What is the volume of the prism given below?

Answer:

C. 6 kg

Step-by-step explanation:

Let m represent the mass of plates on one side of the barbell. Then the total weight of the barbell is ...

2m +24 = 60 . . . . . kilograms

m +12 = 30 . . . . . . . divide by 2

m = 18 . . . . . . . . . . . subtract 12

The mass of plates on one side of the barbell must total 18 kg. If they all have the same mass, then that must be a divisor of 18. In whole numbers, that would include plates of mass 1, 2, 3, 6, 9, 18 kg.

The only one of these on your list of answer choices is ...

6 kg

Answer:

b) true

c) false

d) true

e) true

Step-by-step explanation:

b) Any line that contains an interior point of a circle is a secant of the circle. The center is an interior point, so a line that contains the circle center is a secant.

__

c) Chords of different lengths intercept arcs of different measures

__

d) Any line perpendicular to a radius at the point where the radius meets the circle is a tangent to the circle. The endpoint of a diameter is the endpoint of a radius, so a line perpendicular there will be a tangent.

__

e) The measure of an inscribed angle is half the measure of the intercepted arc, so all inscribed angles that intercept equal arcs are equal.

The statement 'If a line contains the center of a circle, it is a secant of the circle.' is true. The statement 'If 2 chords intersect a circle, they intercept equal arcs.' is false. Statements 'If a line is perpendicular to a diameter at one of its endpoints, then it is tangent to the circle.' and 'Inscribed angle that intercept equal arcs are equal.' are both true.

b) True. If a line contains the center of a circle, it does pass through the circle at two points, therefore it's a secant of the circle.

c) False. Two chords intersecting inside a circle do not always intercept equal arcs. The length of the arcs they intercept depends on their distance from the center of the circle, not on the mere fact that they intersect.

d) True. If a line is perpendicular to a diameter at one of its endpoints, it does indeed result in a tangent to the circle. This is because the line touches the circle at exactly one point (the endpoint), fulfilling the definition of a tangent line.

e) True. Inscribed angles that intercept (cut off) equal arcs are indeed equal. This is a basic theorem in circle geometry.

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Answer:

An outlier is the number that is much smaller or larger than the other numbers.

In this case it is 29 :)

Answer:

D:  29

Step-by-step explanation:

D:  29 is your outlier.  It's quite different from the commonest values (which are in the range 8 - 17).

Answer:

The second photo.

Step-by-step explanation:

If you use a graphing calculator, you can easily find the answer.

Answer:

  see below

Step-by-step explanation:

Comparing the given equation to the standard-form equation of a circle ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . circle centered at (h, k) with radius r

we find that ...

  h = 2, k = -5, r = 2

So, the circle you're looking for is centered at (2, -5) and has a radius of 2.

Answer:

100 in²

Step-by-step explanation:

Since the figures are similar

the linear ratio of sides = a : b , then

ratio of areas = a² : b²

ratio of sides = 15 : 21 = 5 : 7

ratio of areas = 5² : 7² = 25 : 49

let the area of the smaller figure be x then by proportion

[tex]\frac{25}{x}[/tex] = [tex]\frac{49}{196}[/tex] ( cross- multiply )

49x = 4900 ( divide both sides by 49 )

x = 100

Area of smaller figure is 100 in²

Answer:

B. A hamburger sells for $5 but costs $0.15 to make, giving a net income of $3.35.

Step-by-step explanation:

It's the right answer, for many wrong reasons:

- The units aren't the same... since the 5 is expressed in dollars and the the costs would be expressed in cents.

- There could only have one production cost per burger... so it's not a second variable.  

- Of course, the calculation in the statement is also wrong ($5.00 - $0.15 doesn't equal $3.35)

So, for all these three reasons, that statement cannot be expressed in the given equation.

