let lines x and y be parallel, and let lines z and w be parallel. if angle a is the angle formed by lines y and z, and angle b is the angle formed by lines w and x, if the measure of angle a is 25 degrees, what is the measure of angle b?

Answer:

A = 5,752.60

Step-by-step explanation:

P = $3,500

r= 5%

t = 10

k = 4

A = P(1 + r/k)^kt

= 3,500(1 + 0.05/4)^4*10

= 3,500(1 + 0.0125)^40

= 3,500(1.0125)^40

= 3,500(1.6436)

= 5,752.6

A = 5,752.60

Total number of students in the graduating class when 60% of the students are going to college is equal to 400 students.

Percent of students of the graduating class going for college  is equal to 60%

let 'y' represent the total number of students in the graduating class.

Number of students of the graduating class going  to the college are 240.

60% of y = 240

⇒ ( 60 / 100 ) × y = 240

⇒ y = 240 × ( 100 / 60 )

⇒ y = 400 students.

Therefore, when 240 students of the graduating class going for a college then total number of students in the graduating class is equal to 400 students.

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Answer:

B; the angles of the triangle and the hypothnuse can be multiplied.

Answer:

21

Step-by-step explanation:

You got it right.

Answer:

y = 8x - 64

Step-by-step explanation:

Start with y = mx + b, the slope-intercept equation.  Replace m with 8, x with 7 and y with -8:

-8 = 8(7) + b, or

-8 - 56 + b, or

b = -64

Then the desired equation is

y = 8x - 64

Option # 4

Total cost (   $ )     Cost of groceries(   $ )      grocery  pick-up service( $)

15                           10                                                 5

25                          20                                                 5

35                           30                                                 5

45                           40                                                 5

Here we can see that the price difference of total cost and cost of groceries is 5$ which is our  grocery  pick-up service

now lets check  options

#1  since cost of groceries is given 75 $ so total cost will be 80 $ because our grocery  pick-up service is 5 $

#2  Here we can see that on adding Cost of groceries and  cost of grocery  pick-up service ,we are getting our total cost .So yes it is an additive relationship

#3 yes all the given data is independent

#4 Here on the basis of prepeared chart  we can see that grocery  pick-up service cost is 5$ not 10$

so option #4 is incorrect

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Answer:

Step-by-step explanation:

10

Answer:

Han OS New Visa OS de OS OS

17. <

18.=

19.>

20.>

21.3.021,3.12,3.121,3.21

22. 1.03,1.03,1.3,1.39

23.

A measure of center refers to a statistical means of determining the center of a dataset.

A measure of variation refers to a way of determining the spread of data points in a dataset.

A measure of relative standing is a way of comparing the individual data points to the remaining dataset.

To measure the center for a dataset with outliers, the most appropriate way to obtain an accurate result will be by using the median.

A median is a form of measurement that is unaffected by outliers or extreme values. This measurement can help a person to obtain the exact values for the center point.

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Answer:

13.4

Step-by-step explanation:

The tree to the shadow forms a right angle triangle, so to calculate the distance from the tree tip to the shadow tip we can use pythagoras.

a^2 +b^2 = c^2

12^2 +6^2 = 144 +36 = 180 =c^2

Square root of 180 is approx 13.42.

To the nearest 10th = 13.4

Answer:

Step-by-step explanation:

a. (I) x = 65

(ii) vertically opposite angles are equal.

b. (i) 71 degrees

(ii) alternate interior angles are equal

c. (i) z = 180 - 71 = 109 degrees

(ii) angles on a line add up to 180 degrees

Answer:

x = 65°, y = 71°, z = 44°

Step-by-step explanation:

x and 65 are vertical angles and congruent, thus

x = 65°

y and 71 are alternate angles and congruent, thus

y = 71°

The sum of the 3 angles in a triangle = 180°, thus

z = 180° - (65 + 71)° = 180° - 136° = 44°

Hence

x = 65°, y = 71° and z = 44°

Answer:

8.3

Step-by-step explanation:

Use the pythagorean theorem: a2 + b2 = c2 a2 would be 24.1 and c2 would be 25.5. square them then subtract a2 from b2. then find the square root of your answer which is 8.3

To solve the given differential equation by separation of variables, we'll rearrange the equation and integrate both sides.

