Find x to the nearest hundredth.
16
X
40°
OA. x = 24.89
OB. x = 13.43
O C. x 10.28
OD. x = 12.26

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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No, the given two fractions/ratios do not form a proportion.

Two ratios are said to be forming proportions if and only if the reduced forms of fractions of the two ratios are the same or are equal to each other.  For example - [tex]\frac{3}{6}[/tex] and [tex]\frac{1}{2}[/tex] are in proportion because [tex]\frac{3}{6}[/tex] when reduced to the simplest form gives [tex]\frac{1}{2}[/tex] which is the same as the other given ratio.

In the given question, one ratio given is [tex]\frac{1}{3}[/tex] and the other one is [tex]\frac{28}{36}[/tex]. Reducing the second ratio to the simplest form we get [tex]\frac{7}{9}[/tex]. Clearly, the two fractions are not equal. Hence, the given two ratios are not in proportion.

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The graph of the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

Is in the image at the end.

Here we have the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.

Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.

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The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

We have,

To write the equation 6y + y = 5 in slope-intercept form (y = mx + b), we need to simplify the equation and isolate the y variable on one side.

Starting with the equation 6y + y = 5:

Combining the like terms on the left side gives us:

7y = 5

To isolate the y variable, we divide both sides of the equation by 7:

y = 5/7

Now the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, since the equation only contains the variable y and no x, the slope (m) is not present, and the y-intercept (b) is 5/7.

Therefore,

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

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Answer:

f(x) has the most x intercepts

Answer:

Step-by-step explanation:

No, this shape does not belong in a group of shapes that have more than one pair of perpendicular sides.

In order to determine if the shape belongs to a group of shapes with more than one pair of perpendicular sides, we need to examine the number of right angles in the shape.

A right angle is a 90-degree angle, and shapes with perpendicular sides have right angles at their intersections. By counting the number of right angles in the shape, we can determine if it has more than one pair of perpendicular sides.

If the shape has only one right angle, then it does not have more than one pair of perpendicular sides. But if it has two or more right angles, then it would belong to the group of shapes that have more than one pair of perpendicular sides.

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The number of bags of rice that would be needed to make 80 recipes is 48.664 bags.

1 recipe = 3.5 Cups of rice

If

1 cup of rice = 158 grams

1 bag of rice = 2 pounds

2.2 lbs. = 1 kg,

1kg = 1000 g

80 recipes = 3.5 cups 80

= 280 cups

1 cup of rice = 158 grams

280 cups = 158 × 280

= 44,240 grams

1kg = 1000 g

44,240 grams = 44.24 kg

2.2 lbs. = 1 kg; x lbs = 44.24

2.2/1 = x/44.24

x = 2.2 × 44.24

x = 97.328 pounds

1 bag of rice = 2 pounds ; x bags = 97.328 pounds

1/2 = x/97.328

97.328 = 2x

x = 48.664 bags

Hence, 48.664 bags of rice is needed for 80 recipes.

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Answer:

x = 6
JN = 10

Step-by-step explanation:

if the values of SN and SP are the same, so are the corresponding sides next to the right angles.
which means:
if SP = SN, then JK = LM.
Use the reverse version of the function for calculating LM (3x + 2).
-2 * 1/3
Now apply that function to 20.
(20-2)/3
= 18/3
= 6.
x = 6
Now JK is a chord.
and Radius SQ intersects JK at a perpendicular right angle (at point N).
So JN would be half the length of JK.
20/2 = 10.
JN = 10

The domain for n in the given Geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio (r).

In the given geometric sequence, the first term (a1) is -9 and the common ratio (r) is 5. Therefore, the sequence can be written as:

-9, -9 * 5, -9 * 5^2, -9 * 5^3, ...

To determine the domain for n, we need to determine the values of n for which the sequence is defined. In a geometric sequence, the term number n represents the position of a term in the sequence.

In this case, the first term corresponds to n = 1, the second term corresponds to n = 2, and so on. The domain for n consists of all the positive integers starting from 1, as the sequence extends indefinitely.

Therefore, the domain for n in the given geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.

the domain does not include zero or negative values, as these positions in the sequence do not exist. The sequence only starts from the first term (n = 1) and continues indefinitely in the positive integer domain.

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The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321.  the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.

To determine the largest absolute value:

We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.

To determine the smallest absolute value:

We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.

To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.

Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

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Answer:

  38.9 in²

Step-by-step explanation:

You want the area of the composite figure that is an 8-inch square with a semicircle removed.

The missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...

  A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²

The area of the square without the semicircle removed is ...

  A = s² = (8 in)² = 64 in²

After removing the semicircle from the square, the remaining area is ...

  A = square area - semicircle area

  A = 64 in² -25.1 in² = 38.9 in²

The area of the figure is about 38.9 square inches.

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Answer:

The area of the rectangle is 168 ft².

Step-by-step explanation:

Formula: A = lw

where l and w are the length and width of the rectangle respectively.

We're given with the length and the width as

a = 12 ft

b = 14 ft

Let's solve for the area using the formula above.

A = lw

A =  12ft(14ft)

A = 168 ft²

Area of the given heptagon = 364 square unit.

The given figure is regular heptagon,

length of each side = 10

Distance between Centre and edge = 10.4

Since we know that,

A seven-sided polygon with seven angles, seven vertices, and seven edges is known as a heptagon. They may have the same or different length dimensions. It is a closed figure, and a regular heptagon is one with all equal seven sides.

Now,

Perimeter of the given heptagon = 7x10

                                                       = 70

Area of heptagon = perimeter x 10.4/2

                              = 70 x 5.2

                              = 364

Hence,

Area = 364 square unit.

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The interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65), and the observed proportion of 0.55 falls within this interval, indicating that it is within the margin of error of the simulation results.

To create an interval containing the middle 95% of the data based on the simulation results, we can calculate the lower and upper bounds of the interval.

Let's analyze the simulation results and find the appropriate values.

Out of 200 simulations, we observe that the proportion of students who preferred Candidate A ranges from a minimum of 0.35 (35%) to a maximum of 0.65 (65%).

Since the simulations assume a 50-50 split, we can consider these values as the lower and upper bounds for the middle 95% of the data.

To find the range of the middle 95% of the data, we calculate the difference between the upper and lower bounds.

Upper bound: 0.65

Lower bound: 0.35

Range: 0.65 - 0.35 = 0.30  

To find the interval containing the middle 95% of the data, we divide the range by 2 and add/subtract it from the midpoint.

The midpoint is the average of the upper and lower bounds.

Midpoint: (0.65 + 0.35) / 2 = 0.50

Range / 2: 0.30 / 2 = 0.15

Lower bound of the interval: 0.50 - 0.15 = 0.35

Upper bound of the interval: 0.50 + 0.15 = 0.65

Therefore, the interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65).

Now let's compare the observed proportion from the poll to this interval. The poll indicates that out of a random sample of 80 students, 44 students said they would vote for Candidate A.

To calculate the observed proportion, we divide the number of students who preferred Candidate A (44) by the sample size (80).

Observed proportion: 44/80 = 0.55

The observed proportion of 0.55 is within the margin of error of the simulation results.

It falls within the interval (0.35, 0.65), indicating that the observed proportion is consistent with the simulation and aligns with the assumption of a 50-50 split in the population.

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The missing sides of the triangle are

x = 6.32

y = 7.48

z = 11.83

The missing side x is calculated using similar triangles rules as below

x / 10 = 4 / x

cross multiply gives

x² = 40

x = √40 = 6.32

Other sides will solved by Pythagoras theorem.

the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let y be the required distance

y² = 6.32² + 4²

y² = 55.94

y = √55.94

y = 7.48

z² = 6.32² + 10²

z² = 139.94

z = √139.94

z = 11.83

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Using the proportion principle , Orange Juice has a greater percentage of water than Apple juice

To determine which juice has a greater percent of water, we need to calculate the percentage of water in each juice.

Percentage of water = (Water content / Total content) * 100

Water content = 32 ounces

Total content = 80 ounces

Percentage of water in apple juice = (32 / 80) * 100 = 40%

Water content = 48 ounces

Total content = 64 ounces

Percentage of water in orange juice = (48 / 64) * 100 = 75%

Comparing the percentages, we can conclude that orange juice has a greater percentage of water (75%) than the apple juice (40%).

Therefore, the orange juice contains a higher percentage of water.

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Complete question :

an 80 ounce bottle of apple juice contains 32 ounces of water a 64 ounce bottle of orange juice has 48 ounces of water which juice has a greater percent of water

Answer:

(a) - [tex]y=-2x+18[/tex]

(b) - [tex]y=\frac{1}{2} x-\frac{9}{2}[/tex]

Step-by-step explanation:

Given the equation of a line, which we'll call line 1, find the following.

(a) - The equation of a line, which we'll call line 2, that is parallel to line 1 and travels through the point (9,0)

(b) - The equation of a line, which we'll call line 3, that is perpendicular to line 1 and travels through the point (9,0)

Given:

[tex]3y+6x=-6[/tex]

(1) - Write the equation of line 1 in slope-intercept form

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Slope-Intercept Form:}}\\y=mx+b\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ b \ \text{is the y-intercept of the line}\end{array}\right}[/tex]

[tex]3y+6x=-6\\\\\Longrightarrow 3y=-6-6x\\\\\Longrightarrow y=-\frac{6}{3} -\frac{6}{3}x \\\\\therefore \boxed{y=-2x-2}[/tex]

Thus, we can conclude the slope of line 1 is -2.

(2) - Answering part (a)

To find a line that is parallel to line 1, the slopes must be the same, -2. Use the point-slope form for a line to find the equation for line 2.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Point-Slope Form:}}\\y-y_1=m(x-x_1)\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ (x_1,y_1) \ \text{is a point the line passes through}\end{array}\right}[/tex]

[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=-2 \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=-2(x-9)\\\\\therefore \boxed{\boxed{ y=-2x+18}}[/tex]

Thus, the equation for line 2 is found.

(2) - Answering part (b)

To find a line that is perpendicular to line 1, the slope of line 3 must be the opposite-reciprocal of line 1's. Once again, use the point-slope form of a line to find the equation of line 3.

[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=\frac{1}{2} \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=\frac{1}{2}(x-9)\\\\\therefore \boxed{\boxed{ y=\frac{1}{2} x-\frac{9}{2} }}[/tex]

Thus, the equation of line 3 is found.

Formulas with free variables are said to be expressions in formal logic that is known to have variables that are not bound by quantifiers.

Variables are placeholders with changeable values in logic. A free variable in a formula has no quantifier and can take any value.

Formula meaning varies with variable values. Formulas containing variables that are not assigned specific values are frequently employed to convey  open statements or propositions that require further specification.

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In practice, we shall use in formulas other symbols, namely defined pred- icates, operations, and constants, and even use formulas informally; but it will be tacitly understood that each such formula can be written in a form that only involves and as nonlogical symbols.

Concerning formulas with free variables, we adopt the notational conven- tion that all free variables of a formula

(u1,..., Un)

are among u1, ..., un (possibly some u are not free, or even do not occur, in ). A formula without free variables is called a sentence.What is the meaning of "formulas with free variables"?

Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are the Payroll Summary Report and the Retirement Contribution Report.

Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are:

Payroll Summary Report: This report provides a summary of the payroll transactions for the period, including details of employee wages, deductions, and employer contributions.

It should include a specific section or breakdown for retirement contributions, showing the individual employee contributions and the corresponding employer contributions.

By reviewing this report, one can ensure that the retirement contributions have been accurately calculated and remitted.

Retirement Contribution Report: This report specifically focuses on the retirement contributions made by both employees and the employer.

It should provide a detailed breakdown of the contributions for each employee, including the employee's contribution amount, the employer's matching or non-elective contribution amount, and any additional details related to the retirement plan.

This report allows for a comprehensive review of the retirement contributions to verify if they match the expected amounts based on employee records and plan guidelines.

By comparing the information in these reports with the employees' individual contribution records and the retirement plan requirements, it is possible to verify that the retirement contributions were accurately remitted for the most recent payroll period.

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Step-by-step explanation:

3/8 = 0.375

1/9 = 0.1111111111

Answer:

Step-by-step explanation:

Answer:

402.12 or just 402

Answer: To calculate the distance the beetle walks diagonally across the table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the two sides of the right triangle formed by the table are 160 cm and 90 cm. Let's call the hypotenuse (the distance the beetle walks) "d."

So, applying the Pythagorean theorem, we have:

d^2 = 160^2 + 90^2

Simplifying:

d^2 = 25600 + 8100

d^2 = 33700

Taking the square root of both sides:

d ≈ √33700

d ≈ 183.54 cm

Therefore, the beetle walks approximately 183.54 cm diagonally across the kitchen table.

Answer:

C. 50 cm²

Step-by-step explanation:

The volume of a triangular pyramid is calculated using the following formula:

Volume = (1/3) * Area of the base * Height

For Question:

length: 5cm

Breadth:5cm

Height : 6 cm

Now,

Volume = ⅓* Area of the base * Height

Volume = ⅓*length*breadth*height

Volume= ⅓*5*5*6=50 cm³

To solve the compound inequality 2y + 3 ≥ -9 or -3y < -15, we'll solve each inequality separately and then combine the solutions.

First, let's solve the first inequality: 2y + 3 ≥ -9.

Subtract 3 from both sides:

2y ≥ -12

Divide both sides by 2 (note that dividing by a positive number does not change the inequality direction):

y ≥ -6

Next, let's solve the second inequality: -3y < -15.

Divide both sides by -3 (remember to reverse the inequality direction when dividing by a negative number):

y > 5

Now, let's combine the solutions. We have y ≥ -6 or y > 5.

In interval notation, we can express the solution as (-∞, -6] ∪ (5, ∞). This means that the solution includes all real numbers less than or equal to -6, as well as all real numbers greater than 5.

Answer:9.5

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

i jus did this question