For problems 1 – 6, perform the conversions.
1. 7
16
= % 2. 4
3
5 = __ %
3. Express 55% as a fraction in simplified form: ___
4. Express 248% as a mixed number in simplified form: __
5. 0.00031 = __ % 6. 6.005 = __ %
7. Gigi spent 12% of her birthday money on a new pair of sunglasses. What fraction of her
birthday money did she spend on the new sunglasses?
8. Veronica and her friends went out for pizza to celebrate the volleyball team’s victory.
Their total bill for the pizza and soft drinks was $27.50. They left a 20% tip for their
server. How much tip did they leave?

Answer:

Answer would be triangle CAB

Given:-

To find:-

Solution:-

As we know that in a right angled triangle,

[tex]\implies \sin\theta =\dfrac{p}{h} \\[/tex]

And here;

On substituting the respective values, we have;

[tex]\implies \sin20^o = \dfrac{12}{x} \\[/tex]

[tex]\implies 0.342 =\dfrac{12}{x} \\[/tex]

[tex]\implies x = \dfrac{12}{0.342} \\[/tex]

[tex]\implies \underline{\underline{ x = 35.087}} \\[/tex]

Hence the value of x is 35.087 .

and we are done!

The length of the missing side of the given triangle above which is adjacent to angle 20° is 35.09.

To calculate the length of the missing side of the triangle, the formula given below is used. Such as:

Sin ∅ = opposite/hypothenuse.

Where ∅ = 20°

opposite = 12

hypotenuse = X

That is;

sin 20° = 12/X

make X the subject of formula;

X = 12/sin20°

X = 12/0.342020143

X = 35.09

Therefore the length of the missing part of the given triangle which is adjacent to angle 20° is 35.09.

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The area of the composite figure is the sum of the area of the sector and the triangle . Therefore, the area of the composite figure is 95.52 cm².

This composite figure is created by placing a sector of a circle on a triangle. The area of the composite figure can be found as follows:

The composite figure is a combination of a sector and a right triangle. Therefore, the area of the composite figure is the sum of the area of the sector and the area of the right triangle.

area of the composite figure = area of the triangle + area of the sector

Hence,

area of the composite figure =  1 / 2 bh + ∅ / 360 × πr²

area of the composite figure = 1 / 2 × 6 × 8 + 82 / 360 × 3.14 × 10²

area of the composite figure = 48 / 2 + 25748 / 360

area of the composite figure = 24 + 71.5222222222

area of the composite figure = 95.5222222222

Therefore,

area of the composite figure = 95.52 cm²

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Answer:

The answer is 25

Using the data points given, the equation is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].

What is an ellipse?

An ellipse is a locus of a point that moves in such a way that its perpendicular distance from a fixed straight line (directrix) and its distance from a set point (focus) remain constant. which is smaller than unity, i.e. eccentricity(e).

We are given that the center of the ellipse is at (4,-2), and a vertex is at (9,-2).

We know that the distance from the center to a vertex is a, where a is the length of the semi-major axis.

Therefore, we have -

a = 9 - 4 = 5

Since the point (4,3) is on the ellipse, we can use the distance formula to find the length of the semi-minor axis -

c = distance from (4,-2) to (4,3)

c = [tex]\sqrt{((4-4)^2 + (3-(-2))^2}[/tex]

c = 5

Now, we can use the equation of an ellipse -

[tex]\frac{\Big(\frac{(x - h)^2}{a^2}+ (y - k)^2\Big)}{b^2} = 1[/tex]

where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.

Plugging in the values we have found, we get -

[tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex]

Therefore, the equation for the ellipse is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].

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Answer:

The multiplication equation that shows how the denominators of 3/4 and 5/6 are related is:4 × 6 = 24To write an equivalent fraction with a denominator of 4, we need to find a number that, when multiplied by 4, gives us 24. That number is 6. So, we can multiply both the numerator and denominator of 3/4 by 6 to get:(3/4) × (6/6) = 18/2418/24 is equivalent to 3/4, but it has a denominator of 24 instead of 4. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 6.(18/6) ÷ (24/6) = 3/4Therefore, the equivalent fraction of 3/4 with a denominator of 4 is 3/4 × 6/6 = 18/24, which simplifies to 3/4.

The circumference of the circle is 144.44 yards

The circumference of a circle is the total distance around the edge of the circle. It's computed using the following formula:

Circumference = 2πr.

where r is the circle's radius and represents the ratio of a circle's circumference to its diameter by a mathematical constant π that roughly equals 3.14159.

We can also use the formula below whenever we have the diameter of the circle given

c = πd

where d is the diameter of the circle (the distance across the circle passing through the center).

From the image given, the circumference of the circle is given as;

c = 2πr

r = 23yd

c = 2 * 3.14 * 23

c = 144.44

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Using percentage, we can get that 7ml of the 70% solution will be needed.

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form.

In this context, "%" is read as "percent" or "percentage" to represent a percentage. By "division by 100," the percent symbol can always be changed to a fraction or decimal equivalent.

In the given question we get the equation,

35(245) + 0.75x = 0.4(245+x) = 98 + 0.4x

85.75 + 0.75x = 98 + 0.4x

0.35x = 98-85.75 = 12.25

x = 12.25/.35 = 35 mL of 75% solution

mixed with 245 mL of 35% it yields 280 mL of 40% so,

35 is within 5 of 40

75 is within 35 of 40

35/5 = 7

245/35 = 7

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The total surface area of the rectangular prism is 94 cm2.

Surface area is the measurement of the total area of a three-dimensional object. It is the sum of all the areas of the faces or surfaces of a 3D shape.

The total surface area of a 3D object is the sum of the areas of all its faces. The formula to calculate the total surface area of a 3D object is:

Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height)

Where Length, Width, and Height are the dimensions of the 3D object.

For example, if you have a rectangular prism with Length = 5 cm, Width = 4 cm, Height = 3 cm, then the total surface area is:

Total Surface Area = 2(5 cm x 4 cm) + 2(5 cm x 3 cm) + 2(4 cm x 3 cm)

 = 40 cm2 + 30 cm2 + 24 cm2

 = 94 cm2

Therefore, the total surface area of the rectangular prism is 94 cm2.

In conclusion, the formula to calculate the total surface area of a 3D object is: Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height). Examples can be used to better understand the concept and apply the formula to solve for the total surface area.

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Answer: a. To shift the graph downwards 5 units, we subtract 5 from the function, to shift it left 3 units, we add 3 to the input (the x-value), to stretch the graph vertically by a factor of 4, we multiply the function by 4, and to reflect it about the x-axis, we multiply the entire function by -1. Thus, the new function is:

g(x) = -4(1/2)^(x+3) - 5

b. To find the y-intercept, we set x=0 in the equation and solve for y:

g(0) = -4(1/2)^(0+3) - 5 = -9

Thus, the y-intercept is (0, -9).

c. The domain of the function g(x) is all real numbers, since there are no restrictions on the input x.

d. The range of the function g(x) is (-∞, -5], since the function is shifted downwards 5 units and stretched vertically by a factor of 4, which means that the maximum value of the function is -5, and it can take any value less than or equal to -5. The reflection about the x-axis does not change the range.

Step-by-step explanation:

Answer:

f(x)  :  exponential growth

g(x);  exponential growth

h(x):  exponential growth

j(x):   exponential decay

Step-by-step explanation:

In an exponential function such as
[tex]m(x) = a \cdot b^x[/tex]

the factor that determines whether it is a growth or decay function depends entirely on the value of b since x cannot be negative

If b > 1, it is a growth function

If b < 1 then it is a decay function

If b = 1 neither growth or decay function values are constant

In this context
f(x) has b = 2 > 1 . Hence it is a growth function
g(x) has b = 3 > 1 hence growth function
h(x) has be = 3/2 > 1; hence growth function
j(x) has be = 0.5 < 1 hence decay function

Answer:

O f(x)  :  exponential growth

O g(x);  exponential growth

O h(x):  exponential growth

O j(x):   exponential decay

Step-by-step explanation: I used to do this before :)

After answering the provided question, we can conclude that As a result, expression the likelihood that the sample mean book cost of 36 UCF students exceeds $1,278.6 is approximately 0.0427, or 4.27%.

In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators.  Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification. \

[tex]P(x > 1278.6) = P(z > (1278.6-1245)/(102/36)) P(z > 1.72) = 0.0427 P(z > 1.72) = 0.0427[/tex]

As a result, the likelihood that the sample mean book cost of 36 UCF students exceeds $1,278.6 is approximately 0.0427, or 4.27%.

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Answer:

x = 13.44 (2 d.p.)

y = 13.44 (2 d.p.)

Step-by-step explanation:

The interior angles of a triangle sum to 180°. Therefore, the missing angle of the given triangle is 45°. This means the triangle is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle in that the measures of its sides are in the proportion x : x : x√2 where:

As the given triangle is a 45-45-90 triangle, sides x and y are the same length.

As the hypotenuse (side opposite the right angle) is 19 units in length, then x√2 = 19.  To find the length of x (and y), solve for x:

[tex]\implies x\sqrt{2} = 19[/tex]

[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{19}{\sqrt{2}}[/tex]

[tex]\implies x= \dfrac{19\sqrt{2}}{2}[/tex]

[tex]\implies x=13.44\; \sf units\;(2\;d.p.)[/tex]

Answer:

=2

Step-by-step explanation:

You divide by five on each side of the = and then after that you should have X equals two!

The statement that must always be true fοr the median οf the triangle is RM = KM.

The statement that must always be true fοr the centrοid οf the triangle is RM = KM. Since, RM and KM are bοth part οf the median that cοnnect at the centrοid and are divided intο 2 halves.

A median in a triangle is a line segment that jοins οne οf the triangle's vertices tο the midway οf the οther side. There are three medians in every triangle, and they all cοme tοgether at the centrοid. The segment frοm the vertex tο the centrοid is twice as lοng as the segment frοm the centrοid tο the midpοint οf the οppοsing side.

The centrοid is the centre οf mass οf the triangle and splits each median intο twο segments. A median divides a triangle intο six smaller triangles οf equal size, passing thrοugh the centrοid οf each οf these smaller triangles, amοng οther nοtewοrthy qualities.

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Answer:

4/6 = 23

Step-by-step explanation:

Answer: Since there are 500 tumblers in each batch, there are a total of:

500 tumblers/batch × 3 batches = 1500 tumblers

To make a set of 3 tumblers with one tumbler of each color, we can choose one tumbler from each batch. There are 500 choices for the tumbler from the red batch, 500 choices for the tumbler from the yellow batch, and 500 choices for the tumbler from the purple batch. Therefore, there are:

500 choices for the first tumbler × 500 choices for the second tumbler × 500 choices for the third tumbler = 500^3 = 125,000,000 possible sets of 3 tumblers.

However, we are interested in the number of sets that can be made from the available tumblers. Each set requires one tumbler from each batch, and since there are 500 tumblers in each batch, we can make:

500 sets/batch = 500 sets/batch × 3 batches = 1500 sets

Therefore, we can make a total of 1500 sets of 3 tumblers from the available tumblers.

Step-by-step explanation:

On solving the provided question we cans ay that As a result, the ball function remains in the air for 5 seconds.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

The function f(x) = -6t(t-5) reflects the football's height at time t. When the football lands, its height will be zero.

To determine the time the ball is in the air, we must first determine when f(t) = 0. As a result, we may set the equation to zero and solve for t:

-6t(t-5) = 0

This equation is valid for t = 0 or t = 5. When the ball is tossed, time t = 0 occurs, and time t = 5 occurs when the ball strikes the ground. The time the ball is in the air is calculated as follows: time in air = t final - t initial = 5 - 0 = 5 seconds.

As a result, the ball remains in the air for 5 seconds.

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Therefore, the budgeted production for the year is 69,087 units.

factors

given by the question.

To determine the budgeted production for the year, we need to consider the following factors:

Projected sales for the year: 67,577 bicycles

Estimated January 1 inventory: 6,048 units.

Desired December 31 inventory: 7,558 units

The formula to calculate the budgeted production is:

Budgeted Production = Projected Sales + Desired Ending Inventory - Beginning Inventory

Using the values given in the problem, we can calculate the budgeted production as follows:

Budgeted Production = 67,577 + 7,558 - 6,048

Budgeted Production = 69,087 units

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Answer:

$18 were given to each class

Step-by-step explanation:

90÷5=18

1. Have you taken a gap year in the past, or are you considering taking one in the future?

2. What do you think are the key benefits of taking a gap year?

3. Do you think taking a gap year is a beneficial educational experience?

4. Are there any downsides to taking a gap year, in your opinion?

5. What advice would you give to someone considering taking a gap year?

6. Do you think taking a gap year would provide skills/experiences that you couldn't gain elsewhere?

Answer: 13/25

Step-by-step explanation:

1. We can see here that the modes of the given set of numbers will be: 12, 13, 14, 19.

2. The word in the sentence that is the mode is: the.

3. The mode of x is: 7

The mode of y is: - 2

In statistics, the mode is the value or values that occur most frequently in a given dataset. It is one of the most common measures of central tendency, along with the mean and the median.

To find the mode of a dataset, you need to look for the value that appears most often. If there is more than one value that occurs with the same highest frequency, the dataset is said to be bimodal or multimodal.

If no value appears more frequently than any other, the dataset is said to have no mode.

4. Modal class: 4-

Modal class: 12 - 20

5. Knowing the modal size of glass that its customers purchase can provide several benefits for the small company that sells glass. Here are some ways in which the company could benefit:

6. We can actually find the total frequency of the other three classes by subtracting the frequency of the first class from the total number of observations:

Total Frequency of the three classes = Total number of observations -Frequency of the first class

= 115 - 84 = 31

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The average rate of change of the number of farm²⁶ in the US between 1950 and 1970 would be = 8.3 farms/year

From the given graph above which shows the relationship between the number of farms and years. The line drawn from the origin shows an irregular relationship between the two variables.

The number of years between 1950 and 1970 = 20 years.

The number of farms that existed for those 20 years =5.2- 2.8 = 2.4 years

Therefore the average rate of change = 20/2.4 = 8.3 farms/year.

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Anju earned $30 by doing 10 chores. So, if Anju does 10 chores, she can earn money up to $30?

An equation is a mathematical statement that indicates the equality of two expressions. It is made up of one or more variables, constants, and mathematical operations. An equation consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equal sign (=).

The purpose of an equation is to find the value(s) of the variable(s) that satisfy the given conditions. To solve an equation, we need to isolate the variable on one side of the equation and simplify the other side of the equation until we obtain a solution or solutions.

The equation shows that the amount of money Anju earns is directly proportional to the number of chores she does. Each chore is worth $3, so if Anju does c chores, she earns 3c dollars.

For example, if Anju does 5 chores, she can use the equation to find how much money she earned:

3c = d

3(5) = d

15 = d

So, Anju earned $15 by doing 5 chores.

Similarly, if Anju does 10 chores, she can use the same equation to find her earnings:

3c = d

3(10) = d

30 = d

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Answer:  independent variable Dependent variable

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[tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

What is hyperbola ?

A hyperbola is a type of conic section that has two separate parts, called branches, which are mirror images of each other. It is defined as the set of all points in a plane, such that the difference between the distances from two fixed points, called foci, is a constant. Hyperbolas have many applications in science, engineering, and mathematics.

Given two LORAN transmitters located at the coordinates [tex]$(x_1, y_1)$[/tex] and [tex](x_2, y_2)$[/tex], where unit distance on the coordinate plane is measured in miles.

Let the coordinates of the receiver be [tex](x,y)$.[/tex]

The distance from the receiver to the first transmitter is given by [tex]$\sqrt{(x - x_1)^2 + (y - y_1)^2}$[/tex], and the distance from the receiver to the second transmitter is given by [tex]\sqrt{(x - x_2)^2 + (y - y_2)^2}$.[/tex]

Since the difference in the distances from the receiver to these transmitters is 180 miles, we have:

[tex]$$\sqrt{(x - x_1)^2 + (y - y_1)^2} - \sqrt{(x - x_2)^2 + (y - y_2)^2} = 180$$[/tex]

Squaring both sides, we get:

[tex]$$(x - x_1)^2 + (y - y_1)^2 - 2\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} + (x - x_2)^2 + (y - y_2)^2 = 180^2$$[/tex]

Rearranging, we get:

[tex]$$(x - x_1)^2 + (y - y_1)^2 - (x - x_2)^2 - (y - y_2)^2 = 4\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} - 180^2$$[/tex]

Using the identity $a^2 - b^2 = (a + b)(a - b)$, we can simplify the left-hand side as:

[tex]$$4x(x_2 - x_1) + 4y(y_2 - y_1) = 4\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} - 180^2$$[/tex]

Squaring both sides again and simplifying, we get:

[tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

Therefore, [tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

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The calculated volume of the prism with the dimension 6 1/2 cm by 2 1/2 cm by 2 1/2 cm is 325/8 cm³

To find the volume of a rectangular prism, we need to multiply its length, width, and height.

In this case, the length is 6 1/2 cm, the width is 2 1/2 cm, and the height is also 2 1/2 cm.

First, we need to convert the mixed numbers to improper fractions.

6 1/2 = 13/2

2 1/2 = 5/2

Now, we can multiply the three values together to find the volume:

Volume = length x width x height

Volume = (13/2) x (5/2) x (5/2)

Volume = (13 x 5 x 5) / (2 x 2 x 2)

Volume = 325/8

Therefore, the volume of the rectangular prism is 325/8 cm³

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The ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.

A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).

If 80 cents οf every dοllar gοes directly tο prοgram services, then 20 cents οf every dοllar is spent οn staff salaries.

This can be written as a ratiο οf 20 cents tο 100 cents, οr simplified tο 1:5.

Therefοre, the ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.

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