What is the volume of this prism?

The amount of salt in the 20% salt solution and 60% salt solution will be 15 qt and 10 qt, respectively.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Let x be the amount of salt in the 20% salt solution. Then the amount of the salt in the 60% salt solution will be (25 - x). Then the equation will be given as,

0.20x + 0.60(25 - x) = 25 x 0.36

0.20x - 0.60x + 15 = 9

0.40x = 15 - 9

0.40x = 6

x = 6 / 0.40

x = 15 qt

Then the value of (25 - x) will be

25 - x = 25 - 15

25 - x = 10 qt

The amount of salt in the 20% salt solution and 60% salt solution will be 15 qt and 10 qt, respectively.

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Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

-5

Step-by-step explanation:

y=3x+b

M(2,1)

Answer:

y = ((x-2)^2) -3

Step-by-step explanation:

vertex = ( 2 , -3)

y = (x-k)^2 + h

where k and h are (k,h)

so 2 replaces k and h replaces 3

so y = (x - 2)^2 -3

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

24 questions

Step-by-step explanation:

you would make the percentage a decimal and times that by how many problems.

Answer:

24 problems

Step-by-step explanation:

I like to do it like this: I find out what 10 percent is, so I divide it by 10. 30/10=3. 10 percent plus 10 percent is 20 percent. That's 6. 100 percent minus 20 is 80 percent. 30 - 6 is 24. Hope this helps.

Answer:

(4.80 x 0.05) + 4.80

Step-by-step explanation:

Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

Answer:

13 1/8 km

Step-by-step explanation:

Given the man walks 3 3/4 km in 1 hour,

=> Speed of the man = 15/4 kmph

Distance walked by the man in 7/2 hours (3 1/2 hours) is,

= 15/4 * 7/2 = 105/8 km = 13 1/8 km

Answer:

2/3

Step-by-step explanation:

1 and 2 are taken away, therefore you have 3, 4, 5, and 6 left as options to roll. So the answer is 4/6 since there's 4 numbers, but simplified it's 2/3.

Answer:

There are six possible outcomes when rolling a die, each of which is equally likely. Of these six outcomes, three are greater than 2 (3, 4, 5) and three are not (1, 2, 6). Therefore, the odds in favor of rolling a number greater than 2 are 3 to 3, or simply 1 to 1. Alternatively, we could express this as a probability: the probability of rolling a number greater than 2 is 3/6, or 1/2, since there are three favorable outcomes out of a total of six possible outcomes.

Step-by-step explanation:

Answer:

-45.46

Step-by-step explanation:

Answer:

wouldn't it be 90 degrees?

Step-by-step explanation:

Answer:

Understanding basic business math is necessary for profitable operations and accurate record keeping. Knowing how to add, subtract, multiply, divide, round and use percentages and fractions is the minimum you need to price your product and meet your budget.

Answer:

length : 8 m

width : 13/2 = 6.5 m

Step-by-step explanation:

area of rectangle = l(ength)×w(idth) = 52

l = 2w - 5

=> (2w - 5)×w = 52

=> 2w² -5w - 52 = 0

we know, when transforming this quadratic equation into a multiplication of two expressions of w, that we need to have 2w and w (to make 2w²), and then which 2 numbers multiply to 52 and add to -5 (when one is multiplied by 2 due to 2w) : -13 and 4

=> (2w - 13)×(w + 4) = 0

=> 2 solutions for w :

2w-13 = 0

2w = 13, w = 13/2

w+4 = 0, w = -4

negative values for a side length of a shape do not make sense, so the only usable solution is w = 13/2

=> l = 2w - 5 = 13 - 5 = 8

For any value of k and h = -18, the system will have infinitely many solutions.

Hence, option (b) is the correct choice.

A coefficient matrix in linear algebra is a matrix made up of the coefficients of the variables in a group of linear equations. In order to solve systems of linear equations, the matrix is employed.

The system will have infinitely many solutions when the determinant of the coefficient matrix is equal to 0.

The determinant can be calculated from the upper triangular matrix as the product of the diagonal elements, which is 0 * (-20) * (h + 18) = 0.

Therefore, the system will have infinitely many solutions when h + 18 = 0,

or h = -18.

This means the answer is (b) any value of k and h = -18.

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The cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.

To calculate the cost of the ending inventory under FIFO method, we need to first determine the cost of goods sold (COGS) for the month.

The cost of goods sold for the month would be:

300 units x $7 = $2,100

90 units x $8 = $720

20 units x $8 = $160

210 units x $9 = $1,890

Total COGS = $4,870

To calculate the cost of the ending inventory, we need to determine the cost of the remaining 390 units on hand.

Under FIFO, the cost of the ending inventory is based on the cost of the most recent purchases.

Therefore, the cost of the ending inventory would be:

20 units x $8 = $160 (from the 410 units purchased at $8)

370 units x $9 = $3,330 (from the 210 units purchased at $9 and the remaining 160 units of the 410 units purchased at $8)

Total cost of ending inventory = $3,490

Therefore, the cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.

