Determine the equation for the line of best fit to represent the data.

[tex]\text{Given that}~ x = 2,~ y = 3 ~ \text{and}~ z = -2\\\\\textbf{a)}\\\\2(x-y)=2(2-3) = 2(-1) = \boxed{-2}\\\\\textbf{b)}\\\\4x+3y-z = 4(2) +3(3) -(-2) = 8+9+2=\boxed{19}\\\\\textbf{c)}\\\\-2(3z+y) = -2[3(-2) +3] = -2(-6+3) = -2(-3) = \boxed{6}[/tex]

Answer:

a = 1.07

b = 1.96

r = 96%

Step-by-step explanation:

In an exponential function, modeled by f(x) = a(b)ˣ, a is the initial value and b is the growth factor. If we apply this formula to the given function y = 1.07(1.96)ˣ, we can see that the initial value, a, is 1.07, and the growth factor, b, is 1.96.

Now, to break down b, 1.96, into a rate, you simply set it equal to the problem’s given (1 + r) equation to find the rate.

1.96 = 1 + r

So r = .96

Now, we just have to convert .96 into a percentage to get a growth rate of 96%.

Step-by-step explanation:

an average of $3 per student would mean

sum(all students $) / 45 = 3

sum(all students $) = 3×45 = 135

x students have $5.

therefore (45-x) students have $2.

5x + 2(45-x) = 135

5x + 90 - 2x = 135

3x = 45

x = 15

so, 15 students have $5, and 45-15 = 30 students have $2.

Answer:

B. survey a random sample of 7th-grade students

Step-by-step explanation:

this answer would make the most sense because it is a example of a random statistical question.

Answer:

See below in bold.

Step-by-step explanation:

Let t be the number of tulips you buy and r be the number of rose bushes.

a.

The system is:

t + r = 13

4t + 10r = 100

b.

Solving:

4t + 10r = 100

t + r = 13           Multiply this by 4:

4t + 4r = 52      Subtract this from the first equation:

0 + 6r = 48

r = 8.

Now substitute for r in  t + r = 13:

t + 8 = 13

t = 5.

c.

To  buy 13 plants and spend  $100 you need to buy 5 tulips and 6 rose bushes.

Answer:

Reese's Peanut Butter Cups: 10.8

York Peppermint Patties: 2.6

Step-by-step explanation:

Let Reese's Peanut Butter Cups be r and York Peppermint Patties y.

Step 1: Make equations.

1) If you buy 3 bags of Reese's Peanut Butter Cups and 6 bags of York Peppermint Patties, it costs $48.

[tex]3r + 6y = 48[/tex]

2) If you buy 4 bags of Reese's Peanut Butter Cups and 3 bags of York Peppermint Patties, it costs $51.

[tex]4r + 3y = 51[/tex]

Step 2: Solve the system of equations.

We have system of equations. I'll solve them by elimination.

[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 4r + 3y = 51[/tex]

Multiply the second equation with 2 so we'll get 6y.

[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 8r + 6y = 102[/tex]

Now let's subtract second equation from first and solve for r.

[tex]3r - 8r + 6y - 6y = 48 - 102\\-5r = -54\\r = \frac{-54}{-5}\\r = \$10.8[/tex]

To get y let's substitute the value of r in first equation.

[tex]3r + 6y = 48\\3 \cdot 10.8 + 6y = 48\\32.4 + 6y = 48\\6y = 15.6\\y = \$2.6[/tex]

Answer:

a=17/33

Step-by-step explanation:

c=11a ----(1)

3c=17 ---- (2)

Substitute equation (1) into equation (2)

3(11a)=17

33a=17

Divide both side by 33

a=17/33

Answer

8.08

Use the distance formula:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

where (x1, y1), (x2, y1) are points

[tex]\rightarrow \sf d =\sqrt{(7-(-8))^2 + (4-(-2))^2}[/tex]

[tex]\rightarrow \sf d =\sqrt{(15)^2 + (6)^2}[/tex]

[tex]\rightarrow \sf d =3\sqrt{29}[/tex]

This is the length of diameter.

Then radius:

· diameter/2

[tex]\sf \cdot \dfrac{3\sqrt{29} }{2}[/tex]

[tex]\sf \cdot 8.0777[/tex]

[tex]\sf \cdot 8.08 \ \ (rounded \ to \ nearest \ hundreth)[/tex]

Answer:

x=6

Step-by-step explanation:

6(x-3)=18

Then divide both sides by 6

x-3=3

Add 3 to both sides

x=6

Answer:

x = 6

Explanation:

use distributive property: a(b + c) = ab + ac

change sides

add integers

divide both sides by 6

The mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

From the data given in the box plot, we can conclude that the mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

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Answer:

e.  0.308.

Step-by-step explanation:

I can't draw the tree diagram but the answer is

P(red first) = 7/14 = 1/2

P( then black)  = 4/13

P(red then black) = 1/2 * 4/13 = 2/13

P(black first) = 4/14 =  2/7

P( then red)  = 7/13

P(black then red) =2/7 * 7/13 = 2/13

So Probability of red and black in any order

= 2/13 + 2/13  = 4/13

= 0.308.

karen's conclusion is valid because the association does imply causation.

An association claim asserts that a particular level of one variable is expected to be related to a specific level of another variable. As two variables are related, they are said to be correlated, which means that when one variable varies, the other variable tends to change as well. 

An association claim must include at least two variables that are measured rather than manipulated.

While an association claim just acknowledges a connection between two variables, a causal claim goes a step further by claiming that one of the factors is responsible for altering the other.

Therefore, we can conclude that the claim which states that:

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Answer:

Association does not equal Causation, since Karen's theory does not have any evidence to prove causation, her theory is invalid.

Step-by-step explanation:

The density become by the elemental composition of the person has will be 0.258 and hence, option (A) will be correct.

In science, density is defined as the ratio of an object's mass to volume. Technical and statistical density assessments are done using a technique. The theory is applicable to the laws of nature in sciences like physics, where the emphasis is on things and matter.

Because density affects so many aspects of life, comprehending it is crucial. Which cells will float high in the atmosphere and which will sink lower depends on density, according to physics.

Given that the element has

Volume = 16 cubic inch

weight = 4.13 pound

Since density = weight / volume

density = 4.13/16

density = 0.258 which is matching through option (A) hence it will be correct.

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Answer:

1/3

1/2

Step-by-step explanation:

Sum being greter than 8, means 9,10,11,12 (12 is max as 6+6)

You can get 9 in these ways, (6+3),(5+4),(4+5),(3+6)

For 10, (6+4),(5+5),(5+5),(4+6)

For 11, (6+5),(5+6)

For 12 (6+6),(6+6)

Each outcome has probability of 1/6 x 1/6 = 1/36

There are 12 outcomes hence 12(1/36) = 12/36 = 1/3

Part b is 1/2 because half of dice has odd numbers.

Answer:

a point

a line

a line segment

a ray

and an angle in a triangle

Step-by-step explanation:

(a).  From the graph the x estimates of the turning points are

-1.8 and 1.1.

(b).  The solutions are where the graph crosses the x axis .. They are:

x = -3, 0 and 2.

A polynomial is defined as the sum of the same variables having different powers.

Here we have the two third-degree polynomials

x³+x²-6x=0

For this the value of the variable at the turning point of the graph will be

at x=-1.8 and 1.1.

The another equation is :-

x³+x²-6x=0

The solution of the equation will be x = -3, 0 and 2. where the graph crosses the x-axis.

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DOES THE GRAPH SHOW A LINEAR FUNCTION?

[tex] \sf \large \color{grey}{YES IT SHOWS A GRAPHIC LINEAR}[/tex]

Answer:

yeah, cuz it's a line that's straight

Answer:

16807

Step-by-step explanation:

7 * ((sqrt49)^4 =  7 * 7^4  = 7^5 = 16807

The age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the age of the grandsons is x years and

age of the grandfather's age is y years

Here some data are misprinted, so we are assuming the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

Then according to the problem:

12x = y  (as in 1 year, there are 12 months)

y -x = 77 (as difference in age is 77)

After solving both equations, we get:

x = 7 years and y = 84 years

Thus, the age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

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The linear function that represents the line y - 2 = 4(x - 3), in slope-intercept form, is expressed as: D. f(x)y = 4x - 10.

