Factorise completely 49xy+56x​

The area of the shaded region for the circle is derived to be equal to 73.4 square centimeters.

The shaded region is the segment area in the circle, so it is derived by subtracting the area of the segment from the area of the circle as follows:

area of the circle = 22/7 × 5 cm × 5 cm

area of the circle = 78.57 cm²

area of sector = 80/360 × 22/7 × 5 cm × 5 cm

area of sector = 17.46 cm²

area of triangle = 5 cm × sin40° × 5 cm × cos40°

area of triangle = 12.31 cm²

area of the segment = 17.46 cm² - 12.31 cm²

area of the segment = 5.15 cm²

area of the shaded region = 78.57 cm² - 5.15 cm²

area of the shaded region = 73.42 cm²

Therefore, the area of the shaded region for the circle is derived to be equal to 73.4 square centimeters.

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Answer:

Question 1: 27

Question 2: nothing wrong with the table

Question 3: Not sure which one to pick

Question 4: 15

Question 5: There is not enough data

Step-by-step explanation:

[tex]Question[/tex] #1

In the first picture we can see that if we add up all the frequencies we can conclude to: 2+15+8+2

= 27.

Thus the answer to question 1 is, 27

[tex]Question[/tex] #2

By looking at the FIRST picture what I can conclude is that there should be nothing wrong with the table. ( Not 100% sure )

Thus the answer to question 2 is, nothing wrong with the table

[tex]Question[/tex] #3

For this one I am not sure.

[tex]Question[/tex] #4

Well by looking at the SECOND picture I can conclude by adding:

1+8+4+2 = 15

Thus the answer to question 4 is, 15

[tex]Question[/tex] #5

Well looking at it judging by the picture given what I can conclude is that there is not enough data for the frequency.

Thus the answer to question 5 is, there is not enough data

Answer:

#1 A- 42

#2 D- Should be a row for 58

#3 A- Asking people leaving the library if they like to read

#4 C- 13

#5- Nothing wrong with the table

a) The slope of the graph from ( 0 , 1 ) and ( 2 , 4 ) = 3/2

b) The slope of the graph from ( -2 , 1/4 ) and ( -1 , 1/2 ) = 1/4

c) No , the slope is not a constant

d) No , the graph is not linear

Given data ,

Let the exponential equation be represented as A

Now , the slope of the graph from ( 0 , 1 ) and ( 2 , 4 ) is given by

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 4 - 1 ) / ( 2 - 0 )

m = 3/2

And , slope of the graph from ( -2 , 1/4 ) and ( -1 , 1/2 ) is given by

m = ( 1/2 - 1/4 ) / ( -1 - ( -2 ) )

m = ( 1/4 )

And , the slopes are not same for the line , so it is not constant and line is not a linear equation

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The four basic logic gates are AND, OR, NOT, and XOR.

1. AND Gate: This gate takes two or more inputs and produces an output of 1 (true) only if all the inputs are 1 (true).
2. OR Gate: This gate takes two or more inputs and produces an output of 1 (true) if at least one of the inputs is 1 (true).
3. NOT Gate (Inverter): This gate has only one input and inverts it, producing an output of 1 (true) if the input is 0 (false) and vice versa.
4. XOR Gate (Exclusive OR): This gate takes two inputs and produces an output of 1 (true) if either, but not both, of the inputs are 1 (true).

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The slope of the line represented by the graph include the following: C. m = 3.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (9 - (-3))/(2 - 0)

Slope (m) = (9 + 3)/(2)

Slope (m) = 12/4

Slope (m) = 3.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 3.

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Note tha the function that is graphed is f(x) = 1/(x+3) + 2. See same attached.

The function f(x) = 1/(x+3) + 2 is a rational function with a vertical asymptote at x = -3. The graph of the function is a hyperbola that is shifted 2 units up from the standard hyperbola.

As x approaches positive or negative infinity, the function approaches the horizontal line y = 2.

Thus, it is correct to state that it is the function that is graphed.

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Since DL is a perpendicular bisector of chord GA, the diameter is equal to 52 feet.

In Mathematics and Geometry, a perpendicular bisector is a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Generally speaking, the product of the segment lengths for each chord is a constant. Therefore, we can determine this constant as a product of the segment lengths with respect to the bisected chord as follows:

24 × 24 = 576 ft²

For the missing segment length of the diameter's chord (DO), we have:

DO × 36 = 576 ft²

DO = 576/36

DO = 16 ft.

Therefore, the total length of the diameter is given by;

DL = DO + OL

DL = 16 + 36

DL = 52 ft.

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Answer:

x = -2

Step-by-step explanation:

5x + 2x = -8 - 6

7x = -14

x = -2

The yield on a corporate bond is A = 9.14 %

Given data ,

Face value of the bond (FV) = $1000

Purchase price of the bond = $850

Fixed interest rate = 8%

The annual interest payment (I) can be calculated as a percentage of the face value:

I = (Fixed interest rate / 100) * FV

Substituting the given values:

I = (8 / 100) x 1000 = $80

The yield (Y) can be calculated as:

Y = (Annual interest payment / Purchase price) * 100

Substituting the calculated values:

Y = (80 / 850) x 100 = 9.41%

Hence , the yield on the corporate bond is 9.41%

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Yes, you can be certain that there are at least two guests who had the same number of handshakes. This is due to the Pigeonhole Principle.

As the party organizer, you shake hands with all 80 guests, which means you have 80 handshakes. The guests can have a minimum of 0 handshakes (if they don't shake hands with anyone except you) and a maximum of 79 handshakes (if they shake hands with everyone except themselves). There are 80 guests (excluding yourself), so there are 80 "pigeonholes" for the number of handshakes. The range of possible handshakes among the guests is from 0 to 79, which creates 80 possible outcomes or "pigeons."

According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons. In this case, there are 80 pigeonholes (guests) and 80 pigeons (possible handshakes). Therefore, at least two guests must have had the same number of handshakes.

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In a simple undirected graph with 8 vertices and 27 edges, the maximum degree for a vertex is 7, since a vertex can connect to all other vertices. To determine the number of vertices that can have degree 7, we will consider the properties of simple graphs and the relationship between vertices, edges, and degrees.

In a simple graph, there are no self-loops or multiple edges between the same pair of vertices. Therefore, the maximum number of edges in a simple graph with n vertices can be calculated using the formula:

[tex]Max edges = n(n-1)/2\\[/tex]

For our graph with 8 vertices, the maximum number of edges is:

Max edges = 8(8-1)/2 = 8(7)/2 = 28

Since our graph has 27 edges, it is almost a complete graph (which would have 28 edges). To figure out how many vertices can have a degree of 7, we can examine the degrees of other vertices.

If we have one vertex with degree 7, the remaining 7 vertices will be fully connected to each other, forming a complete subgraph with 7 vertices. The number of edges in this subgraph is:

Edges = 7(7-1)/2 = 7(6)/2 = 21

The total number of edges in the graph, including the vertex with degree 7, is 21 + 7 = 28. Since our graph has 27 edges, we need to remove one edge from this configuration. We can remove one edge between two of the vertices that are not the vertex with degree 7. By doing this, we maintain the degree 7 for the first vertex while reducing the degrees of two other vertices to 6.

Therefore, in a simple undirected graph with 8 vertices and 27 edges, 1 vertex can have a degree of 7.

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The answer is d. 75. The sample size needed is approximately 189, which corresponds to option c.

To estimate the required sample size, we can use the formula:

n = (Z^2 * σ^2) / E^2

where:
Z = the Z-score associated with the desired level of confidence (0.95 = 1.96)
σ^2 = the population variance (484)
E = the desired margin of error (5)

Substituting these values, we get:

n = (1.96^2 * 484) / 5^2
n = 74.4096

Rounding up to the nearest integer, the required sample size is 75.

Therefore, the answer is d. 75.

To find the required sample size for estimating the population mean with a desired margin of error of 5 or less and a 0.95 probability, you can use the following formula:

n = (Z^2 * σ^2) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (in this case, 0.95), σ^2 is the population variance, and E is the margin of error.

Given the population variance (σ^2) of 484 and a desired margin of error (E) of 5, we can use the Z-score for a 95% confidence level, which is 1.96. Plug these values into the formula:

n = (1.96^2 * 484) / 5^2

n ≈ 189

Therefore, the sample size needed is approximately 189, which corresponds to option c.

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The probability that a randomly selected child will be a six-year-old is given by P ( A ) = 1/2

Given data ,

Let the probability that a randomly selected child will be a six-year-old be represented as P ( A )

Now , the total number of children in the day care = 8

The number of 6 year olds in the day care = 4

So , P ( A ) = number of 6 year olds in the day care / total number of children in the day care

On simplifying , we get

P ( A ) = 4/8

P ( A ) = 1/2

P ( A ) = 0.5

Hence , the probability is 1/2

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The actual amount of money that Mitchell bought the computer after the discount deductions would be = $80.36

The original price of the computer = $98

The percentage discount = 18% of cost price.

That is ; 18/100 × 98/1

= 1764/100 = $17.64

Therefore the discounted price of the computer = original price - discount price = 98-17.64 = $80.36

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Answer: The slope-intercept form of the equation of a line is y = mx + b, where "m" is the slope and "b" is the y-intercept.

We know that the slope of the line is 2/7. We can also find the y-intercept by plugging in the coordinates of the given point (7,0) and solving for "b".

0 = (2/7) * 7 + b

0 = 2 + b

b = -2

So the equation of the line in slope-intercept form is:

y = (2/7)x - 2

Step-by-step explanation:

Answer:   [tex]y=\frac{2}{7}x-7[/tex]

Step-by-step explanation:

m=slope=2/7

point(7,0)

put into point-slope formula

[tex](y-y_{1})=m(x-x_{1)}[/tex]    where    [tex](x_{1} ,y_{1)} =(0,7)[/tex]

[tex]y-7=\frac{2}{7}(x-0)[/tex]        now put into slope- intercept(y=mx+b) form by simplifying, 0 goes away, and add 7 to both sides

[tex]y=\frac{2}{7}x-7[/tex]          b is your y-intercept, where it hits y-axis

The binary multiplication of 10011 and 1011, assuming unsigned integers, is 1000101 (209 in decimal).

To perform the binary multiplication of 10011 (19 in decimal) and 1011 (11 in decimal), follow these steps:

1. Write down the two binary numbers, with the larger one on top:
  10011
x  1011

2. Starting from the rightmost digit of the bottom number, multiply it by the entire top number, writing the product below, aligned with the current digit:
  10011
x  1011
  -----
    10011   (1 * 10011)

3. Move one position to the left in the bottom number, and repeat step 2. Add a zero to the rightmost position of the product to account for the place value:
  10011
x  1011
  -----
    10011
  00000   (0 * 10011)

4. Continue this process for each digit in the bottom number:
  10011
x  1011
  -----
    10011
  00000
 10011   (1 * 10011)

5. Finally, add all the products together:
  10011
x  1011
  -----
    10011
  00000
 10011
  -----
1000101   (final product)

So, the binary multiplication of 10011 and 1011, assuming unsigned integers, is 1000101 (209 in decimal).

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a) There is no enough evidence of an increase in life expectancy.

b) P-value=0.07.

The P-value indicates that this sample result is not rare to happen (is greater than the significance level) even if the mean of the population is still 87 hours.

We have to perform a hypothesis test on the mean, with known standard deviation of the population.

The null hypothesis, which we will reject or not, states that the life expectancy has not increase (it stays equal or less than 87 hours).

The null and alternative hypothesis are

H₀: μ ≤ 87

H₁ : μ > 87

The significance level is α=0.01.

The z-value is

z = 1.5

The P-value for z is = 0.06681

The P-value (0.07) is greater than the significance level (0.01), so the effect is not significant. We fail to reject the null hypothesis.

There is no enough evidence of an increase in life expectancy.

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complete question:

D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, the company believes that there has been an increase in the life expectancy of its "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours.

(a) Use a 0.01 level of significance, and test to determine if there has been an increase in the life expectancy of the "D" size batteries.

(b) What is the p-value associated with the sample results? What is your conclusion, based on the p-value?

One situation in which a social service agency may want to perform a regression analysis is when they are trying to determine the factors that contribute to the success or failure of their programs.

For example, let's say the agency runs a job training program and they want to know which factors (such as age, education level, or prior work experience) are most strongly correlated with program completion and employment outcomes for participants.

Performing a regression analysis can help the agency identify these key factors and assess their relative importance. This information can then be used to make targeted improvements to the program, such as adjusting the curriculum or offering additional support services to address specific barriers to success.

Additionally, the results of the regression analysis can be used to make a stronger case for the effectiveness of the program to funders and stakeholders. By being able to demonstrate a clear link between program participation and positive outcomes, the agency may be more likely to receive continued support and funding for their services.

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The first quartile for 1 - 3 is Q₁ = 756660.5 (b) The 5th decile for 5 - 6 is D5 = 2724770.5and (c)  The 80th percentile for 7 - 9 is 775346.4

Recall that a quartile is a statistical term used to measure the spread of values above and below the mean

the first quartile is represented by Q1

Q₁ = 1/4 (n+1)th term

Q₁ = 1/4 (3026641+1)

Q₁ = 3026642/4

Q₁ = 756660.5

b) The 5th decile can be calculated using the formula 5 (n+1) / 10, where 5 is the middle data point of any given set of numbers. This means that half of the scores lie above and below the distribution

This implies that D5 = 5 (n+1) / 10

D5 = 5(5449540 + 1) / 10

D5 = 5*5449541 /10

D5 = 27247705/10

D5 = 2724770.5

c) The 80th percentile is a measure of how well you are performing compared to other test takers.

It is calculated by dividing the number of points you scored by 100 and then multiplying that number by 50 to get an ordinal rank

the 80th % = n/100 * 80

80th percentile = 969183/100 * 80

80th Percentile = 969183 *80 = 775346.4

From the calculation, it means that Saudi Arabia has less cases of

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Answer:

48. 192

Step-by-step explanation:

In order to get from 3/4 to 3/16, one way would be to divide by 4. Another way is to multiply 3/4 by 1/4.

You can test whether multiplying by 4 works by multiplying 3/4 by 4 and 3 by 4.

When 3/4 is multiplied by 4, it would equal 12/3 which will simplify to 3. This can be done again with 3*4=12.

So the answer would be 12*4 = 48 and 48*4 = 192.

The statement "If x is a nontrivial solution of Ax=0​, then every entry in x is nonzero" is False.

A nontrivial solution means that there is at least one nonzero entry in x. However, it doesn't imply that every entry in x must be nonzero. It's possible to have a mixture of nonzero and zero entries in a nontrivial solution.

If x is a nontrivial solution of Ax=0, it means that x is a nonzero vector in the null space of A. This implies that A x = 0, which means that the linear combination of the columns of A given by x results in the zero vector.

However, this does not necessarily mean that every entry in x is nonzero. For example, consider the matrix A given by:

A = [1 0 1;

0 1 1;

1 1 2]

The null space of A contains the vector x = [-1; 1; 1], which is a nontrivial solution of Ax = 0. However, this vector has one entry that is zero and two entries that are nonzero.

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The depreciation expense in year 2 using the declining-balance method at twice the straight-line rate is $10,400, not one of the options provided.

To calculate the depreciation expense for year 2 using the declining-balance technique at double the straight-line rate, we must first estimate the straight-line rate and the double-declining rate.

The straight-line rate of depreciation is calculated as follows:

Straight-line rate = 1 / Estimated useful life

Straight-line rate = 1 / 5 = 0.2 or 20%

The double-declining rate of depreciation is calculated as follows:

Double-declining rate = Straight-line rate x 2

Double-declining rate = 20% x 2 = 40%

Using the double-declining rate of depreciation, the depreciation expense for year 1 can be calculated as follows:

Depreciation expense year 1 = Beginning book value x Double-declining rate

Depreciation expense year 1 = $50,000 x 0.4 = $20000

The beginning book value for year 2 is calculated as follows:

Beginning book value year 2 = Cost - Accumulated depreciation year 1 - Residual value

Beginning book value year 2 = $50,000 - $20,000 - $4,000 = $26,000

Using the double-declining rate of depreciation, the depreciation expense for year 2 can be calculated as follows:

Depreciation expense year 2 = Beginning book value year 2 x Double-declining rate

Depreciation expense year 2 = $26,000 x 40% = $10,400

Therefore, the correct answer is not among the options provided.

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Answer:

1 False

2 True

3 True

4 False

The total cost for 13 rides is 46 $.

Amount to be paid as entry fee = 20 $

Amount to be paid in each ride = 2 $

Therefore, total cost for 13 rides, P = 20 + (2 x 13)

P = 46 $

Total cost for r rides, P' = (20 + 2r) $

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After substitution, we get (u + v) X v = u X v + 0, which simplifies to (u + v) X v = u X v thus proving that (u + v) X v = u X v for any vectors u and v in V3.

To prove the statement (u + v) X v = u X v for any vectors u and v in V3, we will use the properties of the cross product. First, we know that the cross product is distributive over addition, meaning that (u + v) X v = u X v + v X v.

However, we also know that the cross product of a vector with itself is zero, since the angle between the two vectors is zero degrees. Therefore, v X v = 0.

Substituting this into the previous equation gives us (u + v) X v = u X v + 0, which simplifies to (u + v) X v = u X v.

Therefore, we have proven that (u + v) X v = u X v for any vectors u and v in V3.

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Answer:

Step-by-step explanation:

you could break up a term, like the y term.

x+2y+2y+9   this is equivalent

The P-value is 0.1611.

P-value = 0.1602

You are given a z-test statistic of -0.99, and you want to find the corresponding P-value. The P-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, given that the null hypothesis is true.

Step 1: Identify the z-test statistic
The z-test statistic is given as -0.99.

Step 2: Find the cumulative probability associated with the z-test statistic
Using a z-table or a statistical software, you can find the cumulative probability associated with a z-test statistic of -0.99.

Step 3: Determine the P-value
The cumulative probability you find in Step 2 is equivalent to the P-value since the alternative hypothesis is of the form p < p₀, and the P-value is the area under the z curve to the left of the calculated value of the test statistic.

P-value = (z curve area to the left of -0.99)

After finding the cumulative probability in a z-table or using a statistical software for a z-score of -0.99, you get:

P-value = 0.1611 (rounded to four decimal places)

So, the P-value is 0.1611.

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In case-control studies, the indirect measure of association between frequency of exposure and frequency of outcome is known as the odds ratio.'

The answer to your question is odds ratio. In case-control studies, odds ratio is used as an indirect measure of the association between frequency of exposure and frequency of outcome. It compares the odds of exposure in cases to the odds of exposure in controls, and provides an estimate of the strength of the association between exposure and outcome. While other measures such as population risk difference and attributable risk may also be calculated in case-control studies, odds ratio is the most commonly used measure of association.

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