The following angle measures could form a triangle
(a)
111º, 28°, 31°
A True
B False


(b)
Explain why the angle measures form a triangle or do not form a triangle,

a. The periodic deposit should be $643.28 (rounded to the nearest cent).

b. $15,438.72 of the $27,000 comes from deposits, and $11,561.28 comes from interest.

a. To determine the periodic deposit, we can use the formula for the future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, FV = $27,000, r = 8% / 4 = 2%, n = 6 x 4 = 24 (since there are 4 quarters in a year and the time period is 6 years).

Substituting these values into the formula, we get:

$27,000 = Pmt x [(1 + 0.02)^24 - 1] / 0.02

Solving for Pmt, we get:

Pmt = $643.28

b. The total amount contributed by deposits is:

$643.28 x 24 = $15,438.72

To find the amount of interest earned, we subtract the total deposits from the financial goal:

$27,000 - $15,438.72 = $11,561.28

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On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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Answer:

1) a

6x - 28 》 14

<=> 6x 》 42

<=> x 》 7

2) c

x/9 + 2 < 5

<=> x/9 < 3

<=> x < 27

Step-by-step explanation:

....... .........

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Answer:

T = 5c +5d,    where unit of the equation is $.

Step-by-step explanation:

Cost of 1 large cheese  pizza = $5

No. of large cheese pizza = c

therefore

cost of c  large cheese pizza = c*Cost of 1 large cheese  pizza = $5c

Cost of 1 large one topping  pizza = $6

No. of large one topping pizza = d

therefore

cost of d  large one topping pizza = d*Cost of 1 large one topping  pizza =             cost of d  large one topping pizza = $6d  

Total cost of  c  large cheese pizza and cost of d  large one topping pizza

= $5c +$6d

total cost is represented by T

thus, T = $5c +$5d  Answer

Answer:

36720 different desserts

Step-by-step explanation:

(1020x3)x12=36720

Answer:

0.72

Step-by-step explanation:

first you take 1.60 and find 10 percent of it once you find that you times it by 4.5.

Answer:

$6.48

Step-by-step explanation:

10 = 0.16

1.60-0.16=1.44

1.44x4=5.76

1.44/2=0.72

5.76+0.72=6.48

The value of angle x in the triangle is 15°

Given: the triangle ABC with equal sides of 9 units.

Since the triangle has equal sides, it will also have equal angles (i.e. it is an equilateral triangle).

Thus, <A = <B = < C =  4x°

Since the sum of angles in a triangle is 180°. We have:

<A + <B + < C = 180°

4x + 4x + 4x = 180°

12x = 180

x = 180/12

x = 15°

Therefore, the value of x is 15°

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The value of the dependent variable when the value of x is 15 is approximately 74.9.

To perform a regression run and compute the value of the dependent variable when the value of x is 15, you can use the following steps:

Save the equation of the regression line, which is:

Use the equation to compute the value of the dependent variable when the value of x is 15. Substituting 15 for x in the equation gives:

Therefore, the value of the dependent variable when the value of x is 15 is approximately 74.9.

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Complete Question:

Given the following data, compute a regression run, save the equation and then use the formula to compute the value of the dependent variable when the value of X is 15. (Please round your answers to two decimal places)

Х : 30 3 14 22 16 5 18 32 4 17

Y : 67 57  53  78  90  97  92  44 58 70

Answer:

None,

they are all correct.

Step-by-step explanation:

A)

3/4 - 75%

4/5 - 80%

3/4 < 4/5

B)

5 ÷ 6 = .83333333333

5/6 > .83

C)

2 ÷ 3 = .666666666

2/3 > .66

D)

1 ÷ 3 = .33333333333

1/3 > .3

Thus,

all of the given statements are correct.

Hope this helps :)

Answer:  Therefore, at the start of the game, Peter had 80 marbles and Jack had 80 marbles.

Step-by-step explanation:

The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

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Answer:

The answer is 1/20.

Step-by-step explanation:

-When you want to share it equally, you must divide by 2, but only the denominator.

-This is because 1/10=0.1 and you would divide 0.1 by 2 and get 0.05.

-0.05 is equivalent to 1/20.

Answer:

i think it would be a; When the price of housing increases, more homeowners want to sell their house.

Answer: 10.90

Step-by-step explanation:

5.18 for candy and 5.72 for pretzels

1.20 + 3.12 = 4.32

4.32 x 1.20 = 5.18

5.2 x 1.10 = 5.72

5.18 + 5.72 = 10.90

hope this helps

plz mark brainleist

Answer:

The length is 13 feet and the width is 5 feet

Step-by-step explanation:

Let w represent the width

Since the length is 3 more than twice the width, it can be represented by 2w + 3

Using this, set up an equation and solve for w:

w + (2w + 3) = 18

3w + 3 = 18

3w = 15

w = 5

So, the width is 5

Use 2w + 3 to find the length:

2w + 3

2(5) + 3

= 13

The length is 13 feet and the width is 5 feet

Answer:

the length is 13 feet and the width is 5 feet

Step-by-step explanation:

Answer:

A - The first one

Step-by-step explanation:

Answer:

The first line.

Step-by-step explanation:

The line starts off at 0,

then it goes to the left of the line -3 times.

Then it goes to the left -1.5 times.

this means it goes one and a half.

so it would land on the line after -4.

Answer:

1/2 I think

Step-by-step explanation:

9 3/8 becomes 8 11/8- 8 7/8= 4/8= 1/2

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

\(9\frac{3}{8} -8\frac{7}{8}\)

Let's convert these to improper. To do this, we will multiply the denominator by the whole number and then add the numerator. The denominator will remain the same. We are just changing the numerator.\(9\frac{3}{8} =\frac{(8*9)+3}{8} =\frac{72+3}{8}= \frac{75}{8}\\8\frac{7}{8} =\frac{(8*8)+7}{8} =\frac{64+7}{8}= \frac{71}{8}\)

Let's subtract:

\(\frac{75}{8} -\frac{71}{8} \\\\\frac{4}{8}\)

\(\frac{4}{8}\) can be reduced to \(\frac{1}{2}\)

AnswerAnswer:   C

Step-by-step explanation:c

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.

What is Perimeter?

Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.

Given : sides of the fence

            s₁ = 4x + 5

            s₂ =  y − 7

            s₃ = 3x − 2

We know that, perimeter of a triangle is sum of all three sides.

So, Perimeter of the fence =  s₁+ s₂+ s₃

                                            = 4x + 5 + y − 7 + 3x − 2

                                            = 7x + y - 4 ft.

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Explanation:

The scale 1 cm : 85 km becomes 10 cm : 850 km when we multiply both parts by 10. We do this so that the "1 cm" becomes "10 cm". At this point, we have our answer.

You could also solve it like so

(1 cm)/(85 km) = (10 cm)/(x km)

1/85 = 10/x

1*x = 85*10

x = 850

Answer: The answers are y=1+i, x=–1+i, and y=1–i, x=–1–i.

Step-by-step explanation: Solve for the first variable in one of the equations, and then substitute the result in the other equation.

Answer:

\(0.63\)

Step-by-step explanation:

Randomly selected orange can be organic or non-organic.

\(0.19/(0.19+0.11)\)

\(0.19/0.3\)

\(=0.63333333333\)

Answer:

x is 34.28 rounded to the nearest hundredth

Step-by-step explanation:

Since it is a right-angled triangle, using Pythagoras' rule, SOH/CAH/TOA;

Viewing the known variables, Opposite(19), Adjacent(x), and Theta(29°);

tan 29° = 19 / x (cross multiply, making x the subject of the formula);

x = 19 / tan 29° = 34.276 = 34.28 rounded to the nearest hundredth

x = 34.28