Solve for x. Round your answer to the nearest tenth.
4.8 in
7.4 in

Answer:

C

Step-by-step explanation:

twenty-one and ninety-five thousandths

Answer:

Radius = 4.95 cm

Step-by-step explanation:

I am assuming you need the radius of the base of the cylinder.

Volume = 1.54 * 1000 = 1540 cm^3

Volume = πr^2h so:

1540 =  π*r^2*20

r^2 = 1540/20 π = 24.510

r = 4.95 cm.

They were based on four key areas

1) Representation,

2) Reasoning and Proof

3) Communication,

4) Problem Solving,

1) Representation:

Students are being challenged to present a mathematical concept in multiple ways. There are five different ways to depict thought:

1) Plaything models

2) Still images

3) Printed signs

4) Verbal/written communication

5) actual circumstances or settings

2) Reasoning and Proof:

The habit of reasoning should serve as a backdrop for the development of key mathematical concepts. Asking questions is the key! Why not? Invite students to make conjectures and then to develop, improve, and assess them since mathematics includes discovery. Additionally, let pupils investigate and articulate their own logic. It's frequently beneficial to expand on what kids already know while teaching them.

Students can use technology and manipulatives to solve problems and test their hypotheses at this point.

3) Communication:

Both a method of transmission and a part of what it means to "do" mathematics, communication in mathematics encompasses both. Teachers must create a safe space where students can attempt to share their ideas in the beginning. Since kids don't naturally communicate in math, teachers must be patient while they learn to do so.

4) Problem solving:

Mathematical problem solving is defined as "participating in a task for which the solution approach is not known beforehand. Students must employ previously learned information to create a solution, and by doing so, they obtain new mathematical understandings. Problem-solving exercises ought to be a regular element of math classes. Problems can be derived from real-world applications and experiences.

Hence we get the required answer.

Learn more about Mathematical thinking here:

brainly.com/question/25870256

#SPJ4

Answer:

Estimated=189

Exact=190.026

Step-by-step explanation:

Estimated values

20.7 to nearest whole number= 21

9.18 to nearest whole number= 9

Product means multiplication

Estimated product of 20.7 and 9.18

=21×9

=189

Exact product of 20.7 and 9.18

=20.7 × 9.18

=190.026

It has 3 decimal places

Answer:

The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number,

is

✔ 189

.

The exact product of 20.7 and 9.18 has

✔ 3

decimal places.

Step-by-step explanation: Hope this helps(:

Answer:

13 cm

Step-by-step explanation:

c = Circumference=pid= 81.64 To find the radius of a circle you can just divide the diameter by 2.pi = 3.14d = diameter=c/3.14 Pi is always 3.14 or 22/7.d = 81.64/3.14d = 26r= radius= 26/2radius=13 cm

Answer: 13 inches

Step-by-step explanation:

This retirement planning scenario involves saving a fixed amount per year, earning a specified interest rate, and determining the final retirement account balance, lump-sum investment amount, annual withdrawal in retirement, and required interest rate for a specific savings goal. The details are as follows:

a. retirement account balance of approximately $536,144.37

b. The lump sum required would be approximately $60,319.79.

c. With an account balance of $536,144.37, the annual withdrawal would be approximately $46,914.90.

d.  It would take approximately 16 years until the savings are depleted.

e. Through trial and error, it can be determined that an interest rate of approximately 10.47% is needed to achieve the desired savings goal.

a. The retirement account balance on the day of retirement can be calculated by using the formula for the future value of an ordinary annuity. In this case, saving $4,500 per year for 35 years with an annual interest rate of 5.5% will result in a retirement account balance of approximately $536,144.37.

b. To achieve the same retirement savings goal with a lump-sum investment today, the present value of an ordinary annuity formula can be used. The lump sum required would be approximately $60,319.79.

c. Assuming a retirement duration of 17 years and a desire to exhaust the savings with the 17th withdrawal, the annual withdrawal can be calculated using the formula for the annuity payment. With an account balance of $536,144.37, the annual withdrawal would be approximately $46,914.90.

d. If the decision is made to withdraw $90,000 per year in retirement, the number of years until the savings are exhausted can be determined using the formula for the number of periods in an annuity. It would take approximately 16 years until the savings are depleted.

e. If the maximum affordable annual saving is $900 and the goal is to retire with $1,000,000, the required interest rate can be calculated using the formula for the rate of return. Through trial and error, it can be determined that an interest rate of approximately 10.47% is needed to achieve the desired savings goal.

These calculations provide insights into the financial aspects of retirement planning and can help individuals make informed decisions about their savings, investments, and withdrawal strategies based on their specific goals and constraints.

Learn more about rate of return here:

https://brainly.com/question/30761579

#SPJ11

The cook made 9 servings of baked beans.

We have,

To find the number of servings of beans, we need to divide the total amount of baked beans by the number of baked beans per serving.

Total amount of baked beans = 7 1/2 pints

Amount of baked beans per serving = 5/6 pint

Number of servings of beans = (7 1/2) ÷ (5/6)

Converting 7 1/2 to an improper fraction:

7 1/2 = (2 × 7) + 1 = 15/2

Number of servings of beans = (15/2) ÷ (5/6)

To divide fractions, we can multiply by the reciprocal of the divisor:

Number of servings of beans = (15/2) × (6/5)

Number of servings of beans = 45/5

Number of servings of beans = 9

Therefore,

The cook made 9 servings of baked beans.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

I think that it is y=15x+35

Step-by-step explanation:

15*x is how many hours and you have to pay $35 regardless to rent the boat

Answer:   If x and y vary directly, it means that their ratio remains constant. We can use this relationship to solve the problem.

Let the constant of variation be represented by k. Then we can write:

y = kx

To find k, we can use the given information that "y is 88 when x is 11":

88 = k(11)

Solving for k, we get:

k = 8

Now that we know k, we can use the formula to find y when x is 7:

y = kx

y = 8(7)

y = 56

Therefore, when x is 7, y is 56.

Step-by-step explanation:

Answer:

when x is 7, y is 56.

Step-by-step explanation:

Please mark branliest

Answer: 16

Step-by-step explanation:

6−2+12

=4+12

=16

Answer:

The anwser is 16

Step-by-step explanation:

1 Simplify  6−2  to  4.

4+12

2 Simplify.

16

16

(a) Proof by contraposition:

To prove the theorem by contraposition, we assume that the product ab is not invertible and show that either a or b is not invertible. Suppose ab is not invertible, which means that there exists a nonzero vector x such that abx = 0. Multiplying both sides of the equation by a^(-1) on the left, we get a^(-1)abx = a^(-1)0. Simplifying, we have (a^(-1)a)bx = 0, which gives bx = 0. Since x is nonzero, this implies that b must be singular, and thus not invertible.

(b) Proof of the converse by contraposition:

To prove the converse of the theorem by contraposition, we assume that either a or b is not invertible and show that the product ab is not invertible. Suppose a is not invertible. Then there exists a nonzero vector x such that ax = 0. Multiplying both sides by b on the right, we have axb = 0b, which simplifies to abxb = 0. Since xb is nonzero, this implies that ab is not invertible.

(c) Proof by contradiction:

To prove the theorem by contradiction, we assume that the product ab is not invertible and show that this leads to a contradiction. Suppose ab is not invertible, which means that there exists a nonzero vector x such that abx = 0. Assume both a and b are invertible. Then we can multiply both sides of the equation by a^(-1) on the left to obtain a^(-1)abx = a^(-1)0, which simplifies to xb = 0. However, this contradicts the assumption that x is nonzero, thus proving that ab must be invertible.

(d) Proof of the converse by contradiction:

To prove the converse of the theorem by contradiction, we assume that either a or b is not invertible and show that this leads to a contradiction. Suppose a is not invertible. Then there exists a nonzero vector x such that ax = 0. Assume that ab is invertible. We can multiply both sides of the equation by b^(-1) on the right to obtain axb^(-1) = 0b^(-1), which simplifies to ax = 0. However, this contradicts the assumption that x is nonzero, thus proving that ab cannot be invertible.

(e) Two-part proof:

Part 1: If A and B are invertible matrices, then the product AB is invertible.

Proof: Assume A and B are invertible matrices. Since A is invertible, there exists an inverse matrix A^(-1) such that AA^(-1) = A^(-1)A = I, where I is the identity matrix. Similarly, B has an inverse matrix B^(-1) such that BB^(-1) = B^(-1)B = I. Now, let's consider the product AB. We can express AB as (AB)(B^(-1)A^(-1)). By associativity, this simplifies to A(BB^(-1))A^(-1) = AIA^(-1) = AA^(-1) = I. Thus, AB has an inverse matrix and is therefore invertible.

To learn more about contraposition click here : brainly.com/question/12151500

#SPJ11

There is about a 33.7% probability that a case of 48 cans will contain at least two cans with a defective ball.

To solve this problem, we can use the binomial distribution. Let's define "success" as getting a can with no defective ball and "failure" as getting a can with at least one defective ball.

The probability of success in one can is:

P(success) = 1 - P(failure) = 1 - 0.025 = 0.975

The probability of failure in one can is:

P(failure) = 0.025

Now, let's define X as the number of cans in a case of 48 that have at least one defective ball. We want to find the probability that X is greater than or equal to 2.

We can use the binomial distribution formula to calculate this probability:

P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

P(X = 0) = (0.975)^48 ≈ 0.223

P(X = 1) = 48C1 (0.975)^47 (0.025)^1 ≈ 0.44

where 48C1 is the number of ways to choose one can out of 48.

Therefore, the probability that a case of 48 cans will contain at least two cans with a defective ball is:

P(X ≥ 2) ≈ 1 - 0.223 - 0.44 ≈ 0.337

Learn more about Binomial distribution:

https://brainly.com/question/15246027

#SPJ11

Answer:

I believe that the answer would be d

Step-by-step explanation:

The first store has 30% right off the gate and the second store offers 10% off, then an additional 20, therefor amounting to 30% as well.

Also i did the math for the actual price that it would be but when I subtracted the two i didnt get any of the answers.

\(Median = \: ( \frac{n + 1}{2} ) \\ = \frac{5 + 1}{2} \\ = \frac{6}{2} \\ = 3th \: term\)

3th term is 14 which is median

Answer:

2n^2 - 5n +11

Question:

Charlotte has been working for her company for x years. Travis has been working for the same company exactly 3 years longer than Charlotte. What is the range of the relationship?

A- y>0

B- y>3

C. y<3

D. 0

Answer:

y > 3

Step-by-step explanation:

Number of years Charlotte has worked = x

Number of years Travis has worked = y. ie, y = 3+x

Let's assume the function reaches its lowest point at 3. There could also be a higher value for this function.

We now have:

f(x) = y > 3

Since Travis has been working for the same company exactly 3 years longer than Charlotte the range of the relationship is y>3

Answer: y>3

Step-by-step explanation:

just did this and got it right

Therefore, The smallest set of integers guaranteed to have a difference that is a multiple of 14 is 15. This is due to the Pigeonhole Principle and the 14 possible remainders when dividing integers by 14.

The smallest set of integers for which we are guaranteed there exist two whose difference is a multiple of 14 is 15. This can be explained by considering the possible remainders when dividing integers by 14. There are 14 possible remainders (0 to 13), but if we choose 15 integers, then by the Pigeonhole Principle, at least two of them must have the same remainder when divided by 14. The difference between these two integers will be a multiple of 14, as their remainders are the same. Therefore, the smallest set of integers required is 15.
Therefore, The smallest set of integers guaranteed to have a difference that is a multiple of 14 is 15. This is due to the Pigeonhole Principle and the 14 possible remainders when dividing integers by 14.

To know more about multiplication visit:

https://brainly.com/question/1135170

#SPJ11

To the nearest square foot, the area of the lawn that receives water from the sprinkler is 877 square feet.

To find the area of the lawn that receives water from the sprinkler, we need to find the area of the circular region that is covered by the sprinkler. The radius of this circular region is 18 feet, which means the area of the circle is pi times 18 squared, or approximately 1017.87 square feet.

However, the sprinkler only covers an angle of 305°, which means it leaves out a small portion of the circle. To find this missing area, we need to subtract the area of the sector that is not covered by the sprinkler.

The total angle of a circle is 360°, so the missing angle is 360° - 305° = 55°. The area of this sector can be found by multiplying the area of the full circle by the ratio of the missing angle to the total angle:

Area of sector = (55/360) x pi x 18 squared

Area of sector ≈ 141.2 square feet

Finally, we can find the area of the lawn that receives water from the sprinkler by subtracting the area of the missing sector from the area of the full circle:

Area of lawn = 1017.87 - 141.2

Area of lawn ≈ 876.67 square feet
To learn more about :  square feet

https://brainly.com/question/29020717

#SPJ8

So, based on the theoretical likelihood, we anticipate that 35 times out of 140 repeats, both spins will be odd numbers.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.

Here,

The theoretical probability of both spins being odd numbers is 9 over 36, which means that for every 36 times the experiment is repeated, we expect 9 of those times to result in both spins being odd numbers.

If the experiment is repeated 140 times, we can use the theoretical probability to estimate the number of times both spins will be odd numbers as follows:

140 * (9/36) = 35

So, based on the theoretical probability, we predict that both spins will be odd numbers 35 times out of 140 repetitions.

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

Answer:

Step-by-step explanation:

Then, the total time, which is 2 hours, is equal to x plus 7x, or 8x. So the amount of time he spends in the automobile is x=1/4 hour. The distance he travels in 1/4 hour at 28 mph is 7 miles.

pls mark brainliest

Answer:

yes indeed..... (wdm? u never finished the question)

Step-by-step explanation:

Answer:

The theocratical probability of rolling a two is 2/6 or 1/3. The theocratical probability of rolling a five is 5/6.

Step-by-step explanation:

The frequency of a class is the number of data points that fall within the class is 1.

To determine the frequency of each class in the table shown, we must first divide the data points into the respective classes. The classes are 1003, 1062, 1063, 1122, 1123, 1182, 1183, 1242, 1243, 1302, 1303, and 1362.

For the class 1003, the frequency is 1, since there is only one data point (1003) in this class.

For the class 1062, the frequency is also 1 since there is only one data point (1062) in this class.

For the class 1063, the frequency is also 1 since there is only one data point (1063) in this class.

For the class 1122, the frequency is 1 since there is only one data point (1122) in this class.

For the class 1123, the frequency is 1 since there is only one data point (1123) in this class.

For the class 1182, the frequency is 1 since there is only one data point (1182) in this class.

For the class 1183, the frequency is 1 since there is only one data point (1183) in this class.

For the class 1242, the frequency is 1 since there is only one data point (1242) in this class.

For the class 1243, the frequency is 1 since there is only one data point (1243) in this class.

For the class 1302, the frequency is 1 since there is only one data point (1302) in this class.

For the class 1303, the frequency is 1 since there is only one data point (1303) in this class.

For the class 1362, the frequency is 1 since there is only one data point (1362) in this class.

Therefore, the frequency of each class in the table shown is 1.

Learn more about frequency here :

https://brainly.com/question/5102661

#SPJ4

Answer:

Not me

Step-by-step explanation:

Answer:

my brain cant take that in to answer it mate

Step-by-step explanation:

sorry I couldnt help!!

Love: Deku <3

Answer:

The measure of each angle of  abc is equal to the corresponding angle of  a'b'c' when coincides with the other three triangles. The measures of the angles of the triangle are preserved as the figure rotates.

Step-by-step explanation:

If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

Learn more about nearly horizontal

brainly.com/question/32554312

#SPJ11

Answer:

First one: X= 11.5

Second one: W = 3

X= 41.4°

Third one: 516.8

Step-by-step explanation:

Remember SOH CAH TOA when dealing with trigonometry and study the diagrams well

We discovered the value, which is \(-31/6\), to solve the equation.

The process of equating or creating equality; Equalization is the idea of equating death with darkness. Equilibrium: a state of equal balance. Mathematics. an assertion that two quantities are equal by an expression or statement, frequently mathematical.

In mathematics, an equation is an expression or even a statement that consists of two algebraic expressions that have the same value and are divided from one another by the equal symbol. It is an otherwise stated proposition that has been quantitatively quantified. A chemical equation is said to be balanced if the quantity of each kind of atom in the reaction is identical on both the reactant and product sides.

To solve the given equation we get

\(3\frac{1}{3}*(-2\frac{1}{4} ) +1\frac{5}{6}\)

To convert these fraction value (mixed fraction) into simple fraction

\(\frac{10}{3} *-\frac{9}{4}+\frac{11}{6}\)

\(-\frac{15}{2}+\frac{11}{6}\)

Take LCM of 2 and 6

\(\frac{-45+11}{6}\)

\(=\frac{-34}{6}\)

To know more about equation visit:

https://brainly.com/question/10413253

#SPJ1

Answer:

Jan spent 3 months at the first gym and 9 months at the second gym.

Step-by-step explanation:

Given that:

1 year = 12 months

x = months at gym one

y = months at other gym

According to given statement;

x+y=12      Eqn 1

85x+50y=705     Eqn 2

Multiplying Eqn 1 by 50

50(x+y=12)

50x+50y=600     Eqn 3

Subtracting Eqn 3 from Eqn 2

(85x+50y)-(50x+50y)=705-600

85x+50y-50x-50y=105

35x=105

Dividing both sides by 35

\(\frac{35x}{35}=\frac{105}{35}\\x=3\)

Putting x=3 in Eqn 1

3+y=12

y=12-3

y=9

Hence,

Jan spent 3 months at the first gym and 9 months at the second gym.