Let f(x) =4x-1 and g(x)=2^x+3. Find (f-g) (5)

Answer:

12f

Step-by-step explanation:

3f + 3f + 3f + 3f = 12f

Answer:

180-142 is angle a

The equation of the product is 4y³ and 2y² multiplied by 3y and 5 is equal to 24y⁴ plus 15y³.

4y³ x 2y² = 8y⁵

8y⁵ x 3y = 24y⁴

24y⁴ x 5 = 15y³

24y⁴ + 15y³ = 24y⁴ + 15y³

The product of 4y³ and 2y² multiplied by 3y and 5 is equal to 24y⁴ plus 15y³. To calculate this product, the first step is to multiply 4y³ and 2y² together. This will give us 8y⁵. Then, we multiply 8y⁵ by 3y to get 24y⁴. Finally, we multiply 24y⁴ by 5 to get 15y³. When we add 24y⁴ and 15y³, we get the final answer 24y⁴ plus 15y³. This calculation shows us how to multiply two expressions and then add them to get the product of four terms.

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The two widely used metrics of variation are the coefficient of variation (CV) and the standard deviation (SD).

Coefficient of variation (CV) is a measure of relative variation and is often used to compare variation between populations or groups with different means. It is calculated as the ratio of the standard deviation to the mean, multiplied by 100 to express the result as a percentage. It's a dimensionless value, which means it can be used to compare the variation of different variables that are measured in different units.

Standard deviation (SD) is a measure of the amount of variation or dispersion of a set of values. It is calculated as the square root of the variance, which is the average of the squared differences from the mean. Standard deviation is a measure of absolute variation and is typically used to describe the spread of data within a single population or group.

Both of these metrics are important in understanding the variation within a population, with the CV being useful in comparing different groups and SD being used to describe the spread of data within a single group.

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Answer:

Step-by-step explanation:

use the point-slope form of the equation if a straight line:

Y - y1 = m(x - x1)

Y - 1 = F(x - 5)

Y = Fx - 5F + 1

Answer:

y = -4x + 1

Step-by-step explanation:

We find the equation of a line passing through two given points using the generalized slope-intercept which is

y = mx + b

m is the slope(gradient) of the line and b is the y-intercept i.e. the y-value where it crosses the y-axis. This is nothing but the value of y when x  0

Start by finding the slope first

Slope, m = (y2-y1)/(x2-x1)  

Taking(x1, y1) as (-1, 5) and (x2, y2) as (2, -7)

we get

y2 - y1 = -7 -5 = -12

x2 - x1 = 2 - (-1) = 1 2 + 1 = 3

m = -12/3 = -4

Equation would be
y = -4x + b

To find b, choose a known value for x and its corresponding y value and solve for b

Let's take (-1, 5)

Subbing this into the equation gives

5 = (-4)(-1) + b

5 = 4 + b

or b = 1

So the equation of the line in slope-intercept form is

y = -4x + 1

The width of the cooling tower at the base of the structure as calculated from the data is 40 meters.

The equation which is given is ,

x²/400 -(y-90)²/1600=1

To calculate the width,

Cooling tower width =2√400

=2×20

=40 meters

Therefore the width is 40 meters.

A cooling tower is a type of heat removal device which uses water to remove waste heat from a process and discharge it into the atmosphere.

Similarly, an industrial cooling tower works by removing heat from water by evaporating little percentage of the water that is recirculated through the unit. When warm water and cooler air mingle, the latent heat of vaporization is released, causing the water to cool.

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The width of the cooling tower at the base of the structure is 16 meters.

x = 16 meters

x^2/400 - (y - 110)^2/2304 = 1

x^2/400 = (y - 110)^2/2304 + 1

400x^2 = 2304(y - 110)^2 + 2304

400x^2 = 2304y^2 - 514240y + 2574304

x^2 = 514240y/400 - 2574304/400 = 514.6y - 6435.76

x = √(514.6y - 6435.76)

For y = 0, x = 16 meters

Therefore, the width of the cooling tower at the base of the structure is 16 meters (rounded to the nearest whole number).The width of the cooling tower at the base of the structure is 16 meters.

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The value of the central angle EJF formed by the given polygon is; 20°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, the number of sides of the given polygon when completed will be 18 sides. Thus, we can say that;

Central angle = 360/18

Central angle = 20°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠E = ∠F = [180 - 20]/2

∠E = ∠F = 80°

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Answer: -170

Step-by-step explanation:

-4(2(-3)+7(5))-6(-3)^2

-4(-6+35)-6(9)

-4(29)-54

-116-54

-170

Answer:

-170

Step-by-step explanation:

-4(2(-3) + 7(5)) - 6(-3)^2

-4 ( 29) -54

-116-54

-170

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2000\\ P=\textit{original amount deposited}\dotfill &\$1800\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}[/tex]

[tex]2000 = 1800\left(1+\frac{0.048}{12}\right)^{12\cdot t} \implies \cfrac{2000}{1800}=(1.004)^{12t}\implies \cfrac{10}{9}=1.004^{12t} \\\\\\ \log\left( \cfrac{10}{9} \right)=\log(1.004^{12t})\implies \log\left( \cfrac{10}{9} \right)=t\log(1.004^{12}) \\\\\\ \cfrac{\log\left( \frac{10}{9} \right)}{\log(1.004^{12})}=t\implies 2.20\approx t\qquad \textit{about 2 years and 73 days}[/tex]

Answer:

x = 18.8

Step-by-step explanation:

The triangles are similar triangles.

We can write the following equation to find the value of x based on the above mentioned information:

[tex] \frac{26}{35} = \frac{14}{x} [/tex]

26x = 35×14

26x = 490

x = 18.8 approximately

The  percent of phones have a battery life less than 5 hours or greater than 5.5 hours is 52.27%.

A z-score, also known as a standard score, provides information on how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve. The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviations (which would fall to the far right of the normal distribution curve). You must be aware of the mean and population standard deviation in order to use a z-score.

Given the talk time battery life of a group of cell phones

Mean = μ = 5 hours

standard deviation = σ = 15 minutes = 0.25 hours

to calculate P(5 > x > 5.5)

formula for z score is

z = (x - μ)/σ

x = 5

z = (5 - 5)/.25

z = 0

P-value from Z-Table:

P(x < 5) = 0.5

P(x > 5) = 1 - P(x<5) = 0.5

at x= 5.5

z = (5.5 - 5)/.25

z = 2

P-value from Z-Table:

P(x < 5.5) = 0.97725

P(x > 5.5) = 1 - P(x < 5.5) = 0.02275

P(5 < x < 5.5) = P(x < 5.5) - 0.5 = 0.47725

for P(5 > x > 5.5) = 1 - P(5 < x < 5.5) = 1 -0.47725

P(5 > x > 5.5) = 0.52275

percent = 0.52275 x 100 = 52.27%

Hence the percent at   P(5 > x > 5.5) is 52.27%.

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The triangles that are congruent are triangle xyz and triangle def.

Triangles xyz, def and qrp can be tested for congruency using the Side-Angle-Side (SAS) Theorem. The SAS theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of a second triangle, then the two triangles are congruent.

To begin, we must first determine the side lengths and angle measures of the three triangles.

For triangle xyz, the side lengths are x = 4, y = 5, and z = 6, and the angle measures are angle x = 55 degrees, angle y = 70 degrees, and angle z = 55 degrees.

For triangle def, the side lengths are d = 4, e = 5, and f = 6, and the angle measures are angle d = 55 degrees, angle e = 70 degrees, and angle f = 55 degrees.

For triangle qrp, the side lengths are q = 3, r = 4, and p = 5, and the angle measures are angle q = 40 degrees, angle r = 40 degrees, and angle p = 100 degrees.

Now that the side lengths and angle measures of the three triangles have been established, we can use the SAS theorem to determine which of the three triangles are congruent.

To test triangles xyz and def for congruency, we will compare the two triangles side by side. We can see that the side lengths of xyz and def are equal (x = d = 4, y = e = 5, and z = f = 6). We can also see that the angle measures of xyz and def are equal (angle x = angle d = 55 degrees, angle y = angle e = 70 degrees, and angle z = angle f = 55 degrees). Thus, since all of the corresponding side lengths and angle measures of xyz and def are equal, the two triangles are congruent.

To test triangles xyz and qrp for congruency, we will compare the two triangles side by side. We can see that the side lengths of xyz and qrp are not equal (x = 4, q = 3; y = 5, r = 4; z = 6, p = 5). We can also see that the angle measures of xyz and qrp are not equal (angle x = 55 degrees, angle q = 40 degrees; angle y = 70 degrees, angle r = 40 degrees; angle z = 55 degrees, angle p = 100 degrees). Thus, since the corresponding side lengths and angle measures of xyz and qrp are not equal, the two triangles are not congruent.

Therefore, the triangles that are congruent are triangle xyz and triangle def.

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Answer: A & C

Step-by-step explanation:

I got it right on edge <3

Let E be the region enclosed by the paraboloids z = x² + y² and z = 2 – x² - y² , then ∫∫∫(√x² + y²)dV is equals to the [tex]∫^{\pi}₀∫^{1} ₀∫^{2 - {r}^{2}} ᵣ₂ r² dz dr dθ ,[/tex].

We have two equations of paraboloids are z = x² + y² and z = 2 – x² - y² . Let E be the region enclosed by the (1) and (2). We have to determine the value of volume integral ∫∫∫(√x² + y²)dV in polar form. Now, change the Cartesian co-ordinates (i.e., x and y) into polar coordinates ( i.e., r and θ ). In polar coordinates, x = r cosθ ; y = r sinθ then, x² + y² = (r cosθ)² + (r sinθ)²

= r²cos²θ + r²sin²θ = r²(sin²θ + cos²θ)

= r² or √x² + y² = √r² = r

Plugging the value in curve equation,

z = x² + y² = r² and z = 2 – x² - y² = 2 - r²

i.e., z varies from r² to 2 - r²

and θ varies from 0 to π ( see in graph) and r varied from 0 to 1. Also, dxdy = r dr dθ. So, the triple integral or volume integral in polar coordinates is

[tex]∫^{\pi}₀∫^{1} ₀∫^{2 - {r}^{2}} ᵣ₂ r² dz dr dθ ,[/tex]

Hence, we get the required expression in polar coordinates.

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The average cost of the model is 60 dollars. Therefore, the advertisement is definitely correct.

The small store that specializes in work boots sells 3 different models of boots. The prices of these 3 models are as follows: $10, $75, and $95.

An advertisement for this store correctly states that the average cost of the boots sold there is $60.00. Therefore, let's find if the advertisement for this store is correct.

Hence,

average cost = sum of the cost of the different models of boot / number of models

average cost = 10 + 75 + 95 / 3

average cost = 180 / 3

average cost = 60 dollars

Therefore, the advertisement is correct.

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Answer:

b = 8

Step-by-step explanation:

cos Θ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{PQ}{QR}[/tex] = [tex]\frac{b}{14}[/tex]

given cos Θ = [tex]\frac{4}{7}[/tex] , then equate the 2 expressions , that is

[tex]\frac{b}{14}[/tex] = [tex]\frac{4}{7}[/tex] ( cross- multiply )

7b = 56 ( divide both sides by 7 )

b = 8

Their annual state income tax could be $4050  if there is $2,000 deduction for married couples and $900 for each dependent or child.

What is percentage?

percentage can be defined as the product of ratio of given value , total value and hundred.

Given,

The Cabrera family makes $92,800 annually and has 2 children. The state in which they live allows a $2,000 deduction for married couples and $900 for each dependent or child. The tax rate is 4.8%.  

As it is a family so $2,000 deduction for married couples

and they are having two childs so we will deduct another $1800 .

so now the actual amount  = $92800 - $2000 - $1800

Amount = $90000

The tax rate = 4.5%

that is amount to be paid = 4.5 % of 90000

= 4.5 / 100  *  90000

= 45/1000  *  90000

= 45 * 90

= 4050

Hence, Their annual state income tax could be $4050 .

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Answer:

[tex]f(-1)=-11\\f(0)=16\\f(2)=22[/tex]

Step-by-step explanation:

[tex]\displaystyle f(-1)=3(-1)-8=-3-8=-11\\f(0)=3(0)+16=16\\f(2)=3(2)+16=6+16=22[/tex]

The cost of each window, rounded to the nearest dollar is $280.

Estimation of a number is a reasonable guess of the actual value to make calculations easier and realistic.

Estimation means approximating a quantity to the required accuracy.

This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer.

The total cost = $5820

Number of windows = 28

Cost of one window = 5820/28

Cost of one window = $208 (estimated)

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The length of truck is equal to 6.325 feet.

In Mathematics, there are two (2) main types of percentage change and these include the following:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase = [Final value - Initial value]/Initial value × 100

Based on the information provided above, we have the following parameters about the car and truck;

Length of car = 5.5 feet.

Percentage increase in length of truck = 15%.

Now, we can calculate the length of the truck by using this mathematical expression;

Length of truck = 115/100 × 5.5

Length of truck = 1.15 × 5.5

Length of truck = 6.325 feet.

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The distance that the cyclist would ride in 8 seconds is; 97.6 yards

The general form of the equation of a line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Now, from the function table, we are given the coordinates;

(2, 24.4), (3, 36.6), (5, 61), (6, 73.2)

Now, we can find the slope from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

m = (36.6 - 24.4)/(3 - 2)

m = 12.2

At x = 0, we have;

12.2 = (24.4 - y)/(2 - 0)

2(12.2) = 24.4 - y

y = 24.4 - 24.4

y = 0

Thus, the equation is; y = 12.2x

Thus, at 8 seconds, we have;

y = 12.2(8)

y = 97.6 yards

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The probability that the man is standing where he started when he is finished is 1/2

Given is that a large, regular hexagon is drawn on the ground, and a man stands at one of the vertices. The man flips a coin. If the coin lands heads, he walks counterclockwise along the edge of the hexagon until reaching the next nearest vertex. If the coin lands tails, he walks clockwise around the hexagon until reaching another vertex.  The man flips the coin a total of six times.

Now, for either all heads or all tails, the person will land at same place. So, we can write that -

number of favorable outcomes = N{F} = 6

total number of favorable outcomes = N{T} = 12

P{E} = N{F}/N{6}

P{E} = 6/12

P{E] = 1/2

Therefore, the probability that the man is standing where he started when he is finished is 1/2.

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The value of given expression -[tex]a^{2}[/tex] - 2bc - | c |  is 9 .

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given expression,

-[tex]a^{2}[/tex] - 2bc - | c |

Given values are a = -3 ,  b = -5 , c =2 .

By substituting given values we get,

= -(-3*-3) - 2 * (-5)(2) - |2|

= -9 - (-20) - 2

= 20-11

= 9

Hence , The value of given expression is 9 .

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The value of given expression - - 2bc - | c |  is 9 .

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

In mathematics, a variable is a symbol, usually a letter, that represents a value or a set of values. Variables are used to represent unknown or changing values in mathematical expressions and equations.

Given expression,

- - 2bc - | c |

Given values are a = -3 ,  b = -5 , c =2 .

By substituting given values we get,

= -(-3*-3) - 2 * (-5)(2) - |2|

= -9 - (-20) - 2

= 20-11

= 9

Hence , The value of given expression is 9 .

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Answer:

3x+6

Step-by-step explanation:

This problem is quite simple, all you need to do is you multiply the 3 on the outside of the parenthesis times x, which results in 3x, next multiply 3 times 2 and it becomes a six.

If the length of one side of a square is increased by 20%, then the perimeter will increase by 40%.

To solve this, consider a square with side lengths. The perimeter of this square is 4s. If we increase the side length by 20%, the new side length is 1.2s. The perimeter of the new square is 4(1.2s) = 4.8s. The increase in the perimeter is 4.8s - 4s = 0.8s, or 80% of the original perimeter. Since the original perimeter was 4s, this is an increase of 80% of the original perimeter or 40% of the original side length.

Therefore, the correct answer is d) 40%.

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If the length of one side of a square is increased by 20%, then the perimeter will increase by 20%.

Therefore the answer is c) 20%.

Let length of the one side of a square be a. Then the new length after 20% is

a + 0.20a = 1.20a

Perimeter of a square is the sum of length of all four sides. Thus initial perimeter of the square is

a + a + a + a = 4a

New perimeter of the square with side 1.2a is thus calculated by

4×1.2a = 4.8a

Percentage increase in perimeter can be calculated by

(4.8a - 4a)/ 4a × 100, that is

[tex]=\ \frac{4.8a\ -\ 4a}{4a}\ 100[/tex]

= 0.8a/4a × 100

= 20%

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Answer:

£ 15347.06

Step-by-step explanation:

 First find 19.5% of 19064.67.

        Decreased amount = percentage of decrease * total amount

                                          = 19.5% * 19064.67

                                          = 0.195 * 19064.67

                                         = £ 3717.61

Amount after decrease = 19064.67 - 3717.61

                                       = £ 15347.06

The algebraic representation of the reflection in the image is the one in option A.

(x, y) → (-x, y)

Here we have an image with two moons, such that one is the reflection of the other.

Notice that the reflection is across the vertical axis (it is the y-axis). So the y-values don't change after the reflection, only the x-values change.

So we will have a change of sign on the x-value, then the reflection must be written as:

(x, y) → (-x, y)

In this way we can conclude that the correct option is A.

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Answer:

Subtract 2 from both sides to get:

2 x = 4 w

Then, you could divide both sides by 2 to get:

x = 2 w

Therefore, the value of x is 2 w.

Answer:

x=7

Step-by-step explanation:

2x-0.4=1+1.8x

Subtract 1.8x from both sides

0.2x-0.4=1

Add 0.4 to both sides of the equation

0.2x=1.4

Divide both sides by 0.2

x=7

Answer:

-9

-4

1

|-2|

|-3|

|-5|

|-6|

Step-by-step explanation:

| |

This symbol means whatever number inside of it turns to positive

Answer:

-9

-4

1

|-2|

|-3|

|-5|

|-6|