The coefficient of xy in the product of (4x2 + 2y) and (3x + y2) is

Find 10-3. Write the subtraction fact two ways.

love history [14]

This is a problem of fact families, but what is fact families? Well it is a family of four things. Two of them are additions and two of them are subtractions. So this question asks about fact families by writing the subtraction fact two ways. So we have:

 $10-3$

First way. So let's take the number 10 and explain this problem using triangles. Let's say that we have 10 triangles in the beginning:

Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

So I want to take away 3 triangles, then by taking away 3 what is left? Well the answer is 7:

Δ Δ Δ Δ Δ
Δ Δ

That is, if we subtract 3 from 10 then the result is:

$10-3=7$

Second way. In this subtraction we take the same 10 triangles:

Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

Now I want to take away 7 triangles, then by taking away 7 what is left is 3:

Δ Δ Δ

That is, if we subtract 7 from 10 then the result is:

$10-7=3$

4 0

2 years ago

What is the 8th term of the binomial expansion (x + y)10?

12345 [234]

We can use the Pascal's Triangle to solve this problem. This pascal's triangle is shown in the figure below. To build the triangle, begin with the number 1 at the top, then continue placing numbers below it in a triangular pattern. In this way, each number are the numbers directly above added together. So, the expression:

$(x+y)^{10}$

Can be extended as follows, for n = 10:

$(x+y)^{10}=x^{10}+10x^{9}y+45x^{8}y^2+120x^{7}y^3+210x^{6}y^4+252x^{5}y^5+210x^{4}y^6+120x^{3}y^7+45x^{2}y^8+10xy^9+y^{10}$

So, the 8th term of the binomial expansion is:

$120x^{3}y^7$

4 0

2 years ago

Which of the graphs below represent the function f(x) = − x3 + 4x2 − x + 3? You may sketch the graph to compare.

Alekssandra [29.7K]

Answer:

Please see the attachment.

Step-by-step explanation:

$\text{Given function:}f(x)=-x^3+4x^2-x+3$

Now we find the x and y intercept of f(x)

For x-intercept: Put f(x)=0 and solve for x

So, x=3.92 (Just before 4 on x-axis)

For y-intercept: Put x=0 and solve for f(0)

So, y=3 (Passes through y-axis at 3)

End Behavior: Third degree function

$x\rightarrow -\infty , f(x)\rightarrow \infty$

$x\rightarrow \infty , f(x)\rightarrow -\infty$

Possible graph of the f(x). Please see the attachment.

7 0

2 years ago

Read 2 more answers

Pete has 4 packs of gumballs. Each pack has 5 gumballs. If Pete gives the same number of gumballs to 6 friends, how many gumball

Illusion [34]

Answer: Each friend will get 3 gumballs.

Step-by-step explanation:

Given: Pete has 4 packs of gumballs. Each pack has 5 gumballs.

Total gumballs he has = 4 x 5 = 20

Now , if he needs to divide them into 6 friends , then each friend will get (20 ÷ 6) gumballs

$20\div 6=\dfrac{20}{6}=\dfrac{18+2}{6}=\dfrac{3\times6+2}{6}=3\dfrac26$

So each friend will get 3 gumballs.

5 0

2 years ago

A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchas

Nataly_w [17]

Answer:

The p value obtained and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidenc to reject the null hypothesis, and we can said that at 5% of significance the proportion of new laptop's with fully charge for the new model is significantly higher compared to the old model.

Step-by-step explanation:

1) Data given and notation n

n=100 represent the random sample taken

X=96 represent the laptop's arrived with fully charged batteries.

$\hat p=\frac{96}{100}=0.96$ estimated proportion of laptop's arrived with fully charged batteries.

$p_o=0.85$ is the value that we want to test

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the new model’s rate is at least as high as the previous model.:

Null hypothesis: $p \leq 0.85$

Alternative hypothesis: $p > 0.85$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.96 -0.85}{\sqrt{\frac{0.85(1-0.85)}{100}}}=3.08$

4) Statistical decision

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level is not provided, but we can assume $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =P(z>3.08)=0.0010$

So based on the p value obtained and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidenc to reject the null hypothesis, and we can said that at 5% of significance the proportion of new laptop's with fully charge for the new model is significantly higher compared to the old model.

4 0

2 years ago