The radius of a small ornament in the shape of a sphere is 2 inches. What is the approximate volume of the ornament? Use 3.14 for pi. Round to the nearest tenth of a cubic inch.

Answer: Fourth Option

[tex]x =4[/tex]

Step-by-step explanation:

First we write the equation

[tex]log_2(x) = 2- log_2(x-3)[/tex]

Now we use the properties of logarithms to simplify the expression

[tex]log_2(x)+log_2(x-3) = 2[/tex]  

The property of the sum of logarithms says that:

[tex]log_a (B) + log_a (D) = log_a (B * D)[/tex]

Then

[tex]log_2[x(x-3)]= 2[/tex]  

Now use the property of the inverse of the logarithms

[tex]a ^ {log_a (x)} = x[/tex]

[tex]2^{log_2[(x)(x-3)]}= 2^2[/tex]  

[tex](x)(x-3))}= 4[/tex]  

[tex]x^2-3x -4=0[/tex]

 [tex]x^2-3x -4=(x-4)(x+1)=0[/tex]

Then the solution are

[tex]x= -1[/tex] and [tex]x= 4[/tex]

We take the positive solution because the logarithm of a negative number does not exist

Finally the solution is:

[tex]x =4[/tex]

Answer:

• zero: -4, -4/3, 7

• positive: -4 < x < -4/3 . . . or 7 < x

• negative: x < -4 . . . or -4/3 < x < 7

Step-by-step explanation:

Zeros of the function are at x=-4, -4/3, +7. These are the values that make each of the individual factors be zero. For example, x-7=0 when x=7.

The function will be negative for x-values left of an odd number of zeros. It will be positive for x-values left of an even number of zeros (including left of no zeros, which is to say right of all zeros). This is because the sign of the factor giving rise to the zero changes for x-values on either side of that zero. (This is not true for zeros with even multiplicity, as the sign does not change at those.)

Answer:

Not sure if this is correct but maybe it is 34?

Answer: [tex]tan(x)=\±\frac{3}{4}[/tex]

Step-by-step explanation:

You know that [tex]sin(x)=\frac{3}{5}[/tex] and you can identify that. Then:

[tex]sin^2(x)=(\frac{3}{5})^2[/tex]

[tex]sin^2(x)=\frac{9}{25}[/tex]

Remember that:

[tex]cos^2(x)=1-sin^2(x)[/tex]

Then [tex]cos^2(x)[/tex] is:

[tex]cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}[/tex]

Apply square root to both sides to find cos(x):

[tex]\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}[/tex]

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

Then, this is:

[tex]tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}[/tex]

[tex]tan(x)=\±\frac{3}{4}[/tex]

Answer:

y = -1/4 x + 15.

Step-by-step explanation:

y = 4x - 2 has a slope of 4 ( = the coefficient of x).

The line  at right angles to it will therefore of a slope of -1/4.

Using the point-slope form of a line the line t which passes through (4, 14) is found as follows:

y - 14 = -1/4(x - 4)

y = -1/4x + 1 + 14

y = -1/4x + 15

Answer:

A. ) 125.6 in.

Step-by-step explanation:

Hope I helped :)

Answer:

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=d\pi[/tex]

d - diameter

We have d = 40in. Substitute:

[tex]C=40\pi\ in[/tex]

[tex]\pi\approx3.14\to C\approx(40)(3.14)=125.6\ in[/tex]

The answer is 1/9 or about 11%.

Answer:8

Step-by-step explanation: it’s right

Answer: 1 5/8 or 13/8. They are the same.

Step-by-step explanation to find the amount of books she reads in 4 1/3 says, first you need to find how much she reads in 1 day.

3/4 divided by 2 = 3/4 x 1/2=3/8.

Now you need to multiply 3/8 by 4 1/3 to find how many books she can reed in a day. 4 1/3= 13/3. 13/3 x 3/8= 39/24 = 13/8 = 1 5/8

Answer: 2.888889

Step-by-step explanation:

3/4 book    4 1/3 book

------------- =  ---------------

2 days          x days

4 1/3= 13/3

3/4= 0.75

1.5x= 13/3

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

1.5      1.5

 x=  2.888889 books

30 ≥ g [keyword - "no more than"

4 ≤ i [keyword - "at least"]

The diameter of the sphere is approximately 19.82 units.

To calculate the diameter of a sphere given its volume, we'll use the formula for the volume of a sphere:

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

Where:

- [tex]\( V \)[/tex] is the volume of the sphere,

- [tex]\( \pi \)[/tex] is a mathematical constant (approximately equal to 3.14159),

- [tex]\( r \)[/tex] is the radius of the sphere.

Since we have the volume, we rearrange the formula to solve for the radius:

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

Substituting the given volume [tex]\( V = 3052.08 \)[/tex], and the value of[tex]\( \pi \)[/tex], we can find the radius:

[tex]\[ r = \sqrt[3]{\frac{3 \times 3052.08}{4 \times 3.14159}} \][/tex]

[tex]\[ r \approx \sqrt[3]{\frac{9156.24}{12.56636}} \][/tex]

[tex]\[ r \approx \sqrt[3]{729.128} \][/tex]

[tex]\[ r \approx 9.85 \][/tex]

Now, to find the diameter, we double the radius:

[tex]\[ \text{Diameter} = 2 \times r \][/tex]

[tex]\[ \text{Diameter} = 2 \times 9.85 \][/tex]

[tex]\[ \text{Diameter} \approx 19.82 \][/tex]

So, the diameter of the sphere is approximately 19.82 units.

To recap, we first found the radius of the sphere using the formula for volume, then we doubled the radius to find the diameter.

Complete question:

The volume of a sphere is 3052.08 units cubed what is its diameter?

Hello There!

Before getting started, we should remember that the top surface and the bottom surface of any cylinder are congruent to each other.

First, we use the formula pi*radius^2 to find the area of a circle since there is always a circle in a cylinder.

Next, we multiply pi*radius^2 * height because a cylinder has a height too.

HOW TO SOLVE

First, we multiply 3.14 which is equal to pi by 25 because the radius is 5 and in the formula we used, it states radius squared so 3.14 multiplied by 25 and then multiplied by the height of our cylinder which equals 6.

Once we multiply, we get a product of 471.

Our final answer is 471.units^3

Answer:

348

Step-by-step explanation:

Answer:

-a^2 -4a +3a +12

-a^2 -1a +12

Step-by-step explanation:

Answer:

405.80

Step-by-step explanation:

So, we know Carlos ran 21 miles per week, for 12 weeks....

That makes 21 mi/wk x 12 weeks = 252 miles.

Then we know each km is 0.621 mile.

So, we divide 252 miles by 0.621 mile/km to get= 405.80 km

Dividing miles by miles/km gives us the unit we want (km).

There was a trap in this question, because if instead of dividing the 252 miles by 0.621 you would have multiplied it, you would have gotten another answer listed... just not the right one. :-)

Answer:

$9259.26

Step-by-step explanation:

The school receives $20 on $75.

We can calculate the percentage by using the values.

20/75 = 0.27%

The school recieved 0.27% of the payment.

Now we know the target amount and percentage, we can calculate the principal amount here.

Let x dennote the worth on which the school will recieve 2500 dollars. [tex]2500 = x * 0.27\\x = \frac{2500}{0.27}\\ x = 9259.26[/tex]

$9259.26 worth of ribbon has to be sold for the school to get $2500 ..

it's the first one !!! so it's A

Winona's bowling scores have a mean of 204.6, a median and mode both of 195.

To find the mean, median, and mode of Winona's bowling scores, we follow these steps:

The bowling scores are 195, 180, 195, 212, 208, 231, 179, 246, and 195.

Mean: (195 + 180 + 195 + 212 + 208 + 231 + 179 + 246 + 195) / 9 = 1841 / 9 = 204.6

The mean score is 204.6.

To find the median, we first arrange the scores in ascending order: 179, 180, 195, 195, 195, 208, 212, 231, 246.

The median, or the middle score, is the fifth one since there are an equal number of scores on either side of it, which is 195.

