Find the surface area of the composite figure.

What does 1/4 plus 2/5 equals? Simplify your answer, if possible. 5th grade math.

BigorU [14]

Answer:

13/20

Step-by-step explanation:

5 0

3 years ago

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Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

ladessa [460]

Answer:

(-2, 4, -2)

x=-2, y=4, z=-2.

Step-by-step explanation:

So we have the three equations:

$4x-y-2z=-8\\-2x+4z=-4\\x+2y=6$

And we want to find the value of each variable.

To solve this system, first look at it and consider what you should try to do.

So we can see that the second and third equations both have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.

Therefore, let's first isolate the variable in the second and third equation.

Second Equation:

$-2x+4z=-4$

First, divide everything by -2 to simplify things:

$x-2z=2$

Subtract x from both sides. The xs on the left cancel:

$(x-2z)-x=2-x\\-2z=2-x$

Now, divide everything by -2 to isolate the z:

$z=-\frac{2-x}{2}$

So we've isolated the z variable. Now, do the same to the y variable in the third equation:

$x+2y=6$

Subtract x from both sides:

$2y=6-x$

Divide both sides by 2:

$y=\frac{6-x}{2}$

Now that we've isolated the y and z variables, plug them back into the first equation. Therefore:

$4x-y-2z=-8\\4x-(\frac{6-x}{2})-2(-\frac{2-x}{2})=-8$

Distribute the third term. The -2s cancel out:

$4x-(\frac{6-x}{2})+(2-x)=-8$

Since there is still a fraction, multiply everything by 2 to remove it:

$2(4x-(\frac{6-x}{2})+(2-x))=2(-8)$

Distribute:

$8x-(6-x)+2(2-x)=-16\\8x-6+x+4-2x=-16$

Combine like terms:

$8x+x-2x-6+4=-16\\7x-2=-16$

Add 2 to both sides:

$7x=-14$

Divide both sides by 7:

$(7x)/7=(-14)/7\\x=-2$

Therefore, x is -2.

Now, plug this back into the second and third simplified equations to get the other values.

Second equation:

$z=-\frac{2-x}{2}\\ z=-\frac{2-(-2)}{2}\\z=-\frac{4}{2}\\z=-2$

Third equation:

$y=\frac{6-x}{2}\\y=\frac{6-(-2)}{2}\\y=\frac{8}{2}\\y=4$

Therefore, the solution is (-2, 4, -2)

3 0

3 years ago

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To make iced tea, 5 tea bags can be added to 1 gallon of water. Find how many bags can be used for 4 gallons of water

Nata [24]

Answer:

20 tea bags

Step-by-step explanation:

if 5 is 1 gallon then you do 5x4=20

4 0

3 years ago

Step 1 of 3: Each year a nationally recognized publication conducts its Survey of America’s Best Graduate and Professional Schoo

lukranit [14]

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: Starting salary of a graduate at a top business school

X: GMAT score of the business school

The sample used had a size n=20

The estimated regression equation was ^Y= -92040 + 228Xi

The correlation coefficients were r= 0.81

You need to know if r is statistically significant at a 0.05 level:

Assuming the hypotheses are:

H₀: There is a linear correlation between the variables of interest

H₁: There is no linear correlation between the variables of interest

α: 0.05

This test is two-tailed.

The p-value for a r=0.81 and n=20 is 0.000015

Using the p-value approach, the decision rule is:

If p-value ≤ α, reject the null hypothesis

If p-value > α, do not reject the null hypothesis

In this case, the p-value is less than α, the decision is to reject the null hypothesis.

At a 5% level, you can conclude that the coefficient of correlation is statistically significant.

4 0

3 years ago

john is a proud owner of a herd of cows 12 of them are brown and 32 are black what is the ratio of brown cows to the total numbe

Burka [1]

Answer:

12:44, or if simplified 3:11

Step-by-step explanation:

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).

6 0

3 years ago

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