Identify the domain and range of
each function.
y = 3.5x
The domain of this function is
The range of this function is
DONE

Hello,

a) Volume of the figure = Volume of light blue rectangular parallelepiped - volume of dark blue rectangular parallelepiped

Volume of rectangular parallelepiped = lengh × high × height

Volume of light blue rectangular parallelepiped :

V = (x + 2) × (x + 5) × (2x + 1)

V = (x² + 5x + 2x + 10) × (2x + 1)

V = (x² + 7x + 10) × (2x + 1)

V = 2x³ + 15x² + 27x + 10

Volume of dark blue rectangular parallelepiped :

V = x × 3 × (x + 5)

V = 3x(x + 5)

V = 3x² + 15x

Polynomial function, in standard form, to model the volume of this solid :

V = 2x³ + 15x² + 27x + 10 - (3x² + 15x)

V = 2x³ + 15x² - 3x² + 27x - 15x + 10

V = 2x³ + 12x² + 12x + 10

b) We have to solve 2x³ + 12x² + 12x + 10 = 208

⇔ 2x³ + 12x² + 12x - 198 = 0

⇔ 2(x - 3)(x² + 9x + 33) = 0

⇔ x = 3 or x² + 9x + 33 = 0

a = 1 ; b = 9 ; c = 33

Δ = b² - 4ac = 9² - 4 × 1 × 33 = -51 < 0 ⇔ Δ < 0 ⇒ no solution

So if the volume of the solid is 208 cubic inches, the value of x is 3

Express  the following in the form kx^n where k and n are constants.

(a) y=x^3

(b)y=3x^-1

(c) y=x^3/27

To express each of the following in the form kx^n where k and n are constants.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given that:

y=1/27x^3

express each of the following in the form kx^n where k and n are constants.

(a) y^1/3

Let y^1/3=x

by cubing both sides we get,

y=x^3

The equation in the form of  kx^n

where,

k=1

n=3

(b) 3y^-1

Let 3y^-1=x

3/y=x

y=3/x

By simplify

y=3x^-1

The equation in the form of  kx^n

where,

k=3

n=-1

(c) √(27y)

Let (27y)^1/3=x

by cubing both sides we get,

27y=x^3

y=x^3/27

The equation in the form of  kx^n

where,

k=1/27

n=3

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Frequency is a physical quantity that relates to the number of cycles made by a wave per second. Therefore the required expression for the frequency of the lower note is:  [tex]\frac{2}{3}[/tex] f

A wave is a phenomenon that propagates through a material medium without any permanent effect on the molecules of the medium. It transmits energy from one end of the medium to another. Examples are sound waves, light waves, electromagnetic waves, etc.

The propagation of a wave gives rise to frequency. Which can be defined as the number of cycles made by a wave per second. And it is measured in Hertz.

Let the frequency of the higher note be represented by f, and that of the lower note by [tex]f_{l}[/tex]. Thus, we have;

[tex]f_{l}[/tex] = [tex]\frac{2}{3}[/tex] f

Therefore, the expression for the frequency of the lower notes is   [tex]\frac{2}{3}[/tex] f.

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Answer: B) The function is decreasing

Step-by-step explanation:

As x increases, y decreases.

Hello,

U (n +1) = Un + 6

Un = Uo + nr

U9 = 7 + 9 × 6 = 7 + 54 = 61

Answer:

nth term = 6n + 1.

Step-by-step explanation:

The first term a1 = 7 and the common difference d =  6.

nth term = a + d(n - 1)

= 7  + 6(n - 1)

= 6n + 1.

The correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.

Here we are given that

KL = NR

JL = MR

Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.

So for the triangles to be congruent by SAS, angle L must be congruent to angle R.

∠L=∠R

Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.

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Answer:

B  

Step-by-step explanation:

L=R

We don’t know the number of employees remaining at the company.

We don’t know the total number of employees remaining at the company.

The classification consists of gender, division, and employment type.

It doesn’t matter what order those attributes come in. A person who is male, age group 6, and employment type 10 has the same classification as someone who is of employment type 6, male, and age group10.

Therefore since order does not matter it is a combination question.

Assuming only two genders are allowed (you didn’t say and some people think there are about 10 of them)

It is either 120 (2 times 6 times 10) or "None of the above" if you believe there are more than 2 genders.

2×6×10=120

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The speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.

We assume the speed (rate) of the plane in still air to be x kilometers per hour, and the speed (rate) of the wind to be y kilometers per hour.

Thus, flying against the wind, the acting speed (rate) for the plane will be x - y kilometers per hour.

Flying with the wind, the acting speed (rate) for the plane will be x + y kilometers per hour.

We are given that flying against the wind, the airplane travels 6230 kilometers in 7 hours.

Thus, speed (rate) = 6230/7 kilometers per hour = 890 kilometers per hour.

Equating this to the derived speed of the airplane flying against the wind, we get x - y = 890 ... (i).

We are given that flying with the wind, the airplane travels 10480 kilometers in 8 hours.

Thus, speed (rate) = 10480/8 kilometers per hour = 1310 kilometers per hour.

Equating this to the derived speed of the airplane flying with the wind, we get x + y = 1310  ... (i).

Now, on adding equations (i) and (ii), we get:

2x = 2200,

or, x = 1100.

Substituting x = 1100 in (ii), we get:

x + y = 1310,

or, 1100 + y = 1310,

or, y = 1310 - 1100 = 210.

Thus, the speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.

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The simplified form of the given expression is 2015

The given expression is (x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022

The expression can be simplified as shown below

(x-2)(x+2)(x²+4) - (x²+3)(x²-3) + 2022

x(x+2)-2(x+2)(x²+4) - x²(x²-3) +3(x²-3) + 2022

(x²+2x-2x-4)(x²+4) - (x⁴-3x²+3x²-9) + 2022

(x²-4)(x²+4) - (x⁴-9) + 2022

x²(x²+4) -4(x²+4) - (x⁴-9) + 2022

(x⁴+4x²-4x²-16) - (x⁴-9) + 2022

(x⁴-16) - (x⁴-9) + 2022

x⁴ -16 -x⁴ +9 + 2022

x⁴ -x⁴ -16 +9 +2022

= 2015

Hence, the simplified expression is 2015

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The statement "The value of a is positive, so the vertex is a minimum" is correct.

Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

From the table we can find the quadratic function:

f(x) = ax² + bx + c

Plug (x, y) on the above function.

a + b + c = 3 ...(1)

9a + 3b + c = -3 ...(2)

25a + 5b + c = -5 ...(3)

After solving the above equations:

a = 0.5

b = -5

c = 7.5

The value of a is positive.

Thus, the statement "The value of a is positive, so the vertex is a minimum" is correct.

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Answer:

15 in.

Step-by-step explanation:

P = 2(L + W)

36 = 2(L + 3)

18 = L + 3

L = 15

Answer:

Hello! The answer is 15 in.

Step-by-step explanation:

The formula for the perimeter of a rectangle is 2l + 2w. We can substitute our w-value since it's provided for us:

2l + 2(3) = 36

Now, we can solve the equation:

2l + 6 = 36

     -6.    -6

----------------

2l = 30

--     --

2     2

l = 15 in

A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.

Correlation coefficients are used to evaluate the strength of the linear relationship between two variables.

When the correlation coefficient value is less than zero, it indicates a bad association, while a number higher than zero indicates a good relationship.

There is no correlation between the two variables being compared, as shown by a correlation coefficient of zero.

The idea of a negative correlation, also referred to as an inverse correlation, is essential to the construction of diversified portfolios that may be better able to withstand portfolio volatility.

It is often done by entering data into a calculator, computer, or statistics application because computing the correlation coefficient requires time.

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Answer:

0,4

Step-by-step explanation:

X is 0 and Y is 4 it'll be touching the vertical line

Answer:

0,4

Step-by-step explanation:

Answer:

x = 145°

Step-by-step explanation:

x and 35° are a linear pair and sum to 180° , that is

x + 35° = 180° (subtract 35° from both sides )

x = 145°

It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated

1. Part A:

Since the points in the scatter plot shows a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.

The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to  1.

Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with a negative slope.

r =  + 1 is a perfect positive correlation: the points will adjust perfectly to a line with a positive slope.

r = 0 means that the variables are not correlated at all.

Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows another thing.

Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.

2. Part B.

A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.

Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.

Thus, the scenario could be:

Amount of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

        50                                                     40

        25                                                     80

        12.5                                                  160

        6.25                                                 320

The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.

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Answer:

The each have to place 2 subscriptions

Step-by-step explanation:

Adriana

E (earnings) = 6 + 2*x where x is the number of subscriptions

Sophie

E (earnings) = 4 + 3x

For them to earn the same amount, their right sides must be equated.

4 + 3x = 6  + 2x                    Subtract 2x from both sides

4 + 3x - 2x = 6+ 2x  - 2x       Combine

4 + x = 6                                Subtract 4 from both sides

4 - 4 + x = 6 - 4

x = 2

The given multipliers are factors of 9, the possible number will have 1 as first and last digit which gives the number as 101

The given numbers are;

18, 27, 36, 45, 54, 63, 72, 81, 99

Given that the first and the last figures are those of the multipliers, we have;

The first and last and last digit of the number can be 1, which gives;

Possible numbers includes; 11 and 101

By trying the possible numbers, the difference found is presented as follows;

99 × 11 = 1089 (The first and the last digit are not the same as the multiplier)

90 × 11 = 990

90 × 101 = 9090

The correct option is therefore 101

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As Convex polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The

Convex Polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.

Lets simplify the given problem,

If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

1070 =[n - 2] x 180, where n = number of sides

[tex]1070 =180n - 360180n =1070+360180n =1430n = 1430 / 180[/tex]

n = 7.94 number of sides. Since this is not a whole number, will simply round it up to 8.

Hence the number of sides is 8

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The solution to the inequality |x + 3| - 2 < 0  is -5 < x < -1 as shown in the graph attached

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is an expression used to show the non equal comparison of two or more numbers and variables.

Given that:

|x + 3| - 2 < 0

Hence:

(x + 3) - 2 < 0   and -(x + 3) - 2 < 0

x < -1 and x > -5

The solution to the inequality |x + 3| - 2 < 0  is -5 < x < -1 as shown in the graph attached

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Answer: The answer to the question is Answer Choice "B"

Step-by-step explanation:

Proof that It's actually correct as you can see it on the screenshot :)

Answer:

two and a half to three and one third

Step-by-step explanation:

a)The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.

Statistical inference is the process of drawing conclusions about populations or scientific truths from data. There are many ways to make inferences, including statistical modeling, data-driven strategies, and the explicit use of designs and randomization in analyses.

Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or population probability distribution.

First, a preliminary assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted H0.

An alternative hypothesis (denoted Ha) is then defined, which is the opposite of what is stated in the null hypothesis. The hypothesis testing procedure involves using sample data to determine whether or not H0 can be rejected. If H0 is rejected, the statistical conclusion is that the alternative hypothesis Ha is true.

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Answer:

5$

Step-by-step explanation:

it is 5 because the difference of 8 and 3 is 5

Answer:

Animal books make up (3/20) of all books

Step-by-step explanation:

Let X be the total number of books, made up of nonfiction, animal, and all others.

(3/5)X are nonfiction books.

Of the nonfiction books, 1/4 are animal books:  (3/5)*(1/4)X = (3/20)X are animal books

[This means that Nonfiction, less animal books is:  (3/5)X - (3/20)X]

Animal books make up (3/20) of all books.

Answer:

.7 pi    Radians

Step-by-step explanation:

There are pi radians in a 180 degrees :

   pi / 180   * 126  = .7 pi  Radians

Answer:

[tex]\frac{7}{10} \pi[/tex] or 0.7π radians

Explanation:

For converting degree to radians, multiply by π/180

Here given:

Conversion:

126° × π/180 = [tex]\frac{7}{10} \pi[/tex] or 0.7π

Similarly (additional),

     1) 100° = 100 × π/180 = [tex]\frac{5}{9} \pi[/tex]

     2) 320° = 320 × π/180 = [tex]\frac{16}{9} \pi[/tex]

Started in Quadrant II and ended in Quadrant IV.

==========================================================

Explanation:

Refer to the diagram below. It shows how the four quadrants are labeled using roman numerals. We start in the upper right corner (aka northeast corner) and work counterclockwise when labeling quadrant I, II, III, and IV in that order.

The green point A is located in quadrant II in the northwest. Meanwhile point B in red is in the southeast quadrant IV.

Therefore, we started in quadrant II and ended in quadrant IV which points us to choice C.

The function rule for the table is A. s = 4c

From the table, it can be seen that when the cans of soup is 1, the number of serving is 4. Also, when it's 2, the number or servings is 8.

This implies that:

4/1 = 8/2

= 4.

Therefore, the function rule for the table is s = 4c

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Answer:

0.18

Step-by-step explanation:

Answer:

y=10x

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

y−y1=m(x−x1)  to find the line parallel to y=10x−45

.

Answer: [tex]\frac{7\sqrt{3}}{2}[/tex]

Step-by-step explanation:

[tex]\sin 60^{\circ}=\frac{x}{7}\\\\\frac{\sqrt{3}}{2}=\frac{x}{7}\\\\x=\frac{7\sqrt{3}}{2}[/tex]

Answer:

True

Step-by-step explanation:

The 'base' of the line has length zero.

Answer:

True.

Step-by-step explanation:

You take 2 points and find gradient of a line and if you get a constant. For example, m=5. Then 5 over 0 (the denominator is what matters, it must be 0) and that's how you know it's a vertical line and has undefined slope.