Find the volume of this sphere.
Use 3 for pie.
V≈ [?]cm³
V = πr³
10 cm

Answer:

cbrt(x+1)-3=y

Step-by-step explanation:

The inverse of a function is when the domain and range are swapped. So to find the inverse simply swap the x and y in the equation and then solve for y.

[tex]y = (x+3)^3-1\\x=(y+3)^3-1\\x+1=(y+3)^3\\\sqrt[3]{x+1}=y+3\\\sqrt[3]{x+1}-3=y[/tex]

Answer:

111 cm^2

Step-by-step explanation:

h = 11.4

d = 5  so  r (radius) = 2.5

Surface Area of a Cone Formula: πr^2 + πrs

s represents the slant height of the cone, lets represent this with a drawing.

We have the values of h and r, but we don't have the value of s, meaning we have to find it. We can do this by using pythagorean theorem.

a^2 + b^2 = c^2

These three values can come together to create a right triangle which we can seperate from the rest of the diagram, now we can find s.

s = √(11.4^2 + 2.5^2)   so  s = 11.67

now that we have all of the pieces, we can plug back into the original surface area formula. πr^2 + πrs

π(2.5^2) + π(2.5)(11.67) = 111.29 cm^2 or 111 cm^2

The surface area of the solid cone requiring paint will be 111 square cm.

Let d be the diameter of the base circle, l be the slant height, and h be the height of the cone.

Then the lateral surface area of the cone will be

SA = πrl + πr²

Then the slant height is given as

l² = r² + h²

The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.

Then the radius of the base circle will be

r = 5 / 2

r = 2.5 cm

The length of the slant height will be

l² = 11.4² + 2.5²

l² = 136.21

 l = 11.67

Then the surface area of the solid cone requiring paint will be

SA = π × 2.5 × 11.67 + π × 2.5²

SA = 29.18π + 6.25π

SA = 35.43π

SA = 111.3

SA ≈ 111 square cm

The surface area of the solid cone requiring paint will be 111 square cm.

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Answer:

-4

+3

12

-0.5, 12.25

x = -0.5

Step-by-step explanation:

The x intercepts are the values of x when y = 0 ie the roots of the equation
[tex]-x^2 -x +12 = 0[/tex]

or

[tex]x^2 + x - 12 = 0[/tex]

We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3

y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12

Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x

Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5

Plugging this value of x into the original function gives the vertex y value
[tex]y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25[/tex]

The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5

The graph of the quadratic function shows these values

Answer:

3/5 ..................................  6/9

Step-by-s4tep explanation:

Answer:

300 meters per minute

Step-by-step explanation:

Step 1

Determine the fraction of the total distance for each part of the race.

Given:

[tex]\begin{aligned} \implies \sf 2nd\:part & = \sf \dfrac{2}{5}\:of\:remaining\:distance\\ & = \sf \dfrac{2}{5} \times\left(1-\dfrac{4}{9}\right)\\& = \sf \dfrac{2}{9}\:of\:total\:distance\end{aligned}[/tex]

[tex]\begin{aligned}\implies \sf 3rd\:part & = \sf 1-1st\:part-2nd\:part\\& = \sf 1-\dfrac{4}{9}-\dfrac{2}{9}\\& = \sf \dfrac{1}{3}\:of\:total\:distance\end{aligned}[/tex]

Step 2

Determine the distance of the third part of the race.

