Lin says that 23 is a prime number. Is Lin correct?

Answer:

96 sq yards

Step-by-step explanation:

40-24 is 16, and 16/2 is 8. 8 is the second length, so 8 times 12 is 96 which is the area

The simple interest using I = prt if Oliver borrowed $1,500 to purchase a riding lawn mowerat the rate of f 12% for 6 monthsis

The concept that will be used is the concpt of simple interest and thei can be calculates using the simple interst formular which is

I = [(prt)/100]

where p = principal =  $1,500

     I = intereste rate

     t=time

Then this can be expressed as

I= (prt)/100

I =  ($1,500* 6/12 * 12 )/100

=  $90

In conclusion the simple interest is now  $90 which is the second option that is given.

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Answer:

$3,550 dollars

Step-by-step explanation:

6.4% off savings

- a total of $2,400

The percentage is that indicating the hundredth total amount in the saving account before withdrawing such that 6.4% of that is $2400 is $37500.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Let's suppose the total amount of money before withdrawing x.

It is known that x% of y is given as, (x/100)y.

Therefore,6.4% of x is (6.4/100)x = 0.064x

The 6.4% of the x is 2400

So, 0.064x = 2400

x = 2400/0.064 = $37500

Hence "The percentage is that indicating the hundredth total amount in the saving account before withdrawing such that 6.4% of that is $2400 is $37500.".

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The area of the parallelogram is \(\sqrt{132}\).

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.

Given that,

vertices k(1, 1, 3), l(1, 3, 5), m(6, 9, 5), and n(6, 7, 3)

Area of Parallelogram = |KL × KN|

KL = (1, 1, 3) - (1, 3, 5) = (0, 2, 2)

KN = (1, 2, 3) - (3, 7, 3) = (2, 5, 0)

Area of the parallelogram = cross product of two vectors, represented by the adjacent sides.

Area of Parallelogram = |(0, 2, 2) × (2, 5, 0)|

                                    = |i(2 × 0 - 5 × 2) - j(0 × 0 - 2 × 2) + k(0 × 5 - 2 × 2)|

                                    = |i(-10) - j(-4) + k(-4)|

                                    = |-10i + 4j - 4k|

                                    = \(\sqrt{(-10)^{2}+(4)^{2}+(-4)^{2} }\)

                                    = \(\sqrt{100+16+16}\)

                                    = \(\sqrt{132}\)

Hence, The area of the parallelogram is \(\sqrt{132}\).

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The speed of the man in the question is: 6 km/hr

The formula to find the average speed when given distance and time is expressed as:

Average Speed = Distance/Time

Let the speed of the man be x.

At this speed(X), the total time he takes to travel 108km is 108/X.

Now, If he had travelled 2km/hour faster, his speed would have been X + 2 km/hour.

At this speed, he could have arrived at the destination 4.5 hours earlier.

This means that the time taken to travel would have been (108/x) - 4.5 hours if his speed had been (X + 2) km/hour.

So, according to the question, we have:

(108/X) - 4.5 = 108/ (X + 2) ----------- (1)

Solving this equation, we get X = 6 or -4. So, his speed is 6km/hour.

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Answer:

0.49

Explanation:

Given the expression:

tan 26°

Evaluating using calculator

tan 26° = 0.4877

Hence the decimal rounded to the nearest hundredth is 0.49

Answer:

0.49 to nearest hundredth

Step-by-step explanation:

tan 26⁰ = 0.48773

A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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The given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

According to the given question.

We have two planes

2x - 4y + 3z = 5

and,

x + 8y + 10z = 3

Since, two planes are perpenicular if

\(a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0\)

Where \(a_{1}\), \(b_{1}\) and \(c_{1}\) and \(a_{2}\), \(b_{2}\) and \(c_{2}\) are the direction ratios of planes.

And the two planes are parallel to each other if

\(\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }\)

Here, the direction ratios of plane 2x + 4y + 3z = 5 are 2, -4, and 3  and the direction ratios of plane x + 8y + 10z = 3 are 1, 8, and 10

Now,

2(1) + (-4)(8) + 3(10)

= 2 - 32 + 30

= 0

Since, the sum of the product of the direction ratios of  the two palnes is 0. Therefore, the given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

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Answer:

Kinda confusing, (probably just me) but I think it may be 1,400 rabbits last year.

We can rewrite dz/du and dz/dv as: \(dz/du = (1 + u + 3ln(v))e^{(u+ln(v))} dz/dv = (3 + u + 3ln(v))e^{(u+ln(v))/v}\)

To find dz/du, we need to take the partial derivative of z with respect to u while treating v as a constant:

dz/du = (∂z/∂x)(∂x/∂u) + (∂z/∂y)(∂y/∂u)
     = (e^(x+y))(1+3y) + (x+3y)e^(x+y)
     = (x+4y)(e^(x+y))

To find dz/dv, we need to take the partial derivative of z with respect to v while treating u as a constant:

dz/dv = (∂z/∂x)(∂x/∂v) + (∂z/∂y)(∂y/∂v)
     = (e^(x+y))(3/(v)) + (x+3y)e^(x+y)
     = (x+3y+3)(e^(x+y))/(v)

Note that the domains of u and v must be such that x=u is defined and y=ln(v) is defined (i.e. u must be any real number and v must be greater than zero).
Hi! To find dz/du and dz/dv, we will first find the partial derivatives of z with respect to x and y, and then use the chain rule.

Given z = (x + 3y)e^(x+y), x = u, and y = ln(v).

First, let's find the partial derivatives of z with respect to x and y:

∂z/∂x \(= (1 + 3y)e^{(x+y)} + (x + 3y)e^{(x+y)}= (1 + x + 3y)e^{(x+y)}\)

∂z/∂y = (3e^(x+y)) + (x + 3y)e^(x+y) = (3 + x + 3y)e^(x+y)

Now, we'll find the partial derivatives of x and y with respect to u and v:

∂x/∂u = 1 (since x = u)

∂x/∂v = 0 (since x is independent of v)

∂y/∂u = 0 (since y is independent of u)

∂y/∂v = 1/v (since y = ln(v))

Now, using the chain rule, we can find dz/du and dz/dv:

dz/du = (∂z/∂x)(∂x/∂u) + (∂z/∂y)(∂y/∂u) = (1 + x + 3y)e^(x+y)(1) + (3 + x + 3y)e^(x+y)(0)

dz/du = (1 + x + 3y)e^(x+y)

dz/dv = (∂z/∂x)(∂x/∂v) + (∂z/∂y)(∂y/∂v) = (1 + x + 3y)e^(x+y)(0) + (3 + x + 3y)e^(x+y)(1/v)

dz/dv = (3 + x + 3y)e^(x+y)/v

Since x = u and y = ln(v), we can rewrite dz/du and dz/dv as:

dz/du = (1 + u + 3ln(v))e^(u+ln(v))

dz/dv = (3 + u + 3ln(v))e^(u+ln(v))/v

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Answer: 7, 28, 63, 112, 175, 252, ...

Step-by-step explanation:

7, 28, 63, 112, ...

7*1, 7*4, 7*9, 7*16, ...

7*1², 7*2², 7*3^2, 7*4², ...

Hence, 7n², n=1, 2, 3, 4, ...

7*5²=

7*5*5=

175

7*6²=

7*6*6=

252

Thus,

7, 28, 63, 112, 175, 252, ...

To solve this problem, let's assume the speed of the current is "x" mph. When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. Therefore, the speed of the boat relative to the water is 11 - x mph.

When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the speed of the boat relative to the water is 11 + x mph.

Now, let's calculate the time taken for each leg of the journey:

Time taken to go 40 miles upstream = Distance / Speed
Time taken to go 40 miles upstream = 40 / (11 - x) hours

Time taken to go 70 miles downstream = Distance / Speed
Time taken to go 70 miles downstream = 70 / (11 + x) hours

According to the problem, these times are equal. So, we can set up the equation:

40 / (11 - x) = 70 / (11 + x)

To solve this equation, we can cross-multiply:

40 * (11 + x) = 70 * (11 - x)

440 + 40x = 770 - 70x

Now, let's solve for x:

110x = 330

x = 3

Therefore, the speed of the current is 3 mph.

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Answer:30 x 96 feet = 10 x 32 yards

Step-by-step explanation:Convert 30 x 96 feet to yards

To convert length x width dimensions from feet to yards we should multiply each amount by the conversion factor. One foot equals 0.333333 yards, in order to convert 30 x 96 feet to yards we have to multiply each amount of feet by 0.333333 to obtain the length and width in yards. In this case to convert 30 x 96 feet into yards we should multiply the length which is 30 by 0.333333 and the width which is 96 by 0.333333. The result is the following:

30 x 96 feet = 10 x 32 yards

Definition of foot

A foot (symbol: ft) is a unit of length. It is equal to 0.3048 m, and used in the imperial system of units and United States customary units. The unit of foot derived from the human foot. It is subdivided into 12 inches.

Definition of yard

A yard (symbol: yd) is a basic unit of length which is commonly used in United States customary units, Imperial units and the former English units. It is equal to 3 feet or 36 inches, defined as 91.44 centimeters.

Meters to yards formula and conversion factor

To calculate a foot value to the corresponding value in yards, just multiply the quantity in feet by 0.333333 (the conversion factor).

Meters to yards formulae

yards = feet * 0.333333

The factor 0.333333 is the result from the division 1 / 3 (yard definition). Therefore, another way would be:

yards = feet / 3

Using our feet to yards converter you can get answers to questions like:

- How many yards are in 30 x 96 feet?

- 30 x 96 feet is equal to how many yards?

- How to convert 30 x 96 feet to yards?

- What is 30 x 96 feet in yards?

- How many is 30 x 96 feet in yards?

Hope this helped :)

Answer:

The orthocenter is the intersection point of the altitudes of a triangle.

Step-by-step explanation:

There are three altitudes in any triangle, one for each side.

To evaluate the integral by reversing the order of integration, we first need to draw the region of integration. From the given limits of integration, we can see that the region is a rectangle with vertices at (0,4), (0,12), (11,4), and (11,12).

Now, we can reverse the order of integration by integrating with respect to y first, and then x. The new limits of integration will be y = 4 to y = 12 and x = 0 to x = 11e^(2y/3).

So, the new integral will be:

∫(0 to 11) ∫(4 to 12) 3y e^(2x/3) dy dx

We can evaluate this integral using integration by parts. Integrating with respect to y gives us:

∫(0 to 11) [3y^2/2 e^(2x/3)] from y = 4 to y = 12

Simplifying this expression gives us:

∫(0 to 11) [36e^(2x/3) - 6e^(8x/3)]/2 dx

Now, integrating with respect to x gives us:

[27e^(2x/3) - 9e^(8x/3)] from x = 0 to x = 11

Substituting these values and simplifying gives us the final answer:

(27e^22/3 - 9e^88/3) - (27 - 9) = 27e^22/3 - 9e^88/3 - 18

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To maintain the CG and balance in the system, the third box weighing 20 pounds should be placed 4 feet forward of the CG.  The CG is the point where the weight of the object is evenly distributed, and it is crucial for maintaining balance.

First, let's calculate the total weight of the system. We have two boxes weighing 15 pounds and 10 pounds, and a third box weighing 20 pounds. The total weight is 15 + 10 + 20 = 45 pounds.
Next, we need to find the moment caused by the two boxes already placed. The moment is the product of the weight and its distance from the CG.
For the 15-pound box, the moment is 15 pounds * 4 feet = 60 pound-feet.
For the 10-pound box, the moment is 10 pounds * 2 feet = 20 pound-feet.

To keep the CG unchanged, the total moment of the system must be zero. This means that the moment caused by the third box must balance out the moments of the other two boxes.

Let's denote the distance from the CG to the third box as 'x' feet. The moment caused by the third box is 20 pounds * x feet.
So, to maintain balance, the equation becomes:
60 pound-feet + 20 pound-feet = 20 pounds * x feet.
Simplifying this equation, we get:
80 pound-feet = 20x feet.
To solve for 'x', we divide both sides by 20:
4 = x.
Therefore, the third box should be placed 4 feet forward of the CG to maintain balance.

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Answer:

x=1.875

Step 1: you need to multiply the brackets.

-2(5x+8) = -10x-16

-10x-16=14+6x

Step 2: you want to put the x on one side, so take away 6 x from both sides

-10x-6x=-16x, 6x-6x=0

-16x-16=14

Step 3: add 16 to both sides so the whole numbers are on one side

-16+16=0, 14+16=30

-16x=30

Step 4: finally, divide the whole by the number of x, so 16

x=1.875

If you need to round it to a significant figure:

1 Sf: x=1.9

2Sf: x=1.78

3 Sf: the final answer only has three figures after the decimal.

Step-by-step explanation:

Hope this helps, have a wonderful day!

