2 3/5 multiplied by 5/6

Answer:

The rate of decay is 12% or .12

Step-by-step explanation:

Answer:

y = 1/4x + 9

Step-by-step explanation:

Hello!

Equation of a line: y = mx + b

A line that is perpendicular has the opposite reciprocal slope.

Since this line has the slope -4:

Our new line is y = 1/4x + b

Next, our line goes through point (0,9). This is our y-intercept, which can be used as our "b" value. Y -intercepts have an x-value of 0.

OUr equation is y = 1/4x + 9.

Answer:

180

Step-by-step explanation:

Answer:

A 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Step-by-step explanation:

We are given the weights, in the ounces, of a sample of 12 boxes below;

Weights (X): 21.88, 21.76, 22.14, 21.63, 21.81, 22.12, 21.97, 21.57, 21.75, 21.96, 22.20, 21.80.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                         P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean weight = \(\frac{\sum X}{n}\) = 21.88 ounces

            s = sample standard deviation = \(\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }\)  = 0.201 ounces

            n = sample of boxes = 12

            \(\mu\) = population mean weight

Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, \(\mu\) is ;

P(-1.796 < \(t_1_1\) < 1.796) = 0.90  {As the critical value of t at 11 degrees of

                                                  freedom are -1.796 & 1.796 with P = 5%}  

P(-1.796 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 1.796) = 0.90

P( \(-1.796 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(1.796 \times {\frac{s}{\sqrt{n} } }\) ) = 0.90

P( \(\bar X-1.796 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+1.796 \times {\frac{s}{\sqrt{n} } }\) ) = 0.90

90% confidence interval for \(\mu\) = [ \(\bar X-1.796 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+1.796 \times {\frac{s}{\sqrt{n} } }\) ]

                                        = [ \(21.88-1.796 \times {\frac{0.201}{\sqrt{12} } }\) , \(21.88+1.796 \times {\frac{0.201}{\sqrt{12} } }\) ]

                                        = [21.78, 21.98]

Therefore, a 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Heya !

Given two points A ( 8 , -4 ) and B ( 1 , - 5 )

To find - slope of line AB

Solution -

\( Slope = \frac{y_{2}-y_{1}}{x_{2} - x_{1}} \\ \\ \dashrightarrow \frac{ -5 - (-4 )}{ 1 - 8 } \\ \\ \dashrightarrow \frac{ - 5 + 4 }{ 1 - 8 } \\ \\ \dashrightarrow \frac{-1}{-7} \\ \\ \dashrightarrow \frac{1}{7}\)

Hence ,

Option ( c ) is correct.

Hope helpful ~

The nth term of the sequence -3, 0, 5, 10, 25, 5, 47 can be represented by the piecewise function:

nth term =

-3 + (n - 1) * 5, if n mod 5 ≤ 5

5 + (n - 1) * 15, if n mod 5 > 5

To find the nth term of a sequence, we need to identify the pattern or rule that governs the sequence. Upon analyzing the given sequence -3, 0, 5, 10, 25, 5, 47, we can observe the following:

The sequence starts with -3 and increases by 5 each time, except for the 5th term, where it increases by 15 (from 10 to 25). After the 5th term, the sequence starts again with 5 and continues to increase by 15 each time.

Based on this pattern, we can divide the sequence into two parts:

Part 1: -3, 0, 5, 10, 25 (increasing by 5 each time)

Part 2: 5, 20, 35, 50, 65 (increasing by 15 each time)

Now, to determine the nth term, we can consider the formula for arithmetic sequences:

nth term = first term + (n - 1) * common difference

For Part 1, the first term is -3 and the common difference is 5. Thus, the nth term for Part 1 is given by:

nth term = -3 + (n - 1) * 5

For Part 2, the first term is 5 and the common difference is 15. Therefore, the nth term for Part 2 can be expressed as:

nth term = 5 + (n - 1) * 15

However, since the sequence alternates between Part 1 and Part 2, we need to determine which part the nth term falls into. For that, we can use modular arithmetic:

If n mod 5 is less than or equal to 5, then the nth term is from Part 1.

If n mod 5 is greater than 5, then the nth term is from Part 2.

Let's calculate a few terms to illustrate this:

For n = 1, the sequence starts with -3, so the 1st term is -3.

For n = 2, we are still in Part 1, so the 2nd term is 0.

For n = 3, Part 1 continues, so the 3rd term is 5.

For n = 4, we are still in Part 1, so the 4th term is 10.

For n = 5, Part 1 ends, and the 5th term is 25.

For n = 6, the sequence starts with 5 in Part 2, so the 6th term is 5.

For n = 7, Part 2 continues, so the 7th term is 20.

For n = 8, we are still in Part 2, so the 8th term is 35.

Based on this analysis, we can conclude that the nth term for the given sequence is:

If n mod 5 ≤ 5:

nth term = -3 + (n - 1) * 5

If n mod 5 > 5:

nth term = 5 + (n - 1) * 15

Therefore, depending on the value of n and the remainder when divided by 5, we can use the appropriate formula to calculate the nth term.

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This example demonstrates a two-step inequality where we first express the savings equation and then solve for the variable 'w' to determine the number of weeks needed to reach the savings goal.

Liam is saving money to buy a new video game console. He has already saved $50 and is saving $10 per week from his allowance. He wants to determine how many weeks it will take for his savings to reach at least $150.

Let:

number of weeks Liam saves = w

total amount of money he saves = S

Step 1: Express the first step of the problem as an inequality.

Liam saves $10 per week, so the amount of money he saves after w-weeks is 10w. We can write the first step of the inequality as:

10w + 50 ≥ 150

Step 2: Solve the inequality.

To isolate 'w', we can subtract 50 from both sides of the inequality:

10w ≥ 150 - 50

10w ≥ 100

Finally, divide both sides of the inequality by 10 to solve for 'w':

w ≥ 10

Therefore, it will take Liam at least 10 weeks to save enough money to reach $150 for the video game console.

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Answer:

See below

Step-by-step explanation:

Answer:

m<VRU = 80°

m<URW = 15°

Step-by-step explanation:

<SRW and <VRT are vertical opposite angles. Vertical opposite angles are equal. Therefore:

\( 2x + 15 = 85 \)

Use this expression to solve for the value of x

\( 2x + 15 - 15 = 85 - 15 \)

\( 2x = 70 \)

\( \frac{2x}{2} = \frac{70}{2} \)

\( x = 35 \)

Find m<VRU by plugging in the value of x in the expression for its angle given.

m<VRU = \( 2x + 10 \(

\( 2(35) + 10 = 70 + 10 = 80 \(

m<VRU = 80°

FIND m<URW.

m<URW = 180° - (m<VRU + m<SRW) (angles on a straight line is 180°)

m<URW = 180 - (80 + 85)

= 180 - 165

m<URW = 15°

The question is incomplete. Here is the complete question.

m∠J and m∠Kare base angles of an isosceles trapezoid JKLM.

If m∠J = 18x + 8, and m∠M = 11x + 15 , find m∠K.

A. 1

B. 154

C. 77

D. 26

Answer: B. m∠K = 154

Step-by-step explanation: Isosceles trapezoid is a parallelogram with two parallel sides, called Base, and two non-parallel sides that have the same measure.

Related to internal angles, angles of the base are equal and opposite angles are supplementary.

In trapezoid JKLM, m∠J and m∠M are base angles, so they are equal:

18x + 8 = 11x + 15

7x = 7

x = 1

Now, m∠K is opposite so, they are supplementary, which means their sum results in 180°:

m∠J = 18(1) + 8

m∠J = 26

m∠K + m∠J = 180

m∠K + 26 = 180

m∠K = 154

The angle m∠K is 154°

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:

Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:

(x^3 - 12x^2) + (-2x + 24)

Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:

x^2(x - 12) - 2(x - 12)

Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:

(x - 12)(x^2 - 2)

Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

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The domain of the function y = √(x + 7) + 5 is all real numbers (all real numbers). Option D.

To determine the domain of the function y = √(x + 7) + 5, we need to identify the values of x for which the function is defined.

In this case, the function includes two operations: addition and square root. To ensure the function is defined, we need to consider the restrictions imposed by each operation.

The square root function (√) is defined only for non-negative real numbers. In other words, the expression inside the square root (√(x + 7)) must be greater than or equal to zero for the function to be defined.

Setting x + 7 ≥ 0, we can solve for x:

x ≥ -7

Therefore, the expression inside the square root (√(x + 7)) is defined for x values greater than or equal to -7.

Additionally, there are no restrictions on the addition operation (+5). It can be applied to all real numbers.

Combining both restrictions, we find that the function y = √(x + 7) + 5 is defined for all real numbers x, since there are no limitations or exclusions. Option D is correct.

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Answer:

0+0=0

Step-by-step explanation:

Expression is another word for equation

Check the picture below.

so the perimeter is 6+16+14+7+8+9 = 60.

Answer:

A

Step-by-step explanation:

\(7n + \frac{1}{5} \)

\( \frac{35n + 1}{5} \)

And

\( \frac{1}{5} + 7n\)

\( \frac{1 + 35n}{5} \)

Answer:

A, because they switched around the order of the expression but it still equals the same thing.

Step-by-step explanation:

Answer:

B) (2x100) + (4x10) + (1x1) + (3x1/10) + (2x1/100) + (4x1/1000)

Answer:

b. undercoverage

c. placebo effect.

e. bias due to a voluntary response sample.

Step-by-step explanation:

Undercoverage because the invitation does not cover for a good amount of university students. It is only given to university students that are nearly

Placebo effect occurs due to the fact that the drug is given to all the sample participants so it will be very difficult differentiating any effect that is above the placebo response. Therefore, the placebo effect is a main problem.

Voluntary Response Bias in survey sampling, this happens due to the fact that sample participants are volunteers that were self selected.

The following problems that are likely to arise with such an experiment is:

B. Undercoverage

C. Placebo effect.

E. Bias due to a voluntary response sample.

B. Under coverage -

C. Placebo effect-

E. Bias due to a voluntary response sample.

Thus, the correct option is B, C and E.

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Given:

Original Value - $29,000

Final Value after 13 years - $15,000

Find: annual rate of change between 1993 and 2006 (13 years)

Solution:

To determine the annual rate of change, we use the formula below:

where a = the initial value, b = the rate of change, x = the number of years, and y = the final value at x year.

Since we already have the values of the variables provided in the question, let's replace them.

Then, solve for b.

Divide both sides of the equation by 29,000.

Power both sides of the equation by 1/13.

The value of b is 0.95055.

Let's subtract this from 1.

Multiply this by 100.

Therefore, the annual rate of change between 1993 to 2006 is -4.95%. We used negative because we are dealing with depreciation. The depreciation rate annually is 4.95%.

If the value of the car continues to drop after an additional 3 years (2006 - 2009) or 16 years from 1993, let's replace "x" in the equation above with 16, and let's use b = 0.95055 to solve for the value of the card in the year 2009.

Type those values in a calculator and solve.

The value of the car in the year 2009 will be approximately $12, 882.42.

Answer:

x=8

Step-by-step explanation:

just do 5x+ 1 =41 solve and your done

Answer:

8 i took the test

Step-by-step explanation:

The fractions are rewritten as so that they have a common denominator as  107/100

A fraction can be described as the part of a whole element, variable or number.

The several types of fractions are;

From the information given, we have that;

13/25 and 11/20

To rewrite the fractions, we have to determine the lowest common multiple

13/25 + 11/20

52 + 55 /100

Add the numerators , we have;

107/100

Hence, the fraction is 107/100

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The electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

The electric field is a vector field that represents the force experienced by a charged particle due to an electric charge distribution. It is a measure of the electric force per unit charge at a particular point in space. The electric field is defined as the negative gradient of the electric potential, which is the energy per unit charge that a charged particle would have at that point in space. The electric field can be used to calculate the force experienced by a charged particle in the presence of other charges, and is a fundamental concept in the study of electromagnetism.

The electric field force between two point charges is given by Coulomb's law:

F = k * (q₁ * q₂) / r²

where k is the Coulomb constant (8.99 x 10⁹ N m²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between the charges.

To calculate the work done by the electric field force, we need to find the force at the initial distance (0.30 m) and the final distance (1.05 m), and then subtract the work done at the initial distance from the work done at the final distance.

