A computer can sort x objects in t seconds, as modeled by the function
below:
t=0.003x^2 +0.001x
How many objects are required to keep the computer busy for exactly 7
seconds?
Round to the nearest whole object.

ANSWER

[tex]x = 5 {y}^{2} + 10[/tex]

EXPLANATION

The given equation is :

[tex]y = 5 {x}^{2} + 10[/tex]

To find the inverse of this function, we interchange x and y to obtain:

[tex]x= 5 {y}^{2} + 10[/tex]

We simplify this function to solve for y.

Therefore the equation that needs to be simplified to find the inverse of the given function is

[tex]x = 5 {y}^{2} + 10[/tex]

The correct choice is is the first option.

Answer: x = 5y2 + 10

Step-by-step explanation: A is the correct answer on the Quiz!

The domain of the given function is:

                  [tex]x\geq 5[/tex] i.e. [5,∞)

Domain of a function--

The domain of a function is the set of all the possible values of x for which the function is defined.

That is it is the collection of all the points except the excluded values of the function.

The function f(x) is a square root function which is given by:

          [tex]f(x)=2\sqrt{x-5}[/tex]

We know that the domain of the function depends on the domain of the square root quantity.

We know that: a square root function is well defined when the quantity under the square root is non-negative

i.e.

[tex]x-5\geq 0\\\\i.e.\\\\x\geq 5[/tex]

Answer:

12 gallons of 20% salt solution

Step-by-step explanation:

Let

x -----> the number of gallons of 20% salt solution

we know that

20%=20/100=0.20

40%=40/100=0.40

25%=25/100=0.25

so

0.20(x)+0.40(4)=0.25(x+4)

Solve for x

0.20x+1.60=0.25x+1

0.25x-0.20x=1.60-1

0.05x=0.60

x=12 gallons

By solving a linear equation, we will see that we must use 12 gallons of 20% salt solution.

If we mix x gallons of 20% salt with 4 gallons of 40% salt, we will have a total mass of (x + 4 gall).

And the concentration on the left side is the known one, and we want the concentration of the mixture to e 25%, so we will have that:

x*0.20 + 4gal*0.40 = (x + 4gal)*0.25

(the percentages must be written in decimal form).

Now we can solve this linear equation for x:

x*0.20 + 4gal*0.40 = (x + 4gal)*0.25

4gal*0.40 = x*0.25 - x*0.20 + 4gal*0.25

4gal*0.40 -  4gal*0.25 =  x*0.25 - x*0.20

4gal*0.15 = x*0.05

(4gal*0.15)/0.05 = x = 12

So you should use 12 gallons of the 20% salt solution.

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Answer: 0.5

Step-by-step explanation:

1-5 is half

and 6-10 is half

The probability that the number she chooses is greater than 5 is 5/10 or 1/2.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Elena randomly chooses a number from 1 to 10.

We have to find the probability that the chosen number is greater than 5.

Total amount of numbers from 1 to 10 = 10

The numbers greater than 5 from 1 to 10 are 6, 7, 8, 9 and 10.

Amount of numbers greater than 5 = 5

Probability = Number of desired outcomes / Total number of outcomes

                  = 5 / 10

                  = 1/2

Hence the required probability is 1/2.

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Answer:

[tex]6x^{13}y^{17}[/tex]

Step-by-step explanation:

We need to multiply

[tex]3x^8y^9.2x^5y^8[/tex]

We know the exponent rule of multiplication:

[tex]x^a y^b . x^cy^d = x^{a+c}y^{b+d}[/tex]

If the bases are same the powers are added.

So,

[tex]=3*2 *x^8*x^5*y^9*y^8\\=^{8+5}y^{9+8}\\=6x^{13}y^{17}[/tex]

So, the answer is:

[tex]6x^{13}y^{17}[/tex]

Final answer:

Bred can paint the wall in 6 different ways using 8 horizontal stripes, considering a maximum of 2 colors out of blue, red, and white with enough paint for 5 stripes of each color.

Explanation:

The question at hand involves combinatorics, which is a branch of mathematics dealing with combinations and permutations. Bred can paint a wall with 8 horizontal stripes using at most 2 colors from the options of blue, red, and white, with enough paint for 5 stripes of each color. Since he is using at most 2 colors, we need to calculate the number of combinations for each pair of colors as well as the individual colors. The possible pairs with their respective numbers of combinations are blue-red, blue-white, and red-white. For blue-red and blue-white, he can paint 5 blue stripes and 3 stripes of the other color, while for red-white, he can paint 5 red stripes and 3 white stripes.

The combinations for each pair would be:

Blue-Red: 5 blue + 3 red

Blue-White: 5 blue + 3 white

Red-White: 5 red + 3 white

Additionally, Bred can choose to use only one color. Thus, for each of the colors blue, red, and white, there will only be one way to paint the wall.

Therefore, the total different ways Bred can paint the wall are the sum of the combinations for each pair plus the individual color options:

For pair Blue-Red: 1 way

For pair Blue-White: 1 way

For pair Red-White: 1 way

Only Blue: 1 way

Only Red: 1 way

Only White: 1 way

Adding these up gives us a total of 6 different ways to paint the wall.

if you add all the x points together the girl will have more text messages

Answer: 537-254=283

Hope this helped!

Answer:

The answer is 283.

Step-by-step explanation:

Subtract the total of 537, by the number of people playing instruments, 254.

537 - 254 = 283

283 is the number of people without instruments.

Hope this helps! :)

Answer:

(f * g)(x) = 4x^3 - x^2

[tex]4x^{3}-x^{2}[/tex]

Step-by-step explanation:

We have been given the following functions;

f(x) = 4x - 1

g(x) = x^2

We are required to determine;

(f * g)(x)

This simply means we shall be finding the product of the two functions given;

(f * g)(x) =  f(x)*g(x)

(f * g)(x) =  x^2 * (4x - 1 )

we open the brackets by multiplying each term by x^2

(f * g)(x) = x^2(4x) + x^2(-1)

(f * g)(x) = 4x^3 - x^2

Answer:

A.

Step-by-step explanation:

four terms are needed. 1-4

so that eliminates bottom 2 choices

Answer:

The correct option is A) [tex](7+3\cdot 1)+(7+3\cdot 2)+(7+3\cdot 3)+(7+3\cdot 4)[/tex].

Step-by-step explanation:

Consider the provided series.

[tex]\sum_{n=1}^{4}(3n+7)[/tex]

Substitute the value of n = 1,2,3 and 4 respectively.

[tex](3\cdot 1+7)+(3\cdot 2+7)+(3\cdot 3+7)+(3\cdot 4+7)[/tex]

Which can be written as:

[tex](7+3\cdot 1)+(7+3\cdot 2)+(7+3\cdot 3)+(7+3\cdot 4)[/tex]

Therefore, the correct option is A) [tex](7+3\cdot 1)+(7+3\cdot 2)+(7+3\cdot 3)+(7+3\cdot 4)[/tex].

Answer:

he received about 750,000 letters a month.

Step-by-step explanation:

multiply the letters received per day=25,000

by the number of days in the month=30

so: 25,000 × 30= about 750,000 letters

Answer: You've probably already seen the basic method for graphing straight lines; namely, make a T-chart, plot some points, put your ruler against them, and draw the line. But the "nice" form of a straight line's equation (being the slope-intercept form, y = mx + b) can make graphing even simpler and faster.

Step-by-step explanation:

The equation of the line must be 2x - 1

The equation of the line that represents an equation of a line with a slope of 2 and a point on the line of (1, 2) can be written in the form:

[tex]y-y_0=m(x-x_0)[/tex]

m is the slope of the line

(x0, y0) is the point on the line

Substitute the given parameters into the formula to have:

[tex]y-2=2(x-1)\\y - 1= 2x - 2\\y = 2x -2+1\\y = 2x-1[/tex]

Hence the equation of the line must be y= 2x - 1

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Hi I am gonna I wanna go to see the

Answer:

10/3 hours

Step-by-step explanation:

12x=15x-10

12x-15x=15x-10-15x

-3x=-10

-3x/-3=-10/-3

x=10/3

Answer: Sally will catch up with Jane after 50 minutes.

Step-by-step explanation:

Since we have given that

Speed of Jane of biking = 12 mph

After 10 minutes,

Speed of Sally of biking = 15 mph

Let the distance be 'x'.

According to question, our required equation becomes,

[tex]\dfrac{x}{12}-\dfrac{x}{15}=\dfrac{10}{60}\\\\\dfrac{5x-4x}{60}=\dfrac{1}{6}\\\\\dfrac{1x}{60}=\dfrac{1}{6}\\\\x=10\ miles[/tex]

Thus, total distance would be 10 miles.

So, the time taken by Sally to catch up with Jane is given by

[tex]\dfrac{10}{12}=\dfrac{5}{6}\times 60=50\ minutes[/tex]

Hence, Sally will catch up with Jane after 50 minutes.

Answer:

No, the inverse function does not pass the vertical line test.

Step-by-step explanation:

Remember that [tex]h(x)=y[/tex]. To find the inverse of our function we are going to invert x and y and solve for y:

[tex]h(x)=x^2+3[/tex]

[tex]y=x^2+3[/tex]

[tex]x=y^2+3[/tex]

[tex]x-3=y^2[/tex]

[tex]y=\pm\sqrt{x-3}[/tex]

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

Now we can graph our function an perform the vertical line test (check the attached picture).

Remember that the vertical line test is a visual way of determine if a relation is a function. A relation is a function if and only if it only has one value of y for each value of x. In other words, a relation is a function if a vertical line only intercepts the graph of the function once.

As you can see in the picture, the vertical line x = 15 intercepts the function twice, so the inverse function h(x) is not a function.

We can conclude that the correct answer is: No, the inverse function does not pass the vertical line test.

Answer:

a. No, the inverse function does not pass horizontal line test

Step-by-step explanation:

h(x) = x² + 3

y = x² + 3

y - 3 = x² ⇒  x² = y - 3

[tex]\sqrt{x^{2} } = \sqrt{y-3} \\[/tex][tex]

x =  \sqrt{y - 3} , -\sqrt{y-3}[/tex]

h^{-1} x = \sqrt{x - 3} , -\sqrt{x-3}[/tex]

The function h^{-1} x fails the horizontal line test, it is not a one to one function.

So, option a is correct

For this case we have that by definition, the domain of a function, is given for all the values for which the function is defined.

We have:

[tex]f (x) = \frac {x + 1} {x ^ 2-6x + 8}[/tex]

The given function is not defined when the denominator is equal to zero. That is to say:

[tex]x ^ 2-6x + 8 = 0[/tex]

To find the roots we factor, we look for two numbers that when multiplied give as a result "8" and when added as a result "-6". These numbers are:

[tex]-4-2 = -6\\-4 * -2 = 8[/tex]

Thus, the factored polynomial is:

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

That is to say:

[tex]x_ {1} = 4\\x_ {2} = 2[/tex]

Makes the denominator of the function 0.

Then the domain is given by:

All real numbers, except 2 and 4.

Answer:

x |x≠2,4

Answer:

is d on edge

Answer:

x = sugar cookies dough

y = chocolate chips cookies

13x + 6y = 252

8x + 12y = 288

x = 12, y = 16

Step-by-step explanation:

x = sugar cookies dough

y = chocolate chips cookies

Equation

13x + 6y = 252 ------------ Equation 1

8x + 12y = 288 ------------ Equation 2

Equation 1 x 2

26x + 12y = 504 ------------ Equation 3

Equation 3 - Equation 2

18x = 216

x = 12

Sub x = 12 into Equation 1

13 (12) + 6y = 252

156 + 6y = 252

6y = 96

y = 16

The cost of one package of sugar cookie dough is $12 and one package of chocolate chip cookie dough is $16 .

Equation is what relates an unknown variables with other known variables by an equal sign.

It is asked to find

cost of each of one package of sugar cookie dough

one package of chocolate chip cookie dough.

Let the price of sugar cookies dough packet be $x

Let the price of  chocolate chips cookies packet be $y

Then from the given data

13x + 6y = 252

8x + 12y = 288

On solving the equations by elimination method

18x = 216

x = 12

On substituting x = 12

13 (12) + 6y = 252

156 + 6y = 252

6y = 96

y = 16

Therefore the cost of one package of sugar cookie dough is $12 and one package of chocolate chip cookie dough is $16 .

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let's firstly convert the mixed fractions to improper fractions and then sum them up.

[tex]\bf \stackrel{mixed}{2\frac{2}{8}}\implies \cfrac{2\cdot 8+2}{8}\implies \stackrel{improper}{\cfrac{18}{8}}~\hfill \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{18}{8}+\cfrac{9}{4}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)18+(2)9}{8}}\implies \cfrac{18+18}{8}\implies \cfrac{36}{8}\implies \cfrac{9}{2}\implies 4\frac{1}{2}[/tex]

Log base 3 of 4 + log base 3 of 11= log base 3 of 4•11; Answers is 11

Answer:

The number is 6

Step-by-step explanation:

We let the number be x. If we subtract -2 from x we obtain the following result;

x - (-2)

This can be simplified to yield the following result;

x - (-2) = x + 2

we use the rule that negative multiplied by negative yields a positive sign.

We are further informed that the result of the above operation is 8, therefore;

x + 2 = 8

Solving for x yields;

x = 8 -2

x = 6

the number that we are looking for is 6.

The question asks us to find the number that results in 8 when -2 is subtracted from it. To solve this, we can set up an equation. Let x be the number we are looking for:

x - (-2) = 8

We know that in subtraction, we change the sign of the subtracted number and then follow the addition rules. This means our equation becomes:

x + 2 = 8

Now we subtract 2 from both sides to find the value of x:

x = 8 - 2

x = 6

Thus, the number that we are looking for is 6.

Answer:

B. 2

Step-by-step explanation:

To find the slope of the line, use the slope formula. Use the coordinates of the two red dots to find the slope of the line.

slope = y2-y1 / x2-x1

         = 2-(-2) / 3-1

         = 4/2 = 2

Hope this helps!

The answers here is

B. 2

Answer:

I would say C Sets 2 and 3 contain outliers.

Step-by-step explanation:

Set 2 has an outlier of 90, and set 3 contains an outlier of 40. 40 is not as much of an outlier as 90, so I'm not absolutely sure.

Answer:

-Sets 2 and 3 contain outliers.

Step-by-step explanation:

Mean is the average value of the set. Mean deviation is the difference of the values of the set when compared to the mean.

In set 1 the values are between 50 and 60. This means that the mean will also be between 50 and 60.

In set 2 there is one outlier that is 38. So, the range of the values are between 38 and 90. More values are between 30 and 40 so the mean will be in this range. So (90 - the mean in the range between 30 and 40) will be a large number.

The same goes for set 3.

Answer:

the answer is the second one 45

Answer:

C) 24

Step-by-step explanation:

1. Since the perimeter of a triangle is the sum of its three sides, you can write the following expression, solve for x and get the value of each side.

[tex]2x+(2x+2)+(2x+4)=24\\2x+2x+2+2x+4=24\\6x+2+4=24\\6x+6=24\\6x=24-6\\6x=18\\x=\frac{18}{6}\\x=3[/tex]

2. So, replacing the value of x, you can calculate the values of each side of the triangle:

First side:

[tex]2x=2(3)=6[/tex]

Second side:

[tex](2x+2)=(2(3)+2)=6+2=8[/tex]

Third side:

[tex](2x+4)=(2(3)+4)=6+4=10[/tex]

As the larger side is the third one, it is the hypotenuse. So, the base and the  height.

3. The formula to find the area of the right triangle is given by the expression:

[tex]A=\frac{b*h}{2}[/tex]

Where b is the base and h is the height of the triangle, so replacing the values we found, we have the following:

[tex]A=\frac{8*6}{2}[/tex]

[tex]A=\frac{48}{2}[/tex]

[tex]A=24[/tex]

Therefore the answer is C) 24

For the circumference, you actually multiply by 20 because of the formula πd = C [OR 2πr = C]. You meant to double the radius.

Answer:

Option C. is the correct option.

Step-by-step explanation:

A bag contains 10 red, 6 blue and 4 green jelly beans.

A jelly bean is chosen at random from the bag then probability that the ball is blue will be = [tex]\frac{\text{Total number of blue balls}}{\text{Total number of balls in the bag}}[/tex]

P(B) = [tex]\frac{6}{20}[/tex]

Now we know that probability that the ball picked from the bag is not blue

= 1 - P(B)

= 1 - [tex]\frac{6}{20}[/tex]

= [tex]\frac{20 - 6}{20}[/tex]

= [tex]\frac{14}{20}[/tex]

= [tex]\frac{7}{10}[/tex]

Therefore, option C. is the correct option.

The probability is the ratio of non-blue jelly beans to the total, resulting in 7/10. The correct answer is C) 7/10.

To determine the probability that a randomly chosen jelly bean from the bag is not blue, we first need to find the total number of jelly beans:

Total number of jelly beans = 10 + 6 + 4 = 20

Next, we need to calculate the number of jelly beans that are not blue:

Number of non-blue jelly beans = 10 + 4 = 14

The probability of choosing a jelly bean that is not blue is given by the ratio of non-blue jelly beans to the total number of jelly beans:

Probability = Number of non-blue jelly beans / Total number of jelly beans = 14 / 20 = 7 / 10.

Answer:

A

Step-by-step explanation:

because youre doing more bushels its adding and youd be solving for d

Answer:700in (squared)

Step-by-step explanation:

Answer:

700in^2

Step-by-step explanation:

The side facing us: 10*15=150. There are 2 of those sides, so 150*2=300

Right and left: 8*10*2=160

Top and bottom: 15*8*2=240

300+160+240=700

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]