Find the volume of the trapezoidal prism

[tex]xy \\\\=\left(\log_{5\sqrt 5} ~125 \right)\left(\log_{2\sqrt 2} ~64 \right)\\\\=\left(\log_{5\sqrt 5} ~5^3 \right)\left(\log_{2\sqrt 2}~2^6 \right)\\\\=\left(3\log_{5\sqrt 5} ~5 \right)\left(6\log_{2\sqrt 2} ~2 \right)\\\\=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5\sqrt 5\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2 \sqrt 2 \right)}\right)\\\\[/tex]

[tex]=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5^{\tfrac 32}\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2^{\tfrac 32} \right)}\right)~~~~~~~~~~~;\left[\sqrt a = a^{\tfrac 12}~~ \right]\\\\=\left( 18 \cdot \dfrac{\ln5}{\tfrac 32\ln5^} \cdot \dfrac{\ln 2}{\tfrac 32 \ln 2 }\right)\\\\\\=18 \cdot \dfrac 23 \cdot \dfrac 23 \\\\=\dfrac{72}9\\\\=8[/tex]

Answer:

(x-4)² -11 where a = 4, b = 11

Step-by-step explanation:

The final form (x-a)² - b evaluates to x² - 2ax + a² -b

Matching

x² - 8x    +  5    

x² - 2ax  +  a² -b

This gives us -2ax = -8x or -2a = -8 or a = 4

and a² - b = 11 ==> 16 - b = 11 or b =5

Rewritten form is

(x-4)² -11

Answer:

Option 2

Step-by-step explanation:

Checking whether P(A) × P(B) = P(A∩B) :

Since this does not obey the Multiplication rule of probability, these events are not independent.

So, the answer is :

No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)

Answer:

Option B

Step-by-step explanation:

Option A should be true if they are independent

So

They are dependant

Answer:

New area is 1/9th the original area

Step-by-step explanation:

Original area   =   L x W

now reduce the side lengths

   1/3 L   x    1/3 W

   1/3 * 1/3   * L x W

       1/9   L x W       <===== the new area is 1/9th the original area

Answer:

28 grapes in total

Step-by-step explanation:

grapes are shared in the ratio 2 : 5 = 2x : 5x ( x is a multiplier )

Eva gets 12 more grapes than Dora , then

5x = 2x + 12 ( subtract 2x from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

total grapes = 2x + 5x = 7x = 7 × 4 = 28

Eva gets 5x = 5 × 4 = 20

Dora gets 2x = 2 × 4 = 8

that is Eva gets 12 more than Dora

The probability P (sum of 12 OR <5) is 7/36 because the total outcomes are 36.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total outcomes = 36

The probability that the sum is 12:

P(A) = 1/36

The probability that the sum is less than 5:

P(B) = 6/36

The probability:

P(sum of 12 OR <5) = 1/36 + 6/36 = 7/36

Thus, the probability P (sum of 12 OR <5) is 7/36 because the total outcomes are 36.

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Answer:

[tex]-3x^2 * x = -3x^3\\y * y = y^2[/tex]

[tex](-3x^2y)(5xy^2 + xy)\\[/tex]

Use F.O.I.L, (First Outer Inner Last) to multiply. Start with -3x^y * 5xy^2

Start with similar terms

[tex]-3x^2 * 5x = -15x^3\\y * y^2 = y^3\\Therefore,\\-15x^3y^2[/tex]

Move onto the xy portion of the problem

[tex]-3x^2y(xy)\\[/tex]

Start with similar terms

[tex]-3x^2 * x = -3x^3\\y * y = y^2\\Therefore,\\-3x^3y^2[/tex]

Combine the two together

[tex]-15x^3y^3 - 3x^3y^2\\[/tex]

The answer is Option A

Answer:

   44. (1) -15x³y³ - 3x³y²

Step-by-step explanation:

Question 44

Answer:  BC = 80

Step-by-step explanation:

One of the many Pythagoean Triplets is 18, 80, and 82. This is the only one with 18 as one of the sides other than the hypotnyse.

Answer: The final price is less than the original

Step-by-step explanation:

    Let us break this down a bit.

The original price is $500

-> At the beginning, the price was marked up by 20%

-> At the end, the price at the beginning of the season is marked down by 20%

    We are solving for: "How does the final price compare with the original price of $500​"

        First, we will find the price at the beginning.

-> Please note a percent divided by 100 becomes a decimal

20% / 100 = 0.2

$500 * 0.2 = $100

$500 + $100 = $600

     Now, we will find the price at the end.

$600 * 0.2 = $120

$600 - $120 = $480

     The final price is less than the original price of $500.

Answer:

Step-by-step explanation:

price marked up by 20%= 500+ [tex]\frac{20}{100}[/tex]×500

                                        =$600

price marked down by 20%= 600- [tex]\frac{20}{100}[/tex]×600

                                             =$480

the final price is less than the original price

The GCF is 4

The polynomial factors to [tex]4(3x^2+x+5)[/tex]

==========================================================

Further explanation:

Ignore the x terms

We're looking for the GCF of 12, 4 and 20

Factor each to their prime factorization. It might help to do a factor tree, but this is optional.

Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.

We can then factor like so

[tex]12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)[/tex]

The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.

The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).

Answer:

the answer is k=-4 hope this helps

Answer:

Negative number Addition and Subtraction.

Step-by-step explanation:

Ok so, 1-(-4)+ to 5

and 2-(-3) also = to 5 so you can kinda see a pattern if you get this 1 has to subtract by 5 bc 1-5=-4 and the same for the others so I hope I get this right and it helps.

y=x+-5

Answer:

145 is the outlier

Step-by-step explanation:

When compared to the other values, 145 is an exceeding highly value. Hence, it can be considered an outlier in the data set.

The completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)

The polynomial expression is given as;

12x⁴ + 39x³ + 9x²

Factor out 3x² from the expression

3x²(4x² + 13x + 3)

Expand

3x²(4x² + 12x + x + 3)

Factorize the expression

3x² * 4x(x + 3) + 1(x + 3)

Factor out x + 3

3x²(4x + 1)(x + 3)

Hence, the completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)

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Step-by-step explanation:

[tex] {x}^{2} + 6x - 2 = {x}^{2} + 2px + {p}^{2} + q[/tex]

[tex]2p = 6[/tex]

[tex] {p}^{2} + q = - 2[/tex]

[tex]p = 3[/tex]

[tex] {3}^{2} + q = - 2[/tex]

[tex]q = - 11[/tex]

p=3, q=-11

Answer:

h=4

Step-by-step explanation:

Answer:

1%

Step-by-step explanation:

0.04c multiplied by 100 is 4.

Answer:

1%

Step-by-step explanation:

Mostly because you see 0.04c is exactly 1% of 4c. Which means a hundred 0.04c will be required to get 4c.

D

--

x=9.4cos(58°)

because the cosine function uses the ratio of the adjacent side to that of the hypotenuse.

9.4 is the hypotenus the ration is 58 degrees I believe

[tex]\\ \rm\Rrightarrow cosA=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow cos58=\dfrac{x}{9.4}[/tex]

[tex]\\ \rm\Rrightarrow x=9.4cos58[/tex]

Option D

The trend line is a strong fit for the data on yellow-spotted salamanders.

A graph can be described as a pictorial representation of data. A trend line is used to show the direction of the data plotted. The trend line shown is positive. This means that as the number of spots increases, the weight of the salamander increases. The trendline is strong because most of the dots lie along the trendline.

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Answer:

x = 9

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{x}[/tex] 729 = 3 then

729 = x³

note 729 = 9³ , so

9³ = x³ ( equating the bases) , gives

x = 9

Answer:

13

Step-by-step explanation:

Volume to find radius: [tex](3\frac{V}{4\pi})^1^/^3[/tex]

Substitute: [tex](3\frac{9198.1}{4\pi})^1^/^3[/tex]

Solve: [tex](3(732.3))^1^/^3[/tex]

[tex]2196.9^1^/^3[/tex]

13≈r

Answer: 5/12

Step-by-step explanation: basically divide each number (10 &24) by 2

Answer:

(10-4)/2 , (2-8)/2

6/2 , -6/2

Midpoint = (3,-3)

Answer:

y = mx + b

y = 1/3x + b

Use (2,4) to find b

4 = 1/3(2) + b

b = 4 - 2/3

b = 12 - 2

3

b = 10/3

The equation will be:

The equation will be: y = 1/3x + 10/3

Answer:

C) [tex]3\cdot10^{-6}[/tex]

Step-by-step explanation:

Divide the two numbers:

[tex]\displaystyle \frac{6\cdot10^{-2}}{2\cdot10^{-8}}=\frac{6}{2}*\frac{10^{-2}}{10^{-8}}=3\cdot10^{-2-(-8)}=3\cdot10^{-2+8}=3\cdot10^{6}[/tex]

Thus, C is the correct choice.

Answer:

is A

Step-by-step explanation:

To answer this item, note that what needs to be done is to substitute -4 to all x's in the equation. That is,

                    F(x) = 2^x

will become,

                    F(-4) = 2^(-4) = 1/16 or 0.0625

Answer:

The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex] but in this case we see that a diameter is being used therefore we can get rid of the 2 and the r because that is what the diameter and just replace d into there like this [tex]C=d*\pi[/tex].

We can then input the value and we get that [tex]C=5*\pi[/tex] which then just narrows down to [tex]C=15.708[/tex].

Hope this helps!  Let me know if you have any questions

Answer:

2.8

Step-by-step explanation:

Just substract 7.2 from 10

You get: 2.8

Answer:

2.8

Step-by-step explanation:

because 7.2 plus 2.8 equals

Answer:

H=4.243

Step-by-step explanation:

Formula: A^2+B^2=C^2

(3)^2+(3)^2=C^2

9+9=C^2

sqrt18=C

C=4.242640....

Answer:

(6.5,-6)

Step-by-step explanation:

(7+6)÷2= 6.5

(-5+-7)÷2=-6