Answer:

20/27

Step-by-step explanation:

Answer:

Step-by-step explanation:

angle A =angle B (because they are alternate interior angles)

5x-12=2x+24

5x-2x=24+12

3x=36

x=36/3

x=12

angle A=5x-12

5*12-12

60-12

48

angle B=2x+24

2*12+24

24+24

48

Answer: 103.62

Step-by-step explanation: 3.14 times 33 is equal to 103.62

The correct option for calculating the degrees of freedom for the between-group estimate in ANOVA is: c. k - 1

Here's a step-by-step explanation:

1. ANOVA, or Analysis of Variance, is a statistical method used to compare the means of multiple groups to determine if there are significant differences between them. In this context, "k" represents the number of groups being compared, and "N" represents the total number of observations.

2. Degrees of freedom (df) are used in statistical tests to account for variability in the data. They are essentially the number of values that can vary independently in the calculation of a statistic.

3. In ANOVA, there are two types of degrees of freedom: between-group (df_between) and within-group (df_within).

4. To calculate the between-group degrees of freedom (df_between), we use the formula: df_between = k - 1. This is because there are k groups being compared, and each group contributes one degree of freedom, minus one since we are comparing the groups against each other.

5. The within-group degrees of freedom (df_within) would be calculated using the formula: df_within = N - k, which accounts for the total number of observations minus the number of groups.

In summary, to compute the degrees of freedom for the between-group estimate in ANOVA, you would use the formula df_between = k - 1.

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the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

We know that odd consecutive numbers means the difference between the numbers will be 2

So, let the first odd number be x

Second number will be = x + 2

Third number will be = x + 2 + 2 = x + 4

Now, we are given that, the sum of these odd integers is 153

So, we get the equation as:

x + x + 2 + x + 4 = 153

3 x + 6 = 153

3 x = 153 - 6

3 x = 147

x = 147 / 3

x = 49

Largest integer = x + 4 = 49 + 4 = 53

Therefore, we get that, the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

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The interval of convergence for the power series is the set of all values of x for which the series converges. The table mentioned in your question likely shows the values of x for which the series converges or diverges.

The interval of convergence for a power series is determined by finding the values of x for which the series converges absolutely. The convergence or divergence of a power series can be determined using various tests, such as the ratio test or the root test.
Once the interval of convergence is found, it can be summarized as a range of values for x. For example, if the interval of convergence is (-3, 5], then the series converges for all values of x between -3 and 5, inclusive.

Hence, the interval of convergence for a power series is the set of all values of x for which the series converges, and it can be determined by finding the values of x for which the series converges absolutely.

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Answer:

\(210547\)

Hope this helps. :)

Answer:

210547

Step-by-step explanation:

Multiply 526, 367.50 by 40 percent than the answer you get from that subtract from 526,367.50 then you get 210547.

Hope this Helps!

:D

Answer:

\(m^{12}\)

Step-by-step explanation:

Answer:

6x^2+3x+1

Step-by-step explanation:

Simplify by combining like terms

I think that the answer would be 6x^2+3x+1.

Answer:

Step-by-step explanation:

To find the difference in temperature between the day's high and low, we need to subtract the low temperature from the high temperature.

The high temperature is 18 degrees, and the low temperature is -6 degrees.

So, the difference in temperature between the day's high and low is:

18 degrees - (-6 degrees)

= 18 degrees + 6 degrees

= 24 degrees

Therefore, the difference in temperature between the day's high and low is 24 degrees.

Answer:

Rafael will read 240 pages.

Step-by-step explanation:

Let's start by setting up the unknowns:

x = # of Rafael's pages

x/2 = # of Philippe's pages

(3/4)x = # of Denise's pages

Set these all equal to 540:

(x) + (x / 2) + (3/4(x)) = 540

Let's multiply both sides by 4 to make this easier.

4x + 2x + 3x = 2160

9x = 2160

x = 240

x was the # of Rafael's pages, so Rafael will read 240 pages. This means that Philippe will read 120 pages (one-half of Rafael), and Denise will read 180 pages (three-fourths of Rafael). Adding these all up will get you 540 pages, so it checks out.

Hope this helps!

To find the circumference we have to calculate

where r=6

therefore we have that the answer is