Jeff can weed the garden twice as fast as his sister Julia. Together they can weed the garden in 3 hours. How long would it take each of them working alone?
A) 4.5 hours; Julia 9 hours
B) 7.5 hours; Julia 15 hours
C) 4.5 hours; Julia 2.25 hours
D) 0.5 hours; Julia 1 hours

The correct representation of the given set using the listing method is {2, 3, 4, 5}. The second option is correct.

The set {x | x I, 2 ≤ x ≤ 5} can be represented using the listing method.

Here, the set consists of all values of x that satisfy the condition 2 ≤ x ≤ 5. The values of x within this range are 2, 3, 4, and 5.

Therefore, the set can be represented as:

{2, 3, 4, 5}

This set includes all the values of x that are greater than or equal to 2 and less than or equal to 5, as indicated by the condition 2 ≤ x ≤ 5.

The elements listed in the set are 2, 3, 4, and 5, and no other values are included.

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Answer:

D) The relationship between y-intercepts cannot be determined.

Step-by-step explanation:

We have been given two different functions f(x) and g(x). Now we need to find about what can be determined about their y-intercepts. Then match with the correct choice from the given choices:

A) The function f(x) has a higher y-intercept.

B) The function g(x) has a higher y-intercept.

C) They both have the same y-intercept.

D) The relationship between y-intercepts cannot be determined.

We know that y-intercept is the y of function value when x=0.

In the table of g(x), we don't see any point that has x=0

So we can't find the y-intercept for g(x)

Hence correct choice is :

D) The relationship between y-intercepts cannot be determined.

The answer is:

C) They both have the same y-intercept.

In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.

So,

- Finding the equation of the g(x):

Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-8}{1-(-1)}=\frac{-8}{2}=-4[/tex]

Now, calculating the value of "b" using the first point (-1,8)  and the slope of the function, we have:

[tex]y=mx+b[/tex]

[tex]y=-x+b[/tex]

[tex]8=-4(-1)+b[/tex]

[tex]b=4[/tex]

So, the equation of g(x) is:

[tex]y=-4x+4[/tex]

- Comparing the y-intercepts of f(x) and g(x):

Finding the y-intercept of f(x),  by making "x" equal to 0, we have:

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

We have that the function f(x) has its y-intercept at "y" equal to 4.

Finding the y-intercept of g(x), by making "x" equal to 0, we have:

[tex]y=-4x+4[/tex]

[tex]y=-4*(0)+4[/tex]

[tex]y=4[/tex]

We have that the function g(x) has its y-intercept at "y" equal to 4.

Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:

C) They both have the same y-intercept.

Have a nice day!

I'm going to assume that you meant y = mx + b not y = my + b

To do this move 7x to the right side by subtracting it to both sides

(7x - 7x) - y = 8 - 7x

0 - y = 8 -7x

-y = 8 - 7x

Y still isn't full isolated! There is still the negative sign that you have to get rid of. To do this divide -1 to both sides

-y/-1 = (8 - 7x)/ -1

y = -8 + 7x

y = 7x - 8

Hope this helped!

~Just a girl in love with Shawn Mendes

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} n&a_n\\ \cline{1-2} 1&4\\ &\\ 2&\stackrel{4(-3)}{-12}\\ &\\ 3&\stackrel{-12(-3)}{36}\\ \cline{1-2} \end{array}\qquad \impliedby \textit{common ratio of "r" is -3} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=-3\\ a_1=4\\ n=15 \end{cases} \\\\\\ S_{15}\implies \displaystyle\sum\limits_{i=4}^{15}~4(-3)^{i-1}[/tex]

Answer:

[tex]\sum_{n=4}^{15}4(-3)^{n-1}[/tex]

Step-by-step explanation:

The given sequence is 4, -12, 36

We can see there is a common ratio

[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-12}{4}=(-3)[/tex]

[tex]\frac{a_{2} }{a_{3} }[/tex] = [tex]\frac{36}{-12}=(-3)[/tex]

Therefore, the given sequence is a geometric sequence.

Now we have to determine the sigma notation of the sum for term 4 through term 15.

Since explicit formula of the sigma can be represented as

[tex]T_{n}=a(r)^{n-1}[/tex]

where [tex]T_{n}[/tex] = nth term

a = first term

n = number of term term

r = common ratio

and sum is denoted by [tex]\sum_{n=1}^{n}a(r)^{n-1}[/tex]

Now for the given sequence sigma notation will be

[tex]\sum_{n=4}^{15}4(-3)^{n-1}[/tex]

can the answer not being an integer?

The angle of elevation is at angle D

So the answer would be 13.8

Answer:

I believe it is surface area

Answer:

Step-by-step explanation:

c

For this case we must find the quotient of[tex]6x ^ 2 + 23x + 20[/tex] between [tex]5 + 2x.[/tex]

As you can see in the figure, we must build a quotient in such a way that when multiplied by the divisor, we eliminate the terms of the dividend until we reach the remainder.

Answer:

[tex]3x + 4[/tex]

See attached image

Answer:

[tex]w=11[/tex]

Step-by-step explanation:

we have

[tex]5=w/2.2[/tex]

Solve for w

That means----> isolate the variable w

Multiply by 2.2 both sides

[tex](2.2)*5=(2.2)*w/2.2[/tex]

Simplify

[tex]11=w[/tex]

Rewrite

[tex]w=11[/tex]

The solution to the equation 5 = w/2.2 is 11

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

5 = w/2.2

Rewrite the equation as follows

w/2.2 = 5

So, we have

w = 5 * 2.2

Evaluate the product of 5 and 2.5

So, we have

w = 11

Hence, the solution to the equation is 11

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For this case we have a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Rewriting the equation we have:

[tex]3k ^ 2-4k-7 = 0[/tex]

So we have to:

[tex]a = 3\\b = -4\\c = -7[/tex]

The solutions will come from:

[tex]k = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Thus, the value of "b" is -4

Answer:

[tex]b = -4[/tex]

Let the number = X

Then to get four less you need to subtract 4 from x so you have X-4.

Then that equals 17, so the equation would be:

x - 4 = 17

The equation of the sentence 'four less than a number is 17' is  x – 4 = 17

Let the number be x

Four less than the number means x - 4

Therefore,

Four less than a number is 17 means x – 4 = 17

Therefore, option x – 4 = 17 is the correct answer

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Answer:

[tex]\large\boxed{x=\dfrac{11}{2},\ y=\dfrac{86}{35}}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}12x-14y=-8\\-8x-14y=-52&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}12x-14y=-8\\8x+14y=52\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad20x=44\qquad\text{divide both sides by 20}\\.\qquad x=\dfrac{44:4}{20:4}\\\\.\qquad x=\dfrac{11}{5}\\\\.\qquad\boxed{x=2.2}\\\\\text{Put the value of x to the second equation}\ 8x+14y=52:[/tex]

[tex]8(2.2)+14y=52\\17.6+14y=52\qquad\text{subtract 17.6 from both sides}\\14y=34.4\qquad\text{divide both sides by 14}\\y=\dfrac{34.4:2}{14:2}\\\\y=\dfrac{17.2\cdot10}{7\cdot10}\\\\y=\dfrac{172:2}{70:2}\\\boxed{y=\dfrac{86}{35}}[/tex]

The solution to the system of equations is: [tex]\[x = 2.2, \quad y = 2.457\][/tex]

To solve the system of linear equations:

[tex]\[12x - 14y = -8\]\[-8x - 14y = -52\][/tex]

We can use the method of elimination to find the values of x and y.

First, let's eliminate y by subtracting the second equation from the first equation. Before that, we should multiply the equations to have the same coefficients for y with opposite signs:

Multiply the first equation by 1:

12x - 14y = -8

Multiply the second equation by -1:

8x + 14y = 52

Now, add the two equations:

[tex]\[(12x - 14y) + (8x + 14y) = -8 + 52\][/tex]

Simplifying this, we get:

[tex]\[20x = 44\]Solve for \(x\):\[x = \frac{44}{20}\]\[x = \frac{22}{10}\]\[x = 2.2\][/tex]

Now that we have x, we can substitute this value back into one of the original equations to find y. Using the first equation:

12x - 14y = -8

Substitute x = 2.2:

[tex]\[12(2.2) - 14y = -8\]\[26.4 - 14y = -8\][/tex]

Subtract 26.4 from both sides:

[tex]\[-14y = -8 - 26.4\]\[-14y = -34.4\][/tex]

Divide both sides by -14:

[tex]\[y = \frac{-34.4}{-14}\]\[y = 2.4571 \approx 2.457\][/tex]

Thus, the solution to the system of equations is:

[tex]\[x = 2.2, \quad y = 2.457\][/tex]

To ensure accuracy, let's substitute x and y back into the original equations and verify that they hold true.

Check the first equation:

[tex]\[12(2.2) - 14(2.457) = -8\]\[26.4 - 34.398 = -8\]\[-7.998 \approx -8 \quad \text{(approximately correct)}\][/tex]

Check the second equation:

[tex]\[-8(2.2) - 14(2.457) = -52\]\[-17.6 - 34.398 = -52\]\[-51.998 \approx -52 \quad \text{(approximately correct)}\][/tex]

Answer:

45pairs

Step-by-step explanation:

15x3=45

ANSWER

B. 1

EXPLANATION

The given function is

[tex]f(x) =\left \{ {{x^{2} +3 (if) -5 \leq x< 1} \atop {x (if) 1 \leq x \leq 5 }} \right.[/tex]

This is a piece-wise defined function.

We want to find f(1)

We substitute x=1 into f(x)=x because, 1 belongs to the interval,

1≤x≤5

f(1)=1

The correct answer is B.

Answer: f(x^-1) = x/5 - 3/5

Step-by-step explanation:

1. Replace f(x) with y

2. Swap the positions of x and y to make x = 5y + 3

3. Solve for y by subtracting 3 from both sides and dividing each side by 5

The inverse of the function is f(x) = (x-3)/5 if the function f(x) is 5x +3 by taking the subject as x in the parent function.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have a function:

f(x) = 5x+3

To find the inverse of the function, take the subject x and the value of x.

f(x) - 3 = 5x

x = (f(x) - 3)/5

Replace the f(x) →x and x →f(x)

f(x) = (x-3)/5

Thus, the inverse of the function is f(x) = (x-3)/5 if the function f(x) is 5x +3 by taking the subject as x in the parent function.

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4.02, 5, 7.3, 19, 23, 23, 34, 35, 41, 42

(Numbers are organized in ascending order from smallest to largest)

0.55

Hope this helps :)

Answer: 0.55

This is the answer... hope this will help y'all. If I'm wrong, please tell me. Thanks ☺️

Answer:

It’s B

6x log (4)

Answer:

Point I

Step-by-step explanation:

Point I is the farthest away from the line of best fit

Answer:

Whoa that's easyyyy

Step-by-step explanation:

Point I because it's not close to the others and it's not anywhere near becing connected to another letter

Answer:

ROI = 66.67%

Step-by-step explanation:

Given:

josh investment= $12,000

Received sum= $20,000

ROI=?

ROI is the return on investment that gives the loss or gain in any investment and is calculated by the following formula:

ROI= (interest/investment) x 100

Finding interest:

interests= received sum- investment

              = 20,000-12,000

              =8000

Putting values in ROI formula we get:

ROI= (8000/12000) x 100

      = 66.67%

Hence the return on investment is 66.67%!

Answer:

A  Open circle at 6, line going to the right

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

We know the area is greater than 24

24 < l*w

One dimension is 4

24 < 4*w

Divide each side by 4

24/4 < 4w/4

6 < w

The other dimension must be greater than 6

Open circle at 6, line going to the right

Here,

[tex]1.578 \times {10}^{ - 5} miles = 1 \: inches \\ 1 \: miles = \frac{1}{1.578 \times {10}^{ - 5} } \: inches\\ 1425 \: miles = \frac{1}{1.578 \times {10}^{ - 5} } \times 1425 inches\\ = 9.03 \times {10}^{7} inches[/tex]

I hope it helps you

Answer:

[tex]\large\boxed{the\ radius\ R=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The formula of a volume of a sphere:

[tex]V=\dfrac{4}{3}\pi R^3[/tex]

We have

[tex]V=\dfrac{1}{6}\pi[/tex]

Substitute:

[tex]\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi[/tex]        divide both sides by π

[tex]\dfrac{4}{3}R^3=\dfrac{1}{6}[/tex]          multiply both sides by 3

[tex]3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}[/tex]

[tex]4R^3=\dfrac{1}{2}[/tex]          divide both sides by 4

[tex]R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}[/tex]

Answer:

$2.04

Step-by-step explanation:

Note that: 1 yard = 3 feet.

First, change the amount of yard (6) to feet:

6 x 3 = 18

6 yard = 18 feet.

Note: 18 feet = $36.72

Find the cost per foot (1 feet). Note the equal sign, what you do to one side, you do to the other. Divide 18 from both sides.

(18 ft)/18 = ($36.72)/18

1 ft = 36.72/18

1 ft = 2.04/1

1 ft = $2.04

~

Answer:

$2.04

Step-by-step explanation:

36.72/6

So that would make the answer $2.04

ANSWER

about 44.64

EXPLANATION

The standard deviation is the square root of the variance.

So we can write the equation or formula;

[tex]standard \: \: deviation = \sqrt{variance} [/tex]

From the question, it was given that, the variance is 1992.8

To find the standard deviation, we plug in the given value of the variance.

[tex]standard \: \: deviation = \sqrt{1992.8} [/tex]

Take your scientific calculator and the given square root.

You should obtain:

[tex]standard \: \: deviation = 44.64078852[/tex]

We round to the nearest hundredth to obtain; 44.64

Answer:

The best measure of location or center is the median.

The best measure of spread or dispersion is the interquartile range (I.Q.R).

Step-by-step explanation:

The data set is skewed to the left since most of the data values fall in the upper end of the distribution. In other words the data set is negatively skewed since it is tailed to the left.

For any skewed data set;

The best measure of location or center is always the median. This is because the median is robust to outliers unlike the mean.

On the other hand, the best measure of spread or dispersion is the interquartile range (I.Q.R).

Answer:

B and D

Step-by-step explanation:

Answer:

5.50 + 75g <= 15

5.50 - 5.50 + 75g <= 15 - 5.50

75g <= 9.5

75g / 75 <= 75 / 15

g = 5

Step-by-step explanation:

Answer:

x<2

Step-by-step explanation:

-x+8>6

-x>6-8

-x>-2 (flip the sign)

x<2

Answer:

x < 2

Step-by-step explanation:

-x+8>6

Subtract 8 from each side

-x+8-8>6-8

-x > -2

Divide each side by -1.  Remember to flip the inequality

-x/-1 < -2/-1

x < 2

Answer:

One of the many reasons of this is because the diet soda is less dense than the normal soda, therefor, it will float even though there's the same amount of liquid in each can, and the cans weigh the same amount

I hope this helps

Step-by-step explanation:

Answer:

The options in the question are missing, but the answer is "The can of diet soda will float due to the Archimedes principle.

Step-by-step explanation:

Now, Archimedes Principle can be defined as,

when a body is partially or completely immersed in a fluid, the body losses its weight in the fluid equal to the amount of fluid displaced by this body.

Notice that the phenomena of floating and sinking is based on Archimedes principle. If, the weight of body is higher than the amount of liquid it displaced, body will sink and if the weight of body is lower than the amount of liquid it displaced, then it will float. Now, in comparison of regular can with diet can, one needs to notice that diet can is slightly lighter due to absence of sugar in the liquid it contained. But the volume of both regular and diet can are same. When immersed, both displace same amount of water, but the weight of diet can is slightly lesser than the amount of water it displaced, so it floats, while on the other hand, the weight of normal can is slightly higher than the amount of water it displaced, so it sinks.

Answer:

5.625π m³

Step-by-step explanation:

The formula for the volume of a cylinder of radius R and length L is:

V = π·R²·L.

Here, V = π·(1.5 m)²(2.5 m) = 5.625π m³

Answer:

Step-by-step explanation:

Givens

r = 1.5 meters.

h = 2.5 meters.

Formula

V = pi * r^2 * h

Solution

V = pi * 1.5^2 * 2.5

V = pi * 2.25 * 2.5

V = 5.625 pi

Answer:

The polynomial that represent the volume of the box is [tex]V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the box is equal to

[tex]V=LWH[/tex]

we have

[tex]L=(x+3)\ in[/tex]

[tex]W=x\ in[/tex]

[tex]H=(x+1)\ in[/tex]

substitute in the formula

[tex]V=(x+3)(x)(x+1)\\V=(x^{2} +3x)(x+1)\\V=x^{3}+x^{2} +3x^{2} +3x\\ V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]