4. The middle school is located at (0, 0) on
a coordinate plane. Town Hall is located
4 miles directly east of the middle
school. The fire station is located 2 miles
directly north of Town Hall.
How many miles long is a straight
line between the school and the fire
station? Round to the nearest tenth.

Answer:

To show that T<0,2> (0,1), we need to evaluate the transformation T at the point (0,1) and check if the result is in the range of T.

T<0,2> (0,1) means that the transformation T takes the point (0,1) in the input space to a point in the output space that has coordinates (0,2).

Let's evaluate T at (0,1):

T<0,2> (0,1) = D3(0,1) + (0,1)

= (0+0, 3+1)

= (0, 4)

The output point (0,4) is not equal to (0,2), which means that T<0,2> (0,1) is false. Therefore, T<0,2> does not map the point (0,1) to (0,2).

To determine if T<0,2> (x,y) = D3 (x,y) is a true statement for any point (x,y), we need to check if the transformation T always equals the function D3.

T<0,2> (x,y) = (x, 3+y)

D3(x,y) = (x,y,3)

Since T and D3 have different ranges (T has a range of R^2 and D3 has a range of R^3), the statement T<0,2> (x,y) = D3(x,y) is not true for any point (x,y).

Therefore, we cannot equate T<0,2> and D3, and the statement T<0,2> (x,y) = D3 (x,y) is false for any point (x,y).

Answer:

x = 8

Step-by-step explanation:

4(x + 3) = 44 ( divide both sides by 4 )

x + 3 = 11 ( subtract 3 from both sides )

x = 8

Answer:

Step-by-step explanation:

I just knew now I forgot sorry lol

Answer:

15%

Step-by-step explanation:

The ratio of the surface areas to cube A to cube B is 12 : 7 .

What is known as a cube?

Six faces, eight vertices, and twelve edges make up the three-dimensional shape of a cube. An example of a prism in particular is a cube. These are the calculations for the volume of the cube formula: Amount = (side) 3.

                      The cube's face's diagonal length is equal to 2. (edge) Cube's cube's diagonal length is three (edge) 12 is the perimeter (edge). Each number multiplied by itself is a square number. The squared sign is (insert square symbol). Up to the number 100, the square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. A number multiplied by itself three times is a cube number.

The ratio of the volumes of cube A to cube B is  =  1728 : 343

                                                                       = 12 : 7

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The volume of the solid is 284π/3 cubic inches.

To find the volume of the solid, we need to break it down into simpler shapes and then calculate their volumes separately.

The solid is made up of a cylinder and a hemispherical hole cut from the top of it. Let's first calculate the volume of the cylinder. The height of the cylinder is given as 12 inches and the radius can be calculated as half of the hypotenuse of the triangle (which is 10 inches). Therefore, the radius of the cylinder is 5 inches.

The formula for the volume of a cylinder is Vcylinder = πr^2h, where r is the radius and h is the height. Substituting the values, we get:

Vcylinder = π(5^2)(12) = 300π cubic inches

Now, let's calculate the volume of the hemispherical hole. The rim of the hole is 3 inches thick, which means the radius of the hole is (5 - 3) = 2 inches. The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3.

Substituting the values, we get:

Vhemisphere = (2/3)π(2^3) = 16π/3 cubic inches

Now, the volume of the solid can be found by subtracting the volume of the hemispherical hole from the volume of the cylinder:

Vsolid = Vcylinder - Vhemisphere

Vsolid = 300π - 16π/3

Vsolid = 284π/3 cubic inches

Therefore, the volume of the solid is 284π/3 cubic inches.

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Answer:

Step-by-step explanation:

18

Answer:

$0.50

Step-by-step explanation:

We know

A package of 8 hot dogs is on sale for $4

What is the price per hot dog?

4 / 8 = $0.50

So, the price per hot dog is $0.50

8×4=32

11-8=3

4×3=12

12÷2=6

32+6=38

=38inch^2

it might b wrong tho?

A double number line means the values of two different quantities are expressed in two separate lines such as corresponding values align. Here 1ml of blue water will need 3 ml of yellow water.

Here double line represents the relation between yellow water and blue water required to produce green water. 5ml of blue water needs 15ml of yellow water.

So the ratio is 5 : 15

3. One division in the line for blue water represents 1ml and 1 division in yellow water line is 3 ml.

We can also solve it using proportions

5 : 15 :: 1: x

5/15 = 1/x

x = (1×15)/5 = 3 ml

4. For 11 ml of blue water, it will require 33 ml of yellow water.

5. For 8 ml of blue water, 24 ml of yellow water is needed.

6. If we know the volume needed with 1ml of blue water, we can multiply that volume with any quantities of blue water to calculate the volume needed. For example 4 ml of blue water needs 4×3 = 12 ml of yellow water.

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The complete question is as below.

The other day, we made green water by mixing 5 ml of blue water with 15 ml of yellow water. We want to make a very small batch of the same shade of green water. We need to know how much yellow water to mix with only 1 ml of blue water.

1. On the number line for blue water, label the four tick marks shown.

2. On the number line for yellow water, draw and label tick marks to show the amount of yellow water needed for each amount of blue water.

3. How much yellow water should be used for 1 ml of blue water? Circle where you can see this on the double number line.

4. How much yellow water should be used for 11 ml of blue water?

5. How much yellow water should be used for 8 ml of blue water?

6. Why is it useful to know how much yellow water should be used with 1 ml of blue water?

No, the result is not significant at 1 percent level for the p-value of 0.802.

Results are significant at a certain level,

Compare the p-value to the significance level (known as alpha).

The significance level is typically set at 0.05 or 0.01.

Here, the p-value is 0.802, which is much larger than 0.01.

This implies here we cannot reject the null hypothesis at a 1% significance level.

Or , the result is not statistically significant at a 1% level.

If the significance level was 5%  that is equal to 0.05.

The result would not be significant at 5% level either.

If the significance level was 10% which is equal to 0.10.

Then the result would be significant as the p-value is less than 0.10.

Therefore, for the given p-value 0.802 result is not significant at 1%.

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Answer:

2500

Step-by-step explanation:

Total spectator 9500

Men 6375

Women and children = 9500-6375= 3125

Women X

Children 4X

If women and children = 3125

4x + X = 3125

5x = 3125

Divide both sides by 5

X = 625

Women 625

Children 625x4 = 2500

Answer:

A. X = -4

Step-by-step explanation:

[tex]-6x-24=3x+12\\-9x=36\\x=-4[/tex]

The domain of the piecewise function g of x is all real numbers, except for x = 2, which is the point at which the two functions overlap. Therefore, the domain is (–∞, 2) ∪ (2, ∞).

A domain is a collection of computers and devices connected to one another through a network. It is a logical grouping of computers and devices, such as a local area network (LAN) or a wide area network (WAN). Each device within the network is assigned a unique address, allowing it to communicate with other devices within the network. Domains can also be used to control access to resources, such as files, folders, printers, and databases. Domains can be used to authenticate users and set permissions, which determine the type of access a user has to the domain’s resources. This is commonly used in businesses and organizations to ensure that only authorized personnel have access to sensitive information.

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Answer:

0.03125

Step-by-step explanation:

[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex](r)^{n-1}[/tex]  

[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{(7-1)}[/tex]

[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{6}[/tex]

[tex]a_{7}[/tex] = 0.03125

Helping in the name of Jesus.

The correct answer is d. 9.9498.

To find the standard deviation of a distribution, we use the formula:

Standard deviation = √[(∑(x - mean)2)/n]

First, we need to find the mean of the distribution. The mean is the sum of all the values divided by the number of values. In this case, the mean is:

mean = (35 + 250)/5 = 57

Next, we need to find the sum of the squared differences between each value and the mean. This is:

∑(x - mean)2 = (35 - 57)2 + (250 - 57)2 = 485 + 37249 = 37734

Finally, we divide this sum by the number of values and take the square root to get the standard deviation:

Standard deviation = √(37734/5) = √7546.8 = 9.9498

So the standard deviation of the distribution is 9.9498.

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This confirms that our polynomial function has the correct y-intercept.

To find a polynomial function with the given properties, we can use the fact that the zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times that zero appears as a factor in the polynomial.

Since we are given a triple zero at x = 1, this means that (x - 1)^3 is a factor of the polynomial. Similarly, since we are given a double zero at x = 3, this means that (x - 3)^2 is a factor of the polynomial.

To find the y-intercept, we can set x = 0 and solve for y. Since the y-intercept is given as (0, 27), this means that the constant term of the polynomial is 27.

Putting all of this information together, we can write the polynomial function as:

f(x) = 27(x - 1)^3(x - 3)^2

This is a polynomial function that satisfies the given properties. It has a triple zero at x = 1, a double zero at x = 3, and a y-intercept of (0, 27).

We can check our answer by plugging in the values of x and seeing if the function equals zero:

f(1) = 27(1 - 1)^3(1 - 3)^2 = 0
f(3) = 27(3 - 1)^3(3 - 3)^2 = 0

Both of these values equal zero, which confirms that our polynomial function has the correct zeros. Additionally, when we plug in x = 0, we get:

f(0) = 27(0 - 1)^3(0 - 3)^2 = 27

This confirms that our polynomial function has the correct y-intercept.

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To simplify the complex fraction ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2))), we can use the common denominator method.

Step 1: Find the common denominator for the numerator and denominator of the complex fraction. The common denominator for the numerator is (f^(3))(a^(3)) and the common denominator for the denominator is (f^(2))(a^(2)).

Step 2: Multiply each term in the numerator and denominator by the common denominator to get rid of the fractions.

Numerator: ((1)(a^(3))-(1)(f^(3)))/(f^(3))(a^(3))

Denominator: ((1)(a^(2))-(1)(f^(2)))/(f^(2))(a^(2))

Step 3: Simplify the numerator and denominator by combining like terms.

Numerator: (a^(3)-f^(3))/(f^(3))(a^(3))

Denominator: (a^(2)-f^(2))/(f^(2))(a^(2))

Step 4: Divide the numerator and denominator by the common factor (f^(2))(a^(2)).

Simplified fraction: (a-f)/(f^(1))(a^(1))

Step 5: Simplify the final fraction by canceling out the common factors.

Final answer: (a-f)/(fa)

Therefore, the simplified complex fraction is (a-f)/(fa).

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Answer: 1

Step-by-step explanation:

3(x-2) = 4x+2

3x-6 = 4x+2

To move 3x, deduct it on both sides of the equation.

3x - 6 - (3x) = 4x + 2 - (3x)

0 - 6 = [1]x +2

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

Answer:

The area of the whole rectangle is 28 cm^2

Step-by-step explanation:

since both triangles are congruent, they have the same area. 14 x 2 = 28

sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.

Suppose sin θ = -3/5, sin ɸ = 20/29. Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. We can find sin(θ + ɸ) and cos(θ + ɸ) by using the following formulas: sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ and cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ.

First, we need to find cos θ and cos ɸ. Since θ is in Quadrant IV, cos θ is positive. We can use the Pythagorean identity, sin² θ + cos² θ = 1, to find cos θ:

cos² θ = 1 - sin² θ
cos² θ = 1 - (-3/5)²
cos² θ = 1 - 9/25
cos² θ = 16/25
cos θ = √(16/25)
cos θ = 4/5

Similarly, since ɸ is in Quadrant l, cos ɸ is also positive. We can use the Pythagorean identity to find cos ɸ:

cos² ɸ = 1 - sin² ɸ
cos² ɸ = 1 - (20/29)²
cos² ɸ = 1 - 400/841
cos² ɸ = 441/841
cos ɸ = √(441/841)
cos ɸ = 21/29

Now we can plug in the values of sin θ, sin ɸ, cos θ, and cos ɸ into the formulas for sin(θ + ɸ) and cos(θ + ɸ):

sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ
sin(θ + ɸ) = (-3/5)(21/29) + (4/5)(20/29)
sin(θ + ɸ) = -63/145 + 80/145
sin(θ + ɸ) = 17/145

cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ
cos(θ + ɸ) = (4/5)(21/29) - (-3/5)(20/29)
cos(θ + ɸ) = 84/145 + 60/145
cos(θ + ɸ) = 144/145

Therefore, sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.

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Step-by-step explanation:

The area A of a rectangle is given by multiplying its length and width. In this case, the length is 7x - 1 units and the width is 2x + 3 units. Therefore, the area of the rectangle is:

A = (7x - 1)(2x + 3)

= 14x^2 + 19x - 3

Hence, the area of the rectangle is 14x^2 + 19x - 3 square units.

Answer:

14x^2+19x-3

Step-by-step explanation:

you have to times them together so

(7x-1)(2x+3)

14x^2+21x-2x-3

=14x^2+19x-3

Answer:

cos G = 3/5

sin G = 4/5

tan G = 4/3

Step-by-step explanation:

I(9, 12)

GH = 9

HI = 12

(GI)² = 9² + 12²

GI = 15

For <G:

opp = HI = 12

adj = GH = 9

hyp = GI = 15

cos G = adj/hyp = 9/15 = 3/5

sin G = opp/hyp = 12/15 = 4/5

tan G = opp/adj = 12/9 = 4/3

Step-by-step explanation:

remember the triangle in a circle, when you learned about sine, cosine and the other trigonometric functions ?

this looked the same way, just that the circle was the norm-circle with radius 1.

here, now, the radius is larger, so every function line is also multiplied by the actual radius.

but the principles are the same.

sine is the up/down leg of the right-angled triangle.

cosine is the left/right leg.

tangent is sine/cosine.

I = (9, 12)

so, Pythagoras gives us the radius (line GI) :

GI² = GH² + HI² = 9² + 12² = 81 + 144 = 225

GI = sqrt(225) = 15

sin(G) × GI = HI

sin(G) × 15 = 12

sin(G) = 12/15 = 4/5 = 0.8

cos(G) × GI = GH

cos(G) × 15 = 9

cos(G) = 9/15 = 3/5 = 0.6

tan(G) = sin(G)/cos(G) = 4/5 / 3/5 = (4×5)/(5×3) =

= 4/3 = 1.333333333...

The expression when evaluated is -5

From the question, we have the following parameters that can be used in our computation:

6(− 2/3 ) − 1.5 + ( 1/2 )

To solve the given expression, we need to apply the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed.

Using the order of operations, we can simplify the given expression as follows:

6(− 2/3 ) − 1.5 + ( 1/2 ) = -4 − 1.5 + 0.5

Evaluate

6(− 2/3 ) − 1.5 + ( 1/2 ) = -5

Hence, the solution is (b) - 5

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Probability of selecting a marble at random and then put it back into the bag will be [tex]\frac{7}{36}[/tex]

The likelihood that something will occur is known as the probability.  Because we don't know how something will turn out, we might talk about the probability of one result or the potential for several outcomes. The study of events that fit into a probability distribution is known as statistics. The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

Number of purple marble=16

Number of blue marble=12

Number of white marble=14

Number of brown marble=6

The Probability is =[tex]\frac{12+14+6}{16+12+14+6}[/tex] ×  [tex]\frac{14}{16+12+14+6}[/tex]

=[tex]\frac{32}{48}[/tex] × [tex]\frac{14}{48}[/tex]

=[tex]\frac{7}{36}[/tex]

Hence, Probability of selecting a marble at random and then put it back into the bag will be      [tex]\frac{7}{36}[/tex].

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Answer:

78

Step-by-step explanation:

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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Answer:

C. a 55 degree angle

Step-by-step explanation:

180 degrees-125 degrees=55.

Answer:

Twenty Seven (27) cubic yards

Answer:

volume =27 cubic yards

Step-by-step explanation:

Volume = Base Area x Height

Volume= 3·3·3

Volume= 27