Here is a regular pentagon.
Calculate the size of the interior angle marked c.
C
Co

Given ΔABC, the measure of b include the following: D. b = 11.690 units.

In Mathematics and Geometry, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

a + c + b = 180°

53 + 58 + b = 180°

b = 180° - 111

b = 69°

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

sin69/b = sin53/10

b = 10sin69/sin53

b = 11.690 units.

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Answer:

-------------

First determine the interest and then use the formula for ordinary interest.

Calculate the interest:

Use the ordinary interest formula:

Plug in the values and solve for Time:

Isolate the Time variable:

Tara would have to pay back the loan in approximately 120 days.

The radical expression √(3x + 12) − 1 = √(5x + 9) when solved for x has a solution of x = -1

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

√(3x + 12) − 1 = √(5x + 9)

The above equation can be solved using trial by error method

Set x = -1

So, we have

√(3(-1) + 12) − 1 = √(5(-1) + 9)

Evaluate

2 = 2

The above equation is true for x = -1

Hence, the solution is x = -1

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Answer:

1) 4

2) 6

3) 10

4) 30°

5) 48°

6) 55°

7) 68°

8) 148°

9) 102°

10) 48°

The correct answer choices for the complementary angles as well as congruent angles  are:

Complementary angles are two angles that when they are summed up give the sum of 90 degrees (90°).

The complementary angle in the given question is as follows:

5 and 6 since their sum are 90 degrees.

Congruent angles are two or more angles that are equal in size.

An example of congruent angles from the given question is 8 and 10 since they are vertically opposite angles.

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The annual percentage rate is 6.81%.

What is compound interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.

Principal = $1135

Total Amount = $132.51 * 9 = $1192.59

Time = 9 months = 9/12 years = 0.75 years

Now using compound interest formula,

=> Amount =[tex]P(1+r)^n[/tex]

=>[tex]$1192.59 = $1135 * (1+r)^{0.75[/tex]

=>[tex](1+r)^{0.75 = 1.0507[/tex]

Taking log both sides , we get ,

=> 0.75 ln(1+r) = ln(1.0507)

=> 1 + r = e0.0659

=> 1 + r = 1.0681

=> r = 0.0681

rate = 6.81%

Hence the annual percentage rate is 6.81%.

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Tom and Keira will owe $182,002 in federal income tax for 2022.

To calculate the federal income tax that Tom and Keira will owe in 2022, we need to first determine their taxable income.

Assuming that Tom and Keira have no dependents, their standard deduction for 2022 is $25,900. Therefore, their taxable income is:

Taxable income = Combined income - Standard deduction

Taxable income = $208,264 - $25,900

Taxable income = $182,364

To determine their federal income tax, we need to use the tax brackets and rates for 2022. According to the IRS, for married filing jointly status, the tax rates for 2022 are as follows:

10% on taxable income up to $21,450

12% on taxable income over $21,450 up to $87,850

22% on taxable income over $87,850 up to $183,250

24% on taxable income over $183,250 up to $351,600

32% on taxable income over $351,600 up to $431,200

35% on taxable income over $431,200 up to $666,450

37% on taxable income over $666,450

To calculate the federal income tax owed, we need to apply the appropriate tax rates to the corresponding income brackets. In this case, the taxable income falls within the following brackets:

$21,450 at 10% = $2,145

($87,850 - $21,450) at 12% = $7,026

($183,250 - $87,850) at 22% = $24,457

($351,600 - $183,250) at 24% = $42,336

($431,200 - $351,600) at 32% = $25,280

($666,450 - $431,200) at 35% = $80,758

($182,364 - $666,450) at 37% = $0

Therefore, the total federal income tax owed for 2022 is:

Total federal income tax = $2,145 + $7,026 + $24,457 + $42,336 + $25,280 + $80,758 + $0

Total federal income tax = $182,002

Therefore, Tom and Keira will owe $182,002 in federal income tax for 2022.

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Answer: 125

Step-by-step explanation:

V=lwh

=(5)(5)(5)

=125

OD. 16.27

cylinder 4:3 the ratio if their volumes is (4/3)^3, which simplies to 64/27.So the correct answers is D.

The center of the circle shown is point S

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

The circle

By definition, the center of a circle is the point that is equidistant to all points on the circumference of the cirlce

In the given circle, the point that satisfies the above definition is the point S

This means that the circle can also be called the circle S

Hence, the center of the circle shown is S

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Answer:

Step-by-step explanation:

First mulitply the current salary by 11.5% to find the increase.

Change 11.5% into a decimal by moving the decimal two places to the left.

11.5% becomes .115.

22000 × .115 = 2530 - the increase

22000 + 2530 = 24530 GBP

The new gross salary.

We need more information about the property and the specific services required to determine the price of Hillary's home.

Answer:

Unfortunately, without additional information, it is impossible to determine the price of Hillary's home. The range of closing costs provided does not provide enough information to calculate the price of the home.

To determine the price of the home, we would need to know either the exact amount of the closing costs or additional information about the home's value, such as its appraised value or sale price.

Therefore, we cannot determine the price of Hillary's home based on the given information.

Step-by-step explanation:

We only know that the estimated closing costs for her home range from $11,600 to $40,600. Closing costs can vary based on a variety of factors, such as the location of the home, the type of mortgage, and the specific fees charged by the lender and other parties involved in the transaction.

To determine the price of Hillary's home, we would need additional information, such as the appraised value of the home, the amount of the down payment, and the specific closing costs that were incurred.

The height of the square pyramid is 58.95 units.

To find the height of the square pyramid, we can use the Pythagorean theorem. Let's call the height "h".

The slant height is the hypotenuse of a right triangle with legs equal to half the length of one side of the square base and the height of the pyramid. The length of one side of the square base is given as 22, so the length of half a side is 11. Using the Pythagorean theorem, we get:

[tex]h^{2}[/tex] + [tex]11^{2}[/tex] = [tex]60^{2}[/tex]

Simplifying, we have:

[tex]h^{2}[/tex]  + 121 = 3600

Subtracting 121 from both sides, we get:

[tex]h^{2}[/tex]  = 3479

Taking the square root of both sides, we get:

h ≈ 58.95

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Answer:

For all answers: x = -17, y = -19, (-17,-19)

Step-by-step explanation:

Substitution:

We plug x = y+2 into the second equation

[tex]-2(y+2)+y=15\\-2y-4+y=15\\-y-4=15\\y=-19[/tex]

Plugging back into x = y+2 we get that x = -17

Elimination:

We move y to the other side in Equation 1 and then subtract y.

[tex]x-y=2\\-2x+y=15\\-x=17\\x=-17\\y=-19[/tex]

Plugging X into x-y = 2 we get that y = -19

What method you prefer is up to you

Answer:

Step-by-step explanation:

The missing values in the table are:

Distance 800 m 1200 m

Time Taken _______ _______
The time taken to walk 800m in Table 2 is not provided, so the blank space remains unfilled.

Answer: m=6.2, direction is 57.84 degrees north of east

Step-by-step explanation:

Break up each into x and y parts of the vector

first part only has a y

<0, 4.5>

2nd <2, 0>

3rd  use trig

sin 30 = y/1.5

y=.75

cos30 =x/1.5

x=1.3

<1.3, .75>

Add all x's and y's

<3.3, 5.25>   to find magnitute use pythagorean

m²=3.3²+5.25²

m=√38.45

m=6.2

to find direction use trig again

tan∅=5.25/3.3

∅=57.84

The number in the given expression is 160.

We have,

Let's call the number "x".

The difference between twice a number and its half is:

2x - (1/2)x = (3/2)x

One-fifth of this difference is 24, so we can set up the equation:

(1/5)(3/2)x = 24

Multiplying both sides by 10 to eliminate the fraction, we get:

3x = 480

Dividing both sides by 3, we get:

x = 160

Therefore,

The number in the given expression is 160.

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The complete question.

One fifth of the difference between twice a number and its half is 24. What is the number.

Answer:

[tex]\left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]

Step-by-step explanation:

When multiplying a constant by a matrix, we have to multiply each element by the constant.

[tex]\dfrac{1}{2} \cdot \left[\begin{array}{c c c c}12 & 64 & 78 & 30\end{array}\right][/tex]

[tex]= \left[\begin{array}{c c c c} \dfrac{12}{2} & \dfrac{64}{2} & \dfrac{78}{2} & \dfrac{30}{2}\end{array}\right][/tex]

[tex]= \left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]

The value of test statistic is -2.23.

What is test statistic?

In statistics, a test statistic is a value calculated from a sample of data that is used to assess the evidence against a null hypothesis.

We can use a one-sample t-test to test the hypothesis:

Null hypothesis: The true population mean cost of weddings is $25,549

Alternative hypothesis: The true population mean cost of weddings is less than $25,549

The test statistic can be calculated using the formula:

t = ([tex]\bar{x}[/tex] - μ) / (s / √n)

where [tex]\bar{x}[/tex] is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (24,342 - 25,549) / (5054 / √60) = -2.23

Rounding to two decimal places, we get t = -2.23.

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Answer:

To find the p-value, we need to first find the corresponding area in the normal distribution table for the test statistic of 1.75.

Since the sample size (n) is greater than 30 and the population standard deviation is unknown, we use the t-distribution to calculate the p-value.

The degrees of freedom (df) for the t-distribution is n - 1 = 20 - 1 = 19.

Using a t-table or calculator, we can find that the area to the right of 1.75 (with df=19) is approximately 0.049.

Since this is a one-tailed test (the alternative hypothesis is that the mean wait time is greater than 2 minutes), the p-value is equal to the area to the right of the test statistic, which is 0.049.

Therefore, the corresponding p-value is 0.049 (rounded to three decimal places).

Step-by-step explanation:

gg

Answer:

Mr. Johnson should be paid $285 for a job requiring 60 hours of work.

Step-by-step explanation:

If Mr. Johnson was paid $190 for 40 hours of work, then we can write:

190/40 = x/60

Where x is the amount he should be paid for 60 hours of work.

To solve for x, we can cross-multiply and simplify:

190 * 60 = 40 * x

11,400 = 40x

x = 11,400/40

x = 285

Therefore, Mr. Johnson should be paid $285 for a job requiring 60 hours of work at the same rate.

The equivalent expression to the given one is the second option:

[tex]log_2( y^4*z^4/x^2)[/tex]

Here you need to remember two logarithmic rules, these are:

[tex]log(x^n) = n*log(x)[/tex]

[tex]log(x) + log(y) = log(x*y)[/tex]

And these work for any base of the logarithm.

Here we start with the expression:

[tex]-2log_2(x) + 4log_2(y)+ 4log_2(z)[/tex]

Using the first one:

[tex]-log_2(x^2) + log_2(y^4) + log_2(z^4)[/tex]

Using the second one:

[tex]log_2( y^4*z^4/x^2)[/tex]

That is the equivalent expression, the second option.

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x² + (y - 3)² = 36; x² + (y + 8)² =36 represent the circles that have a diameter of 12 units and a center that lies on the Y axis.

We know that the abscissa of coordinates of a point on Y axis is 0.

So the equation of a circle center at (0, k) and radius 'r' is given by,

x² + (y - k)² = r²

Here given that the diameter of the circle must be = 12 units

So the radius of the circle = 12/2 = 6 units.

So the equation of the required circle looks like

x² + (y - k)² = 6², where k is an real number.

x² + (y - k)² = 36

So we can see that the equations x² + (y - 3)² = 36; x² + (y + 8)² =36 can be the equation of the required circle.

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According to the information, the maximum infection rate is:  k * 2500 * (5000 - 2500) = 6250k = 40

To address this problem, we can use the law of the infection rate, which states that the infection rate is directly proportional to the product of the number of people infected and the number of people not infected. Therefore, we can write:

where "k" is a constant of proportionality. Since we want to find the number of people infected that produces the maximum infection rate, we can consider the infection rate as a function of the variable "x" representing the number of people infected. Therefore, we can write:

To find the value of "x" that maximizes the infection rate, we can derive this function and set the derivative equal to zero:

This implies that 5000 - 2x = 0, and therefore:

Therefore, the number of infected people that produces the maximum daily rate of infection is 2,500.

However, we must verify that this result is consistent with the information given in the problem. We know that when there are 1,000 people infected, the flu spreads at the rate of 40 new cases per day. Therefore, if we add 1,500 more infected people (for a total of 2,500), the infection rate would be:

If the infection rate is 40 new cases per day, we have:

which implies that:

Therefore, the maximum infection rate is:

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After considering all the given data we conclude that the generated answers to the sub questions are

a) 120 feet

b) 1200 inches

c) 120 inches tall

d) 72

e) 1

f) 1

g) proportional

a. To evaluate the height of the flagpole needed to support a 30 by 42 feet flag, we can apply the ratio of the height of a flagpole to the width of any flag which is 4 to 1.

This projects that the height of the flagpole is be four times the width of the flag. The width of the flag is 30 feet, so the height of the flagpole should be 4 × 30 feet = 120 feet.

b. If the individual have a model of Ft. McHenry that you need to add a flagpole to that will be proportional to the real pole at the fort and the ratio of the model is 1 inch to 10 feet, then you can apply this ratio to determine how tall the individuals model flagpole should be.

The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10

10 × 120 = 1200

to get 1200 inches. This means that your model flagpole should be 1200 inches tall.

c. It is given that a model flagpole that is 8 inches tall; this is not the correct size. To evaluate how tall it needs to be, we can use the same ratio as in part b.

The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10 to get 1200 inches.

This means that your model flagpole should be 1200/10 = 120 inches tall.

d. To evaluate if the model flag and original flag are similar figures, we can compare their corresponding sides.

The original flag has dimensions of 30 by 42 feet, which is equivalent to 360 by 504 inches. The model flag has dimensions of 5 by 6.3 inches. To determine if they are similar figures, we can compare their corresponding sides using ratios.

The ratio of the length of corresponding sides must be equal for two figures to be similar. The length of corresponding sides for these two flags are:

- Original Flag: Length = 360 inches; Width = 504 inches

- Model Flag: Length = 5 inches; Width = 6.3 inches

To compare these lengths, we can divide each length by its corresponding length on the other figure:

- Length Ratio: (360 / 5) = 72

- Width Ratio: (504 / 6.3) = 80

Since these ratios are not equal, these two flags are not similar figures.

To find out what dimensions would make them similar figures, we can use these ratios as scale factors:

Length Scale Factor: (360 / x) = 72

- Width Scale Factor: (504 / y) = 80

Evaluating for x and y gives us:

- x = (360 / 72) = 5

- y = (504 / 80) = 6.3

This means that if we scaled down the original flag by a factor of 72, its dimensions would be equivalent to those of the model flag.

e. To evaluate the ratio of the perimeter of the model flag in comparison to the original flag using the scale factor from part d:

Perimeter Scale Factor: (72 + 80) / 2 = 76

Model Flag Perimeter: (2 * (5 + 6.3)) = 23.6

- Original Flag Perimeter: (2 * (360 + 504)) = 1688

The ratio of these perimeters is:

Perimeter Ratio: (23.6 / (1688 /76)) ≈ 1

This means that the perimeter of the model flag is approximately equal to that of the original flag.

f. To evaluate the ratio of area between these two flags using scale factor from part d:

- Area Scale Factor: (72 × 80) = 5760

- Model Flag Area: (5 × 6.3) ≈ 31.5

- Original Flag Area: (360 × 504) ≈ 181440

The ratio of these areas is:

Area Ratio: (31.5 / (181440 /5760)) ≈ 1

This means that area of model flag is approximately equal to that of original flag.

g. Here relationship between ratios of perimeter and area is that they are both proportional to each other.

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Answer:

n > -2

Step-by-step explanation:

[tex]-2n+1 < 5[/tex]

This is a two-step equation, so the first thing you would do is subtract 1 from both sides of the equation.

[tex]-2n+1-1 < 5-1\\-2n < 4[/tex]

Then, divide -2 from both sides of the equation.

[tex]\frac{-2n}{-2} < \frac{4}{-2} \\[/tex]

The less than symbol will become a greater than symbol because you divided by a negative number.

So the solution is:

[tex]n > -2[/tex]

A.= [tex]$\left( -4,\frac{5\pi}{4}\right)\,\, \left( 4,\frac{-7\pi}{4}\right)[/tex],  B = [tex]$\left( 4,\frac{3\pi}{4}\right)\,\, \left( -4,\frac{-\pi}{4}\right)[/tex],

C=[tex]$\left( -4,\frac{\pi}{4}\right)\,\, \left( 4,\frac{5\pi}{4}\right)[/tex],  D = [tex]$\left( -4,\frac{3\pi}{4}\right)\,\, \left( 4,\frac{7\pi}{4}\right)[/tex]

[tex]$\left( -4,\frac{5\pi}{4}\right) = \left( 4,\frac{5\pi}{4}+\pi = 2\pi + \pi/4\right )\,\,, \left( 4,\frac{-7\pi}{4}\right) =\left( 4,\frac{-7\pi}{4}+2\pi = \pi/4\right)[/tex]

[tex]$\left( 4,\frac{3\pi}{4}\right)\,\, , \,\left( -4,\frac{-\pi}{4}\right) = \left(4,\frac{-\pi}{4}+\pi = 3\pi/4\right)[/tex]

[tex]$\left( -4,\frac{\pi}{4}\right)=\left( 4,\frac{\pi}{4}+\pi = 5\pi/4\right)\,\, ,\,\left( 4,\frac{5\pi}{4}\right)[/tex]

[tex]$\left( -4,\frac{3\pi}{4}\right)=\left ( 4,\frac{3\pi}{4}+\pi = 7\pi/4 \right)\,,\, \left( 4,\frac{7\pi}{4}\right)[/tex]

When [tex]r\geq 0[/tex] and [tex]0\leq \theta < 2\pi[/tex], we call the polar coordinates [tex](r,\theta)[/tex] standard polar coordinates. To convert any given coordinates to standard coordinates 1. if r<0 then replace r with |r| and [tex]\theta[/tex] with [tex]\theta + \pi[/tex]. 2. Now if [tex]\theta < 0 \textrm{ or }\theta\geq 2\pi[/tex], we add a suitable multiple of [tex]2\pi \textrm{ to }\theta[/tex] to bring it inside [0,[tex]2\pi[/tex]) interval.

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