Mathematics College

## Answers

**Answer 1**

A description that is representative of the **data** presented in the graph include the following: B. The amount of rainfall **increases** as an exponential function of time.

What is an exponential function?

In Mathematics and Geometry, an **exponential function** can be represented or modeled by using the following mathematical equation:

[tex]f(x)=a(b)^x[/tex]

Where:

a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or **growth factor**.

Also, the **growth factor** or common ratio can be determined by using this formula;

Common ratio, b = a₂/a₁ = a₃/a₂ = a₄/a₃ = a₅/a₄ = a₆/a₅

In conclusion, we can logically deduce that this graph represents an **exponential function** because it has a** growth factor** or common ratio that remains constant over time.

Read more on **exponential functions** here: brainly.com/question/28246301

#SPJ1

## Related Questions

Si el volumen de una caja de cartón de forma cúbica es de 216 dm³

### Answers

The volume of the **cardboard box** is approximately 13197.402 cubic inches.

The volume of a cardboard box is 216 dm³, we can convert it to the English system of **measurements**.

1 dm (cubic decimeter) is equivalent to 1 liter.

To convert dm³ to cubic inches, we can use the following conversion factors:

1 dm³ = 61.0237 cubic inches

Using this conversion factor, we can calculate the volume of the box in cubic inches:

The cube carton **volume** is 216 dm3 and the cube edge value is 6 dm.

The volume of the cube is calculated by **dividing** the edge values. In other words, volume = edge 3.

To find the edge (side) value, you can solve for the volume formula as follows:

edge 3 = volume.

edge = ∛ volume,

Where ∛ is the cube root.

Applying this **formula** to the given problem gives edge = ∛(216 dm³).

Edge = 6dm. Therefore, the side (edge) value of the cube is 6dm.

Volume (cubic inches) = 216 dm³ * 61.0237 cubic inches/dm³

= 13197.402 cubic inches

Question :- If the volume of a cubic cardboard box is 216 dm³

For more related questions on **cardboard box**:

https://brainly.com/question/28762570

#SPJ8

You pick a card at random, put it back, and then pick another card at random. 5 6 7 8 What is the probability of picking a prime number and then picking a prime number? Simplify your answer and write it as a fraction or whole number.

### Answers

In fraction form, the answer is 1/4, which represents the simplified **probability** of the given event occurring.

To find the probability of picking a **prime number** and then picking another prime number, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Given the four numbers: 5, 6, 7, and 8, we can see that there are two prime numbers (5 and 7) and two non-prime numbers (6 and 8).

The total number of possible outcomes is 4 since there are four cards to choose from.

Now, let's consider the **favorable outcomes**, which are picking a prime number and then picking another prime number.

The probability of picking a prime number on the first draw is 2/4, as there are two prime numbers out of the four total cards.

Since we replace the card before the second draw, the probability of picking a prime number on the second draw is also 2/4.

To find the probability of both events occurring, we multiply the individual probabilities:

(2/4) * (2/4) = 4/16 = 1/4

Therefore, the probability of picking a prime number and then picking another prime number is 1/4.

For more such questions on **probability**

https://brainly.com/question/24756209

#SPJ8

A magnitude of 700 pounds of force is required to hold a boat and its trailer in place on a

ramp whose incline is

10

to the horizontal. What is the combined weight of the boat and its

trailer?

### Answers

The combined **weight** of the boat and its trailer is approximately 4000 pounds.

To determine the combined weight of the boat and its trailer, we need to consider the forces acting on the ramp.

When an object is on an inclined plane, the force acting parallel to the incline can be calculated using the **formula**: Force = Weight * sin(θ), where θ is the angle of **inclination**.

Given that the force required to hold the boat and its trailer in place is 700 pounds, and the **angle** of inclination is 10 degrees, we can rearrange the formula to solve for the weight:

Weight = Force / sin(θ)

Weight = 700 / sin(10°)

Weight ≈ 4000 pounds

It's important to note that this calculation assumes ideal conditions and does not consider other factors such as friction or additional forces.

for more such questions on **angle**

https://brainly.com/question/31615777

#SPJ8

grade > R3 Compare and order rational numbers using number lines FMS

) What sign makes the comparison true?

0.75

D) You can use the number line to help.

+

0

### Answers

**Answer:**

**Step-by-step explanation: 1/4 is 0.25 as a decimal so the answer is 0.75>1/4**

Given h(x) = 4x^2-2x+1, find h (a + 3).

show work

### Answers

h( a + 3) = **4a² - 4a + 13**

Given,

**h(x) = 4x² - 2x + 1**

∴ h(a+3) = 4(a+3)² - 2(a+3) + 1

Now, calculating the three terms** **individually,

**4(a-3)² **= 4(a² + 3²- 2×a×3) {∵ (a-b)² = a² + b² - 2ab}

= 4(a² + 9 - 6a)

= 4a² - 6a + 9

and, **2(a + 3)** = 2a + 3

Adding the calculated terms, we get,

h(a+3) = 4( a + 3 )² - 2( a + 3 ) + 1

⇒ h( a + 3 ) = 4a² - 6a + 9 + 2a + 3 + 1

⇒ h( a + 3 ) = 4a² - 6a + 2a + 9 + 3 + 1

⇒ h( a + 3 ) = 4a² - 4a + 13

Hence, **h( a + 3) **= 4a² - 4a + 13.

For more questions on **evaluations of functions**,

https://brainly.com/question/26582052

A magician wants to know which of her magic tricks is the most popular. She emails a survey to people who previously attended one of her shows, asking them to rank their three favorite tricks. The magician determines that people favor her card trick. Select all the statements that are true about the sampling method.

### Answers

The magician's **sampling method** involves using a survey to collect responses from people who attended her shows. The sample is self-selected and may not be representative of the general population. The survey asks respondents to rank their favorite tricks, allowing the magician to determine the most popular trick based on the rankings provided by the respondents.

Based on the given information, we can identify the following true statements about the sampling method used by the magician to determine the popularity of her magic tricks:

1. The magician uses a** survey** method: The magician emails a survey to people who previously attended her shows. This method involves collecting responses from individuals through a **questionnaire** or survey.

2. The sample consists of people who attended the magician's shows: The survey is sent to individuals who have attended the magician's shows in the past. This ensures that the sample includes people who have direct experience with her tricks.

3. The sample is self-selected: The individuals who respond to the survey are self-selecting. They choose to participate voluntarily, potentially leading to a biased sample. Those who were more interested or had stronger opinions may be more likely to respond.

4. The survey involves ranking favorite tricks: The survey asks respondents to rank their three favorite tricks. This ranking approach allows the magician to determine the most popular trick based on the preferences expressed by the respondents.

5. The sample may not be** representative** of the general population: Since the sample consists only of individuals who attended the magician's shows in the past, it may not be representative of the general population's preferences. Those who have not attended the shows may have different opinions.

for more such questions on **sampling method**

https://brainly.com/question/13219833

#SPJ8

Question 9 of 60

Which symbol correctly compares the fractions below? 3/7 ? 4/14

O A. =

B. >

O C. <

OD. None of these are correct.

SUBMIT

### Answers

My answer is letter B. >

please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the

day?

OA. 5°F

ов. 33°F

OC. 3°F

OD. 33°F

### Answers

**Answer:**

I think its C

**Step-by-step explanation:**

The number of runs scored by a batsman in 20 matches 16,41,13,39,45,28,48,51,67,12,89,30,0,28,35,27,38,32,64,70 (take class intervals of 20 runs and form a frequency distribution table).

### Answers

**Answer:**

Refer below:

**Step-by-step explanation:**

To form a frequency distribution table for the number of runs scored by a batsman in 20 matches, we can use **class intervals** of 20 runs.

The given scores are 16, 41, 13, 39, 45, 28, 48, 51, 67, 12, 89, 30, 0, 28, 35, 27, 38, 32, 64, and 70.

Let's create the frequency distribution table:

**Class IntervalFrequency**

0-19 1

20-39 6

40-59 4

60-79 5

80-99 2

In the table, the class intervals represent **ranges of scores,** and the frequency represents the number of scores falling within each interval.

For example, in the class interval of 0-19, there is one score (0) falling within that range. In the interval of 20-39, there are six scores (16, 13, 28, 30, 28, 27) falling within that range. Similarly, we calculate the frequencies for the remaining intervals.

For more information on ** a frequency distribution table**:

https://brainly.com/question/17114842

https://brainly.com/question/31530115

7) GIVEN AB=DE. m< E = 108°

Determine the value of x and y

### Answers

The **values** of x and y are 35° and 20 ft

What is Pythagoras theorem?

**Pythagoras theorem** staes that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

This means if a and b are the two legs of the triangle and c is the hypotenuse then,

c² = a² + b²

Since triangle DEC and ABC are congruent triangles, then line DC is equal to line AC

therefore DC = 15 ft

Using **Pythagorean theorem**

25² = 15² + y²

y² = 25² -15²

y² = 400

y = √400

y = 20 ft

Since angle C = 45°

therefore;

100+45 +x = 180

x = 180 -145

x = 35°

Therefore the **values** of x and y are 35° and 20ft respectively.

learn more about **Pythagoras theorem** from

https://brainly.com/question/343682

#SPJ1

A student was asked to give the exact solution to the equation

22x+4-9(2) = 0

The student's attempt is shown below:

22x+49(2)=0

22x+24-9(2) = 0

Let 2* = y

y²-9y+8=0

(y-8)(y-1)=0

y = 8 or y=1

So x = 3 or x = 0

(a) Identify the two errors made by the student.

(b) Find the exact solution to the equation.

### Answers

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the **quadratic equation** as (y - 8)(y - 1) instead of

[tex]y^{2} - 9y + 8.[/tex]

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step [tex]"22x + 49(2) = 0,"[/tex] the student incorrectly **expanded **49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step [tex]"y^{2} - 9y + 8 = 0,"[/tex] the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be [tex](y - 8)(y - 1) = y^{2} - 9y + 8.[/tex]

(b) To find the exact solution to the equation, let's correct the errors made by the **student **and solve the equation:

Starting with the original equation: [tex]22x + 4 - 9(2) = 0[/tex]

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the **equation **is x = 7/11.

For more questions on **quadratic equation**

https://brainly.com/question/30164833

#SPJ8

The functions (x) and g(x) are shown on the graph.

f(x) = x²

What is g(x)?

10

-5

f(x)

10%

g(x)

y

(2,8)

5

10

### Answers

**Answer:**

232cm=m887-jjj

**Step-by-step explanation:**

f(x) = x²

What is g(x)?

10

-5

f(x)

10%

g(x)

y

(2,8)

5

10

Both **functions** are **quadratic** **functions**, and their graphs are **parabolas**. The function of g(x) is -x² - 4.

We have,

**Graph** of f(x) = x²:

This is a simple **quadratic** **function**.

The graph of f(x) = x² is a parabola that **opens** **upward**.

As x moves away from 0 in either direction, the function value increases. The **vertex** of the parabola is at the origin (0, 0). The curve is symmetric with respect to the y-axis.

Graph of g(x) = -x² - 4:

This function is also a **quadratic** **function** but with a negative coefficient in front of the x² term.

The graph of g(x) = -x² - 4 is a parabola that **opens** **downward**.

As x moves away from 0 in either direction, the function value decreases.

The **vertex** of the parabola is at (0, -4). Like the previous function, this curve is also symmetric with respect to the y-axis.

Thus,

Both **functions** are **quadratic** **functions**, and their graphs are **parabolas**. that opens upward and downwards.

Learn more about **functions** here:

https://brainly.com/question/28533782

#SPJ5

Solve the system of equations using elimination -3x - 5y = 45 and 2x - 2y = 2

### Answers

The solution to the system of **equations** -3x - 5y = 45 and 2x - 2y = 2 using elimination is x = -9 and y = -6.

1. Start with the given system of equations:

-3x - 5y = 45 ...(1)

2x - 2y = 2 ...(2)

2. Multiply equation (2) by 3 to make the **coefficients** of x in both equations equal:

6x - 6y = 6 ...(3)

3. Add equation (1) and equation (3) together to eliminate x:

(-3x - 5y) + (6x - 6y) = 45 + 6

**Simplify** the equation:

3x - 11y = 51 ...(4)

4. Now we have two equations without the variable x:

3x - 11y = 51 ...(4)

-3x - 5y = 45 ...(1)

5. Multiply equation (1) by 3 to make the coefficients of x in both equations equal:

-9x - 15y = 135 ...(5)

6. Add equation (4) and equation (5) together to eliminate x:

(3x - 11y) + (-9x - 15y) = 51 + 135

Simplify the equation:

-26y = 186

7. **Divide** both sides of equation (6) by -26 to solve for y:

y = -186/26

Simplify the equation:

y = -93/13

8. Substitute the value of y back into equation (1) to solve for x:

-3x - 5(-93/13) = 45

Simplify the equation:

-3x + 465/13 = 45

Subtract 465/13 from both sides:

-3x = 45 - 465/13

Simplify the equation:

-3x = 585/13 - 465/13

-3x = 120/13

9. Divide both sides of equation (8) by -3 to solve for x:

x = (120/13) / -3

Simplify the equation:

x = -40/13

10. Therefore, the solution to the system of equations -3x - 5y = 45 and 2x - 2y = 2 is x = -40/13 and y = -93/13, which can be further simplified to x = -9 and y = -6.

For more such questions on **equations**, click on:

https://brainly.com/question/17145398

#SPJ8

11. Find five numbers in A.P., such that their sum is 20 and the product of the first and the last is 15.

### Answers

**Answer: See below**

**Step-by-step explanation:**

I'm assuming that A.P is a list...

The prime factorization of 15 is: 1, 3, 5, 15, which means that the first and last can only be 1 and 15, or 3 and 5.

However, If it were 1 and 15, this would mean that the sum of the other 3 numbers equals 4. Not sure if repetition is allowed.

Option 1: 1 and 15

Other numbers are 1, 1, and 2

Option 2: 3 and 5

Other numbers add up to 13

Only one number between 3 and 5 though, which is 4. Do you know if the list is numbered from least to greatest?

Call the 5 numbers x, x + y, x + 2y, x + 3y, x + 4y, where x is the value of the first number and y is the constant value difference.

Since their sum is 20, 5x + 10y = 20.

Since the product of the first and last number is 15, x^2 + 4xy = 15.

From 5x + 10y = 20, we can see that x + 2y = 4.

-> (x+2y)^2 = 16 -> x^2 + 4xy + 4y^2 = 16 -> 4y^2 = 1.

-> y = 1/2 or -1/2

Replace back into the original equation : 5x + 10.(1/2) = 20 or 5x + 10.(-1/2) = 20

-> 5x + 5 = 20 / 5x + (-5) = 20

-> x = 3 / x = 5.

From the 4 combinations of x and y, we see that (x;y) = (5; -1/2) and (3; 1/;2) would satisfy the second condition.

So, the five numbers that we need to find has 2 different combinations :

(5; 9/2; 4; 7/2; 3) or vice versa (sum = 20)

An organization distributed 240 bottles of hand sanitizer, 480 pieces of face shields and 600 pieces of masks in the bags of item-wise equal number, to a certain people of a village to prevent from Covid-19. Find the greatest number of bags required to pack the items so that 10 bags remained empty.

### Answers

Given statement solution is :- The total number of **bags** distributed is 120 + 10 = 130.

To find the greatest number of bags required, we need to determine the common number of items that can be evenly** distributed **among the bags.