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Answer:

HE=11

EF=25

HF=28

DE=25

CH=14

BE=33

Step-by-step explanation:

The measurements of the missing lengths are; HE = 11, DE = 25, CH = 14, EF = 25, HF = 28 and BE = 33

The centroid is a point in a triangle where all the three medians of the triangle intersects.

Given that,  H is the centroid of the triangle BDF, DF = 50, CF = 42, and BH = 22,

Here, BE, CF and DG are the medians of Δ BDF

We know that,

The centroid divides the medians into two parts always, ratio 2:1

And the medians divide their corresponding sides into two equal parts.

a) HE =

BH/HE = 2/1

Let HE = x, therefore, BH/HE = 22/x = 2/1

HE = 11

b) DE = DF/2 = 50/2 = 25

c) CH = (CF/3)x1 = 42/3 = 14

d) EF = DE = DF/2= 25

e) HF = (CF/3)x2 = 14x2 = 28

f) BE = HE+BH = 22+11 = 33

Hence, Each of the missing measures are HE = 11, DE = 25, CH = 14, EF = 25, HF = 28 and BE = 33

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Answer:

your right!!!

Step-by-step explanation:

Answer:

\(\boxed{135\°,315\°}\)

Step-by-step explanation:

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

\(\theta = 135+180n\)

\(n\) is any integer value.

The value of \(n\) cannot exceed 1 or be less than 0, because the value of \(\theta\) must be between 0 and 360 degrees.

\(\theta = 135+180(0)\)

\(\theta = 135\)

\(\theta = 135+180(1)\)

\(\theta = 315\)

.72 radians is the answer.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

The relation of the arc length of a circle subtended by an angle to the radius of the circle is the definition of an angle in radians.

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Answer:

C; Basketball

Step-by-step explanation:

Although Greg Ridley wants to play for the Scorpions when he grows up, he learns along the way that there are things that are more important, hence the use of the term "treasure."

He learns from this that memories, friendships, and family are all that matters and if having to let go of basketball to sustain the aforementioned elements (which may or may not be an easy thing to do), then it is much more of a necessity than a choice.

Hope this helped! :D

** p = pages, hrs = hours

sorry if it's messy lol I can explain it again if you want

Answer:

4.25 and 51

Step-by-step explanation:

IN GENERAL:

Equivalent ratio are equivalent fractions.

Equivalent fractions:

-if we simplify them they will be the same

for example, 1/2 is the same as 1*3/2*3 = 3/6

- if we divide the numbers on the fractions we get the same result.

for example, 1/2 = 0.5, and 3/6 = 0.5

IN OUR PROBLEM:

-sometimes the numbers are easy to see and you can do it this way

8/34 = 1/?, those are our equivalent fractions

how did we got from 8 to 1 ?...by dividing by 8

how do we get from 34 to ?...by dividing by 8

34/8 = 4.25

our equivalent fraction are 8/34 and 1/4.25

-sometimes just using algebra works better

\(\frac{8}{34} = \frac{12}{x}\),  set up the equivalent fractions and cross multiply

8x = 34*12, divide both sides of the equation by 8

\(x=\frac{34*12}{8}\),solve

x= 51

our equivalent fractions are 8/34 are 12/51

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

Questions 1, 2, and 5 are correct.

Question 3:

To find the common difference, we can subtract the last two numbers.

60 - 47 = 13

So, the common difference is 13

We can add 13 to each term to get the next term.

8 + 13 = 21

21 + 13 = 34

So, 8, 21, 34, 47, 60

Question 4:

To find the common difference, we can subtract the last two numbers.

8/3 - 2 = 2/3

So, the common difference is 2/3

We can add 2/3 to each term to get the next term.

0 + 2/3 = 2/3

2/3 + 2/3 = 4/3

So, 0, 2/3, 4/3, 2, 8/3

Question 4:

Since we are only given the first and last number, we need to find a number we can subtract that we get -13 at the end. The distance between 3 and -13 is 16. We can divide this by 4 since there are 4 numbers before -13.

16 / 4 = 4

Since the number is going down, the common difference is going to be -4.

Subtract find the next terms.

3 - 4 = -1

-1 - 4 = -5

-5 - 4 = -9

-9 - 4 = -13

So, 3, -1, -5, -9, -13

Best of Luck!

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Answer:

436.42 m

Step-by-step explanation:

We are to determine the perimeter of the field

perimeter = perimeter of rectangle + perimeter of the two semicircles

Perimeter of a rectangle = 2 x (length + breadth)

2 x (82 + 53) = 270m

Perimeter of a semicircle = 1/2πD

perimeter of the 2 semicircles = 2 x (1/2 x 3.14 x 53) = 166.42

Perimeter = 270 + 166.42 = 436.42 m

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

75%

Step-by-step explanation:

1/4 is 25

2/4 is 50

3/4 is 75

4/4 is 100

Answer:

Step-by-step explanation: