What is 5/3 times 5

Answer:

6 yards long

Step-by-step explanation:

1/3 yards wide = 2 yards long

Let x = length of the other rug

1 yard wide = x yards long

1/3 : 2 = 1 : x

1/3 ÷ 2 = 1 ÷ x

1/3 × 1/2 = 1 / x

1/6 = 1/ x

Cross product

1*x = 6*1

x= 6 yards

Therefore, the length of the new rug with 1 yard wide is 6 yards long

The first thing to do is to find the ratio of wide to long of the two rugs by representing the long of the second rug with x

It is the simplest method to solve the question

Answer:  C = - 2

Step-by-step explanation: Subtract 3c from 4c.

The outward flux of the vector field F across the boundary of the region D, which is the cube bounded by the planes x = ±1, y = ±1, and ±1, can be found using the divergence theorem.

The outward flux is the integral of the divergence of F over the volume enclosed by the boundary surface.The first step is to calculate the divergence of F. The divergence of a vector field F = P i + Q j + R k is given by div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z. In this case, div(F) = ∂/∂x(5y - 4x) + ∂/∂y(-4z - 5y) + ∂/∂z(-3y - 2x). Simplifying these partial derivatives, we have div(F) = -4 - 2 - 3 = -9.

Applying the divergence theorem, we can relate the flux of F across the boundary surface to the triple integral of the divergence of F over the volume enclosed by the surface. Since D is a cube with sides of length 2, the volume enclosed by the surface is 2^3 = 8.

Therefore, the outward flux of F across the boundary of D is given by ∬S F · dS = ∭V div(F) dV = -9 * 8 = -72. The negative sign indicates that the flux is inward.

In summary, the outward flux of the vector field F across the boundary of the cube D, as described by the given vector components, is -72. This means that the vector field is predominantly flowing inward through the boundary of the cube.

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c) The range of the tangent function is all real numbers. This can be represented as (-∞, ∞) in interval notation

a. The domain of the cosine function (cos) is all real numbers. This can be represented as (-∞, ∞) in interval notation.

The range of the cosine function is [-1, 1]. This can be represented as [-1, 1] in interval notation.

b. The domain of the sine function (sin) is all real numbers. This can be represented as (-∞, ∞) in interval notation.

The range of the sine function is [-1, 1]. This can be represented as [-1, 1] in interval notation.

c. The domain of the tangent function (tan) is all real numbers except the values where the function is undefined, which occur when the input angle is equal to (2k + 1)π/2, where k is an integer. This can be represented as (-∞, (2k + 1)π/2) ∪ ((2k + 1)π/2, ∞) in interval notation.

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Answer:

12

Step-by-step explanation:

Multiply both sides by 4

Answer:

X=12

Hope it helps.

The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.

The sequence we are provided is 2, 4, 7, 10, …

Here, \( a_{1}\) = 2, \( a_{2}\) = 4 and \( a_{3}\) = 7.

A sequence is considered as an Arithmetic sequence if their difference is equal. Represented as -

\( a_{2}\) - \( a_{1}\) = \( a_{3}\) - \( a_{2}\) = \( a_{4}\) - \( a_{3}\) and so on

Now, in the given sequence

⇒\( a_{2}\) - \( a_{1}\) = 4 - 2

\( a_{2}\) - \( a_{1}\) = 2

⇒ \( a_{3}\) - \( a_{2}\) = 7 - 4

\( a_{3}\) - \( a_{2}\) = 3

⇒ \( a_{4}\) - \( a_{3}\) = 10 - 7

\( a_{4}\) - \( a_{3}\) = 3

Since, the difference between the given sequence of terms are not same.

∴ The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.

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Step-by-step explanation:

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Answer:

1

Step-by-step explanation:

So first we do (x^5)^2 which we know is just x^10 because of exponents of powers I believe it's called, basically you just multiply the two powers.

Then you do the bottom half which is x^3 * x^7 and that equals x^10 because of the product of exponent rule,

Then we do x^10/x^10 which = 1 because the same number over the same number is always 1.

Let me know if you have any questions

Answer:

Solving the expression: \(\frac{(x^5)^2}{(x^7)(x^3)}\) the answer is 1

Step-by-step explanation:

We need to solve the expression: \(\frac{(x^5)^2}{(x^7)(x^3)}\)

We know that exponent rule: \((a^m)^n=a^{m*n}\)

Applying this rule in numerator

\(\frac{(x^5)^2}{(x^7)(x^3)}\\=\frac{(x^{5*2})}{(x^7)(x^3)}\\=\frac{(x^{10})}{(x^7)(x^3)}\)

We know the exponent rule: \((a^m).(a^n)=a^{m+n}\)

\(=\frac{(x^{10})}{x^{7+3}}\\=\frac{(x^{10})}{x^{10}}\)

Now, using the exponent rule: \(\frac{a^m}{a^n}=a^{m-n}\)

\(=x^{10-10}\\=x^0\)

We know that \(a^0=1\)

So, \(x^0=1\)

Solving the expression: \(\frac{(x^5)^2}{(x^7)(x^3)}\) the answer is 1

Answer:

106 in²

Step-by-step explanation:

Given that :

Davindra made a paper box that is 8 in. Long, 5 in. Wide, and 1 in. High.

Using the relation :

SA=2lw+2lh+2hw

Surface area :

2(lw + lh + hw)

l = 8 ; w = 5 ; h = 1

Surface area :

2(8*5 + 8*1 + 1*5)

Surface area :

2(40 + 8 + 5)

= 2(53)

= 106 in²

The x-coordinates of the left edges of the rectangles are 1,5/4,6/4,7/4.

The area of this region with a Riemann Sum is 0.7595.

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

Given function is f(x) = 1/x on the interval [1,2] is shown.

The four rectangles of width 1/4 are present.

From the figure we can see that the x coordinate of the left edges of the rectangle are:

1,5/4,6/4,7/4

Now we plug these values in the function to find the height of rectangles.

For x=1 ,f(x) = 1

For x=5/4 ,f(x) = 4/5

For x=6/4 ,f(x) = 4/6

For x=7/4 ,f(x) = 4/7

Now, Area = length*width, and width of each rectangle is 1/4

Area of rectangle 1 = 1*1/4 = 1/4

Area of rectangle 2 = 4/5*1/4 = 1/5

Area of rectangle 3 = 4/6*1/4 = 1/6

Area of rectangle 4 = 4/7*1/4 = 1/7

Total Area is = 1/4+1/5+1/6+1/7  = 0.7595

This is an overestimation of ln(2).

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Answer:

Step-by-step explanation:

Only a straight line can be formed at the intersection of a plane with another plane. The faces of a cube are planes, so a 2-dimensional (planar) cross section of a cube cannot be a curve. It cannot be an ellipse or circle.

The intersection of a plane with a cube can be a polygon with 3, 4, 5, or 6 sides. That is, the 2-D cross section of a cube can be ...

  triangle, rectangle, square, pentagon, hexagon

__

The attachment shows some possibilities.

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

Incorrect Answer Below

Step-by-step explanation:

Problem: We have a total of 28 candies that need to be divided evenly between 4 students.

(Incorrect) Solution: In order to solve this problem we can seperate the total number of candies into single digits and then divide each digit by 4 like so...

2 / 4 = 0.5

8 / 4 = 2

Now that we have the answer of both of these divisions we can simply add these values together to get the number of candies each student will get

0.5 + 2 = 2.5 candies

Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the height of the antenna h and the length of the wire connecting the top of the antenna to the ground d.From the problem statement, we know that d = 7 feet and the angle of elevation θ is 75 degrees. The angle of elevation is the angle between the horizontal and the line of sight to the top of the antenna.We can use the tangent function to find h:tan(θ) = opposite / adjacentIn this case, the opposite side is the height of the antenna h, and the adjacent side is the length of the wire d + 0. This is because the wire touches the ground at a point 7 feet away from the base of the antenna, so the total length of the wire is d + 0.Substituting the values we have:tan(75 degrees) = h / (7 feet + 0)Simplifying:h = (7 feet) × tan(75 degrees)Using a calculator:h ≈ 24.16 feetTherefore, the height of the antenna is approximately 24.16 feet.

Using permutation and combination concept, there are 358,800 different passwords that are possible and the number of more passwords available through this combination is 1054920

(a) To find the number of different passwords that are possible, we can use the permutation formula. Since there are 26 letters in the alphabet and we are choosing 4 letters without repetition, we can write:

Number of possible passwords = P(26, 4)

= 26 x 25 x 24 x 23

= 358,800

Therefore, there are 358,800 different passwords that are possible.

(b) If the numbers 1 through 10 are also available to be chosen only once in addition to the alphabet, we can use the same permutation formula to find the number of different passwords that are possible. Since there are now 36 characters to choose from (26 letters + 10 numbers), and we are choosing 4 characters without repetition, we can write:

Number of possible passwords = P(36, 4)

P(36, 4) - P(26, 4) = 1054920

The number of more passwords available through this combination is 1054920

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20/2 × 7 = ?

= 10 × 7

= 70

\( \: \)

6/2 + 6/1 = ?

= 3 + 6

= 9

\(\huge\mathfrak\blue{Answer}\)

Answer:

0.80

Step-by-step explanation:

I did the math 5 times

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

Answer:

Step-by-step explanation:

a. 110°

b. 70°

c. 110°

d. 70°

e. 110°

f. 70°

g. 110°

Answer: 125/x^18

Step-by-step explanation: this should be the answer

Answer:

\((5 {x}^{ - 6} )^{3} \\ \\ (125 {x}^{ - 18}) \\ \\ = \frac{125}{ {x}^{18} } \)

I hope I helped you^_^

Answer:

y=-.5x+4

Step-by-step explanation:

a Probability that Upper X 0.0013 ,

b. Upper X less than 80 is 0.0228

c  Upper X less than 95 or Upper X greater than 125 is 0.6853.

d 99% of the values are between 76.7 and 123.3 (symmetrically distributed around the mean).

Given a normal distribution with mu equals 100 and sigma equals 10, we can use the cumulative standardized normal distribution table to complete the following parts:

a. What is the probability that Upper X greater than 70?
Using the cumulative standardized normal distribution table, we find the z-score for 70 as (70-100)/10 = -3. We then look up the probability for a z-score of -3, which is 0.0013. Therefore, the probability that Upper X greater than 70 is 0.0013. (Round to four decimal places as needed.)

b. What is the probability that Upper X less than 80?
Using the cumulative standardized normal distribution table, we find the z-score for 80 as (80-100)/10 = -2. We then look up the probability for a z-score of -2, which is 0.0228. Therefore, the probability that Upper X less than 80 is 0.0228. (Round to four decimal places as needed.)

c. What is the probability that Upper X less than 95 or Upper X greater than 125?
Using the cumulative standardized normal distribution table, we find the z-score for 95 as (95-100)/10 = -0.5 and the z-score for 125 as (125-100)/10 = 2.5. We then find the probabilities for each of these z-scores, which are 0.3085 and 0.0062, respectively. To find the probability that Upper X is either less than 95 or greater than 125, we add these two probabilities and subtract from 1 (to account for the overlap): 1 - (0.3085 + 0.0062) = 0.6853. Therefore, the probability that Upper X less than 95 or Upper X greater than 125 is 0.6853. (Round to four decimal places as needed.)

d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?
To find the z-score corresponding to the 99th percentile, we look up the probability of 0.99 in the cumulative standardized normal distribution table, which is 2.33 (rounded to two decimal places). Using this z-score, we can find the corresponding X-values using the formula z = (X - mu)/sigma. Solving for X, we get: X = z*sigma + mu = (2.33)(10) + 100 = 123.3 and X = (-2.33)(10) + 100 = 76.7. Therefore, 99% of the values are between 76.7 and 123.3 (symmetrically distributed around the mean).

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The boiling point of water can be affected by several factors, including pressure. The boiling point of water decreases with decreasing pressure. In this case, the pressure is given as 0.04 bar. At this pressure, water boils at a lower temperature than it would at atmospheric pressure, which is 1 bar.

The correct answer to this question is b. 35.6 C. This is because at a pressure of 0.04 bar, water boils at 35.6 C, which is lower than the standard boiling point of water at atmospheric pressure, which is 100 C.The boiling point of water decreases by about 1 C for every 28.5 millibars (0.0285 bar) of pressure reduction.

So, at a pressure of 0.04 bar, the boiling point of water is about 64 C lower than it would be at atmospheric pressure. Therefore, water boils at 35.6 C at a pressure of 0.04 bar.

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The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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To prove the identity cos(x + y) + cos(x - y) = 2 cos(x) cos(y), we can use the sum and difference of angles formulas for cosine.

We start by applying the sum of angles formula for cosine, which states that cos(a + b) = cos(a) cos(b) - sin(a) sin(b). Applying this formula to the first term of the equation, we have cos(x + y) = cos(x) cos(y) - sin(x) sin(y).

Next, we apply the difference of angles formula for cosine, which states that cos(a - b) = cos(a) cos(b) + sin(a) sin(b). Applying this formula to the second term of the equation, we have cos(x - y) = cos(x) cos(y) + sin(x) sin(y).

Now, substituting these results back into the original equation, we have cos(x + y) + cos(x - y) = (cos(x) cos(y) - sin(x) sin(y)) + (cos(x) cos(y) + sin(x) sin(y)).

Simplifying this expression, we get 2 cos(x) cos(y), which proves the given identity.

Therefore, we have successfully proved that cos(x + y) + cos(x - y) = 2 cos(x) cos(y) using the sum and difference of angles formulas for cosine.

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True, The One Way Repeated Measures ANOVA is used when you have a quantitative DV and an IV with three or more levels that is within subjects in nature.

The statement is true and explained as follows:

The One Way Repeated Measures ANOVA is a statistical technique that is used to analyze data from experiments where the same participants are exposed to multiple levels of an independent variable (IV). This type of experimental design is known as a within-subjects design, as opposed to a between-subjects design, where different participants are used for each level of the IV.

One of the main advantages of using a within-subjects design is that it allows for more efficient use of participants. By exposing each participant to all levels of the IV, the variability between participants is reduced, which in turn increases the power of the statistical analysis.

The One Way Repeated Measures ANOVA is specifically used when the dependent variable (DV) is quantitative, meaning that it can be measured using numerical values. Additionally, the IV must have three or more levels, meaning that there are at least three different conditions that participants are exposed to.

The basic idea behind the One Way Repeated Measures ANOVA is to compare the mean scores of the DV across the different levels of the IV while taking into account the fact that the same participants are being used for each level. This is done by calculating the within-subjects variability, which is the variability in the scores of the DV that is due to individual differences between participants. The within-subjects variability is then compared to the between-subjects variability, which is the variability in the scores of the DV that is due to the different levels of the IV.

The statistical output from the One Way Repeated Measures ANOVA includes an F-test, which compares the within-subjects variability to the between-subjects variability. If the F-test is statistically significant, this indicates that there is a significant difference between at least two of the levels of the IV.

In conclusion, the One Way Repeated Measures ANOVA is a useful statistical technique for analyzing data from within-subjects experiments with a quantitative DV and an IV with three or more levels. By taking into account the fact that the same participants are used for each level, the One Way Repeated Measures ANOVA can provide a more efficient and powerful analysis of experimental data.

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