Write the given equation in exponential form.


log7 = 3

Answer:

[tex]r=\sqrt{\dfrac{75}{\pi}}\approx 4.89\ in[/tex]

Step-by-step explanation:

If the water in the cube rose from 6 inches to 8 inches when the cone was placed in the cube, then the difference in volumes is the volume of the submerged portion of the cone.

Initially, 10 in by 10 in by 6 in:

[tex]V_{initial}=10\cdot 10\cdot 6=600\ in^2.[/tex]

At he end, 10 in by 10 in by 8 in:

[tex]V_{final}=10\cdot 10\cdot 8=800\ in^3.[/tex]

Thus,

[tex]V_{submerged \ cone}=800-600=200\ in^3.[/tex]

Use cone's volume formula

[tex]V_{cone}=\dfrac{1}{3}\pi r^2 \cdot h,[/tex]

where r is the radius of the cone's base, h is the height of the cone.

From the diagram, h=8 in, then

[tex]200=\dfrac{1}{3}\cdot \pi\cdot r^2\cdot 8\\ \\\pi r^2=75\\ \\r^2=\dfrac{75}{\pi}\\ \\r=\sqrt{\dfrac{75}{\pi}}\approx 4.89\ in[/tex]

Answer:

The amplitude  of the given sinusoidal function is 3.5

Step-by-step explanation:

The given sinusoidal function is

[tex]m(x)=-3.5\cos x[/tex]

This function is of the form:

[tex]m(x)=a\cos bx[/tex]

where

a=|-3.5|=3.5 is the amplitude.

Therefore the amplitude of the given sinusoidal function is 3.5

Answer:

3n+21

Step-by-step explanation:

3 × n =3n

3 × (+7) = +21

Answer:

Use distributive property.

3(n+7),

3*n + 3*7=

3n + 21

Hope this helps and have a great day!

Answer:

So first, we can see that two out of four sides of this triangular prism is a square because they have equal side lengths.

The surface area of these two sides should be:

A = a² · 2 = 10² · 2 = 100 · 2 = 200 (ft²)

Next, we need to find the area of the two triangles:

A = bh/2 · 2 = hb = 8 · 12 = 96 (ft²)

Lastly, we have the rectangular base:

A = wl = 10 · 12 = 120 (ft²)

All we need to do now is to add up all of our results:

A = 200 + 96 + 120 = 416 (ft²)

Answer:

[tex]4 \times 3^{3}\\\\4\times3 \times3\times3\\\\108[/tex]

Step-by-step explanation:

Four times three cubed

Given the statement, times means multiplication.

four times three

4        x         3

It says three cubed, where cubed means raised to 3. So that means we right an exponent, and the exponent is 3.

4 x 3³

When we have an exponent, that tells you how many times you will multiply it by itself. So since the exponent is 3, we multiply 3 by itself 3 times.

3³ = 3 x 3 x 3

So 4 x 3³ = 4 x 3 x 3 x 3

Lastly, if we get the product your result will be 108.

4 x 3 x 3 x 3

=4 x 27

= 108

The expression is 4 times 3 cubed. The value equivalent to 4 times 3 cubed is 108.

The expression is 4 times 3 cubed.

To find the value equivalent to 4 times 3 cubed, we need to calculate it.

3 cubed means 3 raised to the power of 3, which is 3 x 3 x 3 = 27.

So, the value equivalent to 4 times 3 cubed is 4 x 27 = 108.

https://brainly.com/question/34132400

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Answer:

B

Step-by-step explanation:

I. Number of men who liked both equally = 18

Number of men who preferred the movie = 35

18 < 35, so this option is false.

II. Number of men preferred the book  = 56

Number of women preferred the book = 28

56 = 2 · 28, so this option is true.

III. Number of women preferred the book = 28

Number of women preferred the movie = 35

28 < 35, so this option is false.

IV. Number of men who preferred the movie = 35

Number of women who preferred the movie = 35

35 = 35, so this option is true.

True options II and IV.

Answer: Alaska

Step-by-step explanation: Alaska has the Earliest United States Time Zone as from Earliest to latest Alaska is 2 PM. Pacific is 3 PM. Mountain is 4 PM. Central is 5 PM. Eastern is 6 PM. Therefore Aleutian/Hawaii is 7 PM. From West, headed East, Each time Zone bumps up 1 hour.

Answer:

23.79

Step-by-step explanation:

one is less than 5 so you just drop it

Answer:

23.79

Step-by-step explanation:

In the number 23.791, the number place holding the 9 is the hundreth's place. Now look at the thousands place, the number place holding the 1.

If the number in the thousands place is 5-9, round up to 23.8

If the number in the thousands place is 1-4, round down to 23.79

Since 1 is smaller than 5, round doqn to 23.79

I hope this helps!

