Find the product of -8 and -7.

-1
1
56
-56

Answers

Answer 1

Answer:

-8-7

= -15

None of the choices

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The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm?

Answers

what we can do is set up an algebraic equation.

our variable can me L for Length

3L+4L+5L=90

now all we have to do is solve

12L=90
---- ----
12 12

L=7.5

now multiple each number in the ratio by 7.5 to find out how long each side is

3 times 7.5 is 22.5
4 times 7.5 is 30
5 times 7.5 is 37.5

the side lengths are 22.5, 30, and 37.5

A jar contains 24 coins: 10 quarters, 6 dimes, 2 nickels, and 6 pennies.What is the probability of randomly drawing _____ ?
1. a penny
2. a quarter
3. a coin that is not a penny

Answers

The probability of randomly drawing a penny is 6/24 or 1/4, since there are 6 pennies out of a total of 24 coins.

How to solve and What is Probability?

The probability of randomly drawing a quarter is 10/24 or 5/12, since there are 10 quarters out of a total of 24 coins. The probability of randomly drawing a coin that is not a penny is 18/24 or 3/4, since there are 18 coins that are not pennies out of a total of 24 coins.

Probability is the branch of mathematics that deals with measuring the likelihood or chance of an event or outcome occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Probability theory is used to make predictions and informed decisions based on available data in various fields, including statistics, finance, engineering, and science.

It involves understanding and analyzing random events, and determining the likelihood of specific outcomes. Probability is an essential tool for decision-making in various applications, such as risk analysis, game theory, and quality control.

To know more about Probability visit:

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Write each number as a power of given base.8/27;base 2/3

Answers

Suppose x=log(8/27)with base 2/3

Then,

(2/3)^x=8/27

(2/3)^x=(2/3)^3

So, x=3

Hence, the value of log(8/37) under base 2/3 is 3.

A ball is thrown down from a balcony with a vertical velocity (in ft/s) given by V(t)= –32t – 10. Chose the inequality that represents the time for which the velocity of the ball will be between –90 and –58 ft/s

Answers

If the ball is thrown downward, it has a negative velocity due to the direction is traveling. By just looking at the magnitude of the velocity 90 is greater than 58, the negative sign only represents that it is moving downwards. So the correct answer is choice 2

Inequalities are used to represent unequal expressions or numbers.

The inequality that represents the time for which the velocity of the ball will be between -90 and -58 ft/s is: $-90 < -32t - 10< -58$

Given

$V(t) = -32t - 10$

$V_1 = -90$

$V_1 = -58$

From the numbering system;

$-90 < -58$ -- i.e. -90 is less than -58.

This means that:

$-90 < V(t) < -58$

Substitute $V(t) = -32t - 10$

$-90 < -32t - 10< -58$

Hence, the inequality that represents the scenario is:

$-90 < -32t - 10< -58$

Answers

Answer:

9 years 4 months

Step-by-step explanation:

To find out how long it will take for Allie's initial deposit of $300to grow to $995 in a savings account with a 13% annual interest rate compounded quarterly, we can use the compound interest formula:

$\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\n\nA=P\left(1+(r)/(n)\right)^(nt)\n\n\textsf{where:}\n\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\n\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\n\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\n\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\n\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}$

In this case:

A = $995
P = $300
r = 13% = 0.13
n = 4 (quarterly)

Substitute the values into the formula and solve for t:

$995=300\left(1+(0.13)/(4)\right)^(4t)$

Simplify the expression inside the bracket:

$995=300\left(1.0325\right)^(4t)$

Divide both sides of the equation by 300:

$(995)/(300)=\left(1.0325\right)^(4t)$

Take natural logs (ln) of both sides of the equation:

$\ln\left((995)/(300)\right)=\ln\left(1.0325^(4t)\right)$

$\textsf{Apply the power law:} \quad \ln x^n=n \ln x$

$\ln\left((995)/(300)\right)=4t\ln\left(1.0325\right)$

Divide both sides of the equation by 4ln(1.0325) to isolate t:

$(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))=t$

$t=(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))$

Evaluate using a calculator:

$t=9.37184241...$

Therefore, it will take 9.37 years for the balance to grow to $995.00.

To determine the number of months, subtract 9 from the value of t and multiply by 12:

$\textsf{Months}=12(9.37184241...-9)=4.46210895...$

Therefore, it will take 9 years and 4 months (rounded to the nearest month) for the balance to grow to $995.00.

Additional comments

In the case of quarterly compounding, the interest is calculated and added to the account balance every three months (once every quarter). So, even though it will take 9 years and 4 months for the balance to reach $995.00, Allie's account will not show this exact amount at that specific time. It will show a balance of $979.61 at 9 years and 3 months, and a balance of $1,011.45 at 9 years and 6 months, so technically, the account balance will still show as $979.61 at 9 years and 4 months.

Answer:

9 years and 4 months

Step-by-step explanation:

In order to calculate the number of years and months it will take for Allie's savings account balance to grow to $995.00, we can use the following compound interest formula:

$\sf A = P\left(1 + (r)/(n)\right)^(nt)$