$5,581 is invested, part at 15% and the rest at 6% . If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 6% by $261.54 , how much is invested at each rate? (Round to two decimal places if necessary.)

The value of "c" in this triangle is approximately 154.2 units long.

The given information is a side length of 61 and two angles, one of which is 142 degrees. To solve for the unknown side length "c", we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

Where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.

In this problem, we know the side length "a" is 61 and the angle opposite that side is 63 degrees. We also know the angle opposite the unknown side "c" is 142 degrees. Using the law of sines, we can write:

61/sin(63) = c/sin(142)

Now we can solve for "c" by multiplying both sides by sin(142) and then dividing by sin(63):

c = (61*sin(142))/sin(63)

Using a calculator, we find that c is approximately 154.2. Rounding to the nearest tenth, we get:

c ≈ 154.2 to the nearest tenth.

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Answer:

117.25

Step-by-step explanation:

Ik this is late but I need the answer for my test later so I’m answering here so I can find it. Also this was right on acellus.

The reason for which the graph is misleading is given as follows:

The x-axis only shows the data for one year.

The statement for this problem is given as follows:

"The yearly spending for the company has drastically decreased".

To state that the yearly spending has decreased, a comparison of the spending for multiple years must be made.

However, on the x-axis of the function, the time in years is shown for only one year, which is the reason why we can say that the graph is misleading.

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The bar graph that correctly displays the data from the list and the table is Graph D.

A bar chart, often known as a bar graph, is a diagram that displays categorical data as rectangular bars with heights or lengths proportional to the values they stand for.

You can plot the bars either vertically or horizontally.

Considering the data given:

The correct bar graph is D.

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Answer:  

552 students are going to the picnic

Using the law of detachment and the law of syllogism,

We can conclude that Sally is too heavy for the bridge, but we cannot conclude that she can cross the bridge.

We have,

Using the law of detachment, we can conclude from statements 1 and statement 3:

If something weighs more than 2,000 pounds, then it weighs more than Jill's car. (Statement 1)

Sally the elephant weighs 2,325 pounds. (Statement 3)

Therefore, Sally weighs more than Jill's car.

Using the law of syllogism, we can then use the conclusion above and statement 2 to conclude:

Sally weighs more than Jill's car.

If something weighs more than Jill's car, then it is too heavy for the bridge. (Statement 2)

Therefore, Sally is too heavy for the bridge.

Therefore,

We can conclude that Sally is too heavy for the bridge, but we cannot conclude that she can cross the bridge.

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The solution is, PV= $45,879.68.

Here, we have,

Explanation:

Giving the following information:

Cash flow= $4,000 annually

n= 20

i= 6% compunded annually

The maximum that an investor should pay is the present value (PV).

First, we need to calculate the future value using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

FV= {4,000*[(1.06^20) - 1]} / 0.06

FV= $147,142.36

Now, we can calculate the present value, we need to use the following formula:

PV= FV/(1+i)^n

PV= 147,142.36/(1.06^20)

PV= $45,879.68

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complete question:

Assuming you are a rational investor, the amount you should be willing to pay for a 20-year ordinary annuity that makes payments of $4,000 per year and you require a 6% rate of return per year is closest to:

The expressions that can be used to represent the above model are

A. The number of fourths in 1.

b. Number of fourths in three

To represent the model, we need to note the range of the figures and the number of bars in each of the specified ranges. For, 0 to 1, there are four boxes which indicate a distribution of four to 1. So, we can say that this expression is the number of fourths in 1.

Also, when we look at it on a wider level, we can say that the number of fourths in 3 is a good descriptor since there are 12 fours in the total range of 3.

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Answer:

KL=45

Step-by-step explanation:

The scale factor of the dilation is k = 5/4

Given data ,

A figure with an area of 25 square units is dilated from a figure with an area of 16 square units

Let the dilation scale factor be k

Now , Given that the original area (A) is 16 square units and the target area (B) is 25 square units, we can write the equation as:

B = k² A

k² = 25/16

Taking square roots on both sides , we get

k = 5/4

Hence , the dilation factor is 5/4

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As we have shown that both line segments PN and PM are equal to (1/2)MN, and hence they are equal in length to each other.

Given that point P lies on the perpendicular bisector l of line segment MN, we know that line segment PN and line segment PM are both equal in length to the distance between point P and the midpoint of MN, which we will call point O. This is because the perpendicular bisector of a line segment passes through the midpoint of the segment, and any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Let us call the length of line segment PM "x". Then, we can express the lengths of line segments PN and PO in terms of x as well. Since P is equidistant from the endpoints of MN, we know that line segment PN has the same length as line segment PO, which is half the length of MN. We can express this relationship mathematically as:

PN = PO = (1/2)MN

Similarly, we can express the length of line segment PM in terms of the length of PO, which is also equal to (1/2)MN. Since line segment PM is equal in length to the distance between point P and the midpoint of MN, we know that:

PM = PO = (1/2)MN

Therefore, we have proved that PM = PN.

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a. The distribution of X bar is  x bar - N(1022, 43.45²).

b. The distribution of x bar is x bar - N(1022, 43.45²).

c.  The probability that one randomly selected auto insurance is more than $990 is 0.1131.

d. a simple random sample of 39 auto insurance policies, the probability that the average cost is more than $990 is 0.887

a. The dispersion of X bar is ordinary with a cruel of 1022 dollars and a standard deviation of 272/√(39) dollars. In this way, X bar - N(1022, 43.45²).

b. The conveyance of x bar is additionally ordinary with the same cruel and standard deviation, so x bar - N(1022, 43.45²).

c. To discover the likelihood that one arbitrarily chosen auto protection is more than $990, able to utilize the z-score equation:

z = (990 - 1022) / 272/√(39) = -1.21. Looking up the comparing region beneath the standard typical dissemination bend, we discover a likelihood of 0.1131.

d. To discover the likelihood that the normally taken toll of a simple random test of 39 auto protections approaches is more than $990, we got to discover the z-score for this test cruel:

z = (990 - 1022) / 272/√(39) = -1.21. Employing a standard typical dispersion table, we discover that the likelihood of a z-score less than -1.21 is 0.1131. Hence, the likelihood of a test cruel more prominent than $990 is 1 - 0.1131 = 0.8869, or 0.887 (adjusted to 3 decimal places). 

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The measure of the arc angles CA and AD are 216° and 46° respectively, while the angle m∠C is equal to 36°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

Diameter BD bisects the angle m∠ABC and the triangles BQC and BQA are identical isosceles triangles so;

m∠QBC = 72/2 = 36°

m∠BQC = 180 - 2(36)°

m∠BQC = 108, also m∠AQB = 108° so;

arc angle CA = 2(108)° = 216°

arc angle CD = arc angle AD so;

arc angle AD = 46°

angles m∠QBC and m∠BCQ are base angles of an isosceles and they are equal so;

m∠C = 36°

Therefore, the measure of the arc angles CA and AD are 216° and 46° respectively, while the angle m∠C is equal to 36°.

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Answer:

Step-by-step explanation:

A=1/2 a p                 a is apothem;  p is perimeter of base

p=22*5 =110

a you need to find by making a triangle with the radius and finding the angle of the right triangle

All external angles of any polygon =360

divide by 5 and then 2 to find triangle

=54

Use tan 54 = a/11

a=15.14

A= 1/2 *15.14 *54

408.8

Answer:

Set your calculator to degree mode.

Using the Law of Cosines:

37^2 = 23^2 + 20^2 - 2(23)(20)(sin C)

1,369 = 929 - 920sin(C)

440 = -920sin(C)

sin(C) = -11/23

C = sin^-1 (-11/23) = 151.4°

To write 8gk³-20g²k²+4g⁴f in standard form, we need to arrange the terms in decreasing order of their exponents.

So we start with the highest degree term:

4g⁴f

Then the next highest degree term:

-20g²k²

And finally, the lowest degree term:

8gk³

Putting it all together, we have:

4g⁴f - 20g²k² + 8gk³

This is the standard form of the expression.

The value of 2x+y when X =4al and y = 3​ is 8al + 3

to find the value of of 2x+y

If X = 4al and y = 3, then:

2x + y = 2(4al) + 3

Simplifying the expression:

2x + y = 8al + 3

Therefore, the value of 2x+y is 8al+3.

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The length of VX is approximately 9.4 yd.

The area of the triangle is approximately 56.4 yd².

The area of triangle = 1/2 * base * height.

To find the area of the triangle, we have to determine its height which is the length of VX.

Apply the sine ratio to find the length of VX:

sin 70 = opposite/hypotenuse

sin 70 = VX/10

10 * sin 70 = VX

VX ≈ 9.4 yd.

The area of triangle = 1/2 * base * height = 1/2 * 12 * 9.4

= 56.4 square yards

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Answer:

800 grams flour ÷ 5 grams flour/biscuit = 160 biscuits

160 biscuits × 3 grams butter/biscuit = 480 grams butter

160 biscuits × 2 grams sugar/biscuit = 320 grams sugar

Katie needs 320 grams sugar.

Kate needs 270g of sugar to make the maximum number of biscuits possible.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Now, Based on the ratio of flour, butter, and sugar of 5:3:2, we can determine that Kate needs;

⇒ 800g + 550g

= 1350g of the mixture.

Hence, For find out the amount of sugar needed, we need to determine the proportion of sugar in the mixture.

We can do this by adding up the ratio numbers;

(5+3+2) = 10.

Then we can divide each ratio number by the total (10) to get the proportion of each ingredient.

So the proportion of sugar in the mixture is 2/10. To find out how much sugar Kate needs, we can set up a proportion:

2/10 = x/1350

We can solve for x by cross-multiplying:

2 × 1350 = 10x

2700 = 10x
x = 270

Therefore, Kate needs 270g of sugar to make the maximum number of biscuits possible.

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Answer:

The answer to your problem is, [tex]ft^3[/tex]

Step-by-step explanation:

In the problem we will use the area formula:

l × w × h

Multiply:

16.5 × 12 × 5 = 990

We look at the options:

990 [tex]ft^3[/tex] is in Option D.

Thus the answer to your problem is, 990 [tex]ft^3[/tex]

Answer:

the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

Step-by-step explanation:

The probability of selecting a quarter or a nickel can be found by adding the probability of selecting a quarter to the probability of selecting a nickel. Since the coins are chosen randomly, the probability of selecting a coin from the jar is the number of coins of that type divided by the total number of coins in the jar.

So, the probability of selecting a quarter is:

P(quarter) = number of quarters / total number of coins

P(quarter) = 80 / (70 + 100 + 80 + 50)

P(quarter) = 0.32

Similarly, the probability of selecting a nickel is:

P(nickel) = number of nickels / total number of coins

P(nickel) = 70 / (70 + 100 + 80 + 50)

P(nickel) = 0.175

To find the probability of selecting a quarter or a nickel, we add these probabilities:

P(quarter or nickel) = P(quarter) + P(nickel)

P(quarter or nickel) = 0.32 + 0.175

P(quarter or nickel) = 0.495

Therefore, the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

The proportion of the tapestries' height to width is 3:2, which means the height is 1.5 times the width.

To find the proportion of the tapestries' height to width using whole numbers and ratio notation, we need to divide the height of the tapestry by its width.

The height of the tapestry is 1.5 meters, and the width is 1 meter. Therefore, the proportion of the tapestry's height to width is

1.5 meters / 1 meter = 1.5 : 1

We can simplify this ratio by dividing both sides by 1, which gives

1.5 : 1 = 3/2 : 1

Therefore, the proportion of the tapestry's height to width using whole numbers and ratio notation is 3:2.

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The value of the arithmetic operation; 0.79 × 12 as required in the task content is; 9.48.

The value of the arithmetic operation; 12.45 × 11 as required in the task content is; 136.95

It follows from the task content that the value of the given arithmetic expressions are to be determined.

By the use of a mathematical calculator; we have that;

0.79 × 12 = 9.48

Also; 12.45 × 11 = 136.95.

Ultimately, the result of the evaluations as required are such that;

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Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

Option C is the correct answer.

We have,

Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

This will give us a single equation in y, which we can then solve for y, and use to find the value of x.

In this case, we can eliminate the x term by adding the equations.

3x + 2y = 4

-3x + y = 2

If we add the two equations, the x term will cancel out:

3x + 2y = 4

(-3x + y = 2)

0x + 3y = 6

Simplifying, we get:

3y = 6

y = 2

Now that we have found the value of y, we can substitute it into one of the equations to find the value of x.

Let's use the second equation:

-3x + y = 2

-3x + 2 = 2

-3x = 0

x = 0

Therefore, the solution to the system of equations is (x, y) = (0, 2).

Thus,

Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

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Since first four points in this table have been plotted on the scatter graph, the points that shows where the last point should be plotted is C.

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) above, the coordinate points and quadrants should be identified as follows;

Point C ⇔  (130, 180) → quadrant I.

In conclusion, we can logically deduce that the each of the intervals on both the x-axis and y-axis is equal to 10 units.

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The coordinates of the reflected triangle are (-1,3) (-3,1) and (-4,5)

Given that we have the graph of the triangle ABC

With the coordinates (1,3) (3,1) (4,5)

The transformation is given as

Triangle ABC is reflected over the y-axis

The rule of this transformation is

(x, y) = (-x, y)

So, we have

Image = (-1,3) (-3,1) and (-4,5)

In (a), we have

The rule of this transformation is (x, y) = (-x, y)

This means that the y-coordinate remains unchanged while the x-coordinate is negated as a result of this reflection.

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The probability that exactly 3 out of 4 people chosen at random favor the new building project is 0.2904.

This problem can be solved using the binomial probability formula. Let X be the number of people who favor the new building project out of the 4 chosen at random. Then X follows a binomial distribution with parameters n = 4 and p = 0.45.

The probability of having exactly k people who favor the new building project out of 4 is given by:

P(X = k) = (4 choose k) * [tex]0.45^{k}[/tex] * [tex]0.55^{4-k}[/tex]

where (4 choose k) is the binomial coefficient.

To find the probability that exactly 3 of the 4 people favor the new building project, we substitute k = 3 in the above formula and evaluate:

P(X = 3) = (4 choose 3) * [tex]0.45^{3}[/tex] * [tex]0.55^{1}[/tex]

= 0.290384375

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The value of this expression if x = -1 and y = -5 is -5/4.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

x²y/4

(-1)² × -5/4

1 × -5/4

-5/4

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Complete Question:

find the value of this expression if x = -1 and y = -5.

x²y/4

Answer:

B

Step-by-step explanation:

56.54867 (the area of the bigger half circle) + 14.137165 (the area of the smaller half circle + 96 (the area of the rectangle) = 166.685835 (rounded up is 166.7 (B)).