the function f(x) = x^2-1 and g(x) = -x^2+4 are shown on the graph

The amount of water needed is 72 liters.

Given that, the ratio of the alcohol and water in a mixture of 72 units is 2 ratio 1, we need to find the amount of water that must be added to the mixture in order to make this ratio 1 ratio 2,

So,

The quantity of water in it = 72 / 3 × 1 = 24

New ratio =

48 / 24+x = 1/2

96 = 24+x

x =72

Hence, the amount of water needed is 72 liters.

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Step-by-step explanation:

First group of five    total score   =    5 * 6.5 = 32.5

Group of fifteen total score         =   15 * 4.5 = 67.5

total score of  20    is    67.5 + 32.5 = 100

Average =  100 /20 = 5.0

The computations of the net profit or loss using the following cost valuation methods are as follows:

FIFO, net profit = $20,000

Weighted Average, net profit = $17,555.54.

The inventory cost valuation methods include FIFO (First In, First Out), LIFO (Last In, First Out), WAC (Weighted Average Cost), and Specific Identification.

Under the FIFO basis, the cost of inventory is evaluated based on the assumption that inventory that are first brought in are the first to be sold.

Under the Weighted Average Cost method, the average cost is computed by dividing the total cost of goods available for sale by the number of units.

Other inventory cost valuation methods include LIFO and Specific Identification.

Cost of Goods Sold = $80,000 ($10,000 x 3 + $12,000 x 2 + $13,000 x 2)

Sales Revenue = $106,000 ($15,000 x 7)

Overhead = $6,000

Net Profit = $20,000 ($106,000 - $80,000 - $6,000)

Weighted Average Cost per tractor = $11,777.78 ($106,000 ÷ 9)

Cost of Goods Sold = $82,444.46 ($11,777.78 x 7)

Sales Revenue = $106,000 ($15,000 x 7)

Overhead = $6,000

Net Profit = $17,555.54 ($106,000 - $82,444.46 - $6,000)

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The slope of the line that contains the points (-3, -1) and (3, -10) is -3/2.

Given two points.

We have to find the slope of the line.

Slope of a line passing through (x, y) and (x', y') is,

Slope = (y' - y) / Ix' - x)

Here two points are,

(-3, -1) and (3, -10)

Slope = (-10 - -1) / (3 - -3)

         = -9 / 6

         = -3/2

Hence the slope of the line is -3/2.

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The value of angle x is determined as 107⁰.

The value of angle x is calculated by applying principle of intersecting chord theorem.

The intersecting chord theorem states that half of the difference between the arc of two intersecting chords is equal to the tangent angle.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠MNP = ¹/₂( arc MLP - arc MP )

x = ¹/₂ [(360 -73) - (73)]

x = ¹/₂ (287 - 73 )

x = ¹/₂ (214)

x = 107⁰

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Answer:

The equation Qd = 50 - 4Px + 0.5I + 10Py - 2Pz represents the demand function for a certain good X, where Qd is the quantity demanded, Px is the price of X, I is the consumer's income, Py is the price of another good Y, and Pz is the price of another good Z.

To solve for the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied. However, without information on the supply function or market conditions, we cannot find the equilibrium price and quantity.

We can use the demand equation to determine the effect of changes in the independent variables on the quantity demanded for the good. For example, an increase in the price of X (Px) would lead to a decrease in the quantity demanded (Qd), while an increase in the price of Y (Py) or a decrease in the price of Z (Pz) would lead to an increase in the quantity demanded (Qd). An increase in income (I) would also lead to an increase in the quantity demanded (Qd).

Note that it is important to understand the context and assumptions underlying the demand function in order to make accurate economic predictions or decisions based on it.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

C)  1/2  and 8

Step-by-step explanation:

-2x + y = 7              Eq. 1

6x + y = 11               Eq. 2

From Eq. 1:

y = 7 + 2x               Eq. 3

From Eq. 2:

y = 11 - 6x              Eq. 4

Equalyzing Eq. 3 and Eq. 4:

7 + 2x = 11 - 6x

2x + 6x = 11 - 7

8x = 4

x = 4/8

x = 1/2

From Eq. 3:

y = 7 +2* 1/2

y = 7 + 1

y = 8

Check:

From Eq. 2

6x + y = 11

6*1/2 + 8 = 11

3 + 8 = 11

Answer:

2.38 s

4.62 s

Step-by-step explanation:

The height of a projectile is given by the function:

[tex]h(t) = -t^2 + 7t + 9[/tex]

where:

To determine the time(s) at which the rocket is 20 ft above the ground, set h(t) = 20 and solve for t.

[tex]-t^2+7t+9=20[/tex]

To solve the equation for t, complete the square.

Subtract 9 from both sides:

[tex]-t^2+7t=11[/tex]

Divide both sides by -1:

[tex]t^2-7t=-11[/tex]

Add the square of half the coefficient of the term with the variable "t" to both sides of the equation:

[tex]t^2-7t+\left(\dfrac{-7}{2}\right)^2=-11+\left(\dfrac{-7}{2}\right)^2[/tex]

Simplify:

[tex]t^2-7t+\dfrac{49}{4}=\dfrac{5}{4}[/tex]

We have now created a perfect square trinomial on the left side of the equation. Factor the perfect square trinomial:

[tex]\left(t-\dfrac{7}{2}\right)^2=\dfrac{5}{4}[/tex]

To solve for t, square root both sides:

[tex]t-\dfrac{7}{2}=\pm \sqrt{\dfrac{5}{4}}[/tex]

[tex]t-\dfrac{7}{2}=\pm\dfrac{\sqrt{5}}{2}[/tex]

Add 7/2 to both sides of the equation:

[tex]t=\dfrac{7}{2}\pm\dfrac{\sqrt{5}}{2}[/tex]

[tex]t=\dfrac{7\pm\sqrt{5}}{2}[/tex]

Therefore, the times at which the rocket is 20 ft above the ground is:

[tex]t=\dfrac{7-\sqrt{5}}{2}=2.38\; \rm s[/tex]

[tex]t=\dfrac{7+\sqrt{5}}{2}=4.62\; \rm s[/tex]

The apex angle |‹aed| of the rectangular base pyramid is equal to 14°.

In a rectangular base pyramid, the base is a rectangle and the apex (or top point) is directly above the center of the rectangle.

The apex angle is the angle formed by the edges of the pyramid at the apex. In a rectangular base pyramid, the apex angle depends on the dimensions of the rectangle base and the height of the pyramid. It can be calculated using trigonometric functions.

The apex angles bec and aed formed by the opposite width of the rectangle base are equal.

In conclusion, the apex angle |‹aed| of the rectangular base pyramid is equal to 14°.

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Answer:

Step-by-step explanation:

[tex]\frac{x}{18} =cot~30\\x=18cot~30=18 \times \sqrt{3} =18\sqrt{3} \\base=36\sqrt{3} \\area~of~triangle=3\times \frac{1}{2} \times36\sqrt{3} \times 18=972\sqrt{3} \approx 1683.55~mm^2[/tex]

Solving the given word problem systematically, Serene Travel Organization offers 12 diverse vacation packages.

To calculate the overall number of distinctive excursion packages that Quiet Travel Organization offers, we ought to duplicate the number of cities by the number of carriers:

Add up to number of get-away bundles = number of cities x number of airlines

Since the agency has 6 cities and 2 aircrafts to select from, we are able substitute those values within the over equation:

Add up to number of get-away bundles = 6 x 2 = 12

In this manner, Serene Travel Organization offers 12 diverse get-away bundles.

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The two-way table constructed from the data showing the numbers of boys and girls that choose each dance category should look like this:

                         Boys      Girls         Total

Fall Fling            82          81             163

Spring Social     62         75             137

Total                 144        156            300

A two-way table is a data display tool that displays the frequencies for two different categories collected from a single group.

A two-way table use rows to represent one category variable and the columns to represent a second category variable, while the cells display the proportions or frequencies of each row and column combination.

The total number of boys in eighth grade = 144

The number of boys who choose to attend the Fall Fling = 82

Therefore, the number of boys who attend the Spring Social = 62 (144 - 82)

The total number of girls in eighth grade = 156

The number of girls who choose to attend the Spring Social = 75

Therefore, the number of girls who attend the Fall Fling = 81 (156 - 75)

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Answer:

62,  82, 163, 300

Step-by-step explanation:

I got this on study island

The volume of the flower vase, can be found to be 2, 199 cm ³.

The volume of the flower vase can be found by subtracting the volume of the cone from the volume of the rectangular prism.

Volume of rectangular prism :
= Length x Width x Height

= 20 x 12 x 10

= 2, 400 cm ³

The volume of the cone is:

=  π x radius ² x height / 3

= π x 4 ² x 12 / 3

= 201. 06 cm ³

Volume of vase:

= 2, 400 -  201. 06

= 2198.94

= 2, 199 cm ³

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The key features of the function f(x) = 2log₃(x+7) graphed below include the following:

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-7, ∞].

Range = [-∞, ∞].

In conclusion, we can logically deduce that this logarithmic function has a vertical asymptote is at x equal to negative seven.

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The requried, perimeter and area of the parallelogram are 18.4 centimeters and 18 square centimeters respectively.

To find the perimeter of parallelogram EFGH, we need to find the length of all four sides and add them up. The distance formula is used to find the length of each side:

EF = √((2-(-1))² + (8-5)²) = √(3² + 3²) = √(18)

FG =√(20)

GH = √(18)

HE = √(20)

Therefore, the perimeter is:

Perimeter = EF + FG + GH + HE = √(18) + √(20) + √(18) + √(20) ≈ 18.4

Similarly,
The area of the parallelogram is given as,
= 18 square centimeters

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We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.

To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.

To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:

Group Size   Frequency   Relative Frequency

1                          9             9/150 = 0.06

2                         52           52/150 = 0.35

3                         27            27/150 = 0.18

4                         38            38/150 = 0.25

5                         16             16/150 = 0.11

6                          6              6/150 = 0.04

7                          5              5/150 = 0.03

8                          7              7/150 = 0.05

We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.

To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:

Number of groups with 5 or more people = 600 x 0.23 = 138

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Answer: x=23

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

When you have a value on the x-axis, your y=0

plug in y=0 to find your x-intercept

1x-2(0)=23

1x=23

x=23

The lengths of the legs, the circumference and the radius of the circles are;

First part; The diameter = 18 units

The second leg = 9 units

Second part; The circumference = 34·π units

Third part; The radius is r = 36 cm

The radius of a circle is the distance from the center to the circumference.

First part;

cos(30°) = 9·√3 ÷ The diameter = (√3)/2

The diameter = (9·√3) ÷ ((√3)/2) = 18

The length of the other leg, using the relationship between special triangles is 18/2 = 9

Second part;

The lengths of the legs of the right triangle indicates that we get;

The square of the diameter, D² = 30² + 16² = 1156

The length of the diameter, D = √(1156) = 34

The formula for finding the circumference of a circle, C, based on the diameter can be presented as follows;

C = π × D

Therefore;

The circumference of the circle, C = π × 34

The circumference of the circle = 34·π units

Third part

The length of the 20° arc = 4·π cm

Therefore;

4·π = 2·π·r × 20/360

Where;

r = The radius of the circle

Therefore;

r = (360/20) × 4·π ÷ (2·π) = 36

The radius of the circle, r = 36 cm

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The steepness of the ramp is approximately 56 feet.

You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground.

Therefore, let's find how steeped the ramp is.

Hence, using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

55² + 10² = c²

c² = 3025 + 100

c² = 3125

square root both sides of the equation

c = √3125

c = 55.9016994375

c = 56 feet

Therefore,

steepness of the ramp = 56 feet

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The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.

One can utilize the Central Limit Theorem (CLT) for proportions to detail the dispersion of the sample proportion. Explained by the CLT, if the size of the sample is sufficiently significant enough, then the distribution with respect to the sample proportion will be mostly indistinguishable from a typical distribution.

np ≥ 10

n(1-p) ≥ 10

Given that both conditions are fulfilled, we can essentially posit that the said sample proportion distribution  is almost normal. In light of this knowledge, it would be pertinent to ascertain the mean (μ) and standard deviation (σ) of the sample proportion distribution.

Mean = p = 0.15

Standard deviation:

= √ ( ( 0.15 x ( 1 - 0. 15 ) ) / 86 )

= 0.03852

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Answer:

92.

Step-by-step explanation:

To find the range of the set of numbers 20, 3, 95, 54, 71, 66, we first need to find the difference between the largest and smallest numbers in the set.

Largest number = 95

Smallest number = 3

Range = Largest number - Smallest number

Range = 95 - 3

Range = 92

Therefore, the range of the set of numbers 20, 3, 95, 54, 71, 66 is 92.

Answer:92

Step-by-step explanation: highest-lowest

it helps to put the terms in order first

95-3=92

The value of Tan A + B is 6.009.

[tex]sin^2 A + cos^2 A = 1sin^2 A = 1 - cos^2 Asin A = sqrt(1 - cos^2 A)sin A = sqrt(1 - (28/45)^2)sin A = sqrt(1 - 784/2025)sin A = sqrt(1241/2025)cos A = 28/45\geq[/tex]

We have to solve for Tan B

[tex]sin^2 B + cos^2 B = 1sin^2 B = 1 - cos^2 Bsin B = sqrt(1 - cos^2 B)sin B = sqrt(1 - (13/12)^2)sin B = sqrt(55/144)Therefore, tanB = sinB / cosB = (sqrt(55/144)) / (13/12) = (12 sqrt(55)) / 143[/tex]

[tex]tan(A+B) = (3207 \sqrt{55}) + 1804 \sqrt{124})) / (3115 - 207 \sqrt{(341)}[/tex]

= 6.009.

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In the circle the measure of arc YP as per the given measurements is equal to option D. 166°

In the circle,

Measure of arc ST = 70°

Measure of arc RS = 96°

Measure of angle YZP = 128°

Arc formed by vertically opposite angles are equal

This implies,

Measure of arc YT = Measure of arc PR

Measure of arc ST + Measure of arc RS + Measure of arc YT = 180°

⇒70° + 96° + Measure of arc YT = 180°

⇒Measure of arc YT = 180° - 166°

⇒Measure of arc YT = 14°

⇒ Measure of arc PR = 14°

Measure of arc YP = 360° - ( Measure of arc (PR + RS + ST + TY ))

⇒ Measure of arc YP = 360° - ( 14° + 96° + 70° + 14° )

⇒Measure of arc YP = 360° -194°

⇒ Measure of arc YP = 166°

Therefore, the measure of arc YP is equal to option D. 166°

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Answer:32 minutes

Step-by-step explanation:

He is running at a rate of 1 mile every 8 minutes. 3 miles in 24 minutes and 4 miles in 32 minutes

The equations to solve the length of the room is

a) y² - 5y = 750

b) 750 - y ( y - 5 ) = 0

c) ( y + 25 ) ( y - 30 ) = 0

Given data ,

Let the area of a rectangular room is 750 square feet.

Let the width of the room is 5 feet less than the length of the room

So , on simplifying , we get

w = l - 5

Area of rectangle = length x width

And , A = l x w

A = l ( l - 5 )

750 = y ( y - 5 )

Therefore , the equation is

a) y² - 5y = 750

b) 750 - y ( y - 5 ) = 0

On simplifying the quadratic equation , we get

c) ( y + 25 ) ( y - 30 ) = 0

Hence , the length of the rectangular room is solved

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The complete question is attached below :

Which equations can be used to solve for y, the length of the room? Select three options.

a) y(y + 5) = 750

b) y² – 5y = 750

c) 750 – y(y – 5) = 0

d) y(y – 5) + 750 = 0

e) (y + 25)(y – 30) = 0