Given:

[tex]\begin{aligned}\sf Distance & = \sf speed \times time\\& = \sf 300 \times 15\\& = \sf 4500 \:\:meters\end{aligned}[/tex]

Step 3

If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:

[tex]\begin{aligned} \sf Total\:distance & = \sf 4500 \times 3\\& = \sf 13500\:meters \end{aligned}[/tex]

Step 4

Determine the distance of the 1st part of the race:

[tex]\begin{aligned}\sf Distance\:of\:1st\:part\:of\:race & = \sf \dfrac{4}{9} \:of\:total\:distance\\& = \sf \dfrac{4}{9} \times 13500\\& = \sf 6000\:meters \end{aligned}[/tex]

Step 5

Determine the speed of the 1st part of the race:

Given:

[tex]\begin{aligned}\sf Speed\:of\:1st\:part\:of\:race & = \sf \dfrac{distance}{time}\\& = \sf \dfrac{6000}{20}\\ & = \sf 300\:meters\:per\:minute\end{aligned}[/tex]

Answer:

39

Step-by-step explanation:

Okay so there are 52 cards in a deck and there are 4 of each card. 4 kings 4 Queens 4 Jacks 4 Ace 4 Twos 4 Threes 4 fours 4 fives 4 sixes 4 sevens 4 eights 4 nines 4 tens. One from each group is a heart there are 13 groups so therefore subtract 13 from 52.

Answer:

Slope is 3/4

Step-by-step explanation:

Gradient means slope. So, to find the slope without using the formula, look at two points then count up until you're in line with the other point, then count right until you reach the other point. Remember it must be written as rise/run.

I hope this explanation makes sense!

The points I will use is (0,-2) and (4,1).

Slope is 3/4.

Hope this helps!

If not, I am sorry.

The value of the expression 2 2/3 - (-3 2/6) is 6

The expression is given as:

2 2/3 - (-3 2/6)

Open the bracket

2 2/3 + 3 2/6

Express as improper fractions

8/3 + 20/6

Rewrite as:

16/6 +20/6

Evaluate the sum

36/6

Evaluate the quotient

6

Hence, the value of 2 2/3 - (-3 2/6) is 6

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Answer:

There were 120 marbles to start

Step-by-step explanation:

Let x be the number of marbles at the start

x* 5/12 = number of marbles given away

1 -5/12 = 7/12 = fraction of marbles left

x * 7/12 = number of marbles left

x * 7/12 = 70

Multiply each side by 12/7

x *7/12 * 12/7 = 70 * 12/7

x =120

There were 120 marbles to start

Answer:

  (c)  (-30, 10)

Step-by-step explanation:

Two points will be on the same graph of a proportional relationship if the ratio of values y/x is the same.

__

The given point (x, y) = (60, -20) has a ratio k = y/x = -20/60 = -1/3.

The offered points have y/x ratios ...

(a) 30/-10 = -3

(b) -15/30 = -1/2

(c) 10/-30 = -1/3 . . . . . . the point you are looking for is (-30, 10)

(d) -30/80 = -3/8

Answer:

B. Matter

Explanation:

When rocks break down and become smaller ex: mountains eventually becoming sand, the matter does not disappear or get destroyed, it becomes smaller particles, but the matter is always preserved.

Hope It Helps!!!

Answer:

matter

Step-by-step explanation:

The conservation of matter states that

Here big matters gets down into smaller pieces

but they are not destroyed

Answer:

t+s = 9

4t+9s=51

tulips and succulents combined is 9 plants

the amount of money they have combined is $51

Answer:

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.

Answer:

0.93

Step-by-step explanation:

Use the chain rule to differentiate both sides of the given equation with respect to [tex]x[/tex] :

[tex]y = 2 f(g(x))[/tex]

[tex]\dfrac{dy}{dx} = y' = 2 f'(g(x)) g'(x)[/tex]

Differentiate again with the product and chain rules to get the second derivative :

[tex]\dfrac{d^2y}{dx^2} = y'' = \boxed{2 f'(g(x)) g''(x) + 2 f''(g(x)) g'(x)^2}[/tex]

(D)

Answer:

[tex]\fbox {400.41 feet}[/tex]

Step-by-step explanation:

Here we need to take the tan ratio of the angle.

