solve the equation check the solution a/a^2-9+3/a-3=1/a+3

Answer:

The expression b/(a +b) does not exist when a = -b or b = -a

Step-by-step explanation:

The expression b/(a + b) does not exist if the denominator a + b = 0.

So, a = - b or b = -a.

So, the expression b/(a + b) does not exist when a = -b or b = -a.

When a = -b values, the denominator a + b = -b + b = 0. This will make the expression b/(a + b) = b/0 = ∞ which undefined or does not exist.

When b = -a values, the denominator a + b = a + (-a) = a - a = 0. This will make the expression b/(a + b) = -a/0 = -∞ which undefined or does not exist.

So the expression b/(a +b) does not exist when a = -b or b = -a

Answer:

The volume of a cone is 1/3 of the volume of the cylinder.

Step-by-step explanation:

The formula for a cylinder is:

V = bh

For a cone:

V = 1/3(bh)

If the radius of both are the same, then the area of the base is the same. The height is also constant, therefore:

The volume of a cone is 1/3 the volume of the cylinder.

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

Example to prove:

Given, radius 2 and height 15:

Cylinder: V = bh (b = πr²)

V = 4π × 15

V = 60π u³

Cone: V = 1/3 (bh)

V = 1/3 (4π × 15)

V = 20π u³

There are 2605 ways to choose a group of 7 people from a group of 8 adults and 7 children, with the condition that at most 6 adults can be selected.

To determine the total number of ways the group of 7 people can be chosen from a group of 8 adults and 7 children, with the condition that at most 6 adults can be selected, we need to consider different scenarios.

Scenario 1: Selecting all children (0 adults):

In this scenario, we choose all 7 people from the group of 7 children. The number of ways to do this is given by the combination formula:

C(7, 7) = 1

Scenario 2: Selecting 1 adult and 6 children:

In this scenario, we choose 1 adult from the group of 8 adults and 6 children from the group of 7 children. The number of ways to do this is given by the product of the number of ways to choose an adult and the number of ways to choose the children:

C(8, 1) * C(7, 6) = 8 * 7 = 56

Scenario 3: Selecting 2 adults and 5 children:

In this scenario, we choose 2 adults from the group of 8 adults and 5 children from the group of 7 children. The number of ways to do this is given by the product of the number of ways to choose 2 adults and the number of ways to choose the children:

C(8, 2) * C(7, 5) = 28 * 21 = 588

Scenario 4: Selecting 3 adults and 4 children:

In this scenario, we choose 3 adults from the group of 8 adults and 4 children from the group of 7 children. The number of ways to do this is given by the product of the number of ways to choose 3 adults and the number of ways to choose the children:

C(8, 3) * C(7, 4) = 56 * 35 = 1960

Adding up the number of ways from each scenario, we get the total number of ways to choose the group of 7 people:

1 + 56 + 588 + 1960 = 2605

Therefore, there are 2605 ways to choose a group of 7 people from a group of 8 adults and 7 children, with the condition that at most 6 adults can be selected.

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Answer: \(\sqrt{3}\) x 8 = 13.8564064606

Step-by-step explanation: The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3 (\(\sqrt{3}\)). Therefore, square root 3 (\(\sqrt{3}\)) is multiplied by the length (8 in our case) of either 6 faces of the cube.

Hope it helped!

Answer:

13.8564064606

Answer:

266.67 feet^2.

Step-by-step explanation:

The scale is 1:40.

That means that if the scale has a width of 4 inches, the room will have a width of 4 * 40 = 160 inches. 160 / 12 = 80 / 6 = 40 / 3 feet.

The length in the model is 6 inches, so the room has a length of 6 * 40 = 240 inches. 240 / 12 = 120 / 6 = 60 / 3 = 20 feet.

The area will then be (40 / 3) * 20 = 800 / 3 = 266.67 feet^2.

Hope this helps!

Answer:

A line traveling to the left with an open dot on x=1.

Explanation:

The inequality x < 1 basically means "less than 1." On number lines, the further left you go, the smaller the number becomes, and the further right you go, the larger the number becomes. So we know that because it's less or smaller than 1, then the line will be to the left. On the other hand, the inequality does not have a line under it to indicate a "less than or equal to 1," just "less than." Therefore, the dot is open. If there were a line under the inequality, then it would indicate "less than or equal to 1" and the dot would be closed.

Answer:

about 7.2 I think

Step-by-step explanation:

if his pay went up all the way to 770 it would be going up either 7.8 or 7.2

Answer:

11/14

Step-by-step explanation:

Answer:

11/14

Step-by-step explanation:

\(\frac{3}{7} *\frac{2}{2}+\frac{5}{14}*\frac{1}{1} \\\frac{6}{14} +\frac{5}{14} =\frac{11}{14}\)

Answer:

because

Step-by-step explanation:

when you make 16-2 it equals= 14

Answer:

yes

Step-by-step explanation:

the lines are perpendicular

Answer:

See below

Step-by-step explanation:

.2 of an hour   is     .2 * 60 min = 12 min

120 min / 10 times = 12 min per trip

The train takes 12 minutes to go around the museum once.

A mathematical arithmetic operation is multiplication. Moreover, it is the practice of repeatedly adding the same expression kinds.

Example: 2 x 3 means that 2 is multiplied by 3 or that 3 is multiplied by 2 times.

A toy train that travels the length of a train museum is present. In two hours, the train travels roughly ten times.

The error in the student's work is converting 0.2 hours to 20 minutes. 0.2 hours is equal to 12 minutes, not 20 minutes.

To correct the student's work, we can multiply 0.2 by 60 to convert it to minutes:

0.2 hours × 60 minutes/hour = 12 minutes

Therefore, it takes 12 minutes for the train to go around the museum 1 time.

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When comparing means of three or more conditions, an analysis of variance (ANOVA) should be used instead of multiple t-tests. This is because using multiple t-tests increases the risk of a type I error, where a significant difference is found when there is none. ANOVA controls for this by using a single test to determine if there is a significant difference between the means. Additionally, using multiple t-tests increases the risk of a type II error, where a significant difference is not found when there is one.

ANOVA is also more likely to detect statistical significance between the means because it takes into account the variability within each condition as well as the variability between conditions. This increases the power of the test and reduces the chances of missing a significant difference between the means.

When using ANOVA, the results can indicate that there are no differences between any of the population means (option a), that at least one of the three population means is different from another population mean (option b), that all three of the population means are different from each other (option c), or that one population mean is different from one of the other population means, but not the other population mean (option d).

Finally, ANOVA provides a measure of effect size, typically reported as r2, which indicates the proportion of variability in the data that can be attributed to the differences between the conditions. This can be useful in determining the practical significance of the results.

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Answer: 21 units²

Step-by-step explanation:

Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is \(\frac{1}{2}(a+b)h\), where a and b are the parallel sides and h is the height.

Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.

\(A=\frac{1}{2}(5+9)*3\)

\(A=\frac{1}{2}(14)*3\) [Adding in the parentheses]

\(A=7*3\) [Multiplying one-half by 14]

\(A=21\) [Multiplying 7 and 3]

The area is 21 units².

Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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Answer:

Press down the brake firmly and smoothly. ...

Don't brake and swerve the car at the same time. ...

Avoid using your transmission for quick stops. ...

Focus on where you want to go, not what you want to avoid.

The equation that represents the circle shown in the graph is:\((x - 2)^2 + (y + 1)^2 = 9.\)

What is circle ?

A circle is a shape in geometry that is defined as a closed curve that is formed by a set of points that are equidistant from a single fixed point called the center. The distance between any point on the circle and the center is called the radius of the circle.

The center of the circle appears to be at the point (2, -1) and the radius seems to be approximately 3 units.

Using the values of the center and radius, we can plug them into the general equation of a circle to obtain the equation that represents the circle:

\((x - h)^2 + (y - k)^2 = r^2\)

Substituting h = 2, k = -1, and r = 3, we get:

\((x - 2)^2 + (y + 1)^2 = 9\)

Therefore, the equation that represents the circle shown in the graph is:\((x - 2)^2 + (y + 1)^2 = 9.\)

Option D is the equation that represents the circle, which is\((x - 2)^2 + (y + 1)^2 = 9.\)

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Ratio compares two things. The length of the trail, in reality, is 6.75 km.

A scaling ratio helps us to compare two things.

Given to us

The scale on the map states that 2 centimeters represent 3 kilometers.

Length of the trail on the map, L = 4.5 cm = 0.045 m

As we know that 2 centimeters represent 3 kilometers. therefore,

\(\rm \dfrac{Map}{Real} = \dfrac{0.02\ m}{3000\ m}\)

We know that the Length of the trail on the map is 0.045 m,

\(\rm \dfrac{L}{L'} = \dfrac{0.02\ m}{3000\ m}\)

Substitute the value,

\(\rm \dfrac{0.045}{L'} = \dfrac{0.02\ m}{3000\ m}\\\\L' = 6750\ m\\\\L' = 6.750\ km\)

Hence, the length of the trail, in reality, is 6.75 km.

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The total number of possible dinner combinations are 15

What are Combinations?

The number of ways of selecting r objects from n unlike objects is calculated by combination. The formula for combination is

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the total number of dinner combinations be = T

Now ,

The values of Starters is represented in set = A

The values of Entree is represented in set = B

The values of Set A = { bread sticks , soup , salad }

The values of Set B = { beef , fish , chicken , shrimp , pork }

Now , the total combinations of possible selection of Starters = ³C₁

The total combinations of possible selection of Entree = ⁵C₁

So , the total number of dinner combinations T = total combinations of possible selection of Starters x total combinations of selection of Entree

And , the equation is

The total number of dinner combinations T = ³C₁ x  ⁵C₁

The total number of dinner combinations T = 3 x 5

The total number of dinner combinations T = 15

Therefore , the value of T is 15

Hence , The total number of possible dinner combinations are 15

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Answer:

Step-by-step explanation:

x^2 =63^2 +61^2 - 2(63)(61)cos142°

x^2= 13746.65

x= √(13746.65)

x≈ 117.246

x= 117

The measure of the acute angles in the right triangle are 10 and 80 degrees.

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.

The sum of angles in a right angle triangle is 180 degrees.  

The other measures of the right triangle are acute angles.

Any angle that measures greater than 0° and less than 90° is called an acute angle.

Hence, let's find the measure of the acute angles

let

x = measure of one acute angle

Hence,

x + 8x + 90 = 180

9x = 180 - 90

9x = 90

x = 90 / 9

x = 10

Therefore, the measure of the acute angles are 10 and 80 degrees.

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Answer:

no solutions

Step-by-step explanation:

I believe there are no solutions for these 2 equations.

Hope this helps!

Answer:

The answer is below

Step-by-step explanation:

Since 1000ml Of Dextrose 25% is needed to be produced from Dextrose 70%. Let us assume that x ml of Dextrose 70% is mixed with a Dextrose 5% to get 1000 ml of Dextrose 25%. Hence:

The amount of Dextrose 5% = 1000 ml - x ml = 1000 - x

25% of 1000 ml = 70% of x + 5% of (1000 - x)

25000 = 70x + 5000 - 5x

Simplifying gives:

65x = 25000 - 5000

65x = 20000

x = 308 ml

Therefore 308 ml of Dextrose 70% was mixed with 692 ml of Dextrose 5% to produce 1000 ml of Dextrose 25%.

Answer:

15

Step-by-step explanation:

The first term, a1, in the geometric series is -3.

What is Geometric Series?

A geometric series is a series for which the ratio of two consecutive terms is a constant function of the summation index. The more general case of a ratio and a rational sum-index function produces a series called a hypergeometric series. For the simplest case of a ratio equal to a constant, the terms have the form

To find the first term, a1, in a geometric series given the sum, Sn = 93, the common ratio, r = 2, and the number of terms, n = 5, we can use the formula for the sum of a geometric series:

Sn = a1 * (1 - r^n) / (1 - r)

Plugging in the given values, we have:

93 = a1 * (1 - 2^5) / (1 - 2)

Simplifying the expression:

93 = a1 * (1 - 32) / (-1)

93 = a1 * (-31)

Now we can solve for a1 by dividing both sides of the equation by -31:

a1 = 93 / -31

a1 = -3

Therefore, the first term, a1, in the geometric series is -3.

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The monthly payment for a bank loan assuming a one-year repayment period and 13.5% interest is To calculate the monthly payment for a bank loan, we can use the formula:

Monthly payment = Total cost / Number of months

Given that the total cost is $1,800 and the repayment period is one year (12 months), we can substitute these values into the formula:

Monthly payment = $1,800 / 12 = $

Now, let's calculate the total cost for the bank loan:

Total cost = Monthly payment * Number of months

Total cost = $ * 12 = $

For the add-on method of interest calculation with a one-year repayment period and 11.5% interest, the monthly payment is $ (main answer).
The add-on method of interest calculation involves adding the interest to the principal amount and then dividing it by the number of months.

Given that the total cost is $1,800 and the repayment period is one year (12 months), we can calculate the interest as follows:

Interest = Total cost * Interest rate

Interest = $1,800 * 11.5% = $

Now, let's calculate the new principal amount:

New principal amount = Total cost + Interest

New principal amount = $1,800 + $ = $

Finally, we can calculate the monthly payment:

Monthly payment = New principal amount / Number of months

Monthly payment = $ / 12 = $

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African Americans faced numerous challenges during the Civil Rights Movement.

The Civil Rights Movement, which spanned from the 1950s to the 1960s, aimed to secure equal rights and end racial segregation and discrimination in the United States. African Americans encountered significant challenges during this period. One of the key challenges was institutionalized racism, which permeated various aspects of society, including education, employment, housing, and voting rights. African Americans were subjected to Jim Crow laws, which enforced segregation and denied them equal treatment under the law. They faced violence, intimidation, and discrimination, particularly in the Southern states. Despite these obstacles, African Americans demonstrated resilience and determination in their pursuit of justice and equality. They organized peaceful protests, sit-ins, boycotts, and marches to demand their rights and challenge discriminatory practices. These efforts ultimately led to significant milestones in civil rights legislation, such as the Civil Rights Act of 1964 and the Voting Rights Act of 1965, which aimed to dismantle segregation and protect the voting rights of African Americans. The Civil Rights Movement remains an important chapter in American history, highlighting both the struggles and triumphs of African Americans in their fight for equality and justice.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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We can say with 90% confidence that the increase in proportion of people satisfied with their financial situation is between 1.05% and 6.71%.

To calculate the confidence interval for the increase in proportion of people satisfied with their financial situation, we need to first calculate the proportions for both years:

Proportion in year 1 = 478/2038 = 0.2342
Proportion in year 2 = 537/1967 = 0.2730

The increase in proportion is:
0.2730 - 0.2342 = 0.0388

To calculate the confidence interval, we can use the formula:
CI = (point estimate ± (critical value x standard error))

The point estimate is the increase in proportion we just calculated: 0.0388

The critical value can be found using a z-table for a 90% confidence level. The z-value for a 90% confidence level is 1.645.

The standard error can be calculated using the formula:
sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

where p1 and n1 are the proportion and sample size for year 1, and p2 and n2 are the proportion and sample size for year 2.

Plugging in the values, we get:
SE = sqrt[(0.2342(1-0.2342)/2038) + (0.2730(1-0.2730)/1967)] = 0.0174

Now we can plug in all the values to get the confidence interval:
CI = (0.0388 ± (1.645 x 0.0174)) = (0.0105, 0.0671)

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The probability that in 8 progeny plants, four or more plants will express the gene is approximately 0.892.

To find the probability that four or more plants will express the gene, we sum up the probabilities of these individual outcomes:P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8). Calculating these probabilities and summing them up will give you the final result.

To calculate the probability that in 8 progeny plants, four or more plants will express the gene, we can use the binomial probability formula.

The binomial probability formula is given by:

\(P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)\)

Where:

P(X = k) is the probability of getting exactly k successes

n is the total number of trials

k is the number of successful outcomes

p is the probability of success in a single trial

C(n, k) is the number of combinations of n items taken k at a time (given by n! / (k! * (n - k)!)

In this case, we want to find the probability of getting four or more plants expressing the gene in 8 progeny plants. Let's calculate it step by step:

\(P(X = 4) = C(8, 4) * 0.20^4 * (1 - 0.20)^(8 - 4)\\P(X = 5) = C(8, 5) * 0.20^5 * (1 - 0.20)^(8 - 5)\\P(X = 6) = C(8, 6) * 0.20^6 * (1 - 0.20)^(8 - 6)\\P(X = 7) = C(8, 7) * 0.20^7 * (1 - 0.20)^(8 - 7)\\P(X = 8) = C(8, 8) * 0.20^8 * (1 - 0.20)^(8 - 8)\)

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