I need help with this Question.

Let the number be n.

Then the expression is:

Answer:

Step-by-step explanation:

Forming the expression,

→ 4x + x

Let's solve the expression,

→ 4x + x

→ 5x

Hence, the answer is 5x.

a) An algebraic expression for the gasoline left in the fuel tank is L = 0.4w.

b) If w = 15.5, the amount of gasoline left in the tank at the end of the journey was 6.2 gallons.

An algebraic expression is a mathematical statement that combines constants and variables together with mathematical operands.

The mathematical operands include addition, subtraction, division, multiplication, etc.

Let L = the amount of gasoline left

Let the full capacity of the fuel tank = w gallons

Gasoline consumed on the journey = 60% = 0.6

L = w - 0.6w

L = 0.4w

If w = 15.5

L = 0.4(15.5)

= 6.2 gallons

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Answer:

[tex]d=-6[/tex]

[tex]a_9=-49[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=-6n+5[/tex]

Therefore, the ninth term in the sequence is:

[tex]a_9=-6(9)+5[/tex]

[tex]a_9=-54+5[/tex]

[tex]a_9=-49[/tex]

Answer:

yes

Step-by-step explanation:

because 4

Answer:

Step-by-step explanation:

average rate of change

[tex]=\frac{25-(-10)}{9-2} \\=\frac{35}{7}\\=5[/tex]

The probability of the event that the first song played by Alan is a rock song is 0.01.

The probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes. But the probability of an event say event "a" not occurring is 1 - a.

We shall calculate for the probability of the event that Alan's first song to be played is a rock song as follows:

probability of playing a rock song = 11/229

probability of not playing a Latin American song = 208/229

probability of not playing a gospel song = 183/229

probability of not playing a country song = 199/229

probability of not playing a rap song = 190/229

probability of not playing a classical song = 204/229

probability of not playing a pop song = 172/229

So,

The probability that the first song played is a rock song = (11/229) × (208/229) × (183/229) × (199/229) × (190/229) × (204/229) × (172/229)

The probability that the first song played is a rock song = 0.05 × 0.91 × 0.80 × 0.67 × 0.83 × 0.89 × 0.75

The probability that the first song played is a rock song = 0.01

Therefore the probability of the event that Alan's first song played is calculated to be 0.01 approximated to 2 decimal places.

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For given equation y = ln(3 - 4 cos(x))​,

dy/dx =  4sin(x) / (3 - 4 cos(x))

In this question, we have been given an equation y = ln(3 - 4 cos(x))​

We need to differentiate y = ln(3-4cosx)​

dy/dx

= d/dx(ln(3 - 4 cos(x))​)

= 1/(3 - 4 cos(x))​ * d/dx(3 - 4cos(x))               .......(by Chain rule)

= 1/(3 - 4 cos(x))​ * [4 sin(x)]

= 4sin(x) / (3 - 4cos(x))

Therefore, for given equation y = ln(3 - 4 cos(x))​,

dy/dx =  4sin(x) / (3 - 4 cos(x))

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If the value of R² in the regression equation is 0.810, the value of R is 0.9

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

Regression equation: y = -2.6x + 10

Value of R2 = 0.810

Rewrite the above parameters properly

So, we have the following representation

y = -2.6x + 10

R² = 0.810

The variable r² represents the coefficient of determination

Recall that

R² = 0.810

This gives

r² = 0.810

Take the square roots of both sides

r = 0.9

Hence, the value of r is 0.9

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1. Dianely's salary can be represented with the following table of values for 5 years as follows:

Year         Salary

1            $40,000

2           $42,500

3           $45,000

4           $47,500

5          $50,000

2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.

An equation is a mathematical statement equating two or more mathematical expressions.

Equations use variables, numbers, mathematical operands, and the equation symbol (=).

Dianely's initial salary = $40,000

Salary raise per year = $2,500

Dianely's salary after n years in equation form, S = 40,000 + 2,500n.

Year         Salary

1            $40,000

2           $42,500 (40,000 + 2,500)

3           $45,000 (42,500 + 2,500)

4           $47,500 (45,000 + 2,500)

5          $50,000 ($47,500 + 2,500)

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The coordinates  of the point that is one half the distance between A and B is (5/2, 11/2)

The point with the distance that is one half the distance between A and B is the midpoint of A and B.

The coordinate of the midpoint of a line is the half x values and y values. Thus: Xm = (X1 + X2)/2 and Ym = (Y1 + Y2)/2

where m is the midpoint

Given: A(-1, -2) and B(6, 12)

X1 = -1, Y1 = -2 and X2 = 6, Y2 = 12

Xm = -1+6 /2 = 5/2

Ym = -2+12 = 11/2

Therefore, the coordinates  of the point that is one half the distance between A(-1, -2) and B(6, 12) is (5/2, 11/2)

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Answer:

76%

Step-by-step explanation:

100%-24%=76%

Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty.

A compound event is made up of two separate events.

Here is a table of probable sums of two die rolls. Die 1 and Die 2 values are listed along the side and top. The figures are roughly near the middle. The sum of Die 1 = 2 and Die 2 = 2 is 4, for example.

          Die 2

Die1    1   2   3   4   5   6

1         2   3   4   5   6   7

2         3   4   5   6   7   8

3         4   5   6   7   8   9

4         5   6   7   8   9   10

5         6   7   8   9   10 11

6         7   8   9   10 11  12

Rolling two dice yields 6 * 6 = 36 possible outcomes, or 36 possible sums. There are 36 occurrences in the sample space.

Looking at the table, a 3 or a 9 happens as the sum 9 times, resulting in 9 of the 36 potential occurrences having a sum of 3 or 9.

Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4

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The equation of the line is x+y-4=0.

What is an equation?

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Main Body:

we know that one point form of a line is

y-y₁= m(x-x₁)   ,  where m= slope

now given is a point (-3,7) and m=-1

y-7 =(-1)(x+3)

x+y-4=0

Hence the answer is x+y-4 =0

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Answer:

64

Step-by-step explanation:

8(x+2) when x=6

replace x with 6

8(6+2)

distribute 8

48+16= 64

The shaded area under the standard normal curve is 2.58%.

According to z-score table,

Area for < 2.23 = 0.9871

Area for >2.23 = 1 - 0.9871

                        = 0.0129

Area for < 2.23 = 0.0129

Total area = 0.0129 + 0.0129

                 = 0.0258

Area percent = 0.0258*100

                      = 2.58%

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84 i think?

im not sure if i did my math properly

Answer:

80

Step-by-step explanation:

40 ÷ 6 = 6.66666667 x 12 = 80

Answer:

60 ways;

GOOD LUCK!

Step-by-step explanation:

The word CHEWY has 5 letters, Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.

Answer: (D) [tex]y=3x-5[/tex]

Step-by-step explanation:

Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].

Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].

The value of y is - 0.326 when x = 7.

A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is typically expressed as x: y or x/y, although it may alternatively be read as x is to y.

Comparatively speaking, a proportional equation states that two ratios are comparable. A ratio is expressed as x: y: : z: w and is understood to mean that x is to y as z is to w. Here, w and y are not equal to 0, therefore x/y Equals z/w.

A connection between two quantities is said to be in inverse proportion if one quantity rises while the other falls, and vice versa. As a result, an inverse ratio is expressed as y ∝ 1/x.

The general equation of proportion is given by

y = k/x²

-4 = k/(-2)²

k = -4(4)=-16

y = -16/x²

When x=7, then

y= -16/49

y= - 0.326

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Step-by-step explanation:

6x-4+60=14x-8

6x+56=14x-8

8x=64

x=8

The missing x and y values in the ordered pair of the equation are:

x = 1

y = -4

Given the ordered pair (x, y) of an equation, y = mx + b, we can find their values by plugging in the given value of either of the x or y coordinates to find the other coordinate value.

The ordered pairs of y = -2x + 4 are given as:

(4, y) and (x, 2)

To find the value of y, substitute x = 4 into the equation y = -2x + 4:

y = -2(4) + 4

y = -8 + 4

y = -4

The value of y is -4.

To find the value of x, substitute y = 2 into the equation y = -2x + 4:

2 = -2x + 4

2 - 4 = -2x

-2 = -2x

-2/-2 = x

1 = x

x = 1

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Answer:

Step-by-step explanation:

You want the result of a division operation performed on numbers written in scientific notation.

In each case, the result number will have a repeating decimal fraction. We show 4 significant figures in the answer. The number of significant figures you need to use will depend on what you're using the answer for. If you are required to match the precision of the numbers here, you will want to use 1 significant figure.

The rules of exponents apply, so the exponent of the result will be the difference of the exponents of numerator and denominator. As always, if the numerator mantissa is smaller than the denominator mantissa, the result will be a fraction, so adjustment of the exponent will be necessary.

  = (5/3)×10^(-10-(-9)) = 1.667×10^-1

  = (1/3.5)×10^(-9-(-9)) = 0.2857×10^0 = 2.857×10^-1

__

Additional comment

Any scientific or graphing calculator and any spreadsheet can accept input in scientific notation and format the output in the same way.

You need to be careful with the way you enter the multiplier. Most calculating platforms accept the E notation shown in the attachment. If you use multiplication (×10^-9, for example), then the denominator number will need to be enclosed in parentheses. The third line of the second attachment shows the result of not using parentheses: the multiplier intended for the denominator instead multiplies the result of the division. (This behavior is required by the Order of Operations.)

Answer:

[tex]y+17=-2(x-14)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

Answer:

Mediterranean Paradise has 30 fewer deluxe staterooms than three times the number of deluxe staterooms on the

Pacific Paradise.

Step-by-step explanation:

The length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.

According to the question,

We have the following information:

A piece of pipe is 40in. long. It is cut in to 3 pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece.

Let's take the length of middle sized piece to be x inches.

Length of longest piece = 3x inches

Length of shortest piece = (3x-23) inches

Now, we have the following expression:

x+3x+3x-23 = 40

7x-23 = 40

Adding 23 on both the sides:

7x = 40+23

7x = 63

Dividing by 7 on both the sides:

x = 63/7

x = 9 inches

Length of longest piece = 3*9 inches

Length of longest piece = 27 inches

Length of shortest piece = (27-23) inches

Length of shortest piece = 4 inches

Hence, the length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.

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If  a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.

Range = 31.5≤  x < 32.5

Range = 31.5≤  10 < 32.5

Hence,

Lowest and greatest possible for 32 grams

Lowest possible = 31.5 grams

Greatest possible =32.4 grams

Since multipack of crisps contain is 10 packets hence.

Least weight = 31.5 grams × 10

Least weight =315

Greatest weight = 32.5 grams × 10

Greatest weight = 325

Therefore 315 and 325 are the weight.

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Using differentiation, 36 feet is the maximum height, in feet, that the object will reach.

In the given question,

An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground.

The position of the object can be modeled using the function [tex]f(t)=-16t^2+32t+20[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object.

We have to find the maximum height, in feet, that the object will reach.

The given function is [tex]f(t)=-16t^2+32t+20[/tex].

To find the maximum height we differentiate the function with respect to t

[tex]\frac{df}{dt}=-32t+32[/tex]

As we know that at the maximum point the slope of the tangent is zero.

So df/dt = 0

So -32t+32=0

Subtract 32 on both side

-32t+32-32=0-32

-32t=-32

Divide by -32 on both side

-32/-32 t = -32/-32

t=1

Therefore at t=1 the function have maximum value. So we put t=1 in the given equation.

[tex]f(1)=-16(1)^2+32\times1+20[/tex]

f(1)=(-16)×1+32×1+20

Simplifying

f(1)=-16+32+20

f(1)=36 feet.

Hence, 36 feet is the maximum height, in feet, that the object will reach.

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Answer:

--------------------------------------

The graph has two local maximums and two local minimums.

The intervals between those points are the increasing intervals.

Refer to the attached, where the intervals are marked.

The intervals are

Answer:

answer,(2)x≥-1

Step-by-step explanation:

it was right

130 units should be manufactured to minimize the cost.

Calculation

by using the quadratic formula

[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]

where, a = 0.15, b = -39 and c = 4500

x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]

Hence, 130 units should be manufactured to minimize the cost of fax machines

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130 units should be manufactured to minimize the cost.

Calculation

by using the quadratic formula

[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]

where, a = 0.15, b = -39 and c = 4500

x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]

Hence, 130 units should be manufactured to minimize the cost of fax machines

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