8 cm What is the area of the circle

Equivalent 5(6x+3y)

STALIN [3.7K]

The equivalent expression is 30x + 15y

Solution:

Given that we have to find the equivalent expression for given expression

Given expression is:

5(6x + 3y)

We can find the equivalent expression by using distributive property

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

By distributive property,

a(b + c) = ab + ac

Therefore, in given expression 5(6x + 3y), 5 can be multiplied with both 6x and 3y

$\rightarrow 5(6x + 3y) = 5 \times 6x + 5 \times 3y$

Multiply the numbers and simplify

$\rightarrow 5(6x + 3y) = 5 \times 6x + 5 \times 3y = 30x + 15y$

Thus the equivalent expression is 30x + 15y

3 0

3 years ago

A student wanted to find the sum of all the even numbers from 1 to 100. He said:

murzikaleks [220]

Answer:

The statements are incorrect as: The sum of even numbers from 1 to 100(i.e. 2550) is not double\twice of the sum of odd numbers from 1 to 100(i.e. 2500).

Step-by-step explanation:

We know that sum of an Arithmetic Progression(A.P.) is given by:

where 'n' denotes the "number" of digits whose sum is to be determined, 'a' denotes the first digit of the series and '' denote last digit of the series.

Now the sum of even numbers i.e. 2+4+6+8+....+100 is given by the use of sum of the arithmetic progression since the series is an A.P. with a common difference of 2.

image with explanation

Hence, sum of even numbers from 1 to 100 is 2550.

Also the series of odd numbers is an A.P. with a common difference of 2.

sum of odd numbers from 1 to 100 is given by: 1+3+5+....+99

.

Hence, the sum of all the odd numbers from 1 to 100 is 2500.

Clearly the sum of even numbers from 1 to 100(i.e. 2550) is not double of the sum of odd numbers from 1 to 100(i.e. 2500).

Hence the statement is incorrect.

Step-by-step explanation:

3 0

3 years ago

List 4 rational numbers between-4 and -3?

lana [24]

-3.1, -3.5, -3.9, -3.8

6 0

3 years ago

Here are summary statistics for randomly selected weights of newborn girls: nequals=174174, x overbarxequals=30.930.9 hg, seq

MaRussiya [10]

Answer:

The 95% confidence interval would be given by (29.780;32.020)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=30.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=174-1=173$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that $t_{\alpha/2}=1.97$ , this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.