37. The sum of first three terms in an arithmetic progression is 24 and the sum of their squares is 224. Find the first three terms of this arithmetic progression.
​

Given:

Kevin bought twelve 8-ounce bottles of water.

1 ounce ≈ 30 ml

To find:

The quantity of water in milliliters

Solution:

We have,

1 ounce ≈ 30 ml

8 ounce ≈ 8×30 ml

8 ounce ≈ 240 ml

It means, one 8 ounce bottle can hold about 240 milliliters of water.

Total number of bottles = 12

So, the quantity of water Kevin buy in milliliters is

\(12\times 240=2880\)

Therefore, Kevin buys 2880 milliliters of water in twelve 8-ounce bottles.

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Answer: 26

Step-by-step explanation: The third length is the hypotenuse or the longest side

Answer:

N=108

Step-by-step explanation:

You just have to add the $90 they need to raise plus the ingredients price to get $108.

The polynomial to represent the volume of the rectangular prism is:

V = (0.5x - 3) × (x - 4) × (x + 5)

Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60

How to calculate the volume (V) of a rectangular prism?
The volume (V) of a rectangular prism can be calculated using the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism respectively.

Here, the length (l) can be represented by (0.5x - 3), the width (w) can be represented by (x - 4), and the height (h) can be represented by (x + 5).

Therefore, the polynomial to represent the volume of the rectangular prism is:

V = (0.5x - 3) × (x - 4) × (x + 5)

Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60

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True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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Answer: ( A )

Step-by-step explanation: basically as the question is what is equivalent to .45 and if you put it like a fraction kinda it will look like this 1\45

Answer: 3/4

Step-by-step explanation:

You have to find one single number that goes into both the numerator and the denominator. In this case, it was 8.

24/8 = 3

32/8 = 4

Answer:

1st one is 3/4

second one is 32

I cant really see the third one

fourth one is $1.03

Step-by-step explanation:

Answer:

yes u are correct

Step-by-step explanation:

x2+16=8x

16=6x

16/6=x

x=2.6666666 or 2/3

Answer:

840

Step-by-step explanation:

3600=450+3.75x

3600-450=3.75x

3150=3.75x

3150/3.75=x

840=x

840

Answer:

(a)

\(r =\lim_{n \to \infty} |\frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}}| = \lim_{n \to \infty} \frac{n+1}{4} = \infty\)

(b)

if r<1, then it converges absolutely

if r>1, then it diverges

if r=1, then the test is inconclusive

Step-by-step explanation:

The ratio test is:

\(\lim_{n \to \infty} |\frac{x[n+1]}{x[n]}| = L\)

if L<1, then it converges absolutely

if L>1, then it diverges

if L=1, then the test is inconclusive

I'm assuming that they used r instead of L. Anyway, to do the ratio test, you plug in n+1 into the equation and make that numerator.

Then you plug in n into the same equation and make that your denominator.

In our case, our equation is \(\frac{2n!}{2^{2n}}\).

So lets plug in n+1 and make that our numerator.\(\frac{2(n+1)!}{2^{2(n+1)}}\)

Now lets plug in n and make that our denominator. \(\frac{2n!}{2^{2n}}\)

Now set up the ratio test.

\(\lim_{n \to \infty} |\frac{x[n+1]}{x[n]}| = L\)

\(\lim_{n \to \infty} |\frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}}| = L\)

if you simplify this, you would get (view image for the steps)

\(\lim_{n \to \infty} |\frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}}| = \lim_{n \to \infty} \frac{n+1}{4} = \infty\)

L = infinity, which is > 1, therefore this series diverges

(a). The value of r from ratio test is greater than 1.

(b). The value of r tell about that the given series is converges or diverges.

The ratio test is given as,

             \(\lim_{n \to \infty} (\frac{x(n+1)}{x(n)} )=r\)

if \(r<1,\) then series converges absolutely

if \(r>1,\) then series diverges

if \(r=1,\) then the test is inconclusive

Given infinite series is,

              \(x(n)=\frac{2n!}{2^{2n} }\)

   \(\lim_{n \to \infty} \frac{\frac{2(n+1)!}{2^{2(n+1)} } }{\frac{2n!}{2^{2n} } } = \lim_{n \to \infty} \frac{n+1}{4}=\infty=r\)

Here, Observed that value of r is greater than 1.

Thus, the given series is diverges.

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Answer:

$280

Step-by-step explanation:

There are 2 ways to do the question.

Method 1: $330-$50=$280

Method 2: 7 days equals to one week=$40.

$40×7=$280

Hope these helps you!

Answer:

c. -19

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given a polynomial in standard form

The leading coefficient is the coefficient of the variable with the largest exponent.

The term with the largest exponent of the variable is

\(\frac{1}{4}\) \(x^{5}\)

Then the leading coefficient is \(\frac{1}{4}\) → A

Answer:

\( \dashrightarrow \: { \tt{4 \sqrt{3} - 5 \sqrt{7} + 2 \sqrt{3} + 6 \sqrt{7} }} \\ \\ \dashrightarrow \: { \tt{(4 - 2) \sqrt{3} + (6 - 5) \sqrt{7} }} \\ \\ \dashrightarrow \: { \tt{2 \sqrt{3} + \sqrt{7} }} \\ \\ \dashrightarrow \: { \tt{ \sqrt{3 \times 4} + \sqrt{7} }} \\ \\ \dashrightarrow \: { \tt{ \sqrt{12} + \sqrt{7} }}\)

Answer:

Step-by-step explanation:

\(4\sqrt{3} - 5\sqrt{7} +2\sqrt{3} +6\sqrt{7}=4\sqrt{3} + 2\sqrt{3} -5\sqrt{7}+6\sqrt{7}\)

                                        \(=(4+2)\sqrt{3}+ (-5 +6)*\sqrt{7}\\\\=6\sqrt{3}+1\sqrt{7}\)

$3400 in past-due business invoices will cost you $503 to collect. The correct option is (a) $503. The Percentage is 58.3%. Option (a) 7/12 58.3% is the correct answer.

1) A total of $503 will be charged to collect $3400 in past-due business invoices. A $27 application fee plus 14% of the total amount collected are charged by the chosen collection agency. Let C be the amount charged for collecting $3400 past-due commercial invoices.

Application fee = $27Therefore, the amount collected is: $3400 - $27 = $3373Amount charged for collecting is $27 + 14% of $3373.

Mathematically, it is expressed as: C = $27 + (14% of $3373)

Simplifying, we get: C = $27 + 0.14 × $3373C = $27 + $472.22C = $499.22

Rounding off C to the nearest cent, we get: C ≈ $499.23

Therefore, a total fee of $503 was incurred to recover $3400 in past-due business invoices. Therefore, the correct option is (a) $503.

2) We have to fill in the percentage that fits the blank. We can use the formula for finding the percentage given below: Percentage = (Fraction / 1) × 100Given fraction is 0.583Percentage = (0.583 / 1) × 100Percentage = 58.3%Therefore, option (a) 7/12 58.3% is the correct answer.

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Answer:

x=6

Step-by-step explanation:

Answer: x=6

Explanation:

1. Add:     15+25=40

2.Subtract 4 from each side:   40=4+6x

3.Divide by 6:   36=6x

4. x=6

The value of   Sin(a + b) =   \(-\frac{3+4\sqrt{15} }{20}\) and value of

Cos (a -b) = 119/400

Given,

In the question;

Sin(a) = 1/4 and cos(b) = -3/5

with a and b both in the interval [\(\frac{\pi }{2} ,\pi\))

To find the sin(a + b) and cos (a - b)

Now, According to the question:

We know that :

Sin (b) =   \(\sqrt{1-cos^2b}\) = 4/5

Cos (a) = - \(\sqrt{1-sin^2a} = - \frac{\sqrt{15} }{4}\)

∴ Sin(a + b) = Sin(a) Cos(b) + Cos(a) Sin(b)

  Sin(a + b) = 1/4. (-3/5) + \(-(\frac{\sqrt{15} }{4} )\) . 4/5

   Sin(a + b)  =   \(-\frac{3+4\sqrt{15} }{20}\)

∴ Cos (a -b) = \(cos^2a -sin^2b\)

Cos (a -b) = \((-\frac{\sqrt{15} }{4} )^2\) - \((\frac{4}{5} )^2\)

Cos (a -b) = 119/400

Hence, The value of   Sin(a + b) =   \(-\frac{3+4\sqrt{15} }{20}\) and value of

Cos (a -b) = 119/400 .

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Answer:

~-1.67

Step-by-step explanation:

Multiply. Note that when you multiply a negative and positive number, your answer will be negative:

5 x (-1/3) = (5 * -1)/3

Multiply, then divide:

5 * -1 = -5

-5/3 = ~-1.67 (rounded to the nearest hundredths).

~

Answer:

-5x/3

It just is, trust me.

The identity of the unknown is hexane, the second unknown is isopropyl alcohol, and the edge length of the jade cube is approximately 1.87 cm.

a. To determine the identity of the first unknown, we can compare the calculated density with the known densities of the liquids. The calculated density can be found by dividing the mass of the sample (3.310 g) by its volume (5.00 mL), giving us a density of 0.6620 g/mL.

Since the calculated density (0.6620 g/mL) is closest to the density of hexane (0.7851 g/mL), it is likely that the first unknown is hexane.

b. To determine the identity of the second unknown, we can use the same approach as in part a. By dividing the mass of the sample (4.061 g) by its volume (5.00 mL), we find the calculated density to be 0.8122 g/mL.

This density is closest to the density of isopropyl alcohol (0.7851 g/mL), so it is likely that the second unknown is isopropyl alcohol.

c. To find the edge length of the jade cube, we can use the formula for the volume of a cube: V = l^3. We know the mass of the cube (15.00 g) and its density (3.25 g/mL), so we can find its volume by dividing the mass by the density:

V = m/d = 15.00 g / 3.25 g/mL = 4.62 mL = 4.62 cm^3

Since the volume is equal to the edge length cubed, we can find the edge length by taking the cube root of the volume:

l = cuberoot(V) = cuberoot(4.62 cm^3) = approximately 1.87 cm.

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Perimeter = 2(8 cm + 6 cm) = 2(14 cm) = 28 cm. We can calculate it in the following manner.

The perimeter of the rectangular piece of cardboard is the sum of all four sides. Using the given measurements of 8 cm by 6 cm, we can calculate the perimeter as follows:

Perimeter = 2(Length + Width)
Perimeter = 2(8 cm + 6 cm)
Perimeter = 2(14 cm)
Perimeter = 28 cm

Therefore, the perimeter of the rectangular piece of cardboard is 28 cm.
Hi! To calculate the perimeter of a rectangular piece of cardboard with measurements 8 cm by 6 cm, you can use the formula: Perimeter = 2(Length + Width). In this case, the length is 8 cm and the width is 6 cm.

Your answer: Perimeter = 2(8 cm + 6 cm) = 2(14 cm) = 28 cm.

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Step-by-step explanation:

5(r + 9) - 2(1 - r) = 1

5r + 45 - 2 + 2r = 1

7r + 43 = 1

7r = -42

r = -6.

Answer:

r = -6

Step-by-step explanation:

Given equation,

→ 5(r + 9) - 2(1 - r) = 1

Now the value of r will be,

→ 5(r + 9) - 2(1 - r) = 1

→ 5r + 45 - 2 + 2r = 1

→ 5r + 2r + 43 = 1

→ 7r = 1 - 43

→ 7r = -42

→ r = -42/7

→ [ r = -6 ]

Hence, the value of r is -6.

Answer:

x2 -12x - 20y = 64

6/50 fraction of all people in the company are women under age of 30 In a company where the ratio of men to women i 3:2.

In a company the ratio of men to women  3:2

30% of the women are under the age of 30.

suppose there are 500 people in the company

then 300 are men and 200 are women

30% of 200 = 200*30/100= 60 women are under 30

60/500= 6/50 women are under 30

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Answer:

Therefore, the answer to how much is in the checking account is $677.

Step-by-step explanation:

The amount in the checking account after all the transactions would be $677.

Here's the breakdown of the transactions:

Starting balance: $910

Bill payment: -$185

Withdrawal for lunch: -$30

Purchase of pants: -$43

Purchase of gift card: -$15

Refund for pants: +$43

Total = $910 - $185 - $30 - $43 - $15 + $43 = $677

An absolute value inequality that models this situation: \(|x-120|\leq 4\)

The required compound inequality representing all possible weights for Mr. Bean.: \(116\leq x\leq 124\)

Given: For the last 20 years,

Mr. Bean has weighed 120 pounds, give or take 4 pounds.

To write: a) An absolute value inequality that models this situation.

b)  a compound inequality representing all possible weights for Mr. Bean.

Computation:

Let x be the actual weight of Mr. Bean,

then

Required absolute inequality:\(|x-120|\leq 4\)

It can be written as

\(-4 \leq x-120\leq 4\)

Add 120 on all sides , we get

\(120-4\leq x\leq120+4\)

\(116\leq x\leq 124\)

The required compound inequality representing all possible weights for Mr. Bean.: \(116\leq x\leq 124\)

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Answer:

m = 36

Step-by-step explanation:

A^2 + B^2 =  C^2

81 +  144 = 225

square root of 225 =  15

n = 15

m = ?

39 = 39

225  + m ^2 = 1521

m^2 = 1296

m = 36.

CHECK :

225 + 1296 =  1521

CORRECT!

Given the equation

Subtract 3 from both sides

Divide both sides by 3

Raise both sides to power 5 to remove the 5th root on the left hand side

Take the cube root of both sides

Subtract 2 from both sides

x + 2 = 32

x = 32 - 2

x = 30

The solution to the equation is x = 30