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This test batch can be chosen is 455 ways. (Option A).

The problem is asking for the number of ways to choose 3 batteries out of a box of 15.

This is a combination problem and the number of ways to choose k items out of a set of n items, without regard to the order of selection, is given by the binomial coefficient:

C(n,k) = n!/(k!(n-k)!)

where ! denotes factorial.

So in this case, we have:

C(15,3) = 15!/(3!(15-3)!) = 151413/(321) = 455

So, the answer is 455.

Therefore, This test batch can be chosen is 455 ways. (Option A).

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Answer:161.56

Step-by-step explanation:

8 x5=40

8 x 7.07=56.56

1/2 x 5 x 5 x 2= 25

8 x 5=40

Add that all together

The dimensions of the paint, obtained by factoring the polynomial function for the area of the tray, 42·x + 135·x + 108 are as follows;

(a) The width of the tray = 6·x + 9

(b) Area of the square paint compartment is 9 in²

(c) The width of the edges is 12 inches

The factors of a polynomial are other polynomials of lesser degree, that when multiplied together, produces the polynomial which is factored.

The area of the paint tray = 42·x² + 135·x + 108 in²

The dimensions of the square paint compartment are the same

Space along the edge of the tray = 2 × space between the squares

(a) The length of the tray obtained from the diagram in the question = 7·x + 12 inches

Using an online tool, we get;

42·x² + 135·x + 108 = 3·(2·x + 3)·(7·x + 12)

The area of a rectangle = Length × Width

Therefore, the width of the tray = The area ÷ The length

Width = (42·x² + 135·x + 108)/(7·x + 12) = 3·(2·x + 3)

(b) Let s represent the side length of each square paint compartment, we get;

Width of four compartments + 3 spaces between compartments = (7·x + 12) - 2 × 2·x

Width of four compartments + 3 spaces between compartments = 4·s + 3·x

4·s + 3·x = (7·x + 12) - 2 × 2·x = 3·x + 12

4·s = 3·x + 12 - 3·x = 12

s = 12/4 = 3

s = 3

The side length of each square = 3 inches

The area of each square paint compartment = s²

s² = 3² = 9

(c) Where the width = 45 inches, we get;

3·(2·x + 3) = 45

2·x + 3 = 45/3 = 15

2·x + 3 = 15

2·x = 15 - 3 = 12

x = 12/2 = 6

x = 6

The width of the edges of the tray = 2·x

2·x = 2 × 6 = 12

The width of the edges of the tray = 12 inches

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Answer:

1 mile

Step-by-step explanation:

1m =160934 cm

what is the questions below

The null hypothesis rejected represents there is evidence the proportion of members engaged in professional networking within last month is different from established percentage.

Using a hypothesis test we have,

Let p be the proportion of employees in the company who engage in professional networking within the last month.

The null hypothesis represents,

The proportion of employees who engage in professional networking within the last month is equal to the established percentage of 55%.

H0: p = 0.55

The alternative hypothesis represents ,

The proportion of employees who engage in professional networking within the last month is different from 55%.

Ha: p ≠ 0.55

Use a two-tailed z-test for the proportion to test this hypothesis, with a significance level of 0.05.

The test statistic is,

z = (p₁ - p) / √(p(1-p)/n)

p₁ is the sample proportion

p is the hypothesized proportion

And n is the sample size.

Here,

p = 0.55

n = 980

p₁ = 500/980

   = 0.51.

Substituting these values, we get,

z = (0.51 - 0.55) / √(0.55(1-0.55)/980)

  = -1.96

The critical values for a two-tailed test with a significance level of 0.05 are ±1.96.

Since the test statistic (-1.96) falls within the critical region.

Reject the null hypothesis

Therefore, there is evidence that the proportion of employees who engage in professional networking within the last month is different from the established percentage of 55%.

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The probability that it is a false negative (test indicates the person does not have the disease when in fact they do) is 0.0348.

This probability indicates that the test's accuracy is 0. 0348; as the likelihood of this inaccuracy is minimal, the test is quite accurate.

The likelihood that a randomly chosen result will be a false negative, meaning that the test will show that the person does not have the condition while in fact they do:

\(P(NP|D) = \frac{4}{115} \\\\P(NP|D) = 0.0348\)

We may infer that the occurrence is unlikely to occur and that the test is reasonably accurate because the probability is less than 0.0500.

Probability is simply the possibility that something will happen. When we don't know how something will turn out, we might talk about the possibility of one result or the likelihood of several. The study of occurrences that fit into a probability distribution is known as statistics.

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Answer:

...............................................................................................5x4

Choosing different initial conditions,  y(0) = c and y'(0) = d, the first three terms of the power series solution are: y2(x) = c + dx + (-2c - 3d/2)\(x^{2}\) + ...

To find the solutions of the differential equation y'' - 2y' - 4 = 0 using power series, we assume that the solution can be expressed as a power series of the form y = ∑(n=0 to ∞) anxn. Substituting this series into the differential equation, we can obtain a recurrence relation for the coefficients an.

For the first solution, let's assume an initial condition where y(0) = a and y'(0) = b. Solving the recurrence relation, we can determine the coefficients of the power series. The first three terms of the solution would be y1(x) = a + bx + (-2a - 3b/2)\(x^{2}\)

For the second solution, we choose a different initial condition, for example, y(0) = c and y'(0) = d. Following the same process as above, we obtain a different set of coefficients, and the first three terms of the solution would be y2(x) = c + dx + (-2c - 3d/2)\(x^{2}\)

It's important to note that these power series solutions may converge only within a certain interval of x-values, determined by the radius of convergence. However, providing the first three terms gives an approximation of the solutions near x = 0.

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Answer:

If the points (-2,-1), (-1,0), (2,3) and (-3,-2) are joined to form a straight line, they would intersect the y-axis at (0,1)

Step-by-step explanation:

Work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number.

Then: divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

False. Calculating standard error is indeed important in statistics, as it serves a different purpose than the regular standard deviation of a single data set.

While standard deviation measures the variability or dispersion within a data set, standard error is used to measure the accuracy of a sample mean as an estimate of the true population mean.
1. Standard deviation measures the dispersion or spread of data points in a single data set. It helps you understand how much the individual data points deviate from the mean (average) of that data set.
2. Standard error, on the other hand, is a measure of how accurate a sample mean is in estimating the true population mean.

It is calculated by dividing the standard deviation of the sample by the square root of the sample size (n).
Standard Error (SE) = Standard Deviation (SD) / √n
3. As the sample size increases, the standard error decreases, indicating that the sample mean becomes a more accurate estimate of the population mean.

This is because larger sample sizes tend to have a smaller sampling error.
4. In hypothesis testing and confidence interval estimation, standard error plays a crucial role.

It helps to determine the margin of error and to assess the significance of differences between sample means.
5. While standard deviation is a useful measure for understanding variability within a single data set, standard error is essential for making inferences about the population based on the sample data.
In conclusion, both standard deviation and standard error are important in statistics as they serve different purposes. Ignoring standard error would lead to inaccurate conclusions about the population mean based on sample data.

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bcx + acy + abz = abc is another form of the equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

bcx + acy + abz = abc is another form of the equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

To find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c, we can use the intercept form of the equation of a plane:

x/a + y/b + z/c = 1

This equation states that any point (x, y, z) on the plane will satisfy this equation.

To see why this is true, note that if x = a, then the left-hand side of the equation is 1, since y/b + z/c = 0 (since the numerator is 0).

Similarly, if y = b, then the left-hand side of the equation is 1, since x/a + z/c = 0.

Finally, if z = c, then the left-hand side of the equation is 1, since x/a + y/b = 0.

To simplify this equation, we can multiply both sides by the denominators a, b, and c:

hence, bcx + acy + abz = abc is another form of the equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

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Answer:

9

Step-by-step explanation:

94% of 150=141

150-141=9

false :) thats ur answer

The limit of anth/n-700 as n approaches infinity is equal to the limit of am/n-2 as n approaches infinity. This is because the sequence an is defined recursively as an = da n-1, where d = 2. Therefore, an is a geometric sequence with first term 1 and common ratio 2.

The limit of a geometric sequence is equal to the first term divided by 1 - the common ratio, so the limit of an as n approaches infinity is 1/(1-2) = -1. The limit of a sequence is the value that the sequence approaches as the number of terms tends to infinity. In this case, we are interested in the limit of anth/n-700 as n approaches infinity.

We can rewrite anth/n-700 as am/n-2, because an = da n-1. Therefore, we need to find the limit of am/n-2 as n approaches infinity.

The sequence am/n-2 is a geometric sequence with first term 1 and common ratio d = 2. The limit of a geometric sequence is equal to the first term divided by 1 - the common ratio, so the limit of am/n-2 as n approaches infinity is 1/(1-2) = -1.

Therefore, the limit of anth/n-700 as n approaches infinity is also equal to -1.

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The percent of the respondents that preferred the new hours is equal to 39%.

In Mathematics and Statistics, a frequency table can be used for the graphical representation of the frequencies or relative frequencies that are associated with a categorical variable or data set.

Based on the information provided about this survey with respect to employees and customers shown in a two-way relative frequency table, the percentage of the respondents that preferred the new hours can be calculated as follows;

Percent new hours = (0.16 + 0.23) × 100

Percent new hours = 0.39 × 100

Percent new hours = 39%.

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Answer:

4

Step-by-step explanation:

d = 8 inches

r = 8/2 = 4 inches

Answer:

4 inches.

Explanation:

If the diameter is a circle, divide the diameter by two and you will have the answer of 4. This gives you the radius.

8 / 2 = 4

Hope this helps. Have a wonderful day.

Step-by-step explanation:

I just answered this.

this turns out to show 28 = 0. and that is never true.

so, this has 0 solutions.

Answer:

x = 25

Step-by-step explanation:

hyp/short leg

Compare large triangle to small triangle

x/15 = 15/9

multiply both sides by 15

x = 15/9 * 15

x = 25

A, B, C, and D are all correct reasons why time-series plots are used.

A: Time-series plots are used to examine the shape of the distribution of the data.
B: Time-series plots are used to identify any outliers in the data.
C: Time-series plots are used to identify trends in the data over time.
D: Time-series plots are used to present the relative frequency of the data in each interval or category.

Time-series plots are a type of data visualization that is used to examine the relationship between two variables over a period of time. The reasons why time-series plots are used include:

A. Time-series plots are used to examine the shape of the distribution of the data. While this is not the primary purpose of time-series plots, they can be used to examine the distribution of the data and identify any patterns or trends that may be present.

B. Time-series plots are used to identify any outliers in the data. Outliers are values that are significantly different from the rest of the data and can have a significant impact on the overall results. Time-series plots can be used to identify these outliers and determine how they may be affecting the data.

C. Time-series plots are used to identify trends in the data over time. This is one of the main purposes of time-series plots, as they allow us to see how the data changes over time and identify any patterns or trends that may be present.

D. Time-series plots are used to present the relative frequency of the data in each interval or category. This allows us to see how often certain values occur within the data and can help us identify any patterns or relationships between the variables.

Overall, time-series plots are a valuable tool for data analysis and can be used to identify trends, patterns, and outliers in the data.

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Answer:

25

Step-by-step explanation:

Find the total by summing the heights of the bars, that is

total = 2 + 5 + 6 + 8 + 3 + 1 = 25

\(19+1,5(10m-8)=127\\\\19+15m-12=127\\\\15m+7=127 \ \ /-7\\\\15m=120 \ \ /:15\\\\\huge\boxed{m=8}\)

Answer:

\(m=8\)

Step-by-step explanation:

\(19 + 1.5(10m-8) = 127\)

Multiply both sides by 10

\(190+15(10m-8)=1270\)

Subtract 190 from both sides

\(15(10m-8)=1080\)

Divide both sides by 15

\(10m-8=72\)

Add 8 to both sides

\(10m=80\)

Simplify

\(m=8\)

The value of the integral (9x + 9y) da over the region r is approximately 14.0625.

To evaluate the given integral using a transformation, we can use the concept of a double integral over a region in the xy-plane.

First, let's define the transformation T from the uv-plane to the xy-plane, where x = 9u and y = 9v. This transformation scales the coordinates by a factor of 9.

Next, let's find the Jacobian determinant of the transformation. The Jacobian determinant of T is given by the absolute value of the determinant of the matrix of partial derivatives of x and y with respect to u and v. In this case, the matrix is:

J(T) = |[∂x/∂u  ∂x/∂v]|
           |[∂y/∂u  ∂y/∂v]|

Taking the partial derivatives, we have:

∂x/∂u = 9   and   ∂x/∂v = 0
∂y/∂u = 0   and   ∂y/∂v = 9

Therefore, the Jacobian determinant is:

J(T) = |[9  0]|
           |[0  9]|

Taking the determinant, we have:

J(T) = (9)(9) - (0)(0) = 81

Now, we can evaluate the integral by transforming it into the uv-plane. The integral becomes:

∬(9x + 9y) dA = ∬(9(9u) + 9(9v))(J(T)) dA

Since x = 9u and y = 9v, we can substitute these expressions into the integral:

∬(9(9u) + 9(9v))(J(T)) dA = ∬(81u + 81v)(81) dA

Now, we need to find the limits of integration in the uv-plane. The region r in the xy-plane corresponds to a parallelogram in the uv-plane with vertices (-1/9, 2/9), (1/9, -2/9), (3/9, 0), and (1/9, 4/9).

Using these vertices, we can determine the limits of integration for u and v:

u ranges from -1/9 to 1/9
v ranges from 2/9 to 4/9

Therefore, the integral becomes:

∬(81u + 81v)(81) dA = ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv

Now, we can evaluate this double integral:

∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv = (81)(81) ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (u + v) dudv

Evaluating the inner integral with respect to u, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + vu [v=2/9 to 4/9] dv

Simplifying further, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(2/9) dv

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (4/81)u^2 du

Combining like terms, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2 + 4/81)u^2 du

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du

Now, we can evaluate the integral:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du = (81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du

Integrating u^2 with respect to u, we get:

(81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du = (81)(81)(85/162) [u^3/3] from -1/9 to 1/9

Plugging in the limits of integration, we have:

(81)(81)(85/162) [(1/9)^3/3 - (-1/9)^3/3]

Simplifying further, we get:

(81)(81)(85/162) [(1/729)/3 - (-1/729)/3] = (81)(81)(85/162) [2/729]/3

Now, we can simplify this expression:

(81)(81)(85/162) [2/729]/3 = (81)(81)(85/162) (2/729)(1/3)

Finally, evaluating this expression, we get:

(81)(81)(85/162) (2/729)(1/3) ≈ 14.0625

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In the morning, the train went 170 miles. in the afternoon the train went 50 more miles. The Train ended up going 220 miles in total.

In the morning, the train traveled 170 miles.

In the afternoon, it traveled an additional 50 miles.

To find the total distance traveled by the train, we need to add the distance traveled in the morning and the distance traveled in the afternoon:

Total distance = Distance traveled in the morning + Distance traveled in the afternoon

Total distance = 170 miles + 50 miles

Total distance = 220 miles

So, the train ended up traveling a total of 220 miles.

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Answer:

On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?

That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Obviously.)

Step-by-step explanation:

The identified scale factor of the triangles is 71 / 37.

Scale factor is the ratio of corresponding sides on two similar figures.

The triangles are similar. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Therefore, let's identify the scale factor of the triangles.

The triangle on the right is a scale copy of the triangle on the left.

Hence,

scale factor = 71 / 37 = 71 / 37

Therefore, the scaled factor of the triangles in fraction form is 71 / 37

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The slant height of the right circular cone with height 12 inches and radius 3.5 inches is 12.5 inches (rounded to the nearest tenth).

The slant height l of a right circular cone, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (slant height in this case) is equal to the sum of the squares of the other two sides (height and radius). The formula to find the slant height l is:
l = √(h² + r²)

where h is the height of the cone and r is the radius of the cone.
Plugging in the given values, we get:
l = √(12² + 3.5²)
l = √(144 + 12.25)
l = √156.25
l = 12.5 inches (rounded to the nearest tenth)

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325%

6.5/2 is 3.25 or