5b+ 11 = 26
Can you help me solve this equation

Answer:

D: 7c + 9t

Step-by-step explanation:

I assume c = car and t = truck

Since it costs 7 dollards PER car and 9 dollars PER truck, you would use 7c+9c as the equation.

The equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

Let's assume that Aj runs x yards each week. Then, the number of yards that Aj walks each week would be (x + 90) yards, since he walks 90 more yards than he runs.

The total distance that Aj covers each week would be the sum of the distance that he runs and the distance that he walks, which is given as 400 yards.

So, we can write an equation as:

Distance covered by Aj = Distance that he runs + Distance that he walks

or,

Simplifying this equation gives:

Therefore, the equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

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The new cost of the order is 62.7% of the original price where still 4.5% sales tax had to pay.

A discount is a reduction in the price of an item or service, usually expressed as a percentage of the original price.

Let's assume the original cost of the order was $x.

        0.6x + 0.027x = 0.627x

Therefore, the new cost of the order is 62.7% of the original price.

For example, if the original cost of the order was $20, then the discounted price is $12 (60% of $20), and the sales tax is $0.324 (4.5% of $12). The final cost of the order would be $12.324.

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To define a default field value in a form or a database, you can use the attribute "default". When you add the "default" attribute to a field, it will automatically assign the specified value to that field if no other value is provided by the user or system.

This can be particularly useful when designing forms or databases that require certain fields to have a value even when the user does not provide one.
For example, in a web form, you might have a "Country" field that requires users to select their country from a dropdown list. By setting a default value for this field, such as "United States," the system ensures that there is always a value associated with that field even if the user does not make a selection.
Similarly, in a database schema, you might have a "DateCreated" field that automatically assigns the current date and time as the default value. This ensures that the date and time are always recorded for each new entry, even if the user does not manually input a value.
In both cases, the "default" attribute allows you to streamline the data collection process and ensure that your forms and databases maintain consistent and complete data. Using default values can also improve the user experience by reducing the amount of input required, making it easier for users to complete forms and submit their data.

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A linear equation can be written as:

\(y = a*x + b\)

Where a is the slope and b is the y-intercept.

Defining x as the number of weeks since the start of the year, we can write the linear equations I and B as:

\(B(x) =\$70 + \$5*x\)

(initial amount plus the amount that he saves each week times the number of weeks)

Similarly, for Ian we have:

\(I(x) = \$30 + \$15*x\)

The graph of these lines can be seen below, where the blue one is I(x) and the green one is B(x).

Now we want to determine how much they had when they had the same amount.

This means that we need to solve:

B(x) = I(x)

Replacing the equations we get:

\(\$70 + \$5*x = \$30 + \$15*x\)

Now we can solve this for x:

\(\$70 - \$30 = \$15*x - \$5*x\)

\(\$40 = \$10*x\)

\(\$40/\$10 = x\)

\(4 = x\)

So they have the same amount of money in week 4, and each one of them has:

\(B(4) = I(4) = \$70 + \$5*4 = \$70 + \$20 = \$90\)

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The probability that a randomly selected utility bill is,

a) P(X < 68) ≈ 0.016 or 1.6%

b) P(81 < X < 90) ≈ 0.1476 or 14.76%

c) P(X > 120) ≈ 0.0912 or 9.12%

To find the probability in each case, we can use the standard normal distribution by converting the given values into z-scores.

a) To find the probability that a randomly selected utility bill is less than $68, we need to find P(X < 68). First, we calculate the z-score using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (68 - 100) / 15 = -2.1333

Using a standard normal distribution table or a calculator, we can find the corresponding cumulative probability for z = -2.1333, which is approximately 0.016. Therefore, the probability P(X < 68) is approximately 0.016 or 1.6%.

b) To find the probability that a randomly selected utility bill is between $81 and $90, we need to find P(81 < X < 90). We calculate the z-scores for both values:

z1 = (81 - 100) / 15 = -1.2667

z2 = (90 - 100) / 15 = -0.6667

Using the standard normal distribution table or a calculator, we find the cumulative probability for z1 and z2: P(z1) ≈ 0.1038 and P(z2) ≈ 0.2514. Then, we subtract P(z1) from P(z2) to find the probability between the two values:

P(81 < X < 90) ≈ P(z1 < Z < z2) ≈ P(z2) - P(z1) ≈ 0.2514 - 0.1038 ≈ 0.1476 or 14.76%.

c) To find the probability that a randomly selected utility bill is more than $120, we need to find P(X > 120). We calculate the z-score:

z = (120 - 100) / 15 = 1.3333

Using the standard normal distribution table or a calculator, we find the cumulative probability for z = 1.3333, which is approximately 0.9088. Since we want the probability of X to be greater than 120, we subtract this value from 1:

P(X > 120) ≈ 1 - P(z) ≈ 1 - 0.9088 ≈ 0.0912 or 9.12%.

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The probability of observing a sample mean lower than 40.8 is 1.1% assuming the data come from a population that follows a normal model. Therefore, option b. is correct.

The p-value is a measure of the evidence against a null hypothesis. In statistical hypothesis testing, the null hypothesis is typically a statement of "no effect" or "no difference" between two groups or variables. The p-value represents the probability of obtaining a sample statistic (or one more extreme) if the null hypothesis is true.

In this context, the p-value is 1.1%, which means that if the null hypothesis were true (i.e., the population mean is equal to 43.80), the probability of obtaining a sample mean lower than 40.8 is 1.1%. This suggests that the data provide some evidence against the null hypothesis and support the alternative hypothesis that the population mean is less than 43.80.

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The correct answer is a. The P-value represents the probability of observing a sample mean as extreme or more extreme than the one observed, assuming that the data comes from a population that follows a normal model.

In this context, a P-value of 1.1% means that there is a low probability of observing a sample mean lower than 43.80, given that the data comes from a normal distribution. This suggests that the observed sample mean is unlikely to have occurred by chance alone, and provides evidence for a significant difference between the sample mean and the hypothesized population mean.

The P-value represents the probability of observing a sample mean as extreme as, or more extreme than, the one obtained from your data (43.80 mpg) if the true population mean is 40.8 mpg. The P-value of 1.1% indicates that there is a 1.1% chance of obtaining a sample mean of 43.80 or more due to natural sampling variation, assuming the population follows a normal model.

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

Step-by-step explanation:

The rate of change of the radius dr/dt = . 75 in/min because the radius is increasing with respect to time. hence, the volume is increasing at a rate of 75π cu in/min when the radius has a length of 5 inches.

Answer:

3,600−−−−−√ is a rational number.I guess

Answer:

B, C, E It is Rational, Perfect square(60*60) and an whole number

Answer:

The surface area of the label is 28 squared inches.

Step-by-step explanation:

The dimensions of juice box are length=2 inches, breadth=1.5 inches and height= 4 inches.

The lateral surface area of a cuboid is given by 2(length+breadth)×height.

Now, lateral surface area of juice box = 2(2+1.5)×4

= 2×3.5×4

= 28 squared inches

Answer:

28 square inches

Step-by-step explanation:

         The label covers the lateral surface area of the box.

  l = 2 in ;  w = 1.5 in ; h = 4 in

    \(\boxed{\text{\bf lateral surface area of cuboidal box = 2h*(l +w)}}\)

                                                                      \(\sf = 2*4 *( 2 +1.5)\\\\= 2 * 4 * 3.5\\\\ = 28 \ in^2\)

Answer:

5

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

because first u have to add it all up then take away

The absolute value of y, and the square root of (xy to the power of z) is \(xy^{z}\)

Floats are a type of number representation that allows us to store very large or very small numbers with a high degree of precision. In computer programming, it is often used to represent real numbers, such as decimals.

In this problem, we are given three float numbers x, y, and z and asked to perform various mathematical operations with them.

Let's start with the first operation: x to the power of z. This means that we want to find x raised to the power of z. This can be written mathematically as xᵃ.

The next operation is x to the power of (y to the power of z). This means that we want to find x raised to the power of y raised to the power of z. This can be written mathematically as x(yᵃ).

The third operation is the absolute value of y. The absolute value of a number is its magnitude, or distance from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. Mathematically, it can be written as |y|.

Finally, we have to find the square root of (xy to the power of a). The square root of a number is the value that, when multiplied by itself, gives the original number.

The square root of 25 is 5 because 5 * 5 = 25. This can be written mathematically as

=> √(xyᵃ).

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Answer:

Angle MJK = 64°

Step-by-step explanation:

In ∆MJL & ∆LJK,

JL= JL ...(common side)

Angle JML = Angle JKL ....( each 90°)

MJ = JK ....( Both measures 7)

Hence, by SAS criteria, ∆ MJL = ∆ LJk

.°. by C.P.C.T , ∠MJL = ∠LJK = 32°

Also,

∠MJK = ∠MJL+∠LJK

∠MJK = 32°+32°

Hiero earns $17.50 per hour and worked 41 hours this week. Under the Fair Labor Standards Act (FLSA), non-exempt employees are entitled to receive overtime pay at a rate of 1.5 times their regular pay for hours worked beyond 40 hours in a workweek.

To calculate Hiero's regular pay for the week, we multiply his hourly rate by the number of regular hours worked, which is 40 hours in this case. Therefore, Hiero's regular pay for the week is:

Regular pay = Hourly rate x Regular hours worked

Regular pay = $17.50 x 40

Regular pay = $700

Now, to determine whether Hiero is eligible for overtime pay, we subtract the number of regular hours worked from the total number of hours worked. In this case, the total number of hours worked is 41. Therefore, Hiero worked 1 hour of overtime, for which he is entitled to receive overtime pay.

To calculate Hiero's overtime pay, we multiply his hourly rate by 1.5 and then by the number of overtime hours worked, which is 1 hour in this case. Therefore, Hiero's overtime pay for the week is:

Overtime pay = Hourly rate x 1.5 x Overtime hours worked

Overtime pay = $17.50 x 1.5 x 1

Overtime pay = $26.25

Therefore, Hiero's total pay for the week, including regular pay and overtime pay, is:

Total pay = Regular pay + Overtime pay

Total pay = $700 + $26.25

Total pay = $726.25

Hiero's regular pay for the week is $700.

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High intercorrelations between two or more independent variables in a multiple regression model are referred to as multicollinearity.

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. With the use of independent variables whose values are known, multiple regression analysis aims to predict the value of a single dependent variable.

Multicollinearity, also known as collinearity, is a phenomena in statistics when one predictor variable in a multiple regression model can be linearly predicted from the others with a high level of accuracy. In this case, minor adjustments to the model or the data may cause the multiple regression's coefficient estimates to fluctuate unpredictably.

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By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

A gradient is a generalization of the tangent curve used for multivariate function, that is, a function with more than one variable. In this case we have a function with one variable, which means that the gradient is equal to the slope:

\(\nabla f = \frac{df}{dx}\)     (1)

Now we proceed to calculate the gradient of the curve:

\(\nabla f = 6\cdot x^{2}-7\)

\(\nabla f = 6\cdot (-2)^{2}-7\)

\(\nabla f = 17\)

By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

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Answer:

below

Step-by-step explanation:

the solution is

$2,400 * 43,560

=$104,544,000

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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The average value of f over the rectangle [0,6] x [0,1] is approximately 3.427.

The average value of a function f over a rectangle R is given by:

avg(f) = (1/Area(R)) * double integral of f over R

Here, f(x,y) = 5e^(yx) + e^y and R = [0,6] x [0,1]

The area of R is given by:

Area(R) = (6 - 0) * (1 - 0) = 6

So, the average value of f over R is:

avg(f) = (1/6) * double integral of f over R

We can evaluate the double integral using iterated integration. First, we integrate f with respect to y from 0 to 1, and then integrate the result with respect to x from 0 to 6:

integral of f(x,y) dy = integral of (5e^(yx) + e^y) dy

= (5x/2)e^(yx) + e^y + C

where C is the constant of integration.

Now, we integrate this result with respect to x from 0 to 6:

integral of [(5x/2)e^(yx) + e^y] dx = [(5/2) * integral of xe^(yx) dx] + integral of e^y dx

= [(5/2) * (1/y)e^(yx) - (5/2)(1/y^2)(e^(yx) - 1)] + ey + C

where C is another constant of integration.

Therefore, the average value of f over R is:

avg(f) = (1/6) * [(5/2) * (1/y)e^(yx) - (5/2)(1/y^2)(e^(yx) - 1) + ey] evaluated from y=0 to y=1 and x=0 to x=6

avg(f) = (1/6) * [(5/2) * (1/e^6 - 1) - (5/2)(1/e - 1/e^6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-6) - (5/2)(e^-1 - e^-6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-6 - e^-1 + e^-6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-1) + e - 1]

avg(f) ≈ 3.427

Therefore, the average value of f over the rectangle [0,6] x [0,1] is approximately 3.427.

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If we randomly select someone who was aboard the titanic, what is the probability that person is a man, given that he died is 1360/1517.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

Probability that person is a man, given that he died,

P(x) = Favorable outcome/Total

= 1360/ 1517.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Given:

\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)

Express 16 as \(4^{2}\): \(x^2+y^2=16\)

\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)

Trignometry,

\(\cos ^2(t)+\sin ^2(t)=1\)

Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:

\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)

Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)

Taking positive square roots as follows:

\(x=4 \cos (t), y=4 \sin (t)\)

Recall that, z = xy.

Now, we have:

\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)

Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)

So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)

Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)

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The values of the given functions are: \(Ay = 0.70711, dy = 0.25\)

We need to find the change in y, Ay when x = 1 and Ax 0.1 =

Find the differential dy when x = 1 and da = 0.1

Formula Used:

To find the differential, we use the formula:

\(dy = f'(x) * da\)

Where dx is the change in x.f'(x) is the derivative of f(x).da is the differential of x.

\(Ay = √√1 \\= √(1/2) \\= 0.70711\)

Now, we are given, \(x = 1 and dx = 0.1\)

Let us first find the derivative of y using the chain rule:

\(dy/dx = (1/2) * 5 * x^(-3/4) * (x^(-1/4))^(-1)\\dy/dx = (1/2) * 5 * x^(-3/4) * x^(1/4)\\dy/dx = (5/2) * x^(-1/2)\)

Substituting \(x = 1,\)

\(dy/dx = (5/2) * (1)^(-1/2)\\dy/dx = 5/2 = 2.5\\\)

Now, we need to find dy when \(x = 1 and dx = 0.1,\)

\(dy = f'(x) * dxdy \\= (5/2) * (0.1) \\= 0.25\)

Hence, \(Ay = 0.70711, dy = 0.25\)

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Answer:

d. -2/3x+5

Step-by-step explanation:

Because the line is perpendicular, the slope must be the inverse of the original slope. The inverse of 3/2 is -2/3. To find the b value, you plug (6,1) into the equation y=-2/3x+b

1=-2/3(6)+b

1=-4+b

5=b

The final equation is y=-2/3x+5

Answer:

Step-by-step explanation: Step 1: Write down the percent divided by 100 like this: 26.5% = 26.5 / 100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point: ...

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them.

This is an example of a comparative study that uses random sampling to ensure representation from different socioeconomic groups and educational backgrounds in the samples. The study aims to compare mathematics knowledge among 15-year-olds in the US and Japan by administering a mathematics achievement test to 1000 students from each country.
Hi! I'd be happy to help with your question. You would like to compare mathematics knowledge among 15-year-olds in the US and Japan by giving a mathematics achievement test to samples of 1000 15-year-olds in each of the two countries, with 200 students from low-income families, 400 students from middle-income families, and 400 students from high-income families in each country. This is an example of a stratified random sampling method.

In this case, the population is divided into different strata based on socioeconomic groups (low-income, middle-income, and high-income families), and then random samples are drawn from each stratum. This ensures that the samples include individuals from all different socioeconomic groups and educational backgrounds, which allows for a more accurate comparison between the two countries.

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Answer: 221 B.C

Step-by-step explanation:

Answer:

221 B.C.

Step-by-step explanation:

The state of Qin, based in the Sichuan plains, eventually won out in 221 B.C. under the leadership of the ruthless King Zheng. The victorious monarch gave himself the title Qin Shi Huangdi (259–210 B.C.), First Qin Emperor.Jun 3, 2019