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The sale price of the car as a percentage of the original price is 142%

Sale price as a percentage of the original price = sale price / buying price

= 1280/900 × 100

= 1.42222222222222 × 100

= 142.22%

Approximately,

142%

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The first four terms of the sequence are 6, -24, 96 and -384

How to determine the first four terms?

The sequence is given as:

an=6(-4)^n-1

When n = 1, we have:

a(1)=6(-4)^(1-1)

This gives

a(1) = 6

When n = 2, we have:

a(2)=6(-4)^(2-1)

This gives

a(2) = -24

When n = 3, we have:

a(3)=6(-4)^(3-1)

This gives

a(3)=96

When n = 4, we have:

a(4)=6(-4)^(4-1)

This gives

a(4)=-384

Hence, the first four terms of the sequence are 6, -24, 96 and -384

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Using the cosine ratio, the value of AD in the diagram is: 2√3π in.

If we have the following given in a right triangle like triangle ADC in the diagram:

AC = 4π (hypotenuse)

AD = ? (adjacent side)

The cosine ratio, CAH would be applied, which is:

Cos 30 = adjacent/hypotenuse

Cos 30 = AD/4π

AD = cos 30 × 4π = √3/2 × 4π [cos 30 = √3/2]

AD = 2√3π in.

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Answer:

40 people

Step-by-step explanation:

480.80 times 40 this equals 19,220

The rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.

Given mechanic first worked 20 hours and mechanic second worked 15 hours and they charged $1650. The sum of rates of first mechanic and second mechanic is $95 per hour.

let the rate charged by first mechanic be x .

let the rate charged by second mechanic be y.

According to question

x +y=95-----------1

20x+15y=1650----------2

Multiply equation 1 by 20 and subtract equation 2 from 1.

20x+20y-20x-15y=1900-1650

5y=250

y=50

put the value of y=50 in 1 to get the value of x.

x +y=95

x+50=95

x=95-50

x=45

Hence the rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.

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Question is incomplete as it should be as under:

Two mechanics worked on a car, the first mechanic worked 20 hrs. and the second mechanic worked 15 hours together. They charged a total of $ 1650.  What is the rate charged per hour for each mechanic if the sum of the two rates per hour was $95 per hour?

Answer:

Hello! The answer to your question is (-7, -4).

Step-by-step explanation:

To solve this problem, you have to use the midpoint formula:

[tex](\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

Now, we can substitute our values in:

[tex](\frac{-9 + -5}{2}, \frac{1 - 9}{2} )\\= (\frac{-14}{2} , \frac{-8}{2}) \\= (-7, -4)[/tex]

Answer:

x=80

Step-by-step explanation:

So normally when x is in the numerator, you multiply both sides of the equation by whatever the denominator is to cancel out the fraction. But in this case since you don't have the fraction alone, you normally want to isolate it first So let's do that

Original equation:

[tex]\frac{x}{4}+7=27[/tex]

Subtract 7 from both sides

[tex]\frac{x}{4}=20[/tex]

Multiply both sides by 4 to cancel out the denominator:

[tex]x=80[/tex]

Answer:

Step-by-step explanation:

the triangles are similar, so same angles

the sum of the interior angles of a triangles is 180°

take away from 180° the know angles and you will have your answer

180 - 62 - 90 =

28°

Answer:

one hundred and two years

Answer:

  42

Step-by-step explanation:

Each ages at the same rate. In 3 years, all will be 3 years older.

The sum of their ages now is ...

  A +J +D = 33

In 3 years, the sum will be ...

  (A +3) +(J +3) +(D +3) = (A +J +D) +(3 +3 +3) = 33 +9 = 42

In 3 years, the sum of their ages will be 42.

The true statements about the function are:

The table of values is given as:

x     f(x)

-3    -15

-2     0

-1      3

0      0

1      -3

2      0

3      15

From the table, the function values do not exceed 0 at the interval 0 to 2.

This means that f(x) ≤ 0 over the interval [0, 2].

Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0

This means that f(x)>0 over the interval (-2,0)

Also from the table, the function values are at least 0 at the intervals greater than 2

This means that f(x) ≥ 0 over the interval [2,∞)

Hence, the true statements are (b), (d) and (e)

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Answer:

The answers are B, C, and D

Step-by-step explanation:

Edge 2023

The greatest sum, difference, product and quotient is 9, 12, 90 and 26 respectively.

Given the numbers -5 1/2, 3. 75, -20. 8, -4, 11 1/4

a. SUM

=8 + [tex]11* \frac{1}{4}[/tex]

= [tex]8 + \frac{45}{4}[/tex]

= [tex]\frac{32 + 4}{4}[/tex]

= [tex]\frac{36}{4}[/tex]

= 9

B. Difference

= 8 - (-4)

= 8 + 4

= 12

C. Product

= [tex]8 * \frac{45}{4}[/tex]

= [tex]2 * \frac{45}{1}[/tex]

= 90

D. Quotient

= [tex]8 * 3. 25[/tex]

= 26

Thus, the greatest sum, difference, product and quotient is 9, 12, 90 and 26 respectively.

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Answer:

84 mm

Step-by-step explanation:

1 cm = 10 mm

8.4 cm = 84 mm

the segment DE is perpendicular to segment AC

==========================================================

Explanation:

The tiny square marker indicates we have a 90 degree angle, which in turn means the two segments DE and AC are perpendicular.

Furthermore, DE is a perpendicular bisector of AC because AC is broken into two equal pieces (AE and EC). The term "bisect" means "split in equal halves". We know that AE = EC due to the small tickmarks on each mentioned segment.

Choice B states "AC is a perpendicular bisector". This is incorrect because AC does not split any segments into two equal pieces. If choice B said "DE is a perpendicular bisector", then it would be correct.

The graph has been shifted to the left and moved up and stretched as scaling is done ,

Reflecting , Rotating , Dilating a function to form a new function is called Transformation.

The graph of the function f(x) = 1/ x is given

and a transformed function is given

The graph has been shifted to the left and moved up and stretched as scaling is done ,

Therefore three types of transformation are done on the parents function.

The transformation can be seen through the graph attached.

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Answer:

a = -4

b=-29

Step-by-step explanation:

First write the radicals in simplest form.

i² = -1

[tex]\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)[/tex]

                                                          [tex]\sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i[/tex]

   [tex]\sf \boxed{a = -4 }\\\\\boxed{b=-29}[/tex]

Answer: 9

Step-by-step explanation:

[tex](f \circ g)(0)=f(g(0))\\\\g(0)=2\\\\\implies f(g(0))=f(2)=\boxed{9}[/tex]

1/216 is the equivalent expression for the given exponent [tex]6^{-3}[/tex].

An algebraic expression is a mathematical expression involving mathematical operations, variables, numbers, and mathematical quantities and combinations of them.

A negative exponent is the reciprocal of the same exponent with a positive value.

The reciprocal of any number is given by the fraction with the number as denominator and 1 as the numerator.

Here the given negative exponent is given by,

[tex]6^{-3}[/tex]

The exponent with positive value of the given negative exponent is given by [tex]6^3[/tex]

Reciprocal of the above exponent with positive value is given by,

[tex]\frac{1}{6^3}[/tex]

So now Calculating the negative exponent we have,

[tex]6^{-3} = \frac{1}{ {6}^{3} } = \frac{1}{216} [/tex]

Hence the equivalent expression for the given negative exponent is 1/216.

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Answer:

3√5 or ≈ 6.71

Step-by-step explanation:

The Distance Formula is d = √((x2-x1)² + (y2-y1)²)

Given Points: (-3, 2) and (0, -4)

          Points: (x1, y1) and (x2, y2)

Find the difference between coordinates:

(x2 - x1) = (0 - (-3)) = 3

(y2-y1) = (-4 - 2) = -6

Square the results and sum them up:

(3)² + (-6)² = 9 + 36 = 45

Now Find the square root and that's your result:

Exact solution: √45 = 3√5

Approximate solution: 6.7082

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Answer:

The new store will have a profit of $5400 after its fifth month.

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

(Use 5 for x)

(R-C)(5) = 9(5) + 9 = 45+9 = 54

The test statistic for the hypothesis would be 1.413.

Given that the participants in its new diet program lose, on average, more than 13 pounds and the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds.

The objective is to text the advertisement's claim that participants in new diet program lose weight, on average, more than 13 pounds.

Hypothesis:

Null hypothesis:H₀:μ=13

Alternative hypothesis:Hₐ:μ>13

Here, μ be the mean weight loss of all participants.

n=30,

Degree of freedom n-1=30-1=29

[tex]\bar{x}[/tex]=13.8 and s=3.1

To test the null hypothesis H₀, the value of test static would be calculated as follows:

[tex]\begin{aligned}t&=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{29}&=\frac{13.8- 13}{\frac{3.1}{\sqrt{30}}}\\ &=\frac{0.8}{0.566}\\ &=1.413\end[/tex]

Hence, the value of the test static for the hypothesis with the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds is 1.413.

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The probability illustrates that the mean of the sample proportions equal the proportion of girls in two births.

The table that describes the sampling distribution of the sample proportion of girls from two births will be:

Girls Probability

0. 0.25

0.5. 0.5

1. 0.25

The mean of the sample proportions equal the proportion of girls in two births. This is illustrated as 1/2.

Also, the result suggest that the sample proportion is an unbiased estimator big the population proportion because rye sample proportion and population proportion are not the same.

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Answer:

B. 44.93

Step-by-step explanation:

The law of sines states
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

where a, b and c are the 3 sides of the triangle and A is the angle opposite side a, B the angle opposite side b and C the angle opposite side c

In this particular problem we have

side a = 44, angle A = 46.7
side c = ? , angle C = 48

So 44/sin(46.7) = c/sin(48) or by multiplying both sides by sin(48)

c = sin(48) * 44/sin(46.7)  = 44.92937 which is 44.93 rounded to 2 decimal places

Answer: No

Step-by-step explanation:

The sum of the interior angles of a polygon with n sides is given by [tex]180(n-2)[/tex]. Setting this equal to 850 degrees,

[tex]180(n-2)=850\\\\n-2=\frac{85}{18}\\\\n=\frac{121}{18}[/tex]

Since this gives n to be a non-integer value, this is an impossible situation since a polygon must have an integer number of side lengths.

Answer:

Yes

Step-by-step explanation:

To find out whether or not a graph is a function, we can do the vertical line test. If the vertical line only touches one point, then the graph is a function. This is because in a function, an input can only have one output.

Answer:

ksb said did bud did did it did did gc victory in suf did did zudbxudng jc fn facing did fjgduf bdyrut during their fyrhfb hi f f7djdufj fhdf. Is A

Answer:

x=7 and x = 1

Step-by-step explanation:

This is pretty much a quadratic in disguise.
If we multiply both sides by x, we get:
x^2-7=6x
move 6x to the left
x^2-6x-7 = 0
We can either use the quadratic formula, or we can use factoring.
with factoring*, we get:
(x-7)(x+1) = 0 , and so the solution to the equation is x=7, and x=-1

*in a equation: x^2+ax+b = (x+c)(x+d), c+d equals a, and c*d equals b

On to the quadratic formula, a=1, b=-6, and c=-7, so:
(6±sqrt(36+4*7))/2 = x
=(6±8)/2
=3±4
x=7 and x = 1

The formula that will help eli determine how much money he will earn in one week is a = 9h + nb

Let

a = (9 × h) + (n × b)

a = 9h + nb

Complete question:

Eli works in an electronics repair shop. he earns 9 dollars an hour plus a bonus for each item her repairs.

write a formula that will help eli determine how much money he will earn in one week

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Step-by-step explanation:

[tex]10x+45 > 120\\10x+45-45 > 120-45\\10x > 75\\\frac{10x}{10} > \frac{75}{10} \\x > 7.5[/tex]

Therefore, Mel has to work at least 7.5 hours or 8 total hours.

The correct options about the dilation are; Options A, B and E

From the given information, find attached a dilated image.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2(x, y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

A) DO, 2 (x, y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

Thus Option A is correct.

B) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

m = 4/(-6+2) = 4/-4

m = -1

Option B is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

Option C is false

d) The vertices of the image are closer to the origin than those of the pre-image.

From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.

Option D is False

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

Option E is correct.

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If sin theta < 0 and tan theta > 0 as described in the task content, then, cos theta < 0 and 180<theta <270.

From the task content, it was described that sin theta < 0 and tan theta > 0.

Upon recall of angle quadrants, it follows that only the 3rd quadrant angles have positive tan values and negative sin values. Hence, it follows that the angle theta is in the 3rd quadrant and also has cos theta < 0.

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