How much, including taxes of 12%, would you pay for an item with a retail price of $194.95?

Answer:

5

Step-by-step explanation:

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

A whole number between 3.75 and 6 is 5.

Answer:-8.5714285714 × 10-1

Step-by-step explanation:

-101/119=-0.85714285714

remember Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

so -0.85714285714 in standard form is -8.5714285714 × 10-1

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:

The IQ score of 122.5 is about 1.5 standard deviations above the mean.

What is an equation?

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

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The z score is given by:

z = (raw score - mean) / standard deviation.

Given a mean of 100 and standard deviation of 15. The IQ score that is 1.5 standard deviations above the mean corresponds to a z score of 1.5, hence:

1.5 = (x - 100)/15

x = 122.5

The IQ score of 122.5 is about 1.5 standard deviations above the mean.

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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 value of  f –1(13) is 4

The table of values is given as:

x –4 0 2 5 9 13

f (x) –11 1 7 16 28 40

A linear function is represented as:

y = mx + b

Where b represents the y-intercept and m represents the slope

From the graph, when x = 0, y = 1.

This means that b = 1

So, we have

y = mx + 1

Also from the graph, when x = 2, y = 7.

So, we have:

7 = 2m + 1

Subtract 1 from both sides

7 - 1 = 2m + 1 - 1

Evaluate the difference

6 = 2m

Rewrite the above equation as:

2m = 6

Divide both sides of the equation by 2

m = 3

Substitute m = 3 in y = mx + 1

y = 3x + 1

The notation  f –1(13) implies that y = 13

So, we have

13 = 3x + 1

Subtract by 1

3x = 12

Divide by 3

x = 4

Hence, the value of  f –1(13) is 4

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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].

The next two terms of the sequence based on the information given is 37 and 50.

It should be noted that from the information given, the numbers illustrated are 5, 10, 17, and 26.

In this case, there is an addition of 2 to the previous difference.

Therefore, 26 - 17 = 9.

The next number will be:

= 26 + 9 + 2 =37

The following number will be:

= 37 + 11 + 2

= 50

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Please see the blue curve of the image attached below to know the graph of the function g(x) = (1/3) · 2ˣ.

Herein we have an original function f(x). The transformed function g(x) is the result of compressing f(x) by 1/3. Then, we find that g(x) = (1/3) · 2ˣ. Lastly, we graph both function on a Cartesian plane with the help of a graphing tool.

The result is attached below. Please notice that the original function f(x) is represented by the red curve, while the transformed function g(x) is represented by the blue curve.

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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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The area of the triangle is 1000 unit square

The area of a triangle is half the base multiplied by the height

The formula is given as;

Area = 1/2 × b × h

From the information given, the base is given as 50 and the height is 40

Area = 1/ 2 × 50 × 40

Area = 1/ 2 × 2000

Area = 1000 unit square

Thus, the area of the triangle is 1000 unit square

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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

The amount that will be in the account after 30 years is $188,921.57.

When an amount is compounded annually, it means that once a year, the amount invested and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.

The formula that can be used to determine the future value of the deposit in 30 years is : annuity factor x yearly deposit

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$2000 x [{(1.07^30) - 1} / 0.07] = $188,921.57

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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 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 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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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].

The solution set of the given inequality has a domain of (-∞, ∞) and the vertex(h,k) = (1, -9)

The solution set for inequality is the set of all solutions for which the inequality is defined. It can also be represented in an interval notation.

Given that:

By rewriting the equation in the parabola standard form 4p(y-k) = (x - h)², we have:

[tex]\mathbf{4\times \dfrac{1}{4}(y-(-9)) = (x-1)^2}[/tex]

Therefore, the parabola properties are:

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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 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: I think its A

Step-by-step explanation: maybe

2x3 i think maybe yes

Answer:

(6, 4)

{second option given}

Step-by-step explanation:

we know that point y is (3, 2)

If we dilate this point by a factor of 2, we will get (6, 4)

why?

when we "dilate" something, we multiply both numbers of that point by a scale factor, we can see that this factor is 2--so we can multiply both 3

(3 ·2 = 6)  and 2 (2 · 2 = 4) to get our new point, (6, 4)

hope this helps! have a lovely day :)

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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There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].

In this problem we must simplify the trigonometric equation by both algebraic and trigonometric means and clear the variable x:

2 · cos x = 4 · cos x · sin² x

2 · sin² x = 1

sin² x = 1/2

sin x = ± √2 /2

There are several solutions:

x₁ = π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₂ = 3π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₃ = 5π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].

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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:

2.92

Step-by-step explanation:

[tex]V=\frac{4}{3}\pi r^3 \\ \\ 105=\frac{4}{3}\pi r^3 \\ \\ r^3=\frac{105}{\frac{4}{3}\pi} \\ \\ r=\sqrt[3]{\frac{105}{\frac{4}{3}\pi}} \\ \\ r \approx 2.92[/tex]

Answer:

13.5

Step-by-step explanation:

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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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