Determine whether the Mean Value theorem can be applied to fon the closed interval [a, b]. (Select all that apply.) f(x) = 9 sin x, [0, 1] a. Yes, the Mean Value Theorem can be applied. b. No, f is not continuous on [a, b]. c. No, f is not differentiable on (a, b). d. None of the above.

Explanation:

x = number of gigabytes of data used

y = total price

Company A has the equation y = 100. The x variable is not involved since the cost is $100 no matter what.

Meanwhile, company B has the equation y = 5x+20

The slope of 5 indicates how much per gigabyte is charged. The 20 at the end is the flat fee, aka y intercept.

If we were to graph those equations, then we'd find they intersect at (16,100) as mentioned.

This means x = 16 and y = 100 pair up together.

It further tells us that both companies charge the same ($100) when x = 16 gigabytes of data are used.

This points us to choice B as the final answer.

Answer:Pass out the pennies and the dimes to your students. Write a couple of problems on the board that will use regrouping. As you write them, write “ones” over the ones column. Write “tens” over the tens column. Have students take out their coins for each problem.

Step-by-step explanation:

Answer:

55000 grams

Step-by-step explanation:

1 kg = 1000 grams  ==> kilo means 1000, so 1 kilogram = 1000 grams

Now multiply 55 kg with the grams-kilograms conversion factor to get the total number of grams Shaina weighs.

55 kg* 1000 grams / 1 kg =

55 * 1000 grams / 1 =  ==> cancel out the kg

55 * 1000 = 55000 grams

The other two angle measures of triangle XYZ are 35° and 75°.

We are given that the triangles PQR and XYZ are similar.

Also, ∠ZXY = 70°  and ∠PRQ = 35°.

Now, we know that when two triangles are similar, then the corresponding angles are same.

Therefore, ∠XZY = ∠PRQ = 35°

Now, in triangle XYZ, we have ∠XZY = 35° and ∠ZXY = 70°.

Since, we know that the sum of the angles of a triangle is 180°.

So, ∠XZY + ∠ZXY + ∠ZYX = 180°

i.e. 35° + 70° + ∠ZYX = 180°

i.e. ∠ZYX = 180° - ( 35° + 70° )

i.e. ∠ZYX = 180° - 105°

i.e. ∠ZYX = 75°

Hence, the other two angle measures of triangle XYZ are 35° and 75°.

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The answer is 35 and 75 which is A and C

Answer:

No, she would need to print out 4536 pages

Step-by-step explanation:

2 x 28 x 81 = 4536

Answer:

No, that does not sound right.

Ms. Stewart needs to print a total of 4,536 pages in this time!

Step-by-step explanation:

This situation is an example of ratios and proportions.

⭐What is a ratio?

⭐What is a proportion?

Let's set up the 1st ratio:

"Every school day, Ms. Stwewart prints out 2 pages of worksheets for each [student]"

1 student/2 pages

Let's set up the 2nd ratio:

"Ms. Stewart is a teacher with 28 students"

28 students/x pages

Now, we want to solve how many pages Ms. Stewart prints in a day for 28 students.

Thus, we need to set up a proportion with these 2 ratios.

Make sure the same units are on the numerator and denominator.

[tex]\frac{1}{2} = \frac{28}{x}[/tex]

Multiply LHS and RHS by [tex]\frac{1}{28}[/tex] to solve for x.

[tex]\frac{1}{2}(\frac{1}{28}) = \frac{28}{x}(\frac{1}{28})[/tex]

[tex]\frac{1}{56} = \frac{1}{x}[/tex]

∴ Ms. Stewart needs to print 56 worksheets for 1 day.

However, this isn't what the problem is asking us. We want to know how many worksheets Ms. Stewart needs to print for the coming school days.

To find out, we need to make another proportion. We only have 1 ratio so far: 56 worksheets/1 day, so we need to make another one for the coming school days.

Let's set up the 2nd ratio:

"There are 81 school days left in this school year."

y worksheets/ 81 days

Thus, we need to set up a proportion with these 2 ratios.

Make sure the same units are on the numerator and denominator.

[tex]\frac{56}{1} = \frac{y}{81}[/tex]

Multiply both sides by 81 to isolate y.

[tex]56(81) = \frac{y}{81}(81)[/tex]

[tex]y = 4,536[/tex]

∴ Ms. Stewart needs to print 4,536 worksheets for the next 81 days!

The rate of change of y with respect to x for a given line is 4/5.

What is the rate of change?

The rate of change is measured by a line's slope. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.

The rate of change of y with respect to x for a given linear function is simply the slope expressed as:

dy/dx = (y2 - y1)/(x2 - x1)

Let us take the first 2 coordinates from the graph which are:

(0, 3) and (5, 7)

Thus;

dy/dx = (7 - 3)/(5 - 0)

dy/dx = 4/5

Hence, the rate of change of y with respect to x for a given line is 4/5.

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Answer:

[tex]y=2^x-5[/tex]

Step-by-step explanation:

The y-intercept occurs when x = 0.

Therefore, substitute x = 0 into each equation to find its y-intercept.

[tex]\begin{aligned}\implies y&=(-4)^0\\&=1\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=2^0-5\\&=1-5\\&=-4\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=3^0+4\\&=1+4\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=(0)^{-4}\\&=0\end{aligned}[/tex]

Therefore, the exponential function that has a y-intercept of (0, -4) is:

[tex]\large\boxed{y=2^x-5}[/tex]

Check the picture below.

The percent increase in the cost to Deb, to fly from Boston to Hartford is  25%

If the airline charges an additional $50 baggage fee then the percent increase would be 41.67%

The percent increase to Deb to fly from Boston to Hartford can be found by the formula:

= ( Cost to fly now - Cost to fly two weeks ago ) / Cost to fly two weeks ago

= ( 375 - 300 ) / 300

= 0. 25

= 25%

If an  additional​ $50 baggage fee is added to the new price, the percent increase is:

= ( (375 + 50 ) - 300 ) / 300

= 41.67%

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In the picture we can see the graph represents of the function f(x)=x²-2x+3 that is curve graph.

Given that,

We have to find the graph represents the function f(x)=x²-2x+3.

We know that,

The quadratic function is f(x)=x²-2x+3.

This is a vertical parabola open downward

The vertex is a maximum

We know,

A vertical parabola's equation in vertex form is equal to

y= a(x-h)²+k

where

a is a coefficient

(h,k) is the vertex

Here

a=1

(h,k)=(0,3)  is vertex

The y-intercept is the point (0,3) is value of y when the value of x is equal to zero (is the same point that the vertex)

The x-intercepts are the points is values of x when the value of y is equal to zero  

Therefore, In the picture we can see the graph represents of the function f(x)=x²-2x+3.

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In the given Fibonacci sequence , 8th number is 13 mad 11th number is 55 .

What is a Fibonacci Sequence?

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it:

In a Fibonacci sequence, the number is equal to the sum of the two preceding numbers.

so the seventh number is 3+5 = 8

8th number is 5+ 8 = 13

11th number is 21+34 = 55

now the sequence becomes 0,1,1,2,3,5,8,13,21,34,55

Hence , the 8th number is 13 mad 11th number is 55.

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Comparing the square root of 18 and twenty three fifths using an inequality is ✓18 < 23/5.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

The square root of 18 will be 4.25

23/5 will be 4.6

Therefore, we can see that 4.6 is greater than 4.25.

In this case, ✓18 is less than 23/5.

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The value for p is 9 and the equation is y = 9x.

What is the proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

We have,

x        y

4        36

8        72

12        108

A proportional relationship between x and y is p,

y = px

p = 36/4 = 9

p = 72/8 = 9

p = 108/12 = 9

Hence, the value for p is 9 and the equation is y = 9x.

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The age of the bones from the skeleton of a prehistoric creature is 8460 years.

The formula to be used for the calculation of age is

ln (N/N₀) = -kt

where, N/N₀ represents represents remaining time

k is constant of proportionality

t is age or time period

The remaining time is 100 - 65 = 35

Remaining time = 35% or 0.35

Keeping the values in the above formula, we have

ln (0.35) = - 0.000124 t

-1.049 = -0.000124 t

t = 8459.67 ≈ 8460 years

Thus, the age of the prehistoric creature is 8460 years.

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As per the exponential growth function, the cost of the same goods and services in January 1, 2013 is $291.54

Exponential growth function:

In statistics, exponential growth function mean  a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given,

The amount of goods and services that costs $200 on January 1, 1997 costs $230.16 on January 1, 2006.

Here we need to estimate the cost of the same goods and services on January 1, 2013 and also assume the cost is growing exponentially. Round your answer to the nearest cent.

Here we know that the value of

Cost on 1997 = $200

Cost on 2006 = $230.16

So, the time difference is

=> 2006 - 1997 = 6

And the amount difference is

=> $30.16

So, based on the exponential growth function, the cost of goods and services at the time of 2013 is

=> 200 + ( 1 + 30.16)⁶

=> 200 + 91.54

=> 291.54

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An equation to represent the monthly cost of Kiara's plan for any number of text messages she sent is c = 0.25x.

An equation is a mathematical statement proving that two or more mathematical expressions are equivalent or equal.

Equations are represented using the equation symbol (=).

Let the monthly cost of Kiara's plan = c

The unit cost per text = $0.25

The number of text messages sent per month = x

Thus, equation c = 0.25x represents Kiara's monthly cell phone cost.

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Write an equation to represent the monthly cost of Kiara's plan for any number of texts.

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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The ounces of butter that are needed to make a pound of jelly is  3 ounce  .

In the question ,

it is given that ,

Samuel is using 1/5 of an ounce of butter to make 1/15 of a pound of jelly.

let the number of ounces of butter needed to make a pound of jelly be "x" .

So , the equation for the situation can be represented as

( 1/5 ounce butter)/(1/15 pound jelly) = x/( 1 pound jelly)

So ,after cross multiplication ,

we get ,

15/5 = x/1

So , x = 3  .

Therefore , the ounces of butter needed is 3 ounce .

The given question is incomplete , the complete question is

Samuel used 1/5 of an ounce of butter to make 1/15 of a pound of jelly. How many ounces of butter are needed to make a pound of jelly ?

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The percentage of students that prefer biology only is; 60%

Percentage can simply be calculated by dividing the value by the total value, and then multiplying the result by 100.

Now, we are told that 29 of the students are girls. Thus;

Number of boys = 100 - 29 = 71 boys

Now, 9 of the girls like biology. Thus, this is;

9% of the total students

20 of the boys prefer physics and this in percentage is;

20% of the total students.

27 people prefer chemistry and this is;

27% of total students

Number of boys that prefer biology = 71 - (20 + 20) = 31

Thus;

Number of students that prefer biology = 29 + 31 = 60 students

This gives a percentage of 60% of the total students.

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The distinction between them is that an integer is a negative number without a decimal point.

All whole numbers and negative numbers are considered integers. This means if we include negative numbers together with whole numbers, we form a set of integers.

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers. In this article, let's learn more about integers, their definition, and their characteristics.

According to our question-

The group of integers that are neither whole nor a natural number are:

As previously noted, the third set of integers lacks a decimal point;

However, the difference between them is that; a negative number without a decimal point is referred to as an integer

From the provided set: only fit into the description of an integer, because

It does not have a decimal point

And that is unfavorable.

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You have an element range of the equation y = 2x - 7 for the domain of 4, 3, 2 with values of -15, -13, and -11.

The difference between the highest and lowest values in a set of numbers is known as the range. Subtract the lowest value in the distribution from the highest to determine it.

Between the lowest and greatest numbers, there is a range. In the example,{4, 6, 9, 3, 7}  the lowest value is 3, and the highest is 9. The range then equals 9 - 3 = 6.

Here the explanation ,

The R domain xx.

R' is the range yy.

Y=2x7 is the equation of a line with slope m=2, and the domain and range of any line with m 0 and m are all real values.

The R domain xx. R is the range "y"

You have a range of -15, -13, and -11.

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Answer:

cost of the remaining amount How much does sheet metal cost per square foot?

Sheet metal costs $13x per square foot

Answer:

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes

Three main categories of probability exist:

The first team will be a team of all males :

Total number of Outcomes = 13C6 = 1716

Number of favourable outcomes = 7C6 = 7

Probability that all member of the first team will be male is =

Number of favourable outcomes/Total number of Outcomes

= 7/1716

the second team is all females, given the first team is all males

Total number of Outcomes = 7C6= 7

Number of favourable outcomes = 1

the probability the second team is all females, given the first team is all males = (Number of favourable outcomes/Total number of Outcomes)

= 1/7.

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complete analysis (carrying out steps A-H in section 4.4 from the Stewart textbook)

results as The graph of f(2) = et te is a straight line with a y-intercept of 1.

A) f(2) = et te

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers

Step B) Find any x-intercepts:

x-intercepts: None

Step C) Find any y-intercepts:

y-intercept: f(0) = e0te = 1

Step D) Find any vertical asymptotes:

Vertical asymptotes: None

Step E) Find any horizontal asymptotes:

Horizontal asymptote: None

Step F) Find any points of inflection:

Points of inflection: None

Step G) Find any symmetry:

Symmetry: None

Step H) Sketch the graph:

The graph of f(2) = et te is a straight line with a y-intercept of 1.

B) f(x) = tan-(+)

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers except -π/2, π/

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Answer: y=-3.46,3.46

Step-by-step explanation:

isolate y

5y^2=60

y^2=12

y=-3.46,3.46

Answer:

Step-by-step explanation:

You have triangles with two sides and the included angle given, or all three sides given. You want the measures of the missing sides or angles.

For triangle ABC, the law of cosines tells us ...

  c² = a² +b² -2ab·cos(C)

Solving for the third side, we get ...

  c = √(a² +b² -2ab·cos(C))

Solving for the angle, we get ...

  C = arccos((a² +b² -c²)/(2ab))

The names of the sides and vertices can be permuted, as long as the angle is between the given sides.

  a = √((7² +9² -2·7·9·cos(35°)) ≈ 5.176

The measure of side 'a' is about 5.2 units.

  C = arccos((8² +7² -10²)/(2·8·7)) = arccos(13/112) ≈ 83.33°

  A = arcsin((8/10)·sin(83.33°)) ≈ 52.62°

  B = arcsin((7/10)·sin(83.33°)) ≈ 44.05°

The last two angles are found using the law of sines:

  sin(A)/a = sin(B)/b = sin(C)/c

  b = √(230² +360² -2·230·360·cos(38°)) ≈ 228 . . . . feet

The third side measures 228 feet.

__

Additional comment

A calculator or spreadsheet can be programmed with the necessary formulas so that you can avoid a lot of repetitive work when you have several of these to solve. You need to make sure angles are treated appropriately, as the default is often radians, rather than degrees.

When solving for angles from three given sides, we like to solve for the largest angle first. That avoids any ambiguity when using the Law of Sines to find the other angles.

When using the Law of Sines to find a second angle after using the Law of Cosines, it can work well to find the smallest remaining angle. (In the first problem, that would be the angle opposite the side of length 7; in the last problem, that would be the angle opposite the side of length 230.)

True Matrix organizations have a flexible structure that brings together specialists from different Areas.

Teams in a matrix organization report to several leaders inside the business. The matrix structure promotes open communication between teams and can assist businesses in producing more creative goods and services. By using this framework, teams are spared the hassle of constantly realigning themselves for new projects.

How can teams be empowered to work fast on challenging projects without being slowed down by reviews and approvals from stakeholders? The solution might lie in organizational structure. Most workplaces have established hierarchies of command so that everyone is aware of who has the final say.

There are two or more management reporting structures in matrix organizations. Team members often have a principal manager for their department, despite the fact that this may at first seem unclear.

Comparable to a traditional organizational structure is reporting to a department manager. For instance, team members in the IT department answer to the head of the department. The vice president of their division is responsible for overseeing the IT department. All reporting lines ultimately lead to the CEO.

In contrast, team members in a matrix organization also report to project managers. It is appropriate to choose a separate manager for each project because tasks associated with them frequently require assistance from employees from different areas, such as IT, marketing, and finance.

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Answer: Total: $5.52
   F=$1.84
   D=$3.68

To get the answer first I did 0.92 times 2. It is $1.84. Next, I did 0.92 times 4. It is $3.68 Then I added them together and got the answers!