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)[/tex]

Let [tex]v=x+y[/tex], so that [tex]\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}[/tex]:

[tex]\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1[/tex]

Now the ODE is separable, and we have

[tex]\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx[/tex]

Integrating both sides gives

[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx[/tex]

For the integral on the left, rewrite the integrand as

[tex]\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v[/tex]

Then

[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C[/tex]

and so

[tex]\csc v-\cot v=x+C[/tex]

[tex]\csc(x+y)-\cot(x+y)=x+C[/tex]

Given that [tex]y(0)=\dfrac\pi2[/tex], we find

[tex]\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1[/tex]

so that the particular solution to this IVP is

[tex]\csc(x+y)-\cot(x+y)=x+1[/tex]

Answer:

True

Step-by-step explanation:

we know that

sin(90°)=1

sin(270°)=-1

sin(-90°)=-sin(90°)=-1

sin(-90°)=sin(270°)

therefore

For sin(x)=-1

the values of x are x=-90° and x=270° ------> is true

Answer:

1. The correct answer option is B.

2. The correct answer option is C.

4. The correct answer option is D.

Step-by-step explanation:

1. [tex]\frac{3}{x^2+14x+48}[/tex] ÷ [tex]\frac{3}{10x+60}[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{3}{x^2+14x+48} \times \frac{10x+60}{3}[/tex]

[tex]\frac{3}{(x+6)(x+8)} \times \frac{10(x+6)}{3}[/tex]

Cancelling the like terms to get:

[tex]\frac{10}{(x+8)}[/tex]

The correct answer option is B. [tex]\frac{10}{(x+8)}[/tex]

2. [tex]\frac{4x^2+36}{4x} \times \frac{1}{5x}[/tex]

Factorizing the terms and then cancelling the like terms to get:

[tex]\frac{4(x^2+9)}{4x} \times \frac{1}{5x}[/tex]

[tex]\frac{x^2+9}{5x^2}[/tex]

The correct answer option is C. [tex]\frac{x^2+9}{5x^2}[/tex].

4. [tex]\frac{\frac{4t^2-16}{8} }{\frac{t-2}{6} }[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{4t^2-16}{8} \times \frac{6}{t-2}[/tex]

[tex]\frac{4(t-2)(t+2)}{8} \times \frac{6}{t-2}[/tex]

Cancelling the like terms to get:

[tex]3(t+2)[/tex]

The correct answer option is D. [tex]3(t+2)[/tex].

Answer:x = -2

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

25=5x+35

25-35=5x

-10=5x/:5

-2=x

x=-2

Answer:

an = 6 (1/4)^(n-1)

Step-by-step explanation:

We're given the first term, a₁ = 6.

The common ratio is a term aₓ divided by the previous term aₓ₋₁.

aₓ = 1/4 aₓ₋₁

aₓ / aₓ₋₁ = 1/4

r = 1/4

Therefore:

an = 6 (1/4)^(n-1)

Your answer is correct, good job!

The recursive rule for a geometric sequence is given a₁ = 6, aₓ = 1/4 aₓ₋₁. The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

[tex]a, ar, ar^2, ar^3, \cdots[/tex]

Thus, the nth term of such sequence would be  

[tex]T_n = ar^{n-1}[/tex]

We have been given the first term,

a₁ = 6.

The common ratio is the term aₓ divided by the previous term aₓ₋₁.

aₓ = 1/4 aₓ₋₁

aₓ / aₓ₋₁ = 1/4

r = 1/4

Therefore:

[tex]a_n = 6 (1/4)^{n-1}[/tex]

Hence, The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].

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Answer:

its the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the answer is B, is this a lesson or a quiz?

Answer:

Y-intercept;

(0, 1)

Asymptote;

Horizontal asymptote: y = -2

Step-by-step explanation:

We have been given the following exponential function;

[tex]f(x) = 3^{x+1}-2[/tex]

The y-intercept of a function is the point where the graph of the function intersects the y-axis. At this point, the value of x is usually 0. Therefore, to establish the y-intercept of the given function we substitute x with 0 in the given equation and simplify;

[tex]y=3^{0+1}-2\\ \\y=3-2=1[/tex]

The y-intercept of the given function is thus (0, 1).

Exponential function of the form;

[tex]f(x)=c.n^{ax+b}+k[/tex]

has a horizontal asymptote y = k. In the function given, k = -2 implying that

y = -2 is a horizontal asymptote of the given exponential function

Answer:

1

Step-by-step explanation:

The production cost of company 1 never gets below 340 (at x=20), found e.g., by equating the derived function to 0.

You can figure out that g(x) = 0.05x^2 -7x + 300, but you already know that company 1 has higher cost based on the example values for g(x).

Answer:

Hi!

The answer is:

Based on the given information, the minimum production cost for company __1__ is greater.

Step-by-step explanation:

You have to find the minimum value of a f(x), so you need to differentiate it, set it to zero and solve for x. Then differentiate the function again and calculate the value of the second derivative at the maximum or minimum points to find out whether it is a maximum or a minimum.

[tex]f(x) = 0.15x^2 - 6x + 400[/tex]

[tex]\frac{df}{dx}=2 * 0.15x - 6 = 0.30x - 6 [/tex] First derivative.

[tex][tex]\frac{d^2f}{dx^2} = 2 [/tex][/tex] Second derivative. Confirm it's a minimum point.

Minimum occurs at:

0.30x − 6 = 0

0.30x = 6

x = 6/0.30

x = 20

Replace x on equation f(x):

f(20) = 0.15 * 20² - 6 * 20 + 400 = 340.

For g(x), the value of minimum cost is:

g(70) = 55.

Answer:

The correct option is D

Step-by-step explanation:

The correct option is D.

They both have the same height, assuming that each coin has same volume, then how can coins in 1 stack have different volume than coins in another stack no matter how you stack them.

Like two cylinders with same base area and height have same volume. Like wise rectangle and parallelogram with same base and same perpendicular height having same area....

D) they have the same volume

The answer is:

The correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

[tex](a^{m})^{n}=a^{m*n}[/tex]

When we have a power of a power, we need to keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

[tex](9^{3})^{3}[/tex]

Then, calculating we have:

[tex](9^{3})^{3}=9^{3*3}=9^{9}[/tex]

Hence, we have that the correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

Have a nice day!

Answer:

The correct answer is option C)  9^9

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (9^3)^3

To find the correct option

(9^3)^3 can be written as, (9³)³

By using above identities,

(9³)³ = 9³ ˣ³

 = 9⁹

Therefore the correct answer is option C).  9^9

For this case we have by definition, that a hemisphere represents half of a sphere.

Its volume is given by:

[tex]V = \frac {2} {3} \pi * r ^ 3[/tex]

Where "r" represents the radius.

Substituting the data and clearing the radio we have:

[tex]\frac {2} {3} \pi * r ^ 3 = 18 \pi\\\frac {2} {3} * r ^ 3 = 18\\r ^ 3 = 18 * \frac {3} {2}\\r ^ 3 = 27\\r = \sqrt [3] {27}\\r = 3[/tex]

Thus, the radius of the hemisphere is 3 inches.

Answer:

[tex]3 \ in[/tex]

Answer: these nats

Step-by-step explanation:verry carefully

Answer:

Step-by-step explanation:

Let x represent the amount invested at the higher rate (6%). Then the amount invested at the lower rate is (2400-x) and the total interest earned is ...

  6%·x + 4%·(2400-x) = 5.5%·2400

Dividing by % and rearranging, we have ...

  x(6 -4) = 2400(5.5 -4)

  x = 2400·(5.5 -4)/(6 -4) = 2400(1.5/2) = 2400·0.75

  x = 1800 . . . . . . . . amount invested at 6%

  2400-x = 600 . . . amount invested at 4%

Maria put $1800 in the 6% account and $600 in the 4% account.

_____

Comment on the solution

You will note that the proportion of the investment that went to the higher interest rate account is (5.5-4)/(6-4). This is the ratio of the mixed interest rate less the lower rate to the difference of account rates. This will be the generic solution to mixture problems, so is worthy of note for that reason.

