If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45

The probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.

Given:

Probability between z = 0 and z = 3.01 is given by

As, P(0<z<3.01)

= P(z<3.01) - P(z<0)

So, the z score values are

P(z<0) = 0.5

and, P(z<3.01) = 0.9987

Hence, the probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.

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13x-2(x+4) = 8x+1 =

13x-2x-8 = 8x+1=

11x-8 = 8x+1

-8 =-3x+1=

-9 = -3x

x = -9/-3 = 3

x = 3

Answer:  For the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]

Step-by-step explanation:  We are given to find the values of [tex]a_1[/tex] and [tex]r[/tex] of the following geometric series:

[tex]2-2+2-2+2-~.~.~..[/tex]

We know that

[tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio of the given geometric series.

We can see that the first term of the given geometric series is 2.

So. we must have

[tex]a_1=2.[/tex]

Also, common ratio is found by dividing a term by its preceding term.

Therefore, the common ratio [tex]r[/tex] of the given geometric series is

[tex]r=\dfrac{-2}{2}=\dfrac{2}{-2}=~.~.~.~=-1.[/tex]

Thus, for the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

[tex](4h^7k^2)^4[/tex]

We need to simplify this :

Here we go:

We will apply :

[tex](a^m)^n=a^{mn}[/tex]

[tex](4h^7k^2)^4\\\\=4^4\times (h^7)^4\times (k^2)^4\\\\=256h^{28}k^8[/tex]

Hence, option 'D' is correct.

Answer with explanation:

The two points on the number line are

  x = -4

  y=3

The distance is a positive Quantity.

So, Distance between x and y can be written as:

  =|x-y| or |y-x|

 =|3-(-4)| or |-4-3|

 =|3+4| or |-7|

 =|7| or |-7|

 =7 Units

The expression will be : =|x-y| or |y-x|

 =|3-(-4)| or |-4-3|

The quadratic formula gives two roots for a quadratic equation. The roots of the equation 2x²+x-6=0 are 1.5 and -2.

The quadratic formula gives the roots of a quadratic equation of the form ax²+bx+c=0. For the equation 2x²+x-6=0, the values of a, b, and c are 2, 1, and -6, respectively.

Using the quadratic formula, we can calculate the roots:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values of a, b, and c into the formula:

x = (-1 ± √(1² - 4*2*(-6))) / (2*2)

Simplifying the expression:

x = (-1 ± √(1 + 48)) / 4

x = (-1 ± √49) / 4

x = (-1 ± 7) / 4

Therefore, the roots of the equation 2x²+x-6=0 are:

x = (-1 + 7) / 4 = 3/2 = 1.5

x = (-1 - 7) / 4 = -8/4 = -2

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a. The perimeter of the triangle is 18 cm. b. The area of the triangle is 24 cm². c. Tiling the triangle at $7 per square centimeter would cost $168.

a. Perimeter:

Perimeter} = 5 + 5 + 8 = 18 cm

b. Area:

  Use Heron's formula since the sides are known:

[tex]\[ s = \frac{5 + 5 + 8}{2} = 9 \] \[ \text{Area} = \sqrt{s(s-5)(s-5)(s-8)} \] \[ \text{Area} = \sqrt{9 \times 4 \times 4 \times 1} = \sqrt{576} = 24 \, \text{cm}^2 \][/tex]

c. Cost to Tile:

  If the cost is $7 per square centimeter:

[tex]\[ \text{Cost} = \text{Area} \times \text{Cost per square centimeter} \] \[ \text{Cost} = 24 \times 7 = 168 \][/tex]

Therefore,

a. Perimeter = 18 cm

b. Area = 24 cm²

c. Cost to Tile = $168

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Given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]

Law of Cosines is given as: [tex]a^2+b^2 - 2abcosC = c^2[/tex]

Given also are the sides of a triangle:

Plug in the values into the Law of Cosines,  [tex]a^2+b^2 - 2abcosC = c^2[/tex] to find [tex]\mathbf{2abcosC}[/tex]

[tex]4^2+5^2 - 2abcosC = 2^2\\\\16 + 25 - 2abcosC = 4\\\\41 - 2abcosC = 4[/tex]

[tex]41 - 2abcosC - 41 = 4-41\\\\-2abcosC = -37[/tex]

[tex]\mathbf{2abcosC = 37}[/tex]

Therefore, given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]

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for the length of the side that is not given:

look at it as part of a triangle with the legs being 4m tall by 6 m wide

 so 4^2 + 6^2 = X62

16+36 = 52^2

square root(52) = 7.211 m

 does it as to round of to nearest whole number? nearest tenth?

round off answer as needed

Answer:

B on edge

Step-by-step explanation:

Answer:

acceleration i think

Step-by-step explanation:

The value of n is 12 .

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

According to the question

The circle will be dilated by a scale factor of 6 .

so,

New radius of the circle R = 6r

As is it dilated by a scale factor of 6

Now ,

The circumference of the new circles = 2πR  

                                                              = 2.6π

                                                              = [tex]12\pi r[/tex]  -------------------- (1)

and given circumference of the new circles = nπ  ---------------------(2)

when we compare both n = 12

Hence, the value of n is 12 .

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Final answer:

In this question, the arrangements of characters sitting together and the options for hamburger toppings are explored using permutations and combinations in Mathematics for High School.

Explanation:

(1) When the elf and the dwarf insist on sitting next to each other, treat them as one entity. Then, there are 4 entities: {elf & dwarf}, hobbit, wizard, man. This gives 4! ways to arrange them, and the elf and dwarf can be arranged within their entity in 2! ways.

So, the total ways are 4! x 2! = 48 ways.

(2) For the hamburger order, since you can choose to include/exclude each topping independently, there are 2 options for each topping (with or without).

Hence, the total ways to order the hamburger are 2⁵ = 32 ways.

Answer:

q=5 sqrt 5 and q=-5 sqrt 5

Step-by-step explanation:

got it right on edge :)

The roots of the quadratic function f(q) = q^2 − 125 are q = -5 and q = 5. Other options listed do not satisfy the function. The roots are found by factoring the equation as a difference of squares.

The roots of the quadratic function f(q) = q2 − 125 can be found by solving the equation q2 − 125 = 0. To find the roots, we need to factor the quadratic or use the square root property since the equation is already set to zero.

We can see that this is a difference of squares equation, so it factors to (q + 5)(q - 5) = 0. Setting each factor equal to zero gives us q = -5 and q = 5.

So, the roots of the quadratic function are q = -5 and q = 5. The other options given (q = 3, q = -3, q = 25, q = -25) do not satisfy the equation f(q) = q2 − 125 = 0, hence they are not roots of this function.

Answer:

Step-by-step explanation:

Givens

Now, remember that all coordinates with the form (a,0), represents points on the x-axis, because the y-coordinate is zero.

In this case, we have negative horizontal coordinates and a null vertical coordinate, like (-a,0).

This points is on the x-axis, because y-value is null. Actually, it's on the negative part of x-axis, because its horizontal coordinate is negative.

Therefore, the right answer is x-axis.

Answer:

Round the value of r to three decimal places.

Step-by-step explanation:

The rounding rule for the correlation coefficient requires three decimal places

this statement is true.

The correlation coefficient in statistics is a parameter which measures the degree of strength of relation between two variables .

Its value lies between -1  to +1 .

The closer the correlation coefficient  will be near to 1 the stronger the correlation will be.

The correlation between two variables can be positive or negative

Correlation coefficients are helpful in determining the  functional relationships among the variables

So higher  magnitude  of correlation coefficients lead to accurate functional relation among variables.

The rounding rule for the correlation coefficient requires three decimal places

this statement is true.

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Final answer:

Using the half-life formula, it would take 24 hours for the amount of carprofen to reduce from an initial dose of 80 milligrams to 10 milligrams.

Explanation:

To calculate the time it will take for the amount of carprofen to decrease from 80 milligrams to 10 milligrams in a dog, given the half-life of 8 hours, the exponential decay formula can be used. The half-life formula is:

[tex]C = C0 \times (1/2)^{(t/T)[/tex]

Let's set up the equation using the given values:

[tex]10 mg = 80 mg \times (1/2)^{(t/8 hours)[/tex]

Now, we solve for t:

[tex]10/80 = (1/2)^{(t/8)[/tex]

[tex]1/8 = (1/2)^{(t/8)[/tex]

To find the exponent t/8 that makes this equation true, we can use logarithms:

log2(1/8) = t/8

-3 = t/8

t = -3 * 8

t = -24 hours

The negative result is due to the fact that we are finding a factor by which the concentration is reduced. To get the actual time elapsed, we take the absolute value:

t = 24 hours

Therefore, it would take 24 hours for the amount of carprofen to reduce to 10 milligrams.

perimeter = 20 +20 +24 = 64 feet

 area = 12^2 + x^2 = 20^2

144 + x^2 = 400

x^2 = 256

x = sqrt(256) = 16 feet

area = 1/2 x 16 x 24 = 192 square feet

 cost = 192 x $2 = $384

Answer:

Step-by-step explanation:

The given equation is:

[tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex]

On solving the above equation, we get

=[tex]\frac{4x^2+36}{(4x)(5x)}[/tex]

=[tex]\frac{4(x^2+9)}{(4x)(5x)}[/tex]

=[tex]\frac{x^2+9}{(x)(5x)}[/tex]

=[tex]\frac{x^2+9}{(5x^2)}[/tex]

which is the required simplified form.

Thus, the simplified form of the given equation [tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex] is [tex]\frac{x^2+9}{(5x^2)}[/tex].

Answer:

in other words that guy said E

Step-by-step explanation: