In ΔABC, the measure of ∠C=90°, AB = 86 feet, and CA = 61 feet. Find the measure of ∠A to the nearest degree

Answer:

Step-by-step explanation:

1)

∠1 = ∠2     {Angles opposite to equal angles are equal}

∠1 = ∠2 = x

x +x + 55 = 180  {angle sum property of triangle}

2x + 55 = 180

        2x = 180 - 55

        2x = 125

          x = 125/2

x = 62.5

∠1 = 62.5

2) ∠2 = 62.5

3) ∠3 = 55         {Vertically opposite angles are congruent}

4) ∠4 + 105 = 180        {linear pair}

∠4 = 180 - 105

∠4 = 75

5) ∠3 + ∠4 + ∠5 = 180 {Angle sum property of triangle}

    55 + 75 +∠5 = 180

            130 + ∠5 = 180

                     ∠5 = 180 - 130

∠5 = 50

The given function is f(x) = { 5 - 5x + 3, if x < 1 4x + 4, if x ≥ 1 }The limit of f(x) can be determined by graphing the function. As x approaches 1 from the right (i.e., x → 1+), the function's right-hand limit can be evaluated. To sketch the graph, we need to plot the two parts of the function separately and then combine them.

As x approaches 1 from the right (i.e., x → 1+), the function's right-hand limit can be evaluated. To sketch the graph, we need to plot the two parts of the function separately and then combine them:For values of x less than 1, we have: f(x) = 5 - 5x + 3 or f(x) = -5x + 8This is a straight line whose slope is -5 and y-intercept is 8. This line passes through the points (0, 8) and (1, 3).When x is greater than or equal to 1, we have: f(x) = 4x + 4This is a straight line whose slope is 4 and y-intercept is 4. This line passes through the points (1, 8) and (2, 12).If we combine these two lines, we get the following graph:We can see from the graph that as x approaches 1 from the right, f(x) approaches 8. Therefore, the right-hand limit of f(x) as x approaches 1 is 8. Hence, the correct option is (A).

Thus, the limit of f(x) can be determined by graphing the function. As x approaches 1 from the right (i.e., x → 1+), the function's right-hand limit can be evaluated. To sketch the graph, we need to plot the two parts of the function separately and then combine them.

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Step-by-step explanation:

The value of the expression can be calculated using the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

The expression is:

2 + [(15 + 3) × 2]

According to PEMDAS, we should first evaluate the expression within the parentheses:

15 + 3 = 18

So, the expression becomes:

2 + [18 × 2]

Next, we perform the multiplication:

18 × 2 = 36

Now, we substitute the result back into the original expression:

2 + 36

Finally, we perform the addition:

2 + 36 = 38

So, the value of the given expression is 38.

Answer:

The height is 12.4 in

Answer:

there is 3 terms I think

Step-by-step explanation:

Answer:

67.5$

Step-by-step explanation:

75$ x .10 = 7.5$

75$ - 7.5$ = 67.5$

Answer:

$67.50

Step-by-step explanation:

First, find the discount.

Multiply the discount rate by the cost.

discount rate * cost

The discount rate is 10% and the cost is $75.

$75 * 10%

Convert 10% to a decimal. Divide 10 by 100 or move the decimal place two spots to the left.

10/100 = 0.10       or         10.0 --> 1.0 --> 0.10

$75 * 0.10

$7.5

Now, find the final price.

Since it is a 10% discount, we must subtract the discount amount from the cost.

cost - discount

The cost is $75 and the discount is $7.5

$75 - $7.5

$67.50

The final price of a item that costs $75 with a 10% discount is $67.50

Answer:

f x−y+2z=0x−2y+3z=−1 divide x−y+2z=0x−2y+3z=−1 by 2

.

x−y+z=0x−y+3z=−1

Step-by-step explanation:

Hope this helps you :)

Answer:

Point form

(4/3, 2/3, −1/3)

Equation Form:

x= 4/3, y= 2/3, z= −1/3

Step-by-step explanation:

Answer:

48 + 30m

Step-by-step explanation:

The perimeter of a hexagon is 6 times its side length.

6(8 + 5m)

= 48 + 30m (Distributive property)

If 'A" denotes the event that student takes statistics and B denotes event that the student is senior, the P(A' or B') is 0.85.

To find P(A' or B'), we want to find the probability that a student is not a senior or does not take statistics (or both).