The mode is the number that appears most often, which is also 195.

Therefore, Winona's mean score is 204.6, the median score is 195, and the mode is 195.

Answer:

well how many tables are there?

Step-by-step explanation:

Answer:

3.4594

Step-by-step explanation:

To change the base of a logarithm

• [tex]log_{b}[/tex] x = [tex]\frac{log_{c}x }{log_{c}b }[/tex]

where c represents the new base

Changing the base from 2 to 10

[tex]log_{2}[/tex] 11 = [tex]\frac{log_{10}11 }{log_{10}2 }[/tex] ≈ 3.4594

Answer:

The height of the water is [tex]60.5\ ft[/tex]

Step-by-step explanation:

step 1

Find the volume of the tank

The volume of the inverted right circular cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=16\ ft[/tex]

[tex]h=96\ ft[/tex]

substitute

[tex]V=\frac{1}{3}\pi (16)^{2} (96)[/tex]

[tex]V=8,192\pi\ ft^{3}[/tex]

step 2

Find the 25% of the tank’s capacity

[tex]V=(0.25)*8,192\pi=2,048\pi\ ft^{3}[/tex]

step 3

Find the height, of the water in the tank  

Let

h ----> the height of the water  

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

[tex]\frac{R}{H}=\frac{r}{h}[/tex]

substitute

[tex]\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}[/tex]

where

r is the radius of the smaller cone of the figure

h is the height of the smaller cone of the figure

R is the radius of the circular base of tank

H is the height of the tank

we  have

[tex]V=2,048\pi\ ft^{3}[/tex] -----> volume of the smaller cone

substitute

[tex]2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h[/tex]

Simplify

[tex]221,184=h^{3}[/tex]

[tex]h=60.5\ ft[/tex]

Answer:

n= -3 and n= -6

Step-by-step explanation:

[tex]n^2 = -18 -9n[/tex]

We need to solve this equation to find the value of n.

Rearranging:

[tex]n^2 +9n +18 =0[/tex]

This is a quadratic equation and we can solve by using factorization method.

We need to make factors of 18n^2 such that their sum is equal to 9n.

So solving,

[tex]n^2 + 9n +18 =0\\n^2 + 6n + 3n +18 =0\\n(n+6) + 3(n+6)=0\\(n+3)(n+6) =0\\=> n+3 =0 \,\, and n+6 =0\\n= -3 \,\,and \,\,n=-6[/tex]

Answer:

f(1) = 2

Step-by-step explanation:

Since y is a function of x, that is;

y = f(x)

f(1) implies the value of y when x = 1.

To obtain this value we draw the vertical line x = 1 and check where the line intersects the graph of f(x).

In this case, the line x = 1 will intersect with the graph of f(x) on the line y = 2. The function f(x) assumes the value 2 between x = 0 and x = 4. Therefore,

f(1) = 2

Answer:

f(1) = 2

Step-by-step explanation:

Answer:42

Step-by-step explanation:

7 multiplied by 6= 42

Insert 6 in the x place and solve

7x

7(6)

^^^The parentheses is the same as saying 7 × 6

so...

42

Hope this helped!

~Just a girl in love with Shawn Mendes

For this case we have the following functions:

[tex]f (x) = - x ^ 2 + 3x + 5\\g (x) = x ^ 2 + 2x[/tex]

We must find (f + g) (x), by definition we have to:

[tex](f + g) (x) = f (x) + g (x)[/tex]

So:

[tex](f + g) (x) = - x ^ 2 + 3x + 5 + (x ^ 2 + 2x)\\(f + g) (x) = - x ^ 2 + 3x + 5 + x ^ 2 + 2x\\(f + g) (x) = 5x + 5[/tex]

ANswer:

See attached image

Answer:

Step-by-step explanation:

see graph below

notice, the x-coordinate is the same for both points, thus is a vertical line.

Check the picture below.

To find the distance between the points (-16, -9) and (-16, -18), subtract the y-coordinates, which gives us a distance of 9 units.

To find the distance between the points (-16, -9) and (-16, -18), we can use the distance formula for two points in a Cartesian coordinate system. However, because the x-coordinates of the two points are the same, this means that the line connecting these two points is vertical, and we can simply subtract the y-coordinates to find the distance.

The distance formula in a two-dimensional Cartesian coordinate system is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Since the x-coordinates are identical, the formula simplifies to:

d = |y₂ - y₁|

Applying this to the points given:

d = |-18 - (-9)|

d = |-18 + 9|

d = |-9|

Therefore, the distance is 9 units.

Answer:

The equation is y = -x + 2.5

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the equation of a line is y = mx + c , where m is the slope

  of the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

- The slope of the line which passes through points (x1 , y1) , (x2 , y2)

  is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

* Lets solve the problem

∵ The line passes through the points (-8.5 , 11) and (5 , -2.5)

- Let point(x1 , y1) = (-8.5 , 11) and point (x2 , y2) = (5 , -2.5)

∴ x1 = -8.5 , x2 = 5 and y1 = 11 , y2 = -2.5

∴ [tex]m=\frac{-2.5-11}{5-(-8.5)}=\frac{-13.5}{5+8.5}=\frac{-13.5}{13.5}=-1[/tex]

∴ The slope of the line is -1

∵ y = mx + c

∴ y = -x + c

- To find c substitute x and y in the equation by the coordinates of

  one of the two points

∵ Point (5 , -2.5) lies on the line

∴ x = 5 at y = -2.5

∵ y = -x + c

∴ -2.5 = -(5) + c

∴ -2.5 = -5 + c

- Add 5 to both sides

∴ c = 2.5

∴ y = -x + 2.5

* The equation is y = -x + 2.5

The slope and y-intercept to get y = -x + 2.5.

The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula, we get m = (-2.5 - 11) / (5 - (-8.5)) = -13.5 / 13.5 = -1.

Next, we use the slope-intercept form of a line, y = mx + b, to find the y-intercept (b). Substituting one of the points and the slope into this equation, for example, (-8.5, 11), gives us 11 = (-1)(-8.5) + b, which simplifies to b = 2.5.

Therefore, the equation of the line is y = -x + 2.5.

Answer:6,916

6,916

How to find the number:

The decimal of seven percent is 0.07. Take that times 9880

For this case we must find the sum of the given series. For this we must expand the series for each value of k.

[tex](-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =[/tex]

Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.

[tex]-1-3-5-7 =\\-16[/tex]

The value of the series is -16

ANswer:

-16

Heya!

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

Things to know before we solve:

The "6" at the top means that the the sequence only goes to the 6th term.

k = 3 represents that the sequence starts with the 1st term.

(-2k + 5) represents the rule of the sequence, we can substitute 3, 4, 5, and 6 to solve for the terms of the sequence.

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

Solving for each term:

3rd term:

-2(3) + 5

-6 + 5

-1

4th term:

-2(4) + 5

-8 + 5

-3

5th term:

-2(5) + 5

-10 + 5

-5

6th term:

-2(6) + 5

-12 + 5

-7

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

Simplifying:

Write these terms in expanded form:

(-1) + (-3) + (-5) + (-7)

Find the sum of the series:

(-1) + (-3) + (-5) + (-7) = -16

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

Answer:

The sum of the series is -16

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

Best of Luck!

Answer:

-60.75

Step-by-step explanation:

-12 / 8 = -3/2

18 / -12 = -3/2

-27 / 18 = -3/2

This is a geometric sequence with a common ratio of -3/2.

an = 8 (-3/2)^(n-1)

The sixth term is:

a₆ = 8 (-3/2)^(6-1)

a₆ = 8 (-3/2)^5

a₆ = -60.75

Answer:

Nvm about those questions the answer is 1440 degrees

Step-by-step explanation:

Answer:

First option

b = (8) * Tan (30)

Step-by-step explanation:

Tan (B) = Oppo. / Adj.

Tan (B) = AC/BC

Tan (30) = b / 8

b = (8) * Tan (30)

Answer

First option

b = (8) * Tan (30)