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2 years ago

Marcel is nearing graduation. He just met with his counselor and she showed him this information.

Mathematics

2 answers:

Troyanec [42]2 years ago

5 0

Answer:

The correct answer option is A. $4,400.

Step-by-step explanation:

Cost of the tuition and fees for 1 year = $12,500

Grants and scholarships for 1 year = $6500

Cost of room and board for 1 year = $8200

Cost for work study for 1 year = $9800

So basically, Marcel pays = (tuition and fees + cost of room and board)

= $12,500 + $8,200 = $20,700

He can pay through the (grants and scholarships + cost for work-study) = $6,500 + $9,800 = $16,300

Therefore, Marcel needs to borrow = $20,700 - $16,300 = $4,400

MrRa [10]2 years ago

4 0

Answer:

The answer is A

Step-by-step explanation:

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Of the 500 sample households in the previous exercise, 7 had three or more large-screen TVs. (a) The percentage of households in

likoan [24]

Answer:

a) The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

$\hat p=\frac{7}{500}=0.014$

And that represent the 1.4%.

b) And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

Step-by-step explanation:

Data given and notation

n=500 represent the random sample taken

X=7 represent the households with three or more large-screen TVs

$\hat p=\frac{7}{500}=0.014$ estimated proportion of households with three or more large-screen TVs

$\alpha=0.05$ represent the significance level (no given, but is assumed)

z would represent the statistic (variable of interest)

p= population proportion of households with three or more large-screen TVs

Part a

The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

$\hat p=\frac{7}{500}=0.014$

And that represent the 1.4%.

Part b

Yes is possible. We hav that $np>10$ and $n(1-p)>10$ so we have the assumption of normality to find the interval.

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.014 - 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.00370$

$0.014 + 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.0243$

And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

4 0

2 years ago

What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2

Margaret [11]

Answer-

$\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}$

Solution-

Given expression is $(x+2)^4$

Applying Binomial Theorem

$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

Here,

a = x, b = 2 and n = 4

So,

$\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i$

Expanding the summation

$=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4$

$=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4$

$=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16$

$=x^4+8x^3+24x^2+32x+16$

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2 years ago

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Triangle XYZ is rotated to create the image triangle X'Y'Z'.

Solnce55 [7]

Answer:

The correct option is;

R0, 180°

Step-by-step explanation:

The coordinates of ΔXYZ are given as follows;

X(-2, 2), Y(1, 2), Z(0, 4)

The coordinates of ΔX'Y'Z' are given as follows;

X'(2, -2), Y'(-1, -1), Z'(0, -4)

Whereby, the coordinates of the point Y' is (-1, -2), we have the rule that describe the transformation of ΔXYZ to ΔX'Y'Z', given as follows

Coordinates of the preimage = (x, y)

Coordinates of the image = (-x, -y)

Which is in accordance with the transformation by rotation 180° about the origin.

7 0

2 years ago

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable i

jek_recluse [69]

Answer:

Option b. continuous random variable

Step-by-step explanation:

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment.

In this experiment the speed is the the random variable.

Now, speed can take any value within an interval.

It can take infinite values within an interval.

Also, speed is always measured and not counted.

Thus, speed is a continuous random variable.

Thus, the correct answer is

Option b) continuous random variable

6 0

2 years ago

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Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is

scZoUnD [109]

Answer:

sin−1(StartFraction 8.9 Over 10.9 EndFraction) = x

Step-by-step explanation:

From the given triangle JKL;

Hypotenuse KJ = 10.9

Length LJ is the opposite = 8.9cm

The angle LKJ is the angle opposite to side KJ = x

Using the SOH CAH TOA Identity;

sin theta = opp/hyp

sin LKJ = LJ/KJ

Sinx = 8.9/10.9

x = arcsin(8.9/10.9)

sin−1(StartFraction 8.9 Over 10.9 EndFraction) = x

7 0

2 years ago

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