Question 4 problem solving ​

The survey method which will produce the best representative sample is option B.  survey 3 randomly selected students from every homeroom.

Sampling methods are methods used to select a sample using specific methods. This includes various types of probability sampling and non probability sampling methods.

Here given that,

a middle school principal wants to change the lunch menu at the school.

It is impossible to survey the whole students in school.

In order for the survey results to be the best representative of the whole school, it is important to survey students representing each class and group.

So when we survey every fifth student who rides in a car to school, survey will be biases to only the students who travels in car.

When the survey only done to seventh grade students, it is also biased.

When the survey is done in art and music classes, again the survey will be biased since only the music students takes place.

If students from every homeroom is selected, it will represent the whole school.

Hence the best method is option B.

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A middle school principal wants to change the lunch menu at the school. The principal surveys the students to determine how the students would feel about the changes. Which survey method will produce the best representative sample? A: survey every fifth student who rides in a car to school B: survey 3 randomly selected students from every homeroom C: survey every tenth seventh grade student during lunch D: survey 5 randomly selected students from every art, drama, and music class

Hello, there!!!!

Given that,

80°,3x° and 2x°are three angles on a st.line.

we have,

2x°+3x°+80°= 180° {The total sum of angles on a st. line is 180°}.

or, 5x°= 180°-80°

or, 5x°=100°

or, x= 100°/5

Therefore the value of x is 20°.

Hope it helps...

The values in the missing places are 26, 52, 14, 40 and 50

A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.

Given is a frequency table with some missing places,

For every missing places, we just need to add or subtract from the total.

Types of food                                             Age

                                            child          adult (18+)              Total

Fruit                                       26                  26                        52

Vegetable                              14                  24                        38

Total                                       40                  50                       90

First missing place = 50-24 = 26

Second missing place = 26+26 = 52

Third missing place = 38-24 = 14

Fourth missing place = 26+14 = 40

Fifth missing place = 90-40 = 50

Hence, The values in the missing places are 26, 52, 14, 40 and 50

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Answer: Ron's z-score is +1.2.

B. 1.2 standard deviation above the mean .

Step-by-step explanation:

Let X deontes the scores of the final exam

Given : Ms. Meyer's statistics class follow a normal distribution with Mean =  82

standard deviation =5.1

Formula : \(z=\dfrac{X-Mean}{Standard \ deviation}\)

Ron scored 88 on the final.

So, put x=88

\(z=\dfrac{88-82}{5.1}=\dfrac{6}{5.1}\approx1.2\)

Ron's z-score is +1.2.

Also, 88= 86+(1.2 x 5.1) = Mean +1.2 x (standard deviation)

i.e.  This means that Ron's final score is 1.2 standard deviation above the mean .

Answer:

A) Upper limit = 7.39

Lower limit = 6.37

Margin of error = 0.51

B)Sample size = 87

C) Upper limit = 2218.50

Lower limit = 1909.50

Margin of error = 154.50

Step-by-step explanation:

We are given;

x¯ = $6.88 per 100 pounds

σ = $1.98 per 100 pounds

n = 45

A) We want to find a 90% Confidence interval. It means the significance level is; 1 - 0.9 = 0.1

Critical z-value for significance level of 0.1 is z = 1.645

Now, margin of error is;

MOE = zσ/√n

MOE = (1.645 × 1.98)/√40

MOE ≈ 0.51

Confidence interval is;

CI = x¯ ± MOE

CI = 6.88 ± 0.51

CI = ((6.88 + 0.51), (6.88 - 0.51))

CI = (7.39, 6.37)

Upper limit = 7.39

Lower limit = 6.37

B) We are given E = 0.35

Thus;

E = zσ/√n

Rearranging, we have;

n = (zσ/E)²

n = (1.645 × 1.98/0.35)²

n ≈ 87

Sample size = 87

C)We are told that the farm brings 15 tons of watermelon to market.

Also, 1 ton = 2000 pounds

Thus;

15 tons = 15 × 2000 pounds = 30000 pounds

Now this is per 100 pounds.

Thus, we can write as: 30000/100 = 300 pounds

So;

x¯ = 300 × 6.88

x¯ = 2064

σ = 1.98 × 300

σ = 594

Critical z-value for significance level of 0.1 is z = 1.645

Now, margin of error is;

MOE = zσ/√n

MOE = (1.645 × 594)/√40

MOE ≈ 154.50

Confidence interval is;

CI = x¯ ± MOE

CI = 2064 ± 154.50

CI = (2064 + 154.50, 2064 - 154.50)

CI = (2218.5, 1909.5)

Upper limit = 2218.50

Lower limit = 1909.50

Answer:

4,896sq

Step-by-step explanation:

just multiply bro

Answer:

104m²

Step-by-step explanation:

\(Area =\frac{b_{12} + b_{2}}{2}*h=\frac{9+17}{2}*8=104m^{2}\)

Answer:

yes

Step-by-step explanation:

An arbitrary right triangle can be partitioned into isosceles triangle by drawing a median from the right angle to the hypotenuse.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Let's take a right angled triangle ΔABC.

