mary drove 156156 miles at a constant rate. if she had driven 99mi/h faster, she could have reduced her driving time by 4545 minutes. find the rate at which she actually drove.

Answer:

$9.01

Step-by-step explanation:

10 percent off of 15 is 8.5 and since sales tax is 6%, that means it adds 0.51 cents to the total, bringing the total to $9.01

Answer:

17.49

Step-by-step explanation:

15x0.10= 1.5
15+1.5= 16.5
16.5x0.06=0.99
16.5+0.99=

The height of a Wolsey Hall student is an example of continuous data. Option 1. is the answer

Continuous data is data that can take any value. An easy way of identifying continuous data is that they are measured and not counted.

For example, height, weight, temperature and length are all examples of continuous data. Over time, some continuous data can change.

Thus, the height of a Wolsey Hall student is an example of continuous data because it is measured and not counted

Note: Other options are NOT continuous data because they include only data that can only be counted in whole numbers or integers, which implies that the data can not be split into fractions or decimals.

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The expression equivalent to 12m(m-3n) using distributive property is 12m² - 36mn.

An expression is combination of variables, numbers and operators.

The given expression is  12m(m-3n) .

Twelve m times m minus three times n.

12m(m-3n).

12m is to multiplied to m minus three n.

12m²-35mn.

Twelve m square minus thirty five times of m and n.

Hence, 12m²-35mn is the expression equivalent to 12m(m-3n) .

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Yes, one can use more than one infinitives in the same sentence. For example : I have to wash my hand to keep myself clean.

Reason for the given statement:

To use two or more infinitives in the same sentence:

Therefore, it is perfectively alright to use more than one infinitives in the same sentence.

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Answer:

Below

Step-by-step explanation:

x = amount of 80% to use

amount of alcohol in ingredients = amount of alcohol in final product

  .8 x   =  .7 (560)

   x = 490 ml

Yes lower production cost increase profit.

Production costs are expenses, such as labor and materials that your company incurs within the course of producing the product that you simply offer to consumers. In common, the lower your generation cost, the higher your benefit, or the sum you've got remaining after you subtract your costs from your sales revenue. lower production costs generally lead to higher profits. When production costs are lower, companies can charge lower prices and still make a profit, or they can keep prices the same and earn higher profits. Lower production costs also reduce the amount of money spent on materials, labor, and other expenses, leaving more of the revenue as profit.

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The transformation equivalent to the reflection across the line q = -1, followed by the reflection across the line p = 2, [tex]r_p \circ r_q[/tex] is a translation of 6 units to the right.

A reflection transformation is one in which the points of the image are mirrored across the line of reflection.

The coordinate of a point (x, y) following a reflection about the y-axis is the point (-x, y)

The line x = -1 is parallel to the y-axis, therefore, only the x-coordinate of the preimage point (x, y) will change following the reflection across the line, q, [tex]r_q[/tex], x = -1

The relative x-coordinate of a point (x, y) to the line x = -1 is x + 1

Therefore, the image of the point (x, y) following the reflection across the line x = -1 and relative to the line is the point (-(x + 1), y) = ((-x - 1), y)

Relative to the x-axis, the point ((-1 - x), y) is (-1 + (-1 - x), y) = (-2 - x, y)

The coordinate of a point (x, y) relative to the line x = 2 is (x - 2, y)

Therefore, the coordinate of the point ((-2 - x), y) relative to the line x = 2 is ((-2 - x) - 2, y) = ((-4 - x), y)

The image of the point ((-4 - x), y) following a reflection across the line x = 2, [tex]r_p[/tex], is (-(-4 - x), y) = ((4 + x), y)

Relative to the y-axis, the coordinate of the image point ((4 + x), y) is ((2 + (4 + x)), y)

((2 + (4 + x)), y) = ((6 + x), y)

The translation equivalent to the transformation, [tex]r_p \circ r_q[/tex] is a translation of 6 units to the right

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The size of the angle to the nearest degree of tan v = 0.9657 will be 44°.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

As per the given,

tan v = 0.9657

Take inverse tan on both sides of the above expression,

v = [tex]tan^{-1} 0.9657[/tex]

v = 44°

Hence "The angle at tan v = 0.9657 will be 44° to the closest degree.".

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Answer: x ≤ -1

Step-by-step explanation:

8 ≤ -4x+4

4x+8 ≤4

4x ≤-4

x ≤ -1

Answer:

Step-by-step explanation:

first open the bracket by multiplying -4 through

8 ≤ -4x + 4

then group like terms and unlike terms  

therefore; 8 - 1 ≤ -4x or -4x ≤ 8-4

-4x ≤ 7 then divide both side by -4

so, ⇒ x ≤ -4/4

x≤-1

The measure of x = 93 degree and y = 36 degree.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.

Given:

As, <QRP= 51

So, <QRP = <QPR= 51 {Angles opposite to equal sides are also Equal}.

In ΔPQR

<P+ <Q+ <R= 180

51 + 51 + <Q= 180

<Q= 180- 102

<Q= 78 degree.

So, <y = 1/2 <Q= 78/20 = 36 degree.

and, In small left Triangle

36 + 51+ x= 180

x = 180 - 87

x= 93 degree.

Hence, the measure of x = 93 degree and y = 36 degree.

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If the value of the land fell to $100000 , then the amount of loss albert can claim in 2022 is $0   .

In the question ,

it is given that ,

the value of the tract land in 2019 that Albert purchased = $140000

and he heard that after the new highway project the property and  land would soon be worth of $200,000 .

after survey the value of the project will be = $180000 ,

after the abandoning of highway project , the value = $100000 .

but Albert cannot claim any loss because there was no transaction.

It is not given that Albert sold the land so neither did he gain or make a loss.

Therefore , the correct option is (e)None of these choices are correct .

The given question is incomplete , the complete question is

Albert purchased a tract of land for $140,000 in 2019 when he heard that a new highway was going to be constructed through the property and that the land would soon be worth $200,000. highway engineers surveyed the property and indicated that he would probably get $180,000. the highway project was abandoned in 2022 and the value of the land fell to $100,000. what is the amount of loss albert can claim in 2022 ?

(a) $100,000

(b) $60,000

(c) $40,000

(d) $80,000

(e) None of these choices are correct.

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The number of red bricks is 6, and there are 8gray bricks.

Here given,

A red brick weighs 9 kg and a gray brick weighs 8 kg. The total number of bricks is 14, with a weight of 120kg.

Let x be a red brick and y be a gray brick.

x + y = 14bricks,

=> x = 14 - y bricks

9x + 8y = 120kg

9(14 - y) + 8y = 120

126 - 9y + 8y = 120

-y = -6

y = 6

14 - 6 = 8

The number of red bricks is 6, and the number of gray bricks is 8.

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The administrative costs is approximately 10% of sponsorship revenue expressed as percentage.

Total amount of money received for equipment = $258,000

Total administrative cost = $27000

Percentage representation of the administrative costs =

= 27000 / 258000 × 100%

= 0.10465 × 100%

= 10.46...%

≈ 10 %

therefore the administrative cost is about 10 % of the whole  sponsorship.

Long before the decimal system, calculations in Ancient Rome were regularly conducted in fractional multiples.

Augustus, for example, levied a centesima rerum venalium tax of one cent on commodities sold at auction. With these fractions, it was similar to computing percentages.

As money denominations grew in the Middle Ages, computations with a denominator of 100 became more widespread, becoming typical in mathematical literature from the late 15th through the early 16th centuries.

Several of these works used similar methodologies to investigate profit and loss, interest rates, and the Rule of Three. By the 17th century, interest rates were expressed in hundredths.

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The volume flow rate of the water passing through the pipe increases by a factor of 6.

Assuming that the initial cross sectional area of the pipe is A m² and the initial velocity of the water is V m/s, the water flow rate is:

= initial flow rate = area × velocity = AV m³/s

As the water speed doubles (2V m/s) and the pipe cross-sectional area triples (3A m²), the volume flow rate becomes:

Final flow rate = 2V × 3A = 6AV m³/s

As a result, the volume flow rate of the water moving through it multiplies by a ratio of six.

The basic equation for cases like these is

Q=AV,

where Q is the volume flow rate, A is the cross-sectional area occupied by the flowing material, and V is the average velocity of flow.

V is considered an average since not every component of a flowing fluid flows at the same rate. If you monitor the waters of a river moving slowly downstream at a consistent rate of gallons per second, you will see that the surface has slower currents here and faster currents there.

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From the  arrangement given, it can be concluded that-

Frank is between Chuck and Bob

What is arrangement?

The way of putting up a particular thing in order for a particular purpose or activity is called arrangement.

From the seating arrangement given,

Andy is on the end: but Eliot isn't

Andy  ___  ___ ___ ___ ___

Eliot is not on the end and Eliot and Doug have three people between them

Andy Elliot ___ ___ ___ Doug

Chuck sits next to Eliot, but not next to Bob

Andy Elliot Chuck ___ Bob Doug

Only Frank is left

Andy Elliot Chuck Frank Bob Doug

So Frank is between Chuck and Bob

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Answer: -7/4

Step-by-step explanation: see attached

Answer:

13.8

Step-by-step explanation:

2b+3a

2(3)+3(2.6)

6+3(2.6)

6+7.8

13.8

The inverse functions required from the given table of values are;

f⁻¹(1) = 1/3

f⁻¹(12) = 1/13

f⁻¹(7) = 1/9

An inverse function also called an anti function is defined as a function, that can reverse into another function. This simply means that, if any function “f” takes x to y then, the we can say that the inverse of the function “f” will take y to x. If the function is denoted by 'f' it means that the inverse function is denoted by f⁻¹(x)

For example, we have the function;

y = 2x + 3, the inverse would be;

f⁻¹(y) = (x - 3)/2

Thus, from the given table;

f⁻¹(1) = 1/3

f⁻¹(12) = 1/13

f⁻¹(7) = 1/9

Thus, we conclude that the inverse functions of f⁻¹(1), f⁻¹(12) and f⁻¹(7) are respectively 1/3, 1/13 and 1/9.

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The equations that represent the pattern are:

P = 3n

P = 2n + 1

Options A and C are the correct answer.

An equation is a mathematical statement of two expressions connected by an equal sign.

Example:

2x = 5 is an equation.

We have,

P = 3 when n = 1.

a) P = 3n

P = 3 x 1 = 3

b) P = n + 3

P = 1 + 3 = 4

c) P = 2n + 1

P = 2x 1 + 1 = 2 + 1 = 3

d) P = 3 - n

P = 3 - 1 = 2

We see that,

P = 3n and P = 2n + 1 gives P = 3 when n = 1.

Thus,

P = 3n and P = 2n + 1 gives P = 3 when n = 1.

Options A and C are the correct answer.

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Amount paid by Ethan to buy a video game on sale of 20% with usual cost of $39.99 is equal to $32 ( nearest cent ).

As given in the question,

Usual cost of Video game bought by Ethan = $39.99

Sale discount received by Ethan on video game = 20%

Let 'x' be the amount paid by Ethan for video game.

Discount amount = 20% of $39.99

                             = ( 20 / 100 ) × 39.99

                             = 799.8/100

                             = $ 7.998

                             = $7.99

Amount to be paid by Ethan 'x' = $39.99 - $7.99

                                                   = $32 ( nearest cent)

Therefore, the amount paid by Ethan to purchase a video game on sale discount of 20% is given by $32.

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Thus , the probability of that  a) a flush (5 cards of the same suit) is  .198% and probability of a 3 card of same rank and2 from single other rank is  0.07612 %

The field of mathematics known as probability studies numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.

Here,

a) It doesn't matter what suit the first card is. Any of the suits may be drawn first, provided that the following four cards are taken from the same deck and have the same suit.

The deck contains 13 of each suit, so after the first card is pulled, there are only 12 of that suit remaining. There are then 11 remaining for the third card, 10 remaining for the fourth card, and 9 remaining for the fifth and final card. The deck will also contain one fewer card overall each time.

(ℎ) = (2   ) ∙ (3   ) ∙ (4ℎ   )\s∙ (5ℎ   )

(ℎ) = [tex]\frac{12}{51} *\frac{11}{50} *\frac{10}{49} *\frac{9}{48}[/tex]

(ℎ) =11880 / 5997600

(ℎ)= 33/16660 = .00198  .198%

c) The probability of a 3 card of same rank and2 from single other rank

Since there are 13  ranks in the cards

So, P =  [tex]\frac{13}{52} * \frac{12}{51} *\frac{11}{50} *\frac{13}{52} *\frac{12}{51}[/tex]

P = 267696/351655200

P=0 .0007612 or 0.07612 %

Thus , the probability of that  a) a flush (5 cards of the same suit) is  .198% and probability of a 3 card of same rank and2 from single other rank is  0.07612 %

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The value of l such that the rectangle and trapezium have the same area will be 18 feet.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

The perimeter of the rectangle = 2( length + width).

As per the given,

Area of rectangle = area of a trapezoid

9 x l = (1/2)(24 + 12)9

9l = 162

l = 18 feet

Hence "The amount of l that must be present for the rectangle and trapezium to share the same area is 18 feet.".

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By using Gram Schmidt process of orthogonalization, it can be calculated that-

Distance from a vector (2; 3; 1)t to the subspace spanned by the vectors [tex](1; 2; 3)^T , (1; 3; 1)^T[/tex] IS 2.51 units

What is Gram Schmidt process of orthogonalization?

In an inner product space, the set of mathematical operations which converts a set of linearly independent vectors into an orthonormal vector that spans the same set as spanned by the original vectors is called Gram Schmidt process of orthogonalization.

Distance from [tex]b=(2,3,1)^T[/tex] to   W= [tex]Span\left \{u_1= (1,2,3)^T,u_2=(1,3,1)^T \right \}[/tex]

Here, Gram Schmidt process of orthogonalization is used

[tex]v_1=u_1=(1,2,3)^T\\ v_2=u_2-\frac{ < u_2,v_1 > }{||v_1||^2}v_1[/tex]

     [tex]=(1,3,1)^T-\frac{(1,2,3)^T.(1,3,1)^T}{(1,2,3)^T.(1,2,3)^T}(1,2,3)^T\\ =(1,3,1)^T-\frac{1+6+3}{1+4+9}(1,2,3)^T\\ =(2/7,11/7,-16/14)^T[/tex]

[tex]v_2 =(2/7,11/7,-8/7) ^T[/tex]

[tex]proj_bW=\frac{(2,3,1)(1,2,3)}{(1,2,3)(1,2,3)}(1,2,3)+\frac{(2,3,1)(2/7,11/7,-8/7)}{(2/7,11/7,-8/7)(2/7,11/7,-8/7)}(2/7,11/7,-8/7)[/tex]

             =(1.42, 5.11,  -0.22)

[tex]b-proj_bW[/tex]=(2,3,1)-(1.42,5.11, -0.22)=(0.58,-2.11,1.22)

Required distance from b onto W=

[tex]||b-pro_bW||=||(0.58,-2.11,1.22)||=\sqrt{(0.58)^2+(-2.11)^2+(1.22)^2}[/tex] = 2.51 units

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Answer and Step-by-step explanation:

Let the cost of each ticket for Jessica be $x. If she sold one of the tickets at a profit of 10%, she got $x + 0.1*x = $1.1x from selling it. Similarly, if she sold the other ticket at a loss of $18, she got $x - $18 from selling it.

Since the difference in the selling prices of the two tickets is $36, we have $1.1x - ($x - $18) = $36. Solving this equation for x, we get $x = $36 / 0.1 = $360. Therefore, the cost of each ticket for Jessica was $360.

To determine whether Jessica made an overall profit or loss, we need to compare the total amount she received from selling the two tickets to the total cost of the tickets. The total amount she received from selling the two tickets was $1.1x + ($x - $18) = $1.1x - $18 + $x = $1.1x = $396. The total cost of the tickets was 2 * $360 = $720. Since $396 < $720, Jessica made a loss of $720 - $396 = $324 overall.

8(−5x−8)=-3x-4−3x−4

-40x-64=-3x-4-3x-4

-40x-64=-6x-8

-36x=-56

[tex]x=\frac{56}{36}[/tex]

[tex]x=\frac{14}{9}[/tex]

Answer: No

Step-by-step explanation:

Answer:

Step-by-step explanation:

A......

By using the concept of intercept, it can be calculated that-

y-coordinate of the y-intercept is -5

What is intercept?

The distance from the origin to the point where the curve cuts the x axis is the x intercept of the curve.

The distance from the origin to the point where the curve cuts the y axis is the y intercept of the curve

The polynomial function is

f(x) = [tex]7x^2-5x+9x^3-5+2x^4[/tex]

For  y-coordinate of y- intercept, we put x = 0

[tex]f(0) = 7(0)^2-5(0)+9(0)^3-5 + 2(0)^4[/tex]

       = -5

y-coordinate of the y-intercept is -5

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a) The amount of water in the tank will be 0 after 5 minutes.

b) As time increases, the amount of water decreases at a rate of -60 L/min.

Here we can see a graph of a linear function that relates the amount of water in an aquarium (vertical axis) with the time (horizontal axis).

The amount of water in the aquarium will reach the 0 liters mark when the line intercepts the x-axis.

We can see that happens for x =  5 minutes

b) We can see that as we move to the right (time flows to the right in that graph) the line goes downwards. This means that the amount of water on the tank decreases as the time increases.

We can see that in 5 minutes, the amount of water goes from 300 lites to 0 liters, so the rate at which the water comes out of the tank is:

R = 300L/5min = 60 liters per minute.

It should actually be written with a negative sign so we are 100% clear that it means that the water is coming out from the tank, so the rate is:

R = -60 L/min

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