If the range of the data is 40, find the mean value by showing your detailed work. 23, 24, 27, 35, 38, X For the toolbar, press ALT+F10 (PC) or ALT-FN-F10 (Mac) ...

Answer:

4 is the answerrrrrr........

Answer:

4........

....

.......

Mathematics is a fundamental subject in education that is essential in the development of an individual’s critical thinking and problem-solving skills. It is one of the primary subjects that are taught in elementary schools and must be taught appropriately for children to understand and gain the required skills. One true statement about mathematics teaching in elementary schools is that it should be student-centered.

Teachers should focus on the child's understanding, individual learning abilities and styles, and progress.The learning experience should not be centered on the teacher but on the students. Teachers should also make the subject engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject. Besides, teachers should develop a personalized learning approach that allows students to learn and understand the subject at their own pace while creating opportunities for individual and group learning. Through such learning approaches, students can develop the required mathematical concepts and competencies such as critical thinking, problem-solving, and decision-making skills that will be beneficial in their future endeavors.

In elementary schools, mathematics teaching should be student-centered. It should be engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject.

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Answer:

8/21

Step-by-step explanation:

2/7 divided by 3/4

Keep

2/7

Change

divided to multiply

Flip

3/4 to 4/3

Multiply

2/7 x 4/3

Multiply the numerators and deniminators to get 8/21

Cannot be simplified so it is the final answer.

Answer:

25

Step-by-step explanation

8x+5x+4x=180-6+1

17x=175

x=25

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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The area of the cylinder is 3, 399. 74 square centimeters

The formula for calculating the area of  a cylinder is expressed with the equation;

A = 2πrh + 2πr²

Given that the parameters are;

From the information given, we have that;

Radius, r = 13.4 centimeters

Height, h = 27 centimeters

Now, subsitute the values, we get;

Area = 2× 3.14 × 13. 4× 27 + 2× 3.14 × (13.4)²

expand the bracket

Area = 2272. 104 + 1127.64

Add the values

Area = 3, 399. 74 square centimeters

Hence, the value is 3, 399. 74 square centimeters

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Answer:

1 cubic foot

Step-by-step explanation:

1*1*1 = 1

Answer:

6 maybe

Step-by-step explanation:

The part of the coordinate plane that is equidistant from the points A(-3, 2) and B(3, 2) is the horizontal line with a y-coordinate of 2.

The points A(-3, 2) and B(3, 2) have the same y-coordinate, which means they lie on a horizontal line. The midpoint of the line segment AB will also lie on this line.

To find the midpoint, we can average the x-coordinates and the y-coordinates of the two points.

The x-coordinate of the midpoint is (-3 + 3) / 2 = 0 / 2 = 0.

The y-coordinate of the midpoint is (2 + 2) / 2 = 4 / 2 = 2.

Therefore, the midpoint of AB is (0, 2).

Since the midpoint lies on the same horizontal line as the points A and B, any point on this line will be equidistant from A and B. This line is parallel to the x-axis and has a y-coordinate of 2.

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The value of z, In the above statistics-based question where the area to the right of z is 0.9803, is approximately 1.81.

In statistics, the standard normal distribution is a specific distribution of normal random variables with a mean of 0 and a standard deviation of 1. The area under the curve of a standard normal distribution is equal to 1, and the distribution is symmetric around the mean of 0.

To find the value of z for a given area to the right of z, we can use a standard normal distribution table or calculator. For example, using a standard normal distribution table, we can find the value of z that corresponds to an area of 0.0197 to the left of z. This value is approximately -1.81. Since the area to the right of z is 0.9803, we can find the value of z by subtracting -1.81 from 0, which gives us approximately 1.81.

Alternatively, we can use the inverse normal distribution function in Excel or another statistical software package to find the value of z directly. For example, the Excel function NORMSINV(0.9803) returns a value of approximately 1.81, which is the same as the value we obtained using the standard normal distribution table.

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Answer:

See solution below

Step-by-step explanation:

Given the expression

\(\frac{cos(x+30)-sin(x+60)}{sin(x)cos(x)} \\\)

Recall that

cos x  = sin(90-x)

cos(x+30 ) = sin (90-(x+30)

= sin(90-x-30)

= sin(60-x)

Substitute

\(\frac{sin(60-x)-sin(x+60)}{sin(x)cos(x)} \\= \frac{sin60cosx-cos60sinx)-sinxcos60-cosxsin60)}{sin(x)cos(x)} \\= \frac{-2cos60sinx)}{sin(x)cos(x)} \\= \frac{-2(1/2)sinx)}{sin(x)cos(x)} \\= \frac{-1}{cos(x)}\\= \frac{1}{cos(x)}\\ \\= -sec(x) Proved\)

Answer:

Yes

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

So -9x is 36,36-2=34

Answer:

34

Step-by-step explanation:

-9(-4)-2

36-2

34

To find the value of f(6), we can use the information given about the function f(x) and its derivative f'(x).The value of f(6) is 44/3.

