Azarai is looking to purchase a new pair of basketball shorts costing $40. The New Jersey state tax rate is 7.5 percent. What final price must he pay??? Plzzz I will give you 100 points

Answer:

1282.82ft³

Step-by-step explanation:

To find the volume of the entire shape, we first need to find the volume of the cone and the cylinder separately.

Let's begin by getting the volume of the cylinder.

The formula to find the volume of a cylinder is:

[tex]V=\pi r^{2}h[/tex]

r = 7 ft

h = 6 ft

Let's plug in our values into the formula.

[tex]V=\pi (7)^{2}6[/tex]

[tex]V=\pi (49)6[/tex]

[tex]V=\pi (294)[/tex]

[tex]V=923.63[/tex]ft³

Now that we have the volume of our cylinder we need to find the volume of the cone.

The volume of the cone can be found by using the formula:

[tex]V=\dfrac{1}{3}\pi r^{2}h[/tex]

Our variables for the cone are:

r = 7 ft

h = 7 ft

[tex]V=\dfrac{1}{3}\pi (7)^{2}(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (49)(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (343)[/tex]

[tex]V=\dfrac{1}{3}1077.57[/tex]

[tex]V=359.19[/tex]ft³

Now that we found both of the volumes of the two shapes, we can then simply get the sum of both volumes to get the total volume of the shape.

Total Volume = 923.63ft³ + 359.19ft³

Total Volume = 1282.82ft³

Answer:

(x, y) ⇒ (-x, y)

Step-by-step explanation:

Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.

The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.

_____

Comment on rotations

A rotation about the origin can be written in the form ...

(x, y) ⇒ (ax -by, bx +ay)

where a^2 +b^2 = 1 and b/a = tan(angle of rotation)

This rigid transformation is an exception to the statement above about multiplication by something other than ±1.

Answer:

1.2g+0.4

Step-by-step explanation:

The equivalent expression should be 1.2g+0.4.

The equation is (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)

= (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)

= 0.7g + 0.6h - 0.4 + 0.8 - 0.6h + 0.5g

= 1.2g + 0.4

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Answer:

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

||Vel_jet_r|| =  465.993 mph

Step-by-step explanation:

We need to decompose the velocity of the wind into a component that can be added  (or subtracted from the velocity of the jet)

The velocity of the jet

500 mph North

Velocity of the wind

50 mph SouthEast = 50 cos(45) East + 50 sin (45) South

South = - North

Vel_ wind = 50 cos(45) mph  East  -  50 sin (45) mph North

Vel _wind =  35.35 mph  East  -  35.35 mph North

This means that the resulting  velocity of the jet is equal to

Vel_jet_r =  (500 mph - 35.35 mph) North + 35.35 mph East

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

An the jet has a magnitude velocity of

||Vel_jet_r|| =  sqrt ((464.645 mph)^2 + (35.35 mph)^2)

||Vel_jet_r|| =  465.993 mph

Answer: (-6) is the answer for your question

Answer:

  1/6

Step-by-step explanation:

The three numbers, a, b, c, satisfy the equations ...

Subtracting the last equation from the first gives ...

  (a +b +c) -(a +b -5c) = (1) -(0)

  6c = 1

  c = 1/6

Now, we know the sum of the first two numbers is 5/6 (five times the last), and the difference of the first two numbers is 1/6 (equal to the last). Then the least of the first two numbers is ...

  (5/6 -1/6)/2 = 1/3

and the third number, 1/6, is shown to be the smallest.

The smallest of these numbers is 1/6.

____

In order, the numbers are 1/2, 1/3, 1/6.

____

Comment on finding the second-smallest number

For ...

We can find b by subtracting the second equation from the first:

  (a +b) -(a -b) = (5/6) -(1/6)

  2b = 4/6 = 2/3 . . . . . simplify

  b = 1/3 . . . . . . . . . . . . divide by 2

Please note that half the difference of the sum and difference is the generic solution to finding the smallest in a "sum and difference" problem.

Answer: - 2.5n+13.5

Explanation:

[tex]11 - 8.5 = 2.5 \\ - 2.5n \times 1 = - 2.5 \\ it \: is \: negative \: as \: the \: sequence \: \\ decreases\\ 11 - - 2.5 = 13.5 \\ - 2.5n + 13.5[/tex]

The explicit rule for the sequence 11, 8.5, 6, 3.5, 1 is to subtract 2.5 from the previous term.

To find the explicit rule, we look for a pattern in the sequence. We can see that each term is decreasing by a constant amount. Let's calculate the difference between consecutive terms:

- The difference between the second term (8.5) and the first term (11) is 8.5 - 11 = -2.5.

- The difference between the third term (6) and the second term (8.5) is 6 - 8.5 = -2.5.

- The difference between the fourth term (3.5) and the third term (6) is 3.5 - 6 = -2.5.

- The difference between the fifth term (1) and the fourth term (3.5) is 1 - 3.5 = -2.5.

Since the difference is constant and equal to -2.5, we can express the nth term of the sequence, [tex]\( a_n \)[/tex], as:

[tex]\[ a_n = a_{n-1} - 2.5 \][/tex]

where [tex]\( a_{n-1} \)[/tex] is the previous term in the sequence. To express this in terms of n, we need to find the first term of the sequence and then apply the pattern. The first term, [tex]\( a_1 \)[/tex], is 11. Since we are subtracting 2.5 each time, the nth term can be written as:

[tex]\[ a_n = a_1 - (n - 1) \cdot d \][/tex]

where [tex]\( d \)[/tex] is the common difference, which is -2.5. Substituting [tex]\( a_1 = 11 \) and \( d = -2.5 \)[/tex], we get:

[tex]\[ a_n = 11 - (n - 1) \cdot (-2.5) \][/tex]

[tex]\[ a_n = 11 + 2.5n - 2.5 \][/tex]

[tex]\[ a_n = 8.5 + 2.5n \][/tex]

Therefore, the explicit rule for the nth term of the sequence is:

[tex]\[ a_n = 8.5 + 2.5n \][/tex]

This rule gives us the terms of the sequence when we substitute n = 1, 2, 3, 4, 5, etc. For example, for n = 1:

[tex]\[ a_1 = 8.5 + 2.5(1) = 8.5 + 2.5 = 11 \][/tex]

which matches the first term of the sequence.

she went a total of 46.75 miles

Answer: OPTION D

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:

 [tex](48inches)(\frac{1foot}{12inches})=4feet[/tex]

- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that  correctly compares 2 feet to 48 inches, you can write:

[tex]ratio=\frac{2feet}{4feet}[/tex]

- Reduce the fraction, then:

[tex]ratio=\frac{1}{2}[/tex]

- You can rewrite it as following:

[tex]ratio=1:2[/tex]

Answer:

D

Step-by-step explanation:

Answer:

  80

Step-by-step explanation:

The square of a binomial is ...

  (a +b)^2 = a^2 + 2ab + b^2

You have a=8q, b=5, so the square is ...

  (8q)^2 + 2(8q)(5) + (5)^2

  = 64q^2 +80q +25

The coefficient missing from your given expression is 80.

Answer:

  2 feet below the ground level at the place where he started.

Step-by-step explanation:

After he adds 12 feet of elevation to the 6 feet above ground level where he launched, Mr Burnam is 6+12 = 18 feet above the ground level where he launched.

If he descends 20 feet, he will be 18 -20 = -2 feet above the ground level where he launched. That is, he is 2 feet below the ground level where he launched. We hope the ground slopes downward somewhat so Mr Burnam is not buried in the ground at that point.

Mr. Burnam ends up at 8 feet above ground.

To determine Mr. Burnam's final position, we need to consider each of his movements:

1. He starts from 6 feet above ground.

2. He ascends 12 feet further, so we add 12 feet to his initial height of 6 feet, which gives us (6 + 12 = 18) feet.

3. Then, he descends 20 feet to meet his wife. We subtract these 20 feet from his current height of 18 feet, which gives us (18 - 20 = -2) feet.

Since he can't be below ground, we adjust the calculation to reflect that he stops at ground level. Therefore, we take the absolute value of the result to find out how far above ground he is after the descent. The absolute value of -2 feet is 2 feet.

Now, we add this to the initial 6 feet from which he launched: (6 + 2 = 8) feet.

So, Mr. Burnam ends up at 8 feet above ground after all the ascending and descending.

Subtract 10k from both sides:

[tex] kx^2+5x-10k = 0 [/tex]

Assuming [tex]k\neq 0[/tex], divide both sides by k:

[tex] x^2+\dfrac{5}{k}x-10 = 0[/tex]

When you write a quadratic equation as [tex]x^2-sx+p [/tex], you know that the two solutions follow the properties

[tex]x_1+x_2=s,\quad x_1x_2=p [/tex]

So, in this case, we have

[tex]x_1+x_2=-\dfrac{5}{k},\quad x_1x_2=-10 [/tex]

Since we know that [tex]x_1=-5[/tex] we have:

[tex]\begin{cases}-5+x_2=-\dfrac{5}{k}\\ -5x_2=-10\end{cases}[/tex]

This system has solution [tex]k=\frac{5}{3},\ x=2[/tex]

Answer:

2

Step-by-step explanation:

One root = -5

We know ,

Other root is 2 .

Answer:

D. (2, 5)

Step-by-step explanation:

On a graph, (2, 5) is the only point in the solution space.

___

You can evaluate the inequality for each of the points to see which works.

A. 4 > 2·4 -3 . . . . false

B. 12 > 2·9 -3 . . . . false

C. 2 > 2·3 -3 . . . . false

D. 5 > 2·2 -3 . . . . TRUE

Answer:

  b² -2ab +a²

Step-by-step explanation:

The first factor can be rearranged to put the minus sign in the middle. Then you have

  (b -a)(b -a) = (b -a)² = b² -2ab +a²

___

If you like, you can also write this as ...

  a² -2ab + b² . . . . . . terms in lexicographical order

_____

The "special product" of interest here is the square of a binomial:

  (p +q)² = p² +2pq +q²

You have p=b, q=-a, so the result is as shown above.

Answer:77

32+27+22+17+12+7+2-3-8-13-15-18=77

Answer:

54

Step-by-step explanation:

The first twelve terms would be, in decreasing order, 32, 27, 22, 17, 12, 7,2, -3, -8,-13,-18,-23.

1. -23+22 = -1

2. -13+12 = -1

3. -18+17 = -1

4. -8+7 = -1

5. -3+2 = -1

Using these five facts, we can simplify this to 32+27 -5(1) = 32+27-5 = 54

Answer:

Step-by-step explanation:

Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...

  9/(n -1) - 9/n = 3/4 . . . . . minutes

Multiplying by (4/3)n(n -1), we get

  12n -12(n -1) = n(n -1)

  12 = n(n -1)

Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...

  (4·450 m)/(9 min) = 200 m/min

Brian completes 3 laps in that 9-minute time, so his rate is ...

  (3·450 m)/(9 min) = 150 m/min

Answer:

184

Step-by-step explanation:

1st step

we simplify (5-1) which is just 4 and (3+7) which is 10

and we also simply 6^2 which is 36

now we plug the simplified terms back in

(4)(36+10)

(4)(46)

184

Answer:

184

Step-by-step explanation:

Subtract: 5 - 1 = 4

Power: 6 ^ 2 = 36

Add: 36 + 3 = 39

Add: 39 + 7 = 46

Multiple: 4 * 46 = 184

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Answer:

The correct answer option is B. c = 25 + 2m.

Step-by-step explanation:

We are given that a movie rental club charges a one time fee of $25 to join and $2 for every movie rented.

We are to determine whether which of the given equations in the answer options represent how much you would spend to join the club and rent movies for a year.

The correct answer option is B. c = 25 + 2m.

One time charges = 25 plus $2 multiplied by the number of movies rented.

Answer:

Step-by-step explanation:

27

Answer:

  √13 units

Step-by-step explanation:

Find points B and C on the figure and locate the line between those points. The number next to the line is its length. Read the length from the diagram.

In a right triangle, the hypotenuse is the side across from the 90 degree angle. Without more information, we can't determine the length of the hypotenuse (BC), but if the lengths of the other two sides or the measurements of the other angles are known, the Pythagorean theorem or trigonometry can be used.  It is expressed as BC^2 = AB^2 + AC^2.

In a right triangle, the hypotenuse is the side that is opposite to the 90 degrees angle. In your right triangle, as you mentioned the sides as BC, I assume you have a triangle ABC where B and C are the two base angles and A is the right angle (90 degrees).

Without additional information such as the lengths of the other two sides (AB, AC), or the measurements of angles B or C, it is impossible to determine the length of the hypotenuse (BC). However, if you do have this information, you can use the Pythagorean theorem or trigonometric ratios to find the length. Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides. It is expressed as BC^2 = AB^2 + AC^2.

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Answer:

$15000 in bonds, $55000 in a CD

Step-by-step explanation:

Let x represent the amount Betsy invests in the B-rated bonds (in thousands). Then she will invest 70-x in a CD. Her interest (in thousands) will be ...

0.15x + .05(70 -x) = 5

0.10x + 3.5 = 5 . . . . . . . eliminate parentheses, collect terms

x + 35 = 50 . . . . . . . . . . multiply by 10

x = 15 . . . . . . . . . . . . . . . subtract 35

Then 70-x = 70-15 = 55

Betsy should invest $15000 in bonds, and $55000 in a CD.

To achieve $5000 in annual interest, Betsy should invest $15000 in B-rated bonds and $55000 in CDs.

Betsy, a recent retiree, requires $5000 per year in extra income. She has $70000 to invest and is considering two options: B-rated bonds paying 15% per year and certificates of deposit (CD) paying 5% per year. To find out how much she should invest in each to realize exactly $5000 in interest per year, we can set up a system of linear equations.

Let x be the amount invested in B-rated bonds and y be the amount invested in CDs. The equations based on the investment and the total interest required would be:

To solve this system, multiply the second equation by 100 to get rid of decimals:

Now, we can multiply the first equation by 5 to get:

Subtracting this from the modified second equation:

Plug the value of x back into the first equation:

Betsy should invest $15000 in B-rated bonds and $55000 in a CD to achieve $5000 in annual interest.

Answer:

A). Sometimes.

Step-by-step explanation:

Sometimes a translation  because it might be a rotation or a reflection.

Translation in geometry always results in a similar figure. Hence, the correct answer is C.

A similar figure compared to the original figure is **always** a translation.

Translation in geometry involves moving a figure without rotating or flipping it. When a figure is translated, all the points move in the same direction by the same distance. This means that a translation produces a figure that is congruent to the original figure.

Answer:

1800

Step-by-step explanation:

Given in the question a polygon of 12 sides

Formula to calculate sum of interior angles of 12-gon is

where n is the number of sides

which in this case = 12

plug values in the formula above

(12 - 2)180

12*180 - 180(2)

2160 - 360

1800

Sum of measurements of the interior angles of a 12sided polygon is 1800

Answer:

=1800°

Step-by-step explanation:

A 12 sided figure is called a do-decagon or a 12-gon. The general formula for calculating the sum of all interior angles of a regular polygon is=180(n-2)

n represents the number of sides of the polygon.

Therefore, the sum of all angles= 180(12-2)

=1800°

Answer:

C. 2

Step-by-step explanation:

Point B is 6-(-4) = 10 units up from point A. A point (F) that partitions that distance in the ratio 3:2 will be 3/(3+2) = 3/5 of the distance from A to B. That is, it will be ...

3/5 · 10 units = 6 units

above A. The y-coordinate of F will be 6 units added to the y-coordinate of point A, -4 +6 = 2.

Answer:

The answer is -3t(t^4 - 6t² - 1) ⇒ third answer

Step-by-step explanation:

∵ -3t^5 + 18t³ + 3t

∵ The common factor is -3t

∴ -3t(t^4 - 6t² - 1)

The observed value when x = 3, estimated to the nearest half unit is y = 4.5.

The observed value is the actual value of the variable. The points on the regression line are called predicted values.

Therefore, the observed value of y when x = 3, estimated to the nearest half unit is y = 4.5. The correct answer is option C.

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Answer:

  $5.25

Step-by-step explanation:

If the friend tripled the first purchase and subtracted twice the second purchase, he would have the cost of 3·8-2·5 = 14 notebooks. 7 notebooks would cost half that amount:

  (3·$11 -2·11.25)/2 = $5.25 . . . . . cost of 7 notebooks

Given dimensions:

Height of the cylinder = 2 m

Volume is increasing at a rate of = 10 m³/min

Radius = 4 inches

Converting radius in meters.

1 inch = 0.0254 meters

4 inches = [tex]4\times0.0254=0.1016[/tex] meters

[tex]\frac{dv}{dt}=10[/tex]

we have to find, [tex]\frac{dr}{dt}=?[/tex]

Volume of the cylinder is given by [tex]\pi r^{2} h[/tex]

= [tex]\pi r^{2} *2 = 2\pi r^{2}[/tex]

Now differentiating with respect to 't'

[tex]\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})[/tex]

[tex]\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})[/tex]

[tex]10=2\pi (2*0.1016)\frac{dr}{dt}[/tex]

[tex]10=2*3.14(0.2032)\frac{dr}{dt}[/tex]

[tex]\frac{dr}{dt}=\frac{10}{1.276}[/tex]

= 7.83 meter per minute.

Answer:

3.7 < √14 < 3.8

Step-by-step explanation:

First approximation

9 < 14 < 16, so

3 < √14 < 4

Second approximation

14 is closer to 16 than to 9.

Is √14 between 3.7 and 3.8? If so, then

 3.7²  < 14 <   3.8²

13.69 < 14 < 14.44. TRUE

The inequality is 3.7 < √14 < 3.8.