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.
If V6x - 9 = x, what is the value of x ?
Answer:
9/5
Step-by-step explanation:
Given that ,
⇒ 6x - 9 = x
⇒ 6x - x = 9
⇒ 5x = 9
⇒ x = 9/5
Final answer:
To solve the equation V(6x - 9) = x, we square both sides, rearrange the resulting quadratic equation, and factor it to find that x = 3 is the solution.
Explanation:
The equation given is V(6x - 9) = x. To find the value of x, we must solve the equation that involves a square root. First, we need to square both sides of the equation to eliminate the square root:
(V(6x - 9))² = x²What is the solution to the equation?
Answer:
x= 27
Step-by-step explanation:
Move constant to the right-hand side and change its sign.
[tex]\sqrt{2x+10}[/tex] = 2+6
Add the numbers.
[tex]\sqrt{2x+10}[/tex]= 8
Square both sides of the equation.
2x+10= 64
Move the constant to the right-hand side and change its sign.
2x= 64-10
Subtract the numbers.
2x= 54
Divide both sides of the equation by 2.
x= 27
PLEASE HELP ME!!! there's an equation: y × 6 for y = 2/3. what the heck is the y?!
Answer:
y equals 2/3. u have to do 2/3 ×6 I'm pretty sure
A jet leaves the Charlotte, North Carolina, airport traveling at an average rate of 564 km/h. Another jet leaves the airport one-half hour later traveling at 744 km/h in the same direction. Use an equation to find how long the second jet will take to overtake the first.
A.
1 17/30 h
B.
2 1/15 h
C.
− 1 17/30 h
Answer:
[tex]A.\ 1\frac{17}{30}\ hours[/tex]
Step-by-step explanation:
[tex]Let\ second\ jet\ overtake\ first\ in\ x\ hours.\\\\[/tex]
Distance covered by first jet:
[tex]Speed\ of\ first\ jet=564\ km/h\\\\Time=x+\frac{1}{2}\\\\Distance\ covered=speed\times time\\\\Distance\ covered=564\times (x+\frac{1}{2})=564x+564\times \frac{1}{2}\\\\Distance\ covered=564x+282[/tex]
Distance covered by second jet:
[tex]Speed\ of\ second\ jet=744\ km/h\\\\Time=x\\\\Distance\ covered=speed\times time\\\\Distance\ covered=744\times x\\\\Distance\ covered=744x[/tex]
[tex]Distance\ covered\ by\ both\ the\ jet\ in\ x\ hours\ is\ equal.\\\\744x=564x+282\\\\744x-564x=282\\\\180x=282\\\\x=\frac{282}{180}=\frac{6\times 47}{6\times 30}\\\\x=\frac{47}{30}\ hours\\\\x=1\frac{17}{30}\ hours[/tex]
It is 9:00. What is the measure of the smaller angle between the hour hand
and minute hand after three minutes? *
Answer:
The hour hand is three-fourths of the way from the "4" to the "5; that is, ... What is the angle between the hour hand and the minute hand at 4:40? ... What is the measure of the smaller angle formed by the hands of an analog watch if the hour hand is on the ... One has to account, however, for the 10 minutes that have passed.Step-by-step explanation:
What is the y-value when x equals -16?
y = -200 - 12(x)
Answer:
Step-by-step explanation:
y = -200 - 12(x)
x = -16
y = -200 - 12(-16)
y = -200 + 192
y = -8
Answer:
y=-8
Step-by-step explanation:
y=-200-12(-16)
y=-200+192
y=-8
How much pure acid is in 440 milliliters of a 19% solution
Answer:
83.6 mL
Step-by-step explanation:
Given 440 mL of 19% acid solution. This means the whole volume of this acid solution is 100%. Let x mL be the volume of pure acid in this solution.
Then
[tex]440\ mL - 100\%\\ \\x\ mL - 19\%[/tex]
Write a proportion:
[tex]\dfrac{440}{x}=\dfrac{100}{19}[/tex]
Cross multiply:
[tex]100\cdot x=440\cdot 19\\ \\x=\dfrac{440\cdot 19}{100}\\ \\x=\dfrac{8,360}{100}\\ \\x=83.60\ mL[/tex]
Final answer:
In 440 milliliters of a 19% solution, there are 83.6 milliliters of pure acid, calculated by multiplying the percentage (converted to a decimal) by the total volume of the solution.
Explanation:
To find out how much pure acid is in 440 milliliters of a 19% solution, you need to use the concept of percentage concentration in chemistry. The percentage concentration tells us how much of a substance is present in a solution compared to the total amount of the solution.
In this case, we have a 19% acid solution. This means that 19% of the solution's total volume is pure acid. To calculate the volume of pure acid, you multiply the total volume of the solution by the percentage (expressed as a decimal).
Calculation:
Convert the percentage to a decimal: 19% = 0.19
Multiply this decimal by the total volume of the solution: 0.19 × 440 mL
This gives us the volume of pure acid: 0.19 × 440 mL = 83.6 mL
So, there are 83.6 milliliters of pure acid in 440 milliliters of a 19% acid solution.
On Saturday sally works 8.25 hours and earns $6.50 an hour. Michelle work 6.75 hours and earns $8.95 an hour. Who earns more? How much more?
Answer:
Sally y= (8.25)(6.5)= $53.63
Michelle y = (6.75)(8.95)= $60.41
Michelle earns more
60.41-53.63= $6.78
please I need your help
Do 5*12 because that's 5*(4+4+4) which the 4s are the base lengths added together. So you have 60 for one part of the figure.
Next, you have 2*4 left to add on to the figure which is 8.
So 60+8=68 is your answer
68 units^2
Hope this helped!
Answer:
The area of the figure is 68ft^2
Step-by-step explanation:
To get the area look for the separate shapes in the figure, there are 2
One has the side lengths of 5ft and 12ft, to get the 12ft length see that one side is segmented into 3 4ft long lines.
5ft * 12ft= 60ft^2
The other shape has the side lengths of 2ft and 4ft
2ft*4ft= 8ft^2
60ft^2 + 8ft^2= 68ft^2
work out the equation of the line which has a gradient of -2 and passes through the point (1,7)
Answer: [tex]y = -2x + 9[/tex]
Step-by-step explanation:
The formula for finding equation of line given slope and one point is given as :
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]x_{1}[/tex] = 1
[tex]y_{1}[/tex] = 7
[tex]m = -2[/tex]
substituting the values into the equation , we have :
[tex]y - 7 = -2 ( x - 1 )[/tex]
[tex]y - 7 = -2x +2[/tex]
[tex]y = -2x + 2 + 7[/tex]
[tex]y = -2x + 9[/tex]
Table 1.19 Frequency of Number of Movies Viewed
1. Using the tables, find the percent of data that is at most two. Which table did you use and why?
2. Using the tables, find the percent of data that is at most three. Which table did you use and why?
3. Using the tables, find the percent of data that is more than two. Which table did you use and why?
4. Using the tables, find the percent of data that is more than three.
To find the percent of data that is at most two or three, locate the corresponding column in the frequency table and divide the frequency by the total number of data points. To find the percent of data that is more than two, subtract the percent at most two from 100.
Explanation:1. To find the percent of data that is at most two, I would look at the table that displays the frequency of the number of movies viewed. I would locate the column that represents 'at most two' and find the corresponding frequency. To calculate the percent, I would divide this frequency by the total number of data points and multiply by 100.
2. To find the percent of data that is at most three, I would use the same procedure as in the previous question, but this time I would find the column representing 'at most three.'
3. To find the percent of data that is more than two, I would subtract the percent of data that is at most two from 100. This is because the percent of data that is at most two includes any data that is less than or equal to two.
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Amanda works at a store that pays her 5% commission on the total amount of clothes she sells last week she sold $1200 worth of clothes what is the amount of commission Amanda earned last week
Answer:
$75
Step-by-step explanation:
Consider the dice A, B, and C below. The opposite sides have the same values as those shown.
A(2,9,4) B(1,8,6) C(3,7,5)
a) If A is rolled against B with the higher number the winner, which should you bet on? Why?
Explain in terms of probability.
b) What if B is rolled against C?
c) Now what about C against A?
Answer:
a) A
b) B
c) C
Step-by-step explanation:
There are 9 different outcomes when 2 die are rolled.
a) A & B : A has a higher chance of winning, i.e probability of 5/9
(A,B) : (2,1) (9,1) (9,8) (9,6) (4,1)
In other 4 possible outcomes, B will win which is a probability of 4/9 (less than 5/9)
b) B & C: B has a higher chance of winning, i.e probability of 5/9
(B,C) : (8,3) (8,7) (8,5) (6,3) (6,5)
In other 4 possible outcomes, C will win which is a probability of 4/9 (less than 5/9)
c) A & C: C has a higher chance of winning, i.e probability of 5/9
(A,C) : (2,3) (2,7) (2,5) (4,7) (4,5)
In other possible outcomes, A will win which is a probability of 4/9 (less than 5/9)
Kittens weigh about 100 grams when born and gain 7 to 15 grams per day. If a kitten weighed 100 grams at birth and gained 8 grams per day, in how many days will the kitten triple its weight
A kitten weighing 100 grams at birth and gaining 8 grams per day will take 25 days to triple its birth weight and reach 300 grams.
To calculate the number of days it will take for a kitten to triple its birth weight, we will use the given rate of weight gain and the initial weight. A kitten weighs about 100 grams at birth and gains 8 grams per day. To triple the kitten's weight, it must reach 300 grams (100 grams multiplied by 3).
First, we find the total weight gain needed for the kitten to triple its weight:
300 grams (desired weight) - 100 grams (birth weight) = 200 grams (weight gain needed).
Next, we divide the total weight gain needed by the daily weight gain to find the number of days:
200 grams (weight gain needed) / 8 grams (daily weight gain) = 25 days.
Therefore, it will take the kitten 25 days to triple its birth weight at a rate of 8 grams per day.
Write an inequality that represents 54 less than 1/2 of a number is more than 233
[tex]\frac{1}{2}[/tex]x - 54 > 233 would be your inequality.
⭐ Answered by Hyperrspace (Ace) ⭐
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The inequality that represents 54 less than 1/2 of a number is more than 233 would be; 1/2 x - 54 > 233
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Given that 54 less than 1/2 of a number is more than 233
Let the number be x.
So, 1/2 of a number means 1/2x
54 less than 1/2 of a number = 1/2 x - 54
Therefore,
Hence, 1/2 x - 54 > 233 would be your inequality.
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Question 3 of 50
Line A in the given graph has what kind of slope?
-1/2
0
undefined
Eight more than seven times a number is 8
Answer:
The number is 0
Step-by-step explanation:
We form an equation using the statement:
8 = 7x + 8
Then we solve it:
8 = 7x + 8
8 - 8 = 7x
0 = 7x
0 ÷ 7 = x
x = 0
Subtract. (5 x 2 −3x−2)−(−2 x 2 −x+10)
Step-by-step explanation:
We have,
(5[tex]x^2[/tex] − 3x − 2) − (− 2[tex]x^2[/tex] − x + 10)
To subtract (5[tex]x^2[/tex] − 3x − 2) − (− 2[tex]x^2[/tex] − x + 10) = ?
∴ (5[tex]x^2[/tex] − 3x −2) − (−2[tex]x^2[/tex] − x + 10)
= 5[tex]x^2[/tex] − 3x − 2 + 2[tex]x^2[/tex] + x - 10
= (5[tex]x^2[/tex] + 2[tex]x^2[/tex]) + ( − 3x + x) + (- 2 - 10)
= 7[tex]x^2[/tex] + ( -2x) + ( - 12)
= 7[tex]x^2[/tex] - 2x - 12
∴ (5[tex]x^2[/tex] − 3x −2) − (−2[tex]x^2[/tex] − x + 10) = = 7[tex]x^2[/tex] - 2x - 12
The height h in feet of a ball thrown vertically upward from the top of a 288-foot tall building is given by h=288+48t-16t^2 where t is in seconds. How long will it take to he penny to strike the ground.
6 sec can take penny to strike the ground.
Solution:
Given data:
[tex]H_0=288[/tex] feet
[tex]V_0=48[/tex] feet
[tex]h(t)=288+48t-16t^2[/tex]
Re-arrange the terms from greatest degree to smallest degree.
[tex]h(t)=-16t^2+48t+288[/tex]
We can solve it by applying quadratic formula,
[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a = –16, b = 48, c = 288
[tex]$t=\frac{-48\pm \sqrt{48^2-4(-16)(288)}}{2(-16)}[/tex]
[tex]$t=\frac{-48\pm \sqrt{2304+18432}}{-32}[/tex]
[tex]$t=\frac{-48\pm \sqrt{20736}}{-32}[/tex]
[tex]$t=\frac{-48\pm144}{-32}[/tex]
Now, write find two t's using plus and minus operation.
[tex]$t=\frac{-48+144}{-32},\ \ t=\frac{-48-144}{-32}[/tex]
[tex]$t=\frac{96}{-32},\ \ t=\frac{-192}{-32}[/tex]
t = –3 (or) t = 6
We cannot write time is negative. so neglect t = –3.
Therefore t = 6.
Hence 6 sec can take penny to strike the ground.
What is the solution set of the given equation?
4y - 6y + 9y = -2
{-2/11}
{2/7}
{2/11}
{-2/7}
Angie and Eric have opened a jumbo bag of candies and counted the number of each color. They have 100 red, 180 green, 90 yellow, and 130 brown candies. Sarah and Laney each take turns drawing a candy, replacing each candy after they draw. If Angie and Eric each draw a candy 500 times, how many times should they expect for Angie to draw a brown candy followed by Eric drawing a red candy?
Answer:
26 times.
Step-by-step explanation:
Total number of candies = 500.
Probability ( Angie drawing a brown candy) = 130/500 = 13/50.
Probability (Eric drawing a red candy) = 100/500 = 1/5.
So Probability ( Angie drawing brown then Eric drawing a red) = 13/50 * 1/5
= 13/250.
Therefore the expectation of the number of times this will happen
= Probability * total number of draws
= (13/250) * 500
= 13 * 2
= 26 times.
Slove for x? X+16=4x-5
Answer:
x=7
Step-by-step explanation:
x+16=4x-5
16=4x-x-5
16=3x-5
3x=16+5
3x=21
x=21/3
x=7
Answer:
x=7
Step-by-step explanation:
Which is the slope of the line that passes through the points (−2,4) and (5,−1)?
Answer:
-1-4=-5
5+2=7
slope=-5/7
Answer:
slope = -5/7
Step-by-step explanation:
URGENT 15 POINTS
Which event has a probability of 1/2? Select two answers.
A.Rolling a number greater than 6 on a six-sided number cube
B.A flipped coin landing on tails
C.A flipped coin landing on heads or tails
D.Picking a blue marble from a bag of 6 red marbles and 4 blue marbles
E.Rolling an odd number on a six-sided number cube
Answer:
C and e
Step-by-step explanation:
there are two sides and its pretty much completely random on which side it lands on 2 sides = 1/2 probrability for each side and for the dice there are 3 odd numbers and 3 even numbers so thats half and half of the dice therefore 1/2 probrability
It is C and E. It can't be A or D or B.
what is 130/15 simplifed
Answer:
26/3Step-by-step explanation:
answer:
5 or 26/3
step-by-step explanation:
either one is okay mine is just simplified all the way :)
A person’s salary is $2500 per month. She receives a 10% raise. What is her new salary, in dollars per month?
* Write an expression using multiplication.
Answer:
Her new salary per month is $2750.