At a distance of 0.30 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (0.30 m)² = 4.02 x 10⁻⁸ N

The work done at this distance is:

W = F * 0.30 m = 1.21 x 10⁻⁷ J

At a distance of 1.05 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (1.05 m)² = 1.33 x 10⁻⁸ N

The work done at this distance is:

W = F * 1.05 m = 1.40 x 10⁻⁷ J

Finally, to find the total work done, we subtract the work done at the initial distance from the work done at the final distance:

W total = W final - W initial = 1.40 x 10⁻⁷ J - 1.21 x 10⁻⁷ J = 1.90 x 10⁻⁸ J.

Therefore, the electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

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With a pound of flour costing $12 and considering that there are 16 ounces in a pound, the cost per ounce is $0.75. Thus, for $3.30, you can purchase 4.4 ounces of flour.

To find out how many ounces of flour can be purchased for $3.30, we need to determine the cost of one ounce of flour.

Given that a pound of flour costs $12, we know that there are 16 ounces in a pound (since there are 16 ounces in 1 pound). So, the cost of one ounce of flour can be calculated as:

Cost of one ounce of flour = Cost of one pound of flour / Number of ounces in one pound

Cost of one ounce of flour = $12 / 16 ounces

Cost of one ounce of flour = $0.75

Therefore, the cost of one ounce of flour is $0.75.

To determine how many ounces of flour can be purchased for $3.30, we divide the total amount of money by the cost of one ounce of flour:

Number of ounces of flour = Total money / Cost of one ounce of flour

Number of ounces of flour = $3.30 / $0.75

Number of ounces of flour ≈ 4.4 ounce

Therefore, for $3.30, approximately 4.4 ounces of flour can be purchased.

In summary, with the given cost of $12 for a pound of flour, and knowing that there are 16 ounces in a pound, we find that one ounce of flour costs $0.75. Thus, for $3.30, approximately 4.4 ounces of flour can be purchased.

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Using it's concept, the average rate of change of the function on the interval [0,2] is of -1.5.

Before going into the average rate of change, the other items are correct.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

\(r = \frac{f(b) - f(a)}{b - a}\)

For the interval [0,2], we have that:

Hence the rate is:

r = (0 - 3)/(2 - 0) = -1.5.

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Answer:

Let x equal the number of hours worked.

a) ƒ(x) = 8x + 1(16)

b) The slope is 8

c) The -intercept represents the money earned

d) For every one hour you work, you will gain eight more dollars

e) Yes, this answer would make sense in the real world because it will show how much money you would make over a given number of hours

f) Take a look at the picture I illustrated below.

Step-by-step explanation:

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To solve this problem, we need to perform the indicated operations in order. The first step is to simplify the expressions inside the parentheses.

(3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

The next step is to combine like terms within each parentheses:

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

Finally, we can add the two expressions:

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

= 56x - 3x² - 8x + 2x³ + 3 + 7

= 56x - 3x² - 8x + 2x³ + 10

The final answer is 56x - 3x² - 8x + 2x³ + 10.

In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.

Using this information, we can set up equations to solve for the variables.

From the given information, we have -

AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)

BE = x + 2

DE = BE = (x + 2) = g (since diagonals bisect each other at point E)

We also know that opposite sides of a parallelogram are parallel.

Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -

10/1 = 2y/1

10 = 2y

y = 5

Now we can use equation (1) to solve for x -

2x - 5 = 5x - 17

12 = 3x

x = 4

Finally, we can use x to solve for g -

(x + 2) = g

(4 + 2) = g

g = 6

Therefore, the values of x, y, and g are 4, 5, and 6, respectively.

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The mass of the 2 meter length of the pipe if the mass of 1 cm³ volume of pipe is 7.2 g is 57,600 g.

Given a pipe.

We have to find the volume of the pipe to find the total mass of the pipe.

Volume of a rectangular prism = Area × height

Area of the pipe = Area of the larger rectangle - Area of smaller rectangle

                           = (12 × 10) + (12-2)(10-2) [ Since the pipe is 1 cm thick on both sides]

                           = 120 - 80

                           = 40 cm²

Height of the pipe = 2 m = 200 cm

Volume of the pipe = 40 cm² × 200 cm

                                = 8000 cm³

Total mass of the pipe = 8000 × 7.2 g

                                     = 57,600 g

Hence the required mass is 57,600 g.

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