Alanis is moving and needs to pack two mirrors the largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror is similar in proportion to the larger mirror Alanis determines that the width of the smaller box needs to be a minimum of 9 inches. what should the minimum length of the box to hold the smaller mirror ?

Answer: x = -3/2

Step-by-step explanation:

-4x + 2(x+4) = -7x - (x+1)

-4x + 2x+8 = -7x -x-1

-2x + 8 = -8x - 1

+2x          +2x

8 = -6x - 1

+1           +1

9 = -6x

/-6    /-6

-9/6  = x

-3/2 = x

The units of water the friends used in one month is 820 units.

The total units of water used as read by the meter = 789 units + 820 units

= 1609 units

Therefore, the friends used a total of 820 units of water.

Complete question:

A water meter shows how many units of water Riya and her friends use.

Riya reads the meter when they move in. It shows 789 units.

She reads the meter again after one month. It reads 820 units.

How many units of water did the friends use in one month?

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Answer:

0.606 < p < 0.674

Step-by-step explanation:

[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.64\pm1.645\sqrt{\frac{0.64(1-0.64)}{540}}\\\\CI_{90\%}\approx0.64\pm0.034\\\\CI_{90\%}=\{0.606,0.674\}[/tex]

Thus, we are 90% confident that the true population proportion is between 0.606 and 0.674

6,000 grams is equivalent to 6 kilograms.

The problem is solved by converting the given dimensions from grams to kilograms. The conversion is from a smaller metric unit to a larger metric unit.

A kilogram is a larger unit of measurement for mass or weight compared to a gram.

The prefix kilo in kilogram means 1000, so one kilogram is equal to 1000 grams.

Therefore, to convert from grams to kilograms, you simply divide the number of grams by 1000.

In this case, 6,000 grams divided by 1000 equals 6 kilograms.

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The equation of the line is (y - 1/12) = -4/3(x - 7/5).

What is the slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be depicted by

tan θ = Δy/Δx

So, the slope of a line is tan.

The given equation of a line is:

3x-4y=7

-4y = -3x + 7

y = 3/4 x - 7/4

The slope of the line is 3/4.

The slope of the line perpendicular to the given line is - 1/m = - 4/3

The point-slope of a line is y - y₁ = m(x - x₁).

The given point is (7/5,1/12)

The equation of the line is

(y - 1/12) = -4/3(x - 7/5)

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Answer:

Step-by-step explanation:

6(x+5) = 6x+30

-2(x-3)=-2x+6

6x+30=-2x+6

8x+30=6

8x=-24

x=-3

Answer: x = -3

Step-by-step explanation:

6(x + 5) = -2(x-3)

1. Distribute: 6x + 30 = -2x + 6

2. Add 2 to both sides: 8x + 30 = 6

3. Subtract 30 on both sides: 8x = -24

4. Divide by 8 on both sides: x = -3

Answer:

From the given information, we know that:

The thousands digit is greater than 6 and less than 8, so it must be 7.

The hundreds digit is the highest even number, so it must be 8.

The tens digit is 6.

The sum of the tens and ones digit is equal to the hundreds digit, so 6 + ones digit = 8.

Solving for the ones digit, we get:

ones digit = 8 - 6 = 2

Putting the digits together, we get the number: 7862.

So, the 4-digit number that satisfies all the given conditions is 7862.

Step-by-step explanation:

Given the clues, the thousands digit is 7, the hundreds digit is 8, the tens digit is 6, and the ones digit is 2; therefore, the 4-digit number is 7862.

Given the hints, we can infer that:

Therefore, the 4-digit number is 7862.

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On solving the provided question we can say that The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.

A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,

The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.

z(180) = (180-185)/4  = -1.25

P(x < 180) = P(z < -1.25)

3)28 C 5

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Answer:

Below

Step-by-step explanation:

The exterior angles for any polygon  sum to 360 °

so

 6 * n   = 360 °     <=====  where 'n' is the number of sides

 n = 60   sides

Answer:

y=-2/3x-0.5

Step-by-step explanation:

y=mx+b is the equation for slopes so I used it and all I needed to find was the y-intercept, which is -0.5

Answer: The future value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

FV = PMT * ( ( (1 + r)^n - 1) / r) * (1 + r)

where PMT = $300, r = 6%/12 = 0.05, and n = 10 years * 12 months/year = 120 months.

Substituting these values into the formula, we get:

FV = $300 * ( ( (1 + 0.05)^120 - 1) / 0.05) * (1 + 0.05)

FV = $300 * ( ( 1.05^120 - 1) / 0.05) * 1.05

FV = $300 * ( ( 2.704813829421526 - 1) / 0.05) * 1.05

FV = $300 * ( 1.704813829421526 / 0.05) * 1.05

FV = $300 * 34.09627658843153 * 1.05

FV = $52,113.63

Therefore, the future value of the annuity due is $52,113.63.

