The camera Melissa wanted for her birthday is on sale at 44% off the usual price. The amount of the discount is $96.80. What was the original price of the camera?

Answer: f(x^2) = x^2 - 5

Using integrals, the desired probabilities and measures are given as follows:

a) P(X < 6) = 0.84375 = 84.375%.

b) P(X < 13) = 1 = 100%.

c) P(6 < X < 8) = 0.15625 = 15.625%.

d) P(X > 5) = 0.31641 = 31.641%.

e) x = 6.434.

The distribution is given as follows, simplifying the operations:

f(x) = 0.09375x - 0.01171875x², 0 ≤ x ≤ 8.

Hence the density function is:

[tex]\int_{a}^{b} f(x) dx[/tex]

[tex]\int_{a}^{b} (0.09375x - 0.01171875x^2) dx[/tex]

[tex]0.046875x^2 - 0.00390625x^3|_{x=a}^{x = b}[/tex]

Applying the Fundamental Theorem of Calculus:

P(a < X < b) = 0.046875b² - 0.00390625b³ - 0.046875a² + 0.00390625a³

Hence, for item a:

P(X < 6) = 0.046875(6)² - 0.00390625(6)³.

P(X < 6) = 0.84375 = 84.375%.

For item b, the entire distribution is below 13, hence:

P(X < 13) = 1 = 100%.

For item c:

P(6 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(6)² + 0.00390625(6)³.

P(6 < X < 8) = 0.15625 = 15.625%.

For item d:

P(5 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(5)² + 0.00390625(5)³.

P(X > 5) = 0.31641 = 31.641%.

For item e:

We have to find b when a = 0 and P(X < b) = 0.9, hence:

0.046875b² - 0.00390625b³ = 0.9.

Using a calculator, the solution in the range of the distribution is given by:

b = x = 6.434.

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Answer:

3

Step-by-step explanation:

i think its 3 because 28 divided by 9 is 3

Answer:

  {-2}

Step-by-step explanation:

You want the solution set for the inequality 4(x +2)² ≤ 0.

The expression on the left cannot be negative, but it can be zero when ...

  x +2 = 0   ⇒   x = -2

The only solution to this inequality is x = -2.

Expressed as a set of solutions, we have ...

  x ∈ {-2}

Answer:

16

Step-by-step explanation:

[tex]-7+3^2\\3^2\\=9\\=-7+9\\=-7+9 = 2\\=2\times \:8\\2\times \:8=16\\\boxed{16}[/tex]

Answer:

Step-by-step explanation:

Point G has coordinates (4, -2).

After reflection across the x-axis it s coordinates will change as per rule:

Applied to point G:

After dilation by a scale factor of 2 the coordinates will change as per rule:

Applied to point G:

Check the picture below.

The expressions that are equal to 7⁸ x 7 are:

B. For (7¹⁸)/7⁹

C. For (7³)³

E. For 7⁴ x 7⁵

Exponential functions now have formula f(x) = bx, where b > 0 and b 1. As in any exponential expression, b serves termed the base and x is called its exponent. The proliferation of bacteria is an example of such an exponential function.

A. For 7³ x 7³

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7³ ⁺ ³

Calculate the sum or difference: 7⁶

Calculate power : 117649

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: False

Solution: False

B. For (7¹⁸)/7⁹

Reduce the fraction: 7⁹

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

C. For (7³)³

simplify using exponent power rule : 7⁹

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

D. For 7⁴ + 7⁵:

Calculate the power: 2401 + 16807

Calculate the sum or difference: 19208

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: False

Solution: False

E. For 7⁴ x 7⁵:

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁴ ⁺ ⁵

Calculate the sum or difference: 7⁶

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

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I understand that the question you are looking for is:

Select all the expressions that are equivalent to 7⁸ x 7.

A. For 7³ x 7³

B. For (7¹⁸)/7⁹

C. For (7³)³

D. For 7⁴ + 7⁵:

E. For 7⁴ x 7⁵

Answer:

none

Step-by-step explanation:

point steeler

The set of months having 31 days will be S = { January, March, May, July, August, October, December }.

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

We know that there are 12 months in a year.

From these months, we get that the months that have 31 days are:

January

March

May

July

August

October

December

The set of months having 31 days will be:

S = { January, March, May, July, August, October, December }

Therefore, we get that, the set of months having 31 days will be S = { January, March, May, July, August, October, December }.

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Answer:

7/10

Step-by-step explanation:

Rewriting 0.7 as a fraction would be 7/10. 0.7 can also be 0.70, and 70/100

3 houseplants will weigh 15 kg (Refer to the tape diagram below).

The weight of 3 household plants will be about 15 kg.

Therefore, the weight of 3 household plants will be about 15 kg (Refer to the tape diagram below).

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The sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11

(6.9 × 10^6) and (5.9 × 10^5)

Sum

= (6.9 × 10^6) + (5.9 × 10^5)

= (6.9 + 5.9) × 10^(6+5)

= 12.8 × 10^11

Therefore, the sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11

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Answer:

[tex]x = \frac{2a}{a - 2} [/tex]

The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].

The Domain of a function f(x) is the set of all values for which the function is defined.

The Range of a function is the set of all values that f takes.

As, [tex]sec x=\frac{1}{cos x}[/tex] , so sec x is defined where [tex]cos x \neq 0[/tex].

It implies, sec(3.14t/4) is defined where [tex]cos(3.14t/4)\neq 0[/tex].

The cosine is 0 at [tex](2n+1)\frac{\pi }{2}[/tex] , where n is any integer.

Now, [tex]\frac{3.14t}{4} =\frac{(2n+1)\pi }{2}[/tex]

         [tex]\frac{\pi t}{4} =\frac{(2n+1)\pi }{2}[/tex]

       [tex]t=2(2n+1)\\t=2+4n[/tex]

Since, the range of cos x is [-1,1], so sec x will never be less than 1, but can grow infinitely large as cos x approaches 0.

Thus, The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].

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The value of the integer number is -1

The statement is given as:

The sum of an integer and 7 times the next consecutive odd integer is 6

Let the integer value be x

So, the next consecutive odd integer is x + 2

When represented as an equation, we have

x + 7(x + 2) = 6

Open the bracket

x + 7x + 14 = 6

Evaluate the like terms

8x = -8

Divide both sides by 8

x = -1

Hence, the value of the integer number is -1

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Answer:

39 is the sum of their ages

Step-by-step explanation:

Hope this helps :)

We the Probability of pulling either fork or spoon as 1.

We are given that:

We have a fork and a spoon in a bag.

Total number of items in a bag = 1 + 1 = 2

Now, we need to tell the probability of either pulling a fork or a spoon.

Now,

Probability of pulling a fork = 1 / 2 = 0.5

Probability of pulling a spoon = 1 / 2 = 0.5

So, the Probability of pulling either of them will be = 1 / 2 + 1 / 2 = 1

Therefore, we the Probability of pulling either fork or spoon as 1.

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4 × 10 then put a 6 by the 10 as an exponent.

The circle has an area of 28.26 ft².

It is assumed that the circle's radius is 3 feet.

The circle's area must be determined.

What is radius of a circle ?

A line segment from a circle's center to its perimeter is known as the radius.

As per the question ;

Radius of circle , r = 3 ft

Area of the circle is given by ;

A = πr²

A = π × 3²

A = 9π

or

A = 9 × 3.14

or

A = 28.26 ft²

Thus , the area of the circle will be 28.26 ft².

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Answer: I'm pretty sure its a verb

Step-by-step explanation:

Answer: ann is 69 and beth is 138

Step-by-step explanation:

Yes; The construction demonstrates how to bisect an angle correctly using technology because Circles D & E have the same radius

How to properly bisect an angle?

In construction of angles and lines, bisection means dividing either a given angle or line segment into two equal parts. This means after the construction, the two parts must have equal measure.

The steps to bisect a line segment are as follows;

1. Draw the required length of the line segment AB.

2. With point A and radius of the compass greater than half of AB, describe arcs above and below the segment.

3. With the same radius as in step 2 and point B, describe two arcs above and below the segment. These would intersect that of step 2 at C and D.

4. Join the points of intersection of the arcs with a straight line CD.

Now, in this given question with the circle, we can see that line AG is the line that bisects the angle EAD.

Now, we see that circles C and D have the same radius and as such the construction demonstrated is correct for that very reason.

Answer: yes

Step-by-step explanation: the construction correctly shows how to bisect an angle using technology because circles D and E have the same radius. 

Answer:

c) 1

Step-by-step explanation:

Solving for the value of s,

→ 3s - 12 = -9

→ 3s = -9 + 12

→ s = 3/3

→ [ s = 1 ]

Thus, option (c) is correct.

There is no number which is satisfying the given conditions.

The first condition is that the number has seven digits.

The second condition is that the number lies between 1000 and 10000.

From these two conditions, we can conclude that there is no number which satisfies all the given conditions. Because there is no seven-digit number which is less than 10000.

Let us assume that the second condition is the number lies between 1000000 and 10000000.

And let the required number be "abcdefg".

The third condition is the digit in the tenth place is 150% of the digit in the thousandth place.

⇒ f = 150 × (d) / 100 = 1.5 × d

The fourth condition is the digit in the hundredth place is the sum of the digit in the tenth place and the digit in the thousandth place.

⇒ e = f + d = 1.5d + d = 2.5d

The fifth condition is the sum of all the digits in the number is 17.

⇒ a + b + c + d + e + f + g = 17

⇒ a + b + c + d + 2.5d + 1.5d + g = 17

⇒ a + b + c + 5d + g = 17

And the last condition is none of the digits is zero.

Using the last condition the possible values for d are either 1 or 2.

Because, if d is 3, then if we take the least possible digit(1) for others, the sum on the LHS is 19, which is greater than 17.

And d can not be 1. Because, if d is 1, then f and e are 1.5 and 2.5 respectively. 1.5 and 2.5 are not valid digits.

Therefore, the value of d = 2.

f = 1.5d = 3

e = 2.5d = 5

If d = 2, then we get a + b + c + g + 10 = 17

⇒ a + b + c + g = 17 - 10

⇒ a + b + c + g = 7

⇒ The possible values for (a, b, c, g) are (4, 1, 1, 1), (1, 4, 1, 1), (1, 1, 4, 1), (1, 1, 1, 4), (2, 2, 2, 1), (2, 2, 1, 2), (2, 1, 2, 2), (1, 2, 2, 2), (2, 3, 1, 1), (3, 2, 1, 1), (1, 1, 2, 3), and (1, 1, 3, 2)...

Therefore there are more than 12 possible answers that satisfy the assumption made.

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The perimeter of the equilateral triangle will be 27x - 48.

It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.

Therefore, the perimeter of the equilateral triangle will be:

= 3(9x - 16)

= 27x - 48

Therefore, the perimeter of the equilateral triangle will be 27x - 48.

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Find the perimeter of the equilateral triangle.

9x - 16

Answer:

D. F

Step-by-step explanation:

Both F and G are not on plane P

Answer:

See explanation

Step-by-step explanation:

Selected theme park admission prices has the lower standard deviation.

Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.

specific home stereo system: 3.99/59=0.0676.

selected theme park admission prices: 4/1499=0.002668

0.0676>0.002668

Answer:

The theme park ahs the lower standard deviation

Answer:

44

Step-by-step explanation:

20 ÷ 5 = 4 minutes per page

4 x 11 pages = 44

Rory can make 43 metaballs from the remaining beef.

Rory has 6 pounds of ground beef on hand for making meatballs.

He makes 9 meatballs with 5/8 pounds of meat per meatball.

We must subtract 5/8 from 6.

There are 43/8 pounds of ground beef remaining.

As a result, the number of 1/8 pound meatballs produced from 21/8 pound ground beef can be calculated as follows:

Therefore, Rory can make 43 metaballs from the remaining beef.

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