( a^2x^3 -5x+3a).(-2a^3x)

The amount John saves off his minimums after 3 months is $450

From the question, we are to determine the amount John saves off his minimums after 3 months

The amount John saves off his minimums after 3 months =

($500 - $350) × 3

$150 × 3

= $450

Hence, the amount John saves off his minimums after 3 months is $450

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There are 32 no.of digits in

[tex]9[/tex] to the power of [tex]33 = 9^33 = 30 9031543826 3261236192[/tex]0641803529.

Step-by-step explanation:  As the exponent is a positive integer, exponentiation means a repeated multiplication:

9 to the 33rd power =[tex]{9*....*9}[/tex] 33times

The exponent of the number 9, 33, also called index or power, denotes how many times to multiply the base (9).

Thus, we can answer what is 9 to the 33rd power as

[tex]9[/tex] to the power of [tex]33 = 9^33 = 30 9031543826 3261236192[/tex]0641803529.

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There exist 32 digits in 9 to the power [tex]33 = 9^{33}[/tex] of

30903154382632612361920641803529.

The power of a numeral stands for how many multiples of the number there exist. The base of the number stands for the number itself and lives in front of the exponent. The exponent stands for the smaller number written above and to the right of the base. Positive exponents result in the base value existing multiplied by itself numerous times.

As the exponent exists as a positive integer, exponentiation signifies repeated multiplication.

9 to the 33rd power [tex]$=9* ........*9*[/tex] 33 times

The exponent of the number 9, 33, even named index or power, indicates how many times to multiply the base (9).

Therefore, we can answer what exists 9 to the 33rd power as 9 to the power of 33 = [tex]9^{33}[/tex] to the power of 30903154382632612361920641803529.

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Answer:

Rational

Step-by-step explanation:

cause I don't know how to explain

Using the combination formula, the probability that Rosa's mom chooses sausage and onion is given by:

B. [tex]\frac{1}{C_{8,2}}[/tex].

The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

2 toppings are chosen from a set of 8, hence the number of options is given by:

[tex]C_{8,2}[/tex].

Sausage and onion correspond to one topping, hence the probability is given by:

B. [tex]\frac{1}{C_{8,2}}[/tex].

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Answer:

2 cubic meters

Step-by-step explanation:

1 Cubic Meter = 61023.7441 Cubic Inch

Using the power rule, the derivatives are given as follows:

a) [tex]f^{\prime}(2) = -\frac{1}{4}[/tex].

b) [tex]f^{\prime}(3) = 30[/tex].

Suppose we have a power function given by:

[tex]f(x) = x^n[/tex]

The derivative of the function is given by:

[tex]f^{\prime}(x) = n \times x^{n-1}[/tex]

Item a:

The function is:

[tex]f(x) = \frac{1}{x} = x^{-1}[/tex]

Then the derivative is:

[tex]f^{\prime}(x) = -x^{-2} = -\frac{1}{x^2}[/tex]

When x = 2, the derivative is:

[tex]f^{\prime}(2) = -\frac{1}{4}[/tex]

Item b:

The function is:

[tex]f(x) = 5x^2[/tex]

Then the derivative is:

[tex]f^{\prime}(x) = 10x[/tex]

When x = 3, the derivative is:

[tex]f^{\prime}(3) = 30[/tex]

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The first subscription option is given by T = 92 while the second subscription option is given as T = 3x. Where T represent the cost of borrowing x number of books.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let T represent the cost of borrowing x number of books.

For the first subscription option:

T = 92

For the second subscription option:

T = 3x

The first subscription option is given by T = 92 while the second subscription option is given as T = 3x. Where T represent the cost of borrowing x number of books.

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The required system hence becomes

3x-y+4>0,

y + 6 > (x + 2)²

When the symbols “>”, “<”, “≥”, “≤”,  are used to connect two real numbers or algebraic expressions, that relationship is known as an inequality.

The Graph is given below of the given problem statement.

Observe that the parabola y=x² has vertex at (0,0) we can shift the vertex to (-2,-6) to get the parabola

y + 6 = (x + 2)²

And the inequality is

y + 6 > (x + 2)²

Hence, this parabola is as required by the problem.

And the line passing through (-3,-5) and (0,4) is

[tex]\frac{\left(y-4\right)}{\left(-5-4\right)}=\frac{\left(x\right)}{-3}[/tex]

The required inequality hence becomes

3x-y+4>0

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Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.

Step-by-step explanation:

Since we have given that

Total number of students and teachers = 409

Let the number of vans be x

Let the number of buses be x+5

Number of students and teachers each bus transported = 55

Number of students and teachers each van transported = 12

According to question,

Total number of students and teachers who rode to the zoo in buses will be

Total number of students and teachers who rode to the zoo in vans will be

Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.

The amount of money she started with is $5750

The given parameters are:

Interest = $115

Rate = 3%

Time = 8 months

The amount she start with (P) is calculated using:

P = I/(RT/12)

This gives

P = 115/(3% * 8/12)

Evaluate the product

P = 115/(0.02)

Divide

P = 5750

Hence, the amount of money she started with is $5750

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Considering the definition of least common multiple, this means that smallest number of packages of each they can buy is 60.

A number is a multiple of another when it contains it exactly n times. In other words, the multiples of a number are the ones you get when you multiply one number by another.

The least common multiple allows us to know what is the smallest number that is a multiple of a certain set of numbers.

One procedure for calculating the least common multiple is to break each number into prime factors. Then the common and uncommon factors are raised to the highest exponent, which must be multiplied.

To calculate the smallest number of packages of each they can buy, you calculate the least common multiple.

First, the decomposition of the numbers into prime factors is carried out:

15= 3×5

12= 2×2×3= 2²×3

Then, the least common multiple is calculated as 2²×3×5

Solving, the least common multiple between 12 and 15 is 60.

Finally, this means that smallest number of packages of each they can buy is 60.

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Answer:

  1.5 mL

Step-by-step explanation:

The abbreviation mcg stands for "microgram," or 10^-6 grams. The abbreviation mg stands for "milligram," or 10^-3 grams. The relationship between these is ...

  1 mg = 1000 mcg

The order for 6000 mcg is an order for 6(1000 mcg) = 6(1 mg) = 6 mg. At 4 mg/mL, the quantity of dexamethasone required is ...

  (6 mg)/(4 mg/mL) = (6/4) mL = 1.5 mL

The nurse will give 1.5 milliliters of dexamethasone.

(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].

(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].

So, the combined areas of the four semicircles is [tex]241\pi[/tex].

The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].

The value of z from the cyclic quadrilateral as described is; 173/22.

Since the quadrilateral TUVW is a cyclic quadrilateral, it follows that the opposite angles of the quadrilateral are supplementary and hence, amount to 180.

On this note, 14z -7 +8z = 360

22z -7 = 180

22z = 180 -7

z = 173/22

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Answer:

i think it is 340

Step-by-step explanation:

The step in which Yvonne first makes an error while solving the quadratic equation by completing the square in step 1.

A quadratic equation is an equation in which the highest power of the variable is two.

Yvonne is solving the quadratic equation, which is,

6x² +24x +7 =0

He is solving the above equation by completing the square.

The first step to solving this quadratic equation by completing the square is, Take the constant value 7 at the opposite side of the equation as,

6x² +24x = -7

Here, the number seven was a positive number, which we have changed to negative because this number brings the other side of the equation.

In the image attached below, the first step of  the Yvonne while solving the equation by completing the square is,

6x² +24x = 7

Here, Yvonne does not change the sign of the number 7 while taking it to another side of the equation.

Hence, the step in which Yvonne first makes an error while solving the quadratic equation by completing the square is step 1.

The table is attached with the answer below

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Answer:

Step-by-step explanation:

difference=1-(-12)=13°F

Answer:

2%

Step-by-step explanation:

You can write it out as equation first.

430*x%=8.60, leave x% alone, so the equation will change into

x%=8.60/430

8.60/430=0.02=2%

therefore, x%=2%

The factored form of the given expression is (x+2)(x-3)

Quadratic equation are equation that has a leading degree of 2. Given the equation below

6=x^2-x

Equate to zero

x^2-x - 6 = 0

Factorize

x^2 - 3x + 2x - 6 = 0

x(x-3)+2(x-3) = 0

x = 3 and -2

Hence the factored form of the given expression is (x+2)(x-3)

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Answer:

Ask your guidance counselor or a college admissions counselor

Step-by-step explanation:

Answer:

Exact form - 13/15

Decimal Form - 0.86

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine

Using the Poisson distribution, the probabilities are given as follows:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The mean is given as follows:

[tex]\mu = 10.6[/tex]

Hence the probability of no dandelions in an area of 1 m² is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-10.6}(10.6)^{0}}{(0)!} = e^{-10.6}[/tex]

The probability of at least one dandelion is:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - e^{-10.6}[/tex]

The probability of at most two dandelions is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-10.6}(10.6)^{0}}{(0)!} = e^{-10.6}[/tex]

[tex]P(X = 1) = \frac{e^{-10.6}(10.6)^{1}}{(1)!} = 10.6e^{-10.6}[/tex]

[tex]P(X = 2) = \frac{e^{-10.6}(10.6)^{2}}{(2)!} = 56.18e^{-10.6}[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = e^{-10.6} + 10.6e^{-10.6} + 56.18e^{-10.6} = 67.78e^{-10.6}[/tex]

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Answer: LCD = 100

Step-by-step explanation:

16/25 = 64/100

13/20 = 65/100

Using it's concept, the set of ordered pairs that represent a function are:

The set of ordered pairs that do not represent a function are:

A relation represents a function if each input X is mapped to only one output Y.

At (1,9), (-3,-2) (1,-4), input 1 is mapped to outputs 9 and -4, hence it is not a function.

At (0, 3), (0, 7), (4,0), input 0 is mapped to outputs 3 and 7, hence it is not a function.

For the other relations, each input is mapped to only one output, hence they are functions.

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Using the t-distribution, the t-statistic for the two-sided test would be of t = 0.7.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The values of the parameters are given as follows:

[tex]\mu = 22, s = 7.043, n = 6[/tex].

The sample mean is:

[tex]\overline{x} = \frac{23 + 35 + 17 + 30 + 20 + 19}{6} = 24[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{24 - 22}{\frac{7.043}{\sqrt{6}}}[/tex]

t = 0.7.

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Answer:

1/55

Step-by-step explanation:the probability of choosing 3 boys.

The probability of choosing the first boy =4/12

The probability of choosing the second boy =3/11

The probability of choosing the third boy =2/10

The probability of choosing the 3 boys will be,

=4/12×3/11×2/10

=24/1320

Answer:

Should be W

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.

Hope this helps!!

The local minima of [tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex] are (x, f(x)) = (-1.5, 0) and (7.980, 609.174)

The function is given as:

[tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex]

See attachment for the graph of the function f(x)

From the attached graph, we have the following minima:

Minimum = (-1.5, 0)

Minimum = (7.980, 609.174)

The above means that, the local minima are

(x, f(x)) = (-1.5, 0) and (7.980, 609.174)

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The evaluation of 84 2/3% to a fraction in its lowest term is [tex]\mathbf{ \dfrac{127}{150} }[/tex]

Fractions are sections or parts of a whole. They are divided into two parts, the numerator, and the denominator.

From the given information, we are to convert a mixed fraction into its lowest terms. By doing that, we are to convert it to an improper fraction.

[tex]\mathbf{= 84 \dfrac{2}{3}\%}[/tex]

[tex]\mathbf{= \dfrac{(84 \times 3)+2}{3} \%}[/tex]

[tex]\mathbf{= \dfrac{254}{3} \%}[/tex]

[tex]\mathbf{= \dfrac{254}{3} \times \dfrac{1}{100}}[/tex]

[tex]\mathbf{= \dfrac{254}{300} }[/tex]

Divide both the numerator and denominator by (2)

[tex]\mathbf{= \dfrac{127}{150} }[/tex]

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