The dimensions of a triangular prism are shown in the diagram.

yaroslaw [1]

125 = 5 * 5 * 5 = 5³

90 = 2 * 3 * 3 * 5 = 2 * 3² * 5

92 = 2 * 2 * 23 = 2² * 23

3 0

4 years ago

The check-cashing store also makes one-month add-on interest loans at 7.8 percent discount interest per week. Thus if you borrow

masya89 [10]

Answer:

APR = 416%

EAR = 5370.60%

Step-by-step explanation:

Given:

Interest rate = 7.8% per week

Now,

In an year there are total 52 weeks

thus,

The APR (Annual percentage rate) = Interest rate × Total weeks in an year

or

APR = 8% × 52

or

APR = 416%

and, EAR ( Effective Annual Rate ) = ( 1 + r )ⁿ - 1

Here,

r is the interest rate per week

n is the total weeks in an year

thus,

EAR ( Effective Annual Rate ) = ( 1 + 8% )⁵² - 1

= ( 1 + 0.08 )⁵² - 1

= 53.7060

or

53.7060 × 100% = 5370.60%

5 0

3 years ago

The number of traffic violations in a city increased from 12 to 16 in a month. What is the percent of increase in the number of

Tems11 [23]

Answer:

33%

Step-by-step explanation:

Percentage increase = $\frac{increase}{initial value}$ x 100%

Number of traffic violations increased from 12 to 16.

Initial value = 12

Final value = 16

increase = Final value - Initial value

= 16 - 12

= 4

Percentage increase = $\frac{increase}{initial value}$ x 100%

= $\frac{4}{12}$ x 100%

= $\frac{1}{3}$ x 100%

= $\frac{100}{3}$ %

= 33.3333%

The percentage increase in the number of traffic violations for the month is 33%.

5 0

3 years ago

Help solve for number 6 please !!<br> :)

Semenov [28]

Answer:

x: {-3, 5}

Step-by-step explanation:

Step 1. Find least common denominator

Step 2. Multiply missing factors on top AND bottom

Step 3. Combine like terms

Step 4. Simplify (get rid of denominator)

Step 5. Solve for x

$\frac{x}{x-5} +\frac{3}{x+2} =\frac{7x}{x^2-3x-10}$ LCD = $x^2-3x-10$ OR $(x-5)(x+2)$

$\frac{x}{x-5}(\frac{x+2}{x+2}) +\frac{3}{x+2}(\frac{x-5}{x-5}) =\frac{7x}{x^2-3x-10}$

$\frac{x(x+2)}{(x-5)(x+2)} +\frac{3(x-5)}{(x+2)(x-5)} =\frac{7x}{(x-5)(x+2)}$

$\frac{x(x+2)+3(x-5)}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}$

$\frac{x^2+2x+3x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}$

$\frac{x^2+5x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}$

$x^2+5x-15=7x$

$x^2-2x-15$

$(x-5)(x+3)$

8 0

3 years ago

Find the smallest power of 10 that will exceed M. Let M = 118,526.65902.

zavuch27 [327]

Answer:

The smallest power of 10 that will exceed $M$ is $10^{6}$ .

Step-by-step explanation:

We can use the following approach to determine the smallest power of 10 that will exceed M. We can transform that number into scientific notation, which is of the form:

$x.y \times 10^{n}$ , $\forall \,x,y\in \mathbb{N}$

Where:

$x$ - Integer part, formed by a digit, which is of the highest order.

$y$ - Decimal part, formed by a digit onwards.

$n$ - Power grade.

The smallest power of 10 that will exceed M is $10^{n+1}$

If $M = 118,526.65902$ , then, the power grade is number of spaces that dot must be moved leftwards. In this case, dot must be moved 5 spaces on the left. The integer part is 1 and the decimal part is 1852665902. Then, the value of $M$ in scientific notation is:

$M = 1.1852665902\times 10^{5}$

Then, the smallest power of 10 that will exceed $M$ is $10^{6}$ .

5 0

4 years ago