⇒ tan 4° = 28/x = 0.0699268119

⇒ x = 28/0.0699268119

⇒ x = 400.41 feet

Answer:

4

Step-by-step explanation:

In triangle JKL, the side opposite the 30 degree angle, JL, is half the length of the hypotenuse, KL. Thus, JL has a length of

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

In triangle JML, the hypotenuse is

[tex] \sqrt{2} [/tex]

times the length of the leg, meaning that x = 4

Answer:

x < 3

Step-by-step explanation:

The last step is to divide by -2. When you divide by a negative number you must reverse (flip) the inequality symbol.

-6 < -2x

-6/-2 > -2x/-2

3 > x

This is the same as

x < 3 (see the pointy side pointing at the x and the wide open side facing the 3)

Answer:

65

Step-by-step explanation:

its simple math

Answer:

x+5=12.          x = 7,

7x=21.            x = 3,

b-2/3=5/6.     b = 1.5,

3/4x=6x=8.    x = 1/3,

45=3(x+1).      x = 14,

22.5+1.5x.      x = 15,

20+(5•9).        $65

Step-by-step explanation:

[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

[tex] \sf \dfrac{2}{15} \div \dfrac{3}{20} = \dfrac{2 \times 20}{15 \times 3} = \dfrac{40}{45} = \dfrac{8}{9} [/tex]

Answer :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \Rrightarrow \dfrac{8}{9} [/tex]

I hope I've helped : )

[tex]\dfrac{1}{50}[/tex]

[tex] \cfrac{2}{15} \times \cfrac{3}{20} [/tex]

[tex] \cfrac{2 \times 3}{15 \times 20} [/tex]

[tex] \cfrac{6}{15 \times 20} [/tex]

[tex] \cfrac{6}{300} [/tex]

[tex] \cfrac{1}{50} [/tex]

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

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Answer:

c ×=4, only

Step-by-step explanation:

4*-8×+16=0

16-32=-16

-16=-16

Answer:

D. x=4 only

Step-by-step explanation:

You can solve using the quadratic equation which is [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]

where in this case a=1, b=-8, and c=16. But there is any easier way to solve the equation. You can solve by completing the square which consists of moving the constant to the right side and then adding [tex](\frac{b}{2})^2[/tex]. To both sides that way you can rewrite the left side as a perfect square binomial. This is because [tex](x+b)^2[/tex] will expand to [tex]x^2 + 2xb + b^2[/tex]. So when you add [tex](\frac{b}{2})^2[/tex] to both equations. You're able to rewrite the left side as [tex](x+(\frac{b}{2}))^2[/tex]. Because once you expand it out, it becomes [tex]x^2 + 2(\frac{b}{2})x + (\frac{b}{2})^2[/tex]. Which simplifies to [tex]x^2 + bx + (\frac{b}{2})^2[/tex] which is the original equation. In this case there is no need to move the constant, which in this case is 16, to the other side. Since if you calculate the value of (-8/2)^2 it's equal to 16! So this can already be written as a perfect square binomial.

So the equation becomes

[tex]0 = (x+\frac{b}{2})^2[/tex]

Plug values in

[tex]0 = (x+(-\frac{8}{2}))^2[/tex]

Simplify

[tex]0 = (x-4)^2[/tex]

Take the square root of both sides

[tex]0 = x-4[/tex]

Add 4 to both sides

[tex]4 = x[/tex]

Answer:

C.

Step-by-step explanation:

The reds are counting up in whole numbers by one integer.

Hope this helps!

If not, I am sorry.

Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, In the graph,

we can see that we have a vertical asymptote at x = -1.

Hence, This means that the denominator of the rational equation becomes zero when x = -1.

So the equation must be:

⇒ y = 1 / (x + 1)

Here, The denominator is x + 1, and as expected, it becomes zero when, x = -1.

Then, we conclude that the correct option is C.

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The t-test might be more useful in actual practice when standard deviation or variance is unknown.

The t-test is used to determine how the averages of various data sets differ from one another.

When variance is not provided, the T-test, a particular kind of parametric test, is used to determine how the means of two sets of data differ from one another. When variance is provided, the Z-test indicates a hypothesis test that determines whether the means of two datasets differ from one another.

Example of t-test: If you flip a coin 1,000 times, for instance, you can discover that the outcome is distributed normally over all trials.

Example of z-test: We are conducting research using information gathered from cohorts of students who have taken Elementary Statistics in the past.

T-tests are typically more suitable when addressing issues with small sample sizes, whereas z-tests are suitable for large sample sizes.

Using the t-test for an ordinal variable, their frequency is not even close to a normal distribution, and the arithmetic mean offers an unsuitable measure of location.

Because we frequently don't know the population standard deviation, Z-Tests have this drawback.

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First term f = 1

If first four terms are f, f + d, f + 2d, f + 3d

f + f + d + f + 2d + f + 3d = 100

4f + 6d = 100 (divided by 2 , both sides )

2f + 3d = 50

2 + 3d = 50

3d = 50 – 2

3d = 48

d = 48/3

d = 16

The arithmetic sequence is 1, 17, 33, 49, ………….

Answer:

[tex]\sf\large\blue{\underbrace{\red{itz \: jass*}}}:[/tex]

Step-by-step explanation:

[tex]\sf\large\green{\underbrace{\red{hlo \: \: sat \: shri \: akal \: ji \: \: \: *}}}:[/tex]

Answer:

The answer is 0.45 pounds for an apple and 0.3 pounds for a pear

Step-by-step explanation:

Answer:

Cost of each apple: [tex]0.45[/tex].

Cost of each pear: [tex]0.30[/tex].

Step-by-step explanation:

Let [tex]x[/tex] denote the cost of each apple. Let [tex]y[/tex] denote the cost of each pear.

The question states that the cost of [tex]4[/tex] apples and [tex]3[/tex] pears is [tex]2.70[/tex]. Thus:

[tex]4\, x + 3\, y = 2.70[/tex].

Likewise, since the cost of [tex]2[/tex] apples and [tex]5[/tex] pears is [tex]2.40[/tex]:

[tex]2\, x + 5\, y = 2.40[/tex].

Solve this system of equations for [tex]x[/tex] and [tex]y[/tex] to find the price of each fruit.

[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 2\, x + 5\, y = 2.40\end{aligned}\right.[/tex].

Multiply both sides of the equation [tex]2\, x + 5\, y = 2.40[/tex] by [tex]2[/tex] to match the coefficient of [tex]x[/tex] in the first equation:

[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & (2\times 2)\, x + (2 \times 5)\, y = (2 \times 2.40)\end{aligned}\right.[/tex].

[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 4\, x + 10\, y = 4.80 \end{aligned}\right.[/tex].

Substitute the first equation from the new equation to eliminate [tex]x[/tex] and solve for [tex]y[/tex]:

[tex]\begin{aligned}& 4\, x + 10\, y - (4\, x +3\, y) = 4.80 - 2.70\end{aligned}[/tex].

[tex]10\, y - 3\, y = 2.10[/tex].

[tex]7\, y = 2.10[/tex].

[tex]y = 0.30[/tex].

Substitute [tex]y = 0.30[/tex] into an equation from the original system to eliminate [tex]y[/tex] and solve for [tex]x[/tex].

[tex]2\, x + 5\, y = 2.40[/tex].

[tex]2\, x + 5 \times 0.30 = 2.40[/tex].

[tex]2\, x = 0.90[/tex].

[tex]x = 0.45[/tex].

Thus, [tex]x = 0.45[/tex] and [tex]y = 0.30[/tex].

In other words, the price of each apple would be [tex]0.45[/tex]. The price of each pear would be [tex]0.30[/tex].

Answer:

m = -3

c = 2

Step-by-step explanation:

This equation is given in slope-intercept form. The general structure of these equations is:

y = mx + c

In this form, "m" represents the slope and "c" represents the y-intercept. As you have been given the entire equation, the only thing you have to do is rearrange the equation to find which values correspond with the variables.

y = 2 - 3x  -----> y = -3x + 2

Therefore,

m = -3

c = 2

Answer:

g(b-3) = -b + 7

Step-by-step explanation:

Plug in the value (b-3) as x into the equation

g(b-3) = -(b-3) + 4

distribute the negative sign

g(b-3) = -b + 3 + 4

combine like terms

g(b-3) = -b + 7

The solution set is 1 ≥ f ≥ -4, and the correct number line is the one in option A.

Here we have the inequality:

-1 ≤ -2f + 1 ≤ 9

To solve this, we need to isolate the "f" on the middle.

First, we can subtract 1 in both sides to get:

-2  ≤ -2f ≤ 8

Now we need to divide both sides by -2, remember that this will change the direction of the symbols:

-2/-2 ≥ f ≥ 8/-2

1 ≥ f ≥ -4

So we need to have a line that starts at -4 and ends at 1, the correct option is number line A.

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The range of the function lies between (0,8) to (1.5,1.25).

Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The given function is:-

f(x) = 3x² -9x + 8

The value of the range will be from (0,8) to ( 1.5,1.25). When we plot the graph of the function the value of the range lies between the points (0,8) to ( 1.5,1.25). The graph is attached with the answer.

The domain of the function will be all the values of the real numbers for the function ranges from ( 0, ∞ ).

Therefore the range of the function lies between (0,8) to (1.5,1.25).

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Your question is incomplete. Below you will find the missing content.

Which series of transformations will not map figure H onto itself?

A. O(x+0, y-2), reflection over y = 1

B. O(x+2, y-0), reflection over x=3

C. O(x+3, y+3), reflection over y = -x +7

D. O(x-3, y-3), reflection over y = -x +2

The correct option is Option D: the series of transformation O(x-3, y-3), reflection over y = -x +2 will not map figure H onto itself.

Here given a square with its 4 vertices at coordinates (2,1), (1,2), (2,3) and (3,2).

By checking all the options

Option A:

1st transformation (x+0, y-2) will map 4 vertices of the square into points of coordinates such as

(2,1) → (2,-1)

(1,2) → (1,0)

(2,3) → (2,1)

(3,2) → (3,0)

next transformation which is the reflection over y=1 gives the coordinates (x,2-y)

(2,-1) → (2,3)

(1,0) → (1,2)

(2,1) → (2,1)

(3,0) → (3,2)

These new points are exactly the same as the vertices of the initial square.

Option B:

1st transformation (x+2, y-0) will map 4 vertices of the square into points of coordinates such as

(2,1) → (4,1)

(1,2) → (3,2)

(2,3) → (4,3)

(3,2) → (5,2)

next transformation which is the reflection over x=3 gives the coordinates (6-x,y)

(4,1) → (2,1)

(3,2) → (3,2)

(4,3) → (2,3)

(5,2) → (1,2)

These new points are exactly the same as the vertices of the initial square.

Option C:

1st transformation (x+3, y+3) will map 4 vertices of the square into points of coordinates such as

(2,1) → (5,4)

(1,2) → (4,5)

(2,3) → (5,6)

(3,2) → (6,5)

next transformation which is the reflection over y=-x+7 gives the coordinates such as

(5,4) → (3,2)

(4,5) → (2,3)

(5,6) → (1,2)

(6,5) → (2,1)

These new points are exactly the same as the vertices of the initial square.

Option D:

1st transformation (x-3, y-3) will map 4 vertices of the square into points of coordinates such as

(2,1) → (-1,-2)

(1,2) → (-2,-1)

(2,3) → (-1,0)

(3,2) → (0,-1)

next transformation which is the reflection over y=-x+2 gives the coordinates such as

(-1,-2) → (4,3)

(-2,-1) → (3,4)

(-1,0) → (2,3)

(0,-1) → (3,2)

These new points are not matching with the vertices of the initial square.

Therefore the correct option is Option D: O(x-3, y-3), reflection over y = -x +2 will not map figure H onto itself.

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