Starting with the given differential equation:

dy - (y - 2)^2 dx = 0

Rearranging the terms:

dy = (y - 2)^2 dx

Now, we can separate the variables:

dy / (y - 2)^2 = dx

Integrating both sides:

∫ dy / (y - 2)^2 = ∫ dx

Let's evaluate the integrals separately.

For the left-hand side:

∫ dy / (y - 2)^2

Using a substitution, let u = y - 2. Then, du = dy.

The integral becomes:

∫ du / u^2

Integrating, we have:

-1 / u = -1 / (y - 2)

Now, for the right-hand side:

∫ dx = x + C

Combining the results:

-1 / (y - 2) = x + C

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For the function g(x) we have:

The function g(x) is given by applying transformations to f(x), the transformations are:

The function is:

\(g(x) = -(x + 2)^2 + 5\)

The graph is the one you can see below:

There you can see that the vertex is at (-2, 5), then the line of symmetry is:

x = -2.

And we have a maximum at the vertex, which is y = 5.

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he Solution:

iven:

The y-intercept of function 1 is:

The y-intercept of function 2 is:

(a) So, the farthest y-intercept from 0 is function 1.

he slope of function 1 is

The slope of function 2 is

he solope of function 3 is -1

The slope of function 4 is 5

(b) hus, the steepest graph is the function with the highest slope.

So, the steepest graph is the graph of function 4 since it has the greatest slope.

(c)

Functions with y-intercept greater than -3 are:

unction 1, function 2, amnd function 4.

Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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The surface area generated when the curve y = 6x + 5, for 0 ≤ x ≤ 4, is revolved about the x-axis is (656π/3) square units.

To find the surface area generated when the curve is revolved about the x-axis, we can use the formula for surface area of revolution. Let's break down the solution step by step:

Step 1: Determine the equation of the curve

The given curve is y = 6x + 5.

Step 2: Determine the limits of integration

The curve is revolved about the x-axis, and the limits of integration are given as 0 ≤ x ≤ 4.

Step 3: Set up the integral for surface area

The formula for surface area of revolution when revolving a curve y = f(x) about the x-axis over the interval [a, b] is:

Surface Area = ∫[a,b] 2πy√(1 + (dy/dx)^2) dx

In this case, y = 6x + 5, so we have:

Surface Area = ∫[0,4] 2π(6x + 5)√(1 + (6)^2) dx

Simplifying:

Surface Area = ∫[0,4] 2π(6x + 5)√(1 + 36) dx

Surface Area = 2π∫[0,4] (6x + 5)√37 dx

Surface Area = 2π∫[0,4] (6x√37 + 5√37) dx

Surface Area = 2π(√37)∫[0,4] (6x + 5) dx

Step 4: Evaluate the integral

Integrating (6x + 5) with respect to x over the interval [0,4]:

Surface Area = 2π(√37) [3x^2/2 + 5x] |[0,4]

Surface Area = 2π(√37) [3(4^2)/2 + 5(4) - 0]

Simplifying:

Surface Area = 2π(√37) [24 + 20]

Surface Area = 2π(√37) [44]

Surface Area = 88π(√37)

Therefore, the surface area generated when the curve y = 6x + 5, for 0 ≤ x ≤ 4, is revolved about the x-axis is (656π/3) square units.


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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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The required question based on number of posters is y = 109.95 + 65x.

The cost of additional posters = 65x, based on the mentioned information.The 100 posters make 1 set. Assuming the total number of posters be x. So, the additional sets will be calculated by the formula = (x - 100)/100.

Now, the equation will be the sum of the cost of first 100 posters and the cost of remaining posters.

y = 109.95 + 65x

Thus, the equation with the total cost (in dollars) as a function of the number (in hundreds) of posters ordered is y = 109.95 + 65x.

