Which of the following functions is most likely to have the smallest value for y if x is large? (Assume k is positive.) a. a direct variation function with a small value for k c. an inverse variation function with a small value for k b. a direct variation function with a large value for k d. an inverse variation function with a large value for k

It will take 5 minutes to paint this cone

Since the area of the base of the cone is doubled, the new base area becomes 2 * 49π in² = 98π in².

The radius of the original cone can be found by using the formula for the area of a circle:

49π = πr^2

r = 7 in

The height of the new cone can be calculated using the same lateral height as the original cone:

h = 8 in

Using the formula for the volume of a cone, we can calculate the volume of the new cone:

V = (1/3)πr^2h = (1/3)π(7^2)(8) = (1/3)π(392)

The surface area of the original cone can be found using the formula for the surface area of a cone:

A = πr^2 + πrs

where s is the slant height of the cone.

s = √(r^2 + h^2) = √(7^2 + 8^2) = √(49 + 64) = √(113)

So, we have

A = πr^2 + πrs = π(7^2) + π(7)(√(113)) = 49π + 7π(√(113))

The surface area of the new cone can be found using the same formula:

A = πr^2 + πrs = π(7^2 * 2^2) + π(7 * 2)(√(113)) = 98π + 14π(√(113))

When the equations are compared, we have

2 * 49π + 7π(√(113)) = 98π + 14π(√(113))

Since the new cone has twice the surface area of the original cone and can be painted at the same rate,

It will take 2.5 * 2 = 5 minutes to paint this cone.

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Answer:

Step-by-step explanation:

I took the test the answer is 4.2

Answer:

13728

Step-by-step explanation:

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.

The answer is 13728.

Answer:12

Step-by-step explanation:

9/12= 3/4   (/3).   3/4=12/16    (x4)

The values of the ratios of the perimeters and areas of the red figure to the blue figure, which are similar figures, in the simplest form are:

The ratio of their perimeters:  28/16

The ratio of their areas:  (28)²/(16)²

What is the ratio?

A ratio is a relationship between two things when it is expressed in numbers or amounts.

The ratio of the perimeter of similar figures = a side length of one figure / corresponding side length of the other figure

The ratio of the areas of two similar figures = square of the length of one figure/square of the corresponding length of the other

Thus:

The side length of Red-figure = 28

The side length of the Blue figure = 16

Therefore:

The ratio of their perimeter = Side length of the red figure / Side length of the blue figure

The ratio of the perimeter of the red figure to the blue figure = 28/16

The ratio of their areas = Side length of the red figure / Side length of the blue figure

The ratio of the areas of the red figure to the blue figure = (28)²/(16)²

Hence, The values of the ratios of the perimeters and areas of the red figure to the blue figure, which are similar figures, in the simplest form are:

The ratio of their perimeters:  28/16

The ratio of their areas:  (28)²/(16)²

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Answer:

1.

x = 5√3

y = 10

2.

x = 2√33 in.

3.

y = 11√3

x = 22

4.

x = 7√2

5.

x = 3 m

6.

x = 16

y = 16√3

Step-by-step explanation:

Recall:

30-60-90 triangle ratio of sides:    1 : √3 : 2

45-45-90 triangle ratio of sides:    1 : 1 : √2

Pythagorean theorem: a² + b² = c²

1.

1 : √3 : 2

5 : x : y

1/5 = √3/x

x = 5√3

1/5 = 2/y

y = 10

2.

a² + b² = c²

8² + x² = 14²

64 + x² = 196

x² = 132

x = 2√33 in.

3.

1 : √3 : 2

11 :  y  : x

1/11 = √3/y

y = 11√3

1/11 = 2/x

x = 22

4.

1 : 1 : √2

7 : 7 : x

1/7 = √2/x

x = 7√2

5.

a² + b² = c²

x² + 4² = 5²

x² + 16 = 25

x² = 9

x = 3 m

6.

1 : √3 : 2

x :   y :  32

1/x = 2/32

2x = 32

x = 16

√3/y = 2/32

√3/y = 1/16

y = 16√3

Answer:

  3.5%

Step-by-step explanation:

You want the percent error in a measured value of 4.16 g/cm³ in relation to a handbook value of 4.018 g/cm³.

The percentage error is calculated as ...

  % error = ((measured) - (actual))/actual × 100%

  = (4.16 -4.018)/4.018 × 100%

  = 0.142/4.018 × 100% ≈ 3.5%

The given numbers, 4.16 and 4.018 have 3 and 4 significant figures, respectively. Their difference will have 2 significant decimal places, as does 4.16, so should be considered to be 0.14. This value has 2 significant figures, so the final answer will have 2 significant figures.

You will note that we kept all of the digits available throughout the computation, rounding to 2 significant figures only at the end.

You will also note that taking differences of numbers of approximately the same value can result in a loss of significant figures.

The end behavior of the polynomial is:

x → ∞, F(X) → ∞

x → -∞, F(X) →-∞

Then the correct option is C.

Here we have the polynomial:

F(x) = x³ + 2x² - 1

And we want to see which ones of the given statements are true. At the end of the answer you can see the graph of the function so you can know how it behaves.

There we can see that there is one relative maximum and one relative minimum, and that the end behavior is:

x → ∞, F(X) → ∞

x → -∞, F(X) →-∞

Then the only correct option is C.

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The  value of the inequality is 1

In equality is a mathematical statement showing that two or more variables or quantities are not equal.

The given inequality is  6<2y+4

Making y the subject of the relation

6-4<2y

⇒2=2y

Making y the subject of the relation by dividing both sides by 2

therefore, y<1

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the Diagram that would support his plan to use ASA is either option A and Option B.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

The Corresponding portions of Congruent triangles are the complete form of CPCT. Triangles may be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles. The following are many congruency rules.

Since All triangles given in the options are congruent we need to find which pair of triangles are supposed to be congruent by the property of ASA.

From ASA:

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and the side included between the angles of the second triangle.

Therefore, Either Option A or Option B is the Diagram that would be supportive of his intention to utilize ASA.

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Savings account B offers a higher APY of 5.25%, compared to the 5.13% offered by savings account A.

Interest is a fee charged by a lender to a borrower for the use of money. It represents the cost of borrowing money and is typically expressed as a percentage of the loan amount. Interest is paid over a period of time and is calculated based on the principal amount of the loan, the interest rate, and the length of the loan term.

Simple interest is calculated only on the principal amount of the loan, while compound interest is calculated on both the principal and the accumulated interest over time. Compound interest results in a faster growth of the loan balance compared to simple interest.

APY (Annual Percentage Yield) is the effective annual interest rate, taking into account the frequency of compounding. It can be calculated as follows:

APY = (1 + (APR / n))ⁿ⁻¹

where APR is the annual percentage rate and n is the number of times the interest is compounded in a year.

For savings account A, with a 5% APR and compounding quarterly, n = 4. So,

APY = (1 + (0.05 / 4))⁴⁻¹ = 0.0513 = 5.13%

For savings account B, with a 5% APR and compounding semiannually, n = 2. So,

APY = (1 + (0.05 / 2))²⁻¹ = 0.0525 = 5.25%

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The inequality and graph of the solutions will be x + 0.80y ≤ 20 and any value on the line or below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Dion is buying a balloon bouquet. His favorite colors are silver and purple. Silver balloons cost $1.00 and purple balloons cost $0.80.

Let 'x' be the number of silver balloons and 'y' be the number of purple balloons. And if he doesn't spend more than $20. Then the inequality is given as,

$1 x + $0.80 y ≤ $20

x + 0.80y ≤ 20

Take any value on the line or below.

The inequality and graph of the solutions will be x + 0.80y ≤ 20 and any value on the line or below.

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Answer:

√121 = 11

diffrence of 164 and 11 = 164 - 11 = 153

number = 153

1600 units were produced , If you spend $3000 on production cost.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The cost of producing X units of a product is 1.25. Per unit plus $1000 in flat production cost.

If you spend $3000 on production cost.

let, x units were produced.

so, we get,

1.25x+1000 = 3000

1.25x= 2000

x= 1600

Hence, 1600 units were produced , If you spend $3000 on production cost.

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Yes, the triangle can have the angle measures  31[tex]\frac{3}{4}[/tex]°, 53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°.

And the first angle is 31[tex]\frac{3}{4}[/tex]°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

The angle measures of the triangle,

= x,  53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°

The angle measure of x = 180 -  53[tex]\frac{1}{2}[/tex]° - 94[tex]\frac{3}{4}[/tex]°

x = 31[tex]\frac{3}{4}[/tex]°

And, yes, the triangle can have the angle measures  31[tex]\frac{3}{4}[/tex]°, 53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°.

Therefore, the first angle is 31[tex]\frac{3}{4}[/tex]°.

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Answer:

3x+24

Step-by-step explanation:

3*x +3*8

=3x+24

Answer:

3x+24

Step-by-step explanation:

3(x+8)

3×x + 3×8

3x+24

Answer:

[tex]22212[/tex].

Step-by-step explanation:

In base-10, for a number to be divisible by [tex]4[/tex], the last two digits must also be divisible. Among all the two-digit numbers formed with "[tex]\texttt{1}[/tex]" and "[tex]\texttt{2}[/tex]", only [tex]12[/tex] satisfies the requirements as the last two digits of [tex]N[/tex].

For a number to be divisible by [tex]9[/tex], the sum of all the digits must also be divisible. For [tex]N\!\![/tex] to be as small as possible, its digits should add up to the smallest multiple, [tex]1 \times 9 = 9[/tex], instead of larger ones such as [tex]18[/tex].

Since the last two digits of [tex]N[/tex] is [tex]\texttt{1}[/tex] and [tex]\texttt{2}[/tex], the other digits of [tex]N\![/tex] would need to add up to [tex]9 - 1 - 2 = 6[/tex]. To minimize the value of [tex]N\!\![/tex], these digits should consist solely of [tex]\texttt{2}[/tex]: [tex]2 + 2 + 2 = 6[/tex]. Therefore, the answer should be [tex]22212[/tex].

The total number of outcomes is 24

If a fair 6-sided die is tossed 4 times in a row, there are 6 possible outcomes for each toss.

So, the number of possible outcomes would be:

6 + 6 + 6 + 6 or  6 * 4

Evaluate

Outcomes = 24

Each of the 4 tosses is independent, so there are 6 options for the result of each toss, and the total number of possible outcomes is obtained by adding the number of options for each toss as calculated above

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Answer:

$5.86

Step-by-step explanation:

The total was $36.31

We were given the price of 1, which was $1.15

$36.31-$1.15 = $35.16 remaining

Since the other 6 friends ordered the same meal, they would have paid the same price, so we would divide by 6

$35.16/6 = $5.86

The volume of a rectangular prism is, 108 unit³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A rectangular prism has a width of 2, a height of 9, and a depth of 6.

Now, We know that;

Volume of rectangular prism = Length × Width × Height

Substitute all the values, we get;

⇒ Volume of rectangular prism = Length × Width × Height

⇒ Volume of rectangular prism = 2 × 9 × 6

⇒ Volume of rectangular prism = 108 unit³

Thus, The volume of a rectangular prism = 108 unit³

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The dimensions of the original piece of rectangular cardboard are 22 in by 40 in

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Given that, Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard, from which she cuts out 9-in squares from each corner. The length of the original piece of cardboard is 18 in more than the width, the volume of the box is 792 in³,

We know that volume of rectangular box = length × width × height

length = x+18-9-9 = x

height = 9

width = x-9-9 = x+18

= (x-18) × x × 9

(x-18)×9x = 792

9x²-162x-792 = 0

x²-18x-88 = 0

Factorizing to find the value of x,

x = 22 and x = -4

Therefore, width of the cardboard = 22 in

Length = 22+18 = 40 in

Hence, the dimensions of the original piece of rectangular cardboard are 22 in by 40 in

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The  inequalities represent the possible lengths for the third side, x is 4 < x < 14, the correct option is D.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. The set of values of the variable involved in the inequality for which the considered inequality holds true is called the solution set for that inequality.

Given;

One side of triangle =5

The other side of triangle=9

Now, the third side is between the difference and the sum of the other two sides;

9-5 < x < 9+5

4 < x < 14

Therefore, the inequality will be 4 < x < 14.

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Answer:

But the 2lbs.

Step-by-step explanation:

Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.

You're welcome.

The slope-point form of a line can be used to determine the equation for a line that is perpendicular to the line g(x) = 4x + 3 and passes through the point (7,3).

The slope of a line perpendicular to g(x) = 4x + 3 is equal to -1/4, which is the negative reciprocal of g(x slope. )'s Consequently, the perpendicular line's slope is 4.

The equation of the line passing through (7,3) with a slope of 4 can therefore be determined using the point-slope form of a line:

y - 3 = 4(x - 7) (x - 7)

Increasing the right side and reducing it:

y - 3 = 4x - 28

28 more on both sides:

y = 4x + 25

Consequently, y = 4x + 25 is the equation for the line perpendicular to g(x) = 4x + 3 and passing through (7,3).

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The equation for a line that is perpendicular to the line g(x) = 4x + 3 and passes through the point can be found using the slope-point form of a line (7,3).

It forms a 90° angle with one particular spot where the line passes. Finding the perpendicular line requires knowledge of coordinates and line equations. The slope should be a/b if the line's equation is (x1, y1) and its coordinates are (ax + by + c = 0).

The slope of a line perpendicular to g(x) = 4x + 3 is equal to -1/4, which is the negative reciprocal of g(x slope. )'s Consequently, the perpendicular line's slope is 4.

The equation of the line passing through (7,3) with a slope of 4 can therefore be determined using the point-slope form of a line:

Let the equation be

y - 3 = 4(x - 7) (x - 7)

simplifying the above equation we get

y - 3 = 4x - 28

y = 4x + 25

Consequently, the equation for the line parallel to g(x) = 4x + 3 and passing through is y = 4x + 25. (7,3).

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Answer:VROOOOOOM

Step-by-step explanation:

E E E EE

Answer:

...............

Step-by-step explanation:

Answer:

184

Step-by-step explanation:

1. big rectangle area = 10*(6+5+5) =160

2. top & bottom triangle = (2*1/2 bottom * h)= 6*4 = 24

total 160 +24 =184

Check the picture below.

The inverse of functions g(x)=2/x - 1 and f(x)= ⁵√(x-1) + 2 are g⁻¹(x) = 2/(x + 1)  and f⁻¹(x) = (x-2)⁵ + 1 respectively

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f.

For g(x)=2/x - 1:

Let g(x) = y

y = 2/x - 1

y + 1 = 2/x

x(y + 1) = 2

x = 2/(y + 1)

Since x = g⁻¹(y)

Thus, g⁻¹(x) = 2/(x + 1)          [We just replace y with x]

For f(x)= ⁵√(x-1) + 2:

Let f(x) = y

y =  ⁵√(x-1) + 2

y -2 =  ⁵√(x-1)

(y-2)⁵ = (x-1)

x-1 = (y-2)⁵

x = (y-2)⁵ + 1

Since x = f⁻¹(y)

Thus, f⁻¹(x) = (x-2)⁵ + 1

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The total number of pieces of pie they eat in all is (1 + b) pieces of pie

Number of pieces of pie eaten each = 1 piece

Number of friends= b

Total pieces of pie eaten by all = (Robert + Number of friends) × Number of pieces of pie eaten each

= (1 + b) × 1

= (1 + b) pieces of pie

Therefore, Robert and his friends are a total of (1 + b) pieces of pie.

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