Prove the following is equivalent: n* (n-1 C 2) = nC2 * (n − 2) .

Answer:

5.60

Step-by-step explanation:

20% of 10 = 2             he gave 2 dollars to his sis

2 - 10 = 8                      now lucas has 8 dollars

30% of 8 = 2.4               he gave 2.40 dollars to his bro

2.4 - 8 = 5.6

now he has 5 dollars and 60 cents

give me brainlest pls pls pls   :>

Answer:

5.60

Step-by-step explanation:

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Answer:

--------------

Average speed equation:

Substitute 350 for d and 5.15 for t:

The average speed must be approximately 68 km per hour.

Answer:

42x+22

Step-by-step explanation:

Answer: 52.381

7(6+5)−13

7(6x+5)−13

7(6x+5)−13

Simplify

1

Distribute

7(6+5)−13

42+35−13

2

Subtract the numbers

42+35−13

42+22

Solution

42+22

52.381

Step-by-step explanation:

Answer:

P is you pass the class, so it's the hypothesis in the conditional. And Q is the conclusion, which ic you got to the next grade.

Step-by-step explanation:

In order to got to the next grade, you need to pass the class.

or

If you pass the class, you go to the next grade.

Answer:

7 + 15x

Step-by-step explanation:

given: sum of seven and the product of fifteen and a number

sum of seven: 7 +

the product of fifteen: 15 ·

a number: x, n, etc

Putting it together: 7 + 15 · x

Simplfiying: 7 + 15x

Hope this helps, have a nice day! :D

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

To know more about the median, visit:

brainly.com/question/300591

#SPJ11

Answer:

x=1

Step-by-step explanation:

2x-6=-6x+2

8x=8

x=1

Answer: They’re a type of soft coral I’m pretty sure

Step-by-step explanation:

The number of penguins is 15.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of dolphins to penguins = 2:5

This means,

For every 2 dolphins, there are 5 penguins.

Now,

For 6 dolphins,

2 dolphins = 5 penguins

Multiply 3 on both sides.

6 dolphins = 15 penguins

Thus,

There will be 15 penguins.

Learn more about ratios here:

https://brainly.com/question/2462048

#SPJ2

Answer + Explanation:

let x be the measure of angle x

let y be the measure of angle y

\(\left \{ {{x + y = 180} \atop {x=24+y}} \right.\)

Now, solve:

plug x = 24 + y into x + y = 180

24 + y + y = 180

24 + 2y = 180

2y = 156

y = 78

Now, plug this back into the equation x = 24 + 78

x = 102

Answer:

x= 102

y= 78

Step-by-step explanation:

x+y=180

x= y + 24

2x-24 = 180

Answer:

Step-by-step explanation:

The two angles are interior angles on the same side of the transversal. They are supplementary.

2x + 50 + 5x - 80 = 180             Combine like terms

7x - 30 = 180                              Add 30 to both sides

7x = 210                                     Divide by 7 on both sides

x = 210/7

x = 30

Answer:

-6 p+4

-6+4

= -2

Step-by-step explanation:

Mark brainliest

p +4= -2

Like the given function is a linear equation with one variable (p). You can solve this equation replacing p for the informed value (-6).

Here it is important to remember the rules to addition of integers numbers:

+  +   Add  Final result (+)  

-   -          Add  Final result (-)  

+  -      Subtract  Final result (the sign of the integer having greater value )

-   +      Subtract  Final result (the sign of the integer having greater value )

If p=-6, then for p+4, you have:

-6+4=-2. The sign is negative because according to the rules to addition of integers numbers, you must use the sign from the larger number, in this case, -6.

Read more about rules for adding integers here:

https://brainly.com/question/18375556

Answer:

more sales than b

Step-by-step explanation:

if they invert more in the thing of a company then they will have more ganancia.

Answer:

y = 2x + 5

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

3y + 2 = 62

3y = 60

y = 20

The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

A quantity that has both magnitude and direction but not position. Examples of such quantities are velocity and acceleration.

Given that,

The equation for the plane through p0(−1,1,9)

The xy-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.

Then the equation of the plane through (-1, 1, 9) that is parallel to the xy-plane has equation

〈x - (-1), y - 1, z - 9〉 • 〈0, 0, 1〉 = 0

x + 1 = 0

y - 1 = 0

z - 9 = 1

z = 1 + 9

z = 10

Therefore,

The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

To learn more about Vector visit :

brainly.com/question/16856030

#SPJ4

Answer:

2

Step-by-step explanation:

rise/run 4/2

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer: C) 4 x 3 cm

Step-by-step explanation:

The only dimension affected by the cut was 5, because the cut was perfectly parallel to the 4x3 face.

The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.

The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.

To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.

Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.

To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.

Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.

If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.

To learn more about chi-square click here: brainly.com/question/32379532

#SPJ11

Answer:

x=0

Step-by-step explanation:

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

Distribute the negative:

2x+2=2+4x

Subtract 2 from both sides:

2x=4x

Subtract 2x from both sides:

0=2x

Divide by 2 on both sides:

0=x

m∠ AEM = 20°

From the given figure, we can see that m∠ AEM is alternate to m∠ ACE

Note that m∠ ACE = 20°

Alternate angles are equal.

If m∠ ACE is alternate to m∠ AEM

Then, m∠ AEM = 20°

Hence, m∠ AEM = 20°

Learn more about alternate angles here:

https://brainly.com/question/24839702

#SPJ1

Answer:

19

Step-by-step explanation:

19 is your answer i guess

Answer:

H

Step-by-step explanation:

The rectangle has a length of (2x + 1) and a width of (5x - 4).

And we want to select the expression that represents the rectangle's area.

Recall that a rectangle's area is simply its length multiplied by its width. Thus:

\(A=(2x+1)(5x-4)\)

Expand by distributing:

\(A=(2x+1)(5x)+(2x+1)(-4)\)

Distribute:

\(A=(10x^2+5x)+(-8x-4)\)

Simplify:

\(A=10x^2-3x-4\)

Hence, our answer is H.

Answer:

3 + 2k

Step-by-step explanation:

1/5(15+10k)

distribute

1/5 * 15 + 1/5 * 10k

3 + 2k

Answer:

3 + 2k

Step-by-step explanation:

First, I am going to explain what the distributive property is. Lets say he had the expression a(b + c). We can "distribute" the a to the b and c:

a(b + c) = ab + ac

We can apply the distributive property to the expression 1/5(15 + 10k):

1/5(15 + 10k)

= (1/5)(15) + (1/5)(10k)

= 3 + 2k

By using the distributive property, we found the expression 3 + 2k.

I hope you find my answer helpful.

Answer:

7x + 1 and 2a - 1

Step-by-step explanation:

(a)

2x + 1 + 5x ← collect like terms

= (2x + 5x) + 1

= 7x + 1

(b)

- 3a + 2 + 5a - 3 ← collect like terms

= (- 3a + 5a) + (2 - 3)

= 2a + (- 1)

= 2a - 1

Answer: y= (5/4)x-4

Step-by-step explanation:

1. Move 5x to the other side and you get -4y = -5x+16

2. Divide everything by -4

Y= 5/4 cause the negs cancel out and -4