Line / has a slope of. The line through which of the following pair of points is
perpendicular to /?
A. (4, 6), (2, 2) B. (8,8), (2, 4)
C. (8,2), (2,4)
D. (6,2), (2, 4)

Answer:

  14.7 quarts

Step-by-step explanation:

Use the given equivalence figures to write a proportion. Solve the proportion for the unknown value.

__

  quarts/liters = x/14 = 1/0.95 . . . . . the conversion is given as 1 qt = 0.95 L

Multiply by 14 to find x.

  x = 14(1/0.95) ≈ 14.7

There are about 14.7 quarts in 14 liters.

_____

Additional comment

You are given a value in liters (14 liters) and asked for the equivalent in quarts. That means you want to change the units from liters to quarts. To do that, you can multiply the given value (14 liters) by a conversion factor that has quarts in the numerator and liters in the denominator. That is what the fraction 1/0.95 is in the above. You will note that units of liters cancel in this equation.

  [tex](14\text{ liters})\times\dfrac{1\text{ quart}}{0.95\text{ liter}}=\dfrac{14}{0.95}\text{ quarts}\approx14.7\text{ quarts}[/tex]

This rule, "use a conversion factor that divides by the units you don't want and multiplies by the units you do want" applies to any units conversion problem. The conversion factor you use should always have equal quantities in the numerator and denominator. (Here, the equal quantities are 1 quart and 0.95 liters.)

You will notice that we treat units just like any variable. They can be multiplied, divided, cancelled, raised to a power. Only terms with like units can be added or subtracted.

The distribution is right skewed.

A box plot is graph that is used to display data. The box plot is made up of two whiskers that are on either sides of a box. The first line on the box is the first quartile, the second line is the median and the third line is the third quartile.

When the median is closer to the bottom of the box, and if the whisker is shorter on the lower end of the box, the data is right skewed.

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Given expression

[tex]\\ \rm\Rrightarrow T(t)=29-5cos\left(\cfrac{2\pi (t-12)}{365}\right)[/tex]

Now

We know according to property of cosine function

This property is enough for our calculations

Let's check

As t represents no of days hence it can't be negative

So

for positive interval

We know that

Hence it's enough for our range [-1,1]

Now

In the expression

Let

[tex]\sf cos\left(\cfrac{2\pi(t-12)}{365}\right)=n[/tex]

Substitute n for lowest and highest value of range

When n=-1

[tex]\\ \rm\Rrightarrow T(\pi)=29-5(-1)=29+5=34°C[/tex]

When n=1

[tex]\\ \rm\Rrightarrow T(0)=29-5(1)=29-5=24°C[/tex]

Answer:

Highest temperature: 34°C

Lowest temperature: 24°C

Explanation:

In a Normal Trigonometry Function: y = A + B sin(x) or y = A + B cos(x)

Maximum value: A + |B|

Minimum value: A - |B|

In this trigonometric function, A = 29, B = -5

Hence find minimum/maximum:

Maximum value: A + |B| = 29 + |-5| = 34

Minimum value: A - |B| = 29 - |-5| = 24

Hence, the maximum/highest temperature is 34°C and minimum/lowest temperature is 24°C in Karachi, Pakistan.

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Answer:

20 mph

Step-by-step explanation:

First problem:

The new speed is 26 mph.

The old speed was x.

The new speed is 30% higher than the old speed.

1.3x = 26

x = 20

Answer: 20 mph

Second problem:

A number, perhaps a percent or a fraction, is missing from the problem.

[tex] \:❏ \: \: \LARGE{\rm{{{\color{orange}{6 {x }^{2} \: + \: 7x \: - 3}}}}}[/tex]

[tex] \large \blue\implies \tt \large \: 6 {x }^{2} \: + \: 7x \: - 3[/tex]

Sum of two factors = 7 = 9 - 2

Product of these two factors = 9 × (-2) = 18

[tex]\large \blue\implies \tt \large \:6 {x}^{2} \: + \: 9x \: - \: 2x \: - \: 3[/tex]

[tex] \: \\ \large\blue\implies \tt \large \:3x(2x \: + \: 3)\: -1(2x \: + \: 3)[/tex]

[tex] \\ \large\blue\implies \tt \large \:(3x \: - \:1 ) \quad \: (2x \: + \: 3) \: = \: 0[/tex]

Thus, (3x - 1) and (2x + 3) are the factors of the given quadratic equation.

[tex]\large\blue\implies \tt \large \:x \: = \: \frac{1}{3} \: \: , \: \: \frac{ - 3}{2} \\ [/tex]

[tex] {6x}^{2} + 7x - 3 \\ \\ {6x}^{2} + 9x - 2x - 3 \\ \\ ( {6x}^{2} + 9x) - (2x + 3) \\ \\ 3x(2x + 3) - 1(2x + 3) \\ \\ (3x - 1)(2x + 3).[/tex]

The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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The complete question is

"In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet. Triangle N Q L has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, Q M, and L P. The length of line segment N S is x + 10 and the length of line segment S R is x + 3.

What is RS?

4 feet, 7 feet, 10 feet, 14 feet"

Answer:

The Length of RS would be 7 ft. so the correct option is B.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Based on the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR,

NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3)

Solve for x

x + 10 = 2x + 6

x - 2x = -10 + 6

-x = -4

x = 4

SR = (x + 3) ft (SR is same as RS)

substitute the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Hence, The Length of RS would be 7 ft. so the correct option is B.

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Answer: B, 7 feet

Step-by-step explanation:

A fourth of a third of two fifths is a thirtieth.

(1 x 1 x 2) / (4 x 3 x 5) = 2 / 60 = 1 / 30

A thirtieth of a number () is fifteen, the number is four hundred and fifty.

= 15 / (1 / 30) = 15 x 30 = 450

forty percent of four hundred and fifty is one hundred and eighty.

(450 / 100) x 40 = 180

Answer:

The number is 450

Step-by-step explanation:

One fourth is 1/4,

One third is 1/3

and two fifths is 2/5

let the number be x.

So,

One fourth of one third of two fifths of x is 15.

that is,

1/4 * 1/3 * 2/5 * x = 15

2/4*3*5* x = 15

2/60 * x = 15

1/30 * x = 15

1 * x = 15*30

x = 450

Therefore the number is 450

Answer:

12x

Step-by-step explanation:

It has no exponent so it is not a polynomial

The ordered pair of the solution for the system of equation area are (2, -3) and (3, -3)

f(x) = x² - 5x + 3

f(x) = -3

Therefore,

-3  = x² - 5x + 3

x² - 5x + 3 + 3 = 0

x² - 5x + 6 = 0

x² - 2x - 3x + 6 = 0

x(x - 2) - 3(x - 2) = 0

(x - 3)(x - 2) = 0

x = 3 or 2

when x = 2

f(x) = 4 - 10 + 3 = -3

when x = 3

f(x) = 9 - 15 + 3 = -3

Therefore, the ordered pair of the solution for the system of equation are (2, -3) and (3, -3)

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One x- value of the solution is : -2 or -8

An Equation is an algebraic statement that shows that two quantities are equal.

Analysis:

for one x-value of a solution, f(x) = g(x)

[tex]x^{2}[/tex] + 7x -24 = -3x - 40

[tex]x^{2}[/tex] +7x +3x -24 +40 = 0

[tex]x^{2}[/tex] + 10x +16 = 0

[tex]x^{2}[/tex] +8x +2x +16 = 0

x(x+8) +2(x+8) = 0

(x+2)(x+8) = 0

x = -2 or -8

In conclusion, the values of x are -2 or -8

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Answer:

18

Step-by-step explanation:

 (6 * 3 )  - (8 * 0)  = 18

Answer:

c = 25.35

Step-by-step explanation:

Comment

Cost (c) = skate rental + time + miscellaneous

Givens

Answer

Cost = 6.35 + 18.00 + 1

Cost = 25.35 , but 24.35 is an hourly charge,

The equation for a circle with a center (-2, 8) and a radius of 9 will be (x + 2)² + (y − 8)² = 81.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

Write an equation for a circle with a center (-2, 8) and a radius of 9.

Then the equation will be

(x + 2)² + (y − 8)² = 9²

(x + 2)² + (y − 8)² = 81

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The probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

A financial planner has three portfolios: A, B, and C.

Each portfolio has stocks and Bond

P(stock) = 0.5

P(bond) = 0.5

Customers are equally likely to choose stocks.

P(stock and bond from B) = P(stock, B) + P(bond, B)

= 0.25×0.5 + 0.25×0.5

= 0.25 or

= 25%

Thus, the probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.

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Answer:

69 meters squared

Step-by-step explanation:

You can split the shape into two small rectangles by drawing a vertical line. Then, you can solve for the areas of the two rectangles separately and then add them together.

The larger rectangle would have an area of 5 * 12, or 60 m^2.
The smaller rectangle would have an area of 3 * 3, or 9 m^2.
Simply add those together and the total area would be 69 m^2.

Answer:

Area is 69 m

Step-by-step explanation:

Answer: (-2, -4)

Step-by-step explanation:

The translation that maps point A onto point B must also map point D onto point C.

Point A maps onto point B after a translation 8 units right and 6 units up, so point C maps onto point D after a translation 8 units left and 6 units down.

Thus, D has coordinates (-2, -4)

The simplification form of the provided polynomial is u¹³ + u⁹ -u⁷ + u⁶ - u³ - 1 after using the distributive property.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have an expression:

[tex]= \rm \left(u^7+u^3+1\right)\left(u-1\right)\left(u^5+u^4+u^3+u^2+u+1\right)[/tex]

After using the distributive property and simply it.

[tex]\rm =\left(u^8-u^7+u^4-u^3+u-1\right)\left(u^5+u^4+u^3+u^2+u+1\right)[/tex]

[tex]\rm =u^{13}+u^9-u^7+u^6-u^3-1[/tex]

Thus, the simplification form of the provided polynomial is u¹³ + u⁹ -u⁷ + u⁶ - u³ - 1 after using the distributive property.

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Answer:

x<9

Step-by-step explanation:

x-6<x/3

3(x-6)<x

3x-18<x

3x-x<18

2x<18

X<18/2

X<9

The value of composite function (koh)(x) is 1/(5+x) after plugging h(x)  = 5+x in the k(x) option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The question is:

if h(x)=5+x and k(x)=1/x which expression is equivalent to (koh)(x)

Answer options are:

We have:

h(x) = 5 + x

k(x) = 1/x

To find the composite function:

(koh)(x):

= k(h(x))

= 1/(5+x)

Thus, the value of composite function (koh)(x) is 1/(5+x) after plugging h(x)  = 5+x in the k(x) option (B) is correct.

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Equation #1:

We move all terms to the left:

-15+4r-(-9)=0

We add all the numbers together, and all the variables

4r-6=0

We move all terms containing r to the left, all other terms to the right

4r=6

r=6/4

r=1+1/2

Equation #2:

We move all terms to the left:

5-y/3-(-1)=0

We add all the numbers together, and all the variables

-y/3+6=0

We multiply all the terms by the denominator

-y+6*3=0

We add all the numbers together, and all the variables

-1y+18=0

We move all terms containing y to the left, all other terms to the right

-y=-18

y=-18/-1

y=+18

Equation #3:

Simplifying

42 = 5x + -8

Reorder the terms:

42 = -8 + 5x

Solving

42 = -8 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

42 + -5x = -8 + 5x + -5x

Combine like terms: 5x + -5x = 0

42 + -5x = -8 + 0

42 + -5x = -8

Add '-42' to each side of the equation.

42 + -42 + -5x = -8 + -42

Combine like terms: 42 + -42 = 0

0 + -5x = -8 + -42

-5x = -8 + -42

Combine like terms: -8 + -42 = -50

-5x = -50

Divide each side by '-5'.

x = 10

Simplifying

x = 10

Step-by-step explanation:

hope it's beneficial.

Draw my attention for further explanations.✨✨

Answer:

[tex]6\sqrt{25}[/tex]

Step-by-step explanation:

[tex]\sqrt{125} = 5\sqrt{5} \\\sqrt{45} = 3\sqrt{5} \\\sqrt{20} = 2\sqrt{5} \\5\sqrt{5} + 3\sqrt{5} -2\sqrt{5} =6\sqrt{25}[/tex]

Answer:

Answer:

horizontal translation    ( this would require an  x - k   or x+k   type of a factor)

Step-by-step explanation:

It DOES have :

    vertical    due to the -9

    horizontal compression due to the  3x

    reflection due to the   -4

Answer:

8

Step-by-step explanation:

If the only zero for this function is at x = - 4 it looks like this:

f(x)  = (x+4)(x+4)        =    x^2 +8x + 16         so j = 8

Answer:

Step-by-step explanation:

x² +jx +k = 0

If there is only one root ( - 4 ), then (x + 4)² = 0

or

x² + 8x + 16 = 0

j = 8 and k = 16

Answer:{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

Step-by-step explanation:

Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.

Random sampling is the method of selecting the subset from the set to make a statical inference.

Utilizing two six-sided number solid shapes, each named with the numbers 1 through 6.

The number of the total events will be given as,

Total events = 6²

Total events = 6 x 6

Total events = 36

The total sample is given below.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.

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Answer: The coefficients of binomial expansions are calculated using Pascal's triangle.

Answer:

The answer would be 6x^2 + 5x - 4 = 0