Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's. If there is no visible coefficient, then enter for the coefficient. If a specific variable is not present in the equation, then enter for the coefficient. Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165. Total amount invested: + + = Total amount earned from investements: + + = Relation of bonds and CDs: + + =

The lateral surface area of the cylinder is 51.22 cm2.
What is surface area?
Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.

The cylinder shown below has a diameter of 5.2 cm on the base and a height of 7.1 cm. The diameter of the base is referred to as 'd' and the height of the cylinder is referred to as 'h'. The lateral surface area of the cylinder can be found by using the formula LSA = 2πrh, where 'r' is the radius of the base. The radius of the base of this cylinder is half of the diameter, or 2.6 cm. Therefore, the lateral surface area of the cylinder is: 2π x 2.6 x 7.1 = 51.22 cm2.

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The total cost of 6 apples and 3 oranges is $6 + $6 = $12.

The total cost of 4 apples and 4 oranges is $4 + $8 = $12.

The total cost of 5 apples and 4 oranges is $5 + $8 = $13.

The total cost of 8 apples and 2 oranges is $8 + $4 = $12.

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The length of PT is 3 units. The solution has been obtained using the concept of transformation.

What is transformation?

A transformation is an operation that moves a polygon or other two-dimensional object on a plane or coordinate system.

The term "pre-image" or "inverse image" refers to the shape in two dimensions prior to any modification. The image is the shape after transformation.

Transformation can be done by translation, rotation, reflection and dilation.

We are given two rectangles ABCD and PRQT

AB = DC = 3 units

AD = BC = 10 units

It can be observed that the rectangles PRQT and ABCD are same but PRQT is rotated.

Since, they are same so,

AB = PT = 3 units

Hence, the length of PT is 3 units.

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Answer:

0.07

Step-by-step explanation:

[tex]0.0007*100=0.07[/tex]

Basically, you move the 7 two places to the left since 100 has 2 zeroes.

All of the angles in an acute triangle are less than 90 degrees. Triangles are referred to as right triangles when one of their angles is 90 degrees.

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles. With three sides and three vertices, triangles are a particular kind of polygon in geometry.

It has three straight sides and is a two-dimensional figure. As a 3-sided polygon, a triangle is included. Three triangle angles added together equal 180 degrees. In one plane, the triangle is contained. When three straight lines cross, a triangle is the result. There are always three sides and three corners to a triangle (angles). A triangle's vertex is the location at which two of its sides meet.

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The values of x from the given figures are 3 √29 and 24 respectively.

What is triangle ?

Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.

Given

In the figure,

The two given triangles are similar ,

So, in the first figure it is given that they are similar ,

√29 / 5  = x / 15

x  = √29 * 15  / 5

x =√29 * 3

x = 3 √29

And in the second figure , here also they gave they are similar

so we get,

12 / 13  =  x /  26

x = 12 * 26 / 13

x = 12 * 2

x = 24

Hence, The values of x from the given similar triangles are 3 √29 and 24 respectively.

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Answer:

To find the coordinates of Q, we can use the concept of proportional division of line segments.

Given that MQ:ON = 2:3, it means that the ratio of the length of MQ to ON is 2:3.

Let's first find the vector that represents the direction of MN, which is the vector pointing from M to N. We can find this by subtracting the coordinates of M from the coordinates of N:

(8,10) - (-12,-5) = (20, 15)

This is the vector <20,15>

Now, we can find the point Q, which is located two thirds of the way from M to N, by multiplying the vector <20,15> by 2/5 and adding the result to the coordinates of M:

Q = M + (2/5) * <20,15>

= (-12,-5) + (2/5) * <20,15>

= (-12,-5) + <8,6>

= (8,1)

So, the coordinates of Q are (8,1)

Answer:

Step-by-step explanation:

The image of the point (-1, 3) is (1, 1).

A translation is a transformation that moves every point in a figure the same distance in the same direction.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

Pint( -1, 3).

Translating unit = 2 units down

According to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, move it to your new x-coordinate, and then take the opposite of the x-coordinate and set it as your new y-coordinate:

Extended Rotation Rules

270°-clockwise rotation [90°-counterclockwise rotation] = (x, y) → (-y, x)

270°-counterclockwise rotation [90°-clockwise rotation] =(x, y) → (y, -x)

and, 180°-rotation = (x, y) → (-x, -y)

Thus, the 270°-counterclockwise rotation [90°-clockwise rotation] will be

[-1, 1] moves to [1, 1].

Hence, the translation is (1, 1).

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The height of the new prism so that its surface area is doubled will be 26.31 cm.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

A right rectangular prism measures 12 cm tall, 3 cm long, and 10 cm wide. A manufacturer would like to double the surface area of this prism.

Then the height of the new prism so that its surface area is doubled will be given as,

2 x 2 x (12 x 3 + 3 x 10 + 10 x 12) = 2(3h + 3 x 10 + 10h)

2(36 + 30 + 120) = 13h + 30

372 = 13h + 30

13h = 342

h = 26.31 cm

The height of the new prism so that its surface area is doubled will be 26.31 cm.

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Macy had 3 appointments.

Logan had 5 appointments.

What is the quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, which is written in the form of "ax^2 + bx + c = 0", where x is the variable and a, b, and c are constants. The solutions to a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.

Part A:

Let x be the number of appointments Macy had.

We know that the total income (60x + 40) must equal 220.

Therefore, the equation representing the situation is:

60x + 40 = 220

To solve for x, we can subtract 40 from both sides:

60x = 180

Finally, we divide both sides by 60 to get:

x = 3

Macy had 3 appointments.

Part B:

Let y be the number of appointments Logan had.

We know that the total profit (70y + 50 - 20y) must equal 300.

Therefore, the equation representing the situation is:

50y + 50 = 300

To solve for y, we can subtract 50 from both sides:

50y = 250

Finally, we divide both sides by 50 to get:

y = 5

Logan had 5 appointments.

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True, free bilirubin is transported by the blood to the liver.

Macrophages begin the disposal of hemoglobin by separating the heme from the globin. They hydrolyze the globin into free amino acids, which can be used for energy-releasing catabolism or recycled for protein synthesis.

Bilirubin

Bilirubin is a red-orange compound that occurs in the normal catabolic pathway that breaks down heme in vertebrates. This catabolism is a necessary process in the body's clearance of waste products that arise from the destruction of aged or abnormal red blood cells.

Hemoglobin

Hemoglobin is a protein in your red blood cells that carries oxygen to your body's organs and tissues and transports carbon dioxide from your organs and tissues back to your lungs.

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As per the given parentage, the highest percentage saying the greens are too fast is females.

In math the term percentage is defined as the number or ratio that can be expressed as a fraction of 100.

Here we have know that the number male players are

Male Golfers                                    Greens Condition              

Handicap                               Too fast                        Fine

Under 15                                       10                             40

15 or more                                     25                           25

And the female players are,

Male Golfers                                     Greens Condition            

Handicap                               Too fast                         Fine

Under 15                                       1                                9

15 or more                                   39                              51

Then the total value of them is calculated as,

                      Too fast                   Fine             Total

Male                   35                          65               100

Female              40                           60               100

So, the group with the highest percentage of too fast is the females.

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The total percentage increase in the investor's stock account was of 4.55%.

The values of the stocks of Company A and Company B, after the increase are given, respectively, by:

Company A: 3300 x 1.04 = $3432.

Company B: 4140 x 1.05 = $4347.

The total values are given as follows:

Before the increase: 3300  + 4140 = 7440.

After the increase: 3432 + 4347 = 7779.

The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:

P = (7779 - 7440)/7440 x 100% = 4.55%.

The total percentage increase in the investor's stock account was of 4.55%.

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For the given function H(t) = -12cos( πt/45 ) + 18 the maximum height is  30 units.

