What is the prime factorization of 168?

22 x 32 x 5
34 x 7
22 x 17
23 x 3 x 7

The median charge is $51. The median of a data set is also called the middle value.

Median is the value of the middle point in a data set. Here is how to find the median.

A sample of the paramedical fees:  $55, $49, $50, $45, $52, and $55. Find the median!

The number of the data is 6.

Let's sort the data form the smallest!

$45, $49, $50, $52, $55, $55

The middle part of the data is $50 and $52. The median is

($50 + $52)/2 = $102/2 = $51

Hence, the median of the data is $51.

Learn more about median here:

brainly.com/question/28060453

#SPJ4

Answer:

[tex]-(220x^2-5x+9)[/tex]

Step-by-step explanation:

[tex]3*2x-9-4x*11*5x-x\\\\-4*11*5xx+3*2x-x-9\\\\-4*11*5xx+6x-x-9\\\\-220x^2 +6x-x-9\\\\-44 5x^2 +6x-x-9\\\\-220x^2+6x-x-9\\\\-220x^2 +(6x-x)-9\\\\-220x^2+5x-9\\\\(-(220x^2-5x+9))[/tex]

Factor -1 out of -220x^2 +5x-9

Answer:

graph C

Step-by-step explanation:

if x ≥ 0

2x + 1 < 5

2x < 5 - 1

2x < 4

2/2 x < 4/2

x < 2

0≤ x < 2

if x < 0

2 (-x) + 1 < 5

-2x < 5 - 1

-2x < 4

-2/-2 x > 4/-2

x > -2

-2 < x < 0

final solution

-2 < x < 2

By using trigonometry it can be calculated that-

Horizontal distance from the base of the skyscraper out to the ship is 1009.91 feet

What is trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\\[/tex]

Trigonometry is a very important tool in mathematics.

Trigonometry is used here

Here, a diagram has been attached

Let AB be the skyscraper and C is the position of the boat

Let the horizontal distance from the base of the skyscraper be x feet

Angle of depression = 48°

Height of the observation deck = 1121 feet

[tex]tan 48 = \frac{1121}{x}\\1.11 = \frac{1121}{x}\\x = \frac{1121}{1.11}\\[/tex]

x = 1009.91 feet

To learn more about trigonometry, refer to the link

https://brainly.com/question/24349828

#SPJ1

Answer: 1009.35

Step-by-step explanation:

1.1 cm is the 1/360th of the circumference. The circle's circumference is 69.72% of the arc that the angle's rays subtend.

We must comprehend and use the relationships between arc length and circumference in this question. By using geometry, we can determine that a circle's central angle is 360 degrees, and that the circle arc is directly proportional to the central angle.

The angle's rays' subtend an arc that is 69.72% the diameter of the circle.

The circumference's length is multiplied by 1/360 to get the 1/360th of the circumference, and the resulting measurement is

s= 1/360 x 396

= 1.1

the circumference is 1.1 cm.

By dividing the subtended arc by the arc length, one may determine the arc that the angle's subtend rays :

n = 276.1/396 x 100%

n= 69.72%

To learn more on circles

brainly.com/question/11833983

#SPJ4

Answer:

A. Same-side interior angles

Step-by-step explanation:

Same-side interior angles are angles that has same-side interior angles sum up to 180 degrees. So, the answer is A.

Answer: A. Same side interior angles

Step-by-step explanation:

because they are inside the parralel lines and they are on the same side of the line going across them

Answer:

a) 80 pence

b) 6 pence

Step-by-step explanation:

The connection fee is the y intercept of the graph

The cost per minute is the slope of the graph

Answer:

Step-by-step explanation:

d.) y=-x+2 and y=x+17

I graphed these system of equations on Desmos and the first 3 showed that the lines are parallel meaning they will never touch meaning that they won't have a solution or that they won't intercept. And for the last one, when I entered the equations it showed the interception, which is (-7.5, 9.5)

(Hopefully this is right)

Answer:

$4950

Step-by-step explanation:

100-45 = 55

55% × 9000 = 4950

Answer:

Step-by-step explanation:

This is the same as before,  two sides are the same length, so we know the angles are also the same.  That is, D and C are equal

180= 106+2a

now algebra again

(180-106)/2 = a

74/2 = a

37 = a

The difference in elevation in meters between the points X and Y is 360.

Why are there contour lines?

A contour line is a line drawn on a topographic map to represent a dip or elevation in the ground.

                  The vertical separation or difference in elevation between contour lines is referred to as a contour interval. Every fifth contour line is a set of bold or thicker lines known as an index contour.

Which 3 types of contour lines are there?

There are three different types of contour lines that you might find on a map: supplemental, index, and intermediate. Index lines are the thickest contour lines, and they are frequently numbered at a specific location along the line. You can see the elevation above sea level from this.

Point X is marked on the contour line of 1,600 m. Point Y is marked on the second contour line between the 1,200 m and 1,300 m contour lines, thus:

2 x 20 = 40

So we have 1,240 m. Having the elevations of the two points, we only need to take the lower value from the larger value:

1,600 - 1,240 = 360 m

So we get a result of 360 m of difference in elevation between the points X and Y.

Learn more about contour lines

brainly.com/question/3543105

#SPJ4

a quadrilateral must be a parallelogram if one pair of opposite sides is congruent and parallel

A quadrilateral with two sets of opposing parallel sides is referred to as a parallelogram.To be a parallelogram, one pair of opposite sides must be congruent and parallel. Congruent means that two sides have the same measurements or length while parallel means that two lines never intersect. For example, if one pair of opposite sides is congruent and parallel, and the other pair of opposite sides is parallel, then the quadrilateral is a parallelogram. This is because the two pairs of opposite sides form parallel lines and the respective pairs have the same length. Therefore, the answer is c. congruent and parallel.

Learn more about quadrilateral here

https://brainly.com/question/13805601

#SPJ4

By complex and real number properties, the resulting electric resistance is equal to R' = 47 / 270 + i 4 / 45 ohms.

Complex numbers are numbers of the form z = a + i b, where a, b are real numbers. The first component is the real component and the second one is the complex one. In this problem we find the case of a combination of two electric resistances described by two complex numbers. This expression must be simplified by means of real number and complex number properties:

R' = 1 / R₁ + 1 / R₂

If we know that R₁ = 4 + i 6 and R₂ = 2 - i 4, then the resulting electric resistance is:

1 / (4 + i 6) + 1 / (2 - i 4)

(4 - i 6) / [(4 + i 6) · (4 - i 6)] + (2 + i 4) / [(2 - i 4) · (2 + i 4)]

(4 - i 6) / (16 - i² 36) + (2 + i 4) / (4 - i² 16)

(4 - i 6) / (16 + 36) + (2 + i 4) / (4 + 16)

(4 - i 6) / 52 + (2 + i 4) / 20

(2 - i 3) / 27 + (1 + i 2) / 10

47 / 270 + i 4 / 45

To learn more on complex numbers: https://brainly.com/question/17162901

#SPJ1

Answer:

2.15

Step-by-step explanation:

The equation before the transformation is g(x) = (x - 0.6) - (x - 0.5)

From the question, we have the following function that can be used in our computation:

g(x) = (x - 1.6) - (x - 1.5)

Also, we have:

Transformation = shifted to the right 1 unit

This means that

g(x) = f(x - 1)

So, we have

f(x) = g(x + 1)

Substitute the known values in the above equation, so, we have the following representation

g(x + 1) = (x - 1.6 + 1) - (x - 1.5 + 1)

Rewrite properly

g(x + 1) = (x - 0.6) - (x - 0.5)

So, the equation is g(x) = (x - 0.6) - (x - 0.5)

Read more about transformation at

brainly.com/question/27224272

#SPJ1

Answer:

No

Step-by-step explanation:

The cost of running six seminars is [tex]10000+1500+6(400+250)=\$15400[/tex].

The revenue earned is about [tex]1500(6)=\$9000[/tex].

Since the revenue is significantly less than the cost, there will not be a profit.

The expression for the number of boxes of donuts bought by Ling is d/6.

We are given that -

Ling bought a ' d ' donut to share with a coworker.

There were 6 donuts in each box. This implies that 1 box contains 6 donuts.

Now, let us write the expression for the number of boxes of donuts bought by Ling as follows -

The number of boxes of donuts = the total number of donuts/donuts in 1 box.

Hence, the number of boxes of donuts = d/6

Thus, the expression for the number of boxes of donuts bought by Ling is d/6.

Read more about Algebraic expressions -

brainly.com/question/4344214

#SPJ4

The situation given in the question occurs due to the lower mortality rate which is seen in women of the age group 50-60.

Discrepancies between men and women's death rates and life expectancy. In general, women live longer than males. This means that, assuming everything else is equal, we should anticipate that women will make up somewhat more than half of the population.

Birth sex ratios are not equal. Males outnumber female births in every country. This means that, assuming everything else is equal, we should anticipate that men will make up somewhat more than half of the population.

The population's gender distribution can be impacted through migration. All other things being equal, we would anticipate that men would make up more than 50% of the population if some countries import a sizable amount of male-dominated labor.

To learn more about gender

brainly.com/question/12097093

#SPJ4

X = [tex](A - CB)^-^1[/tex]CD is the required matrix solution of the equation  [tex]AX(D+BX)^-^1[/tex] = C

we are Given [tex]AX(D+BX)^-^1[/tex] = C:

Multiply both sides by (D+BX):

=> [tex]AX(D+BX)^-^1[/tex] * (D+BX) = C * (D+BX)

=> [tex]AX(D+BX)^-^1[/tex] (D+BX)) = C(D+BX)

=> AX * I = CD + CBX

where I is the identity Matrix of size n×n

=> AX = CD + CBX.

Subtract CBX on both sides and factor:

AX - CBX = (CD + CBX) - CBX

=> AX - CBX = CD + (CBX - CBX)

=> AX - CBX = CD + 0

=> (A - CB)X = CD.

Multiply both sides on the left by [tex](A - CB)^-^1[/tex]:

[tex](A - CB)^-^1[/tex] * (A - CB)X = (A - CB)^(-1) * CD

=> ([tex](A - CB)^-^1[/tex]* (A - CB)) X = [tex](A - CB)^-^1[/tex] CD

=> IX = [tex](A - CB)^-^1[/tex] CD

X = [tex](A - CB)^-^1[/tex]CD.

To know more about matrix click on below link:

https://brainly.com/question/28180105#

#SPJ4

Answer:

(a + 9)(a + 5)

Step-by-step explanation:

a² + 14a + 45

consider the factors of the constant term (+ 45) which sum to give the coefficient of the a- term (+ 14)

the factors are + 9 and + 5 , since

+ 9 × + 5 = = + 45 and + 9 + 5 = + 14 , then

a² + 14a + 45 = (a + 9)(a + 5)

The details of the angles in the diagram used to prove the congruency of the triangles ΔABC ≅ ΔCDA  indicates;

Statements                                               [tex]{}[/tex]   Reasons

1.  ∠D ≅ ∠B                                             [tex]{}[/tex]  1. Given

∠ACB ≅ ∠CAD

2. Therefore; ∠ACD ≅ ∠CAB               [tex]{}[/tex]  2. Angle sum property of a triangle

3.  [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]                             [tex]{}[/tex]               3. Reflexive property

4. ΔABC ≅ ΔCDA   [tex]{}[/tex]                                4. ASA congruency rule

Therefore, the completed flowchart is presented as follows;

∠D ≅ ∠B                   [tex]{}[/tex]              ∠ACB ≅ ∠CAB                [tex]{}[/tex][tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]

∠ACB ≅ ∠CAB                       Angle sum property        Reflexive prop

Reason; Given

            [tex]{}[/tex]                             ΔABC ≅ ΔCDA

                                        [tex]{}[/tex]

What are congruent triangles?

Triangles are congruent if the three sides on both triangles are congruent or if two angles and a non included side in one triangle are congruent to two angles and a non included side of the other triangle

The details of the reasons used to prove the ΔABC ≅ ΔCDA are as follows;

Angle sum property of a triangle

The angle sum property of a triangle indicates that the sum of the three interior angles of a triangle is 180°

Reflexive property

Reflexive property of congruency states that a geometric figure is congruent to itself.

ASA congruency rule

The Angle-Side-Angle, ASA, congruency rule states that the if two angles and a non included side of one triangle are congruent to two angles and a non included side of the other triangle, then both triangles are congruent

Learn more about congruency of triangles here:

https://brainly.com/question/29865889

#SPJ1

The definite integral of the function f shown in the graph below, over the limits from 0 to 3.

In the given question, we have to find the definite integral of the function f shown in the graph below, over the limits from 0 to 3.

On the interval [a, b], the definite integral of a real-valued function f(x) with respect to a real variable x is written as

[tex]\int^{b}_{a}f(x)dx = f(b) - f(a)[/tex]

Any function's definite integral can be written as the upper limit of a sum or, if an anti-derivative F exists for the interval [a, b], as the difference between the values at the points a and b.

[tex]\int^{3}_{0}f(x)dx[/tex] = Area under the curve from 0 to 3

[tex]\int^{3}_{0}f(x)dx[/tex] = 1/2 ×3×12

[tex]\int^{3}_{0}f(x)dx[/tex] = 18

Hence, the definite integral of the function f shown in the graph below, over the limits from 0 to 3 is 18.

To learn more about definite integral of the function link is here

brainly.com/question/29974649

#SPJ4

Answer:

Step-by-step explanation:

4+5(7)

4+ 35

39

I got this answer by simply plugging in the number that was given because it said a =7 I plugged in 7 instead of using a. The same goes to b it said that b=4 so then i plugged in 4 instead of using b.

A. Perpendicular

B. Neither

C. Parallel

D. Parallel

E. Parallel

F. Perpendicular

G. Neither

H. Neither

I. Neither

Answer:

maybe the first answer is 0.035 and the second answer is 0.045

Step-by-step explanation:

Answer:2.8333…

Step-by-step explanation:

you just have to divide

The equal gives the solution for the variable 'c' in the given equation. I.e., c = 2.6.

A solution is the only value that satisfies the equation. It is also said to be the root of the equation.

The given equation is

5c = 13

To solve the equation, divide both sides of the equation by 5.

So, we get

5c/5 = 13/5

⇒ c = 13/5

On converting the fraction into a decimal, we get c = 2.6.

To find whether the solution is correct or wrong, just substitute the value into the equation. If we get L.H.S = R.H.S, then that solution is the valid or correct one.

Substituting the value in L.H.S of the given equation, we get

5c = 5(2.6)

On multiplying,

5c = 13.0 ≈ 13

⇒ L.H.S = R.H.S

Hence, the solution is valid. The value of c is 2.6.

Learn more about an equation here:

https://brainly.com/question/25678139

#SPJ1

The percentile score of 71 on test score is 27 and the score of victor is 71.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula

[tex]R_{100} =\frac{100(N < )+\frac{1}{2} }{N}[/tex]

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60th percentile.

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

To learn more on Statistics click:

brainly.com/question/29342780

#SPJ1

Answer:

---------------------------------

Given:

It gives us:

Divide both sides by 9.60 to find the rate:

Answer:

Therefore, the value of "a" could be 23 or -7 in order for the two points (-5,8) and (3,a) to be 17 units apart.

Step-by-step explanation:

To find the value of "a" such that the two points (-5,8) and (3,a) are 17 units apart, we can use the distance formula to calculate the distance between the two points.

The distance formula is:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for x1, y1, x2, and y2, we get:

distance = sqrt((3 - (-5))^2 + (a - 8)^2)

Simplifying the expression, we get:

distance = sqrt((8)^2 + (a - 8)^2)

distance = sqrt(64 + (a - 8)^2)

Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":

sqrt(64 + (a - 8)^2) = 17

64 + (a - 8)^2 = 289

(a - 8)^2 = 225

a - 8 = 15 or a - 8 = -15

a = 23 or a = -7

Answer: 23 or -7

Step-by-step explanation:

The distance formula is:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for x1, y1, x2, and y2, we get:

distance = sqrt((3 - (-5))^2 + (a - 8)^2)

Simplifying the expression, we get:

distance = sqrt((8)^2 + (a - 8)^2)

distance = sqrt(64 + (a - 8)^2)

Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":

sqrt(64 + (a - 8)^2) = 17

64 + (a - 8)^2 = 289

(a - 8)^2 = 225

a - 8 = 15 or a - 8 = -15

a = 23 or a = -7