Given that f'(x) is continuous, we can apply the Fundamental Theorem of Calculus. According to the theorem:

∫[a to b] f '(x) dx = f(b) - f(a)

In this case, we are given that:

∫[1 to 6] 6 f '(x) dx = 16

We can simplify the integral:

6 ∫[1 to 6] f '(x) dx = 16

Since f'(x) is the derivative of f(x), the integral of 6 f '(x) dx is equal to 6 f(x). Therefore, we have:

6 f(6) - 6 f(1) = 16

Substituting the given value f(1) = 12:

6 f(6) - 6(12) = 16

6 f(6) - 72 = 16

Next, we isolate the term with f(6):

6 f(6) = 16 + 72

6 f(6) = 88

Finally, we solve for f(6) by dividing both sides by 6:

f(6) = 88 / 6

f(6) = 44/3

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Given:

In a number, adding \(1\dfrac{3}{4}\), then multiplying the result by \(2\dfrac{2}{11}\) we get 8.

To find:

The unknown number.

Solution:

Let the unknown number be x.

According to the question,

\((x+1\dfrac{3}{4})\times 2\dfrac{2}{11}=8\)

\((x+\dfrac{1\times 4+3}{4})\times \dfrac{2\times 11+2}{11}=8\)

\((x+\dfrac{4+3}{4})\times \dfrac{22+2}{11}=8\)

\((x+\dfrac{7}{4})\times \dfrac{24}{11}=8\)

Multiply both sides by \(\dfrac{11}{24}\).

\(x+\dfrac{7}{4}=8\times \dfrac{11}{24}\)

\(x+\dfrac{7}{4}=\dfrac{11}{3}\)

Subtract \(\dfrac{7}{4}\) from both sides.

\(x=\dfrac{11}{3}-\dfrac{7}{4}\)

\(x=\dfrac{44-21}{12}\)

\(x=\dfrac{23}{12}\)

\(x=1\dfrac{11}{12}\)

Therefore, the required number is \(1\dfrac{11}{12}\).

Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

Answer:

\(\frac{x^2}{16} +xy+4y^2\) can be factored out as: \((\frac{x}{4} +2\,y)^2\)

Step-by-step explanation:

Recall the formula for the perfect square of a binomial :

\((a+b)^2=a^2+2ab+b^2\)

Now, let's try to identify the values of \(a\) and \(b\) in the given trinomial.

Notice that the first term and the last term are perfect squares:

\(\frac{x^2}{16} = (\frac{x}{4} )^2\\4y^2=(2y)^2\)

so, we can investigate what the middle term would be considering our \(a=\frac{x}{4}\), and \(b=2y\):

\(2\,a\,b=2\,(\frac{x}{4}) \,(2\,y)=x\,y\)

Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:

\((\frac{x}{4} +2\,y)^2\)

Answer:

\(\{3\}\)

Step-by-step explanation:

Strictly speaking, we need to know the point of \(f(x) = 3x\) intersecting \(f(x) = 9\). In other words, we need to solve the equality:

\(3x = 9; \\ x = \frac{9}{3}; \\ x = 3\)

Here it is.

Answer:

Step-by-step explanation:

The triangle ABC(on the right hand side) is mirrored about the y-axis and translated one unit in the direction of the negative y-axis and the result the triangle DFE(on the left hand side)

Note that the same result can be obtained by translating then mirroring.

The Size(Area) is actually the same.

So basically If its coordinates was ( x , y )

it's now ( -x , y-1 )

(- minus) Due to Mirroring

(-1) duo to Translating in the negative direction

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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The circumference of the circle is 81.64 mm.

The formula for the circumference of a circle is:

C = πd

where C is the circumference, π (pi) is a mathematical constant that approximates to 3.14, and d is the diameter of the circle.

Substituting the given value, we get:

C = 3.14 x 26 mm

C = 81.64 mm (rounded to two decimal places)

Therefore, the circumference of the circle is 81.64 mm.

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Answer:

\(b = \sqrt{ \frac{ {c}^{2} }{2 {\pi}^{2} } - {a}^{2} } \)

Answer:

5. C

6. Volume is multiplied by 4

Step-by-step explanation:

Answer:

c²=8

Step-by-step explanation:

You must substitute 2 in for the variable "N" and calculate

The length of the race track is 171m

To determine the length of the race track, we need to know that the length takes the shape of a rectangle

Now, we have that the formula that is used for calculating the perimeter of a rectangle is expressed as;

P = 2(l +w)

Such that the parameters of the formula are;

Substitute the values, we have;

Perimeter = 2(25.5 + 60)

expand the bracket, we get;

Perimeter = 2(85.5)

Perimeter = 171 m

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Answer:

correct you are

Step-by-step explanation:

Answer:

nope it's-2.

Step-by-step explanation:

rise over run the point (0,3) is 2 points above the other one and one point to the left. which is -2/1 which is just -2.

Answer:

I think it is 12

Step-by-step explanation: