Given that ,On May 7,1992, the space shuttle Endeavour was launched on mission STS-49, the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The table gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters.We need to use a graphing calculator or computer to model these data by a third-degree polynomial.

Answer:

D

Step-by-step explanation:

because

( 5 + 2 + 1 ) is (x + y + z)

y = -2/3x + 4 is an equation in slope-intercept form that could be the second equation in the system.

simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given, The solution of a system of equations is (3,2). One of the solutions in the system is 2x + 3y = 12.

From the general formula of Slope intercept form:

y = mx + c

where,

m = slope

c = y-intercept of the equation

Thus in our case,

2x + 3y = 12

=> 3y = -2x + 12

=> y = -2/3x + 4

thus, the Slope of the line = -2/3

and another coordinate (0, 4)

Therefore,  an equation in slope-intercept form that could be the second equation in the system is y = -2/3x + 4.

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Answer:m=-5/4

Step-by-step explanation: The formula for finding slope is y1-y2 / x1-x2 so when plugging in these coordinates, you get -3-(-8)/-6-(-2). When simplified -3-(-8) is 5 and -6-(-2) is -4, so the answer is -5/4. You can also switch the numbers so its -8-(-3) / -2-(-6) and still get the same answer.

Step-by-step explanation:

that's so easy just learn it times

The smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.

The smallest amount of rotation about a vertex from one ray to the other can be calculated using the formula θ = 180° - (α + β), where θ is the measure of the angle of rotation, α and β are the measures of the two rays that are connected by the vertex. The amount of rotation between two rays is measured in degrees, which is equal to the angle between the two rays. The formula used to calculate the amount of rotation is the arctangent of the ratio of the difference in the y-coordinates to the difference in the x-coordinates. For example, if the two rays have measures of 90° and 30°, the smallest amount of rotation from one ray to the other would be 60°. This can be calculated by taking 180° - (90° + 30°) = 180° - 120° = 60°. In conclusion, the smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.

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The change in dollars at the end of the week is - $5

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

Amount spent = $45

Amount gained = $55

Amount spent on gas = $15

The change is then calculated as

Change = Amount gained - Amount spent - Amount spent on gas

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

Change = 55 - 45 - 15

Evaluate

Change = -5

Hence, the change is a deficit of $5

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the set of all z ∈ (-3,1) such that neither 2+z nor 2-3z is in the interval (-1,2].

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities.

the set of all z such that neither 2+z nor 2-3z is in the interval (-1,2].

here, we shall assume two cases,

case first.

z > -1,

2+z > -1

z > -1 -2

z > -3

and,

2-3z > -1

-3z > -3

z > 1

z belongs to ( -3 , 1)

case 2nd,

z<=2

2+z < = 2

z <= 2-2

z ≤ 0

and 2-3z ≤ 2

-3z ≤ 0

z ≤ 0

z is less than equal to 0

So, by above conditions

z belongs to (-3,1).

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The TRUE statements about the inequality y ≤ 150x - 3100 are:

Inequality refers to a mathematical statement claiming the inequality of two or more mathematical expressions.

The following types and inequality symbols represent inequalities:

Check:

Ordered pairs (40, 2900)

y ≤ 150x - 3100

y ≤ 150(40) - 3100

y ≤ 6,000 - 3100

y ≤ 2900

Thus, the true statements about this inequality are Options A and E.

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The maximum area of a triangle with a base and height of 10 cm is 50 cm^2. The dimensions for this would be a base of 5 cm and a height of 5 cm.

1. The area of a triangle is calculated by taking the base multiplied by the height, then dividing by 2.

2. Since the sum of the base and the height of the triangle is 10 cm, the base and the height must be equal.

3. Therefore, the base and the height are both 5 cm, and the area of the triangle is (5 cm * 5 cm) / 2, which equals to 50 cm^2.

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The third side is represented by the inequality 7 < x < 43, where x is the third side.

When you know two sides of a triangle, you can calculate the range for the third side.