Let's assume the number of bags required is represented by 'x'.

The total number of hand sanitizer bottles,** face shields**, and masks distributed is 240 + 480 + 600 = 1320.

If 'x' is the number of bags required, then each bag would contain 240/x bottles of hand sanitizer, 480/x face shields, and 600/x masks.

Since we want an equal number of items in each bag, the values 240/x, 480/x, and 600/x should be integers.

To find the greatest number of bags, we need to find the greatest common divisor (GCD) of 240, 480, and 600. The GCD will represent the maximum number of bags that can be evenly packed.

The GCD of 240, 480, and 600 is 120.

Therefore, the greatest number of bags required to pack the items is 120.

Since 10 bags are empty, the total** number of bags** distributed is 120 + 10 = 130.

For such more questions on **Empty bags calculation.**

https://brainly.com/question/1948466

#SPJ11

draw a box plot for (35,50,50,48,48,32,38,41,48,34,29,23,41,34,43)

### Answers

The **box **plot for the given data set (35, 50, 50, 48, 48, 32, 38, 41, 48, 34, 29, 23, 41, 34, 43) is as follows:

| *

| *

| * * *

| * |

| * | *

| * * | *

| * | * * | *

|-------------

To create a box plot for the given dataset (35, 50, 50, 48, 48, 32, 38, 41, 48, 34, 29, 23, 41, 34, 43), we need to determine the five-number summary, which consists of the minimum, first quartile (Q1), median (Q2), third **quartile **(Q3), and maximum.

First, let's sort the data in ascending order: 23, 29, 32, 34, 34, 35, 38, 41, 41, 43, 48, 48, 48, 50, 50.

The five-number summary is as follows:

Minimum: 23

Q1: 34

**Median**: 41

Q3: 48

Maximum: 50

On a number line, we mark the minimum and maximum values (23 and 50) and draw a box with Q1, Q2 (median), and Q3 (34, 41, and 48). We connect the box with horizontal lines and indicate any **outliers** (values outside the minimum and maximum).

The box plot represents the distribution of the given dataset, with the box indicating the interquartile range and the median, and the whiskers showing the range of the data.

For more such answers on **quartile **

https://brainly.com/question/28169373

#SPJ8

Expand and simplify x(3x + 5)-5(2x - 1)

PLEASE HELP ME AND ANSWER THIS QUESTION !! I need this for my assessment revision

### Answers

The simplified **expression** of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

How to expand and simplify the expression

From the question, we have the following parameters that can be used in our computation:

x(3x + 5)-5(2x - 1)

Open the **brackets**

So, we have

3x² + 5x - 10x + 5

Evaluate the **like terms**

So, we have

3x² - 5x + 5

Hence, the simplified **expression** is 3x² - 5x + 5

Read more about **expression **at

https://brainly.com/question/31819389

#SPJ1

20. Find the value of m in 3:7 = m:21.

A. 3

B. 6

C. 9

D. 12

### Answers

The** value** of **m** in the** ratio** 3:7 is 9.

What is a ratio?

In **mathematics**, a** ratio** is a** comparison** of two or more **numbers** that indicates their **sizes **i**n relation **to each other. A **ratio** compares **two quantities **by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

Given the problem above, we need to find the **value** of **m** for 3:7 = m:21.

We can use** proportionality** in order to find **m**.

So,

[tex]\dfrac{3}{7} =\dfrac{\text{m}}{21}[/tex]

[tex]\rightarrow\text{m}=\dfrac{21\times3}{7}[/tex]

[tex]\rightarrow\text{m}=\dfrac{63}{7}[/tex]

[tex]\rightarrow\bold{m=9}[/tex]

Therefore, the** value** of **m** is 9.

To know more on** ratios**, visit:

https://brainly.com/question/28851311

C. 9 That's my answer

Four more than three times a number is equal to 27.

Write the equation for this problem using X as your variable and then solve the equation for X. Write a Findings Statement with your solution for X.

### Answers

a.) The **equation **for the problem is 3X + 4 = 27. Solving it, we find X = 7.67 (rounded).

b.) The solution for X in the equation "Four more than three times a number is equal to 27" is approximately X = 7.67. This satisfies the statement, as when we multiply 7.67 by 3 and add 4, we get 27.

a.) Let's write the equation for this **problem **using X as the variable. The problem states that "Four more than three times a number is equal to 27." We can translate this into an equation as follows:

3X + 4 = 27

To solve this equation for X, we need to isolate X on one side of the equation. We can do this by **subtracting **4 from both sides:

3X = 27 - 4

3X = 23

Next, we can divide both sides of the equation by 3 to solve for X:

X = 23/3

Therefore, the **solution **for X is X = 7.67 (rounded to two decimal places).

b.) Findings Statement: The solution for X in the equation "Four more than three times a number is equal to 27" is X = 7.67. This means that if we take the number 7.67, multiply it by 3, and add 4, we will obtain 27. Thus, the original statement is satisfied when the unknown number is approximately 7.67.

For more question on **equation **visit:

https://brainly.com/question/17145398

#SPJ8

18

X

24

18

These shapes

are similar.

Find X.

8

12

### Answers

**Answer:**

**Step-by-step explanation:**

between 18 & 24

Can someone fill in the 2 column proof table and explain so I understand?

### Answers

The **two-column proof** should be completed as follows;

Statements Reasons__________

1. m∠A ≅ m∠D, 1. given

m∠B ≅ m∠E

2. ∠A ≅ ∠D, ∠B ≅ ∠E 2. Definition of congruence

3. m∠A + m∠B + m∠C = 180° 3. Triangle Sum Theorem

4. m∠D + m∠E + m∠F = 180° 4. Triangle Sum Theorem

5. m∠A + m∠B + m∠C ≅ 5. Definition of congruence

m∠D + m∠E + m∠F

6. m∠A + m∠B + m∠C ≅ 6. Substitution Property of

m∠A + m∠B + m∠F Equality

7. m∠C ≅ m∠F 7. Subtraction Property of

Equality

8. ∠C ≅ ∠F 8. Definition of congruence

What are the properties of similar triangles?

In Mathematics and Geometry, two **triangles** are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are **congruent**.

Based on the angle, angle (AA) similarity theorem, we can logically deduce the following **congruent triangles**:

ΔABC ≅ ΔDEF

Read more on **triangles** here: https://brainly.com/question/11763540

#SPJ1

Let’s assume these are the 25 coins that were collected:

1966 penny, 1967 nickel, 1966 quarter, 1967 penny, 1965 penny, 1966 half dollar, 1967 quarter, 1965 dime, 1967 dime, 1968 quarter, 1964 dime, 1966 nickel, 1965 nickel, 1967 half dollar, 1966 dime, 1964 nickel, 1969 quarter, 1969 half dollar, 1965 half dollar, 1968 penny, 1968 dime, 1964 quarter, 1965 quarter, 1969 dime, 1968 nickel

To simplify writing each coin out, let’s abbreviate 1966 penny by 6P, and 1967 nickel by 7N, etc. Also, let C be the set that contains all 25 coins. So in our collection, C, we have the following:

6P, 7N, 6Q, 7P, 5P, 6H, 7Q, 5D, 7D, 8Q, 4D, 6N, 5N, 7H, 6D, 4N, 9Q, 9H, 5H, 8P, 8D, 4Q, 5Q, 9D and 8N

A physical model for these coins is found on Material Card 1. If you haven't already done so, cut out a set of coins from this Material Card and use them to do several of the following exercises.

Let S be the subset of coins from 1964, V from 1965, W from 1966, X from 1967, Y from 1968, Z from 1969 and T from 1970. Are P, N, D, Q, H, S, V, W, X, Y, Z and T all subsets of C?

yes

Using the correct notation, write out these 12 sets using the listing method by listing the elements in each set. The only elements in C are those listed above this exercise. Note that 6P is one element in P because 6P is a particular penny in C but 6 is not an element and P is not an element. The difference between how you write the answers here and how you did it in the previous exercise is that you are using proper notation with the braces, and commas in between the elements. List the elements in numerical and alphabetical order.