We know that the total number of students surveyed is 100, and out of those students:

15 seniors take statistics

35 seniors take calculus

18 juniors take statistics

32 juniors take calculus;

The probability P(A' or B') is written as P(A') + P(B') - P(A' and B');

To find the probability of a student not taking statistics, we add the number of students who take calculus (seniors and juniors) and divide by the total number of students:

⇒ P(A') = (35 + 32) / 100 = 0.67;

To find the probability of a student not being a senior, we subtract the number of seniors who take statistics and calculus from the total number of students who take statistics and calculus;

⇒ P(B') = (18 + 32) / 100 = 0.50

= 1 - 0.50 = 0.50;

Next, to find probability of student who is neither senior nor does not take statistics, which is 32 students,

So, P(A' and B') = 32/100 = 0.32;

Substituting the values,

We get,

P(A' or B') = 0.67 + 0.50 - 0.32 = 0.85;

Therefore, the required probability is 0.85.

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The given question is incomplete, the complete question is

A student surveyed 100 students and determined the number of students who take statistics or calculus among seniors and juniors. Here are the results.

               Statistics   Calculus

Senior           15              35

Junior           18               32

Let A be the event that the student takes statistics and B be the event that the student is a senior.

What is P(A' or B')?

A) Translation

hope this helps!

Answer:

translation

Step-by-step explanation:

this is a translation because every point of the shape remain in the same position as it is moved.

The number of cruise passengers must there have been in 2017 is  26.7 million.

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

\(\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}\)

Multiplying both sides by 100;

\(\begin{aligned}&\frac{106.7 x}{100} * 100=28.5 * 100 \\&106.7 x=2850\end{aligned}\)

Dividing both sides by 106.7;

\(\frac{106.7 x}{106.7}=\frac{2850}{106.7}\)

x = 26.7

Therefore, the number of cruise passengers in 2017 must have ranged from 26.7 million.

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Answer:

No

Step-by-step explanation: No, because each input is not compared to exactly one output. The ordered pair that would need to be removed is (5,7) or (5,8). This works because it means that one of the inputs got taken away and can go to exactly one output.

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

To find the percent increase between the average low and high temperatures in July, we need to calculate the difference between the average high and low temperatures and then divide that difference by the average low temperature. Finally, we multiply the result by 100 to get the percentage increase.

The difference between the average high and low temperatures is:

90°F - 69°F = 21°F

To find the percentage increase, we need to divide the difference by the average low temperature and multiply by 100:

Percentage increase = (21°F / 69°F) × 100%

≈ 30.4%

Therefore, the percent of increase between the average low and high temperatures in July is approximately 30.4%, rounded to the tenths place.

In the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

An experimental design known as a randomized block design divides the experimental units into units known as blocks.

The experimental units inside each block are assigned the treatments at random.

We have a fully randomized block design when each block has at least one instance of each treatment.

By ensuring that a crucial predictor of the outcome is fairly distributed amongst research groups to require them to be balanced, something that a completely randomized design cannot guarantee, a randomized block design differs from a completely randomized design.

Therefore, in the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

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Complete question:

R.A. Fisher, a famous statistician, describes a well-known design in his book, Design of Experiments. Five varieties of wheat were compared to determine which gave the highest yield in bushels per acre. Eight farms were available for planting. Each farm was divided into five plots. For each farm, the five varieties were randomly assigned to the five plots with one variety per plot. The varieties were planted on their assigned plots and their yields were measured and compared.

How was randomization incorporated into this study?

A. All five varieties were randomly assigned to the five plots at each farm.

B. The five varieties were randomly assigned to the eight farms - three varieties were planted twice and two varieties only once.

C. It was not incorporated. The wheat seeds were not randomly selected from the population of wheat seeds.

D. Experiment - randomized block design

Answer:

40in³

Step-by-step explanation:

Find the picture of the pyramid attached

Volume of the pyramid = 1/3BH

B is the base area

H is the height of the prism

Base area B = 1/2 * 6 * 5

BAse area = 30/2

Base area = 15in²

Height of the prism = 8inches

Get the volume of the prism

Volume of the prism  = 1/3 * 15 * 8

Volume of the prism = 5 * 8

Volume of the prism = 40 cubic inches

Hence the volume of the prism is 40in³

Answer:

290 in^2

Step-by-step explanation:

front side x 2 = 176

top + bottom = 48

sides x 2 = 66

Sum = 290

Answer:

Total surface area S_tot = 290 in²  thus c. is your answer

Step-by-step explanation:

length l = 8 in

width w = 3 in

height h = 11 in

diagonal d = 13.9283883 in

total surface area S_tot = 290 in²

lateral surface area S_lat = 242 in²

top surface area S_top = 24 in²

bottom surface area S_bot = 24 in²

volume V = 264 in³

Formula and Agenda:

Formulas for a rectangular prism:

Volume of Rectangular Prism:

V = lwh

Surface Area of Rectangular Prism:

S = 2(lw + lh + wh)

l = length

w = width

h = height

d = diagonal

S_tot = total surface area

S_lat = lateral surface area

S_top = top surface area

S_bot = bottom surface area

V = volume

Answer:

9/10 or 0.9

Step-by-step explanation:

Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run

where
rise = y2 - y1
run = x2 - x1

Given points (- 6, - 5) and (4, 4),

rise = 4 - (-5) = 4 + 5 = 9

run = 4 - ( - 6) = 4 + 6 = 10

Slope = rise/run = 9/10 or 0.9

Answer:

x = -3

Step-by-step explanation:

Solve for x:

-5 x + 4 = 2 x + 25

Subtract 2 x from both sides:

(-5 x - 2 x) + 4 = (2 x - 2 x) + 25

-5 x - 2 x = -7 x:

-7 x + 4 = (2 x - 2 x) + 25

2 x - 2 x = 0:

-7 x + 4 = 25

Subtract 4 from both sides:

(4 - 4) - 7 x = 25 - 4

4 - 4 = 0:

-7 x = 25 - 4

25 - 4 = 21:

-7 x = 21

Divide both sides of -7 x = 21 by -7:

(-7 x)/(-7) = 21/(-7)

(-7)/(-7) = 1:

x = 21/(-7)

The gcd of 21 and -7 is 7, so 21/(-7) = (7×3)/(7 (-1)) = 7/7×3/(-1) = 3/(-1):

x = 3/(-1)

Multiply numerator and denominator of 3/(-1) by -1:

Answer:  x = -3

Answer:

x = -3

Step-by-step explanation:

=> 4-5x=2x+25

=> -5x-2x= 25-4

=> -7x = 21

=> x = -21/7

=> x = -3

Using the z-distribution, as we have the standard deviation for the population, it is found that the correct decision is given by:

Reject the null hypothesis. There is enough evidence to oppose the company's claim.

At the null hypothesis, it is tested if the mean is of 2.7 years, that is:

\(H_0: \mu = 2.7\)

At the alternative hypothesis, it is tested if the mean is different of 2.7 years, hence:

\(H_1: \mu \neq 2.7\)

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

The parameters are:

In this problem, the values of the parameters are given by:

\(\overline{x} = 3.1, \mu = 2.7, \sigma = 0.85, n = 25\)

Hence, the value of the test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{3.1 - 2.7}{\frac{0.85}{\sqrt{25}}}\)

\(z = 2.35\)

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, the critical value is of \(|z^{\ast}| = 1.96\).

Since the absolute value of the test statistic is greater than the critical value, the correct decision is:

Reject the null hypothesis. There is enough evidence to oppose the company's claim.

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Answer:

Reject the null hypothesis. There is enough evidence to oppose the company's claim.

Step-by-step explanation:

The test statistic needs to fall within the rejection regions that are above and below the critical z-score associated with a 5% level of significance in order to reject the null hypothesis. Otherwise, we will fail to reject the null hypothesis.

Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

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Answer:

The first three terms are \(3,6,11\)

The 10th term is \(102\)

Step-by-step explanation:

An ordered list of numbers is known as a sequence such that each number in the sequence is called a term.

The nth term is \(a_n=n^2+2\).

To find the first 3 terms, put \(n=1,2,3\)

\(a_1=1^2+2=1+2=3\\a_2=2^2+2=4+2=6\\a_3=3^2+2=9+2=11\)

To find the 10th term, put \(n=10\) in \(a_n=n^2+2\)

\(a_{10} =(10)^2+2=100+2=102\)

Answer:

3x - 2y = 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m = \(\frac{5-2}{4-2}\) = \(\frac{3}{2}\) , then

y = \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, 2 )

2 = \(\frac{3}{2}\) (2) + c = 3 + c ( subtract 3 from both sides )

- 1 = c

y = \(\frac{3}{2}\) x - 1 ← equation in slope- intercept form

multiply through by 2 to clear the fraction

2y = 3x - 2 ( subtract 3x from both sides )

- 3x + 2y = - 2 ( multiply through by - 1 )

3x - 2y = 2  ← in standard form

True. An annuity due is a series of equal payments made at the beginning of each period, while an ordinary annuity is a series of equal payments made at the end of each period.

Because payments made at the beginning of each period earn interest for one additional period, annuity due payments are worth more than equivalent ordinary annuity payments. This means that the present value of an annuity due must be larger than the present value of an equivalent ordinary annuity, assuming the same interest rate and number of payments.

Therefore, if we compare two annuities with the same payment amount, interest rate, and number of payments, the annuity due will always have a larger present value than the ordinary annuity. It is important to understand the difference between these two types of annuities as it can impact the amount of money you receive or need to save for your retirement.

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