex](l\times w)+ 2(\frac{\pi r^2}{2})[/tex]
= [tex](l\times w)+ \pi r^2[/tex]
= [tex]16\times8+\frac{22}{7} \times 4\times 4[/tex]
= 128 + 50.28
= 178.28 square meter
Hence, the perimeter of the garden is 57.14 m and
the total area of the garden is 178.28 sq. m.
the rent is 7.50
write an algebra expression to represent the cost to rent a luxury car for x days
Answer:
Step-by-step explanation:
Rent cost 7.50
For x days the rent to pay = 7.50×n
= 7.50n
An index has a length of 7 cm and width of 4 cm. What it’s perimeter?
Answer:
22
Step-by-step explanation:
7+7+4+4=22
A shelf contains 28 boxes of cereal. Each box has a mass of 375 grams.
Which equation can you use to find the total mass of the boxes?
What is the total mass, m, in grams of all the boxes?
A.28 + 375 = m; m = 403 grams
B.28 x 375 = m; m = 1,050 grams
C.28 x 375 = m; m = 10,500 grams
D.28 x 375 =m; m = 11,500 grams
Answer:
Step-by-step explanation:
each box is 375 grams...and there are 28 boxes
total mass(m) = 28 * 375 = 10,500 grams
The weight of all the boxes of cereals can be found by the equation (C) "28 x 375 = m" and the weight is 10,500 grams.
What are equations?Two expressions are combined by the equal sign to form a mathematical statement known as an equation. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.So, the total mass of all the boxes:
The number of boxes is 28.Each box weighs 375 grams.Then, calculate as follows:
375 × 28 = m375 × 28 = 10,500 gramsSo, option (C) is correct.
Therefore, the weight of all the boxes of cereals can be found by the equation (C) "28 x 375 = m" and the weight is 10,500 grams.
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What is the volume of this square pyramid?
384 cm³
288 cm³
192 cm³
96 cm³
V = Abxh/3 = (12cmx12cm)x8cm/3 = 144cm²x8cm/3 = 384 cm³
Answer:
384 cm³
Step-by-step explanation:
Volume = a^2(h/3)
a = base edge = 12 cm
h = height of pyramid = 8 cm
Volume = 12^2*(8/3)
Volume = 144*(8/3)
Volume = 48*8
Volume = 384 cm³
Solve the 2 step equation 3x+3=15
Subtract the entire equation by 3: 3x = 12
Lastly, divide by 3 to get x alone: x = 4
Answer: 4
Step-by-step explanation:
3x+3=15
-3 -3
3x 12
3 3
x= 4
Trapezoid JKLM is is shown below. What is the length in centimeters, of KL
The complete question is:
Trapezoid JKLM is shown below.
What is the length, in centimeters, of KL ?
A. 12 cm
B. 10 cm
C. 9 cm
D. 6 cm
The mentioned figure is attached.
Answer:
[tex]\large\boxed{option\text{ B. }(\overline{KL})=10cm}[/tex]
Explanation:
1. KL is the hypotenuse of a right triangle; hence, you can use Pythagora's theorem to find its length.
2. The height 8 cm is one leg of the right triangle.
3. The other leg may be found by difference:
[tex]\overline{ML} -\overline{JK}=15cm-9cm=6cm[/tex]
4. Now you can use Pythagora's theorem:
[tex]hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ (\overline{KL})^2=(8cm)^2+(6cm)^2\\ \\ (\overline{KL})^2=64cm^2+36cm^2=100cm^2\\ \\ (\overline{KL})=10cm[/tex]
Andre and Elena are reading the same book over the summer.. Andre says he has read 1/5 of the book. Elena says she has read 20 more pages than Andre. If Elena is on page 55, how many pages are in the book?
There are 175 pages in the book.
Step-by-step explanation:
Given,
Pages read by Elena = 55 pages
Let,
x be the number of pages of book.
Pages read by Andre = [tex]\frac{1}{5}\ of\ total\ pages = \frac{1}{5}x[/tex]
As Elena has read 20 more pages than Andre, therefore,
[tex]\frac{1}{5}x+20=55\\\\\frac{1}{5}x=55-20\\\\\frac{1}{5}x=35[/tex]
Multiplying both sides by 5
[tex]5*\frac{1}{5}x=35*5\\\\x=175[/tex]
There are 175 pages in the book.
Keywords: fraction, variable
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Divide 7.956 . 10-6 by 2.55 - 10-3
Answer: 3.12 x 10^-3
Step-by-step explanation:
Charlie wants to split his bonus of 4,206 so that he will be able to enjoy it throughout the year.how much money should he permit himself to spend the same amount each month
the answer is 350.50, the 4th answer
Mike has a recipe that feeds one person that calls for 3/8 teaspoon of salt. How much salt is needed to make the recipe if he needs to cook the recipe for 8 people? a. 3/64 teaspoon c. 24/64 teaspoon b. 1 3/8 teaspoons d. 3 teaspoons
Answer:
3 teaspoons of salt is needed to cook the recipe for 8 people.
The correct option is d. 3 teaspoons.
Step-by-step explanation:
Given:
Mike has a recipe that feeds one person that calls for 3/8 teaspoon of salt.
Now, to find the quantity of salt is needed to cook the recipe for 8 people.
As, given the unit rate is:
[tex]\frac{3}{8}[/tex] teaspoon salt per person.
So, to get the salt needed to cook for 8 people we multiply 8 by [tex]\frac{3}{8}[/tex] :
[tex]8\times \frac{3}{8}[/tex]
[tex]=\frac{24}{8}[/tex]
[tex]=3\ teaspoons.[/tex]
Therefore, 3 teaspoons of salt is needed to cook the recipe for 8 people.
The correct option is d. 3 teaspoons.
a bookstore employee is given a 20% discount off the retail price of any book. assuming there is no tax, how many dollars does she pay for a book with a retail price of $55?
Answer:
= $ 49.5
Step-by-step explanation:
We are given;
Discount off retail price is 20%Retail price is $55Required to determine the amount paid
Taking the retail price as 100%
Then, amount paid will be (100 % - 10%) 90% of the retail price
Therefore;
Amount paid = 90% × $ 55
= 0.9 × $ 55
= $ 49.5
Thus, the employee paid $ 49.5 for the book.
2 3/4+3 5/8 simplified
[tex]2\frac{3}{4}+3 \frac{5}{8}=6\frac{3}{8}[/tex]
Solution:
Given expression is [tex]2\frac{3}{4}+3 \frac{5}{8}[/tex].
To simplify the expression [tex]2\frac{3}{4}+3 \frac{5}{8}.[/tex]
Let us first convert the mixed fraction into improper fraction.
[tex]2\frac{3}{4}+3 \frac{5}{8}=\frac{(2\times 4) + 3}{4}+ \frac{(3 \times 8)+5}{8}[/tex]
[tex]=\frac{8+ 3}{4}+ \frac{24+5}{8}[/tex]
[tex]=\frac{11}{4}+ \frac{29}{8}[/tex]
Take LCM for the denominators (LCM of 4, 8 = 8) and make the same.
[tex]=\frac{11\times2}{4\times 2}+ \frac{29\times1}{8\times1}[/tex]
[tex]=\frac{22}{8}+ \frac{29}{8}[/tex]
[tex]=\frac{51}{8}[/tex]
Now, divide 51 by 8 and again write it in the mixed fraction.
[tex]=6\frac{3}{8}[/tex]
[tex]2\frac{3}{4}+3 \frac{5}{8}=6\frac{3}{8}[/tex]
Hence, the simplified answer is [tex]6\frac{3}{8}[/tex].
How do I find the area
Answer:
73.12 yd²
Step-by-step explanation:
Find the triangle first
A=½bh
a=½×12×8
a=6×8
a=48->triangle
semicircle=
a=½×pi×r²
a=½×3.14×4²
a=½×3.14×16
a=8×3.14
a=25.12
add these two
48+25.12=73.12 yd²
Megan buys all 40 pounds of the farmers tomatoes. She then buys the remaining vegetables according to the ideal ratios shown above. How many pounds of onions and broccoli does Megan buy from the farmer?
Answer:
40 pounds
Step-by-step explanation:
I see no ratios shown above so I guessed
Do these rates form a proportion?
21 miles in 6hours and 14.3 miles in 3 hours
Answer:
These rates DO NOT form a proportion.
Step-by-step explanation:
Two quantities P and Q are said to be in proportion is and only if:
[tex]\frac{P}{Q} = k[/tex] for all values of P and Q.
here, k = Proportionality Constant.
Case 1: when P = 21 miles , Q = 6 hours
[tex]\frac{P}{Q} = \frac{21}{6} = 3.5[/tex]
⇒ k 1 = 3.5
Case 2: when P = 14.3 miles , Q = 3 hours
[tex]\frac{P}{Q} = \frac{14.3}{3} = 4.76[/tex]
⇒ k 2 = 4.76
As we can see in both the cases, k 1 ≠ k 2
Hence, P is NOT PROPORTIONAL to Q.
So, these rates DO NOT form a proportion.
Find the equation of the line that passes through the point (-1, 2) and that has a
slope of 4.
Oy=2x-1
Oy=-1*+6
Oy= 4x+6
Oy=12-1
Answer:
y = 4x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (- 1, 2) into the partial equation
2 = - 4 + c ⇒ c = 2 + 4 = 6
y = 4x + 6 ← equation of line
Mr.quick bought a new computer system.Regular price was 1580,but he got a 15% discount how much did he pay
Answer:
$1343
Step-by-step explanation:
After subtracting 15% from 100% of the original price, the price Mr. Quick paid is 85% of the original price.
0.85 × 1580 = 1343
Mr. Quick paid 1343 for his computer.
A used car is for sale for $24,000. Jared took a chance and offered the owner 1/4 of the selling price. How much did Jared offer?
Answer:
Jared offer $6,000.
Step-by-step explanation:
Given:
A used car is for sale for $24,000. Jared took a chance and offered the owner 1/4 of the selling price.
Now, to find the price Jared offer.
Selling price = $24,000.
Jared offer = [tex]\frac{1}{4}[/tex] of selling price.
So, to get the price Jared offer:
[tex]\frac{1}{4}\ of\ \$24000[/tex]
[tex]=\frac{1}{4} \times 24000[/tex]
[tex]=\frac{24000}{4}[/tex]
[tex]=\$6000.[/tex]
Therefore, Jared offer $6,000.
Hardy is packing his book collection into a box. Each book measures 4in by 6in by 1 inch. The box he uses measures 24in by 24in by 8 inches.
1. If Hardy fills the box completely, what is the greatest number of books that fit into the box?
2. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.
3. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.
Thank you so much for help! Just a mom who hates volume trying to help her kid with volume.
Answer:
1. 192 books.
2. 96 books.
3. 24 books.
Step-by-step explanation:
1. Let's find the volume of each book and the volume of the box, this way:
Volume of a book = 4 * 6 * 1 = 24 inches ³
Volume of the box = 24 * 24 * 8 = 4,608 inches ³
2. If Hardy fills the box completely, what is the greatest number of books that fit into the box?
Greatest number of books = Volume of the box/Volume of a book
Greatest number of books = 4,608/24
Greatest number of books = 192
3. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.
The height of the box is 8 inches, so it can only can hold 2 or 8 layers of books, since the books are 4 * 6 * 1 inches.
Greatest number of layers = Height of the box/Width of a book
Greatest number of layers = 8/1 = 8
Minimum number of layers = Height of the box/Height of a book
Minimum number of layers = 8/4 = 2
Upon saying that, we have:
Number of books per layer = Greatest number of books/Minimum number of layers
Number of books per layer = 192/2 = 96
4. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.
Number of books per layer = Greatest number of books/Number of layers
Number of books per layer = 192/8
Number of books per layer = 24
A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from the bag. What expression would give the probability that one marble is yellow and the other marble is red?
Answer:
The second choice
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.971
This is the correct answer.
Darcy harvest 8 3/4 acres of corn every 5/6 of an hour. How many acres per hour?
Answer:
The answer is [tex]10\frac{1}{2}\ per\ hour.[/tex]
Step-by-step explanation:
Given:
Darcy harvest 8 3/4 acres of corn every 5/6 of an hour.
Now, to find the acres per hour it takes to harvest.
Darcy harvest = [tex]8\frac{3}{4}=\frac{35}{4}\ acres.[/tex]
The time he took to harvest = [tex]\frac{5}{6}\ hour.[/tex]
So, to get the acres per hour we put formula:
[tex]Distance = \frac{35}{4}\ acres.[/tex]
[tex]Time=\frac{5}{6}\ hour.[/tex]
[tex]Speed=\frac{distance}{time}[/tex]
[tex]Speed=\frac{\frac{35}{4}}{\frac{5}{6}}[/tex]
[tex]Speed=\frac{35}{4}\times \frac{6}{5}[/tex]
[tex]Speed=\frac{210}{20}[/tex]
[tex]Speed=\frac{21}{2}[/tex]
[tex]Speed=10\frac{1}{2}\ per\ hour.[/tex]
Therefore, the answer is [tex]10\frac{1}{2}\ per\ hour.[/tex]
(2x^3-3x^2-19x+30)/(x-3)
Answer:
2x^3 + 3x - 10
Step-by-step explanation:
Mariko says that the graph that passes through (-3,-3), (-3,0), and (-3,3) represents a
linear function. Is she correct? Explain your reasoning.
Answer:
The graph that passes through (-3,-3), (-3,0), and (-3,3) does not represents a linear function.
Step-by-step explanation:
The graph that passes through (-3,-3), (-3,0), and (-3,3) does not represents a linear function. Because if we tried to find the slope for either two pairs of these coordinates. The slope would equal infinity
Lets say we find the slope of (-3,-3) and (-3,0)
[tex]\frac{-3-0}{(-3)-(-3)} =\frac{-3}{0}[/tex] Slope = [tex]\infty}[/tex]
Now lets say we find the slope of (-3,0) and (-3,3)
[tex]\frac{0-3}{(-3)-(-3)} =\frac{-3}{0}[/tex] Slope = [tex]\infty[/tex]
So now we can see that both lines of each slope is parallel to the y-axis which means that the lines a Undefined Slope (also known as Infinite Slope).
Which is NOT a factor affecting your Credit Score? Question 1 options: A.Types of Credit B. Salary C.Payment History D.Length of Credit History
Answer:
B salary
Step-by-step explanation:
Your employment status, salary, and bank account balances are never disclosed on your report and have no bearing on your rating.
What impact of Salary on Credit Score?Although your income has no bearing on your credit score, it's still crucial to understand the five key components of a FICO credit score, the most widely used credit score by lenders.
History of payments (35%): Your credit score is mostly influenced by whether you have a history of making on-time payments on your credit accounts.
Your salary does not directly affect your credit score, but it does affect your ability to pay off credit card debt.
Therefore, Your race, gender, marital status, level of education, religion, political party, or source of income are all factors that are never taken into account when calculating your credit ratings.
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NEED HELP PLEASE!
Fill in the blank with the correct response. If 3/4 = x/8, then x is equal to.
THANKS!
answer x = 8
because 3/4 times 2 equals 6/8 so the solution is 6/8