Function to modeled the height 'H' of the Ferries wheel is given by:

H(t) = -12cos( πt/45 ) + 18

Where 't' represents the time in seconds.

For cosine trigonometric function,

-1 ≤ cosα ≤ 1

Here cos function lies between two values -1 and 1.

Substitute cos( πt/45 ) = 1 or -1

When cos( πt/45 ) = 1

H(t) = -12(1) + 18

⇒H(t) = 6 units

When cos( πt/45 ) = -1

H(t) = -12(-1) + 18

⇒H(t) = 30 units

Maximum height of a required cabin is equals to 30 units.

Therefore, the maximum height of given cabin represented by the function

H(t) = -12cos( πt/45 ) + 18 is equal to 30 units.

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The  value for n that would make the inequality true is 4.5

You should understand that a statement of an order relationship with greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is inequality.

The given inequality is ⁿ⁄₉ > ½

This implies that 2(n) > 1(9)

Opening the brackets to have

2n > 9

Making n the subject of the relation by dividing both sides by 2

2n/2 > 9/2

Therefore n = 4.5

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Answer:

1. yes

2. No

Step-by-step explanation:

1. The triangles are congruent

2. It's not matching

Assuming all the workers employed at the beanbag factory are of equal ability, the beanbag factory invest in more equipment to address the diminishing marginal returns it experiences after the hire of its third worker. So the option B is correct.

It is assumed that all of the factory's employed employees have the same level of skill. Additionally, it must follow that if they are working to their maximum ability, they will be able to accomplish the same amount of work as before.

Since the third man was hired, the quantity of work the three of them have completed has decreased, making it clear that he is to blame for the diminishing returns.

Therefore, it seems sense to fire the individual since he is either not performing to his full capacity or encouraging other employees to do the same.

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12.2 % of the area painted blue of the figure representing a square with attached triangle on one side with perpendicular height 4cm is equal to 4.27 cm² .

Figure having square attached with triangle on one side.

Side length of the square = 5 cm

Area of the square = ( side-length )²

                                = 5²

                                = 25 cm²

Triangle attached on one side of the square with height = 4cm

Area of the triangle = ( 1/2) × base × height

                                = ( 1/2) × 5 × 4

                                = 10 cm²

Total area of the figure = 25 + 10

                                      = 35 cm²

Percent of area painted blue = 12.2% of total area

                                               = ( 12.2 / 100 ) × 35

                                               = 4.27 cm²

Therefore, for the given figure made up of square and triangle area to be painted blue is equal to 4.27 cm².

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Answer:82 cm squared

Step-by-step explanation:

Just draw imaginary lines on the shape to turn it into a bunch of squares and rectangles, then find the area of those and add them together.

Kinda hard to explain since there are multiple ways to do it, but I hope that this still helps!

The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.

The radius of the arch is 9 feet.

The formula for calculating the radius of an arch is [tex]R = (width / 2) / sin(90°)[/tex].

Therefore, the radius of the arch is:

R = (18 ft / 2) / sin(90°) = 9 ft

To calculate the radius of the arch he needs to draw, the person can use the formula R = (width / 2) / sin(90°). In this case, the width of the arch is 18 feet, so the radius of the arch is 9 feet, calculated as R = (18 ft / 2) / sin(90°). The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.

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Answer:

Part A.) 153 Boxes

Part B.) 394 Boxes (395 if rounding up)

Step-by-step explanation:

The inequality used in this situation would be:

3.74x + 25 < 600

3.74 is the price of each box

x is the number of boxes

25 is that deposit

and < 600 is not making $600 in sales

What we need to do is get X alone. First we will subtract 25 from both sides since that's the opposite of +25.

Doing that will get you

3.74x = 575

Next step is to divide 3.74 on both sides since 3.74 is being multiplied by x and division is the opposite.

That will give you X = 153.74. We round down to stay under and we end up with 153.

For part B, we would do the same process, but instead of < 600, we would do >= 1500. Just typing the same steps out.

3.74x >= 1475 since we subtract 25 from both sides

x = 394.38 since we divide 3.74 on both sides. Rounding would get us 394

Answer:

The unit price for a coffee mug is $0.55.

Step-by-step explanation:

The unit price is simply just the price per unit.

We have a 4-pack of coffee mugs that costs $2.20.

He have 4 units and the price per 4 units.

Lets evaluate the price per 1 unit.

[tex]\frac{2.20}{4} =\frac{x}{1}[/tex]

Lets solve for [tex]x[/tex].

Divide [tex]x[/tex] by 1.

[tex]x=\frac{2.20}{4}[/tex]

Divide 2.20 by 4.

[tex]x=0.55[/tex]

The time to calculate her rate along the summit Rate = 1.5 mph

Rate = Distance / Time

To solve this problem, we will first need to calculate the time it took Jane to reach the peak. Since she rode 40 miles uphill, we can use the rate of 5 mph slower than when she reached the peak to calculate this time.

Time = Distance / Rate

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5)

Time = 8 hours

Since Jane spent 2 hours exploring the mountain, the total time it took her to reach the peak was 8 hours. We can now use this time to calculate her rate along the summit.

Rate = Distance / Time

Rate = 12 miles / 8 hours

Rate = 1.5 mph

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Answer:

Step-by-step explanation:

Step 1:

Make a proportion:

10/5 = 22/x

Step 2:

Cross multiply:

10x=22*5

10x=110

Step 3:

Divide by 10 to isolate x:

x=11

Step-by-step explanation:

I Don't even know what the answer is

The best statistical test to be used is multiple linear regression analysis.

Multiple linear regression is a statistical method that allows you to examine the relationship between two or more independent variables (in this case, level of education, gender, and annual income of the student's parents) and one dependent variable (annual income and student loan debt).

It will help you determine how much of the variation in the dependent variable is explained by the independent variables, and the strength and direction of the relationships between the variables.

In this case, this test will allow us to determine the impact of a student's level of education, gender, and the annual income of their parents on their annual income and student loan debt while accounting for the possible confounding effect of the annual income of their parents on these variables.

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Considering that the leading digit is never zero , then the number of 9 digit integers that can contain exactly 5 zeroes are 367416 numbers   .

the number of digits in the number is = 9 digits ;

the number should have exactly five zeroes  ,

the number of ways to pick five of the digit positions for the zeroes, since the first digit can’t be zero is  = ⁸C₅ ,

There are 9 possible digits for each of other 4 positions as  other positions are occupied by 0 ,

So, the total number of possibilities is = ⁸C₅ × 9⁹⁻⁵

Simplifying further ,

we have ,

= ⁸C₅ × 9⁴

= 56 × 6561

= 367416 numbers .

Therefore , there can be 367416 numbers of 9 digits having 5 zeros .

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Starch and protein levels are checked for In order to present the idea of chemical compound variety, it is necessary to test for the presence of starches and protein macromolecules.

Hypothesis: It is a negative result if the biuret reagent remains blue after a test for protein since the reagent itself is blue. The test for protein is positive if a solution is pinkish purple or purple. The starch test solution is a yellowish brown color. We utilized iodine to test for starch in some solutions if any ingredient produced a mixture that was yellowish brown in color. Polysaccharides, monosaccharides, and disaccharides are separated from starch by iodine. Iodine interacts with molecules, changing the color of the molecules, while starch is a coiled polymer of glucose.

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If the 3 times of total number of adults was 17 less than number of children who visited the petting zoo , then the equation to model this relationship is written as c = 3a + 17   ;

let the number of children in the petting zoo be = c ;

and the number of adults in the petting zoo is = a ;

given that the the number of children are 3 times the number of adults ;

that means ⇒ c = 3a ;

and also given that the difference between the number of children and number of adults is 17 .

This situation can be represented as :

⇒ c - 3a = 17 ;

⇒ c = 3a + 17 .

Therefore , the equation to model this relationship is "c = 3a + 17" .

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