Joeph drove 27 mile in 1 1/3 hour. If he drove at a contant rate, how far did he travel in one hour?

Answer:

Let x be the shorter side of the rectangular house. Since the length of the house is two-and-a-half times its width, we can write this as 2.5x. The area of a rectangle is given by the formula length * width, so the area of the rectangular house in terms of x is 2.5x * x = 2.5x^2. This is the expression for the area of the rectangular house in terms of the shorter side x.

Answer:

[tex]2.5x^2[/tex]

Step-by-step explanation:

Let x be the shorter side of the rectangle, which is also its width (w), so:

[tex]w=x[/tex]

Given that the length of the rectangle is two-and-a-half times its width, this means the length (l) can be expressed as:

[tex]l=2.5x[/tex]

The area of a rectangle (A) is the product of its length (l) and width (w):

[tex]A =l \cdot w[/tex]

Substitute the expressions for length and width into the formula for area:

[tex]A=2.5x \cdot x[/tex]

Simplify this expression:

[tex]A=2.5x^2[/tex]

Therefore, the expression for the area of the rectangle in terms of x is:

[tex]\Large\boxed{\boxed{2.5x^2}}[/tex]

The quotient of 3.12 × 10⁸ and 2.6 × 10⁵ is 1.2 × 10².

What is quotient?

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

Given numbers are 3.12 × 10⁸ and 2.6 × 10⁵.

Now divides 3.12 × 10⁸  by 2.6 × 10⁵:

(3.12 × 10⁸)/(2.6 × 10⁵)

Break the number into two fractions:

= (3.12/2.6) × (10⁸/10⁵)

Applying formula a^m/a^n = a^(m-n):

= (3.12/2.6) × (10⁸⁻⁵)

= 1.2 × 10³

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Answer:

15997.787145 cm³

Step-by-step explanation:

The particular solution that satisfies the given initial condition is y = 1. This is the solution to the given initial-value problem.

To solve this initial-value problem, we must first note that the given differential equation is homogeneous. This means that if y is a solution to the given equation, then so is cy, where c is an arbitrary constant. Thus, the first step in solving this initial-value problem is to find the general solution of the homogeneous equation. To do this, we can use the method of separation of variables.

This method involves separating the variables x and y on opposite sides of the equation, and then integrating both sides with respect to their respective variables. Doing this yields:

∫xy2 dy = ∫(y3 − x3) dx

Integrating both sides of the equation with respect to y yields:

y3x2/3 + C1 = x4/4 + C2

where C1 and C2 are arbitrary constants. Rearranging this equation yields:

y3 = 4x4/3 − 4C2x2/3 + 4C1

Now, we can use the given initial condition, y(1) = 1, to determine the value of the arbitrary constants. Substituting x = 1 and y = 1 into the equation yields:

13 = 4/3 − 4C2/3 + 4C1

Solving for C1 and C2 yields:

C2 = 0, C1 = 3/4

With the arbitrary constants determined, we can now find the general solution of the homogeneous differential equation. Substituting the values of C1 and C2 into the equation yields:

y3 = 4x4/3 − 3/4

This equation is the general solution of the given homogeneous differential equation. To solve the initial-value problem, we must now find the particular solution that satisfies the given initial condition. To do this, we can substitute the initial condition, y(1) = 1, into the general solution to obtain:

13 = 4/3 − 3/4

Solving for y yields:

y = 1

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Answer: The answer is 6x^2y(9 - 2y)

Step-by-step explanation: I am not completely sure sorry if its wrong

Option - B : Decision support system is a flexible tool for data analysis, since its reports do not have a fixed format.

  Decision support systems, a subset of business intelligence, are created to help organisations make sensible business decisions based on vast volumes of analysed data. Huge volumes of data are analysed using an interactive information system called a decision support system (DSS) to aid in the direction of business choices. A DSS aids management, operations, and planning levels of an organisation in making better decisions by assessing the importance of uncertainties and the tradeoffs involved in selecting one option over another. A DSS uses a variety of raw data, papers, personal knowledge, and/or business models to aid users in making decisions. A DSS may make use of relational data sources, cubes, data warehouses, electronic health records (EHRs), income projections, sales projections, and other sources.

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Answer:

C. Paying a cell phone bill

Answer:

Rylee

Step-by-step explanation:

Carina ran 7.18

and Rylee 7.16

7 4/25

4÷25= 0.16 7+0.16=7.16

Answer: 26, 28, 30

Explanation:

Let's define a variable x to represent the least of the three consecutive even integers. This means that the three integers are x, x + 2, and x + 4.

We can write the given information as an equation:

3 * (x + 4) = 2 * x + 38

We can solve for x by moving all the terms with x to one side of the equation and all the other terms to the other side:

3 * (x + 4) - 2 * x = 38

Then we can distribute the 3 and the -2 to get:

3 * x + 12 - 2 * x = 38

And then we can combine like terms on each side of the equation:

x + 12 = 38

Finally, we can subtract 12 from both sides to solve for x:

x = 26

Therefore, the three consecutive even integers are 26, 28, and 30.

We can check our solution by substituting these values back into the original equation and verifying that it holds true:

3 * (26 + 4) = 2 * 26 + 38

3 * 30 = 52 + 38

90 = 90

The equation holds true, so our solution is correct.

Answer:

You must babysit for 8 weeks to earn enough money to buy the new gaming chair.

Step-by-step explanation:

To determine how many weeks you must babysit to earn enough money to buy the new gaming chair, we need to write and solve an equation that represents the relationship between the money you have saved, the money you earn each week, and the cost of the gaming chair.

First, we can let w represent the number of weeks you must babysit. Then, we can set up the equation:

Earnings + Savings = Total Cost

Substituting the known values into the equation, we have:

Earnings + Savings = Total Cost

$37.50w + $155.95 = $455.95

To solve the equation, we can first subtract $155.95 from both sides of the equation:

$37.50w + $155.95 - $155.95 = $455.95 - $155.95

$37.50w = $300.00

Next, we can divide both sides of the equation by $37.50 to find the value of w:

$37.50w / $37.50 = $300.00 / $37.50

w = 8

Therefore, you must babysit for 8 weeks to earn enough money to buy the new gaming chair.

If Kurt milked 21 goats, then it will take 7/2 hours.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given

The proportional relationship between the number of hours milking, x, and the number of goats milked by Kurt, y, can be modeled by the equation y = 6x.

We have to find out if Kurt milked 21 goats, and how many hours did it take.

y = 6x

if Kurt milked 21 goats, then

21 = 6x

x = 21/6

x = 7/2

Hence, if Kurt milked 21 goats, then it will take 7/2 hours.

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To find the amount of red and white that Peter needs to add to the large batch, we can set up the following proportion:

(3/5 qt red) : (1 qt blue) : (2/5 qt white) = (x qt red) : (15 qt blue) : (y qt white)

The proportion states that the ratio of red to blue to white in the test batch is equal to the ratio of red to blue to white in the large batch.

Cross-multiplying and solving for x and y gives us:

(3/5)x = 15y

(2/5)y = 15x

Solving the first equation for y and substituting it into the second equation gives us:

(2/5)y = 15x

(2/5)(15x/3) = 15x

x = 9 qt

Substituting this value for x back into the first equation gives us:

(3/5)x = 15y

(3/5)(9 qt) = 15y

y = 6 qt

Therefore, Peter needs to add 9 qt of red and 6 qt of white to the large batch to make it the same color as the test batch.

Answer: 13

Step-by-step explanation: First you have to subtract the remaining amount of people from the total. 162-6=156. Then you have to divide the remaking amount, (people who went on) by the amount of people that can fit in a car to get how many cars are left. 156/12=13.

The probabilities are 1. 27/50, 2. 3/4, 3. 31/100, 4. 25/46, 5. 25/48

What is probability ?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item 1:

54 out of 100 people prefer bacon, hence:

P = 54/100

  = 27/50

Item 2:

Out of 100 people, 54 prefer bacon, 21 prefer sausage but pancakes, hence 54 + 21 = 75 desired outcomes, hence:

P = 75/100

  = 3/4

Item 3:

31 out of 100 people prefer bacon and pancakes, hence:

P = 31/100

Item 4:

Out of 46 people that prefer sausage, 25 prefer french toast, hence:

P = 46 / 25

Item 5:

Out of 48 people that prefer french toast, 25 prefer sausage, hence:

P = 48 / 25

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It will cost $225 to pour 25 yd3 of concrete with 3 workers working at a rate of $15 per hour.

To determine the cost to pour 25 yd3 of concrete, you can use the following formula:

cost = (number of workers * worker rate per hour * number of hours)

In this case, the number of workers is 3, the worker rate per hour is $15, and the number of hours can be calculated by dividing the volume of concrete to be poured (25 yd3) by the rate at which the workers can pour concrete (5 yd3 per hour). Therefore, the number of hours it will take to pour 25 yd3 of concrete is 25/5=5 hours.

Plugging these values into the formula gives:

cost = (3 workers * $15/hour * 5 hours) = $<<3155=225>>225

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The commutative property of addition justifies step 1 and the substraction of the property of equality justifies step 3.

What is the Substitution Property of Equality?

The substitution property of equality is applied by replacing a variable with a number or quantity. For example, if we have:

5x + 3 = 18, if x = 3, we can substitute x = 3 into the equation by applying the substitution property of equality as shown below:

5(3) + 3 = 18

15 + 3 = 18

18 = 18.

We have,

0.4x + 5 + 0.2x = 17

Step 1 : 0.4x + 0.2x + 5 = 17

commutative property of addition

Step 2: 0.6x + 5 = 17

Step 3: 0.6x = 12

substraction of property of equality

so, step 1  :  commutative property of addition

Step 3 : substraction of property of equality

Hence, the commutative property of addition justify for step 1 and the substraction of the property of equality justify for step 3.

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The closest allowable distance that a randomly chosen datum falls within the required 2 standard deviations of the mean is 0.95.

The likelihood that a data is within two standard deviations of the mean

By observation, the distribution depicted in the task content above is a normal distribution.

One can tell the difference between the following .

In the case of a standard normal distribution, 68% of the observations (datum) are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and 99.9% are within three standard deviations of the mean.

On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.

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In calculation, the precise bisector is a line section that separates a point into two equivalent points and parts.

The measure of P Q R is equal to the sum of ∠PQT and ∠TQR if line segment QT is the angular bisector of an angle ∠PQR.

∠PQR is equal to ∠PQT + ∠TQR.

There are three angular bisectors that can be made in a triangle, and all of them meet at the incenter of the triangle because line Q T is the angular bisector of P Q R. As a result, P Q T = T Q R.

BD divides ABC into two angles, ABD and DBC, given that line.

Additionally, given that DBC = 20 x + 16

ABD = 12 x + 24

Therefore, A B C = ABD + DBC (1) and ABD = DBC (2) respectively.

According to the second equation, 12 x + 24 = 20 x + 16 24  16 = 20 x 12 x 8 x = 8 x = 8 8 = 1

As a result, A B D = 12 (1) + 24; A B D = 36;

D B C = 20 (1) + 16; A B C = 36.

As a result of the equation (1), A B C = A B D + D B C;

A B C = 36; A B C = 72.

Therefore, ∠ABC measure 72.

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Full Question = Suppose line BD bisects ∠ABC. If m ∠ABD = 12 x + 24 and m ∠DBC = 20 x + 16, what is m ∠ABC?

In this case, the amount of population of fruit flies doubled in 18 days, meaning the doubling time is 9.5 days.

The doubling time of a population is the amount of time it takes for a population to double in size. In this case, the population of fruit flies started at 182 individuals and grew to 340 in 18 days. To calculate the doubling time, we used the equation (182 x 2^(18/9.5)) = 340, where the 2^(18/9.5) is the exponentiation of the number of days divided by the doubling time. This equation can be rearranged to solve for the doubling time, yielding a result of 9.5 days. This means that the population of fruit flies doubled in size every 9.5 days, which is the doubling time of the population.

182 x 2^(18/9.5) = 340

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Answer:

1.5A

Step-by-step explanation:

To find the current that the motor will require, we can use the formula for power, which is given by:

P = E * I

where P is the power, E is the voltage, and I is the current. Substituting the values for the power and voltage into the formula, we get:

180 = 120 * I

Dividing both sides of the equation by 120, we get:

1.5 = I

Therefore, the current that the motor will require is 1.5 amps.

Step-by-step explanation:

The formula for power is P = E x I, so the current required by the motor is equal to the power divided by the voltage. In this case, the current required by the motor is 180 watts / 120 volts = 1.5 amps.

If a number is assumed then multiply it by 3 and added the result to 1 then its algebraic equation will be 3x+1

According to the question

Assume a Number and multiply it by 2.

To Find:

to write it algebraically

Let the number that was asked to think to be x.

Then it is multiplied by 2 which becomes 2x.

Now the number is multiplied by 3

So, x multiplied by 3 will become 3x.

Then, 3x is added to 1

So, we can write it as 3x+1

Therefore, the equation can be written as 3x+1 algebraically.

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The mean, median, mode and the mean of the extra ten rolls are  

 2.96,2.5,1 and 2.9 respectively  

The mean represents the average of the dataset, the median represents the middle value of the data set, and the mode represents the repeated value in the dataset.

Using the given information we construct the following table

Score     frequency           Cumulative Frequency  (frequency*score)

1                 15                          15                                      15

2                10                          25                                     20

3                7                            32                                      21

4                 5                           37                                      20

5                 6                           43                                      30

6                 7                           50                                      42

thus N= 50 (even) The Median is the average of the 25th and 26th observations. The 25th and 26th observations corresponds to the value 3.

The Median is = 2.5

The modal score = 1

Mode = 3×(median) – 2×(mean)

mean = 2.96

The mean score for the 60 roles is 2.95×60 = 148+sum of the extra ten

                                       sum of the extra ten =29

               Thus mean of the extra ten roles is        

                                                                       = 29/10

                                                                       = 2.9

Hence the mean, median, mode and the mean of the extra ten rolls are  

 2.96,2.5,1 and 2.9 respectively

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Answer:

in Right triangles you can use this formula to find altitude by using two parts which altitude has made on the base

H² = b¹ × b²

So using this formula (which can be proven by triangle similarity) can help us to find x

10² = 4x × x ===>> x =5

Answer:

1w

Step-by-step explanation:

I want points

Answer:

x = - 8, 4

Step-by-step explanation:

x² + 4x - 32 = 0

to factorise , consider the factors of the constant term (- 32) which sum to give the coefficient of the x- term (+ 4)

the factors are + 8 and - 4 , since

+ 8 × - 4 = - 32 and + 8 - 4 = + 4 , then

(x + 8)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 4 = 0 ⇒ x = 4

zeros are x = - 8 , 4

The ratio of junior to adult = 6/5

What is proportion?

An equality between two ratios. According to proportion, if 2 sets of given numbers area unit increasing or decreasing within the same quantitative relation, then the ratios area unit aforesaid to be directly proportional to every different.

Main body:

Given - data in the question

To find answer the question

Solution - Let no of junior, children and adults be x, y, z respectively.

Now, ratio of junior to children = 1/3

So, x = 3y

Ratio of children to adult = 5/2

So, 5y = 2z

.(2)

So, from (1) we get, y = x / 3

So, 5x / 3 = 2z

⇒5x = 6z

⇒ x/z=6/5

Hence, the ratio of junior to adult = 6/5

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Answer:

undefined

Step-by-step explanation:

The slope of a vertical line is undefined since its calculation involves division by zero which is undefined.

Answer: undefined

If 4 cartons are selected at random, the the probability that exactly 3 of them are the deluxe model is 0.3231.

A shipment of 16 televisions contains 7 regular and 9 deluxe models.

The manufacturer failed to mark the model designation on the cartons.

If 4 cartons are selected at random, then we have to find the probability that exactly 3 of them are the deluxe model.

Now 4 cartons selected at random from 16 cartoons of televisions can be selected in ways = [tex]^{16}C_{4}[/tex]

Now simplifying

4 cartons selected at random from 16 cartoons of televisions can be selected in ways = [tex]\frac{16!}{4!12!}\\[/tex]

After simplification

4 cartons selected at random from 16 cartoons of televisions can be selected in ways = 1820

Now 3 of them are the deluxe model, can be selected in ways = [tex]^{9}C_{3}[/tex]

Now simplifying

3 of them are the deluxe model, can be selected in ways = [tex]\frac{9!}{3!6!}\\[/tex]

After simplification

3 of them are the deluxe model, can be selected in ways = 84

Remaining 1 selected from 7 regular model in ways = [tex]^{7}C_{1}[/tex]

Remaining 1 selected from 7 regular model in ways = 7

Therefore the probability that exactly 3 of them are the deluxe model = 84*7/1820

The probability that exactly 3 of them are the deluxe model = 0.3231

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The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey