What is the value of: 45 + 3(8 − 22) − 7 × 6 ÷ 3?

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

1. What is the value of: $45 + 3(8 - 22) - 7 \times 6 \div 3$ ?

Perform the operation inside the parentheses.
$45 + 3(-14) - 7 \times 6 \div 3$
Perform multiplication and division from left to right.
$45 - 42 - 42 \div 3$ $45 - 42 - 14$
Perform addition and subtraction from left to right.
$3 - 14$ $-11$
The correct option is B.
$\boxed{\text{B. -11}}$
2. The distance from the Earth to the Sun is approximately 150,000,000 km. How is this number written in standard form?
To write a number in standard form ( $a \times 10^n$ ), move the decimal point so that there is only one non-zero digit to its left.
$150,000,000 \text{ km} = 1.5 \times 10^n \text{ km}$
Count the number of places the decimal point was moved.
The decimal point was moved 8 places to the left.
$1.5 \times 10^8 \text{ km}$
The correct option is C.
$\boxed{\text{C. } 1.5 \times 10^8 \text{ km}}$
3. Given that $T = \log_{10} 10,000$ , what is the value of T?
Rewrite the number 10,000 as a power of 10.
$10,000 = 10^4$
Substitute this into the logarithm expression.
$T = \log_{10} (10^4)$
Use the logarithm property $\log_b (b^x) = x$ .
$T = 4$
The correct option is D.
$\boxed{\text{D. 4}}$
4. Using mathematical tables, evaluate: $\sqrt{3147} + 8.54^2$
Calculate the square root of 3147.
$\sqrt{3147} \approx 56.100089$
Calculate the square of 8.54.
$8.54^2 = 72.9316$
Add the two results.
$56.100089 + 72.9316 = 129.031689$
Rounding to four decimal places, we get 129.0317. Comparing with the given options, option A is the closest.
The correct option is A.
$\boxed{\text{A. 129.0297}}$
5. Six men working at the same rate can complete digging a shamba in 8 days. How many days will it take 4 of the men to complete the same work?
This is an inverse proportion problem.
The total work done is constant. Let $M$ be the number of men and $D$ be the number of days.
$M_1 D_1 = M_2 D_2$
Given $M_1 = 6$ men, $D_1 = 8$ days. We need to find $D_2$ for $M_2 = 4$ men.
Substitute the given values into the formula.
$6 \times 8 = 4 \times D_2$ $48 = 4 D_2$
Solve for $D_2$ .
$D_2 = \frac{48}{4}$ $D_2 = 12 \text{ days}$
The correct option is D.
$\boxed{\text{D. 12}}$

What is the value of: 45 + 3(8 - 22) - 7 × 6 ÷ 3?

Answer

Step-by-step solution

Perform the operation inside the parentheses.

Perform multiplication and division from left to right.

Perform addition and subtraction from left to right.

To write a number in standard form ( $a \times 10^n$ ), move the decimal point so that there is only one non-zero digit to its left.

Count the number of places the decimal point was moved.

Rewrite the number 10,000 as a power of 10.

Substitute this into the logarithm expression.

Use the logarithm property $\log_b (b^x) = x$ .

Calculate the square root of 3147.

Calculate the square of 8.54.

Add the two results.

This is an inverse proportion problem.

Substitute the given values into the formula.

Solve for $D_2$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions

What is the value of: 45 + 3(8 - 22) - 7 × 6 ÷ 3?

Answer

Step-by-step solution

Perform the operation inside the parentheses.

Perform multiplication and division from left to right.

Perform addition and subtraction from left to right.

To write a number in standard form (a×10na \times 10^na×10n), move the decimal point so that there is only one non-zero digit to its left.

Count the number of places the decimal point was moved.

Rewrite the number 10,000 as a power of 10.

Substitute this into the logarithm expression.

Use the logarithm property log⁡b(bx)=x\log_b (b^x) = xlogb​(bx)=x.

Calculate the square root of 3147.

Calculate the square of 8.54.

Add the two results.

This is an inverse proportion problem.

Substitute the given values into the formula.

Solve for D2D_2D2​.

Try one yourself

Still stuck on this one?

More Mathematics Questions

To write a number in standard form ( $a \times 10^n$ ), move the decimal point so that there is only one non-zero digit to its left.

Use the logarithm property $\log_b (b^x) = x$ .

Solve for $D_2$ .