Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.

Answers

Answer 1

Answer: so... our numbers... let's say the first one is hmmm "a"
so the second and subsequent are
a
a+1
a+2
a+3
a+4

there, 5 consecutive whole numbers or integers for that matter

now, we know the sum of the square of the first three,
is the same as the sum of the square of the last two

so $\bf \begin{cases}a\na+1\na+2\n\textendash\textendash\textendash\textendash\na+3\na+4\end{cases}\qquad (a)^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2$

do a binomial theorem expansion on those, solve for "a"

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The tax on a property with an assessed value of $90,000 is $1,350. Find the tax on a property with anassessed value of $140,000.
a. $1500.00
b. $150.00
c. $2100.00
d. $210.00
e. $750.00

Answers

Answer:

0.015 or 1.5% tax

Step-by-step explanation:

90000x0.015 = 1350

let’s go to the beach each let’s go get away say say what they gonna say the patron on

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Solve the inequality.

Answers

Answer:

y > 9

Step-by-step explanation:

Given inequality:

$-6 > -(2)/(3)y$

To solve the given inequality, we need to isolate y on one side of the equation.

Begin by multiplying both sides of the inequality by 3 to eliminate the fraction on the right side:

$-6 \cdot 3 > -(2)/(3)y\cdot 3$

$-18 > -2y$

Now, divide both sides of the inequality by -8 to isolate y. Remember to reverse the inequality sign, as we are dividing by a negative number.

$(-18)/(-2) > (-2y)/(-2)$

$9 < y$

Therefore, the solution is:

$\Large\boxed{\boxed{y > 9}}$

Use the numbers from 1 to 9 to fill in the blanks to get the smallest possible answer.

Answers

Answer: first blank: 1

second blank: 9

third blank: -7

fourth blank: 2

1x-9=-7

x=2

how many pounds of chamomile tea that costs 18.20 per pound must be mixed with 12lb of orange tea that costs 12.25 per pound to make a mixture that costs 14.63 per pound

Answers

8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.

Step-by-step explanation:

We are given the following in the question:

Chamomile tea:

Unit cost = 18.20 per pound

Amount = x pounds

Total cost =

$18.20* x = 18.20x$

Orange tea:

Unit cost = 12.25 per pound

Amount = 12 pounds

Total cost =

$12.25* 12 = 147$

Total mixture:

Unit cost = 14.63 per pound

Amount = (12+x) pounds

Total cost =

$14.63* (12+x) = 175.56 + 14.63x$

We can write the equation that cost of mixture is equal to cost of chamomile tea and orange tea.

$18.20x + 147 = 175.56 + 14.63x\n\Rightarrow 18.20x- 14.63x = 175.56-147\n\Rightarrow 3.57x = 28.56\n\Rightarrow x = 8$

Thus, 8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.

Judging on the basis of experience, a politician claims that 57% of voters in a certain area have voted for an independent candidate in past elections. Suppose you surveyed 25 randomly selected people in that area, and 18 of them reported having voted for an independent candidate. The null hypothesis is that the overall proportion of voters in the area that have voted for an independent candidate is 57%. What value of the test statistic should you report?

Answers

Answer: z= 1.51

Step-by-step explanation:

Test statistic for proportion is given by :-

$z=\frac{p-P}{\sqrt{(PQ)/(n)}}$

Where n is sample size ,p is the sample proportion , P Is the population proportion and Q =1 - P.

Given : P=57% = 0.57

Q= 1- P = 1-0.57=0.43

n = 25

$p=(18)/(25)=0.72$

Test statistic for proportion will be :-

$z=\frac{0.72-0.57}{\sqrt{(0.57*0.43)/(25)}}\approx1.51$

We should report the value of test statistic z= 1.51

Which fraction is equivalent to 0.36

Answers

Answer: 9/25, Percentage: 36%

Final answer:

The fraction equivalent to 0.36 is 36/100, which can be further simplified to 9/25.

Explanation:

In the subject of mathematics, to convert a decimal into a fraction, one must understand the place value of the decimal. In your case, the decimal 0.36 is in the hundredths place, which means you can express this decimal as 36 over 100. Therefore, the fraction equivalent to 0.36 is 36/100. To simplify this fraction, we can divide both the numerator (36) and the denominator (100) by the greatest common divisor, which is 4. This gives us a simplified fraction of 9/25.