Convert 10.6% to a fraction in the lowest terms.

Answer:

a) [tex]x=\frac{15}{p}[/tex]

b) x=[tex]-3[/tex]

Step-by-step explanation:

First, you distribute the 4 to open the parentheses.

[tex]4px+4=64[/tex]

Subtract 4 to both sides:

[tex]4px=60[/tex]

Divide by 4p on both sides:

[tex]x=\frac{60}{4p}[/tex]

[tex]x=\frac{15}{p}[/tex]

For the second part, substitute the value of p.

[tex]x=\frac{15}{-5}[/tex]

[tex]x=-3[/tex]

Answer:

5500 is correct Answer.

Please mark me as brainlist answer.

A basketball court has symmetry; one half of the court is a mirror image of the other. The entire basketball court ( is 94 feet by 50 feet. On each half-court, painted lines show the free throw lane and circle, as well as the three-point arc, whose distance from the basket varies based on the level of hoops being played.

The borders of the court have their own commonsense names:

Along the length of the court, the borders are the sidelines.

Along the ends, the borders are the endlines, or baselines.

Separating both halves of the court is a midcourt line.

In the very center of the midcourt line is the center circle (12 feet in diameter), where the center toss takes place to begin the game.

The free throw lane is the hub of the action in each half-court. This rectangle is 12 feet wide — 16 feet at the men's pro level. Its length, as measured from the basket to the free throw line, is 15 feet at all levels. An offensive player may not stand inside the lane for more than three seconds unless he or one of his teammates is shooting the ball. After a shot is taken, the count starts over again. A defensive player may remain inside the lane for as long as he desires.

A player fouled by another player sometimes receives free throws, also known as foul shots. She takes these shots (they aren't really "throws") from the free throw line at the end of the lane — 15 feet from the basket. The shots are "free" because a defender does not guard the shooter .The remaining players line up alongside the free throw lane (or behind the shooter) and cannot interfere with the shot. They line up in order, on either side of the lane, of defense-offense-defense-offense. (Up to four players may stand on one side of the lane.) If a player opts not to take a spot (say, for example, the second defensive spot), then a player from the opposing team is permitted to step into that spot. The fans behind the basket usually scream, jump up and down, and wave their hands to try to distract an opposing team's shooter during free throws.

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Answer: u need to send a pic of the angle

Step-by-step explanation:

Answer: Your computer will be worth $1,171.12

Step-by-step explanation:

[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]

Step-by-step explanation:

there is no real number solution for the square root of a negative number.

a sqare root multiplied by itself had to deliver exactly the number inside the square root.

so for sqrt(-49), what can be the answer ?

which number multiplied by itself gives -49 ?

it any negative number at that.

because

a × a = a²

and

-a × -a = a² but definitely not -a².

we get a negative number only, when we multiply a positive number with a negative number or vice versa.

the only solution is complex or imaginary (based on the imaginary number i):

i² = -1

i = sqrt(-1)

so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i

but again, no real solution.

Answer:

12 days for Bailey

2.4 days for Andrew

Step-by-step explanation:

If Andrew is 5 times as fast, then Andrew + Bailey are 6 times as fast as Bailey alone.

That means Bailey would take 2*6 = 12 days to paint alone.

Since Andrew is 5 times faster, he'd only take 12/5 = 2.4 days.

2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

Given two numbers

1)2.7×1012

2) 1.5×108

Two numbers can be equal or one is greater than the other or one is less than the other. there will be no other case rather than these three.

1)2.7×1012=2,732.4

2) 1.5×108=162

The value of the 1st number is 2,732.4 and the value of the 2nd number is 162

1st given number is greater than the 2nd number i.e. 2,732.4>162

Therefore,2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

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The domain is:

D: {-4, 5, 6, 8}

The range is:

R: {-4, 3, 5}

And yes, the relation is a function.

For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).

Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}

The domain is the set of the first values of each pair, so we have:

D: {-4, 5, 6, 8}

The range is the set of the second values of each pair:

R: {-4, 3, 5}

Now, is this a function?

Yes, it is a function, because each input is mapped into only one output.

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The image of image of the point [tex](-7,-3)[/tex] after a rotation of [tex]180[/tex] degrees counterclockwise is [tex](7,3)[/tex]

According to the question statement, point [tex](-7,-3)[/tex] is rotated by [tex]180[/tex]  degrees counterclockwise, we are supposed to find out the image of the point after the rotation.

Point [tex](-7,-3)[/tex] lies in the Third quadrant of the Cartesian Plane.

When it will be rotated by [tex]180[/tex] degrees counterclockwise, it will shift to the first quadrant of the Cartesian Plane.

Therefore the coordinates will become as [tex](7,3)[/tex].

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Answer:

  30 mL/h

Step-by-step explanation:

You want the rate 336 ml in 11.2 h as a rate in simplest form.

The rate can be expressed in simplest form in a number of ways. We usually want rates involving time to be expressed with time units in the denominator:

  (336 mL) / (11.2 h) = 30 mL/h

__

Additional comment

Medicine is often prescribed on a "per day" basis. In 24 hours, this rate would be ...

  (30 mL/h)×(24 h/day) = 720 mL/day

The machine setup to dispense this medicine might use time units of minutes:

  (30 mL/h) / (60 min/h) = (1/2) mL/min

Answer: 20

Step-by-step explanation:

Multiply 2.4*10-4

Calculate 24-4

the answer is (12x^10000)/5

Answer:

The value of x = 2/5

Step-by-step explanation:

=>(5x - 2)²

=> (5x)² + 2² - 2(5x)(2)

=> 25x² -20x +4

=> 25x² -10x -10x +4

=> (5x-2) (5x-2)

=> x = 2/5 or 2/5

The expression of [tex] \mathbf{sec( \theta)}[/tex] in terms of [tex]tan( \theta)[/tex] in Quadrant IV is presented as follows;

[tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]

The given trigonometric functions are;

[tex]sec( \theta)[/tex]

[tex]tan( \theta)[/tex]

[tex] {sec( \theta)}^{2} = {tan( \theta)}^{2} + 1[/tex]

In Quadrant IV, the tangent of an angle is -ve, while the secant is +ve

However, the square of -ve is positive;

Therefore;

[tex] \left({tan( \theta)}^{2} + 1 \right) \: is \: positive[/tex]

Which gives;

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The upper class limits are- 29, 39, 49, 59, 69, 79, 89

The lower class limits are- 20, 30, 40, 50, 60, 70, 80

The class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5

The class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5

And the number of individuals included in the summary is 84.

Here, we are given the following dataset-

Age (yr) when          Frequency

award was won

20-29                       27

30-39                       32

40-49                       15

50-59                       3

60-69                       5

70-79                        1

80-89                       1

Upper class limit is the largest data value that can go in a class.

Thus, the upper class limits are- 29, 39, 49, 59, 69, 79, 89

Lower class limit is the smallest data value that can go in a class.

Thus, the lower class limits are- 20, 30, 40, 50, 60, 70, 80

The class midpoint is the average of the upper and lower limits of a class. Class midpoint = (upper limit + lower limit)/ 2

Thus, the class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5

Class boundary is the midpoint of the upper class limit of a class and the lower class limit of the previous class.

Thus, the  class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5

Frequency gives us the number of individuals/ objects belonging to a particular class.

Thus, the number of individuals included in the summary = 27 + 32 + 15 + 3 + 5 + 1 + 1 = 84

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There will be an outcome of 16380 times.

What is an outcome?

The football team will play 14 games

and each game can result in one of 2

Hence, the total possible number of outcomes for the season is [tex]2^{14}[/tex].

Now, let us explain

Let the result can be represented by an 'ordered set" i.e. 14- box.

|1|2|3|4|5|6|7|8|9|10|11|12|13|14|

Hence, the first box can be filled in 2 ways.

Similarly, all boxes.

Hence, the total number of cases will be,

2*2*2*2.... 14 times

=  [tex]2^{14}\\[/tex]

=16380 times.

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The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.

It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.

Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.

Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.

Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.

Thus, An = A + [(n-1)*d]

A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)

A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)

A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)

Solving equation (1) and (2), we get d = 5 and A = 10.

Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.

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The speed of Makayla and Nathan are 12 mph and 20 mph respectively.

Let the speed of Makayla is 'x' mph.

and the speed of Nathan is 'y' mph.

The total distance travelled by both is 129 miles.

The time taken by each is 6 hours, same for both.

Speed  = distance / time

Distance =  speed × time

Makayla's covered distance = xt

Nathan's covered distance = yt

Total distance = xt + yt

xt + yt = 192

As, Nathan travels 8 mph faster than makayla.

The,

y = x + 8, t = 6 hours substitute;

xt + (x+ 8)t = 192

2x + 8 = 192/6

On simplification;

x = 12 mph (Makayla's speed)

Y = x + 8

y = 12 + 8

y = 20 mph (Nathan's speed)

Therefore, the speed of Makayla and Nathan are x = 12 mph and y = 20 mph respective;y.

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Value of the given expression j³k/h0 is 12

h = 8

j=-1

h = 8

In order to do this, we need to change the values of h, j, and k in the given statement = (-1)^3 (-12) / 8^0  ....(1)

Find the denominator by using (1)

(-1)³ (-12) / 1

Analyze each exponent.

= 12/1

Hence, j³k/h0 = 12

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Complete Question -

What is the value of this expression if h=8 ,j= -1 , and k= -12? j³k/h0

1. The temperature change on each day is as follows:

2. The temperature change on Day 1 was 32.31°C.

3. The temperature changed the most on Day 2.

A temperature change is a process whereby the degree of hotness or coldness varies from one time to another.

In this instance, the temperature changes can be computed by subtracting the temperature at Sunrise from the temperature at Sunset in degrees Centigrade or degrees Fahrenheit, as the case may be.

Daily Temperatures

                   Temperature at    Temperature at   Temperature

                       Sunrise (°C)           Sunset (°C)          Change

Day 1                - 13.94                    18.37                   32.31°C

Day 2                 - 9.12                   28.17                   37.29°C

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1) The intersection of sets A and B is; A ∩ B = {1, 3}

2) The complement of set A is; A' = {4, 5, 6, 9, 10}

We are given the sets;

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 7, 8}

B = {1, 3, 9, 10}

1) The intersection of sets A and B simply means the numbers that are common to both sets. Thus;

A ∩ B = {1, 3}

2) The complement of set A is defined as the set that contains the elements present in the universal set but not in set A. Thus;

A' = {4, 5, 6, 9, 10}

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The value of the expression is  -311/35

The expression is given as

negative 2 and 3 over 5 minus 6 and 2 over 7.

Rewrite properly as

- 2 3/5  - 6 2/7

Express as improper fraction

-13/5 - 44/7

Take the LCM

(-13 * 7 - 44 * 5)/35

Evaluate

-311/35

Hence, the value of the expression is  -311/35

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The coordinates of L are: (8,-4)

Here, triangle is rotated 270° counterclockwise. So the rule that we have to apply here is

(x, y) → (y, -x)

Based on the rule given in step 1, we have to find the vertices of the rotated figure.

(x, y) → (y, -x)

L(4,8) → L'(8.-4)

M(4,3) → M'(3,-4)

N(8,8) → N'(8,-8)

Vertices of the rotated figure are:

L'(8.-4)  M'(3,-4)  N'(8,-8)

Hence we get the desired result.

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The amount paid for the refrigerator is $740.25.

From the information, the sale price of a new refrigerator is $705 and sales tax is figured at 0.05 times the price.

The price of the refrigerator will be:

= $705 + (0.05 × $705)

= $705 + $35.25

= $740.25

Therefore, the amount paid for the refrigerator is $740.25

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Considering the volume of the hemisphere, it is found that she can make 48 cookies.

The volume of an hemisphere of radius r is given as follows:

[tex]V = \frac{2\pi r^3}{3}[/tex]

The radius is half the diameter, hence, for this problem:

r = 11.5/2 = 5.75.

Hence the volume of the bowl in cubic inches is given as follows:

V = 2π(5.75)³/3 = 398.16 cubic inches.

Consider the volume of a single cookie, the number of cookies that she can make is given by:

398.16/8.295 = 48 cookies.

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This relationship is not true.

[tex]1 + \sec^2(x) = 1 + (1 - \tan^2(x)) = 2 - \tan^2(x)[/tex]

and

[tex]\cot^2(x) = \dfrac1{\tan^2(x)}[/tex]

Rewrite the equation in terms of only tangent.

[tex]2 - \tan^2(x) = \dfrac1{\tan^2(x)} \iff \tan^4(x) - 2\tan^2(x) + 1 = 0[/tex]

Factorize the left side.

[tex]\left(\tan^2(x) - 1\right)^2 = 0[/tex]

Solve for [tex]\tan(x)[/tex].

[tex]\tan^2(x) - 1 = 0[/tex]

[tex]\tan^2(x) = 1[/tex]

[tex]\tan(x) = \pm 1[/tex]

[tex]x = \pm\tan^{-1}(1) + n\pi = \pm\dfrac\pi4 + n\pi[/tex]

where [tex]n[/tex] is an integer. That is, the equation only holds for certain values of [tex]x[/tex], as opposed to all [tex]x[/tex], so it's not an identity.

Answer:(-2,2)

Step-by-step explanation:

Answer:

the angle marked X is 60 degree

I will need $1,61,884.2 to pay off the mortgage.

This problem is related to simple interest and we have to calculate the amount after 10 years which is payable in the form of mortgage.

The monthly mortgage payment is $1,345.

Rate of interest is 3.6% per annum.

Time is given to be 10 years.

Simple interest for 10 years = 1345×3.6×10/100

                                            = $ 484.2

So, the total money required to clear the mortgage

= $(1345×12×10) + $ 484.2

= $161400 + $484.2

= $ 1,61,884.2

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Answer:

Step-by-step explanation:

You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.

Let x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).

This area is the product of length and width. The expression factors as ...

  rectangle area = x² -36 = (x +6)(x -6)

If we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:

  (x +6) = 2(x -6)

  18 = x . . . . . . . . . add 12-x to both sides

This is the side length of the square. The rectangle dimensions are ...

  x+6 = 18+6 = 24 . . . . feet long

  x -6 = 18 -6 = 12 . . . . feet wide

The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.

__

Additional comment

The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.

The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.

Alternate solution

Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².

The difference is 36 square feet, so we have ...

  9/4x² -2x² = 36 = x²/4   ⇒   x = √(36·4) = 6·2 = 12 . . . . width of rectangle