One number is 2 less than a second number. Twice the second number is 7 less than 3 times the first. Find the two numbers.

[tex]V=lwh=(3)\left(\frac{4}{3} \right) \left(\frac{3}{5} \right)\\\\V=3\left(\frac{12}{15} \right)\\\\V=\frac{36}{15}=\boxed{\frac{12}{5} \text{ cm}^{2}}[/tex]

No, the cone and the cylinder can't have congruent heights and bases.

The volume of a cylinder of radius R and height H is:

V = pi*R^2*H

And for a cone of radius R and height H is:

V = pi*R^2*H/3

So, for the same dimensions R and H, the cone has 1/3 of the volume of the cylinder.

Here, the cylinder has a volume of 120cm³ and the cone a volume of 360cm³, so the cone has 3 times the volume of the cylinder.

This means that the measures must be different, so the cone and the cylinder can't have congruent heights and bases.

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Answer: Heyaa! ~

When simplifying (2x^2y)3 the answer will be...  6x²y

Step-by-step explanation:

    Multiply the numbers:

Hopefully this helps you! ^^

Answer:

7 years

Step-by-step explanation:

Your equation should read     = 200 * e^(.08 t)  =  350

    solving for t       = 6.99 yrs     ~~ 7 years

Answer:

the fourth option is correct

Step-by-step explanation:

the first equation represents that the cost of 6 bananas is the same as the cost of nine apples. therefore, y is the cost of a single banana and x is the cost of a single apple. the second equation represents the situation of you buying 4 bananas and 2 apples for $8. If x and y represent the cost of each fruit, then the point (x,y) = (1,1.5) means that x, the cost of an apple, is $1.00 and that y, the cost of a banana, is $1.50.

The value of her investment after 8 years is  $8,293.81.

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving.

Given:

P= $5600

r= 5.4%

t= 8 years

Then solve the equation for A

A = P(1 + r/n)^nt

A = 5,400.00[tex](1 + 0.054/4)^{4/8}[/tex]

A = 5,400.00[tex](1 + 0.0135)^{32}[/tex]

A = $8,293.81

Hence, the value will be $8,293.81.

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Answer:

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

Step-by-step explanation:

Given function:

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

Replace f(x) with y:

[tex]\implies y=e^{3x-1}[/tex]

Take natural logs of both sides:

[tex]\implies \ln y = \ln e^{3x-1}[/tex]

Apply the Power Log Law   [tex]\ln x^n=n\ln x[/tex] :

[tex]\implies \ln y = (3x-1)\ln e[/tex]

As [tex]\ln e=1[/tex] then:

[tex]\implies \ln y = 3x-1[/tex]

Rearrange to make x the subject:

[tex]\implies 3x=\ln y +1[/tex]

[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]

Swap x for [tex]f^{-1}(x)[/tex]  and y for x:

[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Answer:

8x^2 +6x +36xy^2+27y^2

Step-by-step explanation:

2x * 4x-2x*-3) -9y-^2(-4x)-9y^2(-3)

The x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2

The equation of the function is given as:

[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]

The x intercept is the x value when h(x) = 0

So, we have:

[tex]8 * \sqrt[3]{x - 6} + 16 = 0[/tex]

Subtract 16 from both sides

[tex]8 * \sqrt[3]{x - 6} = -16[/tex]

Divide both sides by 8

[tex]\sqrt[3]{x - 6} = -2[/tex]

Take the cube of both sides

x - 6 = -8

Add 6 to both sides

x = -2

Hence, the x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2

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The Pattern B is the twice of the Pattern A.  Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Item 11 In the table,

Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10".

Pattern A   10  15  20  25  30

Pattern B   20 30 40  50  60

Then the Pattern B is the twice of the Pattern A.

Then the correct option is C.

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Answer:

Step-by-step explanation:

The values of a, b and c from the given exponential function are 7, 9 and 4 respectively

According to the exponential law of indices

[tex]\sqrt[c]{a^b}[/tex]

This can be written as;

[tex]\sqrt[c]{a^b}=a^{\frac{b}{c} }[/tex]

Given the exponential expression

[tex]7^\frac{9}{4}[/tex]

Compare with the original expression

a = 7, b = 9 and c = 4

Hence the values of a, b and c from the given exponential function are 7, 9 and 4 respectively

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The statements that are true about the dollhouses is: 1,4,5.

The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).

Space inside dollhouse 1:

V = 6 (6) (5) + 1/2 (6) (6) (4)

V=180+72

V=252 inches

The space inside dollhouse 2 can be found using the equation

V = 6 (6) (5) + 1/3 (6) (6) (4)

V=180+48

V=228

The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.

V1=252

V2=228

Hence:

252-228=24 inches cubed

V1 ≥V2

Therefore the statements that are true about the dollhouses is: 1,4,5.

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The net present value is $305.73. The project should be accepted.

Using this formula

Net present value=Cashflow÷(1+Cost of capital)^ time

Let plug in the formula

Net present value=-$2,400+ ($630÷(1+.09)^1) + ($760÷(1+.09)^2) + ($800÷(1+.09)^3) + ($880 ÷(1+.09)^4) + ($380÷(1+.09)^5)

Net present value=-$2,400+ ( $630÷(1.09)^1) + ($760÷(1.09)^2) + ($800÷(1.09)^3) + ($880 ÷(1.09)^4) + ($380÷(1.09)^5)

Net present value=-$2,400+ ($630÷1.09) + ($760÷1.1881) + ($800÷1.295029) + ($880 ÷1.41158161) + ($380÷1.538639549)

Net present value=-$2,400+ $577.98+$639.68+$617.75+623.41+$246.91

Net present value=$305.73

Based on the above calculation the project should be accepted.

Therefore the NPV is $305.73.

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Answer:  c. Level of Significance

This is the alpha value

alpha is a greek letter with the symbol [tex]\alpha[/tex]

A type 1 error is when the researcher rejects the null, but the null was true (meaning the researcher shouldn't have rejected the null).

Answer:

x = 25

Step-by-step explanation:

the line QC is parallel to BR

Then

x/15 = 40/24

Then

24x = 40×15

Then

24x = 600

Then

x = 600/24

Then

x = 25

Answer:

=> Apply law of cosine

[tex]c^2=a^2+b^2-2abcos\left(C\right)[/tex]

=> input value

[tex]z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)[/tex]

=> simplify

[tex]z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}[/tex]

=> calulcation

[tex]z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}[/tex]

=> apply rule: Distance must be greater than 0

which is about 14.51828

Answer:

  dilation by a factor of -1/2 about the center (6, 5)

  (x, y) ⇒ (9 -x/2, 7.5 -b/2)

Step-by-step explanation:

Figure B is half the size of Figure A. It has been rotated, and translated. The single transformation must have all of these effects.

__

The orientation of shape B is the same as that of shape A. The small extension from the rectangle still points counterclockwise relative to the figure's center. However, it points west instead of east, signifying a rotation of 180°. The same 180° rotation can be accomplished by a reflection across a point.

Shape B has half the dimensions of shape A. That means it has been dilated by a factor of 1/2. The reflection across a point can be accomplished by using a negative dilation factor.

The center of the dilation must reside between the two figures in order for "reflection across a point" to be accomplished. Each point on figure A must be twice as far from that center as the corresponding point on figure B.

Corresponding points are (1, 1) on figure A, and (8.5, 7) on figure B. The center of dilation divides the line between these points into the ratio 2:1. That center can be found as ...

  (a, b) = (2(8.5, 7) +(1, 1))/3 = (17+1, 14+1)/3 = (6, 5)

The single transformation that maps figure A to figure B is ...

  dilation by a factor of -1/2 about the center (6, 5)

  (x, y) ⇒ (9 -x/2, 7.5 -b/2)

Answer:

0.8p

Step-by-step explanation:

Hello!

As the questions states, 20% of p is 0.2p.

Simplifying the equation:

0.8p is also 80% of p, which can be translated to 100% - 20% of p.

The equivalent expression is 0.8p.

Answer:

17/8

Step-by-step explanation:

You must type 2* 8 and add 1. That makes 17/8

Hi student, let me help you out! :)

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

We are asked to convert 2 1/8 into an improper fraction (a fraction whose numerator is greater than its denominator).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

These are the steps:

However, we cannot simplify 17/8, so that's our answer.

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

c

Step-by-step explanation:

edge 2023

The probability that event B occurs is 83%. Therefore, option C is the correct answer.

Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.

Given that, events A and B are independent, and the probability that event A occurs is 83%.

If the outcome of one event has no bearing on the fate of the other, the two events are said to be independent events. Instead, we may say that an event is considered independent if it does not affect the likelihood of another event.

Since, the events A and B are independent, if the probability that event A occurs is 83%.

Then, the probability that event B occurs is 83%.

Therefore, option C is the correct answer.

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Answer:

9y

Step-by-step explanation:

Mathematicaly, the product of 9 and a number "y" is:

9y

The given differential equation is not exact, if we convert it to an exact one, we get:

[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]

A differential equation:

[tex]Ndx + Mdy = C[/tex]

Is exact only if:

[tex]\frac{dM}{dy} = \frac{dN}{dx}[/tex]

In this case, we have:

[tex]2ydx + (x - sin(y)^{1/2})*dy = 0\\\\then:\\\\N = 2y\\M = x - sin(y)^{1/2}[/tex]

If we differentiate, we will get:

[tex]\frac{dN}{dy} = 2\\\\\frac{dM}{dx} = 1[/tex]

So, to convert this to an exact differential equation, we need to add a factor 2 to N, this will give:

[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]

This is, in fact, an exact differential equation.

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Answer:

Step-by-step explanation:

-4x + 2 = x - 3

-5x + 2 = -3

-5x = -5

x = 1

y = 1 - 3

y = -2

(1, -2)

The attached image represents the completed Venn diagrams

Diagram 1

We have:

Multiples of 3 and Multiples of 10

When the sets are populated, we have:

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 10 = 10, 20, 30

Both = 30

Next, we complete the circles using the above data values

See attachment 1

Diagram 2

We have:

Multiples of 2, Multiples of 3 and Multiples of 5

When the sets are populated, we have:

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 5 = 5, 10, 15, 20, 25, 30

Multiples of 2 and 3 = 6, 12, 18, 24 and 30

Multiples of 2 and 5 = 10, 20 and 30

Multiples of 3 and 5 = 15 and 30

All = 30

Next, we complete the circles using the above data values

See attachment 2

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Answer:

These are Vertical angles, adjacent angles are next to each other and make up a whole angle, while vertical angles are across and equal the same thing.

X = 81 because 84 and (x + 3) are the same so 84 minus 3 is 81

Hope that helps

Answer:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

Step-by-step explanation:

The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

In the graph, the given straight line passes through two points (0,0) and (2,8).

Therefore, the equation of the straight line becomes:

[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]

where:

Thus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:

[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]

y = 4x

Now, our region bounded by the three lines are:

Similarly, the change in polar coordinates is:

where;

Now

Then:

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

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