N=

Q=

S=

### Answers

The **elements **in numerical and alphabetical order.

N = {5N, 7N},

Q = {4Q, 6Q, 7Q, 8Q, 9Q},

S = {4D, 4N, 4Q}.

N = {5N, 7N}

Q = {4Q, 6Q, 7Q, 8Q, 9Q}

S = {4D, 4N, 4Q}

To clarify, the sets are written in numerical and **alphabetical order,** as follows:

N = {5N, 7N}

Q = {4Q, 6Q, 7Q, 8Q, 9Q}

S = {4D, 4N, 4Q}

In set N, we have the elements 5N and 7N, representing the 1965 nickel and 1967 nickel, respectively.

In set Q, we have the elements 4Q, 6Q, 7Q, 8Q, and 9Q, representing the 1964 quarter, 1966 quarter, 1967 quarter, 1968 **quarter**, and 1969 quarter, respectively.

In set S, we have the elements 4D, 4N, and 4Q, representing the 1964 dime, 1964 nickel, and 1964 quarter, respectively.

It is important to note that the remaining sets (P, D, H, W, X, Y, Z, T, and V) are not **explicitly **listed in this exercise.

However, based on the information given, each of these sets would contain the corresponding coins from the given years.

For similar question on **elements. **

https://brainly.com/question/25916838

#SPJ8

For what value of x is cos(x) = sin(14°), where 0° < x< 90°?

### Answers

The value of x is 76°, which satisfies the equation cos(x) = sin(14°) within the given **range**.

To find the value of x for which cos(x) = sin(14°), we need to determine the **angle **whose cosine is equal to the sine of 14°.

In the given range, 0° < x < 90°, we know that the sine function is positive, and the cosine function is also positive.

Since cos(x) = sin(90° - x), we can rewrite the equation as cos(x) = sin(90° - x) = sin(14°).

So, we have cos(x) = sin(90° - x) = sin(14°).

Using the identity sin(a) = cos(90° - a), we can write the equation as sin(90° - x) = sin(14°).

To find the angle whose **sine **is equal to sin(14°), we can set the angles inside the sine functions equal to each other:

90° - x = 14°

Simplifying the equation:

90° - 14° = x

76° = x

Therefore, the value of x for which cos(x) = sin(14°), within the given range of 0° < x < 90°, is x = 76°.

For more such questions on **range**

https://brainly.com/question/30389189

#SPJ8

Please answer this question! Would be a big help thankyou ever so much!!

Simplify fully

Optional working

3a² + 8a + 5-a² +4a-4

Answer:

### Answers

**Answer:**

The simplified expression is,

[tex]2a^2 +12a +1[/tex]

**Step-by-step explanation:**

[tex]3a^2 + 8a+5-a^2+4a-4\\3a^2-a^2+8a+4a+5-4\\2a^2 +12a +1[/tex]

What is the length of the x-component of the vector plotted below?

5

A. 3

B. 2

C. 4

D. 0

### Answers

The length of the x-component of the **vector **is 3, the correct option is A.

How to find the length of the x-component?

To find the **length **of the x-component, count the number of units between the start of the **vector **(the origin in this case) and the point.

Here we can see that the point is 3 units to the right of the start of the vector, which means that the x-vomponent of the vector is 3.

(and we can see that the y-component is 4) then the vector is <3, 4>

finally we can see that the correct option is A.

Learn more about **vectors** at:

https://brainly.com/question/3184914

#SPJ1

How do u solve this question

Simultaneous equations

2x^2+ y^2=12 and 5x+2y=6

### Answers

The solutions to the **simultaneous equations** are approximately (2.18, -2.45) and (-0.18, 3.45).

