An isosceles triangle with legs of 8 cm and a base of 10 cm in length has a median drawn
from its vertex angle to its base. What is the length of this segment?

Answer

∛(107) ≅ 5

Explanation

The squeeze approach uses approximations of perfect cubes around the number to approximate its cube roots.

Let the cube root of 107 be x

∛(107) = x

x³ = 107

We can then write the perfect cubes around this number

2³ = 8

3³ = 27

4³ = 64

5³ = 125

We can easily see that 107 is between the two perfect cube numbers 64 and 125.

Since 107 is far closer to 125 than 64, the closest approximation for ∛(107) will be x = 5

∛(107) ≅ 5

5³ ≅ 107

Hope this Helps!!!

The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two: , the raw score is relatively lower than the mean.

If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.

A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two:

If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.

To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.

In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.

By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.

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Answer:

\(r = 1.34\)

Step-by-step explanation:

Given

Solid = Cylinder + 2 hemisphere

\(Volume = 10cm^3\)

Required

Determine the radius (r) that minimizes the surface area

First, we need to determine the volume of the shape.

Volume of Cylinder (V1) is:

\(V_1 = \pi r^2h\)

Volume of 2 hemispheres (V2) is:

\(V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3\)

\(V_2 = \frac{4}{3}\pi r^3\)

Volume of the solid is:

\(V = V_1 + V_2\)

\(V = \pi r^2h + \frac{4}{3}\pi r^3\)

Substitute 10 for V

\(10 = \pi r^2h + \frac{4}{3}\pi r^3\)

Next, we make h the subject

\(\pi r^2h = 10 - \frac{4}{3}\pi r^3\)

Solve for h

\(h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}\)

\(h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}\)

\(h = \frac{10}{\pi r^2} - \frac{4r }{3}\)

Next, we determine the surface area

Surface area (A1) of the cylinder:

Note that the cylinder is covered by the 2 hemisphere.

So, we only calculate the surface area of the curved surface.

i.e.

\(A_1 = 2\pi rh\)

Surface Area (A2) of 2 hemispheres is:

\(A_2 = 2\pi r^2+2\pi r^2\)

\(A_2 = 4\pi r^2\)

Surface Area (A) of solid is

\(A = A_1 + A_2\)

\(A = 2\pi rh + 4\pi r^2\)

Substitute \(h = \frac{10}{\pi r^2} - \frac{4r }{3}\)

\(A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2\)

Open bracket

\(A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2\)

\(A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2\)

\(A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2\)

\(A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2\)

Take LCM

\(A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}\)

\(A = \frac{20}{r} + \frac{4\pi r^2}{3}\)

Differentiate w.r.t r

\(A' = -\frac{20}{r^2} + \frac{8\pi r}{3}\)

Equate A' to 0

\(-\frac{20}{r^2} + \frac{8\pi r}{3} = 0\)

Solve for r

\(\frac{8\pi r}{3} = \frac{20}{r^2}\)

Cross Multiply

\(8\pi r * r^2 = 20 * 3\)

\(8\pi r^3 = 60\)

Divide both sides by \(8\pi\)

\(r^3 = \frac{60}{8\pi}\)

\(r^3 = \frac{15}{2\pi}\)

Take \(\pi = 22/7\)

\(r^3 = \frac{15}{2 * 22/7}\)

\(r^3 = \frac{15}{44/7}\)

\(r^3 = \frac{15*7}{44}\)

\(r^3 = \frac{105}{44}\)

Take cube roots of both sides

\(r = \sqrt[3]{\frac{105}{44}}\)

\(r = \sqrt[3]{2.38636363636}\)

\(r = 1.33632535155\)

\(r = 1.34\) (approximated)

Hence, the radius is 1.34cm

The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.

Given :

The volume of a cylinder is given by:

\(\rm V = \pi r^2 h\)

The total volume of the two hemispheres is given by:

\(\rm V' = 2\times \dfrac{2}{3}\pi r^3\)

\(\rm V' = \dfrac{4}{3}\pi r^3\)

Now, the total volume of the solid is given by:

\(\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3\)

Now, substitute the value of the total volume in the above expression and then solve for h.

\(\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3\)

\(\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}\)

Now, the surface area of the curved surface is given by:

\(\rm A = 2\pi r h\)

Now, the surface area of the two hemispheres is given by:

\(\rm A'=2\times (2\pi r^2)\)

\(\rm A'=4\pi r^2\)

Now, the total area is given by:

\(\rm A_T = 2\pi rh+4\pi r^2\)

Now, substitute the value of 'h' in the above expression.

\(\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2\)

Simplify the above expression.

\(\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}\)

Now, differentiate the total area with respect to 'r'.

\(\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}\)

Now, equate the above expression to zero.

\(\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}\)

Simplify the above expression in order to determine the value of 'r'.

\(8\pi r^3=60\)

r = 1.34 cm

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The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Answer:

Whats the question?

The 15th term of the sequence is 119.

What is arithmetic sequence?

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

We can find the common difference between any two consecutive terms in the sequence by subtracting the previous term from the current term. Doing this for the first two terms, we get:

2 - (-7) = 9

So, the common difference is 9. We can use this to find the 15th term as follows:

t15 = t1 + (n - 1)d

where t1 is the first term, d is the common difference, and n is the number of the term we want to find (in this case, n = 15).

t15 = -7 + (15 - 1)9

t15 = -7 + 14 × 9

t15 = -7 + 126

t15 = 119

Therefore, the 15th term of the sequence is 119.

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Answer:

Q1

The exponential growth model for frogs:

F- number of frogs, x- number of years, 1.22 - growth factor

Calculations:

All numbers rounded

Q2

The exponential growth model for bacteria:

B- number of bacteria, x- number of hours, 1.8 - growth factor

Calculations:

All numbers rounded

Q3.

The exponential growth model for fish:

F- number of fish, x- number of months, 1.02 - growth factor

Calculations:

All numbers rounded

Answer:

a) F(12) = 821(1.02)¹² = 1041

b) F(120) = 821(1.02)¹²⁰ = 8838

All numbers rounded

Answer:

C. a quadratic function with a negative value of a

Step-by-step explanation:

It is likely that a quadratic function with a negative value of a would be the best model for this data, as it would represent a parabolic shape that can accommodate a downward trend, followed by an upward trend, in the stock price. The value of "a" determines the direction of the parabola, with a negative value resulting in a downward-facing parabola, which is appropriate for a stock price that starts low and increases over time. This type of function would provide a good fit for the data, especially if there are fluctuations or ups and downs in the stock price over time.

Answer:5+2=?

absolute value of -5 is 5

absolute value of -2 is 2

Step-by-step explanation:

Answer:

A. LM ⊥ MN. D. The triangle is isosceles. E. The triangle is a right triangle.

Step-by-step explanation:

edge 2020 <3

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

Answer: 20

Step-by-step explanation: that is 60%=60*100

=6000 =6000/300   =20 boo who                                                                                                                                          

Answer:

The function g(x) = -x° belongs to the family of constant functions. A constant function is a function where the output value is the same for every input value. In this case, the output value is always 0, regardless of the input value of x.

Answer:

11

Step-by-step explanation:

6^2+9^2=c^2

36+81=c^2

117=c^2

\(\sqrt{117\\\)

11

The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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Answer:

B. y=1/2x+7

Step-by-step explanation:

y2-y1/x2-x1 this finds the slope

Then take one of the coordinates: either (2,8) or (4,9) and plug them into x and y to find b (the y-int)

Answer:

Step-by-step explanation:

(2, 8) (4, 9)

(9 - 8)/(4 - 2) = 1/2

y - 8 = 1/2(x - 2)

y - 8 = 1/2x - 1

y = 1/2x + 7

B is the answer

Answer:

B

Step-by-step explanation:

MOVE TO THE RIGHT 9 TIMES!!

Answer:

slope -1/3 y-intercept (0,4)

Step-by-step explanation:

Answer:

See attached image for the graph

Step-by-step explanation:

Start by finding at least two points on the plane that satisfy the equation, and join them with a line.

Pick good values for "x" that will make the evaluation easy (for example the number "0" and also multiples of "3":

when x = 0  then y = 0/3 - 4 = -4   then the point is (0, -4)

when x = 3 then y = 3/3 -4 = 1 - 4 = -3  then this new point is (3, -3)

when x = 6 then  y = 6/3 - 4 = 2 - 4 = -2  then a third point is (6, -2)

We plot these points on the plane, and join them with a line, s shown in the attached image.

Answer: 14

Step-by-step explanation:

Input Data :

Point 1  ( x A , y A )  = (-4, -8)

Point 2  ( x B , y B )  = (10, -8)

Objective :

Find the distance between two given points on a line?

Formula :

Distance between two points =  √ (x B − x A ) 2 + ( y B − y A ) 2

Solution :

Distance between two points =  √ ( 10 −  − 4 ) 2 + ( − 8 −  − 8 ) 2

=  √ 14 ^2 + 0 ^2

=  √ 196 + 0

=  √ 196 = 14

Distance between points (-4, -8) and (10, -8) is 14

Answer: 14

Step-by-step explanation:

Answer:

The answer of x will be 20

Step-by-step explanation:

Since both angels are the same then you would take 140-20 and then divide  that answer by six and you get 20.

I hold I could Help :)

To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively

Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class

The given parameters that will help us to get the percentage are

Mean height of the class = 152 cm

Mean height of the boys = 158 cm

The standard deviation of the boys = 5 cm

Mean height of the girls = 148 cm

Standard deviation of the girls = 4 cm

(1) The percentage of boys in the class is

Total mean height = 158 +148 = 306

Percentage = 158/306 * 100 = 51.6%

Then the  percentages 51.6/100 * 152 = 78%

(2) The total standard deviation of all the students

Boys + girls = 5+4 = 9 cm

Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively

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\(\text{Given that,}~f(x)=x^3-2x^2\\\\f(i)=i^3-2i^2\\\\~~~~~~=i^2 \cdot i -2(-1)~~~~~;[i^2=-1]\\\\~~~~~~=-i+2\\\\~~~~~~=2-i\)

The expression equivalent to f(i) is 2-i.

The expression is mathematical statement which consist of variables, numbers and connected by at least one operation.

Given that, a function f(x) = x³ - 2x², we need to find the expression equivalent to f(i),

To find the same we will put x = i,

So,

f(i) = i³ - 2i² [i = √-1]

= (√-1)³ - 2(√-1)²

= -i - 2(-1)

= -i+2

= 2-i

Hence, the expression equivalent to f(i) is 2-i.

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