Let C be the right angle in this triangle.

Then AB will be the longest side of the triangle, which is the hypotenuse.

Median of a triangle is the line segment joining the vertex to the midpoint  of the opposite side of the triangle.

Suppose we draw a median from C to the midpoint of AB intersecting AB at a point P.

Then there are two triangles formed ΔAPC and ΔBPC.

AP = BP since P is the midpoint of AB.

PC = PC is the common side for both triangles.

So ΔAPC and ΔBPC are isosceles triangles, because two sides are equal.

Hence any right triangle can be partitioned into two isosceles triangles this way.

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The possible price for the items if the store sells $600 is (c) $40

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

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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The point (1,6) belongs to the solution region of the system of inequalities.

The system of inequalities is given as:

y>1.5^x + 4

y< 2/3x + 6

Next, we plot both inequalities on a graph (see attachment)

From the attached graph, the point (1,6) is on the solution region of the inequalities

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Answer is:

a= 90-70

=20

Answer:

The missing angle is 20°

Step-by-step explanation:

The square by the vertex indicates that this is a right angle. A right angle measures 90°. So what you can do is subtract the 70° from the 90°, to get 20°.

Hope this helps! Have a great day! :)

Answer: \(5.301\) x \(10^{7}\)

Answer: x10^7

Step-by-step explanation: 5.301 = x10^7

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:

The interval for 95% will be given as,

Pr(X) = μ ± 2σ

Pr(X) = 200 ± 2(40)

Pr(X) = 200 ± 80

Pr(X) = (200 - 80, 200 + 80)

Pr(X) = (120, 280)

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

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Answer:

74 inches

Step-by-step explanation:

87

Answer:

Step-by-step explanation:

To find the two consecutive natural numbers whose sum is 575, we can set up the following equation:

x + (x+1) = 575

where x and x+1 are the two consecutive natural numbers.

We can solve this equation by combining like terms:

2x + 1 = 575

Subtracting 1 from both sides, we get:

2x = 574

Dividing both sides by 2, we get:

x = 287

Therefore, the two consecutive natural numbers are 287 and 288. Our final answer is 287, 288.

Answer:

287,288

Step-by-step explanation:

Question

The sum of two consecutive natural numbers is 575. Find the numbers

soln

x +( x + 1) = 575

x + x + 1 = 575

2x + 1 = 575

2x = 575 – 1

2x = 574

\( \frac{2x}{2} = \frac{574}{2} \)

x = 287

since we got x as 287, lets solve(x+1)

by substituting

287 + 1 = 288

hence the consecutive numbers are 287,288

Check

287 + 288 = 575

we are correct.

i hope this helps

Answer:

A

Step-by-step explanation:

If the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

If the triangle on the left had the same area as the circle on the right, it would mean that the triangle would have to be larger than its current size. This is because the area of a circle is determined by the formula A=πr^2, where r is the radius of the circle.

Therefore, if the area of the circle is equal to the area of the triangle, the radius of the circle would have to be equal to the height of the triangle, and the base of the triangle would need to be wider.

This would result in a larger triangle with a greater surface area than the current triangle. The larger triangle would also have a longer perimeter, which would make it more difficult to enclose and would require more material to construct.

Additionally, the larger triangle would have a higher center of gravity, which could make it more difficult to balance and more prone to tipping over.

Overall, if the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

It is important to consider both the area and the shape of an object when determining its practicality and effectiveness in a given situation.

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If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Answer: Both angles are 88 degrees each

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

Work Shown:

Angle ABC is cut in half.

The smaller pieces ABD and DBC are the same measure

angle ABD = angle DBC

10x-42 = 6x+10

10x-6x = 10+42

4x = 52

x = 52/4

x = 13

We then use this to find each angle

angle ABD = 10x-42 = 10*13-42 = 88

angle DBC = 6x+10 = 6*13+10 = 88

Both angles are equal to 88 degrees, so we've confirmed the answer.

