Write an interval using interval notation to describe the set of values shown above.

The two variables are; earnings, y and hours, x in which case, the former is the dependent variable while the latter is the independent variable.

It follows from the task content that Tiya earns $7 an hour mowing her neighbor's lawn.

On this note, it follows that the amount of money earned by Tiya is a dependent variable which solely depends on the number of hours spent on the job, which is the independent variable.

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The story that the fraction given represents is that A. A whiteboard is 2/5 Meyer long and has na area of 1/3 square meter. How wide is the whiteboard?

From the information given, it should be noted that the fraction given is 1/2 ÷ 2/5.

Therefore, this is represented by the story that a whiteboard is 2/5 Meyer long and has na area of 1/3 square meter. How wide is the whiteboard?

In conclusion, the correct option is A.

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The story problem that this division problem represent 1/2 ÷ 2/5 is a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the white board and is denoted as option A.

This is a description which represents a part of a whole.

The area of a rectangular shape of length L and width W is:

A = L×W

W=A/L

Only option A uses 1/2 as the area of the whiteboard and 2/5 is the other side of the board.

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The percentage of students age 15 and above travel to school by bus is 47%

The table of values is given as:

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15                            18                 165

Age 15 and above    65                                 195

Column totals          152          110        98      360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above  = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15           87              18      60        165

Age 15 and above    65          92        38        195

Column totals          152          110        98      360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

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The correlation coefficient is -0.87; strong correlation

The given parameters are:

x = Time spent working out

y = lbs Overweight

Next, we enter the table of values in a graphing tool.

From the graphing tool, we have the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -114.19 / √((22.569)(778.9))

r = -0.8613

Approximate

r = -0.87

This means that the correlation coefficient is -0.87

Also, the correlation coefficient is a strong correlation, because it is closer to -1 than it is to 0

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The standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

In this problem we must determine the equation of the hyperbola in its standard form from the coordinates of the foci and a general equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the general equation of the circle into its standard form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0​

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (semi-major distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

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Answer:

A = 30 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases , then

A = [tex]\frac{1}{2}[/tex] × 4 × (5 + 10) = 2 × 15 = 30 ft²

Answer:

  (a)  6 x (21 ÷ 3) + 8

Step-by-step explanation:

The first step in translating English to math is to understand the English.

The quotient of 21 and 3 is written (21 ÷ 3). Six times that quotient is ...

  6×(21÷3)

When 8 is added to this, it becomes ...

  6 × (21 ÷ 3) + 8

The transformation illustrated in the figure is translation.

Translation is a Transformation process in which the size or shape of a figure is not changed rather it only changes the coordinates of the vertices that make up that shape by moving them from one point to another.

Analysis:

Both shapes are congruent, since all the vertices remain in their respective positions even though they were moved and no change in the shape or size, then the transformation process is Translation.

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[tex]x + y = 55 \\ x - y = 15 \\ \\ 2x = 70 \: \: \: \: \: \: x = 35 \\ y = 55 - x = 55 - 35 = 20[/tex]

The value of x is -23 and the values of AB, BC, and AC are -33, 12 and -21

The equations are given as

AB = 13 + 2x

BC = 12

AC = x + 2

Point B is between A and C on Line AC.

So, we have

AC = AB + BC

This gives

x + 2 = 13 + 2x + 12

Evaluate the like terms

x - 2x = 13 + 12 - 2

This gives

-x = 23

Divide by -1

x =-23

Substitute x =-23 in AB = 13 + 2x and AC = x + 2

AB = 13 - 2 * 23 = -33

AC = -23 + 2 = -21

Hence, the value of x is -23 and the values of AB, BC, and AC are -33, 12 and -21

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Answer:

112°

Step-by-step explanation:

Angles on a line add to 180°.

Answer:

false

correct me if i'm wrong :]

Answer:

True

Step-by-step explanation:

the picture is the explanation and pretty much sus everything up about integers

Answer:

  a. 3641.51

  b.  1641.51

Step-by-step explanation:

The future value formula will tell you the amount in the account in 20 years.

  FV = P(1 +r/n)^(nt)

Principal P is compounded n times per year at annual rate r for t years.

The future value of the account with P=2000, r=0.03, n=12, and t=20 will be ...

  FV = 2000(1 +0.03/12)^(12·20) = 2000(1.0025^240) ≈ 3641.50999

The account value in 20 years will be 3641.51.

The first 2000 of account value is the principal, so the interest is ...

  interest = 3641.51 -2000

  interest = 1641.51

__

Additional comment

Many calculators and all spreadsheets have built-in capability for making this calculation.

Answer: 13 in.

Step-by-step explanation:

All you need to do is divide 26 by 2 in this case.

Using the normal distribution, there is a 0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The estimate and the sample size are:

p = 0.29, n = 207.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion of households spending more than $125 a week is less than 0.31 is the p-value of Z when X = 0.31, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.31 - 0.29}{0.0315}[/tex]

Z = 0.63

Z = 0.63 has a p-value of 0.7357.

0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

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Answer: B

Step-by-step explanation:

The parabola has an open hole at x=2, and the line has a closed hole at x=2.

This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].

This eliminates everything except for B.

Answer:

The graph with a downward trend is the negative correlation

Step-by-step explanation:

Answer:

The Downward Slope or 'C' is the answer.

Step-by-step explanation:

Negative Slopes go down

Positive Slopes go up

Random Slopes are random

Scattered Slopes are scattered but together

The four of them can get to the island if the two women begins the journey first. Detail below:

From the question given, we were told that:

With the above information in mind, we can determine how the four of them can get to the island by following the steps listed below:

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The angle that represents an exterior angle of the given triangle is: D. ∠CAB.

An exterior angle of a triangle is the angle that is located outside a triangle on an extended adjacent side of the triangle.

In the image given, and considering the options we have, ∠CAB is located outside a triangle ABF on an extended adjacent side CF of the triangle.

Therefore, the answer is: D. ∠CAB.

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Answer:

6,4

Step-by-step explanation:

I'm not sure if 4 is correct but 6 definitely is. I hope this helps

Answer:

Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints.

Step-by-step explanation:

Answer:

13200 needs to be less than 78*60+8840,

which is false because 13200 < 13520

Step-by-step explanation:

The truck cannot load 60 boxes as it exceeds the weight limit.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

W=78b+8840

So, b= 60

W= 78 x 66 + 8840

W = 5148 +8840

W = 13988 > 13200 ( limit for the weight)

Hence, the truck cannot load 60 boxes as it exceeds the weight limit.

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Answer:

x ≥ -6

Step-by-step explanation:

x - 4 ≤ 3x + 8

Add 4 to both sides.

x ≤ 3x + 12

Subtract 3x from both sides.

-2x ≤ 12

Divide both sides by -2. Remember to change the direction of the inequality sign since you are dividing by a negative number.

x ≥ -6

Answer:

[tex]x \geqslant - 6[/tex]

Step-by-step explanation:

[tex]x - 4 \leqslant 3x + 8 = = > \\ - 12 \leqslant 2x = = = > \\ x \geqslant - 6[/tex]

I assume you meant [tex]f(x)=8^x[/tex].

Reflecting across the x-axis would give [tex]y=-8^x[/tex].

Reflecting across the y-axis would give [tex]y=8^{-x}[/tex].

The equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds is y(t) = 14sin(πt/8) + 1

Since the motion of the ferris wheel is periodic,it follows a sinusoidal function form.

So, the general form of a sine function y(t) is

y(t) = Asin(2πt/T) + K where

Now since radius of 7m, the maximum value from its lowest point is at y = 2r + 1 = 2 × 7 + 1 = 14 + 1 = 15 at sin(2πt/T) = 1 which is the maximum value for sinФ = 1.

Since the bottom of the wheel is 1m above the ground, its minimum value is y = 1 at t = 0.

Also, it rotates once every 16 seconds, so its period T = 16 s.

So, y(t) = Asin(2πt/T) + K

y(t) = Asin(2πt/16) + K

y(t) = Asin(πt/8) + K

At maximum value

15 = Asin(πt/8) + K

15 = A + K  (1)

At minimum value

1 = Asin(πt/8) + K

1 = A(0) + K  

1 = 0 + K

K = 1

Substituting K into (1), we have

15 = A + 1

15 - 1 = A

14 = A

A = 14

So, y(t) = Asin(πt/8) + K

y(t) = 14sin(πt/8) + 1

So, the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel is y(t) = 14sin(πt/8) + 1

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Answer:

[tex]3\sqrt{3}[/tex]

Step-by-step explanation:

The given is a special right triangle with angle measures 30-60-90

The measure of side lengths for this special right triangle are represented with

a-a[tex]\sqrt{3}[/tex]-2a respectively

Now, since the side length that sees angle measure 30 is given as 3 (represented with a) then the measure of the side length that sees angle measure 60 would be [tex]3\sqrt{3}[/tex]

Answer:

Mate im sorry for replying here but i need points to ask a question.

The size of the corner you need to cut in order for your box to have this area is 0.5 inches

The base length is given as:

Length = 7

When the edges are removed, the new length becomes

New length = 7 - x - x

Evaluate

New length = 7 - 2x

The base width is given as:

Width = 4

When the edges are removed, the new length becomes

New width = 4 - x - x

Evaluate

New width = 4 - 2x

The area of the bottom of the box is calculated as:

Area = New length * New width

This gives

Area = (7 - 2x) * (4 - 2x)

Rewrite as:

A(x) = (7 - 2x) * (4 - 2x)

The area is given as:

Area = 16

So, we have:

(7 - 2x) * (4 - 2x) = 16

Expand

28 - 14x - 8x + 4x^2 = 16

Rewrite as

4x^2 - 14x - 8x + 28 - 16 = 0

Evaluate the like terms

4x^2 - 22x + 12= 0

We have:

4x^2 - 22x + 12= 0

Expand the equation

4x^2 - 24x - 2x + 12 = 0

Factorize the equation

4x(x - 6) - 2(x - 6) = 0

Factor out x - 6

(4x - 2)(x - 6) = 0

Solve for x

x = 0.5 or x = 6

The value of x = 6 is too big for the dimensions of the box.

So, x = 6 is an extraneous solution for the equation

Hence, the size of the corner you need to cut in order for your box to have this area is 0.5 inches

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The interval notation of the possible values of x according to.the given inequalities is; -3 > x and x>= 2.

The interval notation of the given inequalities which describes the possible value of x according to the task content are as follows;

For − 2 x − 2 > 4; we have;

− 2 x > 4 +2

-2x > 6

x < -3.

For − 8 x − 7 ≤ − 23; we have;

− 8 x ≤ − 23 +7

-8x ≤ -16

x >= 2.

Consequently, the interval notation of the given inequalities is; -3 > x and x >= 2.

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The recursive function o f the given sequence will be an = an-1 + 4

The formula for calculating the recursive function of n arithmetic sequence is expressed as
an = an-1 + d

Determine the common difference

d = 19 - 15 = 23 -19

d = 4

The recursive function o f the given sequence will be an = an-1 + 4

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