Martina runs 10.5 miles in 75 minutes
Solution:
Given that,
Martina runs 7 miles in 50 minutes
Therefore, miles ran in 1 minute is:
[tex]Miles\ ran\ in\ 1\ minute = \frac{7}{50}\ miles[/tex]
At the same rate how many miles will she run in 75 mins
Thus, to find the miles ran in 75 minutes:
[tex]Miles\ ran\ in\ 75\ minute = \frac{7}{50}\ \times 75\\\\Miles\ ran\ in\ 75\ minute = 0.14 \times 75\\\\Miles\ ran\ in\ 75\ minute = 10.5[/tex]
Thus she runs 10.5 miles in 75 minutes
what times 10 equals 0.3
To find out what number times 10 equals 0.3, you divide 0.3 by 10. The answer is 0.03.
Explanation:The question you're asking is essentially what number, when multiplied by 10, equals 0.3. This is a basic division problem in mathematics, because when you want to find out what number multiplied by another number gives a certain result, you divide the result by one of the numbers.
In this case, you would divide 0.3 by 10. So, the solution to this problem is: 0.3 / 10 = 0.03.
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The number that times 10 equals 0.3 is 0.03. This exercise relates to understanding decimal places and exponents, where for instance, 10⁻³ represents 0.001 and signifies that the decimal point is shifted three places to the left.
To find what number times 10 equals 0.3, we need to solve the following equation:
x × 10 = 0.3
To find x, we divide both sides of the equation by 10:
x = 0.3 / 10
x = 0.03
Therefore, 0.03 times 10 equals 0.3.
A bag contains 15 navy and 26 violet marbles. A marble is drawn at random.
What is the theoretical probability of drawing a violet marble?
Forty-seven percent of fish in a river are catfish. Imagine scooping out a simple random sample of 25 fish from the river and observing the sample proportion of catfish. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.
The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.0998. The 10% condition is not met because there are less than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is not met because there are less than 250 catfish in the river.
We are unable to determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Answer:
Therefore the correct option is a.) The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Step-by-step explanation:
i) Let p = 0.47
ii) therefore q = 1 - 0.47 = 0.53
iii) sample size, n =25
iii) standard deviation = [tex]\sqrt{\frac{p \times q}{n} } = \sqrt{\frac{0.47 \times 0.53}{25} } = 0.0998[/tex]
Therefore the correct option is
a.) The standard deviation is 0.0998. The 10% condition is met because it
is very likely there are more than 250 catfish in the river.
The standard deviation of the sampling distribution of the sample proportion is 0.0998. To determine whether the 10% condition is met, the total population of catfish should be at least 10 times the sample size.
Explanation:The question asks about determining the standard deviation of the sampling distribution of the proportion of catfish in a river and if the 10% condition is met for the sampling distribution to be approximately normal. First, to calculate the standard deviation of the sampling distribution of the sample proportion (p-hat), we use the formula √[(p(1-p))/n], where p is the population proportion and n is the sample size. In this case, p = 0.47, so 1 - p = 0.53, and n = 25. The standard deviation is then √[(0.47*0.53)/25], which is approximately 0.0998.
Next, the 10% condition checks whether we can consider the population large enough that the sample size doesn't affect the population proportion notably when taking without replacement. This condition states that the sample size, n, should be no more than 10% of the population. If there are indeed more than 250 fish in the river (10 times the sample size), we can be confident that the 10% condition is met. If not, the condition is not met.
Therefore, the correct response would state the standard deviation and appropriately evaluate whether the 10% condition is met based on the estimated number of catfish in the river.
solve this system of equations by using substitution
3x + 5y = 23
y= x + 3
Answer:
x=1
y=4
(1,4)
Step-by-step explanation:
TO SOLVE FOR X:
1. Substitute y=x+3 into the equation. This should look like this:
3x+5(x+3)=23
2. Use the distributive property.
3x+5x+15=23
3. Simplify:
8x+15=23
4. Subtract 15 from both sides. It should now lool like this:
8x=8
5. Divide both sides by 8.
x=1
TO SOLVE FOR Y:
1. Take x and substitute into original statement:
3(1)+5y=23
2. Simplify:
3+5y=23
3. Subtract 3 from both sides:
5y=20
4: Simplify:
y=4
CHECK ANSWER:
y=x+3
1. Substitute your answers
4=1+3
2. Simplify
4=4
3. Check for Truth. Is 4=4?
Yes. So your final answer is:
x=1
y=4
(1,4)
Use the drop-down menus to complete the statement about the inequality m ≥ 2.
