Heather used a graphing utility to find the equation of the line of best fit in this scatter plot. VA PW1ALG131_Using Models from Data After reading equation of the line from the graphing utility, Heather wrote in her notebook that the line of best fit is represented by the equation y = 0.77x + 1.34. Heather likely an error when writing the equation of the line in her notebook because the slope and the y-intercept of the equation she recorded.

Answer:

Step-by-step explanation:

Area of trapezoid:

[tex] \frac{1}{2} \times \: sum \: of \: parallel \: sides \: \times height[/tex]

plugging the values:

[tex] \frac{1}{2} \times (21 + 5) \times 2[/tex]

Calculate the sum

[tex] \frac{1}{2} \times 26 \times 2[/tex]

Reduce the numbers with G.C.F 2

[tex]13 \times 2[/tex]

Calculate the product

[tex]26[/tex] feet squared.

Hope this helps...

Best regards!

Answer:

x = -7

Step-by-step explanation:

5x+8=3x-6

Subtract 3x from each side

5x-3x+8=3x-3x-6

2x+8 = -6

Subtract 8 from each side

2x+8-8 = -6-8

2x = -14

Divide by 2

2x/2 = -14/2

x = -7

Answer: x= -7

Step-by-step explanation:

[tex]5x+8=3x-6[/tex]

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

[tex]5x+8-8=3x-6-8[/tex]

[tex]5x=3x-14[/tex]

[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]

[tex]5x-3x=3x-14-3x[/tex]

[tex]2x=-14[/tex]

[tex]\mathrm{Divide\:2\:\:on\:\:both\:sides\:}[/tex]

[tex]-14/2=-7[/tex]

[tex]x=-7[/tex]

Answer:

(a) The probability that the average of the draws will be in the range 80 to 120 is 1.

(b) The probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample selected is quite large, i.e. n = 400 > 30, then the sampling distribution of sample means will be approximately normally distributed.

Compute the mean and standard deviation of sample mean as follows:

[tex]\mu_{\bar x}=\mu=100\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{400}}=1[/tex]

So, [tex]\bar X\sim N(100, 1)[/tex]

(a)

Compute the probability that the average of the draws will be in the range 80 to 120 as follows:

[tex]P(80<\bar X<120)=P(\frac{80-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{120-100}{1})[/tex]

                            [tex]=P(-20<Z<20)\\\\=P(Z<20)-P(Z<-20)\\\\=(\approx1)-(\approx0)\\\\=1[/tex]

Thus, the probability that the average of the draws will be in the range 80 to 120 is 1.

(b)

Compute the probability that the average of the draws will be in the range 99 to 101 as follows:

[tex]P(99<\bar X<101)=P(\frac{99-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{101-100}{1})[/tex]

                            [tex]=P(-1<Z<1)\\\\=P(Z<1)-P(Z<-1)\\\\=0.6827[/tex]

Thus, the probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Answer:

x = -7 or x = 2/3

Step-by-step explanation:

I'm assuming you meant solve for x when f(x) = 0.

f(x) = 3x(x + 7) - 2(x + 7)

0 = (x + 7)(3x - 2) -- Both terms have a common factor of (x + 7) so we can group them

x + 7 = 0 or 3x - 2 = 0 -- Use ZPP

x = -7 or x = 2/3 -- Solve

Answer:

Step-by-step explanation:

If you aren't supposed to do this on your calculator, then you'd have to figure out a way to get the bases of 10 to have the same power somehow in order to use the properties of exponents. This is the problem (you multiply the 2 dimensions together to find area, remember):

[tex](5.5*10^5)(4.2*10^4)[/tex]You cannot simply add the exponents on the 10's and say your power is 9...cuz it's not. It needs to be rewritten so that there is a power of 4 on the 10 in the parenthesis on the left. Do that this way:

[tex](5.5*10^4*10^1)(4.2*10^4)[/tex] Now you've got a common power of 4 between the 2 sets of parenthesis. 10 to the first is the same as 10, so multiplying that into the 5.5 gives us

[tex](55*10^4)(4.2*10^4)[/tex]

55 * 4.2 is 231 and 10 to the 4th times 10 to the 4th is 10 to the 8th.

[tex]231*10^8[/tex] But that's not in correct scientific notation. If we move the decimal to places to the left, we have to add 2 to the exponent of 8, giving us, finally,

[tex]2.31*10^{10}m^2[/tex]

Next use the hint to convert that to kilometers:

[tex]2.31*10^{10}m^2*\frac{1km^2}{1*10^6m^2}[/tex]

Dividing like bases means we subtract the lower exponent from the upper. 10 - 6 = 4, so the equivalent number of km squared is

2.31 × 10⁴ km²

Kilometers are comparable to miles, which is how we measure large things, like pieces of land. So it would be better to measure the forest in kilometers squared instead of meters squared.

Answer: 40 inches

Step-by-step explanation:

The woman weight and the seat will be: 145lb + 5lb = 150lb,

her son weight and the seat will be: 95lb + 5lb = 100lb

her daughter weight and the seat will be: 70lb + 5lb = 75lb

Given that the woman is on the left side of the seesaw, 60 inches from the fulcrum. The moment of the woman will be 150 × 60 = 9000

The daughter and son both get on the right side.

If the son sits 60 inches from the fulcrum, his moment will be:

100 × 60 = 6000

The sum of the moment of the son and daughter must be equal to the moment of their mother.

Let the position of the daughter = X

The moment of the daughter will be:

75 × X = 75X

Equate the moment of the mother to the sum of the moment of her children

9000 = 6000 + 75X

Collect the like terms

75X = 9000 - 6000

75X = 3000

X = 3000/75

X = 40

The position the daughter should sit to balance the seesaw is 40 inches away from seasaw to the right.

Louis traveled 7,144 miles

Answer:

75% (I think)

Step-by-step explanation:

1/4 of babies have no hair

2/4 of babies have little hair

1/4 of babies have a lot of hair

Answer:

Step-by-step explanation:

The easiest way to think about increasing area is by taking a square, if you double the dimensions, let's say they were 1 by 1 and then was made into a 2x2 square, you can fit four of the original cube (1x1) into the 2x2. So when the dimensions are doubled the area is quadrupled.

Even easier shortcut:

Take the cube idea, when the dimensions are messed with for anything, (works for volume too) always think of the smaller piece as 1x1 or 1x1x1. Then if the dimensions are double make it 2x2 or 2x2x2. If the dimensions are tripled then do 3x3 or 3x3x3, etc... 1x1=1x1x1, they are both equal to 1. So think of that as the numerator. the 2x2 in this case is equal to 4 so the smaller piece is 1/4 of the bigger one. Shown with volume if you double the dimensions of a cube that was 1x1x1 into 2x2x2. 1x1x1 still equals 1 so that's still the numerator and 2x2x2 is equal to 8 so the 1x1x1 cube is 1/8 of the 2x2x2, in other words you can fit eight 1x1x1 cubes into the 2x2x2 cube.

Hope this helps with area and volume.

Answer:

Triangle in isosceles, scalene or equilateral forms and

quadrilateral in trapezoid, rectangle or square forms

Step-by-step explanation:

Refer to pictures attached

Shapes can be formed are:

when perpendicular  to base

when  angle cross section to base

when base is isosceles triangle and parallel cross section to base,

or angle cross section

when base is scalene triangle and parallel cross section to base,

or angle cross section

when base is equilateral triangle and parallel cross section to base,

or angle cross section

Answer:

The answer is b

Step-by-step explanation:

since 2*9=18 and (x)(2x+3)=2x^2+3x

Answer: B

Step-by-step explanation:

Answer:

8.3miles

Step-by-step explanation:

Here Jeff's sister drives 14 miles

his brother only drives 57/10 miles then the question is only asking the difference between their distance of driving to school knowing fully well that Jeff's sister drive farther than his brother, then we find the difference between their drives which is done bow

14miles -57/10 miles

= 83/10

= 8.3miles

Therefore, Jeff's sister drive 8.3miles farther than his brother

Answer:

The answer is option 2.

Answer:

A. [tex] \frac{7x^2}{6x - 10} [/tex]

Step-by-step Explanation:

To get the quotient, which is the result of

What we get by dividing the above, we would turn the divisor upside down, while the division sign would change to multiplication. This rule applied is known as "multiplying by the reciprocal".

[tex] \frac{7x^2}{2x + 6} [/tex] ÷ [tex] \frac{3x - 5}{x + 3} [/tex]

[tex] \frac{7x^2}{2x + 6} * \frac{x + 3}{3x - 5} [/tex] => multiplying by the reciprocal.

[tex] \frac{7x^2}{2(x + 3)} * \frac{x + 3}{3x - 5} [/tex]

[tex] \frac{7x^2}{2} * \frac{1}{3x - 5} [/tex] => (x + 3) cancels (x + 3)

[tex] \frac{7x^2(1)}{2(3x - 5)} [/tex]

[tex] \frac{7x^2}{6x - 10} [/tex]

Quotient = [tex] \frac{7x^2}{6x - 10} [/tex]

Answer: A

Step-by-step explanation:

Answer: The answer is D . The graph

Step-by-step explanation: It was the answer given on Edge.

Answer:

d

Step-by-step explanation:

Answer:

[tex]x=-1,5[/tex]

Step-by-step explanation:

[tex]x^2-4x-5=0[/tex]

In order to solve this quadratic, we have many methods. We can factor, complete the square, or use the quadratic formula. I'm going to factor since it's the easiest method.

To factor, find two numbers that when multiplied equal a(c) and when added equal b.

a=1, b=-4, and c=-5.

So we want two numbers that when multiplied equals 1(-5)=-5 and when added equals -4.

-5 and 1 are the possible numbers. Therefore:

[tex]x^2-4x-5=0\\x^2+x-5x-5=0\\x(x+1)-5(x+1)=0\\(x-5)(x+1)=0\\x=5, -1[/tex]

Answer:

The correct option is

This is a polynomial function of degree 7 with a leading coefficient of -1

Step-by-step explanation:

Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions

Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1

Which can be expanded as follows

f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;

f(x) = -x⁷ + 2·x⁴ + 1

Which is  polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7  

Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.

Answer:

Step-by-step explanation:

The equation of  a line in slope-intercept form is expressed as y = mx+c

m is the slope of the line

c is the intercept

m = Δy/Δx = y₂-y₁/x₂-x₁

Given the points on a line to be  (3,1) and (−6,4);

x₁ = 3, y₁ = 1, x₂ = -6 and y₂ = 4

m = 4-1/-6-3

m = 3/-9

m = -1/3

To get the intercept c, we will substitute any of the points given and the value of the slope into the equation y = mx+c. Using the point (3, 1) and m = -1/3

1 = -1/3(3)+c

1 = -1+c

c  = 1+1

c =2

Substituting m = -1/3 and c = 2 into the sllpe intercept form of the equation will give;

y = -1/3 x + 2

Hence the  equation for the line in slope-intercept form is y = -1/3 x + 2

Answer:

41/99

Step-by-step explanation:

There are two types of non terminating decimals. These are: Simple and Mixed

The one that you wrote up here is Simple, Since 41 is the only number that goes on repeating itself.

And mixed non terminating decimal is like 0.352 whereas 52 keeps repeating itself.

So when you change a non terminating decimal the denominator is always 9. But it depends on the decimal whether it is simple or mixed.

Since the decimal you wrote is simple and 2 digits keep on repeating themselves the denominator will be 99.

And the numerator will be the decimal number that keeps repeating itself without the repeating bar.

Therefore, the answer is 41/99.

Hope it helps ;) ❤❤❤

Answer:

[tex]2ab - 6a + 5b - 15[/tex]

Step-by-step explanation:

Given

[tex]2ab - 6a + 5b + \_[/tex]

Required

Fill in the gap to produce the product of linear expressions

[tex]2ab - 6a + 5b + \_[/tex]

Split to 2

[tex](2ab - 6a) + (5b + \_)[/tex]

Factorize the first bracket

[tex]2a(b - 3) + (5b + \_)[/tex]

Represent the _ with X

[tex]2a(b - 3) + (5b + X)[/tex]

Factorize the second bracket

[tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

To result in a linear expression, then the following condition must be satisfied;

[tex]b - 3 = b + \frac{X}{5}[/tex]

Subtract b from both sides

[tex]b - b- 3 = b - b+ \frac{X}{5}[/tex]

[tex]- 3 = \frac{X}{5}[/tex]

Multiply both sides by 5

[tex]- 3 * 5 = \frac{X}{5} * 5[/tex]

[tex]X = -15[/tex]