Step-by-step explanation:

Answer:

              The area of the quadrilateral is C: 12 square feet.

Step-by-step explanation:

               In the photo, the quadrilateral is divided into two triangles, both having a base length of 4 feet and a height of 3 feet. Therefore, we can find the area of the entire quadrilateral by adding the areas of the two triangles together. Since the triangles have a base length of 4 feet and a height of 3 feet, their individual areas will be [tex]4*3*\frac{1}{2} =12*\frac{1}{2} = 6[/tex] square feet. As there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the quadrilateral, which would be [tex]6 * 2=12[/tex] square feet. Hence, we can conclude that the correct answer will be C.

Have a great day! Feel free to let me know if you have any more questions :)

The scale factor of dilation is 4/9

From the question, we have the following parameters that can be used in our computation:

The triangles

Given that the right is the scaled copy of the left

We have the following representation

Scaled factor = Right/Left

Substitute the known values in the above equation, so, we have the following representation

Scaled factor = 4/9

Hence, the scale factor is 4/9

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The number of monthly payments required to pay off the loan of $128,000 at 4% interest is 232.48 which is equivalent to approximately 232 payments.

To determine the number of monthly payments required to pay off a loan, you can use the formula for loan amortization: n = (-log(1 - B/A * r)) / log(1 + r)

Where: n = number of monthly payments, A = loan amount ($128,000), B = monthly payment ($611.09), r = monthly interest rate (4% / 12 months = 0.0033)

The number of monthly payments for the loan is plugged and computed as:

n = (-log(1 - $128,000/$611.09 * 0.0033)) / log(1 + 0.0033)

n = (-log(1 - 0.0208)) / log(1.0033)

n = (-log(0.9792)) / log(1.0033)

n = 21.8068 / 0.093984

n = 232.48 payment.

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On solving the provided question, we can say that by unitary method, Total capital of the firm  = Rs. 85,000

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Heena and Sudha share profits and losses equally.

If the capital of Teena is 1/5 of the total capital which is equal to Rs. [tex]90,000[/tex] 1/5 of Total capital = Rs. [tex]90,000[/tex]

Total capital = Rs. 90,000 × 5 =  4,50,000,  capital of all partners = Rs. [tex]1,20,000 + Rs. 80,000 + Rs. 90,000 + 60,000 + Rs. 15,000[/tex]

Total capital of all partners = Rs. [tex]3,65,000[/tex]

Total capital of the firm  = Rs. [tex]85,000[/tex]

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Answer:Steve

Step-by-step explanation:

Answer: The equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is:       y = 3x - 4.

Step-by-step explanation:

To find the equation of a line passing through two points, we can use the point-slope form of a line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.

Step 1: Find the slope of the line (m)

The slope of the line can be found using the two points:

m = (y2 - y1) / (x2 - x1)

Plug in the values of x1, x2, y1, and y2 from the two given points:

m = (2 - (-1)) / (0 - 1) = 3

Step 2: Write the equation using the point-slope form

Use the point-slope form and the slope from step 1, and one of the given points:

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

Step 3: Simplify the equation

y + 1 = 3x - 3

Step 4: Solve for y

y = 3x - 4

So, the equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is y = 3x - 4.

The direction of the sum of the two vectors is along the west direction

Assuming vector A is pointing west ward and vector B is pointing eastward

The direction of vector A to the horizontal is negative solved by

= -6 cos 30

= -5.196

Adding both vectors

= vector A + vector B

= -5.196 + 5

= -0.196

Hence the direction is to the west since it is negative

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Answer:

the correct answer is letter A

sum of two complementary angle is 180•

[tex]180 - 49 = y = 131[/tex]

If the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

If the quotient of two functions f(x) and g(x) is a constant k, meaning f(x)/g(x) = k for all x, then it follows that:

f(x) = k.g(x)

Taking the derivative of both sides with respect to x, we get:

f'(x) = k.g'(x) + g(x).d(k)/dx

Since the constant k is a constant and not a function of x, its derivative with respect to x is zero, so we can simplify the equation to:

f'(x) = k.g'(x)

Thus, we can see that if the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other, with the constant of proportionality equal to k.

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The ratio of the amounts of money that they each get:

1 : 3 : 3/2

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Let's represent the amount of money that Jan gets as x.

Then, the amount of money that Freda gets is 3x,

and the amount of money that Pieter gets is:

= (1/2) x 3x

= 3/2 x (x)

The ratio of the amounts of money that they each get can be written as:

⇒ x : 3x : 3/2 x (x)

⇒ 1 : 3 : 3/2

So, Jan gets 1 unit of money, Freda gets 3 units of money, and Pieter gets 3/2 units of money.

