Find the value of x in the equation, 3^2x-1 = 81

The answers are given as:

Ai. The price at Store B would be $583 / 1.21 = $481.82

ii. The price at Store A would be $1200 * 1.21 = $1452.

b. The percent increase in membership from 2020 to 2021 is 13.64%

A.

i. If the price at Store A was $583, the price at Store B would be $583 / 1.21 = $481.82 (approximately).

ii. If the price at Store B was $1200, the price at Store A would be $1200 * 1.21 = $1452.

b. The percent increase in membership from 2020 to 2021 is ((12,500 - 11,000) / 11,000) * 100 = 13.64% (approximately).

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Answer:

A.  19.8

B.  15.9

Step-by-step explanation:

A.  

To find the geometric mean between two numbers, you multiply them together and then take the square root of the product.

28 × 14 = 392

[tex]\sqrt{392}[/tex] = 19.799 ≈ 19.8

B.

7 x 36 = 252

[tex]\sqrt{252}[/tex] = 15.8745 ≈ 15.9

The value of the measure of the arc or angle indicated are,

⇒ m ∠DCE = 54°

⇒ m ∠MON = 53°

Now, We can simplify as,

4) As shown in figure,

m arc DE = 360° - (121° + 131°)

m arc DE = 360° - 252°

m arc DE = 108°

So, We get;

⇒ m ∠DCE = m DE / 2

⇒ m ∠DCE = 108 / 2

⇒ m ∠DCE = 54°

4) As shown in figure,

m arc MN = 360° - (109° + 145°)

m arc MN = 360° - 254°

m arc MN = 106°

So, We get;

⇒ m ∠MON = m MN / 2

⇒ m ∠MON = 106 / 2

⇒ m ∠MON = 53°

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The graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

To solve the inequality -4.4 ≥ 1.6x - 3.6, we can follow these steps:

Add 3.6 to both sides of the inequality to isolate the term with x:

-4.4 + 3.6 ≥ 1.6x - 3.6 + 3.6

-0.8 ≥ 1.6x

Divide both sides of the inequality by 1.6

-0.8 / 1.6 ≥ 1.6x / 1.6

-0.5 ≥ x

So, the solution to the inequality is x ≤ -0.5.

Now, from the solution the graph for the inequality start with closed dot from 0.5 and move towards the points -0.6, -0.7, -0.8, ....

Thus, the graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

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The solution of  f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1

option C is correct.

Here, we have,

given that,

the functions are:

f(x) = x^3+6x^2+x^1/2

g(x) = x^1/2

so, we have,

f(x)/g(x)

= x^3+6x^2+x^1/2 / x^1/2

= x^3/ x^1/2  +6x^2/ x^1/2  +x^1/2/ x^1/2

=x ^5/2 + 6x^3/2 + 1

Hence, The solution of  f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1

option C is correct.

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Answer:

8 feet

Step-by-step explanation:

Let b be the length of the base. Then the height is b+6 ft.

The area of the parallelogram is given by:

Area = b(b + 6) = 160

Solving for b, we get,

[tex]b^2 + 6b - 160 = 0[/tex]

Factoring the expression, we get:

(b - 8)(b + 20) = 0

Therefore, b = 8 or b = -20.

Since the base cannot be negative, b = 8.

Therefore, the length of the base of the parallelogram is 8 feet.

Answer:

When an exponent of the power is an even number and the base is a negative number, the value is always positive.

Answer:

It maybe 12,000/120,000

Step-by-step explanation:

12months a year

12+12=24 so,

500×24=12,000

or 120,000

Answer:

The surface area of the hexagonal pyramid is 313.13 square inches.

Step-by-step explanation:

Hexagonal pyramid,

Surface Area = Area of hexagon base + areas of six triangles

b = 6

h = 12.2 (height of the triangle)

A = [tex]\frac{3\sqrt{3} }{2}b + 6(\frac{1}{2} bh)[/tex]

A = [tex]\frac{3\sqrt{3} }{2}b +3bh[/tex]

A = [tex]\frac{3\sqrt{3} }{2}6 +3*6*12.2\[/tex]

A = 93.53 + 219.6

A = 313.13 square inches

To find the measure of each interior and exterior angle of a regular 30-gon, we can use the formula:

In this case, we have a regular 30-gon, so n = 30.

Let's calculate the measures:

Therefore, each interior angle of the regular 30-gon measures 168°, and each exterior angle measures 12°.

Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x = 100[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 20[/tex]

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

[tex] \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }[/tex]

Solving :

[tex] \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }[/tex]

Step 2: Subtracting 10 on both sides :

[tex] \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }[/tex]

We get ,

[tex] \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }[/tex]

Step 3: Dividing both sides by 5 :

[tex] \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }[/tex]

On cancelling , we get :

[tex] \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar[/tex]

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:

a+b>c

a+c>b

b+c>a

In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:

9+13>15 (true)

9+15>13 (true)

13+15>9 (true)

Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.

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The solution of the given equations is: (3,-1).

Here, we have,

from the given graph we get,

1st line passes through ( 0,2 ) and (2,0)

so, equation: y = -x+2 .....1

2nd line passes through ( 0,-4 ) and (4,0)

so, equation: y = x-4 .....2

now, from 1 and 2 we get,

-x + 2 = x -4

or, 2x = 6

or, x = 3

so, we have, y = -1

so, the point of intersection is (3, -1)

Hence, The solution of the given equations is: (3,-1).

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Answer:

  47.5%    (rounds to 48%)

Step-by-step explanation:

You want the probability that a tree has between 240 and 300 apples, given the distribution of numbers of apples is normal with mean 300 and standard deviation 30.

The given diagram shows the center 95% of numbers of apples lies between 240 and 360. The number between 240 and 300 is half that symmetical distribution, so is ...

  95%/2 = 47.5%

The probability a tree will have between 240 and 300 apples is about 47.5%.

__

Additional comment

The figure "95%" is an approximation. A closer value is 95.45%. Hence, a closer value to the probability is 47.7%.

No rounding requirement is shown. To the nearest whole percentage point, the probability would be 48%.

<95141404393>

Answer:

5.85

Step-by-step explanation:

Autumn's bank registry will be :

Transaction Amount Balance

Paycheck $1275.00 $1275.00

Rent $400.00 $875.00

Utilities $75.00 $800.00

Cell Phone $80.00 $720.00

Subway Pass $120.00 $600.00

Groceries $200.00 $400.00

Work Clothes $100.00 $300.00

Entertainment $100.00 $200.00

Savings $200.00 $0.00

As you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:

Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.

By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.

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The value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

To find the value of the expression [tex]n^2 - 11n + 10[/tex], we can follow these steps:

Start with the given expression: [tex]n^2 - 11n + 10.[/tex]

Look for any like terms that can be combined. In this case, there are no like terms.

Since there are no like terms, we can simplify further by factoring the expression. We need to find two numbers that multiply to give 10 (the constant term) and add up to -11 (the coefficient of the middle term, which is -11n).

The numbers that satisfy these conditions are -1 and -10, because

(-1) × (-10) = 10 and (-1) + (-10) = -11.

Now we can rewrite the expression using these numbers:

[tex]n^2 - 11n + 10 = (n - 1)(n - 10).[/tex]

So the factored form of the expression is (n - 1)(n - 10).

Therefore, the value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

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The numerical value of x in the dimensions of the rectangle is 9.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

A = length × width

From the diagram:

Wdith of the rectangle = x - 2

Length of the rectangle = x + 5

Area = 98 ft²

Since area of a rectangle =  length × width:

98 = ( x - 2 )( x + 5 )

Simplify

( x - 2 )( x + 5 ) = 98

Apply distributive property:

x² + 3x - 10 = 98

x² + 3x - 10 - 98 = 0

x² + 3x - 108 = 0

Factor using AC method:

( x - 9 )( x + 12 ) = 0

Hence:

x - 9 = 0 or x + 12 = 0

x = 9 or x = -12

Since, we are dealing with dimensions, we take the positive value.

Hence, the value of x is 9.

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If we know that <C is congruent to <E, we can say that: (a). the two triangles are similar by SAS.

from the question, we have the following parameters that can be used in our computation:

The triangles (see attachment)

Two triangles are similar when the ratio of their corresponding sides are equal and their corresponding angles are congruent.

So, we have

Ratio = BC/AC = 6/3 = 2.

Ratio = FE/DE = 4/2 = 2.

Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.

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Step-by-step explanation:

1 qt = 2 pts     multiply both sides by two

2 qt = 4 pints

Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) [tex]\times[/tex] 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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The area of the slice of pizza is 25.1 inches squared.

The circular pizza has a diameter of 16 inches. Each slice of pizza have a angle of 45 degrees.

Therefore, the area of the slice of pizza can be calculated as follows:

area of the slice of pizza = ∅ / 360 × πr²

where

Therefore,

r = 16  /2

r = 8 inches

area of the slice of pizza = 45 / 360 × 3.14 × 8²

area of the slice of pizza = 45 / 360 × 3.14 × 64

area of the slice of pizza = 9043.2 / 360

area of the slice of pizza = 25.12 inches²

area of the slice of pizza = 25.1 inches²

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Below are the right probabilities for each scenario;

8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]

9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]

10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].

11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex];  P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]

For the compounded probability, we can solve them the following way;

8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32

b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16

c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4

9. There are 28 total students and 6 total outcomes on a standard die.

P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14

10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.

P(both flights delayed) = 6/14 × 8/12 = 2/7

11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.

a) P(nickel, then quarter)  = (6/25) × (5/24) = 1/20

b) P(penny, then not a dime)  = (4/25) × (15/24) = 1/10

c) P(both dimes) = (10/25) × (9/24) = 3/20

d) P(both nickels) = (6/25) × (5/24) = 1/20

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Answer:

Step-by-step explanation:

it is only moving 3 to the right, so shift the green dot to (3,0)

I used desmos . com for the graph

Answer:

  x = 2

Step-by-step explanation:

You want the value of x that satisfies x|x| = 4.

The absolute value function splits the domain of the equation into two parts.

For x < 0, the equation is ...

  x(-x) = 4

  x² = -4

There are no real solutions in this domain.

For x ≥ 0, the equation is ...

  x² = 4

  x = √4 = 2

The only solution is x = 2.

__

Additional comment

In the attachment, we have rewritten the equation to ...

  x|x| -4 = 0

The graphing calculator readily identifies x-intercepts, so this is a convenient way to find the solution. You will notice that for x < 0, the graph is of -x²-4, which is never zero.

<95141404393>

Answer: C-Cylinder

Step-by-step explanation:

In this problem, you are rotating the rectangle on the x axis. If you rotate it along this side, the rectangle makes it a cylinder.

Para aquellos que necesitas este respuesta en español: En este problema, estás girando el rectángulo sobre el eje x. Si lo giras a lo largo de este lado, el rectángulo lo convierte en un cilindro.

I hope this helps!

Answer:

The correct answer is (C), cylinder.

Explanation:

When the rectangle is rotated around the axis shown, it will create a three-dimensional shape with two parallel bases that are connected by a curved surface. This shape is called a cylinder.

Answer:

-6

Step-by-step explanation:

Because two lines that are parallel have the same slope

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

Answer:

B.  90 tickets

Step-by-step explanation:

For t tickets sold, we want the revenue equal to the cost.

25t = 450 +20t

5t = 450 . . . subtract 20t

t = 90 . . . . . divide by 5

90 tickets is the break-even point.

___

:D