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3 years ago

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Which equation demonstrates the distributive property? A) 14 + 77 = 91 B) 14 x 77 = 77 x 14 C) 14 + 77 = 7(2 + 11) D) (2 + 11)7

= 7(2 + 11)

2 answers:

sergey [27]3 years ago

8 0

Answer:

C)14 + 77 = 7(2 + 11)

Step-by-step explanation:

You multiply the sum of the number that is the same as multiplying each addend by that number and then you add the two products.

Hope this helped

Vikki [24]3 years ago

8 0

A) 14 + 77 = 91 - it's the sum

B) 14 × 77 = 77 × 14 - it's a commutative property <em>a × b = b × a</em>

C) 14 + 77 = 7(2 + 11) - it's a distributive property <em>a(b + c) = ab + ac</em>

D) (2 + 11)7 = 7(2 + 11) - it's a commutative property <em>a × b = b × a</em>

<h3><em>Answer: </em>C) 14 + 77 = 7(2 + 11)</h3>

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Please help me answer this!!!!

garik1379 [7]

<h3><u>Answer</u><u>:</u></h3>

$7 \frac{1}{2}$

<h3><u>Explan</u><u>ation</u><u>:</u></h3>

First, convert any mixed numbers to fractions. An easy way to convert:

$4 \frac{1}{2} = 4 \times 2 + 1$

<h3>=</h3>

$\frac{9}{2} \div \frac{3}{5}$

Then, apply the fractions formula for division.

$\frac{9 \times5 }{2 \times 3} = \frac{45}{6}$

Then, simplify.

$\frac{45}{6} = 7 \frac{1}{2}$

5 0

3 years ago

If X denotes the number of heads in n tosses of a coin, what is the standard deviation of the random variable X? Does this stand

vfiekz [6]

Answer:

$\sigma=\sqrt{np(1-p)}=\sqrt{n*0.5(1-0.5)}=\frac{\sqrt{n}}{2}$

As we can see the deviation is proportional to the value of n and if n increase then the deviation increases too. So then the deviation would be larger when n gets larger.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

We can define the following random variable X ="Number of heads in n tosses of a coin".

We assume that the coin is fair and then $P(H)= 0.5$ for any trial so then we can model X with the following distribution:

$X \sim Bin (n, p=0.5)$

For this distribution the mean and variance are given by:

$E(X)=np=n*0.5=\frac{n}{2}$

$Var(X)= np(1-p) = n*0.5*(1-0.5) = 0.25 n = \frac{n}{4}$

And the deviation would be just the square root of the variance and we got:

$\sigma=\sqrt{np(1-p)}=\sqrt{n*0.5(1-0.5)}=\frac{\sqrt{n}}{2}$

Does this standard deviation get larger or smaller when n gets larger?

As we can see the deviation is proportional to the value of n and if n increase then the deviation increases too. So then the deviation would be larger when n gets larger.

3 0

3 years ago

the axis of symmetry for the graph of the function is f(x) = 1/4x2 bx 10 is x = 6. what is the value of b?

Lady bird [3.3K]

we have

$f(x)=\frac{1}{4} x^{2} +bx+10$

This is a vertical parabola open upward

The axis of symmetry is equal to the x-coordinate of the vertex

The vertex is the point (h,k)

the equation of the axis of symmetry is $x=h$

In this problem

$x=6$

so the x-coordinate of the vertex is $h=6$

<u>Convert the quadratic equation in vertex form</u>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-10=\frac{1}{4} x^{2} +bx$

Factor the leading coefficient

$f(x)-10=\frac{1}{4}(x^{2} +4bx)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-10+b^{2}=\frac{1}{4}(x^{2} +4bx+4b^{2})$

Rewrite as perfect squares

$f(x)+(b^{2}-10)=\frac{1}{4}(x+2b)^{2}$

$f(x)=\frac{1}{4}(x+2b)^{2}-(b^{2}-10)$

remember that

$h=6$

so

$(x+2b)=(x-6)$

$2b=-6$

$b=-3$

substitute in the equation

$f(x)=\frac{1}{4}(x-6)^{2}-((-3)^{2}-10)$

$f(x)=\frac{1}{4}(x-6)^{2}+1$

therefore

<u>the answer is</u>

$b=-3$

8 0

4 years ago

Read 2 more answers

The perimeter of a parallelogram is 72 meters. The width of the parallelogram is 4 less than its length. Find the length and the

hram777 [196]

Perimeter = 72m
length = x
width = x - 4

P = 2l + 2w
72 = 2x + 2(x - 4)
72 = 2x + 2x - 8
72 = 4x - 8
72 + 8 = 4x
80 = 4x
80/4 = x
x = 20

Therefore, the length = 20m and width = 16m

8 0

3 years ago

Celia simplified the expression Negative 4 x (1 minus 3) minus (2 x + 2). She checked her work by letting x = 5 in both expressi

guapka [62]

Answer:

6x-2

Step-by-step explanation:

-4x(1-3)-(2x+2)

= 4x+12x-2x-2

6x-2

(simplify)

8 0

2 years ago