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The answer  is , (a) the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%).  , (b) we cannot definitively conclude that the results contradict the expectation.

A confidence interval is a range of values that is used to estimate the true value of an unknown parameter, like a population mean or proportion, based on a sample of data. It is a statistical measure of the precision and reliability of an estimate, and it provides a measure of the uncertainty or margin of error associated with the estimate.

a. To construct  95% confidence interval for percentage of yellow peas, we can use  following formula as :

CI = p ± z*(√((p*(1-p))/n))

Where:

p = proportion of yellow peas = 152/(431+152) = 0.2613

z = z-value for a 95% confidence interval = 1.96 (from standard normal distribution table)

n = sample size = 431+152 = 583

Plugging in the values, we get:

CI = 0.2613 ± 1.96*(√((0.2613*(1-0.2613))/583))

CI = 0.2613 ± 0.0365

CI = (0.2248, 0.2978)

Therefore, the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%).

b. The expected percentage of the yellow peas is 25%. Since the lower limit of the confidence interval is 22.48%, which is less than 25%, it suggests that the actual percentage of yellow peas may be lower than expected. However, since the confidence interval does include 25%, we cannot definitively conclude that the results contradict the expectation.

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Answer:

mark me brilliant

Step-by-step explanation:

There are a total of 4+2=6 students in the seventh grade and 9+1=10 students in the eighth grade, so there are a total of 6+10=16 students in the class.

The probability of selecting a boy from the seventh grade is 2/4 = 1/2, and the probability of selecting a boy from the eighth grade is 9/10.

To find the probability of both events happening, we multiply the probabilities:

P(selecting a boy from seventh grade AND selecting a boy from eighth grade) = (1/2) x (9/10) = 9/20.

Therefore, the probability that the students selected for the competition are both boys is 9/20.

The graph of equation 1/2(x+1)=(y – 5)^2 looks like graph of a horizontal parabola.

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

How to graph equation?

one-half(x + 1) = (y – 5)^2, written symbolically, is (1/2)(x - [-1]) = (y – 5)^2

or x + 1 = 2(y – 5)^2.

Because the y term is squared, we know immediately that the graph is a horizontal (not vertical) parabola.  

This equation can be written as

x = 2 - 1

The standard equation of a horizontal parabola with vertex (h, k) is

x = c + h.  Comparing this to the given quadratic:  

we see that k = 5 and h = -1.  This tells us that the vertex of this graph is (-1, 5), and that the graph is stretched horizontally because c = 2 is greater than 1.

To graph this, it's best to make a short table of points, as follows, remembering that y is the independent value and x depends on y through the equation given above.

y    x = 2(y – 5)^2 - 1    (x, y)

0    x = 49                    (49, 0)

2    x = 2(-3)^2 - 1         (17, 2)

1   x = 2(-4)^2 - 1          (31,  1)

vertex (already found) (-1, 5)

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Answer:

Step-by-step explanation:

The value of A when we rewrite 6^x as A^x/4 is 3/2

An algebraic expression can simply be defined as a mathematical expression that consists of terms, factors, constants, coefficients and variables.

They are also known as expressions made up of arithmetic operations, such as;

From the information given, we have that;

The function is given as;

6^x

Here, the coefficient or rather the base is 6

To determine the value of A when ^^x is given as A^x/4

The value of A would be;

6/4 = 3/2

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Answer:

Step-by-step explanation:

2 hour

Step-by-step explanation:

City A to City B : 1580 miles

Plane speed (C) to City B from A : 400 miles per hour

Plane speed (D) to City A from B : 390 miles per hour

Time taken for plane (C) :

=1580 ÷ 400

=3⁹/²⁰ hours

Time taken for plane (D) :

=1580 ÷ 390

=4²/³⁹ hours

Finding time difference

= 4²/³⁹ - 3⁹/²⁰

=469/780

Finding midpoint

= 469/780 ÷ 2

=469/1560

Total

= 3⁹/²⁰ + 469/1560

= Aprroximately 3¾ hours

The calculated approximation of log(15/2) is 0.9

From the question, we have the following parameters that can be used in our computation:

log(10) = 1.1

log(11) = 1.2

log(6) = 0.9

Also, we have

log(15/2)

Applyingthe quotient logarithmic law, we have

log(15/2) = log(15) - log(2)

15 and 2 cannot be derived directly from 10, 11 and 6

So, we solve independently using a calculator

log(15) = 1.2

log(2) = 0.3

Substitute the known values in the above equation, so, we have the following representation

log(15/2) = 1.2 - 0.3

Evaluate

log(15/2) = 0.9

Hence, the approximation is 0.9

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The given trinomial is [tex]2a^2+5ab+7b^2[/tex]. The trinomial can be factored as (2a+7b)(a+b).

A trinomial is an algebraic expression consisting of three terms. It can be written in the form ax² + bx + c, where a, b, and c are constants and x is a variable. Trinomials are also used to solve equations, such as quadratic equations.

To factor this trinomial, we will first split the trinomial into two groups. The two groups are (2a, 7b) and (a, b).

Now we will multiply the first terms of both the groups.

We will get 2a × a = 2a².

This is the first term of the trinomial. Now we will multiply the second terms of both the groups.

We will get 7b × b = 7b².

This is the last term of the trinomial. Now we will multiply the first term of the first group and the second term of the second group.

We will get 2a × b = 2ab.

This is the middle term of the trinomial.

Hence, the trinomial can be factored as (2a+7b)(a+b).

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Step-by-step explanation:

(a) Proportion of minority jurors = 2/12 = 1/6 = 0.1667

(b) Using binomial distribution, P(2 or fewer minorities) = P(0 minorities) + P(1 minority) + P(2 minorities)

P(0 minorities) = (0.53)^12 ≈ 0.005

P(1 minority) = 12C1 (0.47)(0.53)^11 ≈ 0.048

P(2 minorities) = 12C2 (0.47)^2(0.53)^10 ≈ 0.18

P(2 or fewer minorities) ≈ 0.005 + 0.048 + 0.18 ≈ 0.2339

(c) OA. The number of minorities on the jury is unusually low, given the composition of the population from which it came.

A 95% confidence interval for the population mean length of engineering conferences is 3.70, 4.26.

The error bound based on the information will be 0.28.

95% confidence interval for the population mean length of engineering conferences is:

= 3.98 +- (1.969 (0.142)

= 3.98 +- 0.218

= 3.70, 4.26

The error bound based on the information will be:

= (1.96( (0.142)

= 0.28.

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Answer:

45.73 square feet.

Step-by-step explanation:

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius.

We can rearrange this formula to solve for r:

r = C / 2π

Plugging in the given value of C = 24 feet, we get:

r = 24 / (2π)

r ≈ 3.819 feet

Now that we know the radius of the circle, we can use the formula for the area of a circle to find the approximate area of the park:

A = πr^2

Plugging in the value of r, we get:

A ≈ π(3.819)^2

A ≈ 45.73 square feet

Therefore, the approximate area of the circular park is 45.73 square feet.

Answer: A = 45.82 ft²

Step-by-step explanation:

Given:

C= 24 ft

Formulas needed:

C=2[tex]\pi[/tex]r    where r is radius

Circumference is the perimeter of the circle.  Length of outside line

and

Area:

A=[tex]\pi r^{2}[/tex]

Area the measurement of the shape or area that you want to cover.

Solution:

C=2[tex]\pi[/tex]r              >substitute C=24     and solve for r

24=2[tex]\pi[/tex]r            > divide both sides by 2[tex]\pi[/tex]

[tex]\frac{24}{2\pi }[/tex]  = r               >use 3.14 for [tex]\pi[/tex]

[tex]\frac{24}{2*3.14}[/tex]  = r          >plug into calculator

r=3.82

Now that we have r   we can solve for A

A=[tex]\pi r^{2}[/tex]

A=(3.14)(3.82)²     >plug into calc

A = 45.82 ft²

Answer:

okay?

Step-by-step explanation:

is this a true or false

For the experiment by Cliff, the bar graph will most likely have the same height for the number of times each letter appears.

For the experiment by Devon, the bar graph will most likely have the same height for the number of times the letter A, E, and U appears and the same height for the number of times O and I appear. However, the height of the bar graphs for O and I will most likely be half that of A, E, and U.

For the experiment by Cliff, the probability of the letters appearing is given below:

The letters have equal chances of being picked, hence, their probabilities are equal.

Probability = 1/5

For the experiment by Cliff, the probability of the letters appearing is given below:

The letters A, E, and U have equal chances of being picked, hence, their probabilities are equal.

P(A) = 1/4

P(E) = 1/4

P(U) = 1/4

The letters O and I have equal chances of being picked, hence, their probabilities are equal.

P(O) = 1/8

P(I) = 1/8

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The volume of the right pyramid is 23 1/3 cm³. The correct option is E,

Given that the length of the side of the right pyramid is 3.75 cm, While the height of the pyramid is 5 cm. Therefore, the volume of the given right pyramid is:

Volume = (1/3) × (side length)² × Height

              = (1/3) × (3.75 cm)² × 5 cm
              = 23.33 cm³

              = 23 1/3 cm³

Hence, the volume is 23 1/3 cm³.

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The complete question must be:

What is the volume of the right pyramid with the base lenght of 3.75 cm and height of 5cm?

A. 186 and 2-thirds centimeters cubed

B. 84 centimeters cubed

C. 25 centimeters cubed

D. 23 and 1-third centimeters cubed

E. 18 and 2-thirds centimeters cubed

Answer:

240 cubic inches.

Step-by-step explanation:

To calculate the volume of the sandcastle decoration in the fish tank, we can use the formula:

Volume of the decoration = Total volume of water after adding the decoration - Volume of water before adding the decoration

The volume of water before adding the decoration is the volume of the rectangular prism formed by the fish tank, which is:

Volume of water before = Length x Width x Height

= 16 x 15 x 12

= 2,880 cubic inches

After Kyle added the sandcastle decoration, the water level rose to 13 inches. This means the volume of water in the tank increased by the volume of the decoration. The new volume of water in the tank is:

Volume of water after = Length x Width x Height

= 16 x 15 x 13

= 3,120 cubic inches

Therefore, the volume of the sandcastle decoration is:Volume of decoration = Volume of water after - Volume of water before

= 3,120 - 2,880

= 240 cubic inches

Therefore, the volume of the sandcastle decoration in the fish tank is 240 cubic inches.

Answer:

Step-by-step explanation:

i sorry dont know

Using the given percentages, we can see that 126 students preferred cola.

To find this number, we just need to multiply the correspondent percent by the total number of students.

First, write the percent in decimal form, to do so, divide it by 100%.

20% of the students preferr cola, so we need to write:

20%/100% = 0.2

And the total number of students is 630, so the number that preffered cola is:

0.2*630 = 126

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Answer: The median amount of sales each day was $7,000.

Step-by-step explanation:

To find the median amount of sales each day, we need to arrange the sales amounts in order from smallest to largest. Doing so, we get:

4,000 5,000 6,000 7,000 8,000 9,000

Since there are an odd number of values, the median is the middle value, which is 7,000. Therefore, the median amount of sales each day was $7,000.

The middle value of this dataset is 7,000, so the median amount of sales each day is $7,000.

The value that divides the mathematical numbers or expressions in half is known as the median. The midway number of data points is known as the median value. Then, organize the data points in ascending order before calculating the median.

Given information:

Gert's Groceries recorded the total amount of sales each day.

To find the median of a set of data, we need to order the data from least to greatest and then find the middle value(s).

4,000 5,000 6,000 7,000 8,000 9,000

The middle value of this dataset is 7,000, so the median amount of sales each day is $7,000.

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The probability that the mean IQ score of people in the sample is less than 98 is 0.2533, which is rounded to four decimal places.

Probability is a branch of mathematics that deals with the likelihood of a certain event or outcome occurring. Probability is based on the concept of counting and measuring the chances of something happening. It can be used to provide insight into how likely a certain outcome is to occur, and can be used to make decisions about the future. Probability can also be used to analyze data, identify patterns, and make predictions.

The probability that the mean IQ score of people in the sample is less than 98 can be calculated using the z-score. The z-score is calculated by subtracting the mean from the given value, 98, and then dividing the difference by the standard deviation, 15.0. This gives a z-score of -0.67.

Using the z-table, the probability of the mean IQ score of people in the sample being less than 98 can be calculated. The probability is 0.2533. Therefore, the probability that the mean IQ score of people in the sample is less than 98 is 0.2533, which is rounded to four decimal places.

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Answer:

Step-by-step explanation:

X axis come first then the y axis, p needs to start at 3 then go 4 units up and 3 units to the left and then you get (3,4)

Answer:

x = 9

Step-by-step explanation:

The measure of angle M is half of the sum of the big arc minus the little arc it intersects.

We also know ∠M = 4x +4

∠M= 1/2(mArc CK - mArc LN)

Substitute in values

4x +4 = 1/2(15x + 12 - 67)

Combine like terms

4x + 4 = 1/2(15x - 55)

Multiply (what's in side the parenthesis by 1/2)

4x + 4 = 7.5x - 27.5

Isolate the x. Add 27.5 to both sides

4x + 31.5 = 7.5x

Subtract 4x from both sides

31.5 = 3.5x

Divide both sides by 3.5

9 = x

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{d}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ d=\sqrt{ 17^2 - 15^2}\implies d=\sqrt{ 289 - 225 } \implies d=\sqrt{ 64 }\implies d=8 \\\\\\ \stackrel{\textit{radius is half the diameter}}{r=\cfrac{8}{2}}\implies r=4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4\\ h=15 \end{cases}\implies V=\pi (4)^2(15)\implies V\approx 754~cm^3[/tex]

1) There are 3.4 * 10^1 in Mexico than in Canada.

2) The number of ounces that were consumed is 20.8 * 10^7 ounces

3) The number of ounces of the students at the community college is 1.25 * 10^1 that of the students in the University.

Scientific notation is a way of writing very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to a power.

1) Ratio of people in Mexico to those in Canada;

1.3 * 10^8/3.8 * 10^7

= 3.4 * 10^1 : 1

2) Number of Ounces consumed by students = 5.2 * 10^4 * 4 * 10^3

= 20.8 * 10^7 ounces

3) Ratio of the number drank by community college to University

= 4 * 10^3/3.2 * 10^2

1.25 * 10^1

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[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_4(y)=2\implies 4^2=y\implies 16=y\hspace{5em} {\Large \begin{array}{llll} \log_4(16)=2 \end{array}}[/tex]

Answer:

Step-by-step explanation:

1. -Growth because its increasing

  -asymptote y=0  boundary

  -domain (-∞,+∞)  where does x exist

  -range (0, +∞)    where does y exist

  - y-int (0,2)   plug x into equation or look where it hits y-axis

2.  Decay because its decreasing

   - asymptote y=4

   - domain  (-∞,+∞)

   -range (4, +∞)

   y-int (0,7)

3.  growth

y=-3

domain: (-∞,+∞)

range: (-3, +∞)

(0, -2.25)

4.  decay

y=3

domain  (-∞,+∞)

range (3, ∞)

y-int (0,5)

Answer: b

Step-by-step explanation:

Answer: 1/4

Step-by-step explanation: The probability that the company will hire two women for positions is : 1/4 because..

The total number of possible outcomes = 4.

The event in which two women are chosen = 1.

or (1/2)*(1/2) = 1/4

Keeping a temperature record can help Lamar and others stay informed about the climate in their area and make informed decisions based on that information.

Lamar has been recording the high temperature in degrees Fahrenheit for his city over several days and has recorded them in a table. It is essential to keep a record of the temperature to track the weather patterns and make predictions about future weather conditions.

By having this data, Lamar can analyze the temperature trends in his city over time. He may notice that certain times of the year tend to be warmer or cooler than others or that some days are unusually hot or cold.

This information can be valuable for planning outdoor activities or making decisions about the best time to travel

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Round off 87654 to the nearest hundred?

Marching into my territory,eh?

we need to look at the tens and ones digit of the number. The digit in the hundreds place is 6, which tells us that the number is already in the thousands place.

The tens digit is 5, which is greater than or equal to 5. This means we need to round up the hundreds place to the next digit. Therefore, the rounded number to the nearest hundred is 87700.

One of the function that satisfies all four statements is f(x) = 2 - [tex]e^{3-x}[/tex] , for x ≤ 3.

The function that satisfies all four statements is a decreasing function with a horizontal asymptote y = 0 that intersects the x-axis at x = 3. One possible function that satisfies all four statements is:

f(x) = 2 - [tex]e^{3-x}[/tex], for x ≤ 3

Explanation:

Statement 1, The domain of the function is x ≤ 3 because the expression [tex]e^{3-x}[/tex] becomes undefined for x > 3.

Statement 2, The range of the function is y ≥ 0 because the exponential term [tex]e^{3-x}[/tex] is always positive and subtracting it from 2 will always result in a non-negative value.

Statement 3, The x-intercept of the function is 3 because f(3) = 0, which means the graph intersects the x-axis at x = 3.

Statement 4, When x decreases, the function increases because the exponential term [tex]e^{3-x}[/tex] becomes smaller and smaller as x decreases, which causes the entire expression 2 - [tex]e^{3-x}[/tex] to increase.

Correct Question :

Write a function for which all four statements are true.

Statement 1: The domain of the function is x ≤ 3.

Statement 2: The range of the function is y ≥ 0.

Statement 3: The x-intercept of the function is 3.

Statement 4: When x decreases, the function increases.

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Required true statements are f and d are vertical, d and e supplementary, g and are adjacent, d and g are complementary and f and e are linear pair.

What is the value of d?

Here d is the opposite angle of f.

We know opposite angles are always equal.

So, according to question f = 71° then d = 71°.

Now we need to check given statements are true or false.

1) Given d and f are adjacent.

We know, adjacent angles always have same vertex.

But angle f and d don't have any common vertex.

So, we can say d and f are not adjacent.

2) Given d and e are complementary.

From the picture, sum of d and e is 180°.

We know, sum of two complementary angles is 90° always.

So, this statement is also not true.

3) f and d are vertical.

Vertical angles are always opposite each other where two line cross.

Here it is clear f and d are opposite and they made by two line cross.

So, f and d are vertical is a true statement.

4) d and e supplementary.

Already said sum of d and e is 180°.

We sum of two supplementary angles is 180° always.

So, This is the true statement.

5) Here g and f have common vertex.

So, g and f are adjacent is the true statement.

6) Here value of g is (90-71) = 29°

So, sum of g and d is 90°.

Therefore, g and d are complementary.

7) Here d and g are not opposite.

So, they are not vertical.

8) Linear pair means, two hands of two common line

Here, f and e have two hands of two common line.

So, they are a linear pair.

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