Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y-
intercept to the nearest integer.
X
y
y =
5 6
12 -2
r=
7
00
8 9 10 11 12
3
-1-4
6
0
Identify the correlation coefficient. Round to the nearest thousandth if necessary.

The length of the radius of the sphere is 15 in.

It is a three-dimensional figure and has a diameter and a radius and the volume of a sphere is 4/3πr³.

We have,

Volume of the sphere = 14130 in³

So,

4/3πr³ = 14130 _____(1)

Solve for r.

4/3 x 3.14 x r³ = 14130

keep r on one side and the rest on the other side.

r³ = 14130 x 3 / 4 x 3.14

Cube root on both sides.

r³ = 3375

∛r³ = ∛3375

[ 15 x 15 x 15 = 3375 ]

So,

r = 15

Thus,

The radius of the sphere is 15 in.

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Answer:  x=3, y=-1

Step-by-step explanation:

2x+y=5

2y=2x-8

In equation 1, y=5-2x.

Substitute this value in equation 2.

2(5-2x)=2x-8

10-4x=2x-8

Thus,

4x+2x=10+8 (collecting terms)

6x=18

x=3

Now, we said earlier that y=5-2x.

Therefore, y=5-2(3) [because x=3]

y=5-6

y=-1

Hope this helps :]

The probability of picking three black cards in a row, without replacement, from a standard deck of 52 playing cards is 2/17, or approximately 0.1176 (rounded to four decimal places).

The probability of picking a black card on the first draw = 26/52 = 1/2

        (since there are 26 black cards in the deck)

The probability of picking a black card on the second draw, given that a one was picked on the first draw and the card is not replaced = 25/51,    

        (since there are now only 25 black cards left out)

The probability of picking a black card on the third draw, given that the ones picked on the first two draws are not replaced = 24/50 = 12/25,

        (since there are now only 24 black cards left out)

To pick three black cards in a row, we need to multiply the probabilities of each individual draw = (1/2) * (25/51) * (12/25) = 6/51

Simplifying this fraction, we get = 6/51 = 2/17

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Answer: 0.1 decimal 1/9 fraction

Step-by-step explanation:

Answer:

0.1 or 1/9 i think so but I am sure

There are 10 cars in a race, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.

An arrangement of particulars in a specific order is appertained to as a permutation. Then, the factors of sets are arranged in a direct or successional order. For case, the set A = ,6 has a permutation of 2, which is. There's no other way to organise the factors of set A, as you can see.

There are 10 cars in the race,

Three cars finish the race in the 1st ,2nd and 3rd order

1st finish the race have 10 chances

P(A) = 10

2nd finish the race have 9 chances

P(B) = 9

3rd finish the race have 8 chances

P(C) = 8

The number in which this can be put,

= P(A) x P(B) x P(C)

= 10*9*8

=720 ways

Therefore, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.

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The conclusion is that the bag filling machine appears to be working correctly at this setting.

Based on the information provided, the manufacturer conducted a hypothesis test to determine if the bags are underfilled at the 420 gram setting. The null hypothesis (H0) is that the bags are not underfilled, while the alternative hypothesis (H1) is that the bags are underfilled.

Since the manufacturer failed to reject the null hypothesis at the 0.01 level of significance, this means that there is not enough evidence to support the claim that the bags are underfilled at the 420 gram setting. In other words, the bag filling machine appears to be working correctly at this setting.

It's important to note that the conclusion may change if the sample size or the level of significance is different. Additionally, other factors such as the accuracy of the measuring device used or the consistency of the banana chips themselves may also impact the results.

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The inequality 26/9 > x represents a line with an open circle at 26/9 going toward positive infinity represented by an arrow.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality [tex]2\frac{8}{9} > x[/tex].

26/9 > x.

Now, As the inequality is strictly greater than 26/9 it would be represented by a line open circled at 26/9 and going towards +∞.

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The second option has the better value-for-money.

To find the price per gram, you need to take the quotient between the cost and the mass for each case.

The first brand costs $29.49 for 250 grams, then the cost is:

c = $29.49/250g = $0.12 per gram.

The other brand costs $69.99 for 750 grams, then the cost per gram is:

C = $69.99/750g = $0.09 per gram

We can see that the second option has the better vale-for-money.

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Answer:

113.75

Step-by-step explanation:

13$ x 8.75 h (45 minutes is 3/4 of an hour) = $113.75

keeping in mind that an hour has 60 minutes, so you're really getting paid $13 per 60 minutes, so now, 8 hours and 45 minutes is just 8*60 + 45 = 525 minutes.

[tex]\begin{array}{ccll} \$&minutes\\ \cline{1-2} 13 & 60\\ x& 525 \end{array} \implies \cfrac{13}{x}~~=~~\cfrac{60}{525} \\\\\\ \cfrac{ 13 }{ x } ~~=~~ \cfrac{ 4 }{ 35 }\implies 455=4x\implies \cfrac{455}{4}=x\implies 113.75=x[/tex]

Volume of solid generated by revolving the plane region about the y-axis is [tex]\pi \left(\frac{1392}{7}\right)[/tex]

The shell method formula is used to find the volume of a solid of revolution, formed by rotating a region about a line that is parallel to one of its sides.

The formula for the shell method is V = 2π* ∫r(x)h(x) dx where V is the volume of the solid, r(x) is the distance between the axis of revolution and the curve being rotated and h(x) is the height of the shell at x.

The shell method can be used when the region is more easily described by an equation in one variable. In contrast, the disk/washer method is used when the region is more easily described by an equation in two variables.

It is a powerful tool for solving many types of problems in calculus, physics and engineering. The shell method formula helps to determine the volume of a solid of revolution, which is an important concept in various fields of study.

Given:

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

y = 27

x = 0

Shell method:

V = [tex]2\pi \int\limits_c^d p(y)h(y) dy[/tex]

Then the volume of a solid is

V = [tex]2\pi \int\limits_0^4x(27 - x^\frac{3}{2})dx[/tex]

= [tex]2\pi \left[ \int\limits_0^4 27x dx - \int\limits_0^4 x^\frac{5}{2}dx\right][/tex]

[tex]= 34\pi \left[\frac{x^2}{2} \right]_0^4 - \frac{4}{7} \pi \left[ x^\frac{7}{2} \right]_0^4[/tex]

[tex]= 34\pi \left(\frac{4^2}{2} \right) - \frac{4\pi}{7}(4)^\frac{7}{2}[/tex]

[tex]= 4\pi \left( \frac{68}{7} - \frac{2^7}{7} \right)[/tex]

[tex]= 4\pi \left( \frac{476 - 128}{7} \right)[/tex]

[tex]4\pi \left( \frac{348}{7} \right)[/tex]

[tex]= \pi \left( \frac{1392}{7} \right)[/tex]

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PLEASE GIVE BRAINLIEST
thank you and have a good day :)

Answer:

5.6294995342131E-32

Step-by-step explanation:

the common ratio is 1/5, therefore with the equation an = a x r

                                                                                                       n-1

we can figure out the answer to this by plugging in the common ratio for r,

and n as the number in the sequence that we want to obtain.

a is simply the first number (1000)

Step-by-step explanation:

x current age of the father

y current age of the son

first equation (x-4)+(y-4)=27 so x=27+4+4-y=35-y

second equation (y+5) : (x+5)= 2:7

so (y+5)*7=(x+5)*2

let's replace x we found at the first equation with the one at second equation

(y+5)*7=(35-y+5)*2

7y+35=(40-y)*2

7y+35=80-2y

7y+2y=80-35

9y=45

y=5

x=35-y=35-5=30

Answer:

11

Step-by-step explanation:

Let's call the number of games of Balloon Bouncer that Amy played as "x".

Amy started with 35 tokens and used 2 for Roll-and-Score, so she had 35 - 2 = 33 tokens left.

Each game of Balloon Bouncer costs 3 tokens, so the total number of tokens used for Balloon Bouncer games is 3x.

Therefore, the equation to find the number of games Amy played is:

33 = 3x

Solving for x, we get:

x = 11

So Amy played 11 games of Balloon Bouncer.

Answer: 3g + 3 = 35

Step-by-step explanation:

The statement is incorrect. The replacement of three 2s with two threes will change the sum.

For example, consider the set {2, 2, 2}. The sum of this set is 6. However, if we replace three 2s with two threes, the new set becomes {3, 3}, and its sum is 6, which is different from the original sum. Hence, replacing a set of three 2s with a set of two threes does change the sum. An integer is a  whole number that can be positive, negative, or zero. Integers are numbers that don't have any fractional or decimal component. Some examples of integers are: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, and so on. The set of integers is denoted by the symbol "Z", which stands for Zahlen, the German word for "numbers". Integers are an important mathematical concept used in many branches of mathematics and science, including algebra, number theory, and computer science.

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Complete Question

In any set of positive integers the replacement of a set of three 2s with a set of two threes will not change the sum" State whether the statement was correct or incorrect.

The ordered pair (2,10) means that the cost to feed 200 animals is of $10,000.

The general format of an ordered pair is given as follows:

(x,y).

The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.

The variables for this problem are given as follows:

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The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11

From the question, we have the following parameters that can be used in our computation:

The graphs

The lines are absolute function graphs, and they can be represented as

y = a|x - h| + k

Where

Vertex = (h, k)

For the blue line, we have

(h, k) = (2, -5) and (x, y) = (0, -4)

So, we have

-4 = a|0 - 2| - 5

2a = 1

a = 1/2

So, the equation is y = 1/2|x - 2| + 5

For the red line, we have

(h, k) = (-2, 3) and (x, y) = (0, -11)

So, we have

-11 = a|0 + 2| + 3

2a = -14

a = -7

So, the equation is y = -7|x + 2| - 11

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The snail moves a distance of 40 yards in one hour as it moves at a speed of 2 feet per minute.

We can start by converting the speed of the snail from feet per minute to yards per hour, since the distance moved is given in yards per hour.

There are 60 minutes in an hour, so the snail's speed in yards per hour is:

2 feet per minute * 60 minutes per hour * (1/3) yards per foot = 40 yards per hour

Hence,

The snail moves a distance of 40 yards in one hour.

Since we are given that the snail has moved a total of 3 yards, we can find the amount of time it took by dividing the distance by the rate:

time = distance / rate

time = 3 yards / 40 yards per hour

time = 0.075 hours or 4.5 minutes

Therefore, the snail will move a distance of 3 yards after 4.5 minutes and distance of 40 yards in one hour.

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The Average daily balance of the given scenario is $2083.

Suppose we're given that:

P_v = Present value of the loan amount

r = rate of interest (compound interest) per period of time

n = number of period of time in which loan is to be paid off

P = A fixed period payment needed to be done for paying off the loan in n number of periods.

Then, we get:

[tex]P = \dfrac{r\times P_v}{1 - (1 + r)^{-n}}[/tex]

Given;

APR= 25%

Cost of wheels and tires= $1500

Time=14days

Cost of brake calipers and leaking= $500

Time=30days

Now,

P= 25x2000/1-(1+25)^-30

P=50000/24

P=2083

Therefore, the monthly balance of loan will be $2083.

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By determining the value of x when y = 0, (x, 0), and the value of y when x = 0, respectively, the x-intercept and y-intercept are determined (0, y).

A two-variable equation with a line-shaped graph is referred to as a linear equation. A collection of coordinate plane points that are all the solutions to the linear equation make up the graph. If all of the variables have true numerical values, the equation can be graphed by first drawing a sufficient number of points to identify a pattern, then connecting those points to include all of the points.

A linear equation is represented in standard form as

Ax+By=C,A,B≠0

The equation for y must first be solved before you may graph a linear equation in its usual form.

The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).

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If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h  .

A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.

We have to find the rate at which the radius is changing after 6.5 hours.

So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.

Volume Of Sphere is  V = (4/3)πr³ and dV/dt = -11 ft³/h ;

So,  dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt)  ;

derivative of volume formula with respect to "r", we get:

⇒ dV/dr = 4πr²   ;

Substituting the given values in chain rule equation, we get:

⇒ -11 = (4/3)πr² × dr/dt  ;

⇒ dr/dt = -11/((4/3)πr²)

For  rate of change of the radius when t = 6.5 hours, we find the radius at that time.

The initial volume of the snowball = 260 ft³.

After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be:  V = 260 - (11 × 6.5) = 188.5 ft³   ;

So , V = (4/3)πr³

⇒ 188.5 = (4/3)πr³

⇒ r³ = (188.5 × 3 / (4π))   ;

≈ 3.55ft

Now we substitute r = 3.55 feet

⇒ dr/dt = -11/[(4/3)π(3.55)²]  ;

⇒ dr/dt ≈ -0.208 ft/h  ;

Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing  .

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The inverse of f(x) has no restriction on the domain.

The graph of the inverse function is given below.

The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = (x - 3)²

The inverse of f(x).

Step 1:

Make f(x) = y

y = (x - 3)²

Step 2:

Interchange x and y

x = (y - 3)²

Step 3:

Solve for y.

square root on both sides.

x² = y - 3

y = x² + 3

So,

[tex]f^{-1}[/tex](x) = x² + 3.

a)

[tex]f^{-1}[/tex](x) = x² + 3

we see that for any values of x, [tex]f^{-1}[/tex](x) is a function.

So,

There is no restriction on the domain.

b)

The graph is given below.

c)

The inverse equation is

[tex]f^{-1}[/tex](x) = x² + 3.

Thus,

The inverse of f(x) has no restriction on the domain.

The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.

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Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.

Acceleration is the rate of change of the velocity of an object with respect to time.

Jonathan's initial velocity, u = 12 m/s East

His final velocity, v = 5 m/s East

The time taken, t = 23 seconds

We can use the formula for acceleration:

a = (v - u) / t

Substituting the given values, we get:

a = (5 m/s - 12 m/s) / 23 s

a = -7 m/s / 23 s

a = -0.3043 m/s^2 East

Therefore, Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.

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The average velocity from 4 to 8 seconds is given as follows:

v = [position at 8 seconds - position at 4 seconds]/4.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

The change in the distance from 4 to 8 seconds is given as follows:

position at 8 seconds - position at 4 seconds

The change in the time from 4 to 8 seconds is given as follows:

8 - 4 = 4 seconds.

Hence the velocity is of:

v = [position at 8 seconds - position at 4 seconds]/4.

The problem is incomplete, hence the general procedure to obtain the average velocity was presented.

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Answer:

Step-by-step explanation:

The profit is £1,370. Then the percentage profit of the company will be 124.54%.

A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.

The profit is given as,

Profit = Selling price - Cost price

The number of pins left after the donation to charity is given as,

⇒ (1 - 0.35) x 1,000

⇒ 0.65 x 1,000

⇒ 650 pins

The selling price when 60% are sold for £3 and 40% are sold for £5 is given as,

Selling price = 0.60 x 650 x £3 + 0.40 x 650 x £5

Selling price = £1,170 + £1,300

Selling price = £2,470

The cost price is given as,

Cost price = £1.10 x 1,000

Cost price = £1,100

The profit is given as,

P = £2,470 - £1,100

P = £1,370

Then the percent of profit is given as,

P = [(£1,370) / £1,100] x 100

P = 124.54%

The profit is £1,370. Then the percentage profit of the company will be 124.54%.

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Answer:

Step-by-step explanation:

A square is a 4 sided polygon in which all of its side lengths are equal and the diagonals are also be

The distance is decreasing with time meaning that the object is going back to the starting point.

When distance decreases with time, it means that the object is moving towards its starting point or moving in the opposite direction from its initial position. In other words, the object is moving backwards or reversing its direction of motion.

Distance is a measure of the total amount of ground covered by an object in motion, while time is a measure of how long it takes the object to cover that distance. If the object is moving towards its starting point, it means that it is covering less and less distance over time, or the distance it covers is decreasing.

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Answer:

taking your points

Step-by-step explanation:

The given statement about the intermediate value theorem is false

The given statement is

"Intermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"

But according to Intermediate value theorem "if a continuous function f with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"

So if we takes discontinuous function the given statement will be wrong

Therefore, the statement is false

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