Answer:

[tex](-7x^2+3)(x-3)[/tex]

Step-by-step explanation:

We can take "common" from first 2 terms and common from next 2 terms. Shown below:

[tex]-7x^3+21x^2+3x-9\\-7x^2(x-3)+3(x-3)\\(-7x^2+3)(x-3)[/tex]

That's how we do it. We can't simplify, or factor, any further.

Answer:

i think value 35

Step-by-step explanation:

Answer:

f(x) = -8(4)x

Step-by-step explanation:

The reflection of the point (x,y) across  the x-axis is the point (x,-y).

Having said this, to reflect the function y=g(x) = 8(4x) over the x-axis, we just need to evaluate the equation in the point: (x,-y).

y = 8(4x) ⇒ -y = 8(4x) ⇒ y = -8(4x)

Then f(x) = -8(4x)

Attached you will find the graph of g(x) (blue) and f(x) (red),

Answer:

[tex]f (x) = -8(4x)[/tex]

Step-by-step explanation:

The transformation that reflects the function [tex]g(x)[/tex] on the axis is:

[tex]y = -g (x)[/tex].

Therefore if we have the function

[tex]g (x) = 8 (4x)[/tex] and we call [tex]f (x)[/tex] to the transformation that relieves g (x) on the x axis then:

[tex]f (x) = -g (x)\\\\f (x) = -8(4x)[/tex]

Finally the equation for f(x) es:  [tex]f (x) = -8(4x)[/tex]

The answer is:

The value of x is 3.9 units.

From the statement we know that the sum of the distances AB and BC is equal to 9.7 units, so, we need to write one equation to create a relation between the given distances and the total distance (AB + BC)

So, writing the equation, we have:

[tex]AB+BC=AC\\\\2x-3+(x+1)=9.7[/tex]

Now, adding like terms, we have:

[tex]2x-3+(x+1)=9.7[/tex]

[tex]2x+x-3+1=9.7[/tex]

[tex]3x-2=9.7[/tex]

[tex]3x=9.7+2[/tex]

[tex]x=\frac{9.7+2}{3}=\frac{11.7}{3}=39.9[/tex]

Hence, we have the value of x is 3.9 units.

Have a nice day!

Answer: the answer is 6.

Step-by-step explanation:

a p e x

Answer:

ΔADC ≅ ΔCBA by the SSS congruence postulate

Step-by-step explanation:

This is because of the following:

AD ≅ CB

DC≅AB

lastly, AC≅AC,

however ΔADC ≅ ΔABC by the SSS congruence postulate is also true since ΔABC and ΔCBA is just the same triangle. We can name our triangle in the both the same way.

Answer:

31%

Step-by-step explanation:

100- 75 = 25

25/81 = 0.308 = 31%

First, find what percentage of the total price the jeans are. Price of jeans divided by total cost paid

75/81=.9259 the jeans were 92.59% of the total cost; the rest is tax. So you subtract 92.59% from 100% (the total cost paid) and get 7.41% sales tax

Answer:

A) −13

Step-by-step explanation:

(x + 6)^2 = 49

Take the square root of each side

sqrt((x + 6)^2) = ±sqrt(49)

x+6 = ±7

Subtract 6 from each side

x+6-6 = -6  ±7

x =-6  ±7

Separating into 2 parts

x = -6+7          x = -6-7

x = 1               x = -13

Where is 'the following'?

(I'll Answer in comments just give detail)

Answer:

range

Step-by-step explanation:

this is because it is asking the not central which is range.

Final answer:

John and Ramona are closing in on each other on a collision course with a combined speed of 35 mph over a distance of 24 miles. After doing the calculation, we find that it will take them approximately 41.14 minutes to meet.

Explanation:

To find out how long it will take John and Ramona to meet, we can assume they are moving towards each other on a collision course. We do this by adding their speeds together since they are moving in opposite directions. John cycles at a speed of 20 mph and Ramona cycles at 15 mph, so the combined speed at which they are closing in on each other is 20 mph + 15 mph = 35 mph.

The distance between them is 24 miles. To calculate the time it takes for them to meet, we divide the total distance by their combined speed:

Time = Distance / Speed

Time = 24 miles / 35 mph

Time = 0.6857 hours

Since time is often represented in minutes, we multiply the decimal by 60:

0.6857 hours * 60 minutes/hour = 41.14 minutes

Therefore, it would take approximately 41.14 minutes for John and Ramona to meet.

The area of the square is 36 squared inches, because it is a square with a side of 6 inches.

The two semicircles have a radius of 3 inches. If we subtract their areas from the area of the square, we have

[tex]36-2\left(\dfrac{\pi\cdot 3^2}{2}\right) = 36-9\pi[/tex]

The shaded region is half of this area, so the answer is

[tex]\dfrac{36-9\pi}{2} \approx 7.7[/tex]

36 minus 9 multiplied by Pi . Then divide that answer by 2 to get 7.7

The value of the expression for 121 is 11

Answer:

36

Step-by-step explanation:

If s is the side length, then the area of the square is

A = s^ = (6)^2 = 36

This is how you were expected to answer this question.  However, the actual correct answer is 36 cm^2.

Answer:

36

Step-by-step explanation:

Its rly easy 48.58+3.60=52.18

Answer:

A. 6

Step-by-step explanation:

f(x) = x² − 12x + 7

To complete the square, we first factor the leading coefficient to make it 1 (which it already is).

Then, we take half the second coefficient, square it, and then add to both sides.  So (-12/2)² = (-6)² = 36.

f(x) + 36 = x² − 12x + 36  + 7

Then we factor the perfect square:

f(x) + 36 = (x − 6)² + 7

Then solve for f(x) by subtracting and simplifying:

f(x) = (x − 6)² + 7 − 36

f(x) = (x − 6)² − 29

So the value of a is 6.

Answer:

[tex]\boxed{\text{\$11 500}}[/tex]

Step-by-step explanation:

$1437.50 = 12.5 % of price

[tex]\text{Price} = \text{100 \%} \times \dfrac{\text{\$1437.50}}{\text{12.5 \%}} = \text \$11 500}[/tex]

The price of the motorcycle before tax was [tex]\boxed{\textbf{\$11 500}}[/tex]

Answer:

$36.75

Step-by-step explanation:

Answer: the sales tax alone is $36.75

the above ground pool with the sales tax is 561.75

Step-by-step explanation:

525x.07 =36.75

525x1.07=561.75 or another way you could do it is 525+36.75=561.75

Answer:

20 square units

Step-by-step explanation:

You count how many across the parallelogram is (which is 4) and you count how high it is (which is 5). Then you multiply 5×4* which equals 20 square units.

*The reason you do this is because base×hieght=area

Answer:

20 square units

Step-by-step explanation:

Area of a parallelogram formula = base times height

To find the length of the base we take end points of the base and use distance formula

[tex]distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Two points are (1,0) and (5,0)

Distance = [tex]\sqrt{(5-1)^2+(0-0)^2}[/tex]

[tex]=\sqrt{4^2} =4[/tex]

Length of base = 4 units

Now we find out the height between B (1,0) and D (1,5)

Height =[tex]\sqrt{(1-1)^2+(5-0)^2}=\sqrt{5^2}= 5[/tex]

Height = 5

Area of the parallelogram = base times height

= [tex]4 \cdot 5= 20[/tex]

So area = 20 square units

T o find the median if there are two numbers in between find the mean or the average. To do that add up the 2 middle numbers then divide by 2 that's your median

Answer:

D

Step-by-step explanation:

To shift down:

F(x)-b

To shift up:

F(x)+b

To shift right:

F(x-b)

To shift left:

F(x+b)

ANSWER

D. The graph of G(x) is the graph of F(x) shifted 7 units down.

EXPLANATION

The given assumption is that:

G(x)= F(x)-7

This implies that, our parent function is F(X).

Since 7 is subtracted from F(x) to obtain the graph of G(x), it means that shifting the graph of F(x) down by 7 units gives us the graph of G(x).

D. The graph of G(x) is the graph of F(x) shifted 7 units down.

Answer:

[tex]96\ basketballs[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder (hollow drum)

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=48\ in[/tex]

[tex]r=24\ in[/tex]

substitute

[tex]V=\pi (24)^{2} (48)[/tex]

[tex]V=27,648\pi\ in^{3}[/tex]

step 2

Find the volume of one basketball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=6\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ in^{3}[/tex]

step 3

Find the maximum number of basketballs that the cylindrical drum contains

so

Divide the volume of the cylinder by the volume of one basketball

[tex]27,648\pi/288\pi=96\ basketballs[/tex]

Answer:

(D)

Step-by-step explanation:

Slope : ( y2 - y1 )/( x2 - x1)

slope : ( -2 - 4 )/( - 3 + 4)

slope: ( -6 )/( 1 )

slope : -6

Answer:

Step-by-step explanation:

Factor −16t2+20t

−16t2+20t

=4t(−4t+5)

Answer:

4t(−4t+5)

or

Let's simplify step-by-step.

−16t2+20t

There are no like terms.

Answer:

=−16t2+20t

The equation f(t)=-16t^2+20 when solved gave t = 0 and t = 1.25.

To solve the quadratic equation f(t)=-16t^2+20t, we first need to rearrange it into the standard form of a quadratic equation at^2 + bt + c = 0. We can simplify the original equation by dividing all terms by -4, which will reverse the signs:

4t^2 - 5t = 0

Now, this equation can be factored, giving us:

t(4t - 5) = 0

This means our equation has two possible solutions for when it equals zero:

t = 0 or 4t - 5 = 0

Solving the second part for t gives us t = 5/4 or 1.25.

Therefore, the equation f(t) = -16t^2 + 20t has two solutions for t: t = 0 and t = 1.25.