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The three consecutive integers according to the expression will be 6, 8, 10

In the given question, there is an expression stated that tells the condition for a sequence in which a number is represented by 'n'. The expression is the sum of three even integers whose sum is equal to four times the smallest of numbers.

The expression is n + (n + 2) + (n + 4) = 4n. We have to find out the values for each of the numbers.

Here, First Number = n

Second number = (n + 2)

Third Number = (n + 4)

Now, We will calculate the given expression to find out the value of n.

=> n + (n + 2) + (n + 4) = 4n

=> 3n + 6 = 4n

=> n = 6

We get the smallest number n = 6 which is the first number, the second number is 8, and the third number is 10.

Hence, the numbers are 6, 8, and 10.

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The value of the missing angles are; m∠ABC = 36° and m∠DBC = 41°

We are given that;

m∠ABD = 77°

Addition angle postulate states that the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together.

Now, by addition angle postulate, we can say that;

m∠ABC + m∠DBC = 77°

Now, we are given that;

m∠ABC = (5x - 4)°

m∠DBC = (5x + 1)°

Thus, by substitution property, we have;

(5x - 4)° + (5x + 1)° = 77

10x - 3 = 77

10x = 77 + 3

10x = 80

x = 8

Thus;

m∠ABC = (5(8) - 4)°

m∠ABC = 36°

m∠DBC = (5(8) + 1)°

m∠DBC = 41°

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Answers in bold

[tex]\begin{array}{|c|c|} \cline{1-2}k & P(X = k)\\\cline{1-2}0 & \boldsymbol{0}\\\cline{1-2}1 & \boldsymbol{0}\\\cline{1-2}2 & \boldsymbol{0.04}\\\cline{1-2}3 & \boldsymbol{0.18}\\\cline{1-2}4 & \boldsymbol{0.41}\\\cline{1-2}5 & \boldsymbol{0.37}\\\cline{1-2}\end{array}[/tex]

Note: The P(x) values for k = 0 and k = 1 are not actually zero, but they are small enough that they round to 0 when rounding to two decimal places.

=======================================================

Explanation:

I used a spreadsheet to compute the values in bold.

The specific command is called BINOMDIST

The template is BINOMDIST(k,n,p,0)

Let me know if you have any questions about how to use that function in a spreadsheet.

Also, I used the function called ROUND to round each value to 2 decimal places.

Example calculation

=ROUND(BINOMDIST(4,5,0.82,0),2)

This calculates the result of 0.41 and it corresponds to the value k = 4

Don't forget about the equal sign up front when computing these commands in the spreadsheet. Otherwise, it'll stay as text form.

-------------------

If you want to use a TI83 or TI84 calculator, then press the button labeled "2nd". Then press the button labeled "VARS". Scroll down until you reach "binompdf".

The template is binompdf(n,p,k)

So for example, type in binompdf(5,0.82,4) to get the P(X) value for k = 4

If you aren't able to access a spreadsheet or a TI83/84 calculator, then search out "binomial distribution calculator" and there are plenty of free ones to pick from.

In my opinion, a spreadsheet is the best option since the given data is already in tabular form. Also, many real world situations and careers use spreadsheets everyday.

The surface area of a cone is given by the sum of the areas of the lateral surface and the area of the circular base.

The area of the circular base is given by:

Where r is the radius of the base.

The area of the lateral surface is given by:

Where s is the length of the slant.

Since s=17 in and the radius is half the diameter, r=8 in, the area of the cone is:

To the nearest hundredth, the area of the cone in square inches, is:

The logarithm of the number 6.5 is log(6.5) = 0.8129

This is the number that represents the power by which a fixed number known as the base must be raised to result in another number.

The number is given as

6.5

The logarithm of the number is then represented as

log(6.5)

There are several ways to calculate the logarithm of the number

Some of which are:

In this case, the only way is by using a calculator

Using a calculator, we have

log(6.5) = 0.8129

Hence, the logarithm of 6.5 is 0.8129

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We can divide the given figure into different rectangular faces:

Faces 1 and 3 have the same measure, also 2 and 4, and faces 5 and 6.

Faces 1 and 3 have the following dimensions: L=100cm W=50cm.

Faces 2 and 4 have the following dimensions: L=100cm W=35cm.

Faces 5 and 6 have the following dimensions: L=50cm W=35cm.

The surface area of a rectangular face is given by:

Thus, the surface areas of the given faces are:

The surface area of the net is the addition of all of these surface areas:

A population proportion's 95% confidence interval is 0.45416 ≤ P ≤ 0.66584.

Given sample size n is 318, the probability of success,

p = x ÷ n = 181 ÷ 318 = 0.56

A population proportion's 95% confidence interval is calculated as follows:

(p -  [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n) , p +   [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n)

(0.56 - 1.96 √ ((0.56(1 - 0.56) ÷ 318) , 0.56 + 1.96 √ ((0.56(1 - 0.56) ÷ 318))

(0.56 - 1.96 × 0.054) , (0.56 + 1.96 × 0.054)

(0.45416 , 0.66584)

95% confidence interval for a population proportion of 0.45416 ≤ P ≤ 0.66584.

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Answer:

(-7, 5) is correct.

Step-by-step explanation:

[tex]2x + 3y = 1[/tex]

[tex] - 2x - y = 9[/tex]

Add these two equations, and then solve for y.

[tex]2y = 10[/tex]

[tex]y = 5[/tex]

Substitute this value of y into 2x + 3y = 1, and solve for x.

[tex]2x + 3(5) = 1[/tex]

[tex]2x + 15 = 1[/tex]

[tex]2x = - 14[/tex]

[tex]x = - 7[/tex]

So (-7, 5) is the correct solution.

Here, we want to solve find the value of the expression

We start by opening up the brackets and then, we bring together like terms

We have this as;

Solution

- The ordered list from the least to the greatest is:

- Thus, using the arrangement of the numbers, we can rearrange using the letters.

O, N, L, P, M

Final Answer

O, N, L, P, M (OPTION C)

The critical value (tα/2) for a 95% confidence interval for the sample size 15 is 2.009.

We have to find the critical value tα/2 for 95% confidence interval, we are given the sample size.

First we will find the alpha value to get the critical value.

=100%-95%

=1-0.95

=0.05

α=0.05

α/2=0.05/2

α/2=0.025

degrees of freedom(df)= n-1=15-1=14

We will use degrees of freedom and α/2 values to find the critical value that is tα/2.

By using the t table we get the critical value  of tα/2=2.009.

Therefore, the critical value for 95% confidence interval with sample size of 15 is 2.009.

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A function that models the population of 400 birds decreasing at an annual rate of 6% is  [tex]f(x) = 400(1 - 0.06)^{t}[/tex] where t is the time period.

The Exponential decay formula aids in determining the quick decrease over time, i.e. the exponential decrease. The exponential decay formula is used to calculate population decay, half-life, radioactivity decay, and so on.

Its general form is f(x) = a (1 - r)ⁿ.

Where a = the initial amount

1 - r = decay factor and n = time period.

Given:

The initial population of birds, P = 400

Rate of decay, r = 6% = 0.06

Time = t years

By using the exponential decay formula,we get

[tex]f(x) = P (1 - r)^{t}[/tex]

[tex]f(x) = 400(1 - 0.06)^{t}[/tex]

Therefore, the function that models the population of 400 birds decreased at an annual rate of 6% is  [tex]f(x) = 400(1 - 0.06)^{t}[/tex].

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The perimeter is 54 inches

The area is 108 square inches

The perimeter of the triangle is:

15 in + 15 in + 24 in

= 54 in

The area is:

(1/2)(24)(9)

= 108 sq. in

SOLUTION

Note that for an inequality to be graphed with an open circle the inequality sign must be either less than or greater than

Therefore the inequalities are:

Given:

The vertices are P (-4, -5), L (1, -7), and K (-9, 8).

The vector is < -6,3 >.

Aim:

We need to find the image of the vertices when translating given vertices along the vector.

Explanation:

The translation vector <-6,3> means each point is being moved 6 units to the left and 3 units up.

For each vertex, we subtract 6 from each x value and add 3 to each y value.

Final answer:

Problem

Solution

For this case we can find the remain angle with this operation:

180 -39-90= 51º

And then we can use the sines law and we can do this:

And solving for x we got:

x= 14*sin(39)/sin (90) = 14*sin 39= 8.81

ANSWER

0.01175 metres

EXPLANATION

We want to find how many metres are in 11.75 millimetres.

There are 1000 millimeters in 1 meter:

We will simply divide 11.75 milimetres by 1000

1000 millimetres = 1 metre

SOLUTION

We want to find the distance that the top edge of the calendar is from the ceiling.

The diagram below will help us

From the diagram above x is the distance we want to find

We can see that the entire wall is 9 ft long,

Distance from the foot of the calender to the floor is 5 1/4 ft and

Halve of the calendar is 2/3 ft

So the whole calendar is

So, to find x, we will add length of the calendar which is 4/3 ft to distance from the foot of the calender to the floor which is 5 1/4 ft and subtract this from height of the wall which is 9 ft

We have

Hence the answer is

Given:

Given the equation

Required: Point at which the equation crosses the y axis.

Explanation:

At y -axis, the value of x is zero. Substitute 0 for x in the equation of y.

So, the point at which the equation cross the y-axis is (0, 5).

Final Answer: The point at which the equation cross the y-axis is (0, 5).

The simplified expression of the fraction expression is (b) One group of 4/6, with 1/6 remaining.

The fraction expression is given as

ten StartFraction 1 Over 12 EndFraction bars.

Rewrite the fraction properly

So, we have

Ten 1/12 bars

This can be represented as

10 * 1/12

Rewrite 10 as 10/1

So, we have the following equation

10 * 1/12 = 10/1 * 1/12

Evaluate the products of the numerator

So, we have the following equation

10 * 1/12 = 1/1 * 10/12

Evaluate the products of the denominator

So, we have the following equation

10 * 1/12 = 10/12

Simplify the fraction

10 * 1/12 = 5/6

Split the fraction

10 * 1/12 = 4/6 + 1/6

This means that, the result is

Quotient = 4/6 and remainder = 1/6

Hence, the true statement about the fraction is (b)

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Complete question

Which did you include in your response? Check all that apply?

Use ten 1/12 bars.

The following are the reasons for sampling:

1. To bring the population to a manageable number

2. To reduce cost

3. To help in minimizing error from the despondence due to large number in the population

4. Sampling helps the researcher to meetup with the challenge of time.

Therefore, the answer is:

c. Sampling is so easy.

Answer:

7315.55

Step-by-step explanation:

just dont be lazy solve it.

Given that 1kg=2.2 pound, also there is 14 pounds in 1 stone

There are 9 stones totally,so totally 9 stones will have 405 pounds

To convert into kilogram to should divide pounds by 2.2

Thus 183.705 is the required answer.

In a chemical reaction, atoms are neither CREATED nor DESTRUCTED. According to science, each side of the equation must contain the SAME amount of atoms.

You must place COEFFICIENTS in front of the chemical formulas in the equation in order to make it equal.

What does a chemical reaction always involve?

Only atoms from the reactants can end up in the products of a chemical reaction. No atoms are destroyed or made into new ones. When reactants come into touch with one another, the bonds between their atoms are broken, and the atoms then reorganize and form new bonds to create the products.

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Given,

The coordinates of the points is,

The coordinates of the mid point is:

Hence, the mid point of the line segment is (-1,2).

Answer:

indetermination

Step-by-step explanation:

Hope this helps

Fraction - A,C,D is the incorrect option that means 18 >17 is the correct option B

Equivalent fractions with the same denominator should be used to compare fractions with different denominators. Comparing fractions: If the denominators are the same, the numerators can be compared. The greater fraction is the one with a larger numerator.

Now, comparing the fraction,

first of all write the fraction in simplest form then cross multiplication.

1.   [tex]\frac{29}{35} < \frac{20}{30}[/tex]

[tex]\frac{29}{35} < \frac{2}{3}[/tex]

87 < 70

This option is wrong.

2.    [tex]\frac{18}{34} > \frac{16}{32}[/tex]

[tex]\frac{9}{17} > \frac{1}{2}[/tex]

18 >17

This option is correct.

3.    [tex]\frac{14}{21} > \frac{17}{24}[/tex]

[tex]\frac{2}{3} > \frac{17}{24}[/tex]

48 > 51

This option is wrong.

4.   [tex]\frac{20}{15} < \frac{28}{23}[/tex]

[tex]\frac{4}{3} < \frac{28}{23}[/tex]

92 < 84

This option is wrong.

Hence, option b is correct.
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Step-by-step explanation:

probabilities are always

desired cases / totally possible cases

24 cans in total, 4 of them are diet, therefore 20 of them are regular.

2 cans are picked.

for the first can

the probability to pick a diet can is

4/24 = 1/6

the probability to pick a regular is

20/24 = 5/6

a)

to pick 2 diets, the first one has to be diet.

that leaves 23 cans with 3 being diet.

so, the probability for the second can being diet too is

3/23.

as combined event the probability to pull 2 diet cans is

1/6 × 3/23 = 1/2 × 1/23 = 1/46 = 0.02173913...

≈ 0.0217

b)

now the same for picking 2 regular cans.

the first one has to be regular :

5/6

that leaves for the second one 23 cans and 19 of them regular

19/23

combined this gives the probability

5/6 × 19/23 = 95/138 = 0.688405797...

≈ 0.6884

this is not unusual.

what would be considered "usual" or "unusual" ?

c)

one of them is diet, and one of them is regular.

the simple answer ?

it is the only other option, when the cans are not of the same type. it is the opposite of the sum of a) and b).

so, it is

1 - 0.688405797... - 0.02173913 = 0.289855072...

≈ 0.2899

but what to do, if we want to calculate it directly ?

it is the case that either

1. the first can is diet and the second can is regular,

or

2. the first can is regular and the second can is diet.

case 1.

the first can is diet = 1/6

leaving 23 cans with 20 being regular

the second can being regular = 20/23

together

1/6 × 20/23 = 1/3 × 10/23 = 10/69 = 0.144927536...

case 2.

the first can is regular = 5/6

leaving 23 cans with 4 diets.

the second can being diet = 4/23

together

5/6 × 4/23 = 5/3 × 2/23 = 10/69 = 0.144927536...

in an "exclusive or" situation we can add the probabilities.

so, the probability of having exactly one can diet and exactly one can regular is

0.144927536... + 0.144927536... = 0.289855072...

≈ 0.2899

we were correct in the first place !

To find how many Costco employees are, we can use the formula of