Substitute -15 for X in [tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

[tex]2a(b - 3) + 5(b + \frac{-15}{5})[/tex]

[tex]2a(b - 3) + 5(b - \frac{15}{5})[/tex]

[tex]2a(b - 3) + 5(b - 3)[/tex]

[tex](2a + 5)(b - 3)[/tex]

The two linear expressions are [tex](2a+ 5)[/tex] and [tex](b - 3)[/tex]

Their product will result in [tex]2ab - 6a + 5b - 15[/tex]

Hence, the constant is -15

Answer:

172.83 kg

Step-by-step explanation:

A cylindrical container has a radius (r) of 0.3 meter and a height (h) of 0.75 meter and density of 815 kg/m³.

The density of a substance is the mass per unit volume, it is the ratio of the mass of a substance to the volume occupied. The density is given by the formula:

Density = Mass / volume

The volume of a cylinder is given as:

V = πr²h

V = π × (0.3)² × 0.75 = 0.212 m³

Density = Mass/ volume

Mass = Density × Volume

Mass = 815 kg/m³ × 0.212 m³

Mass = 172.83 kg

Answer:

The answer is 173

Step-by-step explanation:

The other guy's answer was correct, but he forgot to round up to the nearest whole number so just in case you didn't notice the question saying that!

Step-by-step explanation:

Keeping,  one angle FDE, many triangles are possible since length of no segment is fixed and only one angle is fixed.

At many instances, triangle ABC and DEF have same angle measurements. Referring to the image attached here.

As point G moved on the ray EF, many triangles with same angle measurements as of ABC can be formed.

Answer:

Since no segment length is fixed and only one angle is fixed, multiple triangles are possible while maintaining one angle FDE. Triangles ABC and DEF frequently have the same measured angles. referring to the picture that is attached. Numerous triangles with the same angle measurements as ABC can be constructed when point G moves along ray EF.

Step-by-step explanation:

Answer: g(1) = 9

Step-by-step explanation:

g(x) = 3(1/4)^(x-2) - 3

g(1) = 3(1/4)^(1-2) - 3

g(1) = 3(1/4)^(-1) - 3

g(1) = 3(4) - 3

g(1) = 12 - 3

g(1) = 9

Hey there! :)

Answer:

Slope = 2/5.

Step-by-step explanation:

Use the slope formula to solve for the slope of the line:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates of each point into the equation:

[tex]m = \frac{8 - 6}{10 - 5}[/tex]

Simplify:

m = 2/5. This is the slope of the line.

Answer:

(-4, y) and (4, y), where y is any real number.

Step-by-step explanation:

The point (-4; 7.5) is 4 units from the y axis.

All points that lie on the line x = -4 and the line x = 4 have the same distance from the y-axis of 4 units.

Answer:

B

Step-by-step explanation:

to find the inverse of a function, repalace f(x) with x, and replace x with y, proceed to solve for y and the answer you get is B

Answer:

B

Step-by-step explanation:

f(x)=5x/3+5

y=5x/3+5

x=5y/3+5

now solve for y

3x=5y+15

5y=3x-15

y=3x/5-3 or 3(x-5)/5

Answer:

[tex]4\sqrt{2}\\\\7\sqrt{2} \\\\13\sqrt{2}[/tex]

Step-by-step explanation:

Well the diagonal using pythagora's theorem:

[tex]x\sqrt{2}[/tex] where x is the lenght is the side of the square

so when x=4

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

when x=7

[tex]7\sqrt{2\\}[/tex]

when x=13

[tex]13\sqrt{2}[/tex]

The length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].

Given side of squares.

We have to calculate the length of diagonal.

We know that in square shape,

length of diagonal [tex]=\sqrt{2} a[/tex], here a is the side of square.

So when square has a side of 4 then its diagonal becomes [tex]4\sqrt{2}[/tex].

when square has a side of 7 then its diagonal becomes [tex]7\sqrt{2}[/tex].

when square has a side of 13 then its diagonal becomes [tex]13\sqrt{2}[/tex].

Hence the length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].

For more details on length of diagonal of square follow the link:

https://brainly.com/question/16716787

Answer:

£32.4

Step-by-step explanation:

£100 = 216 Swiss francs

x        =  70 francs

70 x 100=7000/216=32.4