Thomas took three 100-point quizzes, and the mean score for the three quizzes was 87 points. If the highest score is taken away, the mean of the remaining two scores would be 83.5 points. If the lowest score is taken away, the mean of the remaining two scores would be 89 points. What is the highest score?

Answer:

>

Step-by-step explanation:

since we know that w=4 then all we need to do if fill out the equation so we get 3*4^2+1    10*4+8 so then we just need to solve the equation

3*4^2+1    10*4+8

3*16+1     10*4+8

48+1       40+8

49          48

so since we know that 49 is bigger then 48 we have to put > to show that 49 is bigger or greater than 48

The value of n in the given congruent triangle is 6.

Congruent triangles have the same corresponding angle measures and side lengths.

Given that two congruent triangles, Δ ABC ≅ Δ XYZ,

Since, we know that, corresponding parts of congruent triangle are equal,

Therefore,

AB = XY

5n+8 = 38

5n = 30

n = 6

Hence, the value of n in the given congruent triangle is 6.

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Answer:

It’s 55

Step-by-step explanation:

180- 125=55

Answer:

This is a same side interior angle. I just learned this in class so don't blame me if your wrong, ur taking advice from a 4th grader dude.

Answer is: x

read the explanation lol

Step-by-step explanation:

So we know angle 3 and 4 is=180

7 and 8 =180

but 4 and 7 ALSO add up to 180, I think you can do this now. It's mental math.

Hint: 125+x=180

now, let's keep in mind that a year has 12 months, thus 3 months is really 3/12 of a year

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (4500)(0.04)(3) \implies \boxed{I = 540} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ I = (4500)(0.04)(\frac{1}{4}) \implies \boxed{I=45}\)

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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A.) let's solve for T :

plugging in the values of x and y,

value of T = 3

B.) Expansion of 3g(8 + 3)

that's all...

Answer:

not factorable

81x^2+1

Step-by-step explanation:

A correlation measures the strength, direction, and form of the relationship between two variables, x and y. The strength of the relationship refers to how closely the variables are related, with values ranging from -1 to 1.

A value of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other decreases. A value of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other also increases. A value of 0 indicates no correlation, meaning that the variables are not related.

The direction of the relationship refers to whether the variables move in the same direction or opposite directions. A positive correlation indicates that the variables move in the same direction, meaning that as one variable increases, so does the other.

A negative correlation indicates that the variables move in opposite directions, meaning that as one variable increases, the other decreases.

The form of the relationship refers to the pattern of the relationship between the variables. The form can be linear, meaning that the relationship between the variables can be described by a straight line, or nonlinear, meaning that the relationship between the variables cannot be described by a straight line.

Nonlinear relationships can take various forms, such as quadratic, logarithmic, or exponential. The form of the relationship can have important implications for interpreting the correlation coefficient and making predictions based on the relationship between the variables.

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The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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We can continue this process to obtain a power series expansion for the antiderivative.

To evaluate the indefinite integral of \(e^t3 + e^x dx\), we need to integrate each term separately. The antiderivative of \(e^t3\) is simply \(e^t3\), and the antiderivative of is also \(e^x.\) Therefore, the indefinite integral is:

\(\int (e^t3 + e^x)dx = e^t3 + e^x + C\)

where C is the constant of integration.

To evaluate the indefinite integral of e^cos(5t)sin(5t)dt, we can use the substitution u = cos(5t). Then du/dt = -5sin(5t), and dt = du/-5sin(5t). Substituting these expressions, we get:

\(\int e^{cos(5t)}sin(5t)dt = -1/5 \int e^{udu}\\= -1/5 e^{cos(5t)} + C\)

where C is the constant of integration.

Finally, to evaluate the indefinite integral of cos(1/x)dx, we can use the substitution u = 1/x. Then \(du/dx = -1/x^2\), and \(dx = -du/u^2\). Substituting these expressions, we get:

\(\int cos(1/x)dx = -\int cos(u)du/u^2\)

Using integration by parts, we can integrate this expression as follows:

\(\int cos(u)du/u^2 = sin(u)/u + \int sin(u)/u^2 du\\= sin(u)/u - cos(u)/u^2 - \int 2cos(u)/u^3 du\\= sin(u)/u - cos(u)/u^2 + 2\int cos(u)/u^3 du\)

We can repeat this process to obtain:

∫\(cos(1/x)dx = -sin(1/x)/x - cos(1/x)/x^2 - 2∫cos(1/x)/x^3 dx\)

This is an example of a recursive formula for the antiderivative, where each term depends on the integral of the next lower power. We can continue this process to obtain a power series expansion for the antiderivative.

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To evaluate the indefinite integral, we need to find the antiderivative of the given function. For the first question, the indefinite integral of et3 + ex dx is:∫(et3 + ex)dx = (1/3)et3 + ex + C,where C is the constant of integration.

To evaluate the indefinite integral of the given function, we will perform integration with respect to x:

∫(3e^t + e^x) dx

We will integrate each term separately:

∫3e^t dx + ∫e^x dx

Since e^t is a constant with respect to x, we can treat it as a constant during integration:

3e^t∫dx + ∫e^x dx

Now, we will find the antiderivatives:

3e^t(x) + e^x + C

So the indefinite integral of the given function is:

(3e^t)x + e^x + C

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Answer:

It's friday for me so here u go

Step-by-step explanation:

The solutions for u are: u = (-55 + √1025) / 8 and u = (-55 - √1025) / 8.

To solve the equation (4)/(u+5)=-(3)/(2u+10)+2 for u, we need to eliminate the denominators and simplify the expression. Let's begin by multiplying both sides of the equation by (u+5) and (2u+10) to clear the fractions:

4(2u+10) = -3(u+5) + 2(u+5)(2u+10)

Expanding these terms, we get:

\(8u + 40 = -3u - 15 + 4u^2 + 40u + 100\)

Rearranging the equation and combining like terms:

\(4u^2 + 55u + 125 = 0\)

Now, we have a quadratic equation. We can try to factor it, but in this case, the quadratic does not factor nicely. Therefore, we can use the quadratic formula:

\(u = (-b \pm \sqrt(b^2 - 4ac)) / (2a)\)

In this case, a = 4, b = 55, and c = 125. Plugging these values into the quadratic formula, we get:

\(u = (-55 \pm \sqrt(55^2 - 4(4)(125))) / (2(4))\)

Simplifying further:

u = (-55 ± √(3025 - 2000)) / 8

u = (-55 ± √1025) / 8

Since the square root of 1025 is not a perfect square, we cannot simplify it further. Thus, the solutions for u are:

u = (-55 + √1025) / 8 and u = (-55 - √1025) / 8

These are the two possible solutions for the equation.

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a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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The required length of the curve y = sin(2x) for the limits 0 to 2π is equal to 8.944units.

Length of the curve y = sin(2x) from x = 0 to x = 2π,

Use the arc length formula,

L = \(\int_{0}^{2\pi }\)√(1 + (dy/dx)^2) dx

y = sin(2x)

⇒ dy/dx = 2cos(2x)

Plug this into the arc length formula and simplify,

L =\(\int_{0}^{2\pi }\)√(1 + (2cos(2x))^2) dx

L = \(\int_{0}^{2\pi }\) √(1 + 4cos^2(2x)) dx

This integral cannot be solved exactly,

Use numerical methods to approximate the value of the integral.

Use a numerical integration method such as Simpson's rule or the trapezoidal rule.

Using Simpson's rule with a step size of 0.01,

Length of the curve is approximately 8.944 units.

Therefore, the length of the curve for the given limits is equal to 8.944units.

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The given question is incomplete, I answer the question in general according to my knowledge:

What is the length of the curve y = sin2x from x = 0 to x = 2π?

By answering the presented question, we may conclude that Because equation both of these answers are real values, the solution to the equation x2 - 9 = 0 is that it has two real solutions.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation \("x^2 + 2x - 3 = 0,"\)for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

(x-3)(x+3) = 0 is a rewrite of the equation \(x^2 - 9 = 0.\) This suggests that the equation's solutions are x = 3 and x = -3.

Because both of these answers are real values, the solution to the equation x² - 9 = 0 is that it has two real solutions.

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The proportion of the boards that will be greater than 122 inches is 84%

Given :

length of boards is listed as 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch.

we are aske to determine what proportion of the boards will be greater than 122 inches = ?

we have :

μ = 123

σ = 122

now, let x denote the number of boards.

⇒ X ∼N (μₓ , σₓ²) X∼N(123,1)

⇒ P(X>122)=P( X- μₓ/ σₓ >  122-123/1)

⇒ P(Z > -1)

= 0.08413

= 84%

hence we get the value as 84%

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​

Answer:

D; 3-thirds

Step-by-step explanation:

Here is a probability question.

Firstly, we need to understand that the probability of any event is between 0 and 1; it cannot be negative and cannot be more than 1.

So the probability we want to calculate here is simply the probability of drawing a yellow pencil.

The way to go about this is by dividing the number of yellow pencils by the total number of pencils

Mathematically;

Probability of bringing out a yellow pencil= Number of yellow Pencils/ Total number of pencils

From the question, we are told that the number of pencils = number of yellow pencils = 3

Thus the probability will be 3/3 = 1

This cannot be found in the options right?

1 is the same as 3-thirds meaning 3 * 1/3 = 1

The amount borrowed at 8% is $4000, at 10% is $12,000 and at 12% is $8000

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

let x be the amount borrowed at 8%

y be the amount borrowed at 10%

and z be the amount borrowed at 12%

total money borrowed = x+y+z = 24000 equation 1

also x+y = 2z equation 2

substitute 2z for x+y in equation 1

2z+ z = 24000

3z = 24000

z = 24000/3

z= $8000

the interest rate paid on z = 12/100× 8000 = $960

the interest paid on y = 10/100 × y

the interest paid on x = 8/100 × x

total interest paid = 960+10y/100+8x/100= 2480

10y/100+8x/100= 2480-960

10y/100+8x/100= 1520

multiply all terms by 100

8x+ 10y = 15200 equation 3

x+ y = 2z = 2× 8000

x+y = 16000 equation 4

using elimination method

8x+10y = 152000 equation 5

8x+8y = 128000 equation 6

subtract equation 6 from 5

2y = 24000

y = $12000

substitute 12000 for y in equation 4

x+12000= 16000

x = 16000-12000

x = $4000

therefore the amount borrowed at 8%, 10% and 12% are $4000, $12000, $8000 respectively.

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The Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.

To find the Wronskian of y1 = e^(3x) and y2 = e^(-7x), we can use the formula for calculating the Wronskian of two functions. Let's denote the Wronskian as W(y1, y2).

The formula for calculating the Wronskian of two functions y1(x) and y2(x) is given by:

W(y1, y2) = y1(x) * y2'(x) - y1'(x) * y2(x)

Let's calculate the derivatives of y1 and y2:

y1(x) = e^(3x)

y1'(x) = 3e^(3x)

y2(x) = e^(-7x)

y2'(x) = -7e^(-7x)

Now, substitute these values into the Wronskian formula:

W(y1, y2) = e^(3x) * (-7e^(-7x)) - (3e^(3x)) * e^(-7x)

= -7e^(3x - 7x) - 3e^(3x - 7x)

= -7e^(-4x) - 3e^(-4x)

= (-7 - 3)e^(-4x)

= -10e^(-4x)

So, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) is W(y1, y2) = -10e^(-4x).

Note that the order of the functions matters in the Wronskian calculation. If we were to reverse the order and calculate W(y2, y1), the result would be the negative of the previous Wronskian:

W(y2, y1) = -W(y1, y2) = 10e^(-4x).

Since the Wronskian is a constant value regardless of the interval (-∞, ∞) in this case, we can evaluate it at any point. For simplicity, let's evaluate it at x = 0:

W(y1, y2) = 10e^(0)

= 10

Therefore, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.

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The correct simulation to be used is option C. use numbers 0, 1, 2, 3, 4 and 5 to represent the green peppers, 6 to represent yellow peppers and 7, 8 and 9 to represent red peppers.

Simulation is defined as the method to obtain the samples using methods like random digit table.

Given,

Percentage of green peppers = 60%

Percentage of yellow peppers = 10%

Percentage of red peppers = 30%

This indicates that green pepper is 6 times the yellow pepper and red pepper is 3 times the yellow pepper.

So the numbers used muse be 6 numbers for green, 1 number for yellow and 3 numbers for red.

So 0, 1, 2, 3, 4, and 5 represent the green peppers, 6 represent the yellow pepper and 7, 8 and 9 represents the red peppers.

Hence simulation to be used is option C.

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Answer:

0,000003588

Step-by-step explanation:

the answer is 0 :)

Step-by-step explanation:

LOL.......................... -,-

To solve this problem, we need to find a common denominator for 5/8 and 3/12.

The prime factorization of 8 is 2 x 2 x 2, and the prime factorization of 12 is 2 x 2 x 3.

A common denominator for 5/8 and 3/12 is the least common multiple (LCM) of 8 and 12, which is 24 (2 x 2 x 2 x 3).

We can convert both fractions to have a denominator of 24 as follows:

5/8 = (5/8) x (3/3) x (3/3) = 15/24

3/12 = (3/12) x (2/2) x (4/4) = 6/24

Now we can add the fractions:

15/24 + 6/24 = 21/24

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 3:

21/24 = (21/3) / (24/3) = 7/8

Therefore, 5/8 + 3/12 = 7/8.

The answer is (B) 7/8.

Answer:

B 7/8

Step-by-step explanation:

showed work in the picture

Answer:

the option 3 says that the volume of box is true.as volume of box is calculated by (v)= l×b×h

Answer:

Step-by-step explanation:

Volume is a cubic measure. That means that the label you get for volume is the length cubed. For example, if the sides of that box were meaured in inches, your label would be in inches cubed. To get a length cubed, you would multiply. If each of the length, width, and height all measured x, then our volume expression would be x*x*x which is x-cubed.

That should tell you that to find the volume of the box shown, you have to multiply the length, width, and height together. The option you want is C. The word "product" means to multiply, in case that was an issue with determining the correct answer.

Answer:

B.

Step-by-step explanation:

Answer: (d+10) (d+6)

The specific solution to the initial value problem:\(y(x) = 10e^(2x) - 5e^(4x) + e^(-3x).\)

To solve the given initial value problem, we can use the method of finding the roots of the characteristic equation and then applying the initial conditions to determine the specific solution.

The characteristic equation for the given differential equation is obtained by substituting y = \(e^(rx)\) into the equation:

\(r^3 - 3r^2 - 22r + 24 = 0\)

To find the roots of this cubic equation, we can use numerical methods or factorization. In this case, we can observe that r = 2 is a root of the equation. Dividing the cubic polynomial by (r - 2) gives us:

\((r - 2)(r^2 - r - 12) = 0\)

Now, we can factor the quadratic equation \(r^2 - r - 12 = 0:\)

(r - 4)(r + 3) = 0

\(y(x) = 10e^(2x) - 5e^(4x) + e^(-3x).\)

So the roots of the characteristic equation are: r1 = 2, r2 = 4, and r3 = -3.

The general solution for the given differential equation is:

\(y(x) = C1e^(2x) + C2e^(4x) + C3e^(-3x)\)

To find the specific solution, we will use the initial conditions:

y(0) = 16    --->    C1 + C2 + C3 = 16       (Equation 1)

y'(0) = -11  --->    2C1 + 4C2 - 3C3 = -11   (Equation 2)

y''(0) = -181 --->   4C1 + 16C2 + 9C3 = -181  (Equation 3)

To solve this system of equations, we can use various methods such as substitution or matrix methods. Here, we'll solve it using matrix methods.

Rewriting the system of equations in matrix form:

| 1  1  1  |   | C1 |   | 16  |

| 2  4 -3  | x | C2 | = | -11 |

| 4  16 9  |   | C3 |   | -181 |

Using Gaussian elimination or matrix inversion, we can find the values of C1, C2, and C3. The solution is:

C1 = 10, C2 = -5, C3 = 1

Therefore, the specific solution to the initial value problem\(y(x) = 10e^(2x) - 5e^(4x) + e^(-3x).\)

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