Standard Form Instructions: Write the polynomial expression in Standard Form -6-7x^(2)+8x^(5) Standard Form:

The number of bacteria or the number of all the other animals in the table put together is 7.8 x 10⁶.

To compare the number of bacteria to the number of all other animals in the world, we need to use some mathematical estimates. It's important to note that it's almost impossible to count the exact number of bacteria and animals in the world since they are found in vast numbers and diverse environments.

According to some scientific estimates, the number of bacteria on Earth is around 5 x 10³⁰, which is a massive number. In comparison, the total number of all other animals, including insects, birds, and mammals, is estimated to be around 7.8 x 10⁶.

In conclusion, the number of bacteria is much greater than the number of all other animals in the world. Although bacteria are tiny microorganisms, they are present in vast numbers and can be found in almost every environment.

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To solve the equation x^(2)-5x-5=0 using the quadratic formula, we can use the formula x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a=1, b=-5, and c=-5.

Plugging in the values into the formula, we get:

x = (-(-5) ± √((-5)^(2)-4(1)(-5)))/(2(1))

Simplifying the equation, we get:

x = (5 ± √(25+20))/2

x = (5 ± √45)/2

x = (5 ± 3√5)/2

Therefore, the solution set in exact simplest form is x = (5 ± 3√5)/2.

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The sale price of a pair of dress shoes originally at $69.98 with a 25% discount will be $52.49.

To find the sale price, you need to calculate the discount amount and subtract it from the original price.

Step 1: Find the discount amount by multiplying the original price by the discount percentage.
$69.98 x 0.25 = $17.49

Step 2: Subtract the discount amount from the original price to get the sale price.
$69.98 - $17.49 = $52.49

Therefore, the sale price of the dress shoes will be $52.49.

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It is true that the quotient of two integers will always result in a rational numbers, as the quotient of two integers is in fact a fraction.

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(a) Stratified random sampling ensures a representative sample, and Ys is an unbiased estimate of the population mean y.

(b) Proportional allocation allocates sample size in each stratum proportionally to its size, while optimum allocation determines sample size based on variance and cost in stratified random sampling.

(a) Stratified random sampling is a method of sampling that involves dividing the population into smaller groups or strata, and then randomly selecting a sample from each stratum. This is done to ensure that the sample is representative of the population as a whole. The formula for the expected value of the sample mean, E(Ys), in stratified random sampling is:
E(Ys) = Σ wi * E(Yi)
where wi is the weight of the ith stratum, and E(Yi) is the expected value of the sample mean in the ith stratum.
Since Ys is an unbiased estimate of the population mean y, we can prove that E(Ys) = y by substituting y for E(Yi) in the formula:
E(Ys) = Σ wi * y
= y * Σ wi
= y * 1
= y
Therefore, E(Ys) = y, proving that Ys is an unbiased estimate of the population mean y.

(b) Proportional allocation is a method of allocating the sample size in stratified random sampling, where the sample size in each stratum is proportional to the size of the stratum in the population.

This ensures that each stratum is represented in the sample in proportion to its size in the population.

Optimum allocation is another method of allocating the sample size in stratified random sampling, where the sample size in each stratum is determined based on the variance of the stratum and the cost of sampling from the stratum.

This ensures that the sample size in each stratum is optimized to minimize the variance of the sample mean and the cost of sampling.

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The interval that contains a local minimum for this function is (0,2).

A local maximum is present on the graph of the function y = f(x) at the location where the graph shifts from increasing towards decreasing.

Thus, over the span, a local minimum happens (0,2)

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The table for the function is given:

The solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

To solve the inequality 6x + 9 ≥ −(x − 9), we need to first distribute the negative sign on the right side of the inequality. This gives us:

6x + 9 ≥ -x + 9

Next, we need to isolate the variable on one side of the inequality. We can do this by adding x to both sides and subtracting 9 from both sides:

7x ≥ 0

Finally, we can divide both sides by 7 to solve for x:

x ≥ 0

Now, we can write the solution set in interval notation. Since x is greater than or equal to 0, the solution set is [0, ∞).

So, the solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

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The monthly house payment will be $375.84. The annual payment  for A farmer that purchased 265 acres of land for $4,300/acre  will be $75,436.20. The annual payment  of  Larry purchased a new combine that cost $240,500will be $64,514.88.

To calculate the monthly house payment for a home loan of $55,000 at 5.25% APR for 20 years, we can use the formula:

M = P * (r / (1 - (1 + r)^(-n)))

Where M is the monthly payment, P is the principal amount, r is the monthly interest rate, and n is the number of monthly payments.

In this case, P = $55,000, r = 5.25% / 12 = 0.004375, and n = 20 * 12 = 240.