Answer:  

For 4% interest, investment $600

For 6% interest, investment $1,800  

Explanation:  

Maria invested $2,400 into two accounts. One account paid 4% interest and the other paid 6% interest. She earned 5.5% interest on the total investment.

It is a system of linear equations in two variables. Variables are x and y. Solve for x and y using substitution method.

In substitution method: First solve for one variable in terms of another variable and then substitute into another equation.

Further explanation:  

Let $x invested in account which paying 4% interest.

Let $y invested in another account which paying 6% interest.  

Therefore,  x + y = 2400   --------------(1)

                                                                                        = 132

Therefore,  0.04x + 0.06y = 132 -----------(2)

Solve system of equations for x and y , using substitution method.

                     x + y = 2400  

solve for y in terms of x and we get,

                         y = 2400 - x ------------ (3)  

Substitute the value of y into equation (2) and we get,  

                   0.04x + 0.06(2400-x) = 132

                      0.04x + 144 - 0.06x = 132

                                            -0.02x = 132 - 144

                                                     [tex]x=\dfrac{-12}{-0.02}[/tex]  

                                                     [tex]x=600[/tex]

Substitute the value of x into eq(3)  

                                                y = 2400 - 600

                                                y = 1800

In account paying 4% interest, invest $600 and paying 6% interest invest $1,800

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Keywords:

System of equation, Two variable equations, solve for x and y, substitution method, elimination method, cross multiplication method.

Answer:

y=4x+7

Slope m=4 with the equation y2-y1/x2-x1 with any points

y-intercept (0,7)

For this case we have the following system of equations:

[tex]-2x + 5y = -3\\y-15 = 3x[/tex]

We multiply the second equation by -5:

[tex]-5y + 75 = -15x[/tex]

Now we add the equations:

[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]

We find the value of the variable "y":

[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]

THE solution is: (-6, -3)

Answer:

(-6, -3)

Answer:

8.75 cubic feet

Step-by-step explanation:

Your new dresser will be [tex]\frac{2}{5}^{ths}[/tex] larger than your old dresser.

This means that your new dresser wil be

[tex]1+\dfrac{2}{5}=\dfrac{5+2}{5}=\dfrac{7}{5}[/tex]

of your old dresser.

Your old dresser can hold 6.25 cubic feet, so your new dresser can hold

[tex]\dfrac{7}{5}\cdot 6.25=7\cdot 1.25=8.75\ ft^3[/tex]

Final answer:

To find the volume of the new dresser, find 2/5ths of the old dresser's volume (6.25 cubic feet) and add it to the original volume, resulting in a new dresser's volume of 8.75 cubic feet.

Explanation:

To calculate the volume of the new dresser, which will be 2/5ths larger than the old dresser, we will first determine what 2/5ths of the old dresser's volume is, and then add that to the original volume. The old dresser has a volume of 6.25 cubic feet.

Calculate 2/5ths of 6.25 cubic feet: (2/5) × 6.25 = 2.5 cubic feet

Add the additional volume to the original volume to get the new dresser's volume: 6.25 + 2.5 = 8.75 cubic feet

So, the new dresser will hold 8.75 cubic feet of items.

Answer:

Correct answer on ed is C.

Step-by-step explanation:

Just did the exam and it was correct.

The solution is A = ( x - 14 ) / ( x + 4 )

The value of the equation ( h * f * g ) ( x ) = ( x - 14 ) / ( x + 4 )

What is Composition of functions?

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the function f ( x ) be represented as

f ( x ) = ( x - 6 ) / x

Let the function g ( x ) be represented as

g ( x ) = x + 4

Let the function h ( x ) be represented as

h ( x ) = 3x - 2

Now , the equation is ( h * f * g ) ( x )

The equation of composition of functions can be simplified as

h * ( f ( g ( x ) ) ) = h * ( f ( x + 4 ) )

On simplifying the equation , we get

h * ( f ( x + 4 ) ) = h * [ ( x + 4 - 6 ) / ( x + 4 ) ]

h * ( f ( x + 4 ) ) = h * [ ( x - 2 ) / ( x + 4 ) ]

Now , the composition of h * ( f ( g ( x ) ) ) is given by

h ( x ) = 3x - 2

Substitute the value of x as ( x - 2 ) / ( x + 4 ) , we get

( h * f * g ) ( x ) = 3 [ ( x - 2 ) / ( x + 4 ) ] - 2

( h * f * g ) ( x ) = ( 3x - 6 ) / ( x + 4 ) - 2

( h * f * g ) ( x ) = ( 3x - 6 - 2x - 8 ) / ( x + 4 )

( h * f * g ) ( x )  = ( x - 14 ) / ( x + 4 )

Therefore , the value of A is ( x - 14 ) / ( x + 4 )

Hence , the value of ( h * f * g ) ( x )  is ( x - 14 ) / ( x + 4 )

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Minimum: 35

First quartile: 6, 13, 14, 18, 19, 29 (avg. is 16.5)

Median: ≈41.08 (41.0769230769)

Third quartile: 44, 53, 55, 71, 84, 93 (avg. is 66.67)

Maximum: 93

Interquartile range: 50.17

Final answer:

The minimum is 6, the first quartile is 16, the median is 29, the third quartile is 54, the maximum is 93, and the interquartile range is 38.

Explanation:

To find the minimum, first quartile (Q1), median, third quartile (Q3), maximum, and interquartile range (IQR) of the given data set, we first need to organize the data in ascending order, which is already done. Then, we apply the appropriate statistical methods to determine each required value.

Answer:

I believe it would be 40

Step-by-step explanation:

5:3 = x:24

3 times 8 = 24

5 times 8 = 40

There are 40 girls in the chorus.

To express the given information in a linear equation, the setup time and hourly rate per square foot should be considered in the equation y = 4 + (1/1000)x.

To express the information in a linear equation:

Answer:

[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].

Step-by-step explanation:

We want to find the polynomial that will result from expanding:

[tex](x-y)^4[/tex].

Recall that we can use the Pascal's triangle to obtain the coefficient as:

1     4    6   4   1

Also note how the negative sign is going to alternate.

The power of x will decrease from left to right while the power of y increases from left to right

The expansion then becomes:

[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].

Answer:

The Answer is A!!!!

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

0.4 = 4/10 = 2/5

0.4 converted into a fraction is 4/10, 4/10 simplified is 2/5

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

We look for two points through which the line passes to find the slope:

[tex](x1, y1) = (2,2)\\(x2, y2) = (0, -4)[/tex]

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-4-2} {0-2} = \frac {-6} {- 2} = 3[/tex]

So, the line is:

[tex]y = 3x + b[/tex]

We have "b" replacing any of the points:

[tex]-4 = 3 (0) + b\\-4 = b[/tex]

Finally, the equation is:

[tex]y = 3x-4[/tex]

Answer:

[tex]y = 3x-4[/tex]

Answer:

Option B is correct.

Step-by-step explanation:

300 cm^3 of snow melts into 33 cm^3 water. We need to find how much water is produced if 600 cm^3 of snow is melt.

Solving using unitary method:

300 cm^3 of snow melts into water = 33 cm^3

1 cm^3 of snow melts into water = 33/300

600 cm^3 of snow melts into water = 33/300 *600

                                                           = 66 cm^3

So, Option B is correct.

Answer:

[tex]\large\boxed{x=\dfrac{1}{a}}[/tex]

Step-by-step explanation:

[tex]2-4(ax-3)=10\qquad\text{subtract 2 from both sides}\\\\-4(ax-3)=8\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4(ax-3)}{-4}=\dfrac{8}{-4}\\\\ax-3=-2\qquad\text{add 3 to both sides}\\\\ax-3+3=-2+3\\\\ax=1\qquad\text{divide both sides by}\ a\neq0\\\\x=\dfrac{1}{a}[/tex]