To solve the simultaneous equations:

Begin by **rearranging** the second equation to solve for one variable in terms of the other. In this case, we'll solve for y:

5x + 2y = 6

2y = 6 - 5x

y = (6 - 5x)/2

Substitute the **expression** for y in terms of x into the first equation:

[tex]2x^2 + y^2 = 12[/tex]

[tex]2x^2 + ((6 - 5x)/2)^2 = 12[/tex]

Simplify the equation by expanding and combining like terms:

[tex]2x^2 + (6 - 5x)^2/4 = 12[/tex]

[tex]2x^2 + (36 - 60x + 25x^2)/4 = 12[/tex]

Multiply through by 4 to eliminate the fraction:

[tex]8x^2 + 36 - 60x + 25x^2 = 48[/tex]

Rearrange the equation to form a quadratic equation:

[tex]33x^2 - 60x - 12 = 0[/tex]

Solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula here:

[tex]x = (-b ± √(b^2 - 4ac)) / (2a)[/tex]

Plugging in the values from the quadratic equation, we have:

[tex]x = (-(-60) ± √((-60)^2 - 4 * 33 * -12)) / (2 * 33)[/tex]

x = (60 ± √(3600 + 1584)) / 66

x = (60 ± √5184) / 66

x = (60 ± 72) / 66

Calculate the values of x:

For x = (60 + 72) / 66: x ≈ 2.18

For x = (60 - 72) / 66: x ≈ -0.18

Substitute the x values back into the second equation to find the corresponding y values:

For x ≈ 2.18:

5(2.18) + 2y = 6

10.9 + 2y = 6

2y = 6 - 10.9

2y ≈ -4.9

y ≈ -2.45

For x ≈ -0.18:

5(-0.18) + 2y = 6

-0.9 + 2y = 6

2y = 6 + 0.9

2y ≈ 6.9

y ≈ 3.45

Therefore, the solutions to the **simultaneous equations** are approximately (2.18, -2.45) and (-0.18, 3.45).

For such more questions on **Simultaneous Equations Solution**

https://brainly.com/question/15165519

#SPJ8

Insert Parentheses to make the equality true. 1+2x3+4x5=29

### Answers

**Answer:**

**((1+2)x3) + (4x5) = 29**

**Step-by-step explanation:**

Since 4x5 = 20 and 3x3 = 9, and 9 + 20 = 29, we put parenthesis around 1+2,

we get,

((1+2)x3) + (4x5) = 29

This is true because,

(3x3) + (4x5) = 29

(9) + (20) = 29

29 = 29

Pls help i need a quick answer

### Answers

The answer you’re looking for is Option C

What is true about infinite geometric series

### Answers

The true statement about **infinite** geometric series is (b) [tex]\sum\limits^{\infty}_{i=0} {7(\frac{1}{10})^n}[/tex] is not **convergent**

How to determine what is true about infinite geometric series

From the question, we have the following parameters that can be used in our computation:

The **geometric **series

Where, we have

[tex]\sum\limits^{\infty}_{i=0} {7(\frac{1}{10})^n}[/tex]

From the above **geometric series**, we have

**First term**, a = 7

**Common ratio**, r = 1/10 = 0.1

So, the sum of the series is

Sum = a/(1 - r)

This gives

Sum = 7/(1 - 0.1)

Evaluate

Sum = 7.78

From the list of options, we can see that (a), (c) and (d) are not true

Hence, the true statement about **infinite** geometric series is (b) [tex]\sum\limits^{\infty}_{i=0} {7(\frac{1}{10})^n}[/tex] is not convergent

Read more about **sequence **at

https://brainly.com/question/30499691

#SPJ1

Find the slope of the line.

### Answers

**Answer:**

slope = - 8

**Step-by-step explanation:**

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 10) and (x₂, y₂ ) = (4, 2) ← 2 points on the line

m = [tex]\frac{2-10}{4-3}[/tex] = [tex]\frac{-8}{1}[/tex] = - 8