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Answer:

59

Step-by-step explanation:

(2x-1)+(3x+1)+x=180

6x=180

x=30

((2×30)-1)= 59

The mean of distribution will be 60, standard deviation will be 5 and variance will be 24

Given,

The total number of students (n)= 100

The probability of students, completing their homework on time (p)= 60%

= 60 / 100

= 0.6

According to the binomial distribution,

mean = np

= 100 × 0.6

= 60.

Variance = np× (1 - p)

= 100 × 0.6 × 0.4

= 24

Standard deviation = \(\sqrt{variance}\)

= \(\sqrt{24}\)

= 4.89 or 5

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The slope of the tangent to the curve is -5/14.

Apply implicit differentiation and the product rule to the curve:

\(3y^{2} \frac{dy}{dx} x + y^{3} + 2y\frac{dy}{dx} x^{2} + y^{2}2x = 0\)

Do some rewriting

\(3xy^{2}\frac{dy}{dx} + 2x^{2}y\frac{dy}{dx} + y^{3} + 2xy^{2} = 0\)

Factor and move terms without a  \(\frac{dy}{dx}\)  factor to the right side

\(\frac{dy}{dx}(3xy^{2}+2x^{2}y) = -y^{3} - 2xy^{2}\)

Now divide both sides by  \(3xy^{2}+2x^{2}y\)  and factor where you can

\(\frac{dy}{dx} = \frac{-y^{2}(y+2x)}{yx(3y+2x)}\)

\(\frac{dy}{dx} = \frac{-y(y+2x)}{x(3y+2x)}\)

Now evaluate the given point \((2,1)\)

\(\frac{dy}{dx} = \frac{-1(1 + 2(2))}{2(3(1) + 2(2))} = \frac{-1(5)}{2(7)} = \frac{-5}{14}\)

Therefore, the slope of the tangent to the curve is -5/14.

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Answer:

The first option

Step-by-step explaination:

\(9 {xy}^{3} - 4 {y}^{4} - 10 {x}^{2} {y}^{2} + {x}^{3} y + {3x}^{4} + {2x}^{2} {y}^{2} - 9 {y}^{4} \)

\( (- 4 {y}^{4} - 9 {y}^{4} ) + ( - 10 {x}^{2} {y}^{2} + {2x}^{2} {y}^{2}) + 9 {xy}^{3}+ {x}^{3} y + {3x}^{4} \)

\( - 13 {y}^{4} - 8 {x}^{2} {y}^{2} + 9 {xy}^{3} + x {}^{3} y + 3x {}^{4} \)

\( - 13 {y}^{4} + {3x}^{4} - 8 {x}^{2} {y}^{2} + {x}^{3} y + {9xy}^{3} \)

Answer:

Option A. (–13y4 + 3x4 – 8x2y2 + x3y + 9xy3)

Step-by-step explanation:

its correct

Answer:

(3,-9)

Step-by-step explanation:

Xm = (-3+9)/2 = 6/2 = 3

Ym = (-3+(-15)/2 = (-3-15)/2 = -18/2 = -9

Answer:

y = 4x - 3

Step-by-step explanation:

I'm not very sure if this is correct but I used the slope and the y intercept to create a linear equation in slope intercept form.

Answer:

y= 7/2x -3

Step-by-step explanation:

line goes the graph at -3

so b = -3

formula is y = mx + b

ponts on the line are

(2,4

and

(0, -3)

formula

y2-y1/x2-x1

to get the X value or slope

-7/-2 or 7/2

so formula is

y = 7/2x -3

Answer

\(\sqrt[6]{2}\)

Step-by-step explanation:

\(\sqrt{2} = \sqrt[6]{8}\)

\(\sqrt[3]{2} = \sqrt[6]{4}\)

Answer:

$700

Step-by-step explanation:

Store bought computer for $500.

Suggested retail price is 500x.

Store sold it for 0.8(500x).

Store sold it for 1.12(500).

0.8(500x) = 1.12(500)

0.8x = 560

x = 560/8

x = 1.4

Suggested retail price is 500x = 500(1.4) = 700

Answer: $700