Final answer:
Sarah has 1 1/5 cups of nuts and must add 2/5 cup of dried fruit to make a total of 1 3/5 cups of trail mix.
Explanation:
Imagine Sarah is making a trail mix for a hiking trip. She already has 1 1/5 cups of nuts and wants to add more dried fruit to reach a total of 1 3/5 cups of trail mix. To find out how much dried fruit she should add, we can set up the equation:
1 1/5 + x = 1 3/5
Converting mixed numbers to improper fractions gives us:
6/5 + x = 8/5
Subtracting 6/5 from both sides, we find that x (the amount of dried fruit to be added) is:
x = 8/5 - 6/5
x = 2/5
Therefore, Sarah needs to add 2/5 cup of dried fruit to the nuts to make 1 3/5 cups of trail mix.
Austin is using a funnel shown to fill a glass bottle with colored sand Estimate the volume of the funnel number 21 please
Write the first terms of the sequence. Rule:start at 1/2,add1/3
Christopher Christopher just found beautiful yarn for 20% off at his favorite yarn store. He can make one scarf from 2/3 of a ball of yarn. If Christopher buys 12 balls of yarn, how many scarves can he make
(A rectangular prism has a length of 1 1/4 yards, a width of 2 1/2 yards, and a height of 4 yards.
Enter the volume of the prism as a mixed number in simplest form in the box.
Answer:
Step-by-step explanation:
It is given that A rectangular prism has a length of [tex]1\frac{1}{4}[/tex]yards a width of [tex]2\frac{1}{2}[/tex] yards, and a height of 4 yards.
Now, the volume of the prism is given as:
[tex]V=Length{\times}width{\times}height[/tex]
[tex]V=\frac{5}{4}{\times}\frac{5}{2}{\times}4[/tex]
[tex]V=\frac{25}{2}[/tex]
[tex]V=12\frac{1}{2}cubic yards[/tex]
Therefore, the volume of the rectangular prism will be [tex]V=12\frac{1}{2}cubic yards[/tex].
Answer:
V=12 1/2cubic yards.
Step-by-step explanation:
A human society has 73 dogs and cats to be adopted. the number of cats is 10 more than twice the number of dogs. Write a system of linear equations that represent this situation. How many of each animal is up for adoption?
A linear equation of one variable is expressed in the form of ax + b = 0, where a and b are the two integers, and x is a variable.
In the given question, the linear equation can be represented as:
2x + 10 + x = 73.
The number of dogs is 21, and the number of cats available is 52.
Given that:
Total number of dogs and cats = 73
Let the number of dogs be x.
The number of cats, as given is = 10 + 2x
Now, solving for the equation:
x + 10 + 2x = 73
Solving for the variables:
3x + 10 = 73
3x = 73 -10
3x = 63
x = [tex]\dfrac {63}{3}[/tex]
x = 21
The number of dogs available is 21.
The number of cats available is:
2x + 10
Putting the value of x:
2 (21) + 10
52
Thus, the number of dogs is 21, and the number of cats available is 52.
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Explain the Segment of Decant Theorem for Geometry
What shows all like terms in this expression?
4x - 3 + 7x + 1
Answer:
a
Step-by-step explanation:
HELP What is the area of this figure?
The sum of three consecutive even numbers is 48. What are the smallest of these numbers?
Represent the proportional relationship described with an equation where p equals pepperoni and z equals pizza: eighteen pepperoni for each pizza A) p = 18z B) 18p = z C) p = 18 z D) z = 18 p
Answer:
The answer is A. p=18z I just took the test
Answer:
It is A I got it right on usa test prep
Step-by-step explanation:
Jones of Boston borrowed $40,000, 90 day, 10% note. After 60 days Jones made an initial payment of $6,000. Assuming the U.S. Rule what is adjusted balance after the first payment. Use 360 days.
Why is subtracting an expression similar to distributing -1? Explain.
Subtracting an expression is akin to distributing -1 to each term within the expression. This is because subtraction can be viewed as adding the negation of the expression, which involves multiplying each term by -1. So, each term within the expression gets negated when subtracting.
When you subtract an expression, you can think of it as distributing a negative sign (-1) to each term within the expression. Here's a step-by-step explanation:
Start with the expression you want to subtract from, let's call it A.
When you subtract another expression, let's call it B, from A, you're essentially adding the negation of B to A.
The negation of B is obtained by multiplying each term of B by -1.
Distributing -1 to each term of B results in subtracting each term of B individually from A.
