Select the correct answer.
What are the zeros of the quadratic function represented by this graph?
6
21
-X
.
2
2
4
6
-21
W
-61
+
Ο Α. .
1 and 3
OB. -3 and -1
Ос.
-3 and 1
OD.
-1 and 3

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

Step-by-step explanation:

f(2) = 6        (what multiplies 2 to equal 6?)*2 = 6

It seems like x gets multiplied by three. Let's check the next one:

f(-1) = -3

Ah ha! We were right. Let's check one more time:

2 * 3 = 6

-1 * 3 = -3

f(x) just means what is f when x is any number. This function that we covered above is: f(x) = 3x

Answer:

t/7

Step-by-step explanation:

Since the ratio between the amount of water and the time should be the same, 84/12 = 7.

Hence, the ratio is t/7.

Hope this helped!

Answer: $4850

Step-by-step explanation:

The other information related to the question is:

Direct materials = $3.50

Direct labor = $1.10

Variable overhead = $0.45

Fixed overhead = $2.80

Total = $7.85

Based on the information given in the question, the increase in the profit will be calculated as the contribution from the 3000 extra units minus the worker's salary.

Contribution from 3000 units will be:

= (Selling price - Direct materials - Direct labor - Variable overhead) × 3000

= ($25 - $3.50 - $1.10 - $0.45) × 3000

= $19.95 × 3000

= $59850

Increase on Profit:

= $59850 - $55000

= $4850

1. Let us suppose the amount saved = s. 2. The inequality is 62 + s ≥ 100. 3. The value of s is: s ≥ 38. 4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.

A mathematical statement illustrating the relationship between two amounts or expressions that are not always equal is known as an inequality. To represent the connection between the two values, an inequality may employ a number of symbols, including (less than), > (greater than), (less than or equal to), or (greater than or equal to). In algebra and other branches of mathematics, inequalities are frequently used to indicate restrictions, such as limitations on a variable, and to address issues with variables or unknown numbers. An inequality's solution, which may be a range of values rather than a single value, is the collection of all values that meet the inequality.

1. Let us suppose the amount saved = s.

2. The inequality is 62 + s ≥ 100

3. Solving for s we have:

62 + s ≥ 100

s ≥ 100 - 62

s ≥ 38

On the number line, all values greater than or equal to 38 would satisfy this inequality.

4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.

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Answer:

28

After being wrong the questionnaire told me the ans.

Thank you

Step-by-step explanation:

Stay safe, stay healthy and blessed.

Have a great day !

Thank you

Answer: 1100

Step-by-step explanation:

Hope I'm correct!

Answer:

s = 4 m

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 16 m² , then

s² = 16 ( take square root of both sides )

s = \(\sqrt{16}\) = 4 m

Answer:

4m

Step-by-step explanation:

All the sides of a square are equal lengths. So 2 numbers that are the same must equal 16m^2.

A number times itself is known as a square number. The value of this square number is 16 m².

It can be shown like this:

a²= 16 m² or a×a = 16 m²

The reverse of squaring numbers is square root. To find the value of one side you can do √16. √16 = 4. We can check this by substituting (replacing) 4 in the place of 'a' to see if the answer is 16.

a×a = 16 m²

4 × 4 = 16

Therefore, the length of one side of the square equals to 4m.

Answer: linear combo of terms involving x & y, with respective numbers determining their contribution to the expression

The probability of contracting an illness is 0.0475.

According to our question-

D: The patient has the illness

ND: the individual without the disease

TD: The results of the test show the patient has the illness.

P(D) will therefore equal 0.001 since only 0.001 of the population is affected by the disease.

P(ND) = 0.991

Because the test successfully identifies a patient with the condition 99% of the time, P(TD/D) = 0.99.

P(TD/ND) = 0.02 because the test indicates that a healthy person contracts the disease 2% of the time.

We are seeking for P(D|TD) and P(ND|TD), respectively.

According to the Bayes formula, 0.00099/0.00099+0.01982 = 0.00099/0.02081 = 0.0475 = (0.99*0.001)/(0.99*0.001)+(0.02*0.991)

And, \s = 1 - \s = 1 - 0.0475 \s = 0.9525

Therefore,

The likelihood of having an illness is 0.0475.

The likelihood of not having any sick people is 0.9525.

Hence, The probability of contracting an illness is 0.0475.

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Answer:

313

Step-by-step explanation:

First of all you need to find out the surface of the front.

So you need to do 29cm + 29cm = 58cm.

You then have to do 22cm + 22cm = 44cm

So if you add those two numbers up you will get the front surface which is 102cm.

Next, you need to find the surface of the side.

So you need to do 20cm + 21cm = 41cm

After that, you need to find the back surface.

So you need to add 22cm +22cm = 44cm

Then you have to do 21cm + 21cm = 42cm

Add those two together to get 86cm

Then, you need to do the bottom of the shape.

So you need to add 22cm + 22cm (again) = 44cm

You then need to do 20cm + 20cm = 40cm

Add those together to get 84cm

Finally, you need to add 84cm + 86cm + 102cm + 41cm = 313cm

So your answer is:

Surface: 313

Please, send me a picture of your question

Answer:

Dan paid $80 for his luggage

Step-by-step explanation:

$400

-$320

= $80

Jake wants to go to a lil uzi vert concert. A lil uzi vert concert ticket cost $320. The backstage pass is only $400, so Jake pays for that instead. He later figured out that he wanted to lose 50 pounds before the concert in 6 months and for every time he goes to the gym he has to pay $10 he only goes to the gym 8 times and his bank account has $500 on it. How much money did he have left over after going to the gym 8 times? - PS don't worry about this question its just a fake scenario i made for the second part of your question hope this helps!!!

The dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

To determine the dimensions of the can that minimize the cost of the material, we need to find the dimensions that minimize the surface area of the can.

Let's assume the can has a height of h and a radius of r.

The volume of a cylinder is given by:

V = πr²h

Given that the can should hold 500 cubic centimeters of liquid, we have:

500 = πr²h

We want to minimize the cost, which depends on the surface area of the can.

The surface area of the can is the sum of the areas of the top, bottom, and side surfaces.

The cost of the top and bottom surfaces is twice as expensive per square centimeter as the sides.

Let's assume the cost per square centimeter of the sides is c, so the cost per square centimeter of the top and bottom surfaces is 2c.

The surface area of the sides of the cylinder is given by:

A_sides = 2πrh

The surface area of the top and bottom surfaces (each) is given by:

A_top_bottom = 2πr²

The total surface area (cost) is given by:

Cost = 2(2c)A_top_bottom + cA_sides

= 4cπr² + 2c(2πrh)

= 4cπr² + 4cπrh

To minimize the cost, we need to minimize the surface area. To do this, we can express the surface area in terms of a single variable, such as the radius (r) or the height (h).

From the volume equation, we have:

h = 500 / (πr²)

Substituting this value of h into the surface area equation, we get:

Cost = 4cπr² + 4cπr(500 / (πr²))

= 4cπr² + 2000c/r

Now, we can take the derivative of the cost function with respect to r, set it equal to zero, and solve for r to find the critical points:

dCost/dr = 8cπr - 2000c/r² = 0

8cπr = 2000c/r²

8πr³ = 2000

r³ = 250 / π

r ≈ 6.324

Now, we can substitute this value of r back into the equation for h:

h = 500 / (π(6.324)²)

≈ 3.984

So, the dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

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According to the Ratio Test, if the limit of the ratio of consecutive terms is less than 1, the series converges. In this case, the limit is 0, which is less than 1. Therefore, the series ∑(n^3/n!) from n=1 to infinity converges.

To determine the convergence or divergence of the series ∑(n^3/n!) from n=1 to infinity, we can use the Ratio Test.

Step 1: Calculate the ratio of consecutive terms, a_n+1/a_n:
a_n+1/a_n = ((n+1)^3/(n+1)!)/(n^3/n!)

Step 2: Simplify the expression:
a_n+1/a_n = ((n+1)^3/(n+1)!)*(n!/(n^3)) = ((n+1)^3/((n+1)(n!))) * (n!/(n^3)) = ((n+1)^3/(n^3(n+1)))

Step 3: Further simplify the expression:
a_n+1/a_n = (n+1)^2/(n^3)

Step 4: Find the limit as n approaches infinity:
lim (n→∞) (n+1)^2/(n^3) = 0

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The odds of the event happening are: d. 3-to-1.

The odds of an event happening are defined as the ratio of the probability of the event happening to the probability of the event not happening. So, in this case, the odds of the event happening are:

odds of happening = probability of happening / probability of not happening

odds of happening = 0.75 / 0.25

odds of happening = 3

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a mathematical concept that quantifies the chance of a particular outcome or set of outcomes in a random experiment. Probability is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. Probability theory is widely used in many fields, including mathematics, statistics, physics, finance, and engineering, to analyze and model uncertain events and make predictions based on available data.

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The correlation coefficient, denoted as r, is a measure of the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.

To decide if the correlation coefficient is close enough to ± 1 to declare that there is a correlation, we can use the following guidelines:

- If r is close to 0, it indicates that there is little to no correlation between the two variables.
- If r is between 0.1 and 0.3 (or -0.1 and -0.3), it indicates a weak positive (or negative) correlation.
- If r is between 0.3 and 0.7 (or -0.3 and -0.7), it indicates a moderate positive (or negative) correlation.
- If r is between 0.7 and 1 (or -0.7 and -1), it indicates a strong positive (or negative) correlation.

Therefore, if the correlation coefficient is close to ± 1, we can declare that there is a strong correlation between the two variables. However, it is important to note that correlation does not imply causation, and other factors should also be considered before drawing any conclusions.

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If the correlation coefficient is close to +1 or -1, we can declare that there is a strong correlation between the two variables. If the correlation coefficient is close to 0, we can declare that there is a weak or no correlation between the two variables.

To decide if the correlation coefficient is close enough to ± 1 to declare that there is a correlation, we can use the following guidelines:

- A correlation coefficient of +1 or -1 indicates a perfect linear relationship between two variables.
- A correlation coefficient close to +1 or -1, such as +0.9 or -0.9, indicates a strong linear relationship between two variables.
- A correlation coefficient close to 0, such as +0.2 or -0.2, indicates a weak linear relationship between two variables.
- A correlation coefficient of 0 indicates no linear relationship between two variables.

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Answer: -2x²+2x-10

Step-by-step explanation:

Rephrase the expression

Subtract 4x²-7x+6 from 2x²-5x-4

(2x²-5x-4)-(4x²-7x+6)

Expand parenthesis

2x²-5x-4-4x²+7x-6

Put like terms together

(2x²-4x²)+(7x-5x)-(4+6)

Combine like terms

-2x²+2x-10

Hope this helps!! :)

Please let me know if you have any questions

Answer:

sector GPH = 16π yd²

Step-by-step explanation:

area of full circle = πr² = (π)(12²) = 144π yd²

area of 40° segment = (40/360)(144π) = 16π yd²

If the total value of his change is 620 cents, the man has 12 dimes and 20 quarters in his pocket.

Let's assume that the man has x dimes and y quarters in his pocket. We know that he has 32 coins in total,

x + y = 32.

We also know that the total value of his change is 620 cents, which can be expressed as

10x + 25y = 620.

To solve for x and y, we can use either substitution or elimination. Let's use substitution. Solving the first equation for x, we get

x = 32 - y.

Substituting this into the second equation, we get

10(32 - y) + 25y = 620

Simplifying this equation, we get

320 - 10y + 25y = 620

which yields

15y = 300.

Therefore, y = 20, and x = 32 - 20 = 12.

So the man has 12 dimes and 20 quarters in his pocket. We can check that this is correct by verifying that

12(10) + 20(25)

= 120 + 500

= 620.

In summary, we can solve the problem by setting up a system of equations, either using substitution or elimination to solve for the variables, and then checking our answer to make sure it is correct.

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Answer: \(12\sqrt{5}\)

Step-by-step explanation:

\(3\sqrt{88}\)

88 can be rewritten as 8 x 10 and 8 can be rewritten as \(2^2*2\) making a 2 come out of the root.

\(3\sqrt{2^2*2*10}\\ 3*2\sqrt{2*10}\\6\sqrt{2*10}\)

10 can be rewritten as 2 x 5.

\(6\sqrt{2*2*5}\)

2*2 can also be rewritten as \(2^2\) making a 2 come out of the root.

\(6\sqrt{2^2*5}\\ 6*2\sqrt{5}\\ 12\sqrt{5}\)

We can't keep simplifying the root.

Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.

Dilation is a non rigid transformation and does not produce congruent figures.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.

Dilation is a non rigid transformation and does not produce congruent figures.

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Answer:

3. y = 2x - 2

4. y = \(\frac{4}{3}x-1\)

Step-by-step explanation:

3. Slope = 2

Y-intercept = -2

4. Slope = \(\frac{4}{3}\)

Y-intercept = -1

Answer:

3). y = 2x - 2

4). y = (4/3)x - 1

Step-by-step explanation:

3).

First find the slope

(y2 - y1) / (x2 - x1)  or rise/run

(0 - (-2)) / (1 - 0) = 2

2 is your slope

Now use the equation below for using coordinates for finding slope intercept form.

y - y1 = m(x - x1)

y1 = y number of given coordinate

x1 = x number of given coordinate

m = slope

y - 0 = 2(x - 1)

Distribute

y - 0 = 2x + (-2)

Get y by itself by adding 0 to both sides.

y - 0 = 2x + (-2)

  +0           +0

y = 2x - 2

4).

Repeat the same process for 4 as done in 3

Find the slope

(y2 - y1) / (x2 - x1)  or rise/run

(3 - (-1)) / (3 - 0) = 4/3

4/3 is your slope

Now use the equation below for using coordinates for finding slope intercept form.

y - y1 = m(x - x1)

y1 = y number of given coordinate

x1 = x number of given coordinate

m = slope

y - 3 = (4/3)(x - 3)

Distribute

y - 3 = (4/3)x + (-4)

Get y by itself by adding 3 to both sides.

y - 3 = (4/3)x + (-4)

  +3                  +3

y = (4/3)x - 1

Answer:

k = 5

Explanation:

Answer:

K = 5

Step-by-step explanation:

Up so it must be positive and 5 because it says 5

The given statement regarding the GDP of major economies of the world is False.

To determine the accuracy of this statement, we would need to gather data on the real GDP per capita growth rates of major economies between 1982 and 2009 and compare them. Without this data, we cannot definitively say whether the statement is true or false. However, based on historical trends and current economic data, it is unlikely that Italy had the highest growth rate of real GDP per capita during this time period.

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(5000 - 4000)/4000 x 100 = (1000/4000) x 100 = 25%

hope this help! ^^

The amount of Gatorade that Marcus would drink while walking 12 miles depends on several factors such as his personal preference, level of exertion, and the weather conditions.

However, a general rule of thumb is to drink about 8 ounces of fluid (water or sports drink) for every 20 minutes of exercise. If we assume that Marcus takes about 2 hours to walk 12 miles, he would be walking for 120 minutes, and he would need to drink about 48 ounces (8 ounces x 6 cycles of 20 minutes) of fluid during his walk. Therefore, Marcus would drink about 48 ounces of Gatorade (or any other fluid) during his 12-mile walk.

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......,....................................

Answer:

-1/35

Step-by-step explanation:

* means multiply

because of pemdas you should do three multiplication parts first

(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)

1/20 - 3/12 + 6/35

3/60 - 15/60 + 6/35

-12/60 + 6/35

-1/5 + 6/35

-7/35 + 6/35

-1/35

Answer:

3/140

Step-by-step explanation:

1/4 × 2/5 + (-1/6) × 3/2 + 3/7 × 2/5 ​=

= 2/20 - 3/12 + 6/35

**********************************************

We need the LCD of 20, 12, 35.

20 = 2^2 * 5

12 = 2^2 * 3

35 = 5 * 7

LCD = 2^2 * 3 * 5 * 7 = 420

**********************************************

= 42/420 - 105/420 + 72/420

= 9/420

= 3/140

The formula for the final cost, in terms of the original price y, is:

c(y) = y*(0.88)*(1.03)

Let's define y as the original price of the DVD.

We first apply a discount of the 12% of the price, so the new cost will be:

c(y) = y*(1 - 12%/100%)

c(y) = y*(1 - 0.12)

Then we apply a tax of the 3%, this in increase, then we can write this as:

c(y) = y*(1 - 0.12)*(1 + 3%/100%)

c(y) = y*(1 - 0.12)*(1  + 0.03)

c(y) = y*(0.88)*(1.03)

That is the formula that we could use to determine the final cost.

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