How many degrees must Figure A be rotated counterclockwise around the origin in order to line up with Figure B?
A. 90
B. 180
C. 270
D. 360​

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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Answer:9.5

Step-by-step explanation:

Step-by-step explanation:

3/8 = 0.375

1/9 = 0.1111111111

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

To solve this problem, we need to find the circumference of the circular playground and then multiply it by the number of rounds the runner completes.

The circumference of a circle can be calculated using the formula:

Circumference = 2 * π * radius

Given that the radius of the playground is 77m, we can substitute this value into the formula to find the circumference:

Circumference = 2 * π * 77

Now, we need to calculate the distance covered by the runner in 5 complete rounds. Since one round is equal to the circumference, the distance covered in 5 rounds would be:

Distance = 5 * Circumference

Substituting the value of the circumference, we have:

Distance = 5 * (2 * π * 77)

To simplify, we can use an approximation of π as 3.14:

Distance ≈ 5 * (2 * 3.14 * 77)

Calculating further:

Distance ≈ 5 * (6.28 * 77)

Distance ≈ 5 * 483.56

Distance ≈ 2417.8

Therefore, the distance covered by the runner in 5 complete rounds around the circular playground is approximately 2417.8 meters, which can be rounded to 2420 meters (as given in the answer).

Hope this helps!

Answer:

2420

Step-by-step explanation:

Circumference = 2πr

One complete round will be equal to the circumference = 2πr

Five rounds will be five times the circumference

= 5*2πr

= 10πr

[tex]= 10 *\frac{22}{7}*77 \\\\= 10* 22* 11\\\\= 2420[/tex]

The greater number of packages that can fit in the truck is 24000.

The volume of the part of the truck that is being filled is 375 cubic feet.

We have,

To determine the greater number of packages that can fit in the truck, we need to calculate the volume of both the packages and the part of the truck that is being filled.

The volume of a cube-shaped package:

The side length of the cube-shaped package is 1/4 feet.

The volume of a cube is given by V = s³, where s is the side length.

Therefore, the volume of each package is (1/4)³ = 1/64 cubic feet.

The volume of the part of the truck being filled:

The dimensions of the rectangular prism-shaped part of the truck are:

Length = 8 feet

Width = 6(1/4) feet = 6.25 feet

Height = 7(1/2) feet = 7.5 feet

The volume of a rectangular prism is given by V = length × width × height.

Therefore, the volume of the part of the truck being filled is:

8 × 6.25 × 7.5

= 375 cubic feet.

To calculate the greater number of packages that can fit in the truck, we divide the volume of the part of the truck by the volume of each package:

= 375 cubic feet / (1/64 cubic feet)

= 375 × 64

= 24000 packages.

Therefore,

The greater number of packages that can fit in the truck is 24000.

The volume of the part of the truck that is being filled is 375 cubic feet.

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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

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"?

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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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 area of smaller triangle is 59 square feet.

The area of the larger triangle is 105 square feet.

And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.

Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.

Since, the corresponding edges of similar triangles are proportional.

Therefore, y/x=16/12

y=4/3x

Also, the area of larger triangle is 105 square feet.

1/2×4/3x×16=105

The above equation can be written as

1/2×4/3x×4/3×12=105

1/2×x×12=59

Area of smaller triangle  = 59 square feet

Hence, the area of smaller triangle is 59 square feet.

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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.

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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Answer:

Therefore, the expression becomes:

7/1 - 2/6

Now, we need to find a common denominator for the fractions, which is 6:

7/1 - 2/6 = (76)/(16) - 2/6

= 42/6 - 2/6

= (42 - 2)/6

= 40/6

Finally, we can simplify the fraction:

40/6 = 20/3

So, the difference between 5 2/6 and -2 4/6 is 20/3.

Step-by-step explanation:

First, let's subtract the whole numbers: 5 - (-2) = 5 + 2 = 7.

Next, let's subtract the fractions: 2/6 - 4/6 = (2 - 4)/6 = -2/6.

Combining the whole number and fraction results, we have:

7 - 2/6

Now, to simplify this result further, we can express 7 as a fraction with a common denominator of 6:

7 = 7/1

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

Answer:

f(x) has the most x intercepts

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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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

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.

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:

402.12 or just 402

Answer:

-----------------------

In the given right triangle we have an angle of 37° and adjacent leg of 11 units given.

Missing is the length of hypotenuse, x.

Use cosine function:

Plug in known values and solve for x:

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

Answer:

-4

Step-by-step explanation:

i jus did this question

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:

  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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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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