Answer:
The inequality m ≥ 2 has infinity many solutions because 2 and any number to the right of 2 on the number line can be substituted for m to make this inequality true.
What is 4 tens and 6 tenths as a decimal
Answer 4.6
Step-by-step explanation:
Ron decided to use blocking to deal with extraneous factors in his
experiment. If 4 treatments are applied to one of his groups, how many
treatments should be applied to each of his other groups?
A. 3
B. 6
C. 5
D. 4
A study indicated that the citizens of Newport wasted 38,080 gallons of water last year. This year they wasted 20% less. How many gallons did the citizens wasted this year
A gym charges $25 per month plus $4 extra to swim in the pool for an hour. If a member only has $45 to spend each month, at most how many hours can the member swim? Write an equation and demonstrate this on a number line.
please help :(( i gotta hurryy >
The polynomial that represents the area of the given rectangle is [tex]32x^2+16x+2.[/tex]
Step-by-step explanation:
We are given with a rectangle which has the length and breadth.
Also the length and breadth is given in the form of polynomial.
The length of the rectangle = 2(4x+1).
which can also be written as 8x+2.
The breadth of the rectangle= 4x+1
Area of the rectangle A= length × breadth.
⇒A=(8x+2)×(4x+1).
=[tex]32x^2+8x+8x+2.[/tex].
=[tex]32x^2+16x+2.[/tex]
Thus the area of the given rectangle is [tex]32x^2+16x+2.[/tex]
tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $2995 was collected from the sale of 729 tickets. Write and solve a system of linear equations to find the number of tickets sold to students and the number of tickets sold to adults.
Answer:
404 tickets to adults have been sold .
325 tickets to students have been sold .
Step-by-step explanation:
A system of linear equations is a set of two or more first degree equations, in which two or more variables are related.
In this case, a system of two linear equations with two unknowns is solved.
To assemble the system of equations you must first define the variables, which in this case will be:
x: tickets for admission to a high school football game for students.y: tickets for admission to a high school football game for adults.On the one hand, you know that 729 tickets were sold, that is to say that tickets sold for students and adults must add 729. Expressed in an equation this is: x+y=729 equation (A)
On the other hand, you know that during a game, $ 2995 was raised for the sale of those 729 tickets. And you also know that tickets for a high school football game cost $ 3 for students and $ 5 for adults.
Then the proceeds from the sale of tickets for students is 3*x and for adults it is 5*y. And your sum must be $ 2995. Expressed in an equation this is:
3*x + 5*y=2995 Equation (B)
So the system of equations is:
[tex]\left \{ {{x+y=729} \atop {3*x+5*y=2995}} \right.[/tex]
There are several methods of solving a system of equations. In that case, the substitution method will be used, which consists of isolating an unknown element in one of the equations, which will be a function of the other unknown. In the other equation that has not been used, the same unknown is replaced by the expression previously obtained. In this case, the value of variable x in equation (A) will be isolated:
x+y=729 ⇒ x=729-y Equation (C)
Replacing this expression in equation (B) you get:
3*(729-y)+5*y=2995
Solving this equation:
3*729-3*y+5*y=2995
2187+2*y=2995
2*y=2995-2187
2*y=808
y=808÷2
y=404
Remembering that "y" is tickets for admission to a high school football game for adults. this indicates that 404 tickets to adults have been sold .
Replacing this value in equation (C), which is the previously isolated equation, you get:
x=729-y
x=729-404
x=325
Remembering that "x" is tickets for admission to a high school football game for students. this indicates that 325 tickets to students have been sold .
By setting up a system of linear equations, it's found that 325 student and 404 adult tickets were sold.
Explanation:The subject of this question is a linear system, specifically related to the ticket sales at a high school football game. Let's denote 's' as the number of student tickets sold, and 'a' as the number of adult tickets sold. We'll use the following two equations to reflect the given information:
s + a = 729 (This equation represents the total number of tickets sold.) 3s + 5a = 2995 (This equation represents the total cost of tickets sold.)
To solve the system of equations, one method is substitution or elimination. Using the elimination method, you could multiply the first equation by 3, getting 3s + 3a = 2187. Then, subtracting this from the second equation gives 2a = 808. Dividing by 2, we find that a = 404. Plugging this value into the first equation gives s = 729 - 404 = 325. Therefore, 325 student tickets and 404 adult tickets were sold.
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Find the lengths of AB,BC,PQ,and QR. Which segments have equal lengths?
On Friday a local hamburger shop sold a combined total of 304 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
76 hamburgers
Step-by-step explanation:
3x + x = 304
4x = 304
Help with two Math problems.
1: A bag of dog food weighs 20lb. 15% of the weight is oats.
a) Set up an equation OR proportion to find the weight of the oats in the dog food.
b) What is the weight of the oats in the dog food? Show your work.
2: Some students were asked what kind of animals they have at home. The results are in the image:
(a) List the animals in order of popularity from most popular to least popular.
(b) I estimated that 250 students were interviewed. Based on my estimate, how many students have an "other" pet? Show your work.
Answer:
1. a. o = 3b
b. o = 3 pounds
2. a. Most popular animals:
A. Dogs - 67%
B. Cats - 20%
C. Other - 8%
D. None - 4%
E. Horses - 1%
b. 20 students
Step-by-step explanation:
1. a. The equation is:
o = 0.15 *20b
o = 3b
where, o = weight of oats in pounds and b = number of dog food bags
b. Let's find out the weight of the oats in one dog food bag, using our equation:
o = 0.15 *20b
o = 0.15 *20 * 1
o = 3 pounds
2. a. Most popular animals:
A. Dogs - 67%
B. Cats - 20%
C. Other - 8%
D. None - 4%
E. Horses - 1%
b. If 250 students were interviewed, the 8% who answered "other" are:
8% of 250 = 0.08 * 250 = 20 students
You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you
has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium.
How many seats does the auditorium contain? (Hint: Find the number of seats in the first
and last rows)
A. 2,604
B. 2,163
C. 2,422
D. 2,803
Answer: A. 2,604
Step-by-step explanation:
According to the given information the number of sets in rows following arithmetic progression (in short form AP).
Where , 23rd term is 65.
Common difference = 65-63=2
nth term in AP: [tex]a_n=a+(n-1)d[/tex]
For n= 23 , we have [tex]a_{23}=65[/tex] , d= 2
[tex]23=a+(23-1)2\\\\ 23= a+(22)2\\\\ 23=a+44\\\\ a=44-23=21[/tex]
Formula for the sum of first n terms in AP= [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Since, There are 42 rows in the auditorium.
Then,
[tex]S_{42}=\dfrac{42}{2}[2(21)+(42-1)2]\\\\=21(42+82)\\\\=21(124)=2604[/tex]
Hence, the the auditorium contains 2,604 seats.
Thus , the correct answer is A. 2,604
We want to find the total number of seats in the auditorium, knowing that the number of seats is given by an arithmetic sequence.
The correct option is A: there are 2,604 seats in total.
We know that in the row before you (the number 22) there are 63 seats, in your row (number 23) there are 65 seats, and in the next row there are 67 seats, then we can write the 3 terms of a sequence:
[tex]a_{22}= 63\\a_{23} = 65\\a_{24} = 67[/tex]
Is simple to see that this is an arithmetic sequence, such that the difference between consecutive terms is 2, then the number of seats in the n-th row is given by:
[tex]a_n = a_{n-1} + 2[/tex]
or:
[tex]a_n = a_1 + (n - 1)*2[/tex]
Using this second equation, we can find the value of the first term of the sequence:
[tex]a_{23} = 65 = a_1 + 2*(23 - 1)\\\\65 - 44 = a_1 = 21\\[/tex]
Now, if we define d as the difference between consecutive terms in an arithmetic sequence, the sum of the first N terms is given by:
[tex]S(N) = N*(2*a_1 + (N - 1)*d)/2[/tex]
Here we have a total of 42 rows, so we use N = 42.
d =2
a₁ = 21
Then the total number of seats is:
[tex]S(N) = 42*(2*21 + (42 - 1)*2)/2 = 2,604[/tex]
This means that the correct option is A: there are 2,604 seats in total.
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Is this no solution or infinite solutions?
2x+y=2
y=-2x-1
Answer:
infinite solutions
Step-by-step explanation:
Solve 5x + 7 > 17.
{x | x < 2}
{x | x > 2}
{x | x < -2}
{x | x > -2}
Answer:
5x + 7 < 17
5x < 10
x < 2
answer is a
Which statements are true about the multiplication and division properties of rational expressions? Check all that apply.
Answer: A, B, E
Step-by-step explanation:
Answer:
A, B, E.
Step-by-step explanation:
The closure property of multiplication states that the product of two rational expressions is a rational expression.
The commutative property only holds true for the multiplication of rational expressions.
The properties of rational expression multiplication and division are parallel to the properties of rational number multiplication and division.
A circular playground has an area of about 1500 square feet. If the committee decides to double the radius, what is the approximate area of the new playground?
If the committee decides to double the radius, the approximate area of the new playground is; A_new = 6000 sq.ft
How to find the area of a Circle?We are given the area of a circular playground as;
A = 1500 ft²
Formula for area of Circle is;
A = πr²
Thus;
πr² = 1500
r = √(1500/π)
Now, they want to double the radius. Thus approximate area of the new playground is;
A_new = π * [2√(1500/π)]²
A_new = π * [4(1500/π)]
A_new = 6000 sq.ft
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Answer:
c
Step-by-step explanation:
time 4 learning and it was right people :)
Graph: y-3=1/2(x+2)
Where would i graph this please help me just tell me the points dont go over the top with explanation
The plotted line on the graph represents all the points (x, y) that satisfy the equation [tex]\( y - 3 = \frac{1}{2}(x + 2) \)[/tex].
The graph of the equation [tex]\( y - 3 = \frac{1}{2}(x + 2) \)[/tex] has been plotted. Here are the steps to plot this graph:
1. Rearrange the equation: Convert the given equation into slope-intercept form, [tex]\( y = mx + c \)[/tex], which makes it easier to graph.
The given equation is [tex]\( y - 3 = \frac{1}{2}(x + 2) \)[/tex]. By rearranging, you get [tex]\( y = \frac{1}{2}x + 1 + 3 \)[/tex] which simplifies to [tex]\( y = \frac{1}{2}x + 4 \)[/tex].2. Calculate the y-intercept: This is the point where the line crosses the y-axis, which occurs when [tex]\( x = 0 \)[/tex]. Substituting [tex]\( x = 0 \)[/tex] into the equation gives [tex]\( y = 4 \)[/tex]. So, the y-intercept is (0, 4).
3. Calculate the slope: The slope is [tex]\( \frac{1}{2} \)[/tex] which means that for every 2 units the graph moves horizontally to the right, it moves 1 unit up.
4. Plot the y-intercept: Start at the y-intercept (0, 4) on the graph.
5. Use the slope to find another point: From the y-intercept, move right 2 units and up 1 unit to find another point on the line. You could also move left 2 units and down 1 unit for another point.
6. Draw the line: Connect the points with a straight line to complete the graph.
Factor this: a^n+a^n+1
Answer:
1 + 2 a^n
Step-by-step explanation:
Question 16(Multiple Choice Worth 1 points)
(06.02 LC)
Which statement best describes the expression 4y ÷ 9?
9 divided by 4 times y
9 times y divided by 4
4 times y divided by 9
4 divided by 9 times y
Answer:
4 times y divided by 9
Step-by-step explanation:
4y means 4×y which is 4 times y that is divided by 9
Is 1/4 greater than 1/3? Why?
Step-by-step explanation: Notice that the fractions that we're comparing in this problem have different denominators.
When fractions have different denominators, they're called unlike fractions. To compare unlike fractions, we must first get a common denominator.
The common denominator of 4 and 3 will be the least common multiple of 4 and 3 or 12. To get a 12 in the denominator of 1/4, we multiply the numerator and the denominator by 3 which gives us 3/12. To get a 12 in the denominator of 1/3, we multiply the numerator and the denominator by 4 which gives us 4/12.
Now we have the fractions 3/12 and 4/12.
The fraction with the greater denominator is larger so 4/12 is bigger which means that 1/3 is bigger.
1/4 is not greater than 1/3. In fact it is less than 1/3.
We have two fractions, 1/4 and 1/3.
We know that,
For a fraction, when the value of the denominator increases, the value of the fraction decreases.
So here the denominator of 4 is greater than 3.
So 1/4 is less than 1/3.
In other words, 1/4 can be defined as a part when 1 is divided in to 4 parts.
1/3 is one part when 1 is divided in to 3 parts.
So clearly, 1/4 < 1/3.
Hence 1/4 is less than 1/3.
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Helene spends 12% of her budget on transport expenses. Write this percent as a fraction and as a decimal
Answer:
3/25 is the fraction .12 is the decimal
Step-by-step explanation:
In the problem 4x + 10 list a constant.
Answer:
10
Step-by-step explanation:
Constant term consists of natural no.s or numerals
So here the constant is 10
Answer:
In the problem 4x + 10 , 10 is the constant
Step-by-step explanation:
In the problem 4x + 10 , 10 is the constant
As we know
In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
Examples:
In "x + 5 = 9", 5 and 9 are constants.
similarly
In x+ a= b , a and b are constants
so from definition of constant in algebra it is clear that
in
The problem 4x + 10 , 10 is the constant
Leah has The flowers shown she wants to put them in 4 vases with the same number in each case how many flowers does she need to put in each case
The number of flowers she need to put in each case is [tex]\frac{x}{4}[/tex]
What is flowers she need to put in each case?The area of mathematics known as algebra is responsible for helping to express circumstances or problems as mathematical expressions. Divide the total number of flowers by the total number of vases to find the solution. We can still demonstrate how to solve the problem even if we do not have all the quantities.
x = total number of flowers.
There are 4 vases.
Therefore, the number of flowers in each vase will be [tex]\frac{x}{4}[/tex]
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Topic/Objective: Function Applications pp. 228-252
• Write the equation of a linear function and determine the rate of change of the function using a point on the line and the slope of the line.
Write the equation of a linear function and determine the rate of change of the function using two points on the line.
• Determine whether a function is linear or nonlinear using a graph.
• Determine whether a function is linear or nonlinear using a table.
• Determine whether a function is linear or nonlinear using an equation.
• Compare the properties of two linear functions that are represented differently.
Name
Class/Time
Date
Essential Question: How can we model relationships between quantities?
Questions/Voc. Terms/Properties
Define the vocabulary terms below:
Linear function
Nonlinear function
Increasing function
Decreasing function
Constant
How can linear models be interpreted?
How are independent and dependent variables represented on a coordinate plane?
What is the slope and y-intercept of the helicopter altitude from the graph?
What does 35 and 1.2 in the equation represent in the equation?
Describe the situation each equation represents for the water level in other tanks.
How can we represent the water level in a tank that’s empty at first but rises at a rate of 2.1 /s?
What is the process for solving problems involving constant rates?
What is the total cost for movie rental for 1 month? 5 months? 7 months? 1 year?
Is this a linear model? Explain.
What describes the relationship between the independent and dependent variables of the function?
What determines whether a function is linear or nonlinear?
How can we determine if a function is increasing or decreasing?
How can we determine whether a graph is increasing or decreasing?
How can functions be compared?
How can functions be represented?
How can we determine which line has a greater rate of change?
When interpreting a function graph, what key features can we look for?
How can we draw conclusions about an object’s speed?
Example Problems & Steps/Vocabulary Definitions/Property Descriptions
Write/type definitions beside each term below:
p. 228 Copy yellow box
p. 228 Copy purple box
pp. 228-229 Study graph and copy solutions below:
Example 1
A.
B.
pp. 229-230 Copy solution below:
Example 2
A.
p. 230 Copy solution below:
B.
p. 230 Copy solution below:
C.
pp. 231-231 Study table and graph and copy steps below:
Example 1
pp. 232-233 Study table and copy solution below:
Example 2
A.
Study rate of change between values and copy solution below:
B.
p. 234 See yellow box
pp. 234-235 Study tables & graph and copy solutions below:
Example 1
A. y = 2x - 1
B.
pp. 236 See pink box
pp. 236-237 Study graphs and write solutions below:
Example 2
A.
B.
C.
D.
p. 240 See yellow box
p. 240 See paragraph
Study functions pp. 240-244
p. 244 see graph and pink box
p. 246
p. 247 see pink box
Study pp. 247-252
Summary: Connections, Reflections, Analysis about what you learned (3 or more sentences, or you may use the following prompts - be specific):
Today my notes say…
I can use my notes to…
My notes mean…
Answer:
Are the following linear or nonlinear? Circle the correct response.
Step-by-step explanation:
The numder are hard to explain but
You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.
Answer:Your answer i
Step-by-step explanation:You can tell if a table is linear by looking at how X and Y change.
1) In the diagram, l || m. If the measure of angle 3 is 120 find the measure of the following angles
a) angle 4
b) angle 6
c) angle 8
Answer:
a) 60° , b) 120° and c) 60°
Step-by-step explanation:
See the diagram attached to this question.
a) Here, ∠ 4 and ∠ 3 are supplementary angles.
So, ∠ 4 + ∠ 3 = 180° {Here, ∠ 3 is given to be 120°}
⇒ ∠ 4 = 180° - ∠ 3 = 180° - 120° = 60° (Answer)
b) Now, ∠ 3 and ∠ 6 are alternate angles and hence, ∠ 3 = ∠ 6 = 120° (Answer)
c) Here, ∠ 6 and ∠ 8 are supplementary angles.
So, ∠ 6 + ∠ 8 = 180°
⇒ ∠ 8 = 180° - ∠ 6 = 180° - 120° = 60° (Answer)
Emmanuel sold 16 dozen eggs last month. How many eggs did he sell in all?
Answer:
Emmanuel would have sold 192 eggs total
Step-by-step explanation:
one dozen is 12 eggs
16 dozen would be 12 x 16 = 192
Emmanuel would have sold 192 eggs total
Emmanuel sold 16 dozen eggs, and since one dozen equals 12 items, the total number of eggs sold is 192 eggs.
Explanation:The student asked how many eggs Emmanuel sold last month if he sold 16 dozen. To answer this question, we need to understand that one dozen represents 12 items. Therefore, if Emmanuel sold 16 dozens of eggs, we use multiplication to find the total.
First, identify the number of items in a dozen: 12 eggs.Next, multiply the number of dozens sold by the number of items in one dozen: 16 dozens x 12 eggs/dozen = 192 eggs.So, Emmanuel sold a total of 192 eggs last month.
Answering the additional example questions for clarification:
For g., the number is two and the unit is dozen eggs, because 'two' specifies the quantity of dozens, not individual eggs.For h., the unit is dozen eggs because that combines the measurement unit 'dozen' with what's being measured, in this case, eggs.For i., the blank should be filled with the conversion: 1 km = 1000 metersTo identify the number and unit in each quantity provided:
a. The number is one, and the unit is a dozen eggs.b. The number is 2.54, and the unit is centimeters.c. 'A box' is the number, and 'pencils' is the unit.d. The number is 88, and the unit is meters per second.How much cashews at $1.58 per pound must be mixed with walnuts that cost 78 cents per pound to make a mixture of 40 pounds of nuts that cost $1.50 per pound?
Answer:
Cashew= 36 pounds
Walnut= 4 pounds
Step-by-step explanation:
Given: Cost of Cashew= $1.58 per pound
Cost of walnut= $0.78 per pound
Total weight of mixture= 40 Pound
Cost of mixture= $1.50 per pound.
Lets assume the amount of cashew added in the mixture be "x".
∴ Amount of Walnut in the mixture will be [tex](40-x)[/tex]
Now, forming an equation to total cost and weight of mixture.
⇒ [tex]1.58\times x+0.78 \times (40-x)= 40\times 1.50[/tex]
Using distributive property of multiplication
⇒ [tex]1.58x+31.2-0.78x= 60[/tex]
⇒[tex]0.8x+31.2= 60[/tex]
Subtracting both side by 31.2
⇒[tex]0.8x= 60-31.2[/tex]
⇒[tex]0.8x= 28.8[/tex]
Dividing both side by 0.8
⇒[tex]x= \frac{28.8}{0.8}[/tex]
∴ [tex]x= 36\ pounds[/tex]
Hence, Amount of cashew added in the mixture of nuts is 36 pounds.
Next finding the amount of walnut added in the mixture.
subtituting the value of x
Amount of walnut in the mixture= [tex](40-x)[/tex]
⇒ Amount of walnut in the mixture= [tex](40-36)= 4\ pounds[/tex]
Hence, 4 pounds of walnut added in the mixture.
Final answer:
To make a 40-pound mixture of nuts that costs $1.50 per pound, mix 36 pounds of cashews, which cost $1.58 per pound, with walnuts costing $0.78 per pound.
Explanation:
Let's approach this mixture problem using the concept of weighted averages. We know we want to make a 40-pound mixture of cashews and walnuts that costs $1.50 per pound.
The cashews cost $1.58 per pound and the walnuts cost $0.78 per pound. To find out how many pounds of cashews to mix with walnuts, we can set up the equation:
Let x be the amount of cashews needed.
Since the total weight of the mixture is 40 pounds, the amount of walnuts needed would be 40 - x pounds.
Using the equation for the total cost of the mixture: 1.58x + 0.78(40 - x) = 1.50(40),
we solve for x:
1.58x + 31.2 - 0.78x = 600.8x = 28.8x = 36Therefore, to obtain a 40-pound mixture costing $1.50 per pound, a person should mix 36 pounds of cashews with walnuts.