6 What is the answer to this problem

Answer:

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

Step-by-step explanation:

From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.

[tex]V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r[/tex]

Therefore:

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

Answer:

The formula for radius of sphere is r = ∛(3V/4π)

or

r = (3V/4π)¹/³

Step-by-step explanation:

It is given formula for volume of sphere.

Volume of sphere = 4/3 πr³

Where r is the radius of sphere

To find the radius r of sphere

Volume V =  4/3 πr³

r³ = 3V/4π

r = ∛(3V/4π)

Therefore formula for radius of sphere is r = ∛(3V/4π)

or

r = (3V/4π)¹/³

Answer:

[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]

[tex]tan(x) =\±\sqrt{2}[/tex]

Step-by-step explanation:

By definition we know that:

[tex]sin ^ 2 (x) = 1-cos ^ 2 (x)\\\\tan (x) = \frac{sin(x)}{cos (x)}[/tex]

in this case we know that

[tex]cos(x) =\frac{1}{2}[/tex]

So how:

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

Substitute the values of cosine in the function

[tex]sin ^ 2 (x) = 1-\frac{1}{2}[/tex]

[tex]sin ^ 2 (x) = \frac{1}{2}[/tex]

[tex]sin(x) =\±\sqrt{\frac{1}{2}}[/tex]

[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]

Then how:

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

Substitute the values of sine and cosine in the function

[tex]tan(x) = \±\frac{\frac{\sqrt{2}}{2}}{\frac{1}{2}}=\sqrt{2}[/tex]

Answer:

Step-by-step Answer:

This question expects a choice out of the four answers.

We can reason it as follows:

If the angles had been 90-45-45, then the triangle would be isosceles with each leg equal to 14, and the area would be 14*14/2 =  192/2 = 96.

Now one of the base angles has been reduced from 45 to 35 (still assuming a right triangle), the other leg can only diminish, and therefore the area is LESS than 96.

We also realize that changing from 90 to 95 degrees will not change the area by a whole lot, so we are looking for a number LESS than 96, the only of which is 72.8.

The exact value, by solving the triangle,

the opposite side of 35 degrees is 10.483 (using sine rule), and

the area is 73.378 (using A=(1/2)a*b*sin(C), not far from 72.8, if we are looking for the exact value.

10/12 for 1. 12/10 for 2

Answer:

Look at explanation

Step-by-step explanation:

1. How many miles does the herd travel in an hour? : 10 divided by 12 and 10 divided by 1/12

2. How many hours does it take the herd to go 1 mile? : 12 divided by 10 and

1/10 x 12

This answer works on Imagine Math

Answer:

19.87 Pizzas are left

Step-by-step explanation:

To solve, just take 35 the number of starting pizzas and then subtract the number pizzas both of them consumed. So, 35 - 6.8 given 4/5 converts to 0.8 this leaves use with Bob's pizza consumption only at 28.2 pizza's left. Next, we are going to take 28.2 - 8.33 given 1/3 is .3333 repeating this then gives us the answer with having 19.87 pizzas left - although if it asks how many whole pizzas you would say 28 given you can't have .87 of a pizza.

A fraction is a way to describe a part of a whole. The amount of pizza left is 19 13/15.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

Given the total number of pizzas is 35. Also given, Bob eats 6 4/5 pizzas and Dave eats 8 1/3 pizzas. Therefore, the amount of pizza both together eat are,

Amount of pizza Bob and Dave eat = 6 4/5 + 8 1/3

                                                           = 34/5 + 25/3

                                                           = 102/15 + 125/15

                                                           = (102+125)/15

                                                           = 227/15

Amount of pizza left = 35 - 227/15

                                  = (525 - 227)/15

                                  = 298/15

                                  = 19 13/15

Hence, the amount of pizza left is 19 13/15.

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Martin's drink equation = option b, 11.99 + d = 14.48

Nora's calzone equation = option a, c - 3 = 9.49

Hope this helps

Answer:

Step-by-step explanation:

Given is table as follows

1500 75

2800 73

3500 72

4500 70

5000 66

6000 63

8000 60

8500 60

9000 57

9500 55

r -0.98649651

We get correlation coefficient is negative and near -1

Hence there is a strong negative correlation.

Whenever x increases y decreases with almost constant slope.

Answer:

correlation coefficient of the data ---->strong negative linear correlation

interpretation of the correlation coefficient ----> -0.986

Step-by-step explanation:

Answer:

It could be anywhere from eight to 15 members.

Step-by-step explanation:

Answer:

A. Count the members on each team

   Hurdles  = ⅜ × 40 = 3 × 5 = 15

Long jump = ⅘ × 40 = 4 × 8  = 32

Let's look at the two extremes.

B. Most people will compete in only one event

Then the teams will overlap by seven members (Figure 1).

C. All those in Hurdles compete in the Long Jump

Then 15 members will compete in both Hurdles and Long Jump (Figure 2).

Answer:

12 do both hurdles and long jump

Step-by-step explanation:

3/8 of the team does hurdles, so that number is 3/8·40 = 15.

Of those 15, 4/5 do long jump, so there are ...

4/5·15 = 12 . . . hurdlers who do long jump

Answer:

135

Step-by-step explanation:

[tex]\frac{5}{9}\times243=\frac{5\times243}{9}=

\frac{1250}{9}=\boxed{135}

[/tex]

The official formula is 2B+ Ph

where B is the area of a base of the prism, P is the perimeter of a base, and h is the height of the prism (distance between the two bases)

However, length x width x height can also be used

Answer:

c

Step-by-step explanation:

There are 6 red and 2 black balls.

The total number of balls = 2 + 6 = 8

The probability of drawing a black ball first is 2/8 = 1/4

The probability of drawing a red ball second is 6/7

P(black, red)=1/4 * 6/7 = 6/28 = 3/14

C

For this case we must find the inverse of the following function:[tex]f (x) = 4x[/tex]

We follow the steps below:

We change f(x) to y:

[tex]y = 4x[/tex]

We exchange the variables:

[tex]x = 4y[/tex]

We solve for and:

[tex]4y = x[/tex]

We divide between 4 on both sides of the equation:

[tex]y = \frac {x} {4}[/tex]

then y  by [tex]f ^ {-1} (x):[/tex]

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

ANswer:

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

387 customers or 930 customers

(27+12)x10x3 and 1,170

Answer:

Step-by-step explanation:

[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=x^2-2x\\\\g(x)=6x+4\\\\\text{Substitute:}\\\\(f+g)(x)=(x^2-2x)+(6x+4)=x^2-2x+6x+4\\\\\text{combine like terms}\\\\(f+g)(x)=x^2+(-2x+6x)+4=x^2+4x+4\\\\(f+g)(x)=0\Rightarrow x^2+4x+4=0\\\\x^2+2x+2x+4=0\\\\x(x+2)+2(x+2)=0\\\\(x+2)(x+2)+0\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\\\x=-2[/tex]

27\1000 is your rational form.

To simplify (9/100)^3/2, cube 9/100 to get 729/1000000 and then take the square root, which simplifies to 3/100 in rational form.

To simplify (9/100)^3/2 in rational form, we first understand that the exponent 3/2 can be broken down into two steps: first cubing the number, then taking the square root. Cubing 9/100 gives us (9^3)/(100^3), or 729/1000000. Then, taking the square root of this result and multiplying by the convenient factor of 1 in the form of 100/100, we simplify to 3/100, which is the result in rational form.

Answer:

Step-by-step explanation:

10^9 x 0.007

The resulting equation after substituting [tex]\( y = 4x \)[/tex] into [tex]\( x^2 + y^2 = 81 \)[/tex] is [tex]\( x^2 = \frac{81}{17} \)[/tex]

Let's isolate the variable [tex]\( y \)[/tex] in the first equation [tex]\( 3y = 12x \)[/tex]:

Divide both sides by 3 to solve for [tex]\( y \)[/tex]:

[tex]\[ y = 4x \][/tex]

Now that we have an expression for [tex]\( y \)[/tex], substitute it into the second equation [tex]\( x^2 + y^2 = 81 \)[/tex]:

[tex]\[ x^2 + (4x)^2 = 81 \][/tex]

Now simplify the equation:

[tex]\[ x^2 + 16x^2 = 81 \][/tex]

Combine like terms:

[tex]\[ 17x^2 = 81 \][/tex]

Divide both sides by 17 to solve for [tex]\( x^2 \)[/tex]:

[tex]\[ x^2 = \frac{81}{17} \][/tex]

So, the resulting equation after substituting [tex]\( y = 4x \)[/tex] into [tex]\( x^2 + y^2 = 81 \)[/tex] is [tex]\( x^2 = \frac{81}{17} \)[/tex].

4*2=8

4*1.5=6

2*1.5=3

8*2=16

2*6=12

2*3=6

16+12+6=34 ft

Total surface area is sum of area of all parts of surface. The surface area of the box is 34 squared feet.

The area of surface of a figure is sum of area of all sub-parts of it. It is because we want to get the total area of its surface.

For the given case, the box given has:

(its all because of assuming box is cuboid or say  rectangular prism)

Thus,

Surface area of box = twice of (area of top + area + left side + area of back)

Calculating these sub areas:

Area of top = [tex]2 \times 4 = 8 \: \rm ft^2[/tex]

Area of back = [tex]1\dfrac{1}{2} \times 4 = \dfrac{2+1}{2} \times 4 = 6 \: \rm ft^2[/tex]

Area of left side: [tex]1\dfrac{1}{2} \times 2 = \dfrac{2+1}{2} \times 2 = 3 \: \rm ft^2[/tex]

Thus,

Surface area of box = [tex]2(8 + 6 + 3) = 2 \times 17 = 34 \: \rm ft^2[/tex]

Thus,

The surface area of the box is 34 squared feet.

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Answer:

the solution is the last one.

Step-by-step explanation:

We know that for a second grade equation of the type:

ax^2 + bx + c = 0

The solution will be given by the quadratic formula, which states that:

x1 = [-b + sqrt(b^2 - 4ac)]/2a

x2 = [-b - sqrt(b^2 - 4ac)]/2a

So, according to the solution, we have:

x1 = [-5 + 2sqrt(7)]/3

Then:

2a = 3

-b = 5

b^2 - 4ac = 28

Solving each equation:

a = 2/3

b= -5

c = 9/8

None of the alternatives equals the values obtained before. So we can say that the expression is simplified.

Now we knoe what the first and second equation are wrong because b is not equal to -5.

So we have the other two alternatives, where b=-10. This gives us an idea that maybe, the equation is simplified by two. If that's the case:

then:

2a = 6

b= -10

b^2 - 4ac = 112

Then b=-10, a = 3 and c=-1

So the solution is the last one.

Final answer:

The correct quadratic equation with the solutions x = 5 ± 2√7 / 3 is 3x² - 10x - 1 = 0, determined by matching the given solution to the quadratic formula.

Explanation:

The student is asking which of the given quadratic equations has the solutions x = 5 ± 2√7 / 3. The correct equation that yields these solutions must be in the form ax² + bx + c = 0, where a, b, and c are constants.

To determine the right equation, we can work backwards from the given solutions using the quadratic formula:

x = ∛( -b ± √(b² - 4ac) ) / 2a

Comparing the solutions to the standard form obtained by the quadratic formula, we need to match the coefficients such that:

After testing each equation, we find that:

The discriminant for the last equation is (10)² - 4×3×(-1) = 100 + 12 = 112, which is 4×7, confirming that x = 5 ± 2√7 / 3 are indeed the solutions.

Answer: 1

Step-by-step explanation: the cosine function oscillates between the values -1 to 1

The amplitude of this particular function is understood to be 1

The maximum value that a graph of y = cos(x) assumes is y = 1.

In a triangle, the cos function (or cosine function) is the ratio of the base side to the hypotenuse.

cos(0°) = 1

cos(30°) = √3/2

cos(45°) = 1/√2

cos(60°) =  1/2

cos(90°) = 0

Cosine function is a periodic function and the value repeat themselves at an interval of 2π. The maximum value the cosine function achieves is y=1. The graph of the function is shown below:

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Answer:

pennies/first offer

Step-by-step explanation:

you would be rich

1x2=2  2^364= a lot of pennies

the pennies gives u the most money

It’s -125 and you welcome

I think the answer is b) C=.10x+25

Answer: B. C = .10x + 25

Step-by-step explanation: If the original equation uses .05, and that equation is .05x + 25 = C, then increasing it to .10 would mean that the new equation is .10x + 25.

Answer:

Step-by-step explanation:

Look at the picture.

ΔABC and ΔACD are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}[/tex]

We have:

[tex]AB=2+6=8,\ AC=x,\ AD=2[/tex]

Substitute:

[tex]\dfrac{8}{x}=\dfrac{x}{2}[/tex]           cross multiply

[tex]x^2=(8)(2)\\\\x^2=16\to x=\sqrt{16}\\\\x=4[/tex]

Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}f(1)=5\\f(n)=f(n-1)\cdot(-2)\end{array}\right}[/tex]

Step-by-step explanation:

[tex]f(n)=5\cdot(-2)^{n-1}\\\\f(1)\to\text{put n = 1 to the equation of}\ f(n):\\\\f(1)=5\cdcot(-2)^{1-1}=5\cdot(-2)^0=5\cdot1=5\\\\\text{calculate the common ratio:}\ \dfrac{f(n+1)}{f(n)}\\\\f(n+1)=5\cdot(-2)^{(n+1)-1}=5\cdot(-2)^{n+1-1}=5\cdot(-2)^n\\\\r=\dfrac{f(n+1)}{f(n)}=\dfrac{5\!\!\!\!\diagup^1\cdot(-2)^n}{5\!\!\!\!\diagup_1\cdot(-2)^{n-1}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\r=(-2)^{n-(n-1)}=(-2)^{n-n+1}=(-2)^1=-2\\\\\text{Therefore}\\\\f(n)=f(n-1)\cdiot(-2)[/tex]

Answer: ($2.50k) + $5

The distance you can ride is 6 kilometers.

($2.50 x 6) + $5 = $20

Answer:

[tex]2.50d+5\leq 20[/tex]

Step-by-step explanation:

Let d represent distance in kilometers.

We have been given that a taxi ride costs $2.50 per kilometer, so the cost of d kilometers would be [tex]2.50d[/tex] dollars.

We are also told that ride costs a fixed charge of $5, so total cost of d kilometers would be [tex]2.50d+5[/tex] dollars.

You have $20 to spend on taxi fare, so the total cost of riding d kilometers should be less than or equal to 20.

We can represent this information in an inequality as:

[tex]2.50d+5\leq 20[/tex]

Therefore, our required inequality would be [tex]2.50d+5\leq 20[/tex].

For this case we must simplify the following expression:

([tex](-6 ^ {\frac {1} {3}}) ^ {- 2}[/tex]

So, by definition of power properties we have:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex]\frac {1} {(- 6 ^ {\frac {1} {3}}) ^ 2} =\\\frac {1} {(- 6 ^ {\frac {1} {3}}) * (- 6 ^ {\frac {1} {3}})} =\\\frac {1} {(6 ^ {\frac {1} {3}}) * (6 ^ {\frac {1} {3}})} =\\\frac {1} {6 ^ {\frac {2} {3}}}[/tex]

ANswer:

[tex]\frac {1} {6 ^ {\frac {2} {3}}}[/tex]

Answer:

Step-by-step explanation:

1/2 over 4 = 15/4 over x

4/1=/15/4= 60/4*2/1=120/4=30

repeat the step but instead of 15/4 to 21/4

anyways it's 72

Final answer:

The actual distance the Patel family will travel from Smithville to Clarksville is approximately 282.66 miles.

Explanation:

The scale on the map is 12 inches equals 4 miles. To find the actual distance the Patel family will travel from Smithville to Jonesville, we can set up a proportion:

12 inches / 4 miles = 334 inches / x miles

Cross multiplying, we get:

12x = 1336

Dividing both sides by 12, we find that x = 111.33 miles. So, the Patel family will travel approximately 111.33 miles from Smithville to Jonesville.

Similarly, to find the actual distance they will travel from Jonesville to Clarksville, we can set up another proportion:

12 inches / 4 miles = 514 inches / y miles

Cross multiplying, we get:

12y = 2056

Dividing both sides by 12, we find that y = 171.33 miles. So, the Patel family will travel approximately 171.33 miles from Jonesville to Clarksville.

Therefore, the total actual distance the Patel family will travel by the time they reach Clarksville is approximately 111.33 miles + 171.33 miles = 282.66 miles.

ANSWER

84%,0.82,¾,⅓

EXPLANATION

Convert everything to decimals.

[tex] \frac{3}{4} = 0.75[/tex]

[tex] 84\% = 0.84[/tex]

[tex] \frac{1}{3} = 0.333....[/tex]

The last one is already in decimals.

[tex]0.82[/tex]

We can now see clearly, that

[tex]0.84 \: > \: 0.82 \: > \: 0.75 \: > \: 0.3333...[/tex]

This implies that,

[tex]84\% \: > \: 0.82 \: > \: \frac{3}{4} \: > \: \frac{1}{3} [/tex]

Hence from highest to least, we have

84%,0.82,¾,⅓

Answer:

The first choice is correct;

(-∞,∞)

Step-by-step explanation:

We have been given the following functions;

[tex]f(x)=x^{2}-1\\\\g(x)=2x-3[/tex]

We are to determine the domain of (fog)(x).

The composite function, (fog)(x) is obtained by substituting g(x) in place of x in the function f(x);

(fog)(x) = f[g(x)] = [tex](2x-3)^{2}-1[/tex]

Clearly the function will be defined everywhere on the number line since it has no undefined points or domain constraints. The domain is thus;

(-∞,∞)

For this case we have the following functions:

[tex]f (x) = x ^ 2-1\\g (x) = 2x-3[/tex]

We must find [tex](f_ {0} g) (x):[/tex]

By definition of composite functions we have to:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {0} g) (x) = (2x-3) ^ 2-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 9-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 8[/tex]

The domain of the function is given by all the values for which the function is defined.

The function is defined for all real numbers.

Answer:

Domain: (-∞,∞)