find p + q

someone pls help

Answer:

$592.92

Step-by-step explanation:

Bills:

47 ones = 47*1 = $47

22 fives = 22*5 = $110

9 tens = 9*10 = $90

17 twenties = 17*20 = $340

Total Bills: 47+110+90+340 = $587

Coins:

67 pennies = 67*1 = $0.67

12 nickels = 12*5 = $0.60

9 dimes = 9*10 = $0.90

15 quaters = 15*25 = $3.75

Total Coins: 0.67+0.6+0.9+3.75 = $5.92

Total: $587+$5.92 = $592.92

Step-by-step explanation:

=fog(x)

−2x=0

x(x−2)=0

x=0,2

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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No, the average change in population is not the same as it was 50 years ago.

Reason in Support of the Answer:

In many important ways, the demographic future of the United States and the rest of the world is substantially different from the recent past. The world's average population approximately tripled between 1950 and 2010, and the U.S. population nearly doubled.

However, it is anticipated that between 2010 and 2050, both globally and in the United States, average population growth will be substantially slower and will disproportionately favor the oldest age groups. Hence it is seen that the average change in population is never constant. It depends on the demographic trends and conditions, whether the average change in population will be larger or comparatively trivial in the future. And, similarly, it can be said that the average change in population is not the same as it was 50 years ago.

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Answer:

B

Step-by-step explanation:

The domain is the set of input values, which is typically shown on the horizontal axis.

The answer is B.

The domain of the function refers to the possible values of the horizontal axis of the graph.

Hence, the domain is : 6 ≤ g ≤ 12

Answer:

this mean in case of multiplying exponents with same base you should add the exponent and keep base same.

example:

[tex] {6}^{4} \times {6}^{5 } = {6}^{4 + 5} \\ = {6}^{9} [/tex]

Answer:

5

Step-by-step explanation:

[tex]\sqrt{36}=6[/tex]

A whole number between 3.75 and 6 is 5.

Using the normal distribution, the probability that x is of at most 40, represented by option B, is given as follows:

[tex]P(X \leq 40) = 0.1587[/tex]

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 of the distribution are given, respectively, by:

[tex]\mu = 51, \sigma = 11[/tex]

The probability that x is of at most 40 is the p-value of Z when X = 40, hence:

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

[tex]Z = \frac{40 - 51}{11}[/tex]

Z = -1

Z = -1 has a p-value of 0.1587.

Hence the probability is:

[tex]P(X \leq 40) = 0.1587[/tex]

Which is the part to the left of X = 40 of the distribution, hence option B is correct.

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1. The solution to the first percent puzzle is as follows:

                              75%         66²/₃         11¹/₉

          33¹/₃%        25%          22¹/₅%      3⁷/₁₀%

         50%         37¹/₂%          33¹/₃%      5¹/₂%

        50%          37¹/₂%          33¹/₃%      5¹/₂%

2. The solution to the second percent puzzle is as follows:

                           10%             90%

         50%           5%              45%

         50%           5%              45%

A percent puzzle is a puzzle that engages students to practice working with percentages.

The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.

The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.

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2x3 i think maybe yes

Answer:

  (a)  100 meters

Step-by-step explanation:

You want the width at the base of a cooling tower whose walls are modeled by the equation (x/20)² -((y-110)/48)² = 1.

The width at the base will be the difference in the values of x when y=0.

  (x/20)² -((0 -110)/48)² = 1

  (x/20)² = 1 +3025/576

  x = ±20/24√3601 ≈ ±50.01

The width will be 50.01 -(-50.01) ≈ 100 meters.

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519 children chose apple slices.

Given that Daisy's Diner offers a side dish of broccoli, apple slices, or pretzels with their kids' meals, and last weekend, they sold 1,038 kids' meals, and twice as many kids chose pretzels as chose broccoli and 3 times as many chose apple slices as chose broccoli, to determine how many kids chose apple slices, the following calculation must be performed:

Therefore, 519 children chose apple slices.

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Answer:519 children chose apple slices.

Step-by-step explanation:

Answer:

[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]

Step-by-step explanation:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Given quadratic equation:

[tex]x^2-3x-5=0[/tex]

Define the variables:

[tex]\implies a=1, \quad b=-3, \quad c=-5[/tex]

Substitute the defined variables into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}[/tex]

[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]

Therefore, the exact solutions to the given quadratic equation are:

[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]

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Answer:

[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]

Step-by-step explanation:

Quadratic Formula :

[tex]\boxed {\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}}[/tex]

We are given the equation x² - 3x - 5 = 0.

Here,

Solving :

Hence, the solutions are :

[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]

Answer:

f¯¹(x)=x²+12x+36

Step-by-step explanation:

[tex]f(x) = \sqrt{x} - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y = \sqrt{x} - 6 \\ interchange \: x \: and \: y \\ x = \sqrt{y} - 6 \\ swap \: the \: side \: of \: the \: equation \\ \sqrt{y } - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\ \sqrt{y} = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2} + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2} + 12x + 36 \\ domain \: x∈R[/tex]

The given point on the midline of (π, -4), and the minimum point of (π/4, -5.5), give the exact expression for f(x) as; f(x) = 1.5•sin((2/3)•(x - π)) - 4.

The amplitude, a = The difference between the y-values at the minimum point and the midline

Therefore;

a = -4 - (-5.5) = 1.5

d = The difference between the y-values of the midline and the x-axis

Therefore;

d = -4 - 0 = -4

The given function is presented as follows;

f(x) = a•sin(b•x + c) + d

Which gives;

-4 = 1.5•sin(b•π + c) - 4

sin(b•π + c) = 0

(b•π + c) = 0

-c/b = π

c = -b•π

Therefore;

-5.5 = 1.5•sin(b•π/4 + c) - 4

-1.5 = 1.5•sin(b•π/4 + c)

-1 = sin(b•π/4 - b•π) = sin(-3•b•π/4)

-3•b•π/4 = arcsine (-1) = -π/2

-3•b•π/4 = -π/2

3•b/4 = 1/2

b = 2/3

c = -(2/3)•π

Therefore, f(x) = a•sin(b•x + c) + d, gives;

f(x) = 1.5•sin((2/3)•x - (2/3)•π) - 4

By simplification, the exact expression for f(x) is therefore;

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The number of each kind of office supply oscar bought is = markers= (43.2 - 4.2y)/3 notebooks = (43.2-3x)/4.2, sticky notes = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3.

The number of markers he bought = X

The number of notebooks he bought= y

The number of sticky notes he bought= z= 3 + X+y

The amount he paid for markers = $1.05*X

The amount he paid for notebooks = $2.25*y

The amount he paid for sticky notes= $1.95 (3 + X+y)

The total amount he paid is = $49.05

That is;

$49.05 = $1.05x + $2.25y + $1.95 (3 + X+y)

$49.05 = $1.05x + $2.25y + $5.85 + $1.95x + $1.95y

$49.05 - $5.85 = 3x + 4.2y

$43.2 = 3x + 4.2y

Make X the subject of formula,

3x = 43.2 - 4.2y

X = (43.2 - 4.2y)/3

y= (43.2-3x)/4.2

z = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3

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Answer:

50<x<60

Step-by-step explanation:

The triangle can only be formed with these two side lengths if the third side is bigger than (Subtract them)

55 - 5

...and smaller than (Add them)

55 + 5

55-5 < x < 55+5

50 < x < 60

The correct statement regarding the probabilities is given as follows:

P(Male or Type B) > P(Male | Type B)

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there is a total of 200 people, of which 103 are males and 12 are Type B females, hence:

P(Male or Type B) = 115/200 = 0.575

Of the 103 males, 38 are Type B, hence:

P(Male|Type B) = 38/103 = 0.3683.

Hence:

P(Male or Type B) > P(Male | Type B).

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The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.

Herein we must determine a line tangent to the quadratic equation y = 3 · x² at the point P(x, y) = (1, 3) by algebraic means. The slope of the line can be found by using the secant line formula and simplify the resulting expression:

m = [3 · (x + Δx)² - 3 · x²] / [(x + Δx) - x]

m = 3 · [(x + Δx)² - x²] / Δx

m = 3 · (x² + 2 · x · Δx + Δx ² -  x²) / Δx

m = 3 · (2 · x + Δ x)

If Δx = 0, then the equation of the slope of the tangent line is:

m = 6 · x

If we know that x = 1, then the slope of the tangent line is:

m = 6 · 1

m = 6

Lastly, we find the intercept of the equation of the line: (x, y) = (1, 3), m = 6

b = y - m · x

b = 3 - 6 · 1

b = - 3

The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.

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The kind of symmetry that would be shown in the design is an axial symmetry.

It should be noted that an axial symmetry simply means a symmetry around an axis.

In this case, the capital letter E has an acid of symmetry. Therefore, an axial symmetry is appropriate.

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Answer:

24 F

Step-by-step explanation:

Temp increases by 4F per hour.

-8F - 6F = 12F / 3hours

Answer:

13.5

Step-by-step explanation:

The value of x using the alternate exterior angle theorem is 82°

An equation is an expression that shows the relationship between two or more numbers and variables.

An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and scalene.

From the diagram:

x = 82° (alternate exterior angles)

The value of x using the alternate exterior angle theorem is 82°

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The amount it costs to buy 88ft of crow molding is; $143.

It follows from the task content that the cost for 8ft length of a specific width crown molding is; $13.

On this note, it follows that the cost of buying 88ft of the same kind of crow molding can be estimated as;

88 × ($13/8)

= $143.

Therefore, the cost of 88ft of crow molding is; $143.

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I assume [tex]f(x)=0[/tex] otherwise. If [tex]f(x)[/tex] is indeed a proper PDF, then its integral over the support of [tex]X[/tex] is 1.

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = k \int_0^2 (2x + 3x^2) \, dx = 1[/tex]

Compute the integral.

[tex]\displaystyle \int_0^2 (2x + 3x^2) \, dx = (x^2 + x^3)\bigg|_{x=0}^{x=2} = (2^2 + 2^3) - (0^2 + 0^3) = 12[/tex]

Then

[tex]12k = 1 \implies \boxed{k=\dfrac1{12}}[/tex]

The domain of a function is the range of its inverse, and vice versa.

So, the domain is [tex]x > 1[/tex] and the range is [tex]y > 3[/tex].

Answer: [tex](3, \infty)[/tex]

Step-by-step explanation:

q(x) is increasing for [tex]x > 3[/tex].

p(x) is increasing for [tex]x \geq -2[/tex].

So, both functions are increasing for [tex](3, \infty)[/tex].

Answer: I think its A

Step-by-step explanation: maybe

The distance are

a. 42.42

b. 15. 52

80 = 65 + <ABC

<ABC = 80 - 65

= 15

Through the use of sine rule we would have

By using sine rule,

Sine 15/a = sine 135/b =

sin 30/30.

Next we have to solve b by cross multiplying

b = (30× sin135) / sin 30

= 21.21/0.5

b = 42.42 km

Also, the value of a will be:

= (42.42 × sin 15) / sin 135

= 10.98/0.7071

= 15.52

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The probability of E and F expressed as P(E and F) equals;0.12

We are given;

P(E) = 0.2

P(F|E) = 0.6

Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)

Thus;

P(E and F) = 0.2 * 0.6

P(E and F) = 0.12

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