. A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length?

The inequality that represents the least number of days after Monday that Joseph needs to run to reach his goal is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex]  ≤ 6

Number of miles that Joseph run on Monday = [tex]2\frac{1}{2}[/tex] miles

Number of miles that Joseph run each day after that = [tex]1\frac{1}{3}[/tex] miles

The inequality is the mathematical statement that shows the relationship between two expression using an inequality symbol. The inequality symbols are less than, greater than, less than or equal and greater than or equal.

Then the inequality will be

[tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex]  ≤ 6

Where x is the number of days after Monday that Joseph needs to run to reach his goal

Therefore, the inequality is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex]  ≤ 6

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To find out how many percent of computers have the Microsoft operating system installed, we need to add up the percentage of computers that have Windows XP and Windows 7 installed.

First, let's find out how many percent of computers have both Windows 7 and Linux installed:

85% (Windows 7) - 6% (Windows 7 & Linux) = 79% (Windows 7 only)

Next, let's find out how many percent of computers have both Windows XP and Linux installed:

20% (Windows XP) - 4% (Windows XP & Linux) = 16% (Windows XP only)

Finally, let's add up the percentage of computers that have Windows XP and Windows 7 installed:

79% (Windows 7 only) + 16% (Windows XP only) = 95%

So, 95% of the company's computers have the Microsoft operating system installed.

Answer:

o calculate the percentage of computers with the Microsoft operating system installed, we need to find the total number of computers that have either Windows XP or Windows 7 installed.

Microsoft Windows XP operating system is installed on 20% of the company's computers, so 20% of the computers have Windows XP installed.

Microsoft Windows 7 is installed on 85% of computers, so 85% of the computers have Windows 7 installed.

Linux and Microsoft Windows 7 are installed on 6% of computers, so 6% of the computers have both Windows 7 and Linux installed.

Microsoft Windows XP and Linux on 4% of computers, so 4% of the computers have both Windows XP and Linux installed.

All three programs are installed on 2% of computers, so 2% of the computers have all three programs installed.

To avoid double-counting the computers that have both Windows 7 and Linux installed, we need to subtract 6% from the total number of computers with Windows 7 installed. The same applies to the computers that have both Windows XP and Linux installed, so we need to subtract 4% from the total number of computers with Windows XP installed.

The total number of computers with Windows XP or Windows 7 installed is 20% + (85% - 6%) + (20% - 4%) = 20% + 79% + 16% = 115%.

So, 115% of the company's computers have the Microsoft operating system installed.

Step-by-step explanation:

There 144 four digit numbers are made up of four consecutive numbers from 1 to 9

We can approach this problem by counting the number of ways we can choose four consecutive numbers from 1-9 and then arranging them in a four-digit number.

Here we have to use combination

There are 6 possible sets of four consecutive numbers in the range 1-9

= {1,2,3,4}, {2,3,4,5}, {3,4,5,6}, {4,5,6,7}, {5,6,7,8}, and {6,7,8,9}.

For each set, there are 4! = 24 ways to arrange the four numbers into a four-digit number.

So the total number of four-digit numbers made up of four consecutive numbers from 1-9 is:

6 sets × 24 arrangements per set = 144

Therefore, there are 144 such four-digit numbers.

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The balance of Talia's account will grow exponentially if the interest is compounded annually.

The formula for calculating the balance after n years can be represented as:

[tex]B = P * (1 + r)^n[/tex]

where B is the balance, P is the principal (initial deposit), r is the interest rate as a decimal, and n is the number of years. If Talia deposits $100 into her account and the interest rate is x%, the possible balance amounts for the first four years can be calculated as follows:

Year 1: [tex]B = 100 * (1 + 0.01x)^1[/tex]

Year 2: [tex]B = 100 * (1 + 0.01x)^2[/tex]

Year 3: [tex]B = 100 * (1 + 0.01x)^3[/tex]

Year 4: [tex]B = 100 * (1 + 0.01x)^4[/tex]

It is important to note that the interest rate, x, must be provided in order to calculate the exact balance amounts.

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The exponential function for the  population is X = 203.[tex]e^{0.0107.t}[/tex]

The formula for an exponential function is f (x) = ax, where x is a variable and a is a constant that serves as the function's base and must be greater than 0.

Let be supposed that population can be modelled by means of the following exponential function:

X = A.[tex]e^{Bt}[/tex]

Where:

t - Time, measured in years. Where t = 0 for 1970.

A - Initial population, in millions inhabitants.

B - Exponential rate constant, in years.

X - Population, in millions inhabitants.

Each constant is found hereafter:

X = A.[tex]e^{Bt}[/tex]

203 = A.[tex]e^{B*0}[/tex]

203 = A[tex]e^{0}[/tex]

A= 203

X = A.[tex]e^{Bt}[/tex]

X = 203[tex]e^{B.10}[/tex]

226 = 203[tex]e^{B.10}[/tex]

B = 1/10(ln(226/203))

B = 0.0107

The exponential function for the  population is:

X = 203.[tex]e^{0.0107.t}[/tex]

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The cattleman should bid on cows that weigh at least 944.0 pounds, which is the weight corresponding to the top 5% of the normally distributed weights of cows.

To determine the lowest weight cow that the cattleman should bid on, we need to find the weight that corresponds to the top 5% of the weight distribution.

Using the standard normal distribution, we can find the z-score that corresponds to the top 5% of the distribution as follows:

z = invNorm(0.95) ≈ 1.645

where invNorm is the inverse of the standard normal cumulative distribution function, which can be found using a statistical calculator or a standard normal distribution table.

Next, we can use the z-score formula to convert the z-score to a weight value:

z = (x - μ) / σ

Solving for x, we get:

x = z * σ + μ

Substituting the values given in the problem, we get:

x = 1.645 * 74.8 + 825.0

x ≈ 944.0 pounds

Therefore, the cattleman should bid on cows that weigh at least 944.0 pounds.

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Answer:

x=2 , y= (-1/2)

Step-by-step explanation:

3x + 2y = 5
2x + 4y = 2

Consider Equation 1:- (3x+2y=5)

Multiply both sides by 2
2(3x + 2y) = 5*2
6x + 4y = 10

Subtract both equations-
6x + 4y =10
-2x + 4y =2

=> 4x =8
      x = 2

Substitute the value of x in equation 1

3*2 + 2y = 5
6 + 2y = 5
2y = 5-6
2y = (-1)

y = (-1/2)

Hope is helps ;)

Answer: 19x+24

Step-by-step explanation: 12x−8+7x+3212−8+7+32 x12+24+7

Answer: 19x +24

Step-by-step explanation:

The marked price of the radio is Rs 10000.

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

Discount = 10%

VAT = 13%

VAT - Selling price = 1170

Represent the price of the radio with x

Using the above as a guide, we have the following:

Discount = 10% implies 0.9x

VAT = 13% implies 0.9x * 1.13 = 1.017x

So, the difference is

1.017x - 0.9x = 1170

This gives

0.117x = 1170

Divide

x = 10000

Hence, the price of the radio is Rs 10000.

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Answer:36x^13

Step-by-step explanation:

We can solve this problem using the rule of exponents: (am)n = amn.

First, let's simplify the exponent on the first term:

(-3x^5)^2 = (-3x^5) × (-3x^5)

Next, let's multiply this by 4x^3:

(-3x^5)^2 × 4x^3 = (-3x^5) × (-3x^5) × 4x^3

Now, let's multiply the coefficients and combine the exponents:

(-3 × -3)x^(5 + 5 + 3) = 36x^13

Therefore, the answer is 36x^13.

Answer:

No solutions

Step-by-step explanation:

[tex]-8(v+1)=2(1-4v)-9\\-8v-8=2-8v-9\\8=-7\\8\neq-7[/tex]

Hence, there are no solutions to make both sides of the equation true.

well, if a value goes from 88 to 20, it clearly decreased, hmmm 88 - 20 = 68, by 68 units.

so if we take 88(origin amount) to be the 100%, what's 68 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 88 & 100\\ 68& x \end{array} \implies \cfrac{88}{68}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 22 }{ 17 } ~~=~~ \cfrac{ 100 }{ x }\implies 22x=1700\implies x=\cfrac{1700}{22}\implies x\approx 77.3[/tex]

When the cost of 7 books is equal to Rs 300 more than the 5 same books then the cost of a single book is equal to Rs 150.

Let us consider Rs 'x' be the cost of a single book .

Equation to represents the given expression 7 books is equal to Rs 300 more than the 5 same books is :

⇒ 7x = 300 + 5x

Subtract 5x from both the side of the equation we get,

⇒ 7x -5x = 300 + 5x - 5x

⇒ 2x = 300

Divide both the side by 2 we get,

⇒ 2x / 2 = 300 / 2

⇒ x =  Rs. 150

Therefore, the cost of a single book as per the given condition of 7 books is equal to Rs 300 more than the 5 same books is given by          Rs 150.

The above question is incomplete, the complete question is:

If 7 books cost Rs. 300 more than 5 books, find the cost of a book.​

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The expression has 3 terms and 3 factors

The terms are the constant, the r term and the t term

The factors that are in the equation are 1500, 1 and 12

An exponential equation is an equation that involves an exponential function, which has the form f(x) = a^x, where "a" is a constant base and "x" is the exponent. Exponential equations are used to model phenomena that grow or decay at a constant relative rate. The solutions to exponential equations can be found by manipulating the equation algebraically to isolate the variable in the exponent, taking logarithms of both sides, or by using exponential rules such as the power rule or the product rule.

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Answer:

x = 10

Step-by-step explanation:

[tex]-3x+8=5x-72[/tex]

Subtract 5x from both sides:

[tex]-3x+8-5x=5x-72-5x[/tex]

[tex]-8x+8=-72[/tex]

Subtract 8 from both sides:

[tex]-8x+8-8=-72-8[/tex]

[tex]-8x=-80[/tex]

Divide both sides by -8:

[tex]\dfrac{-8x}{-8} =\dfrac{-80}{-8}[/tex]

[tex]\boxed{x=10}[/tex]

The linear equation for A and B will be A=1000+35t and B=700+55t where t=no. of years and A will be same as B in 15 years.

What exactly is a linear equation?

The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.

Now,

As given that High School A currently has 1000 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 55 students each year.

Let A represent the number of students in High School A in t years, and

Let B represent the number of students in High School B after t years.

Then A=initial students+35*no. of years and B=initial students+55*no. of years i.e. A=1000+35t and B=700+55t  

and for A=B

1000+35t=700+55t

55t-35t=1000-700

20t=300

t=15

hence,

          The linear equation for A and B will be A=1000+35t and B=700+55t where t=no. of years and A will be same as B in 15 years.

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The college will have about 640 students who prefer pie. We can calculate percentages based on the student sampling of 225 students (assuming it was a completely random sample, and not one taken just from a specific group, such as football players at half-time).

What is random sample?

To make a prediction, we need to assume that the preferences of the 225 students surveyed are representative of the entire student population of 4,000. We can use the proportion of students who prefer pie in the sample to make an estimate.

The proportion of students who prefer pie in the sample is:

                36/225 = 0.16

We can use this proportion to estimate the number of students who prefer pie in the entire population:

                       4,000 x 0.16 = 640

Therefore, the best prediction about the slices of pie the college will need is that the college will have about 640 students who prefer pie. So the option "The college will have about 640 students who prefer pie" is the correct statement.

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The volume of the silo of cylinder shape containing grain is 8625.24 cubic units.

The volume of the cylindrical shaped grain silo will be calculated by the formula -

Volume = πr²h, where r represents radius and h represents height of the cylinder.

Now, as we know radius is half of the diameter. So, radius = 17/2

Performing division on Right Hand Side of the equation

Radius of the cylinder = 8.5

Keep the values in formula to find the value of volume of silo

Volume = π × 8.5² × 38

Taking square and performing multiplication on Right Hand Side of the equation

Volume = 8625.24 cubic units

Hence, the volume is 8625.24 cubic units.

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Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.

Answer:

The volume of a rectangular prism with length 25 cm and width 40 cm can be calculated as follows:

Volume = Length * Width * Height

Since the height is not given, we cannot calculate the exact volume.

Step-by-step explanation:

Bob tardó 55 minutos en limpiar el garaje, por lo que debemos convertir ese tiempo a segundos para saber cuánto tiempo tardó exactamente.

Sabemos que 1 minuto tiene 60 segundos, por lo que podemos utilizar esta información para convertir los 55 minutos a segundos. La fórmula para realizar esta conversión es:

Segundos = Minutos * 60

Aplicando esta fórmula a los 55 minutos que Bob tardó en limpiar el garaje, obtenemos:

Segundos = 55 * 60

Segundos = 3300

Por lo tanto, Bob tardó 3300 segundos, o aproximadamente 55 minutos, en limpiar el garaje.

Es importante destacar que la conversión de tiempo de minutos a segundos es una operación común en matemáticas y cálculo, y es útil para resolver problemas en los que es necesario trabajar con diferentes unidades de tiempo. Además, entender la relación entre diferentes unidades de tiempo es esencial para realizar cálculos precisos y resolver problemas de manera efectiva.

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First, assign variables to the given information:

We're given:

Plug the second equation into the first and solve using substitution:

[tex]x+y=709\\59+y+y=709\\59+2y=709\\2y=650\\y=325[/tex]

Therefore, 325 adult tickets were sold.

325 adult tickets were sold.

Answer: 11.7 in.

Step-by-step explanation:

I don't really know this stuff myself since I'm in 8th grade, but I can say that AA is 12in. long. I measured the length of A'C, and it was a little shorter than AA. So therefore, I think the answer is 11.7 in. I just wanted to help you out.

The values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.

According to the stem leaf plot the first digit is the stem and the second digit is the leaf.

Hence, the values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.

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The measure of angle A is 83 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In the triangle ABC, ∠A=(12x-1)º, ∠B=10x and ∠C=3x+6

Now we need to find the value of angle A.

We know that from angle sum property that the sum of three angles is 180 degrees.

∠A+∠B+∠C=180

12x-1+10x+3x+6=180

25x+5=180

25x=175

Divide both sides by 25

x=175/25

x=7

Now angle A is 12(7)-1=84-1=83 degrees

Hence, the measure of angle A is 83 degrees.

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The complete question is In Triangle ABC, ∠A=(12x-1)º, ∠B=10x and ∠C=3x+6 then the measure of m∠A

The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.

Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.

Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:

P(Democrat) = 60/100 = 0.6

Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:

P(Woman) = 60/100 = 0.6

Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:

P(Democrat and Woman) = 40/100 = 0.4

To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:

P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)

= 0.6 + 0.6 - 0.4

= 0.8

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Answer:

(a) (0,0)

Step-by-step explanation:
Solving with Elimination method-

Take the first equation-    3x - 2y = 6

Multiply both sides by 2
2(3x - 2y) = 2*6
6x - 4y = 12

Subtract Both the equations-

  6x - 4y = 12
- 6x - 4y = 12
=          0 = 0


The answer is (0,0)

4214.7 is the balance in the account after 2 months .

What does compound and simple interest mean?

A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.

                               Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.

P = $4200

R = 2.1% = 2.1/100 = 0.021  =

    T = 2 month = 2/12 = 1/6

   I = PRT

    = 4200 * 0.021 * 1/6 = 14.7

Amount = P + I = 4200 + 14.7  = 4214.7

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The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.

Let us consider the present age of Earl to be x years.

According to the given question, the present age of Robin is twice that of Earl = 2x

And since it is given that Adam is 8 years younger than Earl, then his age

= x - 8

After 6 years, the age of Earl will be x + 6

Robin's age  will be = 2x + 6

Adam's age will be = x - 8 + 6 = x - 2

According to the given question, Robin's age will be thrice the age of Adam.

Hence, 2x + 6 = 3 (x - 2)

⇒ 2x + 6 = 3x - 6     ⇒ 6 + 6 = 3x - 2x     ⇒ 12 = x

Thus, the present age of Earl is 12 years,

Robin's age = 2x = 2 x 12 = 24 years

Adam's age = x - 8 = 12 - 8 = 4 years

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