2x-[4-3(2^5+18y)] simplify

Answers

Answer 1

Answer: $2x-[4-3(2^5+18y)]\n\n=2x-[4-3(32+18y)]\n\n=2x-(4-96-54y)\n\n=2x-(-92-54y)\n\n=2x+92+54y$

Answer 2

Answer: = 2x - [4 - (96 + 54y)]
= 2x - 4 + 96 + 54y
= 2x + 54y + 92

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Explain what the point (20,160) represents in the context of the situation? Check all boxes that apply A. 160 shirts cost $20B. 20 shirts cost $160
C. 20,160 shirts cost money
D. The total cost of shirts is 20,160

Answers

Answer:

option B is correct option.

Step-by-step explanation:

Explain what the point (20,160) represents in the context of the situation? Check all boxes that apply

Looking at the graph we come to know that 20 shirts cost $160 because x -axis represent number of shirts and y-axis represent Total Cost

So, the point(20,160) means x = 20 and y=160

We have 20 shirts and the cost is $160

So, option B is correct option.

Please correct me if I’m wrong

Answers

Answer:

1 = No, 2 is correct, 3 = No, 4 is correct.

Step-by-step explanation:

A prism has a surface area of 350 mm2.Find the surface area of a scaled image with a scale factor of 2.

Answers

Just put an exponent of '2' on the scale factor and multiply it by the surface area.

Scale factor = 2

$\sf2^2\rightarrow4$

Multiply it:

$\sf350*4=1400~mm^2$

You would mulitply the factor by itself
2^2 = 4

then you would multiply the surface area by 4

350 x 4 = 1400 mm^2

Answer 1400 mm^2

A research firm wants to compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour?

Answers

Answer:

n=97

Step-by-step explanation:

1) Notation and definitions

$\sigma=3$ population standard deviation known

Confidence=90% or 0.9

n sample size required (variable of interest)

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The sample mean have the following distribution

$\bar X \sim N(\mu, (\sigma)/(√(n)))$

2) Calculation for the sample size required

In order to find the critical value we need to take in count that we are finding the interval for the mean with the population deviation known, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_(\alpha/2)=-1.64, t_(1-\alpha/2)=1.64$

The margin of error for the sample mean interval is given by this formula:

$ME=z_(\alpha/2)(\sigma)/(√(n))$ (a)

And on this case we have that $ME =\pm 0.5$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=((z_(\alpha/2) \sigma)/(ME))^2$ (b)

And replacing into equation (b) the values from part a we got:

$n=((1.64(3))/(0.5))^2 =96.83$

And rounded up we have that n=97

Find an equation of the circle that satisfies the given conditions. Endpoints of a diameter are P(-1, 1) and Q(5,9)

Answers

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
$((x_1+x_2)/(2), (y_1+y_2)/(2))$
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

$P(-1,1) \nx_1=-1 \n y_1=1 \n \n Q(5,9) \n x_2=5 \n y_2=9 \n \n(x_1+x_2)/(2)=(-1+5)/(2)=(4)/(2)=2 \n (y_1+y_2)/(2)=(1+9)/(2)=(10)/(2)=5$

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
$d=√((x_2-x_1)^2+(y_2-y_1)^2)$

$(-1,1) \n x_1=-1 \n y_1=1 \n \n (2,5) \n x_2=2 \n y_2=5 \n \n d=√((2-(-1))^2+(5-1)^2)=√(3^2+4^2)=√(9+16)=√(25)=5$

The radius is 5.

$(x-2)^2+(y-5)^2=5^2 \n\boxed{(x-2)^2+(y-5)^2=25}$

Which statements about the system are true? Check all that apply. y = x – 4
3y – x = –7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y–intercept.
The equations represent the same line.
The lines intersect.