write 0.125 as if it was 2 to a power

Answer:

\(6 \frac{2}{3} \) (second option)

Step-by-step explanation:

attached

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

The red will cost him more by $2.21

Step-by-step explanation:

First you multiply the amount of gallons of grey paint and the cost and you get 24.59 x 3= 73.77

The do the same for red

37.99 x 2= 75.98

the red is going to cost him more by 75.98-73.77=  $2.21

Answer:

The answer is 5/6.

Step-by-step explanation:

1/2=3/6, and 1/3=2/6. 2/6+3/6=5/6

The number which is closest to the addition of two fraction numbers, 1/2 + 1/3 is 0.8.

A fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

\(\dfrac{a}{b}\)

Here, (a) is the numerator and (b) is the denominator.

We have to find the addition of two fraction number 1/2 and 1/3. Suppose the value which is closest to 1/2 + 1/3 is n. Thus,

\(n=\dfrac{1}{2}+\dfrac{1}{3}\\\)

Cross multiply to find the addition of two numbers,

\(n=\dfrac{3+2}{6}\\n=\dfrac{5}{6}\\n=0.833\)

Thus, the number which is closest to the addition of two fraction numbers, 1/2 + 1/3 is 0.8.

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Answer:

7/11 or

7

--

11

Step-by-step explanation:

Hope this helps :)

The expression that is equivalent to \(80^{(1/4}\) * x is \(80^{4/x}\)

To determine the equivalent expression to \(80^{1/4}\) * x, let's analyze each option:

\(80/4^{x}\)

This expression simplifies to \(20^{x}\), but it is not equivalent to the original expression.

Applying the power of a power rule, this expression simplifies to \(80^{x/4}\) , which is not equivalent to the original expression.

\(80/x^{4}\)

This expression can be simplified as \(80^{4 x^{4} }\) , which is not equivalent to the original expression.

Therefore, the expression that is option d.

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The maximum score that can be in the bottom 5% of scores is 2.64

The middle 90% of scores lie between 2.88 and 4.56.

(a) We must determine the score that corresponds to the 5th percentile of the normal distribution in order to determine the highest score that may fall inside the lowest 5% of scores.

We may use the standard normal table to determine that the 5th percentile corresponds to a standard normal score of -1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return to the original scale:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

x= 2.64

(b)

We must determine the 5th and 95th percentiles of the normal distribution in order to determine the range of scores that the middle 90% of scores fall inside.

The standard normal table may be used to determine that the 5th percentile corresponds to a normally distributed score of -1.28 and the 95th percentile corresponds to a standard normal rating of 1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return them to their original scale:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

= 2.88 for the 5th percentile

x = 3.6 + 1.28 * 0.75

= 4.56 for the 95th percentile

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Answer:

$2,250 in interest

Step-by-step explanation:

The simple interest formula applicable here is

i = prt, where p is the principal (initial value), r is the interest rate as a decimal fraction, and t is the number of years elapsed.

Here we have i = $15,000(0.0375)(4) = $2,250 in interest

Answer:

f(x) = x2 – 12x + 20

Step-by-step explanation:

if it has those zeros, then it is (x-10)(x-2)

if you multiply that out, you get x^2 - 12x +20

Answer: Jane incorrectly evaluated (-2)² in step 2.

Step-by-step explanation:

\((-2)^{2}=4\), not -4.

Answer:what percent of the yearly sales were for July and September. if the graph shows 123,000​

Step-by-step explanation:

The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

The distance between the two ships after 8 hours is 192 miles.

The problem requires the use of the law of cosines to find the distance between the two ships. To do this, we can use the formula:

c^2 = a^2 + b^2 - 2abcos(θ)

Where:

c is the distance between the two ships,

a and b are the distances traveled by each ship, and

θ is the angle between the two vectors representing the distances traveled.

Since the ships are sailing on different bearings, the angle between their distances traveled will be 180 degrees. Hence, the cosine of this angle is -1.

Given that the ships are traveling at speeds of 24 mph and 28 mph, we can calculate the distances traveled by each ship as follows:

a = 24 mph * 8 hours = 192 miles

b = 28 mph * 8 hours = 224 miles

Using these values in the formula, we can find the distance between the two ships:

c^2 = 192^2 + 224^2 - 2 * 192 * 224 = 36864

c = sqrt(36864) = 192 miles

Therefore, the distance between the two ships after 8 hours is 192 miles.

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Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

Answer:

(Choice B)

(Choice C)

Step-by-step explanation:

The number of particles in 9.89 moles of carbon is solved to be

To determine the number of particles in 9.89 moles of carbon, we can use Avogadro's constant, which is defined as the number of particles (atoms or molecules) in one mole of a substance.

Avogadro's constant is approximately 6.02 x 10^23 particles per mole.

So, the number of particles in 9.89 moles of carbon is:

= 9.89 moles x (6.02 x 10^23 particles/mole)

= 5.95 x 10^24 particles

Therefore, there are approximately 5.95 x 10^24 particles in 9.89 moles of carbon.

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*Please provide a picture of the table next time*

152+ 20n

n is the number of months

after 5 months

152+ 20(5)

=252

after 10 months

152+20(10)

= 352

Each time you need to find the balance for the certain month, replace the n with the number of months.

Hope that helped

Answer:

x = 42

y = 21

Step-by-step explanation:

Since its a right triangle, we have:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

\(sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42\)

\(cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21\)

The answer choice which sin(x + y) - sin(x - y) simplifies to is; 2(cos x)(sin y).

It follows from the task content that the expression given in the task content can be simplified by trigonometric identities as follows;

sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy -cosxsiny)

= 2cosxsiny.

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Answer:

190

Step-by-step explanation:

f(1)=8

f(2)=3f((2-1))-2, f(2)=22

f(3)=3f((3-1))-2, f(3)=64

f(4)=3f((4-1))-2, f(4)=190

Answer:

D. proves \(tan(w + \pi) = tanw\)

Step-by-step explanation:

Given

\(tan(w + \pi) = tan(w)\)

See attachment for complete question

Option D answers the question (See proof below).

Using tangent sum identity, we have:

\(tan(A + B) = \frac{tanA + tanB}{1 - tanAtanB}\)

In this case:

\(A = w\)

\(B = \pi\)

So, we have:

\(tan(w + \pi) = \frac{tanw + tan \pi}{1 - tanw. tan \pi}\)

Note that

\(tan\ pi = 0\)

So:

\(tan(w + \pi) = \frac{tanw + tan \pi}{1 - tanw. tan \pi}\)

\(tan(w + \pi) = \frac{tanw + 0}{1 - tanw * 0}\)

\(tan(w + \pi) = \frac{tanw}{1}\)

\(tan(w + \pi) = tanw\)

Hence: Option D answers the question

Answer:

D. Rewrite tan(w + Pi) using the tangent sum identity. Then simplify the resulting expression using tan(Pi) = 0.

Step-by-step explanation:

test on edge

Answer:

The distance from the store A to the warehouse is of 13.93 miles.

Step-by-step explanation:

The delivery truck drove 5 miles from store A to store B

5 miles south.

13 miles from store B to the warehouse.

13 miles east.

The situation can be represented by:

A

B         Warehouse

In which the distance of A to B is of 5 miles, and the distance of B to the warehouse is of 13 miles. Thus, the distance of store A to the warehouse is the hypothenuse of a right triangle, with sides 5 and 13.

Using the Pytagorean Theorem:

\(h^2 = 5^2 + 13^2\)

\(h^2 = 25 + 169\)

\(h^2 = 194\)

\(h = \sqrt{194}\)

\(h = 13.93\)

The distance from the store A to the warehouse is of 13.93 miles.

Answer:

68,359,375. Using a calculator, you can multiply each new number by 5.

11th term of the given geometric sequence is \(a_{n}= 7(5^{n-1})\)

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Given geometric sequence = 7,35,175,..

Nth term of the geometric sequence \(a_{n}=a_{1}.r^{n-1}\)

\(a_{1}=7\)

\(r=\frac{35}{7}=5\)

Nth term of the geometric sequence

\(a_{n}= 7(5^{n-1})\)

Hence, the Nth term of the given geometric sequence is  \(a_{n}= 7(5^{n-1})\)

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Answer:

p = 13

Step-by-step explanation:

32 = 4p - 20

First, take 20 to the left side.

32 + 20 = 4p

52 = 4p

Now divide both sides by 4.

13 = p

\(-2x+6=12\\2x=-6\\x=-3\)

Answer:

Area = 113.04 m²

Step-by-step explanation:

Area of a circle:

\(\pi r^{2}\)

If we are told to use 3.14 for pi we can now make a new equation:

Area = 3.14×6²

Area = 3.14×36

Area = 113.04m²

Answer:

point slope form= y+4 = -7/8( x-7 )

slope intercept form y = -7x/8 +17/8

Answer: 1. -7/8         2. y+4=(-7/8)(x-7)         3. y= (-7/8)x + (17/8)

Step-by-step explanation: on EDGE

Answer:

62.5 meters per minutes

Step-by-step explanation: