Mathematics College

Q1 - Similar shapes and area
Work out the missing area in each pair of similar shapes.

Answers

Answer 1

The answer for the first shape would be 24cm^2.

The answer for the second shape would be 20cm^2.

The answer for the third shape would be 30cm^2. "30".

What are Shapes?

A shape in geometry can be characterized as an object's form, outline, outer border, or outer surface.

Every object we notice in the world has a form. The objects we see around us may be broken down into several fundamental forms, such as the two-dimensional square, rectangle, and oval, or the three-dimensional rectangular prism, cylinder, and sphere few types of Shape.Shapes establish an object's perimeter and may be distinguished in a variety of ways depending on their characteristics. In a Shape a border that is created by merging the curves, points, and line segments surrounds these forms. The name of each form depends on the structure. Circle, square, rectangle, triangle, and other simple forms are few types of Shape.

The first shape seems to be scaling up. From 3cm to 12cm. So for this you need to multiply. Using the formula that I gave you last time.

3cm times ___ = 12cm. 4 fits in there,

therefore 6cm^2 times 4 = 24cm^2.

The answer for the first one would be 24cm^2. "24" in the blank.

The second shape seems to be scaling down. From 16cm to 8cm. So for this you need to divide.

16cm divided by ___ = 8cm. 2 fits in there,

therefore 40cm^2 divided 2 = 20cm^2.

The answer for the second one would be 20cm^2. "20" in the blank.

The third shape seems to be scaling up.

From 3cm to 4.5cm.

So for this you need to multiply. 3cm times ___ = 4.5cm.

Now since we're dealing with decimals, not whole numbers this time you can't really use guess and check as efficiently. So you do the opposite operation, which in this case the opposite of multiplication is division.

You take 3cm (the original shape's number) and divide it into 4.5cm. So 4.5cm divided by 3cm = 1.5. 1.5 fits in there,

therefore 20cm^2 times 1.5 = 30cm^2.

The answer for the third one would be 30cm^2. "30" in the blank.

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Related Questions

Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) squareroot of (9 + 49^x2) dx

Answers

The indefinite integral of given integral ∫√(9+49x^2)dx is ∫√(9+49x^2)dx = [tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex].

In the given question we have to find the indefinite integral.

The given integral is

∫√(9+49x^2)dx

Now finding the indefinite integral using the C for the constant of integration.

An integral is regarded to be indefinite if it has no lower or upper bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C.

We can write it as:

[tex]\int\sqrt{(9+49x^2)}dx = \int\sqrt{[(3)^2+(7x)^2]}dx[/tex]

Taking common 7^2

[tex]\int\sqrt{(9+49x^2)}dx = 7\int\sqrt{[(3/7)^2+(x)^2]}dx[/tex]

Using the formula

[tex]\int\sqrt{(a^2+x^2)}dx = \frac{1}{2}\times\sqrt{a^2+x^2} + \frac{1}{2}\cdot a^2In|x+\sqrt{a^2+x^2}|+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{(3/7)^2+x^2}+\frac{1}{2}\cdot(\frac{3}{7})^2In|x+\sqrt{(3/7)^2+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{9/49+x^2}+1/2\cdot(9/49)In|x+\sqrt{(9/49)+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+1/2\cdot(9/49)In|x+\frac{\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+(9/98)In|\frac{7x+\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex]

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Solve the equation for v.

0.5v + 0.03 > 2.83

v > 1.3
v < 1.3
v > 5.6
v < 5.6

Answers

Answer:

[tex] \huge{ \boxed{v > 5.6}}[/tex]

Step-by-step explanation:

[tex]0.5v + 0.03 >2.8[/tex]

In order to solve this inequality, first subtract 0.03 from both sides of the inequality to isolate 0.5v

[tex]0.5v + 0.03 - 0.03 > 2.83 - 0.03 \\ 0.5v > 2.8[/tex]

Next divide both sides by 0.5

[tex] \frac{0.5v}{0.5} > \frac{2.8}{0.5} \\ v > 5.6[/tex]

We have the final answer as

[tex] \bold{v > 5.6}[/tex]

A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N). A support cable running to the ground is inclined 71° from the horizontal.

Find the tension in the support cable. Give answer to the nearest whole number.

Answers

The tension in the support cable is 2731 N

How to find the tension in the support cable?

Given that:

A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N) and a support cable running to the ground is inclined 71° from the horizontal.

This can sketch as shown in the attached image. Considering the image:

T is the tension in the support cable

Using trigonometric ratio:

cos 71° = 889/T (adjacent/hypotenuse)

T = 889/cos 71°

T = 2731 N

Therefore, the tension in the support cable is 2731 N

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If u(x) = -2x² +3 and V(x) =
X
what is the range of (u.v)(x)?

Answers

The range of u(x) = {-15, -5,1,3,1, -5, -15} and range of v(x)= {-3,-2, -1,0,1,2,3} for the domain of x = { -3,-2,-1,0,1,2,3}

What is domain and range?

The domain of a function is defined by the set of the values of independent variables and the ranges are the set of values of dependent variables.

The domains act as an input of function where ranges act as an output.

How to find domain and range?

We select domain randomly as domain are the set of independent variables. But how will be the ranges must depend on the function given us.

we are given 2 function u(x) = -2x²+3 and v(x)

for the 1st function the set of domain and ranges are different, but the domain and ranges have the same values for the 2nd function.

we select domain x= {-3, -2, -1, 0, 1, 2, 3}

the ranges for u(x) ={ -15, -5, 1, 3, 1, -5 , -15}

because, u(-3) = -2(-3)²+3 = -15

u(-2) = -2(-2)²+3 =-5

u(0) = 3

similarly, for the same set of x value, v(-3) = -3

v(-2) = -2

v(0) =0

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Two basketball players are trying to have the most
points per game for the season. The current leader has
2112 points in 77 games and the second place player
has 2020 in 74 games. How many points per game did
the leading team score?

Helpppppp

Answers

The leading team has scored 0.13 points per game for the season that the second place player.

What is PPG Statistics?

The average number of points a player scores in a game of a sport, over the course of a series of games, a season, or a career, is known as points per game, or PPG, and it is an important statistic. By dividing the total points by the number of games, it is calculated. Basketball and ice hockey are two sports that frequently use PPG statistics.

First, consider the PPG of the current leader of the season from among the two basketball players.

The total number of points obtained by the current leader is equal to 2112.

The total number of games played by the current leader is equal to 77.

The points per game obtained by the current leader can be calculated as follows,

PPG = Total Points Obtained / Total Number of Games

[tex]\implies PPG=\frac{2112}{77}\\\implies PPG=27.42[/tex]

Now, consider the PPG of the second place player for the season.

The total number of points obtained by the second place player is equal to 2020.

The total number of games played by the second place player is equal to 74.

The points per game obtained by the second place player can be calculated as follows,

PPG = Total Points Obtained / Total Number of Games

[tex]\implies PPG=\frac{2020}{74}\\\implies PPG=27.29[/tex]

Subtracting the points per game of both players, we get

[tex]27.42-27.29=0.13[/tex]

Hence, the leading team has scored 0.13 points per game (PPG) for the season compared to the second place player.

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Chandrani had a Rs 100 note she bought a geometry box for ₹ 37 . 75. Find the amount left with her

Answers

Answer:

The amount left with her si 62.25

50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.

Answers

Negative 2.5 x greater-than-or-equal-to negative 30 is the equivalent expression of 50 minus 2.5 x greater than or equal to 20

How to find an equivalent expression?

Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will give you the same value when you simplify

Given: 50 minus 2.5 x greater than or equal to 20

50 - 2.5x ≥ 20

Subtract 50 from both sides:

-2.5x ≥ 20-50

-2.5x ≥ -30

Therefore, the equivalent expression is "negative 2.5 x greater-than-or-equal-to negative 30"

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Angle ABC is taken by a dilation with centerpoint, P and scale factor of four to angle A’B’C’ the measure of angle, BCA is 75° what is the measure of angle B’C’A’

Answers

Answer:

75°

Step-by-step explanation:

You want to know the measure of the image angle B'C'A' after angle A'B'C' is dilated by a factor of 4 about point P. Angle BCA is 75°.

Dilation

Dilation does not affect angle measures, so angle B'C'A' has the same measure as angle BCA, 75°.

m∠B'C'A' = 75°

6x + 3y = 3 3x - y = 4

Answers

Answer:

x = 1

y = -1

Step-by-step explanation:

Given equations:

6x + 3y = 3 -------------(1)

3x - y = 4 ----------------(2)

Multiply Eq. (2) by 2

2(3x - y) = 4 × 2

6x - 2y = 8 -------------(3)

Subtract Eq. (3) from Eq. (1)

6x + 3y - (6x - 2y) = 3 - 8

6x + 3y - 6x + 2y = -5

3y + 2y = -5

5y = -5

Divide 5 to both sides

y = -5/5

y = -1

Put y = -1 in Eq. (1)

6x + 3(-1) = 3

6x - 3 = 3

Add 3 to both sides

6x = 3 + 3

6x = 6

Divide 6 to both sides

x = 1

[tex]\rule[225]{225}{2}[/tex]

12. The number of liters of fuel used on a trip
varies directly with the number of miles traveled. If
a 120 mile trip requires 12.5 liters of fuel, how
many liters are required for a 504 mile trip?

Answers

Answer:

Step-by-step explanation:

A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game.

Answers

The correct answer is option B which is -1.67 is the expected value.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

You have a higher probability of losing money than gaining it due to the distribution of probability.

There are more chances to lose than win.

As a result, you are expected to lose money.

Only -1.67 is the only negative option, which means that we don't even need to do real math since there's already only one choice.

Hence, the correct answer is option B which is -1.67 is the answer.

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Answer:

You will Gain 5 points.

Step-by-step explanation:

Got it right on the test!

A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?

Answers

The mean and standard deviation of a random variable can be used to describe the distribution of its possible values. In this case, the mean of the random variable X represents the average number of bottles of soda that are bought from the vending machine on a given day, and the standard deviation represents the amount of variation in the number of bottles bought from one day to the next.

To find the mean and standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, you will need to use the mean and standard deviation of X and the price per bottle of soda.

The mean of Y can be calculated using the formula:

mean of Y = mean of X * price per bottle

Plugging in the given values, we get:

mean of Y = 50 * $1.50 = $75

So the mean of the random variable Y, which represents the total revenue from the vending machine on a given day, is $75.

The standard deviation of Y can be calculated using the formula:

standard deviation of Y = standard deviation of X * price per bottle

Plugging in the given values, we get:

standard deviation of Y = 15 * $1.50 = $22.50

So the standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, is $22.50.

Therefore, the mean and standard deviation of Y, the total revenue from the vending machine on a given day, are $75 and $22.50, respectively.

Cameron is deciding between two landscaping companies for his place of business.
Company A charges $25 per hour and a $300 equipment fee. Company B charges $55
per hour and a $150 equipment fee. Let A represent the amount Company A would
charge for t hours of landscaping, and let B represent the amount Company B would
charge for t hours of landscaping. Write an equation for each situation, in terms of t,
and determine the interval of hours, t, for which Company A is cheaper than
Company B.

Answers

Answer:

A = 25t + 300

B = 55t + 150

Less than 5 hours, company B would be cheaper. At 5 hours the cost is equal. After 5 hours, company A would be cheaper.

Step-by-step explanation:

Company B would be cheaper for lower hours.

The the two equation equal to each other and solve for to find out when the costs will be equal.

25t + 300 = 55t + 150 Subtract 25t from both sides

300 = 30t + 150 Subtract 150 from both sides

150 = 30t Divide both sides by 30

5 = t

At 5 hours the cost are the same, after 5 hours company A would be cheaper.

A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?

Answers

The required value of the production at which the company attained the same profit is 4 thousand skin care items.

Given that,

A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t³ + 8t² + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million.

Here,
Plotting the graph of the polynomial equation,

P(t) = –2t³ + 8t² + 2t,
From the graph at x = 4,
The polynomial gives the same value as it gave at x = 1,

Thus, the required value of the production at which the company attained the same profit is 4 thousand skin care items.

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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?

Answers

Using the normal distribution, it is found that a student has to score 0.675 standard deviations above the mean to be publicly recognized.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

z=x-nuo/sigmaIt measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The top 25% is at least the 100 - 25 = 75th percentile, which is X when z has a p-value of 0.75.Looking at the z-table, z = 0.675 has a p-value of 0.75.Hence, a student has to score 0.675 standard deviations above the mean to be publicly recognized.

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Which ordered pair satisfies the inequality? 6x + 5y < -15

Answers

The ordered pair of the inequality 6x + 5y < -15 are (2, 0) and (3, 2).

What is inequality?

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Considering the provided inequality and the provided ordered pairs, we will check it by replacing one by one in the inequality; if the inequality is fulfilled, they are the solution; otherwise, they are not, so we obtain:

(2, 0):

6x + 5y > 2

6(2)+5(0)>2

12+0>2

12>0

Since the inequality holds, then the ordered pair is a solution.

(7, -8):

6x + 5y > 2

6(7)+5(-8) > 2

42-40>2

2>2

Since the inequality is not satisfied, then the ordered pair is not a solution.

(3, 2):

6x + 5y > 2

6(3)+5(2) >2

18+10>2

28>2

Since the inequality holds, then the ordered pair is a solution.

(-8, 6):

6x + 5y > 2

6(-8)+5(6) >2

-48 + 30 > 2

-18 > 2

Since the inequality is not satisfied, then the ordered pair is not a solution.

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can someone help quick? someone gave me the answer but didn’t explain. what’s the inequality? where do i graph this? please give the right answers only

Answers

An inequality that represents the height h, in inches, of a person allowed to ride rollar coaster is h ≥ 48

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Let h represent for the height of any member allowed to ride rollar coaster

From the question we know that everyone's height must be greater that 48 inches.

It means the inequalities would be

h ≥ 48 tall inches

Thus, an inequality that represents the height h is h ≥ 48

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Question 60
Find the probabilities below using a standard 52 card deck.

Answers

By using the concept of probability, it can be calculated that-

1) P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]

2) P(Ace [tex]\cap[/tex] 5) = 0

3) P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4) P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]

5) P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur.

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

1) Number of ace card = 4

Number of '5' card = 4

P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]

= [tex]\frac{8}{52}[/tex]

2) P(Ace [tex]\cap[/tex] 5) = 0

3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)

Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]

P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4) Number of black coloured even numbered card = 10

Number of even numbered card = 20

Number of card of black colour = 26

P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]

= [tex]\frac{36}{52}[/tex]

5) Number of face cards of diamond = 3

P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

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help please very easy proportional relationship due hurry please than u!

Answers

1) h=1/5 k

(10/2 = 1/5, 20/4 = 1/5... etc)

2) k=5/4 h

(5/4 = 5/4, 10/8=5/4... etc)

3) h=5/1 k

(25/5 = 5/1, 30/6 = 5/1 ... etc)

Hope this helps!

Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.

Answers

The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².

What is Area :

The space around a shape's perimeter or boundary is known as its area. To determine the areas of various forms, many mathematical formulae are available.

Area of circle = πr², where r is the radius of the circle. Area of rectangle = lb, where l = length and b = breadth.

Here we have

composed of a rectangle and two semicircles.

Dimensions of the rectangle are,

Length = 14 and breadth = 4

=>Area of the rectangle = 14 × 4 = 56 units²

If we join the two semicircles,

we will have one circle with a diameter of 4 units

=> As we know Radius of the circle = Diameter/2

=> Radius of circle = 4/2 = 2 units

=> Area of the circle = 2πr

= [tex]2 \times\frac{22}{7} \times 2[/tex] = 12.56 unit²

Area of the figure = Area of rectangle + Area of the circle

= 56 units² + 12.56 unit²

= 68.56 unit²

Therefore,

The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².

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is a parallel to b? Explain using angels and measurements. Angel measrment should be part of your explanation.

Answers

Answer:

Not parallel.

Step-by-step explanation:

Given:

m∠9 = 110°m∠8 = 70°

Linear Pair

Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).

Angles 9 and 10 form a linear pair:

⇒ m∠9 + m∠10 = 180°

⇒ 110° + m∠10 = 180°

⇒ m∠10 = 70°

Angles 7 and 8 form a linear pair:

⇒ m∠7 + m∠8 = 180°

⇒ m∠7 + 70° = 180°

⇒ m∠7 = 110°

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

As line p is parallel to line q, and according to the vertical angles theorem and the corresponding angles postulate:

m∠1 = m∠6 = m∠9 = m∠14 = 110°m∠2 = m∠5 = m∠10 = m∠13 = 70°m∠3 = m∠8 = m∠11 = m∠16 = 70°m∠4 = m∠7 = m∠12 = m∠15 = 110°

If line a was parallel to line b, then according to the corresponding angles postulate:

m∠1 = m∠3 = m∠6 = m∠8m∠2 = m∠4 = m∠5 = m∠7

As m∠1 ≠ m∠8 and m∠2 ≠ m∠7 then lines a and b are not parallel.

1.6y+y-4/15y+1 1/6y=2 1/3 pls help

Answers

The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.

What is the domain of the function?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

1.6y+y-4/15y+7/6y=21/3

Move all terms to the left:

1.6y+y-4/15y+7/6y-(21/3)=0

Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R

Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R