Plugging in these values, we get:

M = $55,000 * (0.004375 / (1 - (1 + 0.004375)^(-240)))

M = $375.84

Therefore, the monthly house payment will be $375.84.

#2
To calculate the annual payment for a loan of 265 acres of land at $4,300/acre with a 25% down payment and 6.75% APR over 20 years, we can use the same formula as above, but with different values for P, r, and n.

In this case, P = 265 * $4,300 * (1 - 0.25) = $845,625, r = 6.75% / 12 = 0.005625, and n = 20 * 12 = 240.

Plugging in these values, we get:

M = $845,625 * (0.005625 / (1 - (1 + 0.005625)^(-240)))

M = $6,286.35

Since this is the monthly payment, we can multiply it by 12 to get the annual payment:

A = $6,286.35 * 12 = $75,436.20

Therefore, the annual payment will be $75,436.20.

#3
To calculate the annual payment for a loan of $240,500 for a new combine with a rebate of $4,500, a trade-in of $9,500, and a down payment of $5,000 at 8% APR over 4 years, we can use the same formula as above, but with different values for P, r, and n.

In this case, P = $240,500 - $4,500 - $9,500 - $5,000 = $221,500, r = 8% / 12 = 0.006667, and n = 4 * 12 = 48.

Plugging in these values, we get:

M = $221,500 * (0.006667 / (1 - (1 + 0.006667)^(-48)))

M = $5,376.24

Since this is the monthly payment, we can multiply it by 12 to get the annual payment:

A = $5,376.24 * 12 = $64,514.88

Therefore, the annual payment will be $64,514.88.

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To compare fractions using equivalent fractions, we need to find a common denominator, convert each fraction to an equivalent fraction with that denominator, and then compare the numerators directly.

To compare fractions 3/4 and 7/12 using equivalent fractions, we need to find a common denominator for both fractions. A common denominator is a number that is divisible by all the denominators of the fractions being compared. In this case, the least common denominator (LCD) for 4 and 12 is 12.

To convert 3/4 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 3. This gives us the equivalent fraction of 9/12.

To convert 7/12 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 1. This gives us the equivalent fraction of 7/12.

Now that both fractions have the same denominator, we can compare them directly. We can see that 9/12 is greater than 7/12 since 9 is greater than 7. Therefore, 3/4 is greater than 7/12.

This method allows us to compare fractions with different denominators and make accurate comparisons based on the relative size of the numerators.

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The second largest share of the three entrepreneurs is $291,666.68.

To calculate the second largest share of the three entrepreneurs, we need to first find the total ratio by adding the three individual ratios: 3 + 4 + 5 = 12.

Next, we can find the value of one part of the ratio by dividing the total amount invested by the total ratio: $875,000 ÷ 12 = $72,916.67.

Finally, we can calculate the second largest share by multiplying the value of one part of the ratio by the second largest individual ratio, which is 4: $72,916.67 × 4 = $291,666.68.

Therefore, the amount of the second largest share is $291,666.68.

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Based on the given mean and standard deviation of Sarah's finishing times, we can estimate that approximately 68% of her races will have finishing times between 61.5 and 64.5 seconds.

The empirical rule, also known as the 68-95-99.7 rule, is a useful tool for estimating the percentage of data that falls within a certain number of standard deviations from the mean in a normal distribution.

In this case, Sarah's finishing times in the 400-meter dash are normally distributed with a mean of 63 seconds and a standard deviation of 1.5 seconds. To use the empirical rule, we need to first calculate the z-scores for the lower and upper bounds of the range we're interested in.

For the lower bound of 61.5 seconds:

z = (61.5 - 63) / 1.5 = -1

For the upper bound of 64.5 seconds:

z = (64.5 - 63) / 1.5 = 1

These z-scores tell us how many standard deviations are away from the mean each time. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Since the range we're interested in is within one standard deviation of the mean, we can estimate that approximately 68% of Sarah's finishing times will be between 61.5 and 64.5 seconds.

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Answer: I'd say A

Step-by-step explanation:

-1+1=0

(A). The chest has a volume of 17,600 cubic inches. (B). The cushion covers 880 square inches of the chest. (C). Whereas area is measured in square units, volume is measured in cubic units.

An object's area is determined by its shape. The amount of space a figurine or any other as double geometric shape takes up on a plane depends on its area.

(A). Chest volume is calculated as follows: 40 inches by 22 inches by 20 inches, or 17,600 cubic inches.

(B). The cushion's coverage area for the chest is 40 inches by 22 inches, or 880 square inches.

(C). The units for area are square units, while the units for volume are cubic elements (like as cubic feet or cubic meters) (such as square inches or square meters). This is so because area is the measure of space an item occupies in two dimensions, but capacity means the quantity of space an object occupies in three dimensions. As a result, area is expressed in feet or meters whereas volume is recorded in cubic units.

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The y-intercept of the continuous function in the table is (0, –6) which can be determined by looking at the first point, (0, –6).

A continuous function is a function that is defined for all values of its independent variable, and whose graph is a continuous line without breaks or gaps. It typically means that a function's value for an input can be calculated without having to consider the values of the function for other inputs.

The y-intercept of a continuous function is the point at which the graph of the function crosses the y-axis. It is the point where the x-coordinate is zero. In other words, it is the point where the graph of the function intersects the y-axis.

In the given table, the y-intercept can be determined by looking at the first point, (0, –6). This means that the y-coordinate is –6 when the x-coordinate is 0. Therefore, the y-intercept of the continuous function in the table is (0, –6).

The y-intercept also helps us to determine the slope of the function. The slope is the rate at which the function changes as we move along the x-axis. The slope can be calculated by looking at the change in the y-coordinate for a given change in the x-coordinate.

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The y-intercept οf the cοntinuοus functiοn in the table is (0, –6) which can be determined by lοοking at the first pοint, (0, –6).

A cοntinuοus functiοn is a functiοn that is defined fοr all values οf its independent variable, and whοse graph is a cοntinuοus line withοut breaks οr gaps. It typically means that a functiοn's value fοr an input can be calculated withοut having tο cοnsider the values οf the functiοn fοr οther inputs.

The y-intercept οf a cοntinuοus functiοn is the pοint at which the graph οf the functiοn crοsses the y-axis. It is the pοint where the x-cοοrdinate is zerο. In οther wοrds, it is the pοint where the graph οf the functiοn intersects the y-axis.

In the given table, the y-intercept can be determined by lοοking at the first pοint, (0, –6). This means that the y-cοοrdinate is –6 when the x-cοοrdinate is 0. Therefοre, the y-intercept οf the cοntinuοus functiοn in the table is (0, –6).

The y-intercept alsο helps us tο determine the slοpe οf the functiοn. The slοpe is the rate at which the functiοn changes as we mοve alοng the x-axis. The slοpe can be calculated by lοοking at the change in the y-cοοrdinate fοr a given change in the x-cοοrdinate.

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Complete question:

Which is a y-intercept of the continuous function in the table?

Answer:

A. X = -4

Step-by-step explanation:

[tex]-6x-24=3x+12\\-9x=36\\x=-4[/tex]

Answer:50

Step-by-step explanation:5+5=10 and 5 groups of 10 is 50

Answer:30

Step-by-step explanation:

5x5=25

25+5

30

Answer:

I CAN NOT SEE THAT OML

Step-by-step explanation:

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

The student factored the numerator and denominator incorrectly. Instead of factoring to (x+1)(x+2)/(x+4)(x+2), they factored to (x+1)(x+2)/(x+4)(x+2) = (x+1)/x+4.

Factoring polynomials can be a difficult skill to master, and mistakes in factoring can lead to errors in simplifying rational expressions. Additionally, students may rush through factoring or not double-check their work, leading to careless errors.

Students can avoid mistakes like this by practicing factoring polynomials regularly and double-checking their work. It can also be helpful to write out each step clearly and show all work, so mistakes can be caught more easily.

My advice would be to practice factoring polynomials regularly, and double-check your work when simplifying rational expressions. Also, it is important to take your time and show all work, so mistakes can be caught more easily.

Answer:

[tex]18\frac{1}{24}[/tex] ≅ 18.0416667

Step-by-step explanation:

5 7/8 + 4 1/3 + 7 5/6 = [tex]\frac{433}{24}[/tex]

1.Conversion a mixed number 5 7/8

to an improper fraction: 5 7/8 = 5 7/8

= 5 · 8 + 7/8

= 40 + 7/8

= 47/8

To find a new numerator:

a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8

b) Add the answer from the previous step 40 to the numerator 7. New numerator is 40 + 7 = 47

c) Write a previous answer (new numerator 47) over the denominator 8.

Five and seven-eighths is forty-seven eighths.

2. Conversion a mixed number 4 1/3

to an improper fraction: 4 1/3 = 4 1/3 = 4 · 3 + 1/3 = 12 + 1/3 = 13/3

To find a new numerator:

a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3

b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 3.

Four and one-third are thirteen-thirds.

3. Add: 47/8

+ 13/3

= 47 · 3/8 · 3

+ 13 · 8/3 · 8

= 141/24

+ 104/24

= 141 + 104/24

= 245/24

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(8, 3) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 3 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - forty-seven eighths plus thirteen-thirds is two hundred forty-five twenty-fourths.

4. Conversion a mixed number 7 5/6

to an improper fraction: 7 5/6 = 7 5/6 = 7 · 6 + 5/6 = 42 + 5/6= 47/6

To find a new numerator:

a) Multiply the whole number 7 by the denominator 6. Whole number 7 equally 7 * 6/6= 42/6

b) Add the answer from the previous step 42 to the numerator 5. New numerator is 42 + 5 = 47

c) Write a previous answer (new numerator 47) over the denominator 6.

Seven and five-sixths are forty-seven-sixths.

5.Add: the result of step No. 3 + 47/6= 245/24 + 47/6 = 245/24 + 47 · 4/6 · 4 = 245/24 + 188/24 = 245 + 188/24 = 433/24

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(24, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 24 × 6 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two hundred forty-five twenty-fourths plus forty-seven sixths are four hundred thirty-three twenty-fourths.

For a dish party, Alia needs to seat four people at a round table. There are 24 possible combinations of seating arrangements.

This is because each person has 3 options (clockwise, counter-clockwise, opposite), for a total of 34 or 81 combinations. However, due to symmetry, half of these are the same combinations with the people just shifted around the table, so we are left with 24 total combinations.

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Answer: 200

Step-by-step explanation:

40% of y = 100

40/100 of y = 100

40y/100 = 100

40y = 100 multiplied by 100

40y/40 = 10000

y = 250.

40% of 2 multiplied by 250

40/100 of 500

40 multiplied by 5

answer = 200.

The length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:

11). x = 11√3 and y = 33

12). x = 4√7 and y = 8√7

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

recall that sin60° = √3/2 and cos60° = 1/2

For question 11:

sin 60° = y/22√3 {opposite/hypotenuse}

y = 22√3 × sin 60° {cross multiplication}

y = 22√3 × √3/2

y = 11 × 3

y = 33

cos 60° = x/22√3 {adjacent/hypotenuse}

x = 22√3 × cos 60° {cross multiplication}

x = 22√3 × 1/2

x = 11√3.

For question 12:

sin 60° = 4√21/y {opposite/hypotenuse}

y = 4√21/sin 60° {cross multiplication}

y = 4√21 ÷ √3/2

y = 4√21 × 2/√3

y = 4√7 × 2

y = 8√7

cos 60° = x/8√7 {adjacent/hypotenuse}

x = 8√7 × cos 60° {cross multiplication}

x = 8√7 × 1/2

x = 4√7

Therefore, the length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:

11). x = 11√3 and y = 33

12). x = 4√7 and y = 8√7

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The correct answer is "No, because for each input there is not exactly one output".

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

The relation is not a function because for the input value of 1, there are two possible output values: 0 and 2. In a function, each input can have only one output value. However, in this relation, the input value of 1 is associated with two different output values, so it violates the definition of a function. Therefore, the correct answer is "No, because for each input there is not exactly one output".

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Therefore, f(-2x-5) is \[ \frac{-2(x+4)}{4(x+3)^{2}}=\frac{-2 x-8}{4 x^{2}+24 x+36} \]

(a) To find the value of f(-2), we simply substitute -2 for x in the given function:
\[ f(-2)=\frac{-2-3}{(-2)^{2}+2}=\frac{-5}{6} \]
Therefore, the value of f(-2) is -5/6.

(b) To find f(-2x-5), we substitute -2x-5 for x in the given function:
\[ f(-2x-5)=\frac{-2x-5-3}{(-2x-5)^{2}+2}=\frac{-2x-8}{4x^{2}+20x+27} \]
Simplifying the numerator and denominator, we get:
\[ f(-2x-5)=\frac{-2(x+4)}{4(x+3)(x+3)}=\frac{-2(x+4)}{4(x+3)^{2}} \]
Therefore, f(-2x-5) is \[ \frac{-2(x+4)}{4(x+3)^{2}}=\frac{-2 x-8}{4 x^{2}+24 x+36} \]

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The average number of likes per writer and the average number of comments per writer can be used to determine which website has more user engagement per a single writer

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the average number of likes per writer be L

Let the average number of comments per writer be C

Now , the number of writers for website A = 5

The number of writers for website B = 11

The average number of likes per post for A = 3500 likes

So , the average number of likes per writer A = ( 3500 / 5 ) = 700 likes

And , the average number of likes per writer B = ( 3500 / 5 ) = 700 likes

The number of comments per writer A = ( 500 / 5 ) = 100 comments

The number of comments per writer B = ( 450 / 11 ) = 40.90 comments

Hence , the average number of likes per writer and the average number of comments per writer are solved

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5.6 kilograms.

1000 grams makes ONE kilogram and you have 5000 grams. Then the extra 600 grams are 6/10 of 1000 so it would be .6.