Carlos had $400. He decided to spent 40% of it on clothes, and 50% of the remaining money on video games. How much money did Carlos spend? How much does Carlos have left?

The total surface area of cylinder formed is   924 cm²              

We are given a rectangular sheet of paper of dimensions 44 cm* 14 cm is rolled along its length

So, height of formed cylinder = Length of rectangular sheet = 14 cm

Circumference of base of cylinder = Breadth = 44 cm

Circumference of circle = 2πr

So,

2 × (22/7) × r =44

r = (44×7)/(22×2)

Radius of cylinder is 7 cm

Height = 14 cm

Total surface area of cylinder = 2πr(h+r)

                                                =    2  × 22/7 × 7 (14 +7 )                                      

                                                =     924 cm²                  

Hence the total surface area of cylinder formed is   924 cm²  .  

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A) The rate of change in this situation is -$100 per week.

B) She will have $300 left in her account after five weeks.

Option C : (-4, 6) are the coordinates of B'.

What are meant by coordinates?

Coordinates are two integers (Cartesian coordinates) or often a letter and a number that identify a particular place on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: the horizontal x-axis and the vertical y-axis (vertical).

Given T(ABCD) = (A'B'C'D') and A = (6, -8) , A' = (-2, 4)

If B = (4, -6) then let B' = (x, y)

now, x - 4 = -2 - 6

x = 4 - 2 - 6 = -4

and y - (-6) = 4 - (-8)

y + 6 = 4 + 8

y = 6

Therefore, B' = (-4, 6)

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The statement that must be true for the parallelogram is

Alternate internal angles are pairs of angles that lie on opposite sides of a transversal line intersecting two parallel lines. The angles are on the interior (between the two parallel lines) and are not adjacent to each other.

These angles are equal in measure (i.e., they are congruent), which means that if one angle has a certain degree of measure, the other angle will have the same degree of measure.

In the problem, the diagonal of the parallelogram is the transversal line and it is used to make the alternate internal angle theorem possible

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What is a Right Angle Triangle?

A Right Angle Triangle is a triangle where one of the angles is equal to 90 degrees.

To calculate the values using SOHCAHTOA

 SOHCAHTOA calculate the angles and sides of the right triangle, using trigonometric function sine, cosine, and tangent. There are two triangles in which the adjacent and opposite changes based on which angle is in question, the hypotenuse always stays the same.

Where Sin A = Opposite/ Hypotenuse

            Cos A = Adjacent / Hypotenuse

   And  Tan A = Opposite / Adjacent

For question 1,

If Opposite = PR

Adjacent = PQ

Hypotenuse = QR

Sin A = 14/50

Cos A = 48/50

Tan A = 14/48

For question 2,

If Opposite = PQ

Adjacent = PR

Hypotenuse = QR

Sin A = 48/50

Cos A = 14/50

Tan A = 48/14

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The polygon DEFG is translated 3 units left to get F'(1, 6)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size.

Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). The polygon is translated 3 units left to get F'(1, 6)

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The values of the piecewise functions at the indicated limits using the equations obtained from the graph are;

[tex]\lim \limits_{x \to2^+}\frac{f(x) - 4}{f(x+ 3)} = \underline{-\frac{2}{3} }[/tex]

[tex]\lim \limits_{x\to 3^-}[/tex] f(f(x) + 4) = 7

[tex]\lim\limits_{h\to 0} \frac{f(2+ h)-f(2)}{h}[/tex] DNE

A piecewise function is a function that has rules or definition based on the interval of reference of the function.

The graphed function, f(x), comprising of several piecewise functions, indicates that as x → 2⁺, we get;

The points on the line of the graph are;

(1, 1), and (3, 3)

The slope of the graph as x tends to 2⁺ is therefore;

Slope = (3 - 1)/(3 - 1) = 1

The equation of the line is therefore;

y - 1 = x - 1

y = f(x) =  x

Therefore;

f(x) - 4 = x - 4

f(x + 3) = x + 3

[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{x - 4}{x + 3} | x = 2[/tex]

The piecewise function for the interval, x → 3⁻ is; f(x) = x, therefore;

f(f(x) + 4) = f(x + 4) = x + 4

[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = x + 4, where; x = 3, therefore;

[tex]\lim \limits_{h\to 0} = \frac{f(2 + h)-f(2)}{h}[/tex], can be found as follows;

The equation of the function at x = 2 is; y = f(x) = x

f(2 + h) = 2 + h

f(2) = 2

Therefore;

[tex]\frac{f(2 + h)-f(2)}{h}[/tex] = (2 + h - 2)/h = h/h

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The mean number of hours the students spent listening to music is 31.25 hours.

In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.

Mean = (sum of all values) / (number of values)

For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:

Mean = 9

Therefore, the mean of this data set is 9.

The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.

We can find the mean number of hours spent listening to music using the formula:

mean = (sum of (midpoint of each class) * (frequency of each class)) / (sum of frequencies)

The midpoint of each class can be found by taking the average of the upper and lower class limits.

Using this formula, we get:

mean = ((1.25 + 3.75 + 6.25 + 8.75 + 11.25) * (22 + 15 + 3 + 3 + 1)) / (22 + 15 + 3 + 3 + 1)

mean = (31.25 * 44) / 44

mean = 31.25

Therefore, the mean number of hours the students spent listening to music is 31.25 hours.

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The proof of congruence by SAS, then 2 corresponding sides and the corresponding included angles of both triangles are equal.

Angles who are of same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of same measure, then

[tex]m\angle A = m\angle B[/tex]is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

The SAS postulate , Two sides and the included angle of one triangle are identical to the corresponding two sides and the included angle of another triangle.

In the triangle, the angles mCAD and mACB are congruent.

m∠CAD ≅ m∠ACB

Since m∠CAD and m∠ACB are congruent, AD and BC must also be congruent.

As a result, the SAS Congruence postulate is proven.

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Answer:

c) 6

Step-by-step explanation:

in a 45-45-90 degree triangle the hypotenuse is [tex]\sqrt{2}[/tex] times more than the length of the other sides

3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] is the same as 3(2) or 6

The length of the hypotenuse of the triangle is,

⇒ h = 6

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Base of triangle = 3√2

Length of triangle = 3√2

Now, We can formulate;

⇒ h² = (3√2)² + (3√2)²

⇒ h² = 18 + 18

⇒ h² = 36

⇒ h = 6

Thus, The length of the hypotenuse of the triangle is,

⇒ h = 6

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Answer:

7.5dollars

Step-by-step explanation:

25%/100×$30

Answer:

  EF = 18

Step-by-step explanation:

Given similar triangles DEF and JHI, midpoints G and K of sides DE and HI, with sides marked GF=9, EF=x+8, KI=14, HI=3x-2, you want to know the length of EF.

Corresponding sides in similar triangles are proportional. This means ...

  EF/GF = HI/KI

  (x+8)/9 = (3x-2)/14 . . . . substitute given values

  14(x +8) = 9(3x -2) . . . . multiply by 14·9

  14x +112 = 27x -18 . . . . eliminate parentheses

  130 = 13x . . . . . . . . . . . add 18-14x

  10 = x . . . . . . . . . . . . . divide by 13

Now, we can find EF:

  EF = x+8 = 10 +8

  EF = 18

On solving the provided question, we can say that from the graphs The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.

Prior to technological advancement, the opportunity cost of treating HIV/AIDS rises as the world deviates from its PPF. The potential cost of treating more HIV/AIDS cases falls as a result of technological advancements since less other commodities and services must be sacrificed in order to treat more HIV/AIDS patients. Alternatively, the world might treat more HIV/AIDS patients right now by forgoing the same number of other commodities and services.

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The correct question is -

More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect​ mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and​ now, a cure could be in sight.

​Source: The Guardian​, November​ 30, 2018

Make a graph of the production possibilities frontier with​ HIV/AIDS cases treated on the x​-axis and other goods and services on the y​-axis before and after the advance in technology.

Question content area bottom left

Part 1

The opportunity cost of treating​ HIV/AIDS cases increases as more​ HIV/AIDS cases are treated.

Draw a curve that shows the production possibilities for the world economy that produces​ HIV/AIDS treatments and other goods and services. Label the curve PPF0.

Then draw the PPF that shows the effect of an advance in technology on​ HIV/AIDS treatments. Label the curve PPF1.

Step-by-step explanation:

a normal distribution with mean m and standard deviation d gives us a few regular pieces of information.

for example, we know that 68.2% of all events are within the interval

m ± d

and 95.4% of all events are in the interval

m ± 2d

and 99.7% of all events are in the interval

m ± 3d

that means only 0.3% of all events are outside the interval

m ± 3d = 10.2 ± 3×0.12 = 10.2 ± 0.36

now, when a bag is filled with 9.8 ounces, it is 0.4 off the mean (10.2).

that means it is outside the 10.2 ± 0.36 interval and inside the 0.3% "exception" range.

you have to see it also that way : 0.3% means 3 out of 1000 bags are in that range.

so, yes, it is considered unusual.

Answer:

Width: [tex]9[/tex] Length: [tex]21.[/tex]

Step-by-step explanation:

Let's say [tex]l[/tex] is the length, and [tex]w[/tex] is the width. We can rewrite [tex]l[/tex] as [tex]2w + 3.[/tex] So  [tex]2(2w + 3) + 2w = 60,\\4w + 6 + 2w = 60,\\6w + 6 = 60,\\6w = 54,\\w = 9.\\[/tex]So the length of the rectangle is [tex]2 \cdot 9 + 3 = 21[/tex] and the width is [tex]9.[/tex]

Hope that helps!

Answer:

The solution of the equation is B. 4

Step-by-step explanation:

√x + 2 = x

√x = x - 2

(√x)² = (x-2)²

x = (x-2) (x-2)

x = x² - 4x + 4

x moves to the right

0 = x² - 4x - x + 4

0 = x² - 5x + 4

0 = (x-1) and (x-4)

x-1 = 0 x-4 = 0

x = 1 (not) x = 4

So, the solution to the equation is B. 4

Answer:

this hard

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

P = 72.5 * e^(0.025t)

Step-by-step explanation:

Here's a step by step solution with all the details and calculus involved.

(a) Express P as a function in the form P = Poat.

Since the population is growing continuously at a rate of 2.5% per year, we can use the formula for continuous growth:

P = Po * e^(rt)

where Po is the initial population (72.5 million), r is the continuous growth rate (0.025), and t is the time elapsed in years since 2004.

The continuous growth rate, r, is related to the annual growth rate, g, by:

r = g / 100

So, the continuous growth rate is 0.025.

Substituting the values into the formula for continuous growth, we get:

P = 72.5 * e^(0.025t)

This is the expression for the population as a function of time in the form P = Poat.

(b) Express P as an exponential function using base e.

The exponential function using base e is already in the desired form. So, we can simply write:

P = 72.5 * e^(0.025t)

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a) The rate in this problem is 23 miles.

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel 276 miles.

Unit rate is the ratio of two different units, with denominator as 1.

Given:

A certain car gets 23 miles to the galloon open highway.

a) The rate in this problem is 23 miles

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel

23/ 1 = x/ 12

x= 23 . 12

x= 276 miles

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Answer:

A. (f+g)(x)=-2x^2-2x+8

Step-by-step explanation:

You combine like terms by adding

The equation of the line is (y - 1/12) = -4/3(x - 7/5).

What is the slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be depicted by

tan θ = Δy/Δx

So, the slope of a line is tan.

The given equation of a line is:

3x-4y=7

-4y = -3x + 7

y = 3/4 x - 7/4

The slope of the line is 3/4.

The slope of the line perpendicular to the given line is - 1/m = - 4/3

The point-slope of a line is y - y₁ = m(x - x₁).

The given point is (7/5,1/12)

The equation of the line is

(y - 1/12) = -4/3(x - 7/5)

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Step-by-step explanation:

Your picture looks blurry however I think the graph passes through the points (0,0)(-1,0) and (3,0) so the equation becomes

[tex](x +1)(x - 3)x[/tex]

[tex] {x}^{3} - 2x {}^{2} - 3x + c[/tex]

Where C is the y intercept.

Since C is 0, our equation becomes

[tex] {x}^{3} - 2 {x}^{2} - 3x[/tex]

The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.

The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.

Mathematically, the null and alternative hypotheses can be expressed as follows:

H0: σ = 0.04

Ha: σ ≠ 0.04

where σ represents the standard deviation of the number of accidents per day.

The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.

The interest for the first quarter would be $ 15

The value of the CD when it matures is $ 2, 030. 11

The interest is said to compound quarterly which means that the periodic interest rate per quarter is:

= 3 % / 4

= 0. 75 % per quarter

The interest in the first quarter :

= 0. 75 % x 2, 000

= $ 15

The value of the CD at maturity is:

= 2, 000 x ( 1 + 0. 75% ) ²

= $ 2, 030. 11

Note : 2 periods because 6 months is 2 quarters.

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No one bank is not always better. Factors such as the fees and the charges in one bank may differentiate it from another bank.

No, one bank is not always better than another. The best bank for an individual depends on a variety of factors, including their financial needs and preferences, location, and the fees and charges associated with different banks.

For example, one bank may have lower fees for checking accounts but higher fees for ATM withdrawals or international transactions, while another bank may have higher fees for checking accounts but lower fees for other services.

Other factors that might affect which bank has the better fee structure include the type of account, the minimum balance required to avoid fees, and the level of customer service provided by the bank. Ultimately, the best bank is the one that meets an individual's financial needs at the lowest cost.

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Answer:

10x = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

Step-by-step explanation:

Distributive property of multiplication says every element within every pair of elements is added and multiplied to each other. So the value of 10 times that of 5 is 50.

The area of the shaded portion is [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex].

From the given data,

The equilateral triangle with sides 6.

Equilateral triangle: The amount of space an equilateral triangle takes up in a two-dimensional plane is its area. A triangle is said to be equilateral if all of its sides are equal and all of its interior angles measure 60 degrees. As a result, the area of an equilateral triangle can be determined if its side length is known.

In this problem

area of equilateral triangle=[tex]6^{2}*\sqrt{3}/4[/tex]----->[tex]\frac{9}{\sqrt{3} }[/tex] units²

The internal angles of an equilateral triangle are equal to 60 degrees

The area of a circle=pi*r²

for a circle with radius r=3 units

See the attached figure to better understand the problem

The area of the figure ABC is equal to the area of the circle divided by 6

Area figure ABC=[tex]9* \frac{\pi}{6}[/tex]=[tex]\frac{3}{2} *\pi[/tex]units²

the area of the shaded portion is equal to

⇒[tex]9*\sqrt{3} units^{2} -3*(\frac{3}{2} )*\pi[/tex] = [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex]

[tex]=9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex]

Therefore, the area of the shaded portion is [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex].

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The solution for x in the triangle is x = 51.98 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Using trigonometric ratio:

sin 38° = 32/x  (Sine = opposite/hypotenuse)

x = 32/sin 38°

x = 51.98 units

Therefore, the solution is x = 51.98 units

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