The solution of the given algebraic expression is: ⁷/₁₂ + ⁴/₆q

We are given the algebraic expression as:

¹¹/₁₂ - ¹/₆q + ⁵/₆q - ¹/₃

Combining Like terms gives us:

(¹¹/₁₂ - ¹/₃) + (⁵/₆q - ¹/₆q)

Solving both brackets individually gives us:

((11 - 4)/12) + ⁴/₆q

= ⁷/₁₂ + ⁴/₆q

Thus, we conclude that is the solution of the given algebraic expression problem

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The bank reconciliation reveals various errors and discrepancies between ABC Company's records and the bank statement, including missing deposits, incorrect check charges, outstanding checks, unrecorded interest proceeds, fees, NSF charges, and recording errors.

Upon analyzing the bank reconciliation for ABC Company, several discrepancies between the company's records and the bank statement are identified:

A deposit of Br. 410.90 made after banking hours does not appear on the bank statement. This indicates that the deposit was not processed by the bank before the statement was generated.

A check drawn for Br. 79 was charged by the bank as Br. 973. This suggests an error by the bank in processing the check, resulting in an incorrect charge to ABC Company.

Outstanding checks are checks issued in July but have not yet been paid by the bank. The checks include check numbers 801, 888, 890, and 891, with respective amounts of Br. 100.00, Br. 10.25, Br. 294.50, and Br. 205.00.

A check written for Br. 210 was charged by the bank as Br. 120, indicating an error in the bank's recording.

The proceeds from the collection of an interest-bearing note receivable from David, with a face amount of Br. 500, are not reflected in the bank statement.

A Br. 24.75 interest earned on the average account balance during July is included in the bank statement.

A check for Br. 10, which was recorded in the check register as Br. 100, was returned with the statement. This discrepancy could be due to an error in recording the check amount.

A Br. 5.00 fee was charged by the bank for handling the collection of a note receivable.

A Br. 50.25 check from customer John, deposited by ABC Company, was charged by the bank as Non-Sufficient Funds (NSF), indicating that the customer's check bounced.

A Br. 12.70 service charge was imposed by the bank for the month of July.

Check number 875 was issued on July 20 for Br. 85 but was erroneously recorded in the cash payment journal as Br. 58 for the payment of telephone expenses.

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Answer:

The trinomial is already factored

Step-by-step explanation:

(x+h)^3 expanded is x^3+3x^2h+3xh^2+h^3, and (x+h)^3 is the factored form of the polynomial.

y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

The equation y= -2 -4x in the form of slope intercept form y=mx+b is y=-4x-2.

Where m represents the slope and y intercept is -2.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

The negative reciprocal of -4 is 1/4.

Therefore, the slope of the perpendicular line is 1/4.

The perpendicular line is y=1/4x-2.

We know that the parallel lines have same slope.

y=-4x+3

Hence, y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

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Answer:

95% confidence interval for the proportion of days that IBM stock increases.

(0.45814 , 0.58146)

Step-by-step explanation:

Step:1

Given that a stock market analyst notices that in a certain year, the price of IBM stock increased on 131 out of 252 trading days.

Given that the sample proportion

                      \(p^{-} = \frac{131}{252} = 0.5198\)

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step:2

95% confidence interval for the proportion of days that IBM stock increases.

\((p^{-} - Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p^{-} + Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } )\)

\((0.5198 - 1.96(\sqrt{\frac{0.5198(1-0.5198)}{252} } , 0.5198 +1.96(\sqrt{\frac{0.5198(1-0.5198)}{252} })\)

(0.5198 -  0.06166 , 0.5198+0.06166)

(0.45814 , 0.58146)

Final answer:-

95% confidence interval for the proportion of days that IBM stock increases.

(0.45814 , 0.58146)

Answer:

Domain: (-∞, -4) U (-4,∞)

range: (0,∞)

6 cos(π/2 t) is the best model for the position of the weight.

The motion of the weight on the spring can be modeled by a sine or cosine function because it oscillates back and forth around its equilibrium position.

We know that, the weight is initially pulled down 6 inches from its equilibrium position, so the function should have an amplitude of 6.

The time it takes for the spring to complete one oscillation is 4 seconds, so the period of the function is 4 seconds.

The general form of a sine or cosine function with amplitude A and period T is:

f(t) = A sin(2πt/T) or f(t)

= A cos(2πt/T)

Substituting the given values,

we get:

f(t) = 6 sin(2πt/4) or f(t)

= 6 cos(2πt/4)

Simplifying, we get:

f(t) = 6 sin(π/2 t) or f(t)

= 6 cos(π/2 t)

Therefore,

the function that best models the position of the weight is

s(t) = 6 cos(π/2 t).

So, the answer is option (D).

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The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

7.321852048×10³⁰

Step-by-step explanation: