Explain Mean Value Theorem ​

Answer:

It is 4

Step-by-step explanation:

the slope is -4

hope this helps!!

Answer:

the slope is -4

Step-by-step explanation:

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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The parts of the graph when labelled are :

There is the origin which is where the line starts from. The x-axis represents the independent variable, which is the variable that is being manipulated or changed in the experiment.

The y-axis represents the dependent variable, which is the variable that is being measured or observed. A trend line is a line drawn on the graph that shows the overall pattern or trend of the data. The x and y - intercepts are the points where the trend line crosses the x and y - axis.

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Discuss measures that can be taken to develop the spirit of hard work

Answer:

---------------

Let the numbers be s and l.

We are given that:

Set up equations:

Eliminate l:

Solve for s:

Find l:

Step-by-step explanation:

Possible question so that I can help you with the solution

no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

Step-by-step explanation:

no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

3.759*10^7

Step-by-step explanation:

Step-by-step explanation:

you will end up paying $66 dollars

Answer: 4

Step-by-step explanation:

4+3+5=12

12/3=4

Answer:

(-7,-63)

Step-by-step explanation:

Answer:

n = 195

Step-by-step explanation:

What sample size is necessary such that a 98% confidence interval for the mean, using σ = 3, has a width of pm±0.5?

We solve using Margin of error formula

= z × Standard deviation/√n

Margin of error = ± 0.5

Standard deviation = 3

n = ??

z = 2.326

Hence,

±0.5 = 2.326 × 3/√n

Cross Multiply

±0.5 × √n = 6.978

√n = 6.978/±0.5

√n = ±13.956

Square both sides

n = (±13.956)²

n = 194.769936

Approximately = 195 samples

Answer:

x > -3

Step-by-step explanation:

-3x + 6 < 15

-3x < 15 - 6

-3x < 9

-x < 3

x > -3

A. x > -3

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

−3x + 6 − 6 < 15 − 6

−3x < 9

Step 2: Divide both sides by -3.

−3x/−3 < 9/−3

x > −3

Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer: True

Step by step explanation

Answer:

The answer is 3x12 + 3x6

Step-by-step explanation:

You have to multiply each number inside the brackets by the number outside the brackets

3(12+6)

= 3x12 + 3x6

= 36 + 18

= 54

The baker would need 47. 25 cups of floor

We need to know that proportion is a form of mathematical comparison with two equations made equal to each other.

From the information given, we have that;

baker used 33 3/4 cups of flour to make 15 batches of cookies

This is represented as;

Convert to improper fractions

135/4 cups = 15 batches of cookies

Then, x cups = 21 batches of cookies

cross multiply the values

15x = 708. 75

Divide both sides by the coefficient of x, we have ;

x = 708. 75/15

x = 47. 25 cups of floor

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Answer:

a) Mean of D = -25

Standard deviation of D = 11.18

b) P(N > J ) = 0.9875

Step-by-step explanation:

Given - μₙ = 25, σₙ = 5 , μₐ = 50 , σₐ = 10

where μₙ is mean of nick and  μₐ is mean of jasmine

 σₙ = 5 is standard deviation of nick and σₐ is standard deviation of jasmine

To find - a) Define the random variable D to be the difference between the      amount of time spent on a randomly selected assignment of Jasmine’s and a randomly selected assignment of Nick’s. So D = N – J. Find the mean and the standard deviation of D.

b) Calculate the probability that Nick spent longer doing his assignment than Jasmine did. Show your method clearly.

Proof -

a)

Mean of D = Mean of nick - Mean of jasmine

                  = 25 - 50 = -25

standard deviation of D = √Standard deviation of Nick + jasmine

                                       = √5² + 10² = √25 + 100 = √125 = 11.18

∴ we get

Mean of D = -25

Standard deviation of D = 11.18

b)

We have to find - P(N > J)

If N > J , then D > 0

Now,

The z-score is expressed as

z = \(\frac{0 - (-25)}{11.18} = \frac{25}{11.18} = 2.24\)

Now,

P(N>J) = P (D > 0) = P(Z < 2.24)

                            = 0.9875

⇒P(N > J ) = 0.9875

Step-by-step explanation:

Using the rule of  P E D M A S  :

=3 + (4)  x (-9)

 = 3 - 36 = -33

The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

<95141404393>

Hello-

Here is the way that I learned to multiply decimals. First, remove the decimal points.

2.37 X 1.6

237 X 16

Then you multiply the numbers.

237 X 16 = 3792

Now, we move the decimal point three places to the left on our answer.

3.792

3.792 is our answer.

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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Using simple Subtraction, following is the required data.

point A always begins at 45 and point B at 69,

b) If A moves 2 units to the right, and B moves 2 units to the left, the points will be 20 units apart. (47 - 67)

c) If A moves 2 units to the left, and B moves 2 units to the right, the points will be 28 units apart. (43 - 71)

D) If A moves 10 units to the right, and B moves 10 units to the left, the points will be 4 units apart. (59 - 55)

e) If A moves 12 units to the right, and B moves 12 units to the left, the points will be 0 units apart.

f) A moved units to the left, B moved the same number of units to the right, and the points became 48 units apart.​

We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.

Subtraction can be applied in a variety of real-world situations.

Assume you had five apples and your friend had three. The number of remaining apples may be determined by subtracting: 5 - 3 = 2. Therefore, you are left with 2 apples. Similar to the previous example, if a class has 16 students, 9 of them are girls, we can determine the number of boys in the class by deducting 9 from 16. (16 - 9 = 7). There are 7 lads in the class, as far as we know.

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Answer:

b

Step-by-step explanation:

Answer:

30% increase

Step-by-step explanation:

percentage increase is calculated as

\(\frac{increase}{original}\) × 100%

increase = $35.10 - $27 = $8.10 , then

percentage increase = \(\frac{8.10}{27}\) × 100% = 0.3 × 100% = 30%

Answer:

Step-by-step explanation:

step 1:       35.10-27 =8.1

step 2:       8.1/27 x 100 = 30%

so therefore = 30% increase

Answer:

x > -1/3

Step-by-step explanation:

1. Distribute the 9 to the (2-x) and the -4 to the (2-3x).

       18-9x-8+12x > 9

2. Combine like terms.

       3x+10 > 9

3. Subtract the 10 from both sides.

      3x > -1

4. Divide -1 by 3.

      x > -1/3

Hope this helps! :)

Answer:

En este problema se trata de una función exponencial, donde la cantidad de microbios en el recipiente se duplica cada minuto.

Si x representa el número de minutos transcurridos y y la cantidad de microbios en el recipiente, entonces se puede expresar la función exponencial como:

y = a * (2)^x

Donde "a" es la cantidad inicial de microbios en el recipiente, en este caso a = 1.

Después de 30 minutos, la cantidad de microbios en el recipiente es:

2^30 = 1,073,741,824

Esto significa que si se coloca un solo microbio en el recipiente, se tardará 30 minutos en llenarlo.

Si se colocan 2 microbios en el recipiente, entonces la cantidad inicial de la función exponencial es a = 2, y se busca el valor de x tal que:

2 * (2)^x = 1,073,741,824

Dividiendo ambos lados por 2, se tiene:

(2)^x = 536,870,912

Tomando logaritmos base 2 en ambos lados, se tiene:

x = log2(536,870,912) = 29

Por lo tanto, si se colocan 2 microbios en el recipiente, se tardará 29 minutos en llenarlo.

Step-by-step explanation:

The measure of angle 5 of the exterior hexagon is  m∠5 = 60°.

From the diagram, the shape is a hexagon, so that the total measures of its 6 interior angles are 720 degree.

We assume the interior angles of the hexagon are 1', 2', 3', 4', 5' and 6'.

As all angles 1, 2, 3, 4, 5, 6 are exterior angles of the hexagon, so that we have 6 pairs of supplementary angles: 1 and 1'; 2 and 2'; 3 and 3'; 4 and 4'; 5 and 5'; 6 and 6'.

m∠1 + m∠1' = m∠2 + m∠2' = m∠3+m∠3' = m∠4 + m∠4' = m∠5 + m∠5' = m∠6 + m∠6' = 180⁰

m∠1 + m∠1' + m∠2 + m∠2' + m∠3+m∠3' + m∠4 + m∠4' + m∠5 + m∠5' + m∠6 + m∠6' = 180 × 6 = 1080

(m∠1 + m∠2 + m∠3 + m∠4 + m∠5+m∠6) + (m∠1' + m∠2' + m∠3' + m∠4' + m∠5' + m∠6') = 1080

(m∠1 + m∠2 + m∠3 + m∠4 + m∠5+m∠6) + 720 = 1080

(m∠1 + m∠2 + m∠3 + m∠4 + m∠5 + m∠6)  = 360 (1)

From the question, we know that:

m∠6 = 90

∠1 ≅ ∠2 ≅ ∠3

∠4 ≅ ∠5

Replace ∠1, ∠2 by ∠3; ∠5 by ∠4; ∠6 = 90 in the equation (1), we have;

m∠3 + m∠3 + m∠3 + m∠4 + m∠4 + 90 = 360

3m∠3 + 2m∠4 =270 (2)

As given: m∠4 = m∠3 + 10°

Replace in the equation (2), we have:

3m∠3 + 2 × (m∠3 + 10) =270

3m∠3 + 2m∠3 + 20 = 270

5m∠3 = 270 -20 = 250

m∠3 = 250/5 = 50°

m∠4 = m∠3 + 10° = 50 + 10 = 60°

As ∠4 ≅ ∠5 => m∠5 ≅ m ∠4 = 60°

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Explanation:

Point L is located at (-8, 1) while P is at the point (7,7)

Let's apply the slope formula for these two points

m = (y2-y1)/(x2-x1)

m = (7-1)/(7-(-8))

m = (7-1)/(7+8)

m = 6/15

m = (3*2)/(3*5)

m = 2/5 is the slope of line LP

A slope of 2/5 means that each time you go up vertically 2 units (rise), you move to the right 5 units (run). In short, it's "up 2, over to the right 5". A positive slope means we move upward as we move from left to right.