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To solve proportions in math, you can use the following steps:

"Daffynition decoder" is a word puzzle game in which a code is employed to represent words, phrases, or sentences. To solve the puzzle, use the provided code to decode the words or phrases.

"Daffynition decoder" is a word puzzle game where a code is used to represent words, phrases or sentences. To solve the puzzle, you need to use the provided code to decode the words or phrases.

To solve proportions in math, you can use the following steps:

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The variance of the given frequency distribution is 60.92, and the standard deviation is option (b) 7.80.

To calculate the variance of a frequency distribution, we need to first find the mean or average of the data. The formula for calculating the mean is as follows:

mean (μ) = Σfx / Σf

where Σfx represents the sum of the products of each value and its corresponding frequency, and Σf is the sum of all the frequencies.

Using the given data, we can calculate the mean as follows:

μ = (43 + 85 + 119 + 175 + 204 + 243 + 32*1) / (3+5+9+5+4+3+1)

μ = 13.5

Next, we need to calculate the deviation of each data point from the mean. To do this, we subtract the mean from each value and square the result. The formula for this is:

(x - μ)²

Using this formula, we get the following deviations for each data point:

(4 - 13.5)² = 81.00

(8 - 13.5)² = 30.25

(11 - 13.5)² = 6.25

(17 - 13.5)² = 12.25

(20 - 13.5)² = 42.25

(24 - 13.5)² = 110.25

(32 - 13.5)² = 333.22

Next, we need to multiply each deviation by its corresponding frequency, and then sum up the results. The formula for this is:

Σf(x - μ)²

Using the above deviations and frequencies, we can calculate the sum of squares as follows:

Σf(x - μ)² = 381.00 + 530.25 + 96.25 + 512.25 + 442.25 + 3110.25 + 1 x 333.22

Σf(x - μ)² = 1827.48

Finally, we can calculate the variance by dividing the sum of squares by the total number of observations (Σf). The formula for variance is:

σ² = Σf(x - μ)² / Σf

Using the above values, we can calculate the variance as follows:

σ² = 1827.48 / 30

σ² = 60.92

The standard deviation is the square root of the variance. Therefore:

σ = √(60.92)

σ = 7.80

Therefore, the correction option is (b).

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Complete Question:

Find the variance and standard deviation of the following frequency distribution:

x  4    8 11 17 20 24 32

f   3    5  9 5 4 3 1

Answer: The sum of the two polynomials 3m^2 + 4m + 7 and 4m^2 - 3m + 2 is 7m^2 + m + 9.

Step-by-step explanation:

The completed two-column table that is used to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution. The correct option is option B

B. Substitution

Congruent angles are angles that have the same measurement,

The two-column table is presented as follows;

[tex]{}[/tex]  Statements                                                           Reasons

1. ABCD is a parallelogram with diagonal [tex]\overline{AC}[/tex]  [tex]{}[/tex]     Given

2. [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and [tex]\overline{AD}[/tex]║[tex]\overline{BC}[/tex]  [tex]{}[/tex]                                Definition of a parallelogram

3. ∠2≅∠3, ∠1≅∠4   [tex]{}[/tex]                                           Alt. int. ∠s are ≅

4. m∠2 = m∠3 and m∠1 = m∠4 [tex]{}[/tex]                        Measures of ≅ ∠s are =

5. m∠1 + m∠2 = m∠4 + m∠2 [tex]{}[/tex]                             Addition prop. of equality

6. m∠1 + m∠2 = m∠4 + m∠3[tex]{}[/tex]                              Substitution

7. m∠1 + m∠2 = m∠BAD [tex]{}[/tex]                                    Angle addition property

m∠3 + m∠4 = m∠DCB

8. m∠BAD = m∠DCB [tex]{}[/tex]                                         Substitution

9. ∠BAD ≅ ∠DCB [tex]{}[/tex]                                             Angles are congruent if [tex]{}[/tex]    

[tex]{}[/tex]                                                                          their measures are the same

The missing reason in the partial proof is therefore;  B. Substitution

The abbreviations in the table are expanded as follows;

Alt. int. ∠s are ≅; Alternate interior angles are congruent

Measures of ≅ ∠s are =; Measures of congruent angles are equivalent

Addition prop. of equality; Addition property of equality

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Answer:

Step-by-step explanation:

its 11

ignore bllllllllllldjbjddddddddddddddddddddddddd

The measure of angle R from the triangle PQR is 15.31°.

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

The formula for the cosine rule is c=√(a²+b²-2ab cosC)

In the given triangle PQR, PQ=9 units, PR=12 units and RQ=20 units

PQ²=PR²+RQ² -2×12×20cosR

9²=12²+20² -2×12×20cosR

81=144+400-480cosR

81=544-480cosR

81-544= -480cosR

-463= -480cosR

cosR= 463/480

cosR= 0.9645

∠R=15.31°

Therefore, the measure of angle R is 15.31°.

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