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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 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:

x + 2  (Choice D)

Step-by-step explanation:

The two polynomials are
P1 = 4x² + 5x - 4  

and

P2 = 4x² + 4x - 2

P1 - P2

==>  (4x² + 5x - 4 ) -  (4x² + 4x - 2)

Expanding brackets we get

==> 4x² + 5x - 4 - 4x² - 4x + 2        (signs inside the second parentheses are    

                                                 reversed because of the - sign preceding it)

Group similar terms and add the coefficients

==> (4x² - 4x²) +(5x - 4x) +(-4 + 2)

==> 0 + x + 2

==> x + 2  (Choice D)

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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Answer:

19(42 + 58)

Step-by-step explanation:

19(100)

1900

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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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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Answer:

52°

Step-by-step explanation:

The angle of depression is 90 - angle of elevation

So angle of depression = 90 - 38 = 52°

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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The level curves of the function h(x,y) = 2x-y at c = 0, -2, 2 are y = 2x, y = 2x + 2, y = 2x - 2 respectively.

A level curve (also called a contour line or an isocline) of a function is a curve that represents all the points where the function has a constant value. To find the level curve of a function at a given value of c, we need to set the function equal to c and solve for the variables.

For h(x,y) = 2x-y, we can find the level curves at c = 0, -2, 2 by setting the function equal to c and solving for x and y:

The level curves of h(x,y) = 2x-y at c = 0, -2, 2 are the lines y = 2x, y = 2x + 2, y = 2x - 2 respectively. Each line represents a different value of c and separates the domain of x and y into different regions where the function takes on that constant value.

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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 least certain measurement determines the certainty of the answer.

What guidelines apply when rounding sig figs?

(1) The final digit that is preserved is raised by one if the digit to be eliminated is greater than 5. As an illustration, 12.6 is rounded to 13.

                                      (2) The last digit that remains is left alone if the digit to be dropped is less than 5. As an illustration, 12.4 is rounded to 12.

Which of the following statements best describes the significant figures rule?

Use the following 3 principles to calculate how many significant figures are present in a number: The significance of non-zero digits is constant.

                                   A significant zero is one that comes in between two significant digits. ONLY the decimal part has any significance when there is a final zero or trailing zeros.

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Answer:

D

Step-by-step explanation:

because

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

Answer:7

Step-by-step explanation:

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.

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: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.

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?

Answer:

h = 18 in.

Step-by-step explanation:

Both safes are in the shape of a rectangular prism

The volume of a rectangular prism = L X w X H

where L = length, W = width and H = height

Safe A has volume 18 x 15 x 24

Safe B has volume 20 x 18 x h

Both volumes are equal and we have to find h

Equating both expressions

20 x 18 x h = 18 x 15 x 24

Dividing by 18 on both sides will get rid of the 18 in the product

(20 x 18 x h)/18 = (18 x 15 x 24)/18

20h = 15 x 24

20h = 360

h = 360/20

h = 18 in.

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°

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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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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9 students preferred learning only through videos.

Inclusion-exclusion is a principle used in counting to find the total number of elements in a union of sets by subtracting the elements that are counted multiple times and adding back in the elements that are not counted at all.

The number of students who preferred learning only through videos is 17.

This can be found by using the principle of inclusion-exclusion:

35 students liked to learn through videos

14 students liked to learn through listening and videos

5 students liked all three channels

So, 35 - 14 + 5 = 26 students liked to learn through videos and listening

Therefore, 35 - 26 = 9 students preferred learning only through videos.

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Population Mean is the statistical indicator to its designation or nomenclature.

Therefore,

The formula for the population mean, which is the population's average score on a certain variable, is:  μ = ( Σ Xi ) / N. The population mean is represented by the symbol "."

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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 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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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:

= -10g - 5 + 7h

Step-by-step explanation:

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

Grouping of like terms

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

= -10g - 5 + 7h.