Question 1(Multiple Choice Worth 2 points)

(Graphing Linear Equations MC)

A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 10 + 20x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.

Which graph represents this situation?

graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
Question 2(Multiple Choice Worth 2 points)

(Graphing Linear Equations MC)

A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.


Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38


Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
Question 3(Multiple Choice Worth 2 points)

(Graphing Linear Equations LC)

The table represents a linear relationship.


x −1 0 1 2
y 2 0 −2 −4


Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
Question 4(Multiple Choice Worth 2 points)

(Graphing Linear Equations LC)

Which of the following graphs has a slope of negative three halves and a y-intercept of 2?

graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
Question 5(Multiple Choice Worth 2 points)

(Graphing Linear Equations MC)

A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.

Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 120
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 120
Question 6(Multiple Choice Worth 2 points)

(Graphing Linear Equations MC)

Which graph represents the equation y equals one half times x minus 1?

graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2

(5, 9), open (5), close (9), is the interval graph. This interval is inequitable because:   5 < x ≤ 9

Therefore,

a) Letter A is erroneous since it implies that the graph should have two shaded areas, but this particular graph only has one.

b) Letter B is erroneous because the graph shows that there must be a parenthesis before point 5 because it is open, and point 9 must come after a because it is shaded.

c) The letter c is also wrong because it implies there are two shaded portions in the graph when there is only one.

The complete question is:

Which compound inequality can be represented by the graph below?

A) x < 5 or x ≥ 9

B) 5 ≤ x < 9

C) x ≤ 5 or x > 9

D) 5 < x ≤ 9

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The Percentage of bags with correct weight will be 84%

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, the following can be gotten:

Total number of bags = 2500

Bags with correct weight = 2100

Bags with lower weight = 275

Bags with higher rate = 125

Percentage of bags with correct weight will be:

= 2100 / 2500 × 100

= 84%

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Answer:

125 million

Step-by-step explanation:

[tex]79.4 \times \frac{100}{63.5} = 125.03[/tex]

The cost of car in the year 1983 is 2845

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

The CPI (consumer price index) is a measure of the overall change in prices of goods and services over a certain period of time. It is given by:

CPI = (cost of market basket in a given year / cost of market basket in base year) * 100

Given that:

CPI = 56.9 in 1976, cost of market basket in a given year = x, cost of market basket in base year = $5000

Hence:

56.9 = (x/ 5000) * 100

x = 2845

The cost of car is 2845

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Answer:

calculate = 3.14159

Step-by-step explanation:

convert to degrees 189°

positive angle

[tex] 3\pi \: positive \: angle[/tex]

[tex]\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ (1+a^3)\div (1+a)\implies \cfrac{1+a^3}{1+a}\implies \cfrac{1^3+a^3}{1+a} \\\\\\ \cfrac{~~\begin{matrix} (1+a) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(1^2 - (a)(1)+a^2)}{~~\begin{matrix} 1+a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1^2 - (a)(1)+a^2\implies \boxed{a^2-a+1}[/tex]

Answer:

Below

Step-by-step explanation:

Put the numbers into the pythagorean theorem to see if true

12^2   + 15^2    =   18^2    ??????

144 + 225   =  324   ?????

369 = 324 ??????   <========= not true ....not a triple

Answer:

Sweater: $26

Shirt: $5

Step-by-step explanation:

We can set up two linear equations to form a systems of equations which will allow us to solve for the price of a shirt and sweater.

The first step we want to take is assigning the shirt and sweater to an unknown, so I'll just refer to the price of a shirt as: [tex]S_h[/tex] with the little subscript "h" and I'll refer to the price of a sweater as: [tex]S_w[/tex] with the little subscript "w".

Now the next main thing to understand is we can calculate the total price of something by multiplying the price of an individual item by the quantity. So if I buy an apple for $10, but I buy 10 of them, then the total price would be 10 * 10 or $100. So when Andrea buys 6 shirts, the price of that can be represented as: [tex]6S_h[/tex] and when Anrea buys 7 sweaters the price of that can be represented as: [tex]7S_w[/tex], adding these together should equal 212, since it gives us that buying 6 shirts and 7 sweaters costs a total of $212.

Using this logic with the other case where she buys 10 shirts and 8 sweaters for $258, we can set up the two equations:

[tex]6S_h + 7S_w=212\\10S_h+8S_w=258[/tex]

From here we can use substitution to solve this equation. So let's solve for the [tex]S_h[/tex] on the top equation.

[tex]6S_h+7S_w=212[/tex]

Froom here subtract [tex]7S_w[/tex] from both sides and then divide by 6

[tex]S_h=\frac{212-7S_w}{6}[/tex]

Now we can plug this into the second equation:

[tex]10(\frac{212-7S_w}{6})+8S_2=258[/tex]

Simplifying the division and multiplication on the left side we get:

[tex]\frac{1060}{3}-\frac{70}{6}S_w+8S_w=258[/tex]

From here we can combine the like terms

[tex]\frac{1060}{3}-\frac{22}{6}S_w=258[/tex]

we can simplify the fraction a bit more

[tex]\frac{1060}{3}-\frac{11}{3}S_w=258[/tex]

Now subtract 1060/3 from both sides

[tex]\frac{-11}{3}S_w=\frac{-286}{3}[/tex]

Now divide both sides by -11/3

[tex]S_w=26[/tex]

Now from here we can substitute this back into any equation to solve for the shirt price. Let's use the equation where we solved for the price of the shirt but we just needed to know the price of the sweater.

[tex]S_h=\frac{212-7S_w}{6}[/tex]

Now let's plug in 26 for the sweater price.

[tex]S_h=\frac{212-7(26)}{6}[/tex]

Simplify this and we get:

[tex]S_h=5[/tex]

and now we know the shirt and sweater price!

The slope of the line describes by the table is 0.1.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The table represents Bike ride, where x represents the number of minutes in 'x' and y represents the number of kilometers.

We know, slope(m) = (y₂ - y₁)/(x₂ - x₁).

Slope(m) = (1.0 - 0.5)/(10 - 5).

Slope(m) = 0.5/5.

Slope(m) = 0.1

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Ordering the populations of the 6 different states, written in scientific notations, in order of the greatest to the least value is as follows:

Scientific notation is the standard way of writing very long or short numbers in their shorthand forms.

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10, with the following parts: coefficient, base, and exponent.

For instance, New York's population is 19,700,000 and can be written in scientific notation as 1.97^7.

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The displacements are 2.84 cm, 2.77 cm, 2.83 cm and 2.83 cm respectively.

Instantaneous velocity of the particle at t =,1 is 0.72 cm/s.

a. To find the displacement of the particle at various times t, we can simply plug the given value of t into the equation s = 2 sin(t) + 3 cos(t) and evaluate:

[1, 2]: s = 2 sin(1) + 3 cos(1) = 2.84 cm

[1, 1.1]: s = 2 sin(1.1) + 3 cos(1.1) = 2.77 cm

[1, 1.01]: s = 2 sin(1.01) + 3 cos(1.01) = 2.83 cm

[1, 1.001]: s = 2 sin(1.001) + 3 cos(1.001) = 2.83 cm

b. To find the instantaneous velocity of the particle when t = 1, we need to find the derivative of the equation for displacement with respect to time, which will give us the velocity. The derivative is given by:

v(t) = ds/dt = 2 cos(t) - 3 sin(t)

Plugging in t = 1 into this equation, we find:

v(1) = 2 cos(1) - 3 sin(1) = 0.72 cm/s

So, the instantaneous velocity of the particle at t = 1 is approximately 0.72 cm/s.

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The probability of 35 people being selected before the first person with a phobia being chosen does not provide sufficient evidence to suggest that the ADAA claim is false. To determine if the ADAA claim is false, we would need to perform a statistical hypothesis test to compare the sample proportion of adults with phobias to the ADAA estimate of 8.7%. This would involve collecting data on a random sample of adults, calculating the sample proportion of adults with phobias, and comparing it to the ADAA estimate of 8.7%.

If the sample proportion is significantly different from 8.7%, we can conclude that there is evidence to suggest that the ADAA claim is false. However, without performing a statistical hypothesis test, we cannot make a conclusion about the validity of the ADAA claim based solely on the probability of 35 people being selected before the first person with a phobia is chosen.

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The equation cos (60°) = a/12 can be used to find one of the missing side lengths in the triangle.

Trigonometric identities are equations that are true for all values of the angles in a right triangle. They express the relationships between the angles and sides of a triangle and are used to simplify trigonometric expressions or to prove that two expressions are equal.

One of the trigonometric identities is the SOH CAH TOA.

SOH: sin θ = opposite/hypotenuse

CAH: cos θ = adjacent/hypotenuse

TOA: tan θ = opposite/adjacent

Since angle CBA is 60°, the adjacent side is a, the opposite side is b, and the hypotenuse is 12 units, then:

cos θ = adjacent/hypotenuse

cos (60°) = a/12

Rearranging the equation, we can solve one of the missing side lengths, which is a.

a = 12cos(60°)

Hence, we can use the equation cos (60°) = a/12 to find the length of side a.

The problem seems incomplete, it must have been...

"Which equation can be solved to find one of the missing side lengths in the triangle? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 60 degrees. The length of side C B is a, the length of C A is b, and the length of hypotenuse A B is 12 units.

cos(60°) = 12/a

cos(60°) = 12/b

cos(60°) = b/a

cos(60°) = a/12"

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Answer:

15% tell me if im wrong

Step-by-step explanation:

For the function E(t) = 31 cos (0.11t), the rate at which the number of wolves in the forest is changing at time t = 7 is 22.2549.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function to model the rate at which the number of wolves in a forest is changing is E(t) = 31 cos (0.11t)

Here t is the time measured in weeks.

The time value is given as t = 7

Substitute the value of t in the equation -

E(t) = 31 cos (0.11t)

Apply the arithmetic operation of multiplication -

E(7) = 31 cos (0.11 × 7)

E(7) = 31 cos (0.77)

E(7) = 31 × 0.7179

E(7) = 22.2549

Therefore, the rate value is obtained as 22.2549.

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The claim that the average of a random sample is the same as the average of the population from which it was taken is False.

The sample mean will, of course, differ from the population means. The sample mean, however, is a fair estimation of the population mean if the sample is a simple random sample.

Thus, neither the sample mean nor the population mean is statistically greater or lower. The sample mean will always have a mean that is identical to the mean of the original non-normal distribution. In other words, the population mean is the same as the sample mean.

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The closest value of x that would produce the box with the minimum surface area would be 117 ft.

The volume of a lidless box with height h and a square base with sides of length x is given by V = x^2 * h.

To have a volume of 117 ft^3, we have:

x^2 * h = 117

The surface area of a lidless box is given by:

A = 2x^2 + 4xh

We want to minimize this surface area while still keeping the volume of the box at 117 ft^3. To do this, we need to find an expression for h in terms of x, and then minimize A in terms of x.

From the volume equation, we can solve for h:

h = 117 / x^2

Substituting this expression into the surface area equation, we get:

A = 2x^2 + 4x * (117 / x^2)

= 2x^2 + 466 / x

Now, we can use calculus to find the minimum of A in terms of x.

The derivative of A with respect to x is:

dA/dx = 4x - 466 / x^2

Setting dA/dx equal to zero, we find the critical points:

4x - 466 / x^2 = 0

4x = 466

x = 116.5

We now need to check if x = 116.5 is a local minimum or maximum.

To do this, we need to examine the second derivative of A with respect to x:

d^2A/dx^2 = -932 / x^3

Since the second derivative is negative, this means that A has a local minimum at x = 116.5.

Hence, the value of x that produces the box with a minimum surface area is approximately 116.5 ft.

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Answer:

(3, 4.5)

Step-by-step explanation:

x = [tex]\frac{0 + 6}{2}[/tex] = 3

y = [tex]\frac{3+6}{2}[/tex] = 4.5

Answer:

Find the work required to pump the water out of the spout. (Use 9.8 m/s 2 for g. Use 1000 kg/m 3 as the weight density of water.

Step-by-step explanation:

The solution of the system of equations can be seen in the image at the end, the system has infinite solutions.

Here we have the system of linear equations below:

y = 2x - 2

4x - 2y = 4

To find the solution graphically, we need to graph both of the equations on the same coordinate axis and find the point where the lines intersect.

The graph can be seen in the image below, and there you can see only one line, that is because both of the equation of our system represent the same line, and thus, the system has infinite solutions.

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Answer:

611.05

Step-by-step explanation:

To find the number of cubic feet of water needed to fill Fred's fish tank, we need to calculate the volume of the tank. The volume of a rectangular prism (such as a fish tank) can be found by multiplying the length, width, and height together. Using the given measurements, the volume of Fred's fish tank would be:

8.3 ft * 11.5 ft * 6 ft = 611.05 cubic ft

So, Fred will need 611.05 cubic ft of water to fill his fish tank.

The required solutions are as follows,

(a) The team has zero points in 1 minute of the competition.
(b) The team has two points in 5 minutes of the competition.
(c) After 8 minutes, the team has 3 points.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
From graph,
As at 0 seconds the race started and Monia finished eating a hot dog at 3 minutes. so 1 to 2.9 minutes of race point is zero.

Scorecard with time is given as
1 to 2.9-minute score = 0
3 to 4.9-minute score = 1
5 to 7.9 minutes score = 2

after 8 minutes score = 3

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Answer:

The point (4,0) lies on the line.

All the other answers are not applicable for this situatino.

Step-by-step explanation:

Answer:

f'(2) = 25

Step-by-step explanation:

differentiate f(x) using the power rule

[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant) = 0

f(x) = 2x³ + x² - 3x + 4

f'(x) = 3× 2x² + 2x - 3 = 6x² + 2x - 3 , then

f'(2) = 6(2)² + 2(2) - 3

      = 6(4) + 4 - 3

      = 24 + 1

      = 25

Answer:

To find the value of (a - 1/a)^2 and (a - 1/a), we can start by squaring the given equation:

a^2 + 1/a^2 = 18

(a^2 + 1/a^2)^2 = 18^2

a^4 + 2 + 1/a^4 = 324

a^4 + 1/a^4 = 322

Now, to find (a - 1/a)^2, we can square the difference of a and 1/a:

(a - 1/a)^2 = a^2 - 2 + 1/a^2

We can substitute the value of a^4 + 1/a^4 = 322 into this equation:

(a - 1/a)^2 = 322 - 2

(a - 1/a)^2 = 320

To find (a - 1/a), we can take the square root of (a - 1/a)^2:

(a - 1/a) = √320

And, a^2 + 1/a^2 = 18, we can solve for a,

a^4 - 18a^2 + 1 = 0

(a^2 - 1)(a^2 - 18) = 0

a^2 = 1 or a^2 = 18

a = 1 or a = ±√18

So, in this case, the value of (a - 1/a)^2 is 320 and (a - 1/a) is √320.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Picture?

You didn’t give enough info. Are you able to provide more information? Or a picture?

Step-by-step explanation:

we need to calculate the distances between the points as the side lengths of the triangle.

these side lengths must satisfy the Pythagoras principle :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.

the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.

this is then caked the distance formula, but it is all Pythagoras again.

AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =

= 8² + 0² = 8²

AB = 8

AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20

AC = sqrt(20)

BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52

BC = sqrt(52)

as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.

if this is a right-angled triangle, then

8² = sqrt(20)² + sqrt(52)²

must be true.

but

64 = 20 + 52 = 72

is wrong.

so, the segments do not form a right-angled triangle.

Answer:

x ≥ 4

Step-by-step explanation:

Just treat the equation like you would a regular algebraic equation.

10 + x ≥ 14

10 + x - 10 ≥ 14 - 10

x ≥ 4

As for graphing it, I'm not really sure if you want a proper graph or a number line.

For a number line, put a closed dot on a 4

Answer:

number b is the write answer

Step-by-step explanation:

-2x²-3x+4-4x²+x-2

-2x²-4x²-3x+x+4-2

-6x²-2x+2