A linear function equation is expressed as, y = mx + b, in slope-intercept form.

Given the point-slope equation of the function, y - 2 = 4(x - 3), rewrite in slope-intercept form:

y - 2 = 4(x - 3)

y - 2 = 4x - 12

y = 4x - 12 + 2

y = 4x - 10

The linear function would be: D. f(x)y = 4x - 10

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The best statement that describes the relationship between lines s and t : (C). Lines s and t are parallel.

A line can be defined as a figure that is one dimensional. It is a trace that is made by the movement of points in opposite direction.

Parallel lines can be defined as a group of lines that are of the same orientation. They face the same direction and are on the same axis.

In conclusion, The best statement that describes the relationship between lines s and t : Lines s and t are parallel.

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Answer:

I believe that is the diameter.

Answer:

C. Diameter

Step-by-step explanation:

Circumference: The distance around the edge outside of the circle.

Diameter: The distance across the circle that goes through the center.

Radius: The distance halfway across the circle, which is half the diameter.

Center: The point or dot in the middle of a circle.

Answer:

18

Step-by-step explanation:

the absolute value is 18

radius= 4 m

the volume of the given sphere.

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

[tex]v = \frac{4}{3} \times 3.14 \times {4}^{3} [/tex]

[tex]v = 267.9466667 \: {m}^{3} [/tex]

[tex]v = 267.95 \: {m}^{3} [/tex]

therefore, the volume of the given sphere is 267.95 cubic meters.

[tex]\large\boxed{\bold{Formula: V= \frac{4}{3}\pi{r}^{3}}}[/tex]

[tex]\large\boxed{\bold{\red\pi\red=\red3\red.\red1\red4}}[/tex]

In this question the radius is given so we'll simply have to substitute and solve.

Let's solve!

Substitute the values according to the formula.

Instead of π we are asked to use 3.14

[tex]V= \frac{4}{3}\times\ 3.14\times{4}^{3}[/tex]

Calculator answer:

[tex]\bold{V= 267.9466667 \:{m}^{3}}[/tex]

Now, we can round off to the nearest hundredth.

The value in thousandths place is greater than 5 so, we will have to round up by adding 1 to the hundredths place.

Final answer:

[tex]\large\boxed{\bold{V= 267.95 \: {m}^{3}}}[/tex]

Hence, the volume of the given sphere is 267.95 cubic meters.

Answer: height of a building

Step-by-step explanation:

a^2 + b^2 = c^2

used for finding missing side angle of a triangle

Answer:

0.03

Step-by-step explanation:

You can do this on a calculator.

6 ÷ 161 = 0.0372670807

Hope this helped

Bajo la suposición de que las ciudades se hallan en la misma latitud, la distancia estimada entre las dos ciudades es de aproximadamente 6814 kilómetros.

En esta pregunta asumimos que la Tierra tiene una geometría esférica, de modo que los cálculos de arcos circulares se pueden obtener de manera simple y ágil. Por otra parte, también asumimos que las que la ciudad de Londres se encuentra a la misma latitud que la ciudad de Nueva York.

Es posible determinar la distancia estimada mediante la siguiente ecuación de arco circular:

s = [(θ' - θ) · π/180] · R · cos α     (1)

Where:

Si sabemos que θ' = 7°, θ = - 73°, α = 40° y R = 6371 km, entonces la distancia estimada entre la ciudades de Nueva York y Londres es:

s = [(7+73)/180] · π · (6371 · cos 40°)

s ≈ 6814.420 km

Bajo la suposición de que las ciudades se hallan en la misma latitud, la distancia estimada entre las dos ciudades es de aproximadamente 6814 kilómetros.

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The value of the addition of the numbers 7.8+917.62 will be 925.42.

The method of increasing the number is called the addition. or the sum of the two numbers is termed as the addition.

The addition of the numbers will be done as:-

917.62

 +7.80

925.42

First, arrange the number one to another then add from the unit places you will get your answer.

So the addition of the numbers will be 925.42

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Answer:

Step-by-step explanation:

1.169

Answer:

8^2−38+85+3√8 =111+6√2

(Decimal: 119.485281)