A consumer report revealed the following information about three tubes of toothpaste. A tube of Bright is 60% more expensive than a tube of Fresh and has 25% less volume than Glow. A tube of Glow is 25% less expensive than a tube of Bright and has 100/3 more volume than Fresh. Fresh costs 1. 00$ per unit of volume. What is the number of cents per unit of volume of Glow?

Answer:( 3.5 , -2 )

Step-by-step explanation:

To model the consumer expenditure (revenue for the vendor) as a function of price, we can use a linear equation in the form of:

Expenditure = m * Price + b

Where:

Expenditure represents the consumer expenditure or revenue for the vendor.

Price is the price of the product in dollars.

m is the slope of the linear equation.

b is the y-intercept of the linear equation.

To determine the values of m and b, we need additional data points or information about the relationship between price and consumer expenditure. Without specific data points, it is not possible to determine the exact values of m and b.

However, if you have a specific data set or information on the relationship between price and consumer expenditure within the range of 20 to 32 dollars, I can assist you in calculating the values of m and b using linear regression or provide alternative modeling approaches based on the available information.

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Answer: 45 miles an hour

Step-by-step explanation:

its in the sentence

Answer:

12.5% (I think)

Step-by-step explanation:

75 is the amount of money lost, and 75 is 12.5 percent of 600

Answer:

12.5 percent decrease

Step-by-step explanation:

Use the formula

new-old/old

525 is new price being sold

600 is old price being sold

525-600

-75/600

-1/8

-1/8= -0.125

0.125= 12.5 percent

so 12.5 percent decrease.

99% CI = 0.1252 to 0.1948

This confidence interval suggests that, with 99% confidence, the true proportion of households that have experienced property damage due to a crime lies between 12% and 20%.

SRS stands for Simple Random Sample, which is a sample of a population in which each member of the population has an equal chance of being selected. CI stands for Confidence Interval, which is a range of values that is likely to contain the true population parameter.

To calculate a 99% CI for the true proportion of households that have experienced property damage due to crime, we first need to calculate.

p = 80/500 = 0.16

Standard error = √ (0.16 x 0.84)/500 = 0.0116

Now that we have the sample proportion and the standard error, we can calculate the 99% confidence interval. The 99% confidence interval is equal to the sample proportion plus or minus 3 standard errors.

99% CI = 0.16 ± (3 x 0.0116)

99% CI = 0.16 ± 0.0348

99% CI = 0.1252 to 0.1948

Therefore, we can be 99% confident that the true proportion of households that have experienced property damage due to a crime is between 0.1252 and 0.1948.

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Answer:

Step-by-step explanation:

you the formula x*u

Answer:

1) y= 30

2) y - 45

3) y= 60

4) y = 3

Step-by-step explanation:

Answer:

1. y=30

2. y=45

3. y=60

4. y=3

hope this helps!!!

Answer:

1. x^2-9x+18

2. 2x^2-4x-16

3. 3x^2-19x-14

4. 6x^2 +14x + 8

Step-by-step explanation:

1. (x-3)(x-6)

x^2 - 6x - 3x +18 = x^2-9x+18

2. (2x+4)(x-4)

2x^2-8x+4x-16 = 2x^2-4x-16

3. (x-7)(3x+2)

3x^2+2x-21x-14 = 3x^2-19x-14

4. (3x+4)(2x+2)

6x^2+6x+8x+8 = 6x^2 +14x + 8

Answer:

12+15=27 total students, each car can seat 4, so 27/4=6.75, you would round up to 7 bc you can't have 3/4ths of a car

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

(12+15)÷4=x

(27)÷4=x

6.75=x

round up to 7

Answer:

63 in²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Step-by-step explanation:

Step 1: Define Variables

Base b = 14 in

Height h = 9 in

Step 2: Find Area A

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

sure when i have money

Step-by-step explanation:

i don't have money lol

Answer:

-1,0

0,-2

slope is -2/1

Answer:

View the Screenshot that I have sent.

The statement is false. The arc length of the curve defined by x = 4(3 + y)² on the interval [1, 4] is not approximately 131 units.

To find the arc length of a curve, we use the formula ∫ √(1 + (dx/dy)²) dy, where the integral is taken over the given interval.

In this case, the equation x = 4(3 + y)² represents a parabolic curve. By differentiating x with respect to y and substituting it into the arc length formula, we can calculate the exact arc length over the interval [1, 4].

However, it is clear that the arc length of the curve defined by x = 4(3 + y)² cannot be approximately 131 units, as this would require a specific calculation using the precise integral formula mentioned above.

Therefore, the statement is false, and without further calculations, we cannot determine the exact arc length of the given curve on the interval [1, 4].

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Answer:

all of them

Step-by-step explanation:

Using Gaussian elimination followed by back substitution, we get the solution of the system of equations x = -3z - 11, y = 2z + 2, z is free variable The row operations used were: R2 = R2 - 2R1, R3 = R3 + 2R1, R3 = R3 + 7R2. The corresponding elementary matrices were M1 = [1 0 0; -2 1 0; 0 0 1], M2 = [1 0 0; 0 1 2; 0 0 1], M3 = [1 0 0; 0 1 0; 0 7 1]. The product M3M2M1 was found to be  [1 -6 -8; 0 1 2; 0 0 1]. The matrix MA appears as the row-reduced echelon form of A. The matrix U has a triangular form and the matrix L has 1's along the diagonal and values below the diagonal that were used to eliminate the entries in U.

We perform the following row operations

R2 → R2 - 2R1

R3 → R3 + 2R1

R3 → R3 + 7R2

This gives us the following augmented matrix

[1  3  4 |  1]

[0 -1 -2 | -4]

[0  0  0 |  0]

Now, using back substitution, we get

z = any real number

-y - 2z = -4

x + 3y + 4z = 1

So, our solution is

x = -3z - 11

y = 2z + 2

z is free variable

The elementary matrices corresponding to the row operations used in part (a) are

M1 = [1 0 0; -2 1 0; 0 0 1]

M2 = [1 0 0; 0 1 0; 2 0 1]

M3 = [1 0 0; 0 1 0; 0 7 1]

We compute the product of the elementary matrices as

Mk...M2M1 = [1 -6 -8; 0 1 2; 0 0 1]

We have MA = [1 -6 -8; 0 1 2; 0 0 0], which appears during the row reduction process in part (a) when we have arrived at the row echelon form of the augmented matrix.

U is the upper triangular matrix obtained after performing Gaussian elimination on A, while L is the lower triangular matrix obtained from the product of the elementary matrices found in part (c). They have the property that LU = A, and the determinant of U is the product of the pivots of A (in this case, 1*(-1)*0 = 0).

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The answer is 5 enjoy the answer!

Answer:

Inverse property of multiplication implies that when two number are multiplied, the result is 1. 4 + (-4) = 0. here in this equation is when we multiply 4 and - 4 the answer will not be 1.-8 + (-3) = -3 + (-8) This equation shows the property of multiplicative inverse. The 2 nd equation is showing the inverse of the multiplication property.

Answer:

division

Step-by-step explanation:

because multiplication is the method of something times more by a certain value, if we reverse that effect we divide something.

edit: The dude above might be correct more, cause I think

I answered that wrongly sorry

The number of time constants must elapse before a capacitor in a series rc will be 0.634rc.

Explanation:

Let us denote the equilibrium charge with qₐ

   In the given question

      for the duration we are to obtain the final charge on the capacitor should be 47% of  qₐ

                                 q= qₐ(1-e⁻t/rc)

Where q is the final charge = 47%   = 0.47qₐ

             RC is the time constant

substitute the values:

                                           0.47qₐ= qₐ(1-e⁻t/rc)

                                              e⁻t/rc=0.53

   Taking natural log of both sides

                                  ln(e⁻t/rc) = ln(0.53)

                                     -t/rc = -0.634

                                          t/rc =0.634

                                       t=0.634rc

So the time constant will be t=0.634timeconstants

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Answer:

Option B is the correct option.

Step-by-step explanation:

\( {(4 - 2)}^{3} - 3 \times 4\)

Subtract the numbers

\( = {(2)}^{3 } - 3 \times 4\)

Multiply the numbers

\( = {(2)}^{3} - 12\)

Evaluate the power

\( = 8 - 12\)

Calculate the difference

\( = - 4\)

Hope this helps..

Best regards!!

Answer:

\(\boxed{-4}\)

Step-by-step explanation:

\((4-2)^3-3 \times 4\)

Brackets or parenthesis are to be evaluated first. Subtract the numbers in the brackets.

\((2)^3-3 \times 4\)

Evaluate the power or exponent.

\(8-3 \times 4\)

Multiply the numbers.

\(8-12\)

Finally, subtract the numbers.

\(=-4\)

The solution to the inequality is: x >= 55 or x <= -32.

what is inequality?

An inequality is a mathematical statement that compares two values or expressions and indicates that they are not equal. In other words, an inequality shows the relationship between two values or expressions that are not the same.

To solve the inequality, we need to isolate x on one side of the inequality symbol in each of the two inequalities.

For the first inequality:

3 - 2/5 * x <= -19

Subtracting 3 from both sides, we get:

-2/5 * x <= -22

Dividing both sides by -2/5 (which is the same as multiplying both sides by -5/2), we get:

x >= 55

For the second inequality:

-3/4 * x >= 24

Dividing both sides by -3/4 (which is the same as multiplying both sides by -4/3), we get:

x <= -32

Therefore, the solution to the inequality is:

x >= 55 or x <= -32.

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The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)

= (9 ± √(81 + 144)) / 6

= (9 ± √(225)) / 6

= (9 ± 15) / 6.

We have two possible solutions:

For the positive root:

x = (9 + 15) / 6

= 24 / 6

= 4.

For the negative root:

x = (9 - 15) / 6

= -6 / 6

= -1.

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

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Answer:41.8

Step-by-step explanation:

Gareth has a capital gain of $34,894, which he will need to include in his assessable income.

To determine the amount Gareth has to include in his assessable income, we need to calculate the capital gain or loss on the sale of the rental house. Here's a breakdown of the calculations based on the given information:

Cost Base:

The cost base is the initial purchase price of the house plus any additional costs incurred to acquire or improve the property. In this case:

Cost Base = Purchase Price + Stamp Duty + Initial Repairs + Rates and Taxes + Interest on Loan

Cost Base = $175,000 + $8,425 + $3,100 + $15,300 + $56,000

Cost Base = $257,825

Adjusted Cost Base:

The adjusted cost base takes into account the depreciation deductions claimed (Division 43 deductions in this case).

Adjusted Cost Base = Cost Base - Division 43 Deductions

Adjusted Cost Base = $257,825 - $42,719

Adjusted Cost Base = $215,106

Capital Gain or Loss:

Capital Gain or Loss = Sale Price - Adjusted Cost Base

Capital Gain or Loss = $250,000 - $215,106

Capital Gain or Loss = $34,894

Gareth's assessable income from the sale of the rental house is $34,894. This is calculated by subtracting the adjusted cost base from the sale price, resulting in the capital gain. It's important to note that tax rules and regulations may vary depending on the jurisdiction, so it's advisable to consult a tax professional or accountant for accurate and personalized advice.

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Answer:

13) \(n=-3,-7\)

14) \(b=-4,-8\)

15) \(m=-7\)

16) \(a=-5,-7\)

Step-by-step explanation:

Answer:

76 units

Step-by-step explanation:

In the given figure, a circle with center Q is inscribed in triangle AHD.

Let the circle with center Q touches the side HD at point N.

So, AT & AM, DM & DN and HT & HN are tangents drawn from external points A, D and H respectively.

Since, measure of tangsnts drawn from external point to a circle are equal.

Therefore,

AM = AT = 18

HN = HT = 8

DM = DN = 12

AH = AT + HT = 18 + 8 = 26

AD = AM + DM = 18 + 12 = 30

HD = DN + HN = 12 + 8 = 20

Perimeter of triangle

= AH + AD + HD

= 26 + 30 + 20

= 76 units

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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a. For this study, we should use a one-sample t-test because we are comparing the sample mean to a known population mean and we have the sample standard deviation.

b. The null and alternative hypotheses would be:
H₀: The population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is equal to 9.1 minutes.
H₁: The population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is different from 9.1 minutes.

c. The test statistic can be calculated using the formula:
t = (x - μ₀) / (s / √n)
where x is the sample mean, μ₀ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:
t = (10.1 - 9.1) / (3.51 / √55) ≈ 1.885

d. The p-value can be determined by finding the probability of obtaining a test statistic as extreme as the observed value (or more extreme) under the null hypothesis. Using statistical software or a t-distribution table, the p-value is approximately 0.0656 (rounded to four decimal places).

e. The p-value is 0.0656.

f. Based on this, we should not reject the null hypothesis.

g. Thus, the final conclusion is that the data suggest the population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is not significantly different from 9.1 minutes at the 0.10 level of significance.

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