Solve: ( − )( + ) = �

The exponential form of the given information 3^2x3^3 is 3⁵.

The exponential form is a convenient way of expressing or writing repeated multiplication expressions concerning their bases and power.

From the information given, the given expression can be written in exponential form by using the law of indices.

= 3^2x3^3  

[tex]\mathbf{=3^{2+3}}[/tex]

[tex]\mathbf{=3^{5}}[/tex]

Therefore, we can conclude that the exponential form of the given expression is 3⁵.

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Answer:

10 inches

Step-by-step explanation:

15 days/3 days =5

5 x 2 =10

Answer:

54sqrt(30)

Step-by-step explanation:

3sqrt(24) can be simplified to 6sqrt(6) as 24 can be written as 4 * 6 and 4 is a perfect square

3sqrt(45) can also be written as 9sqrt(5) as 45 can be written as 5 * 9 and 6 is a perfect square

you can multiply 6sqrt(6) * 9sqrt(5) as though the square roots were variables

so

54sqrt(30)

this is your final answer

the rounded answer is 295.770181

For the given inverse functions we have:

a) f⁻¹(5) = 7

b) f(-2) = -3

Remember that if f(x) and g(x) are inverse functions, then:

[tex]f(x) = y\\then\\g(y) = x[/tex]

a) Now we know that:

f(7) = 5

Then if f⁻¹(x) is the inverse, we have:

f⁻¹(5) = 7

b) Now we know that:

f⁻¹(-3) = -2

Again, using the rule for inverse functions, we will have:

f(-2) = -3

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Using the relation between velocity, distance and time, it is found that it took the knight 20 hours to traveled from one kingdom to another.

Velocity is distance divided by time, hence:

v = d/t

On the first day, he traveled at a speed of 10 mph, a distance of d, hence:

10 = d/t

t = d/10

On the second day, he traveled at a speed of 8 mph, a distance of 180 - d, hence:

8 = (180 - d)/t

t = (180 - d)/8

Equaling both equations for t, we find the distance on the first day, hence:

d/10 = (180 - d)/8

8d = 1800 - 10d

18d = 1800

d = 100 miles.

The time on the first day was:

t = 0.1d = 0.1 x 100 = 10 hours.

On the second day he traveled the same amount of time, hence, in total, he traveled 20 hours.

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Answer:

QO < OP < QP

Step-by-step explanation:

The third angle, angle Q, must measure 45° since angles in a triangle add to 180°.

So, OQ < OP < QP.

Answer:

PQ>OP>QO

Greater than symbol goes from largest to smallest

The height of the equilateral triangle is 41. 6 inches. Option C

The formula for finding the height of an equilateral triangle is given as;

h = (a√3)/2

we have a = 48 inches

Let's substitute the value

Height, h = [tex]\frac{48\sqrt{3} }{2}[/tex]

Height = [tex]\frac{48 * 1. 732}{2}[/tex]

Height = [tex]\frac{83. 14}{2}[/tex]

Height = [tex]41. 6[/tex] Inches

Thus, the height of the equilateral triangle is 41. 6 inches. Option C

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Answer:

0.4

Step-by-step explanation:

4+3+2+1 =10

5m÷10 =0.5

(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)

2 : 1.5 : 1 : 0.5

longest piece= 2 (2m)

4+1= 5

2÷5= 0.4

(0.4×4=1.6, 0.4×1=0.4)

1.6 : 0.4

so the shortest piece is 0.4!

By using Microsoft excel to plot the data on a scatter plot, the linear regression equation can best be represented by: A. y = 12.11.1.36^x

A regression line can be defined as a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.

By using Microsoft excel to plot the data on a scatter plot, we can logically deduce that linear regression equation for the x-values and log(y)-values is given by:

y = 12.11.0.30^x

Thus, it can best be represented by: y = 12.11.1.36^x

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Answer:

  (c)  45°

Step-by-step explanation:

A protractor is used to measure angles by aligning one of the sides of the angle with the 0 mark on the protractor scale. Then the value of the angle is read from the same scale where it is crossed by the other side of the angle.

Here, ray BA crosses the outer scale at 0. The other ray of the angle, BC, crosses the outer scale halfway between 40 and 50, obscuring the mark at 45°.

The measure of angle ABC is 45°.

C. 45°

When measuring with a protractor one of the rays should line up with the straight edge of the protractor, then match up the second ray to the tick marks. However, it can be confusing to tell how to read a protractor.

Clockwise

This angle moves clockwise. This means that the second ray is clockwise to the ray at the bottom. When using a protractor that opens up to the left like this, read the top row of the protractor. The second ray matches the 45-degree mark.

Acute vs Obtuse

There is another way to tell which row of numbers to read. By looking at the drawn angle we can tell the angle is acute (smaller than a right angle). So, the measurement must be less than 90. Therefore, the top row must apply in this situation, meaning the angle is 45°.

Answer:

D.  -11

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]

Therefore, the function has three definitions:

[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]

[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]

[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]

f(-4) means to substitute x = -4 into the function.

As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:

[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]

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Answer is D. -11

Answer:

Solution Given:

f(-4) depends on the condition x≤-4,

so

f(-4)=2*-4-3=-8-3=-11

Answer:

Step-by-step explanation:

Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 2.5, \sigma = 0.5[/tex]

The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is one subtracted by the p-value of Z when X = 2.45, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]

Z = -0.1

Z = -0.1 has a p-value of 0.4602.

1 - 0.4602 = 0.5398.

0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.

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The difference of the fractions is 8x/3. Option C is correct.

Given the fraction is 10x/3-2x/3.

When subtracting fractions with the same denominator, just subtract the numerators of the fractions. To find the difference between equal fractions, we subtract the smaller numerator from the larger numerator.

The given expression is 10x/3-2x/3.

Here the denominator in both the fractions are same so, we will take the LCM, we get

10x/3-2x/3=(10x-2x)/3

Now, we will simplify the numerator by subtracting the smaller term from larger, we get

10x/3-2x/3=8x/3

Hence, the difference of the fractions 10x/3-2x/3 is 8x/3 and the correct option is C.

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Answer:

51 Adult tickets were sold that day.

Step-by-step explanation:

Let c = child and a = adult

c + a = 148                      5.50c + 9.00a = 992.50

Change the first equation so that it is either in the form c = or a =and then plug that number into the second equation.

I am going to change the first equation to c = by subtracting a from both sides

c = 148 - a

Now I am going to plug 148 -a for c in the second equation.

5.5(148 - a) + 9a = 992.5 Next distribute the 5.5

814 - 5.5a + 9 a = 992.5 Add the a terms together

814 + 3.5a = 992.5 Subtract 814 from both sides

3.5a = 178.5  Divide both sides by 3.5

a = 51

Answer:

x=3,y=1

Step-by-step explanation:

2^x+y=16,3^x-y=9

16=2^4,9=3^2

x+y=4,x-y=2 add both

2x=6,x=3

3-y=2,y=1

Answer: C, D

Step-by-step explanation:

[tex]x^2 +10x+18=0\\\\x=\frac{-10 \pm \sqrt{10^2 - 4(1)(18)}}{2}\\\\x=\frac{-10 \pm \sqrt{28}}{2}\\\\x=-5 \pm \sqrt{7}[/tex]

The rule for learning the > sign is demonstrating eating with the right hand.

The inequality signs are;

The rule for teaching your students the greater than > sign is by imagining eating with their right hand. The shape of the hand when taking food into the mouth is the greater than sign.

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Answer:

3) 194 feet

Step-by-step explanation:

The other house:

"a house that is 33 ft wide and 50 ft long"

area = LW = (33 ft)(50 ft) = 1650 ft²

This house:

LW = A

L × 22 ft = 1650 ft²

L = 75 ft

P = 2(L + W)

P = 2(75 ft + 22 ft)

P = 194 ft

Answer: 3) 194 feet

Answer:

3) P = 194 ft.

Step-by-step explanation:

[tex]A=wl[/tex]

[tex](30)(50)=22l[/tex]

[tex]1650=22l[/tex]

[tex]l=1650/22=75[/tex]

the dimensions of the house are: (22 × 75)

Perimeter:

[tex]p=2(22)+2(75)=44+150=194[/tex]

Hope this helps

Answer:

31

Step-by-step explanation:

replace the values of a and b in the given term

=2a x 3 + b

2(5) x 3 + (1)

2x5 x 3 + 1

10 x 3 + 1

30 + 1

31

Using the interpretation of the confidence interval, it is found that:

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

Considering the mean and the standard error, the bounds of the interval are:

Hence:

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The surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²

Surface area of the square pyramid

= a² + 2a√a²/4 + h²

where,

Surface area of the square pyramid

= a² + 2a√a²/4 + h²

= 10² + 2(10)√10²/4 + 15²

= 100 + 20√100/4 + 225

= 100 + 20√25 + 225

= 100 + 20√250

= 100 + 20(15.81)

= 100 + 316.2

= 416.2 cm²

Therefore, the surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²

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Answer:

A $1950

Step-by-step explanation:

Food, camper rental and camp site will cost 1350

(120 + 65 + 85)5 = 1350

The trip is 2500 and the car gets  8 miles per gallon  2500/8 = 31.5.  The will need to buy 31.5 gallons of gas at 1.92 a gallon or $600 (31.5 x 1.92).

When we add the cost of gas to the other costs, we get a total of 1950 (1350 + 600)

The point that describes the intersection of line m and line n is; Point W

Intersection of the two lines is defined as the point where the two lines cross or meet each other.

It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.

From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.

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Answer:

1.2 × 107 this is the sciencetific notation for 12 million

..

Answer:

26.556192

Step-by-step explanation:

7.2×10460÷100

20000÷(7.2×10460÷100)

Answer: All real numbers

Step-by-step explanation:

The domain and range of all linear functions is the set of real numbers.