Let x would be the third side.

First, since 25 - 18 = 7, the third leg must be greater than 13. Otherwise, the two smaller legs would not be able to connect to form the third leg.

Second, if we combine 18 with 25 and get 63, the third leg must be smaller than 69. Otherwise, the third leg would be able to reach further than the previous two legs.

This means 7 < x < 43.

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Answer:

52°

Step-by-step explanation:

The angle of depression is 90 - angle of elevation

So angle of depression = 90 - 38 = 52°

Answer:

Length of each side = 3.055

Step-by-step explanation:

The relationship between altitude h and side a of an equilateral triangle is

[tex]h = \dfrac{\sqrt{3} }{2} a\\\\\\\rightarrow a = \dfrac{ 2h}{{\sqrt{3} }}\\\\[/tex]

Given h = √7.

we get

[tex]a = \dfrac{2\sqrt{7} }{\sqrt{3} }\\\\a = 2 \sqrt{\dfrac{7}{3}}\\\\a = 2\times 1.5275\\\\a = 3.055\\\\[/tex]

The number of beads used for Michelle necklace is 70.

Michelle made a bead necklace that was 13 inches long.  The length of the necklace, in inches, is equal to 3 added to one-seventh the number of beads, b.

The number of beads Michelle used for her necklace can be calculated as follows:

number of beads she used for her necklace  = b

Therefore,

13 = 3 + 1 / 7 b

13 - 3 = 1 / 7 b

10 = 1 / 7 b

cross multiply

b = 10 × 7

b = 70

Therefore,

number of beads she used for her necklace  = 70

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The required total income generated by planting corn in 2008 is the amount of $1917.85.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The yield of corn on Mr. Geller's farm since 2001 can be modeled by the function N(t) = 10t + 88.5

Let's find the amount of corn produced in 2008:

N(7) = 10 x 7 + 88.5 = 158.5 (kilograms)

Next, let's find the price of corn in 2008:

P(7) = 81 - 10 x 7 + 1.1 = 12.1 ($/kilogram)

Finally, we can multiply the amount of corn by the price per kilogram to find the total income:

158.5 x 12.1 = 1917.85

Rounding to the nearest cent, the total income generated by planting corn in 2008 is $1917.85.

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Answer:

Step-by-step explanation:

we have a right triangle, therefore with an angle of 90° (red sign) and an angle of 40°, knowing that the sum of the interior angles of all triangles is 180° we remove the known angles from 180° and find the value of angle "?"

180 - 90 - 40 =

50°

The area of the figure/geometric shape U will be 15 yard^2.

What are geometric shapes in mathematics?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now

As the scale factor for similar shapes V and U is 5:1.

Then their area should also be in same ratio.

Given Area of V=75 square yard

Therefore,

                Area of U=75/5

                 Area of U =15 square yard

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In the given oblique triangle , the required value of c using cosine rule is given by c = 34.4.

As given in the question,

In the given oblique triangle ABC,

a = 12 feet

b = 30 feet

∠A = 20°

Let us consider in triangle side opposite to angle A, B, and C are a, b, and c respectively.

Using cosine rule we have,

a² = c² + b² - 2cbcos A

Substitute the values we get,

⇒ 12² = c² + 30² - 2(c )(30) cos 20°

⇒ 144 = c² + 900 - 60c ( 0.9396)

⇒ c² -56.376c + 900 - 144 = 0

⇒ c² -56.376c +756 = 0

using quadratic formula :

c = [ ( 56.376) ± √56.376² -4(1)(756) ]/ 2

  =  [ 56.376 ± 12.42 ] / 2

  =  (56.38 + 12.42) / 2 or (56.38 - 12.42) / 2

  = 34.4 or 21.98

Correct value is c = 34.4

Therefore, using the cosine rule the required values c of the triangle is equal to 34.4 .

The above question is incomplete, the complete question is :

One of the cases for the known measures of an oblique triangle is given. In triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. State whether the Law of Cosines can be used to solve the third side of the triangle .

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Due to weaker aggregate demand, the negative demand shock will cause the aggregate demand curve to move to the left.

Result: A lower output and price level.

Part B:

Explanation of part B

Result of negative supply shock , aggregate demand falls cause the lower demand for the money . This will lead towards the left shift in money demand.(MD 1 TO MD 2(R1 TO R2)

Part c:

Interest rate and bond price are related inversely . Due to negative demand shock the interest rate falls down. vice-versa bond price will rise.

Part D:

Due to fall in the interest rate central banks will follow contractionary fiscal policy which will increase interest rate and reduce the money supply.

Part E :

If the central banks need to increase the money supply by $80 billion. Central banks need to buy securities in exchange of cash .This will Raise the money supply.

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Using the formula for the average value between two numbers, we will see that bag B weighs 11.9 kg

If we have two values x and y, the average value between these two is given by the formula below.

average = (x + y)/2

Here we know that the average between the wheights of bags A and B is 6.4 kg, and A = 0.9kg

Then we can write the equation:

6.4kg = (B + 0.9kg)/2

We can solve that equation for B to get:

2*6.4kg = B + 0.9kg

12.8kg - 0.9kg = B

11.9kg = B

Bag B weighs 11.9 kilograms.

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The most appropriate time-series plot will depend on the data being visualized. The title, axes labels, and scale should all be chosen to accurately describe the data and provide the clearest understanding of the data.

The most appropriate time-series plot for a particular dataset will depend on the data being visualized. The title, axes labels, and scale should all be chosen carefully to accurately describe the data and provide the clearest understanding of the data. For example, for a time series of stock prices, the title could be "Stock Price Over Time", the axes could be labeled "Time" and "Price", and the scale could range from the lowest to the highest stock price. Additionally, the time intervals should be appropriately labeled, such as monthly, quarterly, or annually. It is important to choose the right type of plot to ensure that the data is accurately and clearly represented.

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The complete question is

which of the following time-series plots is the most appropriate? hint: pay close attention to the title, axes labels, and scale should all be chosen to accurately.

The correct option is C for the frequency table.

A table that depicts the frequency of occurrence of a given characteristic according to a specified set of class intervals.

The correct two-way frequency table for the date will look like this:

                                               RAP      ROCK     COUNTRY     TOTAL

Grades 9-10             40           30            55                  125

Grades 11-12            60           25            35                  120

TOTAL                    100          55            90                  245

The sum of the row total is equal to the sum of the column total

125 + 120 = 100 + 55 + 90

245 = 245

The correct option for the frequency table is C.

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The equation of cost of each ticket is 11k = 231 and the exact cost of each ticket is $21.

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

Given,

Kathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same.

So we have to find the cost of each ticket. Write an equation to show your work and the exact cost of each ticket. Compare your answer to your estimate to check for reasonableness.

From the given information ,

The equation to show the work could be ,

231 = k * 11

SO, this is the equation 11k = 231 .

we can say that,

= $231 / 11

= $21

Hence, the equation of  cost of each ticket is 11k = 231 and the exact cost of each ticket is $21

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The Institute of Medicine compared the United States to comparable high-income countries in terms of  various health outcomes.

The findings revealed that the United States had lower rates of birth outcomes than other countries (including infant and maternal mortality). The US also  life expectancy than most other countries, as well as more years lost to alcohol and drug use. Lastly, the US had lower rates of adolescent pregnancy than most other countries.

The Institute of Medicine also calculated the health gap between the US and other countries, which was defined as the difference between the health outcomes of the US and the health outcomes of the other countries. This gap was calculated by subtracting the US health outcome rate from the average of the other countries' health outcome rates. For example, to calculate the infant mortality gap, the infant mortality rate in the US (5.8 deaths per 1,000 live births in 2018) was subtracted from the average infant mortality rate of the other countries (3.5 deaths per 1,000 live births). This resulted in a health gap of 2.3 deaths per 1,000 live births.

Overall, the Institute of Medicine's comparison revealed that the US was lagging behind other countries in terms of various health outcomes.

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Answer:

63

Step-by-step explanation:

the value of the difference between the terms increases by 4 as the series continues.

basically, this shows that the difference between 3 and 12 is 9, the difference between 12 and 25 is 13 (which is 4 more than 9), the difference between 25 and 42 is 17 (which is 4 more than 12), and so on.

using this pattern, all we have to do is find the next difference- the one between 42 and the missing term.

to do this, we take the previous difference, 17, and add 4. this gives us 21.

we then add 21 to 42 to get the next term: 63.

hope this helped, good luck!

Answer:

= -10g - 5 + 7h

Step-by-step explanation:

= -7g +3 - 8 - 3g + 7h

Grouping of like terms

= -7g -3g + 3 - 8 +7h

= -10g - 5 + 7h.

The rate at which shadow is decreasing On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft building on level ground is 60 ft long and is 10.4 inches per minute.

Given,

Height of the building, [tex]h[/tex] = 80 ft = 960 inches

Length of shadow, [tex]x[/tex] = 60 ft = 720 inches

The angle that the sun makes with the ground is increasing,

[tex]\frac{d\theta}{dt} = 0.27[/tex] degree [tex]= \frac{3\pi }{2000} rad/min[/tex]

[tex]tan\theta = \frac{960}{x} \\\frac{d }{dy} tan\theta = \frac{d}{dy} \frac{960}{x} \\sec^{2}\theta \frac{d\theta }{dt} = -\frac{960}{x^{2} } \\\\\frac{dx}{dt} = \frac{(60^{2})(\frac{5}{3})^{2} }{960} \\\\\\\frac{dx}{dt} = 10.4 inches /min[/tex]

Hence, the shadow is decreasing at a rate of 10.4 inches per minute.

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the value of theta in the given complex expression is equal to 16°.

Given, a number. [tex]rcis\theta, is[/tex] expressed by.

cis75° + cis83° + cis91°+.... + cis147°.

we have to find the value of angle in degrees.

The function cisA is a shorthand way of writing the equivalent expression cisA=cosA+i sinA

By definition: CisA=CosA+iSinA

This form simplifies complex arithmetic and allows for the study of complex analysis, as well as reduces the workload in writing the expressions.

now, we have to find the sum of the given expressions.

[tex]cis75+cis83+cis91+...+cis147 as, cis\theta=e^{i\theta}[/tex]

[tex]e^{75i}+e^{83i}+e^{91}+....+e^{147i}\\\\e^{\frac{75\pi}{180} }+e^{\frac{83\pi}{180} }+.....+e^{\frac{147\pi}{180} }[/tex]

on using geometric sum of the series we get,

[tex]Sum=\frac{e^{\frac{75i\pi}{180}}(1-e^{\frac{72i\pi}{180} ) }}{(1-e^{\frac{8i\pi}{180} })}\\ \\\theta=16[/tex]

the value of theta of the angle be 16 degree.

the complete question is.

The number cis 75 + cis 83 + cis91 +...+ cis 147 is expressed in the form r cis(theta), where 0 <= theta < 360.

Find theta in degrees.

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The actual length of the tree based on the information is 19 inches.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches.

The actual length will be:

= 4.75 × 4

= 19 inches

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Complete question

Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches. What is the actual length of the tree?

The dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).

What is a rectangular prism?

A rectangular prism is a solid geometric shape that has three mutually perpendicular rectangular faces, and is also known as a rectangular parallelepiped or a box. It has six faces, eight vertices, and twelve edges.

The shape is defined by three dimensions: length, width and height, and is specified by the three sets of parallel and mutually perpendicular edges that form its six faces. The opposite faces of a rectangular prism are equal in area and parallel to each other. The opposite edges are also parallel and equal in length.

You can’t get a perfect match, but you can get pretty close, with dimensions of (1,8,9), (2,5,7), (3,4,6)

Hence, the dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).

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