Find the degree measure of each angle in the triangle.

The largest value of these integers is 68

We are given that the average of 5 positive integers is 60

Let the five numbers be [tex]x_{1}, x_{2}, x_{3}, x_{4}, x_{5}[/tex]

Therefore,

[tex]\frac{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}}{5} = 60[/tex]

[tex]{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}} = (60)(5)[/tex]

[tex]{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}} = 300[/tex]

Now, let the first (smallest) number be [tex]x[/tex]

Therefore, the last (largest) number will be equal to [tex]x + 10[/tex]

To maximise a number in the sum equation, we'll have to minimise all the other numbers.

Therefore, let it be

[tex]x + x + x + x + (x + 10) = 300[/tex]

[tex]5x + 10 = 300[/tex]

[tex]5x = 290[/tex]

Therefore, [tex]x = 58[/tex]

Now, we took the largest number as [tex](x + 10)[/tex]

Therefore, the largest number is (58 + 10)

The correct answer is 68

To learn more about average problems, refer to:

https://brainly.com/question/12860560

Answer:

yes it is function.........

The approximate difference between the highest and lowest oil production is 4,500,000 barrels per day

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.

Given is a graph of oil production between 1960 and 2010

The lowest oil production was in year 2010 = 5000,000 barrels per day

The highest oil production was in year 1970 = 9500,000 barrels per day

The difference between highest and lowest oil production = 9500,000 - 5000,000 = 4,500,000 barrels per day

Hence, The approximate difference between the highest and lowest oil production is 4,500,000 barrels per day

For more references on approximation, click;

https://brainly.com/question/29669607

#SPJ1

Answer:

8<r

Step-by-step explanation:

5 > r – 3

+3      +3

add 3 to both sides

8>r

move variable to the left and flip the sign

8<r

Large sample significance tests for a single proportion are based on the  statistic binomial. the correct option is A

Significance test can be defined as tests for statistical significance indicate whether observed differences between assessment results occur because of sampling error. Significance tests give a formal process for using sample data to evaluate the likelihood of some claim about a population value.

Therefore a Large sample significance tests for a single proportion are based on the  statistic binomial.

Learn more about significance tests here: brainly.com/question/15414435

#SPJ1

Answer:

To find the cash flows for this project, we need to calculate the net income for each year and then subtract any investments in net working capital and capital expenditures.

In year 0, the firm will incur the following expenses:

- Research and development costs: $490,000

- Cost of the machine: $290,000

- Shipping and installation costs: $59,000

- Increase in net working capital: $145,000

Total expenses in year 0: $490,000 + $290,000 + $59,000 + $145,000 = $984,000

The net income in year 0 is equal to the revenue minus the costs: $690,000 - $340,000 = $350,000.

Therefore, the cash flow in year 0 is:

FCF0 = $350,000 - $984,000 = -$634,000

In years 1, 2, and 3, the firm will incur the following expenses:

- Cost of goods sold: $340,000

- Depreciation: (This can be calculated using the MACRS depreciation schedule. For the first year, the depreciation will be 14.29% of the cost of the machine, or 0.1429 * $290,000 = $41,461. The depreciation in subsequent years can be calculated using the same method.)

- Increase in net working capital: $145,000

Total expenses in each of years 1, 2, and 3: $340,000 + Depreciation + $145,000

The net income in each of these years is equal to the revenue minus the costs: $690,000 - (Total expenses)

The cash flow in each of these years is equal to the net income minus any investments in net working capital and capital expenditures: Net income - Increase in net working capital - Depreciation

Substituting the appropriate values, we get:

Year 1: FCF1 = $690,000 - ($340,000 + $41,461 + $145,000) = $163,539

Year 2: FCF2 = $690,000 - ($340,000 + Depreciation + $145,000)

Year 3: FCF3 = $690,000 - ($340,000 + Depreciation + $145,000)

Note that the depreciation in years 2 and 3 can be calculated using the same method as in year 1.

So, the cash flows for this project are:

Year 0 1 2 3

FCF -$634,000 $163,539

I hope this helps!

Answer:

C. C and E

Step-by-step explanation:

As per the graph, both points C and E are points that are located on both the red and purple graphs.

Answer:

C.  point C and point E

Step-by-step explanation:

The solutions to the given linear-quadratic system of equations are the points where the line and curve intersect.

From inspection of the given graph, the points of intersection are:

Answer:

Step-by-step explanation:

Step-by-step explanation:

the mean score is the sum of all scores divided by the number of scores.

64 = (s1+s2+s3+...+s26+s27)/27

64×27 = (s1+s2+s3+...+s26+s27)

1728 = (s1+s2+s3+...+s26+s27)

now, one of the scores changes from 47 to 74. that means the sum of all scores is increased by 74-47 = 27.

so, we get

1728 + 27 = (s1+s2+s3+...+s26+s27+27)

1755 = (s1+s2+s3+...+s26+s27+ 27)

we still have 27 scores, so for the updated mean we have to divide both sides by 27 again :

1755/27 = (s1+s2+s3+...+s26+s27+27)/27

65 = (s1+s2+s3+...+s26+s27+27)/27

the correct mean is therefore 65%.

Answer: 7

Step-by-step explanation: cause I took the quiz…

The graph of each given piecewise function is shown below .

In the question,

a piece wise function is given ,

we have to sketch the graph of the piecewise function ,

the piecewise function f(x) is  = [tex]\left \{ {-2x-1 , {x\leq 2} \atop -x+4 , {x > 2}} \right.[/tex]

when x ≤ 2 ,

we put x =2 , we get , f(2) = -2*2-1  = -5 .

So , the point is (2,-5) .

when we put x = 0 , f(0) = -2*0 - 1 = -1

so , the second point is (0,-1) .

Now , for x>2  

we put x= 4 , we get f(4) = 0

the point will, be (4,0)

we put x = 6 , we get , f(6) = -2 .

the point will be = (6,-2) .

On plotting all the four points , we get the graph as sketched below .

Therefore , the given piecewise function's graph is shown below.

Learn more about Functions here

https://brainly.com/question/27808693

#SPJ4

On solving the provided question we can say that he probability of getting the following result using the binomial probability formula and the normal curve approximation is P(4, 16, 1/2) = 0.0280.

Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.

P(4,16,1/2) = C(16,4)(1/2) 4(1 - 1/2)16 - 4 = C(16,4)(1/2)16 = 0.02777;

by help of table - P(4, 16, 1/2) = 0.0280

To know more about probability  visit:

https://brainly.com/question/11234923

#SPJ4

Answer:

Area = Length * Width

Area = 5 units * 3 units

Area = 15 units²

(see attachment picture for the graph)

Step-by-step explanation:

Answer: 15 sq units

Step-by-step explanation:

1. graph it out, this will help visually.

2. find the distance/difference between the y's of (3,1) and (3, -2) to find the width, or (-2, -2) and (-2, 1). it is 3.

3. find the distance between the x's of (3,1) and (-2,1), or (3, -2) and (-2, -2). the distance is 5.

4. multiply the lengths together to find the area. :)

Hazel's new balance in the account is $1197

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

Previous balance = $876.21.

$2.39 in interest,

$616.46 in deposits,

$298.06 in withdrawals

Her new balance can be calculated using

New balance = Previous balance + interest + deposits - withdrawals

Substitute the known values in the above equation, so, we have the following representation

New balance = 876.21 + 2.39 + 616.46 - 298.06

Evaluate

New balance = 1197

Hence, the new balance is $1197

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

After evaluating the given integral by changing to polar coordinates we get [tex]7 e^8-31[/tex]

As per the details shared in the above question it is given that,

[tex]$x^2+y^2=64$[/tex]

[tex](x, y)=r(\cos \theta, \sin \theta)[/tex]

[tex]d A=r d r d \theta.[/tex]

Further solving above we get,

[tex]r^2=64 \\\Rightarrow & r=8 . \\0 \leq r \leq 8 ; & 0 \leq \theta \leq \pi / 2[/tex]

The polar coordinate,

[tex]\iint_{R} y e^x d A=\int_0^{\frac{\pi}{2}} \int_0^8 r^2 \sin \theta e^{r \cos \theta} d r d \theta[/tex]

[tex]& =\int_0^8 \int_0^{\frac{\pi}{2}} r^2 \sin \theta e^{r \cos \theta} d \theta ; \\& =\int_0^8\left[-r e^{r \cos \theta}\right]_0^{\pi / 2} d r[/tex]

[tex]=\int_0^8 r\left[-e^{r \cos \left(\frac{\pi}{2}\right)}+e^\alpha\right] d r .[/tex]

[tex]=\int_0^8 r e^r d r-\left.\frac{r^2}{2}\right|_0 ^8[/tex]

Now substituting the value we get,

[tex]7 e^8-31[/tex]

For more such question on Integration.

https://brainly.com/question/20156869

#SPJ4

Note the correct question should be ,

Evaluate the given integral by changing to polar coordinates.

[tex]\iint_R y e^x d A[/tex] , where R is the region in the first quadrant enclosed by the circle  [tex]x^2+y^2=64[/tex].

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

a) To find the type I error probability, we need to find the probability of rejecting the null hypothesis (H0) when it is actually true. In this case,

Since the foam height is approximately normally distributed with a standard deviation of 20 millimeters and we are taking a sample of size n = 10, the standard error of the mean is:

20 : [tex]\sqrt{10}[/tex] = 6.3 millimeters.

This means that the mean of the sampling distribution of the mean is approximately normally distributed with a mean of 175 millimeters and a standard deviation of 6.3 millimeters.

To find the probability of rejecting the null hypothesis when it is actually true, we can use a z-score.

In this case, the z-score for a value of 185 millimeters is:

(185-175)/6.3 = 1.6

We can use a z-table or a calculator to find the probability of getting a value greater than 1.6 standard deviations above the mean in a normal distribution. This probability is equal to 1 - the probability of getting a value less than or equal to 1.6 standard deviations above the mean, which is:

1 - 0.9495 = 0.0505.

Therefore, the type I error probability, or the probability of rejecting the null hypothesis when it is actually true, is 0.0505 if the critical region is x > 185.

b) To find the boundary point of the acceptance region if alpha = 0.05, we need to find the critical value that corresponds to a type I error probability of 0.05.

To find the critical value, we can use the z-score formula:

z = (x - mean) / standard deviation

We can rearrange this formula to solve for x:

x = z * standard deviation + mean

Since we want the probability of getting a sample mean greater than x to be 0.05, we can use a z-table or a calculator to find the z-score that corresponds to a probability of 0.05 in a normal distribution. This z-score is approximately 1.645.

Substituting this value into the formula above, we get:

x = 1.645 * 6.3 + 175 = 185.095

Therefore, the boundary point of the acceptance region if alpha = 0.05 is approximately 185.095 millimeters.

Learn more about probability, here brainly.com/question/11234923

#SPJ4

The upper and the lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds is 224 and 166 metric tons respectively.

The volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table

Assuming that r(t) is increasing for all t in [0,6], a lower estimate is obtained by using left endpoints and an upper estimate is achieved by using right endpoints.  

Lower estimate:  r(0)(1)+r(1)(1)+r(2)(1)+r(3)(1)+r(4)(1)+r(5)(1)

                      = 2+12+20+36+44+52 = 166 metric tons

Upper estimate:  r(1)(1)+r(2)(1)+r(3)(1)+r(4)(1)+r(5)(1)+r(6)(1)

                      = 12+20+36+44+52+60 = 224 metric tons

Midpoint estimate:  r(1)(2)+r(3)(2)+r(5)(2)

                         = 24+72+104 = 200 metric tons

Therefore, the upper and the lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds is 224 and 166 metric tons respectively.

To learn more about estimates refer here

https://brainly.com/question/19426829

#SPJ4

No such c exist from 1 and hence mean value theorem fails, an example is given below.

Consider f(x)=[x] on [-1,1]

Then, f is not differentiable on x=0

Note that,

f'(x)=1  for x>0 and f'(x)=-1 for x<0

The Mean Value Theorem states that if a feature f is non-stop at the closed interval [a,b] and differentiable at the open interval (a,b), then there exists a factor c withinside the interval (a,b) such that f'(c) is same to the feature's common price of extrade over [a,b].

According to near value theorem we need,

a c (-1,1).

f'(c)= f(1)-f(-1)/1-(-1)

=|1|-|-1|/2

=1-1/2=0

i.e., f'(c)=0

While, no such c exist from 1 and hence mean value theorem fails.

To learn more about mean value theorem check the link below:

https://brainly.com/question/19052862

#SPJ4

The leftmost value on the 3rd level of the binary tree with given elements 47, 38, 66, 57, 19, 31, 45, 88 is 19

To build a binary tree first we have to insert 47 into the tree as the root of the tree. The read the next element if it is smaller than the root node, insert it as the left subtree and if it is larger than the root node, insert it as the subtree.

The next element is 38 which is smaller than 47 so it will become the left subtree. The next element is 66 which becomes the right subtree. The next element is 57 is greater than 47 and 38 so it becomes the right subtree below 38. Similarly we go ahead and build a binary tree to find the leftmost value at 3rd level of the binary tree.

To know more about binary tree here

https://brainly.com/question/13864209

#SPJ4

false,  {b}->{a} appears to hold with respect to the given instance.

A variable created in a class that has a unique copy, or instance, for each instantiated object of the class is known as an instance variable in class-based, object-oriented programming. Although not static, an instance variable resembles a class variable.

A variable specified within a class but outside of constructors, methods, or blocks is known as an instance variable. All the constructors, methods, and blocks in the class have access to instance variables, which are created when an object is instantiated. To the instance variable, access modifiers can be applied.

false,  {b}->{a} appears to hold with respect to the given instance.

To know more about instance visit:-

https://brainly.com/question/20533922

#SPJ4

x be the distance (in miles) between point p and where the boat lands on the lakeshore.x = (7 - 3)/(3/4) = 4.5 miles.The boat should be landed 4.5 miles down the shore from point p.

The woman needs to get to a town 7 miles down the shore from point P. She can row the boat 3 miles per hour, and walk 4 miles per hour. The boat needs to be landed 4.5 miles down the shore from point P so she can get to the town in the least time. To figure out this distance, we subtract the 3 miles between the island and point P from the 7 miles between the town and point P. This gives us 4 miles. We then divide 4 miles by the ratio of her rowing rate (3) to her walking rate (4) to get 4.5 miles. Therefore, the boat should be landed 4.5 miles down the shore from point P.

Learn more about distance here

https://brainly.com/question/28956738

#SPJ4

The scale factor of the geometric sequence 200, 100, 50, 25 is ½

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Therefore scale factor= new dimension/ original dimension.

In the sequence 200, 100, 50, 25...., as we take 200 as the original dimension and 100 as the new dimension. From these we can discover that the object is decreasing in shape

Therefore the scale factor = new dimension/ original dimension

scale factor = 100/200

scale factor = ½

therefore the scale factor of the sequence is ½

learn more about scale factor from

https://brainly.com/question/25722260

#SPJ1

When "twice the sum of a number and 3 equals three times the difference of the number and 3," the value of expression is 6.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.

Here,

let x be the number,

2x+3=3x-3

x=6

The value of expression is 6 when "twice the sum of a number and 3 is equal to three times the difference of the number and 3."

To know more about expression,

https://brainly.com/question/1859113

#SPJ4

To generate the most money, the stadiums might set the price at $11.50.A mathematical equation known as a demand function expresses consumer demand as a function of a product or service's pricing and .

The price that customers are prepared to pay and the amount that they're willing to purchase are generally correlated through a demand function. Since the profit function is the sum of these two amounts, this relationship can be converted into one.

m=5−836−30=−36=−1

This is the number of tickets sold that will maximize the revenue because the second derivative is, in fact, negative. Let's go back to the demand function to determine the appropriate ticket price.

R=−x+23\s−x+23=0x=23

R=−1\sp=−12(23)+23=11.5

To know more about demand function visit:

https://brainly.com/question/28198225

#SPJ4

Answer: 2/9 = 0.22

Step-by-step explanation: This is rounded to the nearest hundredth which is in the 2nd place after the decimal point.

Answer:

90%

Step-by-step explanation:

63 of 70 can be written as:

63/70

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

63/70 × 100/100 = (63 × 100/70) × 1/100 = 90/100

Therefore, the answer is 90%

If you are using a calculator, simply enter 63÷70×100 which will give you 90 as the answer.

A height with a z-score of 1 is the lowest, a height with a percentile rank of 80 percent is in the middle, and a height at the third quartile Q₃ is the highest.

A bell-shaped distribution is also known as a normal distribution. It is a symmetrical distribution where the mean, median, and mode are all equal. The distribution has two tails that extend out from the mean in either direction. A height with a z-score of 1 is the lowest because a z-score of 1 is one standard deviation below the mean. A height with a percentile rank of 80 percent is in the middle because it is the 80th percentile, meaning that 80 percent of the data is lower than it. A height at the third quartile Q₃ is the highest because it is the 75th percentile, meaning that 75 percent of the data is lower than it. In ascending order, the heights arranged are III, II, and I.

Learn more about z score here

https://brainly.com/question/15016913

#SPJ4

We may use the instructions provided to build a finite-state machine that simulates a vintage soda machine and can carry out the specified work.

Nickels (5 cents), dimes (10 cents), and quarters are all accepted by the machine (25 cents).

The states should be s, s1, s2, s3, s4, etc.

If we add a nickel to the machine, we move from state s to state s+1 and so on, and the process is the same for a dime and a quarter.

We can build the necessary finite-state machine to simulate an antique soda machine that takes nickels, dimes, and quarters by using x as the input button for soda pop.

A mathematical model of computation is called a finite-state machine (FSM), often known as a finite automaton or just a state machine.

It is an abstract machine that has a limited number of states that it can only be in at any given time. The FSM can change from one state to another in response to some inputs; this change is known as a transition. A set of states, an initial state, and the inputs that trigger each transition comprise an FSM.

To learn more about machine: https://brainly.com/question/388851

#SPJ4