A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.

The amount of profit made by JMP is 102000.

Given,

In the question;

JMP made a profit of $85,000 last year.

If the profit margin increased by 20% this year.

To find the amount of profit made by JMP.

Now, According to the question:

Based on the given condition:

Formulate:

= 85000 x (20% + 1)

Calculate;

85000 x (0.2 + 1)

Calculate the sum or difference

85000 x 1.2

= 102000

Hence, The amount of profit made by JMP is 102000.

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The equation of the line perpendicular to the given line is, y = 3x + 1.

What is slope of the line?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

Consider, the given equation of line

[tex]y = -\frac{1}{3}x+4[/tex]

We have to find the equation of line passes through the point (-2, -5) and perpendicular to the given line.

Here, the point is (-2, 5).

First to find the slope of the line.

Since, the slope of the line, perpendicular to the given line is negative reciprocal of the slope of given line.

Here, the slope of given line is, -1/3.

So, the slope of perpendicular line is [tex]-(\frac{1}{(-\frac{1}{3}) }) = 3[/tex]

Therefore, the slope of the line is 3.

Now to find the equation of the line.

Consider, the point - slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1) = (-2, -5) , m = 3[/tex]

⇒

[tex]y-(-5)=3(x-(-2))\\y+5=3(x+2)\\y+5=3x+6\\y=3x+6-5\\y=3x+1[/tex]

Hence, the equation of line in slope - intercept form, is y = 3x + 1.

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The balance in Lee's account at the end of 6 years is $384,830.53.

The first step is to determine the future value of the initial amount deposited in the savings account.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Balance at the end of 3 years: $17,000 x (1.045)^(3 x2) = $22,138.42

The total value of the account after $42,000 is deposited is:

$42,000 + $22,138.42 = $64,138.42

The future value of $64,138.42 at the end of 6 years is:

Balance at the end of 6 years: $64,138.42 x (1.045)^(3 x2) = $384,830.53

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The answer of the given multiplication is 19.2, 1.7, 15.93 and 0.0512 respectively.

To find the answer, we will simply multiply the given numbers.

i) 3.2 × 6 = 19.2

ii) 8.5 × 0.2 = 1.7

iii) 2.7 × 5.9 = 15.93

iv) 0.32 × 0.16 = 0.0512

Hence, the answers is 19.2, 1.7, 15.93 and 0.0512 respectively.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of x in the second ordered pair is - 0.5 or - 1/2 and that of y in the first ordered pair is 8.

The given ordered pair is (-3,y) and (x,2)

the equation y=-2x+2

In the first step we put the value of x as -3 as given in (-3,y) in the equation y=-2x+2, we get

y=-2(-3)+2

⇒y=6+2

⇒y=8

So the value of y is 8 then the ordered pair will be (-3,8).

Again, in the second step, we put the value of y as 2 as given in (x,2) in the equation y=-2x+2, and we get

2=-2x+2

⇒2x=2-2

⇒2x=0

⇒x=0

So the value of x is 0, and the ordered pair will be (0,2).

The table:

I have provided a photo of the table:

Answer:

[tex]\dfrac{1}{2}[/tex]

Step-by-step explanation:

   Number of cards = 52

 Number of black cards = 13 (club) + 13 (spade)

                                        = 26

[tex]\sf P(\text{getting a black card})=\dfrac{26}{52}[/tex]

                                     [tex]\sf =\dfrac{1}{2}[/tex]

Yes, the graph goes through those two points.

What is Graph?

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Explanation for the answer:

The equation can be graphed by plotting the two given points and drawing a line through them. Such a graph is shown in the attachment.

You can graph a line for any linear equation from any two points that fit the equation. So you can use the points (0, -75) and (15, 0) to graph the line representing the situation.

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The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

The given point K(-2,-5)

If we reflect a point(x,y) along the y-axis then the coordinate after reflection converts as K'(-x,y)

The reflection of K(-2,-5) along the y-axis will be  K'(2,5).

Hence "The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5)".

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Answer:

3x  + 12

Step-by-step explanation:

3(x+1)+9

= 3x  + 3 + 9

= 3x  + 12

Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

WE have been given an expression as 43πr³ represents the volume of a sphere, with radius r.

Terms can be added or subtracted to make a polynomial. They are composed of variables and constants all in multiplication.

So we know that if there is one term, then the polynomial will be called monomial.

Therefore, this expression is a monomial which have inly one term as 43πr³ .

Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.

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The length and breadth expressions where one dimension is the GCF are; 7y and (2y²-5).

Area of a Rectangle

Given that a rectangle is a two-dimensional shape with one of the dimensions being the GCF, as specified in the question;

Consequently, the length and breadth expressions are 7y and (2y²-5) respectively.

Additionally, the rectangle's area when y=2 is; 14(2³) - 35(2) = 52.

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Answer:

C. -16

Step-by-step explanation:

Hope this helps you! :))

16

Step-by-step explanation:

the answer is c

just took a test and I got it right

The equation that models the cost of the van rental is V = $183 + (m - 120)0.39. (first option)

The number of miles that Tim and Jessica can travel roundtrip on vacation is Ashville MC (second option)

The equation that represents the total cost of renting the camper van is a linear equation. A linear equation is an equation that has single variable that is raised to the power of one.

The general form of a linear equation is: y = mx + b

Where:

The form of the linear equation is:

total cost = cost of renting the van + [(total miles driven - 120) x cost per mile)

V = $183 + (m - 120) x 0.39

V = $183 + (m - 120)0.39

Total miles that can be driven if they have to spend $598.74

$598.74 = $183 + (m - 120)0.39

$598.74 = $183 + 0.39m - 46.80

$598.74 = $136.20 + 0.39m

$598.74 - $136.20 = 0.39m

$462.54 = 0.39m

m = $462.54 /0.39

m = 1186

Distance Tim and Jessica can travel from the rental company to the destination = 1186 / 2 = 593 miles

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The value of P=2 and Q=8 as in AP, The difference in two terms is equal between all the terms.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. Sn = n/2[2a + (n 1) d] is the formula to determine the sum of an arithmetic progression. where an is the first term in the arithmetic progression, n is the total number of terms, and d is the common difference. If there is always the same difference between any two consecutive terms in a series of numbers, that progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series.

Here,

18--12=30/3=10

P=-12+10

=-2

Q=-2+10

=8

P=2 and Q=8 as in AP, the difference between the two terms is equal for all terms.

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Answer:

21%

Step-by-step explanation:

126 out of 600=126/600

=0.21 *100 for

21%

The given points gives us a line with constant slope of -2.

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

The points are in the form of ( x, y) , where y= g(x)

Plot these points on the graph and join the points through a line.

Refer to the attachment for the graph.

The slope is constant.

consider any 2 points:

(x,y) = (0,7)

(m,n) =(2,3)

Slope = change in y values/ change in x values

         = (7-3)/(0-2) = 4/-2 = -2

The given points gives us a line with constant slope of -2.

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The ellipse given by x^2+xy+2y^2=7. The y-coordinate(s) of all points are -11.3, 11.2, -5.665, 5.585 where the ellipse has a vertical tangent line.

Differentiation is the process of determining a function's derivative. Differentiating algebraic functions, trigonometric functions, and exponential functions are the three fundamental derivatives.

Given,

Ellipse given,

x²+ xy + y ² = 7

Differentiating:

dy/dx

x²+ xy + y² = 7

d/dx(x² + xy + y²) = d/dx(7)

2x + 1y + x dy/dx + 2y dy/dx = 0

dy/dx = 2x + y/ x + 2y

dy/dx = 0

2x + y = 0

x + 2y = 0

Now, we have 2 equations,

x² + xy + y² = 0

y = -2x

Solving equations by substitution method,

x² + x(-2x) + (-2x)² = 7

x² - 2x² + 4x² = 7

3x² = 7

x = ±√21/3

Using y = -2x

Points are:

( -2√21/3 , √21/3) and (2√21/3 , -√21/3)

±√21/3 = ±1.528

x² + xy + y² = 7 [-11.3, 11.2, -5.665, 5.585]}

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The quotient of 5 divided by 3/10 is equal to 50/3

When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.

So, if we want to divide A by the fraction (b/c), then we can write:

A÷(b/c)

That will be equal to A*(c/b), so:

A÷(b/c) =  A*(c/b)

Here we want to divide 5 by 3/10, then we need to solve:

5÷(3/10)

Using the above rule we will get:

5÷(3/10) = 5*(10/3) = 50/3

That is the quotient.

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Answer:

12 ft, 13 ft , 17 ft

Step-by-step explanation:

let x be the length of the second side , then

one side is x + 1

third side is x + 5

the perimeter P is the sum of the 3 sides, then

P = x + x + 1 + x + 5 ← collect like terms

P = 3x + 6

given P = 42 , then equating gives

3x + 6 = 42 ( subtract 6 from both sides )

3x = 36 ( divide both sides by 3 )

x = 12

x + 1 = 12 + 1 = 13

x + 5 = 12 + 5 = 17

the 3 sides are 12 ft, 13 ft , 17 ft

[tex]{ \pink{ \boxed{ \purple{ \sf{f(3) = 98}}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \tt{f(x) = 2 {x}^{4} - 8 {x}^{2} + 5x - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2( {3})^{4} - 8( {3})^{2} + 5(3) - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2(81) - 8(9) + 15 - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 72 + 8}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 64}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{f(3) = 98}}}}}[/tex]

Answer:

the answer is 18 lol....

The angular value of x is 3° as per the given the given information in the question.

An angle in Euclidean geometry is the figure produced by two rays, called the sides of the angle, that have a common termination, called the vertex of the angle. Angles formed by two rays lie in the plane containing the rays. Angles are also generated by the intersection of two planes. These are referred to as dihedral angles. Two intersecting curves can also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Given,

m ∠GQP=80

m ∠RQP=3+59x

m ∠RQG=32x+4

From the figure,

m ∠RQG+ m ∠GQP= m ∠RQP

32x+4+80°=3+59x

27x=81°

x=3°

Therefore, the value of x=3°

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a) The test statistic is: t = 1.85.

b) The p-value is: 0.0648.

c) The null hypothesis is not rejected.

d) There is not sufficient evidence to conclude that the population mean is different of 4.

The standard deviation is known only for the sample, hence the t-distribution is obtain the test statistic.

The test statistic of the t-distribution is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the variables of the equation are given as follows:

For this problem, the values of these parameters are as follows:

[tex]\overline{x} = 4.32, \mu = 4, s = 4.24, n = 600[/tex]

Hence the test statistic is obtained as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{4.32 - 4}{\frac{4.24}{\sqrt{600}}}[/tex]

t = 1.85.

The p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, with 600 - 1 = 599 df and t = 1.85, hence it is of 0.0648.

Since the p-value is greater than the significance level of 0.01, it is found that the conclusion regarding the null hypothesis is that it is not rejected, meaning that the sample does not give sufficient evidence to conclude that the population mean is different of 4.

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