To satisfy his grandmother's request, Dave needs to mix [tex]\( \frac{1}{5} \)[/tex] cup of fruit for every [tex]\( \frac{1}{3} \)[/tex] cup of nuts.
To find out how many cups of fruit Dave needs to mix for a single cup of nuts, we need to find a common denominator for [tex]\( \frac{1}{5} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex], which is 15.
[tex]\[ \frac{1}{5} \times \frac{3}{3} = \frac{3}{15} \][/tex]
[tex]\[ \frac{1}{3} \times \frac{5}{5} = \frac{5}{15} \][/tex]
So, Dave needs to mix [tex]\( \frac{3}{15} \)[/tex] cup of fruit for every [tex]\( \frac{5}{15} \)[/tex] cup of nuts.
Therefore, to satisfy his grandmother's request, Dave must mix [tex]\( \frac{3}{15} \)[/tex] cup of fruit for a single cup of nuts.
The complete Question is given below:
dave is helping his grandmother make trail mix his grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts. To satisfy his grandmother's request, drave must mix ___ cups of fruit for a single cup of nuts
Which statement best explains the value of 18 − (−5)?
The additive inverse of −5 is +5, so 18 − (−5) = 23.
The additive inverse of −5 is −5, so 18 − (−5) = 23.
The additive inverse of −5 is −5, so 18 − (−5) = 13.
The additive inverse of −5 is +5, so 18 − (−5) = 13.
WALK Heather was out for a leisurely walk at a rate of 3 miles per hour. What was her speed in yards per minute?
A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents time in minutes and p represents how far the paint is spreading.
The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.
Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)
Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate π in this problem. (4 points)
Answer:
r(t) = 3t ; where t represents the time in minutes and r represents how far the paint is spreading.
A(r) = πr²
Part A:
A[r(t)] = π (3t)² = 3.14 * 9t² = 28.26t²
Part B:
r(10) = 3(10) = 30
A(r) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit
Step-by-step explanation:
The cost of producing key chains with the company logo printed on them consists of a onetime setup fee of $205.00 plus $0.70 for each key chain produced. This cost can be calculated using the formula C=205.00+0.70p, where p represents the number of key chains produced and C is the cost. Use the formula to calculate the cost of producing 1700 key chains
What is the average speed (miles/hour) for an object going 1500 feet in 1 minute. Round answer to two decimal places.
there are 3600 seconds per hour
5280 feet per mile
1 foot per second = 3600/5280 = 0.681818 Miles per Hour
60 seconds per minute
so 1500/60 = 25 feet per second
25 x 0.681818 = 17.05 miles per hour
a number divided by 7 is 9
Pittsburgh international airport had approximately 714,587 passengers in august 2009. Write a number that is greater than 714,587.
It takes 1629 digits to number the pages of a book.How many pages does the book have?
the table represents a function. what is the value of f(-1)?
f (-1) = - 3
f (-1) = - 1
f (-1) = 0
f (-1) = 6
The value of f(-1) from the table given is 0
Table of functionsTable of functions are used to find the relationship between variables. The variables x and y can be written as coordinate (x, y)
In order to determine f(-1), we need the value of f(x) at the point where x is 1. From the table, the value of f(-1) is 0
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Diana is going camping with her family. Their campsite is 5/8 mile away. They walk at a steady speed of 2 1/2 miles per hr. How many minutes will It take them to get to the campsite
What is 3^ 2/3 equal to?
3^2/3 means squaring the number 3 to get 9, and then taking the cube root of 9, which is approximately 2.08008.
Explanation:To calculate 3^2/3, we are dealing with an exponential expression where 3 is the base and 2/3 is the exponent. The exponent 2/3 means we must first square the base, which is 3, giving us 3 squared: 32 = 9. Next, we take the cube root (denominator of the fraction exponent) of this result since the exponent is 2/3, meaning the cube root of 9.
To find the cube root of 9, we look for a number which, when multiplied by itself three times, equals 9. Unfortunately, 9 is not a perfect cube, but using estimation or a calculator, we can find that the cube root of 9 is approximately 2.08008. Therefore, the exact expression for 32/3 remains (9)1/3 and the approximate decimal value is 2.08008.
Lucia wants to buy some posters over the Internet. Each poster costs $6.67 and has a shipping cost of $9.99 per order. If Lucia wants to spend no more than $30 for her posters, which inequality shows the maximum number of posters, p, that she can buy?
A professor teaches a small lecture class with 25 students. For a certain class, 22 students attend the lecture. What is the experimental probability that a student is absent?
What's the answer to this!! The highest point on the state of Louisiana is driskall mountain. It rises 535 feet above sea level. Write the elevation of driskall mountain as an integer
two triangles.are.similar, solve for x if au=20x +108, ub=273, bc= 703, uv=444, AV = 372 and AC=589
If two triangles are similar then the corresponding sides are in proportion. Thus,
AB / AU = BC / UV = AC / AV
AB / (20x+108) = 703 / 444
Where AB is equivalent to:
AB = AU + UB
AB = 20x + 108 + 273
AB = 20x + 381
Therefore going back to the first equation:
(20x + 381) / (20x + 108) = 703/444
444 (20x + 381) = 703 (20x + 108)
8880x + 169164 = 14060x + 75924
14060x - 8880x = 169164 – 75924
5180 x = 93240
x = 93240 / 5180
x = 18 (ANSWER)
The correct value of x is [tex]\(\frac{1}{20}\)[/tex].
To solve for x, we need to use the properties of similar triangles. The sides of similar triangles are proportional. Given that triangles AU V and ABC are similar, we can set up the following proportion:
[tex]\[\frac{AU}{AB} = \frac{UV}{BC} = \frac{AV}{AC}\][/tex]
We are given the lengths of the sides as follows:
- (AU = 20x + 108)
- (UB = 273) (which is part of AB, since (AB = AU + UB)
- (BC = 703)
- (UV = 444)
- (AV = 372)
- (AC = 589)
Using the proportion involving the sides AU, UB, UV, and BC, we have:
[tex]\[\frac{AU}{UB} = \frac{UV}{BC}\][/tex]
Substituting the given values, we get:
[tex]\[\frac{20x + 108}{273} = \frac{444}{703}\][/tex]
Cross-multiplying to solve for x, we have:
[tex]\[(20x + 108) \cdot 703 = 444 \cdot 273\][/tex]
Expanding both sides gives us:
[tex]\[14060x + 76184 = 121172\][/tex]
Subtract (76184) from both sides to isolate the term with x:
[tex]\[14060x = 121172 - 76184\] \[14060x = 49888\][/tex]
[tex]\[x = \frac{49888}{14060}\][/tex]
Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20, we get:
[tex]\[x = \frac{2494.4}{703}\][/tex]
Since (2494.4) is very close to (2496), and \(2496\) divided by (703) is (3.55), which is (20) times (0.1775), we can see that:
[tex]\[x = \frac{1}{20}\][/tex]
Therefore, the value of x is [tex]\(\frac{1}{20}\)[/tex].
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.
{}
{a,e}
{a, b, e, g, i, l, o, r, u}
Write 2.95 as the quotient of two integers
The shaded area of the following shape can be found by subtracting the area of the circle from the area of the triangle. True False
a triangle brace has an angle measure of 92 degrees, with a side opposite this angle measuring 10 inches. the base of the triangular brace, which is adjacent to the given angle measure, is 12 inches in length. Which of the following statements is correct
To determine the length of the hypotenuse in a triangle with an angle measure of 92 degrees and a side length of 10 inches, we can use the sine ratio. Calculating the value of Sin(92 degrees) and dividing 10 by that value, we find that the hypotenuse is approximately 10.001525 inches.
Explanation:A triangle brace with an angle measure of 92 degrees and a side length of 10 inches opposite this angle, and a base length of 12 inches adjacent to the given angle. To determine which of the given statements is correct, we need to use trigonometric ratios. We can use the sine ratio in this case.
The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the angle measure is 92 degrees and the side opposite is 10 inches. Let's calculate:
Sin(92 degrees) = Opposite/Hypotenuse
Sin(92 degrees) = 10/Hypotenuse
To solve for the hypotenuse, we can rearrange the equation:
Hypotenuse = 10/Sin(92 degrees)
Using a calculator, we can evaluate Sin(92 degrees) and then divide 10 by that value to find the hypotenuse:
Hypotenuse = 10/0.9998477 = 10.001525 inches (approximately)
Based on this calculation, the correct statement would be that the hypotenuse is approximately 10.001525 inches.
Your class is holding elections to choose a leadership committee of 4 students. If there are 30 students in the class, how many different leadership committees would it be possible to elect?
810,000
27,405
120
657,720
Using the combination formula, it is found that it would be possible to elect 27,405 different leadership committees.
The order in which the students are selected to the committee is not important, which means that the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 students are chosen from a set of 30, thus:
[tex]C_{30,4} = \frac{30!}{4!26!} = 27405[/tex]
It would be possible to elect 27,405 different leadership committees.
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Which of the following points is a solution to the system of linear inequalities
Which of the following points is a solution to the system of linear inequalities?
{2x+y<-5
{-x+y>0
A.
(4, 1)
B.
(–4, –1)
C.
(–8, –21)
D.
(8, 11)
Answer:
(-4,-1) satisfies the given system of inequalities
Step-by-step explanation:
[tex]2x+y<-5[/tex]
[tex]-x+y>0[/tex]
To find out the solution we check with each option
(4,1) , x=4 and y=1 (Plug in x and y values in the given inequalities)
[tex]2(4)+1<-5[/tex]
[tex]9<-5[/tex] False
(-4,-1) , x=-4 and y=-1 (Plug in x and y values in the given inequalities)
[tex]2(-4)-1<-5[/tex]
[tex]-9<-5[/tex] True
Now plug it in second inequality
[tex]-(-4)-1>0[/tex]
[tex]3>0[/tex] True
(-8,-21) , x=-8 and y=-21 (Plug in x and y values in the given inequalities)
[tex]2(-8)-21<-5[/tex]
[tex]-37<-5[/tex] True
Now plug it in second inequality
[tex]-(-8)-21>0[/tex]
[tex]-13>0[/tex] False
(8,11) , x=8 and y=-11(Plug in x and y values in the given inequalities)
[tex]2(8)+11<-5[/tex]
[tex]-9<-5[/tex] false
steps in how to solve
3 times what gives me a sum of 24? im trying to finish my homework so please help.
Create a factorable polynomial with a GCF of 5z. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
The original factorable polynomial 15z^2 + 10z can be rewritten in two different equivalent forms by factoring out the GCF to get 5z(3z + 2) and by applying the Zero Product Property to find its roots z = 0, -2/3.
Explanation:To begin, we will create a factorable polynomial with a Greatest Common Factor (GCF) of 5z. An example might be: 15z^2 + 10z. This polynomial has two terms, and each term includes the GCF of 5z in its make up.
Now, let's rewrite this polynomial in two other equivalent forms using different methods of factorization and simplification.
Form 1: Factor by GCF
In this form, we factor out the GCF from the original polynomial. For our provided example, the GCF is 5z, so we get: 5z(3z + 2).
Form 2: Use the Zero Property
We can also rewrite this polynomial using the Zero Product Property. This naturally complements factoring because it allows us to set the factors equal to zero and solve for z. In this case, this provides the roots of the polynomial but not in factor form: z = 0, -2/3.
Therefore, the original polynomial and the different equivalent forms all represent the same relationship, just expressed in different manners.
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To create a factorable polynomial with a GCF of 5z, multiply it with another term like (4z+2). The resulting polynomial is 20z² + 10z. You can rewrite it in another equivalent form by factoring out the common term from each term, resulting in 2z(8z + 2) = 16z² + 4z.
Explanation:To create a factorable polynomial with a GCF of 5z, we can start by multiplying 5z with another term. Let's say we multiply it with (4z+2). The polynomial becomes 5z(4z+2), which can be expanded to 20z² + 10z. This is one form of the polynomial.
To rewrite the polynomial in another equivalent form, we can factor out the common term from each term of the polynomial. Doing so, we get 5z(4z+2) = 5z * 4z + 5z * 2 = 20z² + 10z. Thus, the second equivalent form is 20z² + 10z.
The third equivalent form can be obtained by factoring out a common term, 2z, from each term: 5z(4z+2) = 2z * (2 * 4z + 2) = 2z(8z + 2) = 16z² + 4z.
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The value of 7 in ___ is 10 times
The value of 7 in ____
3000000000 times 9000000000
There are two 6th grade classes one with 29 students and the other with 31 students. There are 26 male students between the two classes. What is the ratio of female students to total students?
A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches and 50 oranges. How do you distribute the fruit to make the most number of monkeys happy? What is this number?
To make the most monkeys happy we need 20 number of pair of pears, peaches, and oranges. and 20 number of pair of peaches bananas and oranges.
What is sampling distribution?In statistics, sampling distribution refers to the study of multiple random samples drawn from a particular population depending on a specified property. The acquired data paint a clear picture of the changes in the likelihood of the outcomes determined. As a consequence, the analysts are aware of the outcomes ahead of time, allowing them to plan their actions accordingly.
Given, A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches, and 50 oranges. to formulate the equation we need to divide them by 10 and make the pair of three.
Hence,
2pears + 3 bananas + 4 peaches + 5 oranges
2(pears + oranges + peaches) + 2(banana + peach + oranges) + peach +1 orange.
Therefore to make the most monkey happy. we need to make 20 pairs of pears, oranges, and peaches and 20 pairs of banana peaches and oranges.
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I NEED HELP ASAP!!!!!!
4 +12 = 16 crates
16 x 32 = 512 juice boxes
so both A & C are correct