Step-by-step explanation:
Given:
A person’s salary is $2500 per month.
She receives a 10% raise.
Now, to find the new salary.
Salary per month = $2500.
She receives raise = 10% of $2500.
Now, to get the new salary:
[tex]2500+10\%\ \times 2500[/tex]
= [tex]2500+\frac{10}{100} \times 2500[/tex]
[tex]=2500+0.10\times 2500[/tex]
[tex]=2500+250[/tex]
[tex]=2750.[/tex]
Hence, the new salary = $2750.
Therefore, her new salary per month is $2750.
The person's new salary, after receiving a 10% raise, is $2750 per month.
Step 1: Calculate the raise amount:
Raise Amount = Original Salary × Raise Percentage
Raise Amount = $2500 × 0.10 = $250
Step 2: Add the raise amount to the original salary:
To determine the new salary, add the raise amount to the original salary.
New Salary = Original Salary + Raise Amount
New Salary = $2500 + $250 = $2750
Therefore, the person's new salary, after receiving a 10% raise, is $2750 per month.
Expression:
New Salary = Original Salary + (Original Salary × Raise Percentage)
New Salary = $2500 + ($2500 × 0.10)
New Salary = $2500 + $250
New Salary = $2750
Darnell starts the month $952.43 in his checking account. Darnell buys an iPhone 7 for $217.49 with tax included, and two kindle books that each cost $7.99. He pays with his checking account debit card. What is his new balance? The new iPhone 7 is not as awesome as promised, and Darnell returns it. What is his new balance? Explain how returning the phone is like the subtracting a negative number from his balance.
Answer:
Therefore his new balance=$712.95
Therefore his new balance is =$ 930.44
Step-by-step explanation:
Darnell starts the month $ 952.43 in his checking account.
He buys an iPhone 7 for $ 217.49 with tax included and two kindle books that each $7.99.
The price of two books is =$(7.99× 2)= $ 15.98
Total amount that he paid for iPhone 7 and two books is =$(217.49+15.98)
=$233.47
Therefore his new balance = $(952.43- 233.47)
=$712.95
The new iPhone 7 is not as awesome as promised , and Darnell returns it.
He will get the price of iPhone refund.
Therefore his new balance is $(712.95+217.49)
=$ 930.44
Darnell's new balance after purchases is $718.96. When he returns the iPhone 7, his balance is back to $936.45, as subtracting the negative cost of the iPhone is equivalent to adding its price back to his account.
To find Darnell's new balance after his purchases and subsequent return, we need to perform a few calculations based on the transactions. Darnell starts with $952.43 in his checking account. First, he purchases an iPhone 7 for $217.49 and two Kindle books, each costing $7.99. The total cost for the books is $7.99 x 2 = $15.98. We subtract these amounts from his initial balance:
$952.43 - $217.49 = $734.94
$734.94 - $15.98 = $718.96
Therefore, after the purchases, Darnell's new balance is $718.96.
When Darnell returns the iPhone 7, he gets a refund of $217.49, which is like subtracting a negative number from his balance because subtracting a negative is the same as adding a positive. So:
$718.96 + $217.49 = $936.45
After returning the iPhone 7, Darnell's new balance is $936.45.
Round 0.768 to the nearest tenths
0.768 is closest to 0.77, which is closest to 0.8, so there's your answer.
Round up when the number is higher than 5, or round down when lower than 5
What is the next term in the following sequence? -3, 4, 11, 18, ...
Answer:25
Step-by-step explanation: Add 7 to the next term to get the next term.
-3+7=4
4+7=11
11+7=18
18+7=25
Mr. Benton is contemplating which chauffeured car service to take to the airport. The first costs $7 up front and $2 per kilometer. The second costs $19 plus $1 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?
Answer:
12 kilometers
$31 total fare
Step-by-step explanation:
7 + 2x company A
19 + x . Company B
set these equal and solve for x
x is number of kilometers
7 + 2x = 19 + x
2x = 12 + x
x = 12 kilometers
7 x 2 (12) = $31