This process aligns with the distributive property, making subtracting an expression akin to distributing -1 to each term within the expression.
consider the following system with a solution (1,3) equation 1 of the system 2x+y=5 equation 2 of the system x-2y=-5 prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution
To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system. Then we will calculate the solution to the modified system of equations and check if the solution is the same.
Explanation:To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system of equations (1,3). Then we will calculate the solution to the modified system of equations in which the first equation is replaced with the sum of the two equations. If the solution to the modified system is also (1,3), then we have shown that the modified system has the same solution.
Original system:
Equation 1: 2x + y = 5
Equation 2: x - 2y = -5
Substitute x = 1 and y = 3 into the original equations to check if it is a solution:
Equation 1: 2(1) + 3 = 5 => 2 + 3 = 5 => 5 = 5 (true)
Equation 2: 1 - 2(3) = -5 => 1 - 6 = -5 => -5 = -5 (true)
Hence, (1,3) is a solution to the original system of equations.
To create the modified system, we will sum equation 1 and a multiple of equation 2:
New equation 1: (2x + y) + k(x - 2y) = 5 + k(-5), where k is a constant
Expanding and simplifying the equation:
(2 + k)x + (1 - 2k)y = 5 - 5k
Let's substitute x = 1 and y = 3 into the modified equation to check if (1,3) is a solution:
(2 + k)(1) + (1 - 2k)(3) = 5 - 5k
2 + k + 3 - 6k = 5 - 5k
3 - 5k = 5 - 5k
3 = 5 (false)
Therefore, the modified system does not have the same solution as the original system, disproving the statement.
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What number could be added to 0.40 mL for the level of precision to be 0.01mL
Answer:
- 0.39
Step-by-step explanation:
Level of precision = 0.01 mL
We need to find a number which could be added to 0.40 mL for the level of precision to be 0.01 mL .
Let x be a number which could be added to 0.40 mL for the level of precision to be 0.01 mL .
[tex]x+0.40=0.01[/tex]
On subtracting 0.40 from both sides , we get
[tex]x+0.40-0.40=0.01-0.40[/tex]
On solving , we get
[tex]x+0=0.01-0.40[/tex]
We know that [tex]x+0=x=0+x[/tex] where 0 is the additive inverse .
So,
[tex]x=0.01-0.40[/tex]
Here , [tex]0.01-0.40=-0.39[/tex]
Therefore ,
[tex]x=0.01-0.40=-0.39[/tex]
Therefore , -0.39 could be added to 0.40 mL for the level of precision to be 0.01mL
dennis wants to buy a card for his wife. dennis calculates the amount of the card as $4.50. the actual price of the card is $4. what is Dennis's percent error?
Final answer:
Dennis's percent error in estimating the price of the card is 12.5%, calculated by taking the difference between his estimate and the actual price, dividing by the actual price, and then multiplying by 100.
Explanation:
Dennis calculated the amount of the card as $4.50, but the actual price is $4.00. To find Dennis's percent error, we'll need to calculate the difference between his estimated price and the actual price, and then divide that by the actual price. Finally, we'll multiply that number by 100 to get the percent error.
Here's how we'll calculate it:
Divide the error by the actual value: $0.50 ÷ $4.00 = 0.125.
Multiply by 100 to convert to a percentage: 0.125 × 100 = 12.5%.
The percent error in Dennis's estimate is 12.5%.
10p = 66 what is the value of p
Who can help me with #9 a. and b.
Need help with number 12 please, thanks.
Last year, at the Great American Pie Festival, over 16,000 slices of pie was eaten. If each piece of pie is 1/8 of and entire pie, how many pies were eaten at the festival?
Answer:
2,000 pies!
Step-by-step explanation:
Explain how the Quotient of Powers was used to simplify this expression. 2 to the fifth power, over 8 = 22 By finding the quotient of the bases to be one fourth, and cancelling common factors By finding the quotient of the bases to be one fourth, and simplifying the expression By simplifying 8 to 23 to make both powers base two, and subtracting the exponents By simplifying 8 to 23 to make both powers base two, and adding the exponents
Answer:
we can do it by simplifying 8 to [tex]2^3[/tex] to make both powers base two, and subtracting the exponents.
Step-by-step explanation:
We have been given the expression [tex]\frac{2^5}{8}=2^2[/tex]
8 can be rewritten as [tex]2^3[/tex]
Hence, the given expression becomes
[tex]\frac{2^5}{2^3}=2^2[/tex]
After subtracting the exponents on left hand side of the equation we get:
[tex]2^2=2^2[/tex]
we can do it by simplifying 8 to [tex]2^3[/tex] to make both powers base two, and subtracting the exponents.
Answer:
cStep-by-step explanation:
We have been given the expression 2^5/8=2^2
8 can be rewritten as 2^3
Hence, the given expression becomes
2^5/2^3=2^2
After subtracting the exponents on left hand side of the equation we get:
2^2=2^2
we can do it by simplifying 8 to 2^3 to make both powers base two, and subtracting the exponents.
Justin weighs 15 pounds less than Greg weighs. Half of Greg’s weight is 75 pounds less than Justin’s weight. How much does each of them weigh? Greg weighs 200 pounds, and Justin weighs 185 pounds. Greg weighs 190 pounds, and Justin weighs 175 pounds. Greg weighs 180 pounds, and Justin weighs 165 pounds. Greg weighs 170 pounds, and Justin weighs 155 pounds.
Answer:
greg weighs 180 justin weighs 165
Step-by-step explanation:
Helpppp please anyone. I don't understand
stewart draws a triangle , and each side is 2 1/6 inches long. Judith draws a square , each side is 1 5/8 inches long . which figure has the greater perimeter, the triangle or the square?
Upon calculating, it is found that both Stewart's triangle and Judith's square have the same perimeter of 6 1/2 inches. This shows that despite different shapes, their perimeters can be equal if the lengths of their sides are chosen accordingly.
Explanation:The question is about comparing the perimeters of a triangle drawn by Stewart and a square drawn by Judith. Stewart's triangle has each side measuring 2 1/6 inches long, which when converted to improper fraction becomes 13/6 inches. For the triangle, the perimeter is calculated by multiplying the length of one side by three (since a triangle has three sides). The perimeter of Stewart's triangle is 13/6 * 3 = 39/6 = 6 1/2 inches.
Judith's square has each side measuring 1 5/8 inches long, which is equivalent to 13/8 inches. For the square, the perimeter is the length of one side times four (because a square has four equal sides). Thus, the perimeter of Judith's square is 13/8 * 4 = 52/8 = 6 1/2 inches.
Therefore, both the triangle and the square have the same perimeter of 6 1/2 inches.
Your friend invites you to go to an indoor skateboard park. You'd like to go, but since you don't have a helmet or knee pads, you'll have to rent them. You'll also need to but a day pass to enter the park.
Write a formula that will help you determine your total cost.
Let's let:
h = helmet rental
k = knee pad rental
p = cost of day pass
c = total cost
You and your friend are selling tickets to a charity event. You sell 4 adult tickets and 11 student tickets for $148. Your friend sells 7 adult tickets and 5 student tickets for $145. What is the cost of a student ticket?
50 POINTS!!! SHOW YOUR WORK AND ANSWER CORRECTLY OR ELSE A MODERATOR WILL HANDLE YOU! Let f (x) = −x^2 − 5x + 36. What is the value of f(-3)? Show your work. Best answer gets brainliest.
Jessica has the option to switch to a plan that charges $65.00 per month with unlimited text messages. Jessica typically sends about 900 text messages per month. Does it make sense for her to switch to the new plan ? explain.
Jessica has the option to switch to a plan that charges $65.00 per month with unlimited text messages.
Jessica typically sends about 900 text messages per month.
Cost per message under the new plan = $65 / 900 = $ 0.072 per message
It make sense for her to switch to the new plan only if the cost per message in her existing plan is more than $ 0.072
Hope this helps..!!
Thank you :)
The length of a rectangle is 6 inches more than it’s with the perimeter of the rectangle is 24 inches what is the width and length of the rectangle
when writing an equation of a proportional relationship in the form y equals KX what does K represent
Answer:
k = the constant of proportionality .>. sorry this already kinda answered ;w;'
Wesley walked 11 miles in 4 hours if he walked the same distance every hour , how far did he walk in one hour
Wesley walked 2.75 miles in one hour, calculated by dividing the total distance (11 miles) by the total time (4 hours).
The question asks how far Wesley walked in one hour if he walked 11 miles in 4 hours at a consistent pace. To find this, we can calculate his average speed by dividing the total distance by the total time. This gives us an equation: Average speed = Total distance / Total time, which simplifies to: Average speed = 11 miles / 4 hours.
Performing the division, we get an average speed of 2.75 miles per hour. Therefore, Wesley walked 2.75 miles in one hour.