What is the solution to 2x-8 <12?

A. x<2
B. x<8
C. x<10
D. x<40

The 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

To construct a 95% confidence interval for the mean weight of the bags of that specific brand of candies, we can use the following formula:

Confidence Interval = Sample Mean ± (Critical Value)× (Standard Deviation / √Sample Size)

First, let's calculate the critical value. Since the population distribution is assumed to be normal and the sample size is small (n = 16), we can use a t-distribution instead of a z-distribution.

The critical value can be obtained from the t-distribution table or using statistical software. For a 95% confidence level with 15 degrees of freedom (n - 1 = 16 - 1 = 15), the critical value is approximately 2.131.

Now, we can plug in the given values into the formula:

Sample Mean = 2.5 ounces (given)

Standard Deviation = 0.1 ounces (known)

Sample Size (n) = 16 (given)

Critical Value = 2.131 (from t-distribution)

Confidence Interval = 2.5 ± (2.131)× (0.1 / √16)

Calculating the standard error (Standard Deviation / √Sample Size):

Standard Error = 0.1 / √16 = 0.1 / 4 = 0.025

Confidence Interval = 2.5 ± (2.131) × (0.025)

Calculating the bounds of the confidence interval:

Lower Bound = 2.5 - (2.131) ×(0.025)

Upper Bound = 2.5 + (2.131)×(0.025)

Lower Bound ≈ 2.5 - 0.0539 ≈ 2.4461 ounces

Upper Bound ≈ 2.5 + 0.0539 ≈ 2.5539 ounces

Therefore, the 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

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In this question, we are asked to find the success probability for X and hence \($p_{X}$\).

Given brand of dinnerware has three colors: red, white, and blue.

Customers order the red set \($(X)=20 \%$\)

Customers order the white set \($(Y)=45 \%$\)

Customers order the blue set \($=35 \%$\)

Let \($X=1$\) if a randomly chosen order is for a red set, let \($X=0$\)otherwise.

Let \($Y=1$\) if a randomly chosen order is for a white set, let \($Y=0$\)otherwise.

Let \($Z=1$\) if a randomly chosen order is for either a red or white set, let \($Z=0$\) otherwise.

Since given data is in percentage.

We can say out of 100 customers, 20 customers ordered the red set.

\(\begin{gathered}p_{X}=\frac{\text { No.of customers whoordered the redset }}{\text { Totalno.of customers }} \\p_{X}=\frac{20}{100}=0.20\end{gathered}\)

Hence the success probability for \($X\left(p_{X}\right)$ is $0.20$.\)

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The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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Answer:

7

Step-by-step explanation:

4/5 +x =11 /×5

20 +5x =55

5x=55 - 20

5x=35

x=35 :5

x=7

Answer:

x=51/5

Step-by-step explanation:

4/5+x=11

x=11-4/5

have to make the denominators same

x=55/5 - 4/5

x=51/5

Answer:

32

Step-by-step explanation:

Answer:

26.019

Step-by-step explanation:

Answer:

26.01

Step-by-step explanation:

37 degrees plus m mus equal 90 degrees; therefore, the equation that m must satisfy is

subtracting 37 from both sides of the equation gives us

Answer:

w = 2.5

Step-by-step explanation:

Write these 2 equations to represent the problem:

\(l=w+5\\2w+2l=20\)

where w is width and l is length. This can then be solved as a system of equatios. I'll solve by substitution, and as the \(l\) is already solved for at the top:

\(2w+2l=20\\2w+2(w+5)=20\\2w+2w+10=20\\4w+10=20\\4w=10\\w=2.5\)

If you just need the width, then you're already done there. I'll find  the other variable too, and then check it to be sure it's correct.

\(l=w+5\\l=(2.5)+5\\l=7.5\)

Now, confirm that with the second equation:

\(2w+2l=20\\2(2.5)+2(7.5)=20\\5+15=20\\20=20\)

The perimeter of a rectangle is the sum of its side lengths.

The width of the rectangle is 2.5 units

Represent the length with l and the width with w.

So, we have:

\(P =2 \times (l + w)\) --- the formula of perimeter

The perimeter is 20 units.

So, we have:

\(20 =2 \times (l + w)\)

Divide both sides of the equation by 2

\(10 =l + w\)

The length is said to be 5 more than its width.

So, we have:

\(l =5 + w\)

Substitute 5 + w for l in \(10 =l + w\)

\(10 = 5 + w + w\)

\(10 = 5 + 2w\)

Subtract 5 from both sides

\(5 = 2w\)

Divide both sides by 2

\(2.5 = w\)

Rewrite as:

\(w =2.5\)

Hence, the width of the rectangle is 2.5 units

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Given the system of equations:

The solution of the system will be as follows:

Substitute with y into the first equation to find x:

So, the solution of the system is:

Answer:

See below

Step-by-step explanation:

-4x -8y = 8

3x-5y = 16    <===== multiply this equation by   4/3 to get

4x - 20/3 y = 64/3      <=====add to first equation...this will eliminate 'x'

      -8y - 20/3 y = 8 + 64/3       solve for y = -2

   use this value of y in any of the equations to compute x

        -4x - 8(-2) = 8

         -4x = 8-16      shows x = 2

The net of a triangular prism consists of two triangles and three rectangles.

In the net of a triangular prism, we can observe two types of polygons: triangles and rectangles.

First, let's discuss the triangles.

A triangular prism has two triangular faces, which are congruent to each other.

These triangles are equilateral triangles, meaning they have three equal sides and three equal angles.

Each of these triangles contributes two polygons to the net, one for each face.

Next, we have the rectangles.

A triangular prism has three rectangular faces that connect the corresponding sides of the triangular bases.

These rectangles have opposite sides that are parallel and equal in length.

Each rectangle contributes one polygon to the net, resulting in a total of three rectangles.

To summarize, the net of a triangular prism consists of two equilateral triangles and three rectangles.

The triangles represent the bases of the prism, while the rectangles form the lateral faces connecting the bases.

Altogether, there are five polygons in the net of a triangular prism.

It's important to note that the dimensions of the polygons may vary depending on the specific size and proportions of the triangular prism, but the basic shape and number of polygons remain the same.

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The number of cookies in the jar initially was 42

To find out how many cookies were in the jar initially, we can use algebra to represent the problem. Let x be the number of cookies in the jar initially. After Latoya took half of the cookies, Mark took 1/3 of the remaining cookies, Kandi took 1/4 of the remaining cookies, and Shannon took 1 cookie, there are 2 cookies left in the jar.

We can use this information to set up the equation:

x/2 - (x/2)/3 - (x/2)/4 - 1 - 2 = 0.

By solving this equation, we get x = 42. This means there were 42 cookies in the jar initially. To find out how many cookies were there before Latoya came, we just add the 2/3 of a cookie that was left over to the 2 whole cookies we know of.

So, 42+2/3 = 42.67 which means 42 cookies were there before Latoya came.

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The distance from the bottom of the building to the point where the ladder is touching the building for Triangle 2 is 14 feet.

What is triangle?

A triangle is a polygon with three sides and three angles. It is one of the most basic geometric shapes and is often used in geometry, trigonometry, and other branches of mathematics.

Since Triangle 1 and Triangle 2 are similar right triangles formed from the same ladder leaning against the same building, their corresponding sides are proportional to each other.

Let's use the concept of similarity and proportions to solve for the unknown distance in Triangle 2. We can set up the following proportion based on the corresponding sides of the two triangles:

(vertical leg of Triangle 1) : (horizontal leg of Triangle 1) = (vertical leg of Triangle 2) : (horizontal leg of Triangle 2)

We know that in Triangle 1:

the length of the hypotenuse (the ladder) is 16 feet

the length of the horizontal leg (the distance along the ground) is 8 feet

the length of the vertical leg (the distance from the bottom of the building to the point where the ladder is touching the building) is 16 feet

Using the Pythagorean Theorem, we can solve for the length of the vertical leg of Triangle 2:

(vertical leg of Triangle 1) : (horizontal leg of Triangle 1) = (vertical leg of Triangle 2) : (horizontal leg of Triangle 2)

16 : 8 = (vertical leg of Triangle 2) : 7

Simplifying the proportion, we get:

2 : 1 = (vertical leg of Triangle 2) : 7

To solve for the vertical leg of Triangle 2, we can multiply both sides of the proportion by 7:

2 * 7 : 1 * 7 = (vertical leg of Triangle 2)

14 : 1 = (vertical leg of Triangle 2)

Therefore, the distance from the bottom of the building to the point where the ladder is touching the building for Triangle 2 is 14 feet.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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Answer:

A

Step-by-step explanation:

Because B corresponds with 80 and a line segment is 180 degrees b + a =180 and a would be 100.

Answer:

c

Step-by-step explanation:

Answer:

Cc

Step-by-step explanation:

The variance of the length of the critical path is 5.76.

Option A is the correct answer.

We have,

To calculate the variance of the length of the critical path in the Critical Path Method (CPM) with three-time estimates (PERT), we can use the formula:

Variance = (Standard Deviation)²

Given that the standard deviation is 2.4, we can substitute it into the formula:

Variance = (2.4)² = 5.76

Therefore,

The variance of the length of the critical path is 5.76.

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Answer:

x=−2/5

y−2

Step-by-step explanation:

5x+2y=−10

Step 1: Add -2y to both sides.

5x+2y+−2y=−10+−2y

5x=−2y−10

Step 2: Divide both sides by 5.

5x

5

=

−2y−10

5

x=

−2

5

y−2

Answer: x- intercept: (-2, 0)   y- intercept:  (0,_5)

Step-by-step explanation:

True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship.  If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.

In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.

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The area of a 2D form is the amount of space within its perimeter. The total surface area of the square pyramid is 40 meters².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. Therefore, the amount of fabric that Henri will need is equal to the total surface area of the square pyramid.

Total surface area = Area of the base + 4(Area of the triangle)

                               = (4m × 4m) + 4(0.5×4m×3m)

                               = 16 meters² + 24 meters²

                               = 40 meters²

Hence, the total surface area of the square pyramid is 40 meters².

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Maria is 8 years older than her brother, and the sum of their ages is 72 years. How old is her brother?

Maria's brother is 32 years old.

Let's assume that:

As per the provided information, Maria is 8 years older than her brother, so her age can be expressed as \(\large\rm{x+8}\).

The sum of their ages is 72 years, so we can set up the equation:

\(\Large\begin{aligned}\rm{x + (x+8)}& =\rm{72}\end{aligned}\)

Substitute Maria's age into the above equation and solve for x:

\(\Large\begin{aligned}\rm{x + (x+8)}& =\rm{72}\\\rm{2x + 8}&=\rm{72}\\\rm{2x + \cancel{8 \red{-8}}}&=\rm{72 \red{-8}}\\\rm{2x}&=\rm{64}\\\rm{\dfrac{\cancel{2}x}{\cancel{\red{2}}}}&=\rm{\dfrac{64}{\red{2}}}\\\rm{x}&=\bold{32}\end{aligned}\)

\(\therefore\) Maria's brother is 32 years old.

To check our answer, we can substitute \(\large\rm{x = 32}\) into the equation \(\large\rm{x + (x+8) = 72}\):

\(\Large\begin{aligned}\rm{x + (x + 8)}&=\rm{72}\\\rm{\red{32} + (\red{32}+8)} &=\rm{72}\\\rm{32 + 40}&=\rm{72}\\\rm{72}&=\rm{72}\end{aligned}\)

This is true, so our assumption that Maria's brother's age is 32 is correct.

\(\\\\\)

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Answer:

Maria's brother is 32 years old.

Step-by-step explanation:

Let's denote Maria's brother's age as \(\bf{x}\). Since Maria is 8 years older than her brother, her age can be represented as \(\bf{x + 8}\). The sum of their ages is 72, so we can write the equation:

\(\LARGE \boxed {\boxed{x + (x + 8) = 72}}\)

Solving this equation, we get:

Now, we need to isolate \(x\). First, we can subtract 8 from both sides:

Next, we can divide both sides by 2:

So, Maria's brother is 32 years old.

________________________________________________________

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Answer:

d

Step-by-step explanation:

The two types of control charts for variables are the X-bar chart and the R-chart.

Control charts are widely used in statistical process control to monitor and analyze the variability and stability of processes over time. They are used for variables data, which are measurements or observations that can be quantified.

1. X-bar Chart: The X-bar chart is used to monitor the central tendency or average of a process. It tracks the sample means over time to detect any shifts or trends. It helps in assessing whether the process is in control or if there are any systematic variations from the target value.

2. R-chart (Range chart): The R-chart is used to monitor the variability or dispersion within a process. It tracks the ranges (the difference between the highest and lowest values) of samples over time. By analyzing the range values, it helps in understanding whether the process is stable and consistent or if there are any unusual variations or outliers.

Together, the X-bar chart and the R-chart provide valuable insights into process performance and allow for early detection of any deviations or abnormalities, helping organizations maintain quality standards and take appropriate corrective actions when necessary.

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Answer:

11.35 g/mL

Step-by-step explanation:

D = m/v

D = 567.5 g ÷ 50.0 mL (I assume its measured in mL)

D = 11.35 g/mL

Answer:

11.35

Step-by-step explanation:

The answers to each part is below..

Given is a graph as shown in the image.

Therefore, the answers to each part is given above.

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Answer:

below

Step-by-step explanation:

12 + 84/100   = 12.84

Answer: 1.33

Step-by-step explanation: