A composite figure is formed by combining a square and a triangle. Its total area is 60.5 ft2. The area of the triangle is 35.5 ft2. What is the length of each side of the square? Complete the explanation.

Answer:

He is in debt money, therefore he has less than 0$ which means he has a negative sum

Step-by-step explanation:

Answer:

Step-by-step explanation:

Assume that the [tex]20[/tex] mile-per-gallon car consumed all that [tex]75[/tex] gallons of fuel. How far would the cars have travelled?

[tex]20 \times 75 = 1500\; \text{miles}[/tex].

This assumption overestimated the total mileage of the two cars by [tex]1500 - 1325 = 175\; \text{miles}[/tex]. Here's why: for every gallon that the second ([tex]15[/tex] mile-per-gallon) car consumed, this assumption would overestimate the total mileage by [tex]20 - 15 = 5\; \text{miles}[/tex]. Therefore, the overestimation of [tex]175\; \text{miles}[/tex] corresponds to:

[tex]\begin{aligned} & 175\; \text{miles overestimated} \\ & \times \left(\frac{1\; \text{gallon consumed by the second car}}{5\; \text{miles overestimated}}\right)\\ &= \frac{175}{5}\; \text{gallons consumed by the second car} \\ &= 35\; \text{gallons consumed by the second car}\end{aligned}[/tex].

Therefore, the second car consumed [tex]35\; \text{gallons}[/tex]. The first car would have consumed [tex]75 - 35 = 40\; \text{gallons}[/tex].

Verify the results: [tex]40 \times 20 + 35\times 15 = 1325\; \text{miles}[/tex].

Answer:

uh 14

Step-by-step explanation:

i did really just add 12+2

hope it help :)

Step-by-step explanation:

Using Binomial Expansion,

(x + y)³

= 3C0 * x³ + 3C1 * x²y + 3C2 * xy² + 3C3 * y³.

Therefore the coefficient of xy² is 3C2 = 3.

Answer:

The coefficient of the xy² term is 3.

For your question about xy⁵, the coefficient is 6

And for the x²y² question, it is also 6

Step-by-step explanation:

We can simply expand the expression to find the answer:

(x + y)³

= (x + y)(x + y)(x + y)

= (x + y)(x² + 2xy + y²)

= x³ + 2x²y + xy² + x²y + 2xy² + y³

= x³ + 3x²y + 3xy² + y³

So the term term containing xy² has a coefficient of 3

Now, there's actually a simple way to do this, and that's using Pascal's triangle.  If you're not familiar with it, here's a quick representation of the first few lines:

0                                    1

1                                  1     1

2                              1     2     1

3                           1     3     3     1

4                       1      4     6     4     1

5                    1      5    10    10    5    1

6                1      6     15   20   15    6    1

7             1      7     21   35   35   21   7    1

8         1      8     28   56  70   56   28  8   1

You'll notice that each number is simply the sum of the two numbers above it; below 4 and 6 wes see 10, below 20 and 15 is 35, etc.

This is very useful in this case, as the you may notice that the solution to each of the questions asked can be answered by this triangle.  For instance, when we solved (x + y)³, the coefficients of the terms were  1, 3, 3, and 1.  For a perfect square, it's 1, 2 and 1, and so on.  So to get the answers to your questions, you need only look at this triangle.

For example, want the the coefficent of the fourth term in the expansion of (x + y)⁷, it's easy, just look at the seventh row, and look for the fourth number, which would be 35.

But as we're given the x and y powers, but not the position of the term, we need to work that out as well.  Thankfully there's an easy trick to that.  The exponents will always be like this

[tex]x^{n}y^0 + x^{n - 1}y^1 + x^{n - 2}y^2 + ..... + x^2y^{n - 2} + x^1y^{n - 1} + x^0y^{n}[/tex]

where n is the number we're raising the binomial to.

We could put together an equation to solve this, but instead of going through a whole lesson, I'll just update the answer at the top.

Answer:

Angle E

Step-by-step explanation:

Answer:

yes

no

yes

no

hope this helps

Answer:

1. Yes

2. No

3.Yes

4.No

Step-by-step explanation:

I did the test and got it right!

Answer:

the slope of the line passing through (4, 4)  and (9, 1)   is:

Slope = -3/5

Step-by-step explanation:

Given the points on the graph

Here:

(x₁, y₁) = (4, 4)

(x₂, y₂) = (9, 1)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [1 - 4] / [9 - 4]

               = -3 / 5

Thus, the slope of the line passing through (4, 4)  and (9, 1)   is:

Slope = -3/5

Answer: 873.76

First find 1% of 2302 which will be 2302/100=23.02

to find 43% of 2302 multiply 1% of 2302 with 43

43*23.02 = 873.76

Answer:

Contains two 6x6 triangles, contains one 12x3 rectangle, four 2x2 triangles, and two 2x2 squares.

88

Step-by-step explanation:

You only need the area of one side of this shape to find the total area.

((6*6)/2+(3*6)+(2*2)+(2*2))2 = 88. What's inside the parenthesis is the area for one side of the shape, then you can multiply that by two to get the entire area.

Answer:

The village market is better than Sam's Club

Step-by-step explanation:

If you buy 5 more cans of green beans at the village, it will cost $4.40 in total. Therefore if you go buy the beans at Sam's club, the village one will be cheaper.

Answer:

4.16

Step-by-step explanation:

160%=1.6

1.6 times 2.6 =4.16

Answer:

a) 0% probability that one car chosen at random will have less than 49.5 tons of coal

b) 0% probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 56, \sigma = 1.1[/tex]

a. What is the probability that one car chosen at random will have less than 49.5 tons of coal?

This is the pvalue of Z when X = 49.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49.5 - 56}{1.1}[/tex]

[tex]Z = -5.9[/tex]

[tex]Z = -5.9[/tex] has a pvalue of 0

So 0% probability that one car chosen at random will have less than 49.5 tons of coal.

b. What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal?

Now we have [tex]n = 35[/tex], applying the Central limit theorem [tex]s = \frac{1.1}{\sqrt{35}} = 0.1859[/tex]

This is the pvalue of Z when X = 49.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{49.5 - 56}{0.1859}[/tex]

[tex]Z = -35[/tex]

[tex]Z = -35[/tex] has a pvalue of 0

So 0% probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal

Answer:

D: 50% on car payment and college savings

Step-by-step explanation:

225+375 = 600

50% of 1200 is 600

Answer:

Total cost= $141.75

Step-by-step explanation:

Giving the following information:

Bernie's Bargains 6 DVDs for $56.70

Greg's Giveaways 10 DVDs for $99.70

Stan's Steals 8 DVDs for $79.68

First, we need to determine the unitary price of each and choose the lowest one:

Bernie= 56.7/6= $9.45

Greg= 99.7/10= $9.7

Stan= 79.68/8= $9.96

The lowest price is $9.45.

Now, the total cost of 15 DVDs:

Total cost= 9.45*15

Total cost= $141.75

Answer:

149.25

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

simplify 8/10 into 2/5 then 2/5 of 30 is 24

Answer:

0.3

Step-by-step explanation:

0.26?

0.3

Answer:

2 pounds (Specifically 2.2 pounds)

Answer:

2.2lbs

Step-by-step explanation:

Answer:

-x=5 so x=-5 so x is 5 units to the left of 0

Step-by-step explanation:

Answer:

X=x is 13 units to the left of 0.

Use the drop-down menus to complete the statement about −x.

CLEAR CHECK

−x is

units to the

of 0.

Step-by-step explanation:

Answer:

P(x ≥ 30) = 0.3859

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 29, \sigma = 3.4[/tex]

This probability is going to be 1 subtracted by the pvalue of Z when X = 30. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 29}{3.4}[/tex]

[tex]Z = 0.29[/tex]

[tex]Z = 0.29[/tex] has a pvalue of 0.6141

1 - 0.6141 = 0.3859

So

P(x ≥ 30) = 0.3859

Answer:

what fraction ??

Step-by-step explanation:

I don't see the problem

Answer:

7.5

Step-by-step explanation:

10-2.5=7.5

Answer:

[tex]\frac{7}{31} = 0.2258 = 22.58\%[/tex] probability that a randomly selected student prefers hip hop music.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, we have that:

14 students prefer hip hop music

There are 18 + 8 + 20 + 14 = 62 students

So

[tex]p = \frac{14}{62} = \frac{7}{31}[/tex]

[tex]\frac{7}{31} = 0.2258 = 22.58\%[/tex] probability that a randomly selected student prefers hip hop music.

Answer:

the answer is D.

Step-by-step explanation:

Since the square: (3√15) is common in both of them, you only focus on 21 and 9. if you subtract 9 from 21, it will give you 12. so, just add (3√15) to 12, which will give you: 12^3sqrt15

Answer:

A

Step-by-step explanation:

(x-4)^2 = x^2 -4x -4x + (-4)*(-4)

= x^2-8x+16 as required

Answer:

The ranges of value of k are values larger than 0 and lower than 16.

Step-by-step explanation:

Suppose we have a second order polynomial in the following format:

[tex]ax^2 + bx + c = 0, a \neq 0[/tex]

It will have no roots if:

[tex]\Delta = b^2 - 4ac < 0[/tex]

In this question, we have that:

[tex]hx^2 + hx - 4 = 0[/tex]

So, the coefficients are:

[tex]a = h, b = h, c = -4[/tex]

Then

[tex]\Delta < 0[/tex]

[tex]b^2 - 4ac < 0[/tex]

[tex]h^2 - 16h < 0[/tex]

A quadratic function, with a positive(as is 1 in this inequality), will be negative between it's roots.

The roots are:

[tex]h^2 - 16h = 0[/tex]

[tex]h(h - 16) = 0[/tex]

So

h = 0 or h = 16.

The ranes of value of k are values larger than 0 and lower than 16.

Answer:

a

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

divide 1020 by 60

1020 ÷ 60 = 17

meaning that you go 17 mph

Answer:

17 hours.

Step-by-step explanation:

Formula

d = r * t

Givens

t = ?

d = 1020 miles

r = 60 miles per hour

Solution

1020 = 60 * t             Divide by 60

1020/60 = t

17 hours.

Answer: $11.25

Step-by-step explanation:

Answer:

$11.25

Step-by-step explanation:

I assume that x = the 5 videos streamed

5*1.25=6.25

6.25+5 =11.25

y=$11.25