An arithmetic sequence follows a specific pattern where a number is _____________ to get from one term to the next.

Answer:

80 units

Step-by-step explanation:

KN = MN

9x - 5 = 7x + 7

2x = 12

x = 6

KM = 2KL

KM = 2(6x + 4)

KM = 12x + 8

KM = 12(6) + 8

KM = 80

Answer:

80

Step-by-step explanation:

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]

Adding 620 on both sides, we get

[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]

We need to find the y-value for [tex]x=57[/tex].

[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]

[tex]y=183.825+523.25[/tex]

[tex]y=707.075[/tex]

[tex]y\approx 707.1[/tex]

Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.

Answer:

1). AC=8.25cm

2). DB=7cm & EC=14cm

3). See Explanation

Step-by-step explanation:

According To the Question,

Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.

1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 2.5 / 3 = 3.75 / EC

On Solving we get,  

⇒ EC * 2.5 = 3.75 * 3  

⇒ EC * 2.5 = 11.25  

⇒ EC = 11.25 / 2.5  

⇒ EC = 4.5 cm

Thus,  

AC = AE + EC

⇒ AC = 3.75 + 4.50

⇒ AC = 8.25 cm  

Hence the measure of AC is 8.5 cm.

2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 4 / (x-4) = 8 / (3x-19)

on solving we get,

⇒ 3x-19 = 2(x-4)

⇒ 3x-19 = 2x-8

⇒x=11

Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm

And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm

3). If AD=2cm , BD= 4cm , show that BC = 3 DE

Thus, AB = AD + DB = 2+4 = 6cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD/AB = DE / BC

⇒ 2 / 6 = DE / BC

on solving we get

⇒ BC = 3 DE Hence, Proved

Answer:

From top to bottom;

1,1,3,3

Step-by-step explanation:

mathematically, for an even function;

f(x) = f(-x)

what this mean is that;

f(-1) = f(1)

f(-3) = f(3)

f(-5) = f(5)

f(-6) = f(6)

so we have it that;

f(-1) = 1

f(-3) = 1

f(-5) = 3

f(-7) = 3

Answer:

PLZZ MARK ME BRAINLIEST..!

Step-by-step explanation:

Bridgets fish: f , 2f, 3f+2 , 1/2f, 3/5f

Add for total weight: 7 1/10 f +2

Dads fish: 3f+2, 4/5f, 2f+4, 1/2f

Add for total weight:  6 3/10f +6

set the 2 total weights equal:

6 3/10f +6 = 7 1/10f +2

Subtract 6 3/10f from each side:

6 = 8/10f  + 2

Subtract 2 from each side:

4 = 8/10f

Divide both sides by 8/10:

f =  5

Bridget's first fish weighed 5 ounces.

Dads first fish weighed:  2 more than 3 times :3(5) + 2 = 15 +2 = 17 ounces.

Answer:

Yes, the data provides convincing evidence that men and women have different average BF%s

Step-by-step explanation:

The given parameters are;

The number of the subjects ages 20 to 80 = 13,601

The body fat percentage, BF%, for the 6,580 men, [tex]\overline x_1[/tex] = 23.9

The body fat percentage, BF%, for the 7,021 women, [tex]\overline x_2[/tex] = 35.0

The standard error for the difference between the average men and women = 0.144

The null hypothesis, H₀; [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ; [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The test statistic = (35.0 - 23.9)/(0.114) = 97.368

Therefore, given that the z-test is larger than the critical-z, we reject the null hypothesis, H₀, therefore, there is convincing statistical evidence to suggest that men and women have different body average BF%

Answer:

must be parallel

Step-by-step explanation:

They must be parallel.

Answer:

a). 6:51

b). 6:30 am

c). 34 minutes

Step-by-step explanation:

a). Train leaves Westchester at 6:30.

   From the arrival - departure table in column (2),

   Arrival time of the train at middlewich = 6:51

b). Kate has to reach Southam before 9:00 am

   Therefore, time of the latest train that she can catch to get to work on time is 6:30 am

    By this train she can reach at 07:19 at Southam.

c). Duration of journey from Westchester to Eastwick = 06:34 - 06:00

                                                                                        = 00:34

                                                                                        ≈ 34 minutes

Answer:

It is d

Step-by-step explanation:

Answer: 24 square cm.

8*6=48

48/2=24

Answer:

24 cm^2

Step-by-step explanation:

(w*h)/2

Answer:

4/9 of an hour (26.666 minutes)

Step-by-step explanation:

4 * x * 40/60 = 1

x * 160/60 = 1

x=60/160 = 6/16 = 3/8 (this is the rate for one worker)

~~~~~~~~~~~~~~~~

6 * (3/8) * x = 1

x = 4/9

Complete question is;

Which of these is an exponential parent function?

A. f(x) = x

B. f(x) = 2^(x)

C. f(x) = x²

D. f(x) = |x|

Answer:

B. f(x) = 2^(x)

Step-by-step explanation:

> In option A, f(x) = x

This function depicts a straight line with intercept as 0 and slope as 1.

> In option C, f(x) = x²

This function depicts a parabola open up since the leading coefficient is greater than 0.

> In option D: f(x) = |x|

This function depicts a straight line y = x for x > 0 and y = -x for x < 0

In option B f(x) = 2^(x)

This function depicts an exponential function because the x is in the exponent form with a base of 2.

Answer:

The coordinate of point C is (m,m) and the coordinate of point D is (m,0).

Step-by-step explanation:

Square:

In a square, all sides have the same length.

A (0, 0) and B (0, m).

This means that the length of the sides is m.

So:

From A, adding m vertically, we get point (0,m), which is B.

From A, adding m horizontally, we get point (m,0), which I will call D.

From B, adding m horizontally, we get point (m,m), which I will call C.

The coordinate of point C is (m,m) and the coordinate of point D is (m,0).

Answer:

Step-by-step explanation:

[tex]Cos \ 39 = \frac{adjacent \ side}{hypotenuse}\\\\0.7771 = \frac{7}{x}[/tex]

x * 0.7771 = 7

[tex]x =\frac{7}{0.7771}=9.007[/tex]

x = 9

Answer:

g = 48

k = 18

Step-by-step explanation:

h / 10 = 60 / 12

h / 10 = 5

h = 5 x 10

h = 50

40 / h = g / 60

40 / 50 = g / 60

4 / 5 = g / 60

g = ( 60 x 4 ) / 5

= 12 x 4

g = 48

90 / k = 60 / 12

90 / k = 5

k = 90 / 5

k = 18

Answer:

A.

Step-by-step explanation:

A.-6r+6

Answer:

72 cm²

Step-by-step explanation:

Area = 9(8) = 72

..............

Answer:

$843.67

Step-by-step explanation:

We can use a proportion to solve this problem:

12 : 100 = x : 896

x =(896 * 12)/100 = $107,52

896 - 107.52 = $788,48 (price of the computer after the discount)

7 : 100 = x : 788,48

x = (788,48 * 7)/100 = $55,1936

788.48 + 55,1936 = 843,6736 = $843.67 (final price)

Given:

The equation is:

[tex]4\log_2(2x)=x+4[/tex]

The graph of the [tex]4\log_2(2x)[/tex] and [tex]x+4[/tex] are given on a coordinate plane.

To find:

The solution of the given equation from the given graph.

Solution:

From the given graph it is clear that the graphs of [tex]4\log_2(2x)[/tex] and [tex]x+4[/tex] intersect each other at points (1.24,5.24) and (16,20).

It means the values of both functions [tex]4\log_2(2x)[/tex] and [tex]x+4[/tex] are equal at [tex]x=1.24[/tex] and [tex]x=16[/tex].

So, the solutions of given equation are [tex]x=1.24[/tex] and [tex]x=16[/tex].

Therefore, the correct option is only F.

Answer:

use system of equations

Step-by-step explanation:

Set one up for the Smith family and one for the Jones family

Answer:

80°

Step-by-step explanation:

Triangle ABC and CYZ are similar so the angles would also be same

Hi there!

[tex]\huge\boxed{\text{22 cm}}[/tex]

We know that:

Area of a rectangle = l × w

The areas are the same, so:

3x · 4 = 6(3x - 2.5)

Simplify:

12x = 18x - 15

Solve for x:

15 = 6x

x = 2.5

Plug in this value of x to find the perimeter of rectangle B:

P = 2l + 2w

l = 6

w = 3(2.5) - 2.5 = 5

P = 2(6) + 2(5) = 22 cm

Answer:

0.8536

0.29933

Step-by-step explanation:

Given :

Mean amount spent, μ = $230

Standard deviation, σ = $19

1.)

Probability of spending atleast $210

P(x ≥ 210)

The Zscore = (x - μ) / σ = (210 - 230) / 19 = - 1.052

P(Z ≥ -1.052) = 1 - P(Z ≤ - 1.052) = 1 - 0.1464 = 0.8536

2.)

Probability that between $240 and $300 is spent:

P(x < $240) = Zscore = (240 - 230) / 19 = 0.526

P(Z < 0.526) = 0.70056

P(x < 300) = Zscore = (300 - 230) / 19 = 3.684

P(Z < 3.684) = 0.99989

P(Z < 3.684) - P(Z < 0.526)

0.99989-0.70056 = 0.29933

Answer:

sinΘ = √5/3

Step-by-step explanation:

Mathematically, we know that the cos of an angle is the ratio of the adjacent to the hypotenuse

The sine of an angle is the ratio of the opposite to the hypotenuse

So in this case, from the cosine given; adjacent is 2 and hypotenuse is 3

From the Pythagoras’ theorem, we can get the opposite

Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides

Let us have the opposite as x

3^2 = 2^2 + x^2

9 = 4 + x^2

x^2 = 9-4

x^2 = 5

x = √5

This root can be positive or negative

But since the sine is positive, we shall be considering only the positive root

Thus;

sine theta = √5/3

Answer:

C

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (4, - 1 ) and r = 3 , then

(x - 4)² + (y - (- 1) )² = 3² , that is

(x - 4)² + (y + 1)² = 9 → C

The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

Peter sold a cup of lemon juice = $1.25

Peter sold a cup of apple juice =  $2.50

Total number of cups sold = 155 cups

Total amount = $256

Let number of cup of lemon juice be x and

let number of cup of apple juice be y

The equations for the above statements are

[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]

From equation 1,

⇒ [tex]x=155-y[/tex]

Now substitute x in equation 2,

⇒ [tex]1.25(155-y)+2.50y=256[/tex]

⇒ [tex]193.75-1.25y+2.50y=256[/tex]

⇒ [tex]1.25y=256-193.75[/tex]

⇒ [tex]1.25y=62.25\\[/tex]

⇒ [tex]y=\frac{62.25}{1.25}[/tex]

⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]

Now substitute y in equation 1,

⇒ [tex]x=155-50[/tex]

⇒ [tex]x=105[/tex]

Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

Learn more about the system of equation here

https://brainly.com/question/12760602

#SPJ3

Step-by-step explanation:

Length of a rope is 5 meter. it means the rope is 5 meter long..

Answer:

5:15 simplified as 1:3

Step-by-step explanation:

Answer:

In order:

Distributive Property

Subtraction Property of Equality

Division Property of Equality or Reciprocal Property

Step-by-step explanation: