we want to factor the following expression:
x^4+10x+25
which pattern can we use to factor the expression?
U and V are either constant integers or single-variable expressions. ​

Given the function f(x) defined as:

The average value on the interval [1, 4] is given by:

Evaluating the function at x = 4 and x = 1:

Using these values for the average value of f:

Answer:

A

Step-by-step explanation:

With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.

Answer:

A = 5 ounces

B = 1 ounces

C = 4 ounces

Step-by-step explanation:

The 3 foods contain exactly 1800 calories but food A is 100 calories, food B is 500 calories and food C is 200 calories. Thus;

100A + 500B + 200C = 1800 - - - (eq 1)

The 3 meals allows exactly 75 grams of protein while A is 5 grams, B is 6 grams, C is 11 grams.

Thus;

5A + 6B + 11C = 75 - - - (eq 2)

The 3 meals allows exactly 5650 milligrams of vitamin C while A is 400 mg, B is 2050 mg and food C is 400 mg. Thus;

400A + 2050B + 400C = 5650 - -(eq 3)

Solving the 3 equations simultaneously online, we have;

A = 5 ounces

B = 1 ounces

C = 4 ounces

Food A is 5 ounces, Food B is 1 ounce, and Food C is 4 ounces and this can be determined by forming the linear equation in three variables.

Given :

Let the total amount of Food A be 'A', total amount of Food B be 'B', and the total amount of Food C be  'C'.

The linear equation that represents total calories in each food is:

100A + 500B + 200C = 1800  

\(\rm A =\dfrac{ 1800 - 500B-200C}{100}\)      

\(\rm A =18 - 5B-2C\)       --- (1)

The linear equation that represents total protein in each food is:

5A + 6B + 11C = 75    ---- (2)

The linear equation that represents total Vitamin C in each food is:

400A + 2050B + 400C = 5650   --- (3)

Now, substitute the value of 'A' in equation (2).

\(\rm 5(18-5B-2C)+6B+11C=75\)

Simplify the above equation.

90 - 25B - 10C + 6B + 11C = 75

C - 19B = -15

C = 19B - 15     ---- (4)

Now, substitute the value of 'C' in equation (1).

A = 18 - 5B - 2(19B - 15)

A = 18 - 5B - 38B + 30

A = 48 - 43B  --- (5)

Now, substitute the value of A and C obtains in equations (4) and (5) in equation (3).

A = 5 ounces

B = 1 ounce

C = 4 ounces

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Answer:

0.45 = 45% probability that the member uses the golf course but not the tennis courts

Step-by-step explanation:

I am going to solve this question using the events as Venn sets.

I am going to say that:

Event A: Uses the golf courses.

Event B: Uses the tennis courts.

5% use neither of these facilities.

This means that \(P(A \cup B) = 1 - 0.05 = 0.95\)

75% use the golf course, 50% use the tennis courts

This means, respectively, by:

\(P(A) = 0.75, P(B) = 0.5\)

Probability that a member uses both:

This is \(P(A \cap B)\). We have that:

\(P(A \cap B) = P(A) + P(B) - P(A \cup B)\)

So

\(P(A \cap B) = 0.75 + 0.5 - 0.95 = 0.3\)

What is the probability that the member uses the golf course but not the tennis courts?

This is \(P(A - B)\), which is given by:

\(P(A - B) = P(A) - P(A \cap B)\)

So

\(P(A - B) = 0.75 - 0.3 = 0.45\)

0.45 = 45% probability that the member uses the golf course but not the tennis courts

Step-by-step explanation:

I hope this answer is helpful ):

Answer: 11. Is A

Step-by-step explanation:

Answer:

30 square units

Step-by-step explanation:

split shape into other shapes you know how to find the areas of.

the top half is made of 2 triangles and a rectangle, and the bottom half is one large rectangle

A minimum population size of approximately 7373 to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100.

To calculate the minimum population size required to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100, we can use the following formula:

n = [(z-value × SD) / ME]²

Where:

n = the minimum sample size required

z-value = the critical value for the desired confidence level (99% in this case)

SD = the known standard deviation (100 in this case)

ME = the desired margin of error (3 in this case)

First, we need to determine the z-value for a 99% confidence level. Using a standard normal distribution table, we find that the z-value for a 99% confidence level is approximately 2.576.

Substituting the values into the formula, we get:

n = [(2.576 × 100) / 3]²

Simplifying this expression, we get:

n = 7373.08

Therefore, we would need a minimum population size of approximately 7373.

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Answer:

A

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 2 and (a, b) = (3, 1 ), thus

y - 1 = 2(x - 3) → A

The equation of the line with slope 2 that passes through (3, 1) is \((y-1)=2(x-3)\) and this can be determined by using the one-point slope form.

Given :

The line with slope 2 that passes through (3, 1).

The following steps can be used in order to determine the equation of the line with slope 2 that passes through (3, 1):

Step 1 - The one-point form of the line can be used in order to determine the equation of the line with slope 2 that passes through (3, 1).

Step 2 - The equation that shows one-point form is given below:

\((y-y_1)=m(x-x_1)\)

where m is the slope and \((x_1,y_1)\) is the point on the line.

Step 3 - Substitute the values of the known terms in the above equation.

\((y-1)=2(x-3)\)

Therefore, the correct option is A).

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The Area οf the shaded pοrtiοn is given by (16 π -32) inch², the cοrrect οptiοn is A.

A circIe is a rοund shaped figure whοse aII pοints Iie in οne pIane and the distance between the center οf the circIe and aII the pοints οn the circIe is cοnstant.

The area οf the shaded pοrtiοn is equaI tο the difference οf the area οf the arc and  Area οf the TriangIe.

Area οf an Arc =(θ /360) × π r²

Area = (90/360) × π × (8)²

Area οf the arc = 16 π in²

Area οf the triangIe = (1/2) × base × height

Area οf the triangIe = (1/2) × 8 × 8 = 32 in²

Area οf the shaded pοrtiοn = (16 π -32) inch²

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Answer:

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

As per given drawing PQ is the segment bisector of XY.

The point W is the midpoint of XY. As per property of midpoint, XW and WY have equal length.

XW = 13 units, hence:

Answer:

35

Step-by-step explanation:

(-5) - (-4 - 32 - 4)

-5 - (-40)

-5 + 40 =35

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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The expected value of the number of upgrades selected is 1.04.

The given probability mass function provides the probabilities for the number of upgrades purchased per customer. We are asked to find the expected value, which is a measure of central tendency in probability theory. To do this, we need to multiply each possible value of upgrades by its probability and then sum them up.

First, we need to figure out the value of f(3). We know that the sum of all probabilities in a probability mass function is 1. Therefore, we can use the given probabilities to calculate f(3) as follows:

1 = f(0) + f(1) + f(2) + f(3)

1 = 0.50 + 0.20 + 0.06 + f(3)

f(3) = 1 - (0.50 + 0.20 + 0.06)

f(3) = 0.24

Now that we know the value of f(3), we can calculate the expected value as follows:

E(X) = (0 x 0.50) + (1 x 0.20) + (2 x 0.06) + (3 x 0.24)

E(X) = 0 + 0.20 + 0.12 + 0.72

E(X) = 1.04

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Answer:

-1

Step-by-step explanation:

plug in y, subtract 12 from seven, divide -5 by 5

The values of x and y are -1 and 4 respectively.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given are a system of linear equations.

5x + 3y = 7

y = 4

We already have the value of y as 4.

Substituting that value of y = 4 in the first equation 5x + 3y = 7, we get,

5x + (3 × 4) = 7

5x + 12 = 7

Subtracting both sides by 12, we get,

5x + 12 - 12 = 7 - 12

5x = -5

Dividing both sides by 5, we get,

5x / 5 = -5 / 5

x = -1

Hence the value of x is -1 and the value of y is 4.

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The mass, in grams, of substance Y is given the mass of substance x is 1.22 x 10^-6

Standard form is used to condense big numbers into smaller numbers. In order to write a number in standard form, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

In order to determine the mass, multiply 6.10 by 2 and add 2 to -7

6.10 x 2 = 12.2 = 1.22 x 10^-6

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Answer:

Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.

For the larger box:

Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²

Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)

For the smaller box:

Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²

Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.

Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)

The difference in cost between the larger and smaller boxes is:

20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)

The percentage savings can be calculated as follows:

Percentage savings = (difference in cost / cost of larger box) * 100%

= (5.33718 / 20.55986) * 100%

= 25.98%

Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.

The expected value of x is (m+1)/2, and m must be a positive integer.

The expected value of x is the average value of x that we would expect to get if we selected an integer from the set {1, 2, ..., m} many times. To find the expected value of x, we multiply each possible value of x by its probability of being selected and then sum these products. In this case, each integer in the set {1, 2, ..., m} has an equal probability of being selected, so the expected value is (1 + 2 + ... + m) / m = (m(m+1)) / 2m = (m+1) / 2. So the expected value of x is (m+1)/2, and m must be a positive integer.

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Answer:

Step-by-step explanation:

Statements                                 Reasons

DA  ≅ WG                                   Given

WA ≅ DG                                    Given

DW ≅ WD                                  Reflexive property

ΔDAW ≅ ΔWGD                        SSS

Answer:

\(10 = 2x - 20 \\ 10 + 20 = 2x \\ \frac{30}{2} = \frac{2x}{2} \\ 15 = x\)

The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.

Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.

If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.

Therefore, the parabola x = √(y - 9) opens upwards.

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1)  \(\frac{30}{75}=\frac{100}{x}\) and Number of orders on Monday = 250

2) \(\frac{100}{15}=\frac{x}{12}\) and percentage of amount She spends = 80%.

A percentage is created when twο ratiοs are equal tο οne anοther. We write prοpοrtiοns tο cοnstruct equivalent ratiοs and tο resοlve unclear values. a cοmparisοn οf twο integers and their prοpοrtiοns. Accοrding tο the law οf prοpοrtiοn, twο sets οf given numbers are said tο be directly prοpοrtiοnal tο οne anοther if they grοw οr shrink in the same ratiο.

1) Cοffee οrder thrοugh app = 30%

Cοffee οrder thrοugh app οn Mοnday = 75

Nοw tοtal οrder οn Mοnday = x.

Tοtal percentage οf οrder = 100%.

Nοw using prοpοrtiοn,

=> \(\frac{30}{75}=\frac{100}{x}\)

=> x = \(\frac{100\times75}{30}\)

=> x = 250.

2) Payment for completing chores per week 100% = $15

Cost of video game x% = $12

Now using proportion,

=> \(\frac{100}{15}=\frac{x}{12}\)

=> \(x = \frac{100\times12}{15}\)

=> x = 80%.

Hence the answers are,

1)  \(\frac{30}{75}=\frac{100}{x}\) and Number of orders on Monday = 250

2) \(\frac{100}{15}=\frac{x}{12}\) and percentage of amount She spends = 80%.

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The number 842 is the number whose digit 4 is ten times larger than in the number 384

To solve the problem, we need to find a number in which the digit 4 is ten times larger than in the number 384.

In the number 384, the digit 4 is in the ones place, which means that its value is 4.

To find a number in which the digit 4 is ten times larger, we need to find a number in which the digit 4 is in the tens place and its value is 10 times larger than 4, which is 40.

The only answer option that fits this description is 842. In this number, the digit 4 is in the tens place and its value is 40, which is ten times larger than its value in the number 384.

Therefore, the correct answer is 842.

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Answer: 5on x axis 2 on the y axis

Answer:

The answer would be (5,2)

:D Have a Great Day :D

Answer:

-6x²

36

Step-by-step explanation:

1 / (1 + 6x²) = 1 / (1 − r)

Therefore, r = -6x².

The third term, r², is 36x⁴.

Let's draw the situation.

Based on the sum of segments property, we can define the following equation.

Replacing the given expressions, we have

Let's solve for x

We use this value to find BC.

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Check the picture below.