The volume of the sphere is
500
-n cubic units.
3
What is the value of x?
O4 units
O 5 units
O 8 units
O 10 units

Answer:

-7

Step-by-step explanation:

63/9 but there is an odd number of negative numbers so negative answer

Answer:

The fraction of the pocket money she left is 1/8.

Step-by-step explanation:

Let the total pocket money is p.

Spent on Monday = p/2

Amount left = p - p/2 = p/2  

Spent on Tuesday = 2/3 of p/2 = p/3

Amount left = p/2 - p/3 = p/6

Spent on Wednesday = 1/4 of p/6 = p/24

Amount left = p/6 - p/24 = p/8

So, the fraction of the pocket money she left is 1/8.  

Answer:

8/15

Step-by-step explanation:

The ratio of perpendicular to base is tan B .

Here ,

=> tan B = 8 ft/ 15ft

=> tan B = 8/15

Answer:

20

Step-by-step explanation:

f = 2f - 20

f - 2f = - 20

- f = - 20

f = 20

Answer:

126

Step-by-step explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

[tex]$^9C_4$[/tex]

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

[tex]$^9C_4=\frac{9!}{4!(9-4)!}$[/tex]

      [tex]$=\frac{9!}{5! \ 4!}$[/tex]

     [tex]$=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$[/tex]

    = 126

Answer:

-24.4 ≥ w

Step-by-step explanation:

-13.4 ≥ 6.7 + 4.3 + w

-13.4 - 6.7 - 4.3 ≥ w

-24.4 ≥ w

Answer:

answer will be the integer only which was added to zero

Answer:

B.

Step-by-step explanation:

Since the numbers in the root is all the same, lets say [tex]\sqrt{2}[/tex] is a variable.

7x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex]

Group with like terms:

7x[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

Combine like terms:

8x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

There you have it! Since all the square roots are the same thing, we can treat them like variables.

the answer is B..................

answer:

to test whether agraph is linear

Answer:

2/60 = 1/30 = 3.3%

Step-by-step explanation:

Answer:

the answer is -3

Step-by-step explanation:

0.7x - 1.4 = -3.5

add 1.4 to both sides of the equation

you're left with 0.7x = -2.1

then divide both sides by 0.7

you're left with your answer of -3

Answer:

Step-by-step explanation:

z = (k*x*y) / w²

Where,

k = constant of proportionality

z = 72 when x = 80, y = 30 and w = 5

z = (k*x*y) / w²

72 = (k * 80 * 30) / 5²

72 = 2400k / 25

Cross product

72 * 25 = 2400k

1800 = 2,400k

k = 2,400/1800

k = 24/18

= 4/3

k = 1 1/3

k = 1.33

find z when x = 20, y = 60 and w=9

z = (k*x*y) / w²

z = (1.33 * 20 * 60) / 9²

z = (1596) / 81

Cross product

81z = 1596

z = 1596/81

z = 19.703703703703

Approximately,

z = 19.7

Answer:

B

Step-by-step explanation:

B was missed. You have to convert this from hours into minutes before you can deal with seconds.

Hello!

8 × 3 + 10 - 13 × 2 =

= 24 + 10 - 13 × 2 =

= 24 + 10 - 26 =

= 34 - 26 =

= 8

Good luck! :)

Answer:

8

Step-by-step explanation:

According to bdmas rule

First multiply 8 and 3 or 13 and 2

Then, there will be 24 + 10 - 26

Then add 24 + 10, there will be 34

and again minus by 26

Then finally answer will be 8

Answer:

The number of FM listereners are 24000.

Step-by-step explanation:

Let the listeners of FM are p and thus the istereners of AM are 5p.

According to the question,

p + 5 p = 144000

6 p = 144000

p = 24000

The number of FM listereners are 24000.

Answer:

[tex]10x - \frac{1}{x} = 3 \\ 10x = 3 + \frac{1}{x} \\ 10x = \frac{3x + 1}{x} \\ 10x \times x = 3x + 1 \\ 10 {x}^{2} = 3x + 1 \\ 10 {x}^{2} - 3x - 1 = 0 \\ 10 {x}^{2} - 5x + 2x - 1 = 0 \\ 5x(2x - 1) + 1(2x - 1) = 0 \\ (5x + 1)(2x - 1) = 0 \\ \\ 5x + 1 = 0 \\ 5x = - 1 \\ x = \frac{ - 1}{5} \\ \\ 2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2} [/tex]

hope this helps you.

Have a nice day!

Answer:

160=130+x

x=160-130

x=30

Answer:

(C) 0.3(10 + 4h) = 0.25(6h)

Step-by-step explanation:

Here's what we know about Fernando's fees:

$10 is the initial fee

$4 is the hourly fee (h)

Saves 30% (also written as 0.3) of the total cost (includes initial and hourly fee)

Here's what we know about Brenna's fees:

No initial fee

$6 is the hourly fee (h)

Saves 25% (also written as 0.25) of the total cost (just the hourly fee because she doesn't have an initial fee)

We want to find which hour Fernando and Brenna will have saved the same amount of money.

To do this, let's first set up an equation for Fernando and Brenna separately:

Fernando's equation:

0.3(10 + 4h) = how much money he saves from the total cost

Brenna's equation:

0.25(6h) = how much money she saves from the total cost

Now we set them equal to each other:

0.3(10 + 4h) = 0.25(6h)

There's your answer!

Hope it helps (●'◡'●)

Answer:

is there is no value of April

Step-by-step explanation:

so the value of the month April is zero

Answer:

2.5 years

Step-by-step explanation:

The given amount invested, which is the principal, P = $16,800

The simple interest rate, R = 5% per annum

The intended total value of the investment, A = $18,900

The simple interest on the principal, I = A - P

∴ I = $18,900 - $16,800 = $2,100

The formula for the simple interest, I, is given as follows;

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Therefore, we have;

[tex]T = \dfrac{I \times 100}{P \times R}[/tex]

Plugging in the values, gives;

[tex]T = \dfrac{2,100 \times 100}{16,800 \times 5} =2.5[/tex]

The time it will take the investment to grow to $18,900 is T = 2.5 years

Answer:

20

Step-by-step explanation:

3 (b + a) = c

3 (4 + 5) = 7

12 + 15 = 7

27 = 7

27 - 7

20

[tex]\huge\boxed{ \sf{Answer}} [/tex]

Given,

[tex]a = 5 \\ b = 4 \\ c = 7[/tex]

And the equation we need to solve is,

[tex]3(b + a) = c[/tex]

To find the answer, you need to substitute the values of a, b & c in the equation.

[tex]3(b + a) = c \\ 3b + 3a = c \\ ( 3 \times 4) +( 3 \times 5) = 7 \\ 12 + 15 = 7 \\ 12 + 15 - 7 = 0 \\ = 27 - 7 \\ = 20[/tex]

↦ The answer is 20.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

Step-by-step explanation:

Six liters of paint will cover 50 square meters.

  6L ⇒ 50m²

then,

  1L ⇒ 50/6 m²

  9L ⇒ 50 × [tex]\frac{9}{6}[/tex] m²

       ⇒ 75 m²

Answer:

[tex]\rm\displaystyle 0,\pm\pi [/tex]

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

===========================

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]

factor out tanγ:

[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]

divide both sides by tanαtanβ-1 and that yields:

[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]

multiply both numerator and denominator by-1 which yields:

[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]

recall angle sum indentity of tan:

[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]

let α+β be t and transform:

[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]

remember that tan(t)=tan(t±kπ) so

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]

therefore when k is 1 we obtain:

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]

isolate -α-β to left hand side and change its sign:

[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]

when is 0:

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]

likewise by Opposite Angle Identity we obtain:

[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]

isolate -α-β to left hand side and change its sign:

[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]

and we're done!

Answer:

-π, 0, and π

Step-by-step explanation:

You can solve for tan y :

tan y (tan a + tan B - 1) = tan a + tan y

Assuming tan a + tan B ≠ 1, we obtain

[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]

which implies that

y = -a - B + kπ

for some integer k. Thus

a + B + y = kπ

With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.

It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so

[tex]B=\frac{\pi }{2} - a + k\pi[/tex]

but with the given limitation we must have k = 0, because 0 < π/2 - a < π.

On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again

k = 0, so we obtain

[tex]\frac{\pi }{2} - a=-a[/tex]

a contradiction.

Answer:

x = 27.5.

Step-by-step explanation:

There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.

So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.

With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.

Therefore, x = 27.5.

Answer:

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

Step-by-step explanation:

Given

[tex]\{(5, -9), (6, -6), (-3, 8), (9, -6)\}[/tex]

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

[tex]\{(1, -1), (-5, 7), (4, -9), (-9, 7)\}[/tex]

[tex]\{(8, -9), (-3, -6), (-4, 4), (1, -5)\}[/tex]

Required

Which is not a function

An ordered pair is represented as:

[tex]\{(x_1,y_1),(x_2,y_2),(x_3,y_3),..........,(x_n,y_n)\}[/tex]

However, for the ordered pair to be a function; all the x values must be unique (i.e. not repeated)

From options (a) to (d), option (b) has -6 repeated twice. Hence, it is not a function.

Answer:

See below

Step-by-step explanation:

Let side AB equal x. Since triangle ABC is equilateral, sides AB, BC, and Ac are all the same length, x. In any isosceles triangle(equilateral is a type of isosceles triangle) the median is the same as the altitude and angle bisector. This means we can say that AD is also a median. A median splits a side into two equal sections, so we can say BD = DC = x / 2. We are given that DC = CE, so we can also say CE = DC = x / 2. Now, we can use the pythagorean theorem to find the length of AD. So we get the equation:

AB^2 - BD^2 = AD^2

We have the values of AB and BD, so we can substitute them and solve for AD:

x^2 - (x/2)^2 = AD^2

x^2 - x^2 / 4 = AD^2

AD^2 = 3x^2 / 4

AD = x√3 / 2

DE is equal to the sum of DC and CE because of segment addition postulate, so we can say DE = DC + CE = x / 2 + x/ 2 = x. We can again use the pythagorean theorem to find the length of AE:

AD^2 + DE^2 = AE^2

(x√3 / 2)^2 + x^2 = AE^2

3x^2 / 4 + x^2 = AE^2

AE^2 = 7x^2 / 4

AE = x√7 / 2

Now, we know(from before) that AE squared is 7x^2 / 4. We can say EC squared is x^2 / 4 because EC is x / 2 and x / 2 squared is x^2 / 4. We can also notice that AE squared is 7 times EC squared because 7x^2 / 4 = 7 * x^2 / 4

Therefore, we can come to the conclusion AE^2 = 7 EC^2

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes 4 2 3 5 5 3 1

Juice (milliliters) 177 234 202 140 155 210 265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice

Step-by-step explanation:

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes             4        2      3        5       5      3        1

Juice (milliliters)  177    234   202   140   155   210   265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

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