Suppose that f is differentiable for all x and that f (x)≤2 for all x. If f(1)=2 and f(4)=8 then f(2) has the value equal to a.3 b.4 c.6 d.8

If n is a multiple of 8, then n is even, according to commutativity. However, n is not an even number. As a result, n is not a multiple of 8.

Commutativity is a mathematical term that explains sums that can be shifted about and still produce the same solution.

'Commutative' is derived from the term 'commute,' which means to move and go around; thus, commutative equations feature integers that can be moved within the equation.

In mathematics, commutative law is one of two laws relating to number operations of addition and multiplication that are symbolically written as

a + b = b + a and ab = ba.

To know more about Commutativity

brainly.com/question/778086

#SPJ4

Answer:

[tex]x= \boxed{25}\;\; \sf meters[/tex]

[tex]y= \boxed{15}\;\; \sf meters[/tex]

[tex]z= \boxed{58}\;\; \sf degrees[/tex]

Step-by-step explanation:

Similar Triangles

If ΔWXY ~ ΔQRS then:

Therefore:

[tex]\implies \sf WX : QR = XY : RS = WY : QS[/tex]

[tex]\implies (15+x) : 30 = 20 : y = 32 : 24[/tex]

[tex]\implies \dfrac{15+x}{30}=\dfrac{20}{y}=\dfrac{32}{24}[/tex]

Solving for x:

[tex]\implies \dfrac{15+x}{30}=\dfrac{32}{24}[/tex]

[tex]\implies 15+x=\dfrac{30 \cdot 32}{24}[/tex]

[tex]\implies x=\dfrac{30 \cdot 32}{24}-15[/tex]

[tex]\implies x=25[/tex]

Solving for y:

[tex]\implies \dfrac{20}{y}=\dfrac{32}{24}[/tex]

[tex]\implies 20 \cdot 24=32y[/tex]

[tex]\implies y=\dfrac{20 \cdot 24}{32}[/tex]

[tex]\implies y=15[/tex]

If ΔWXY ~ ΔQRS then:

Therefore, solving for z:

[tex]\implies m \angle W = m \angle Q[/tex]

[tex]\implies 40^{\circ} = z-18^{\circ}[/tex]

[tex]\implies z=40^{\circ} +18^{\circ}[/tex]

[tex]\implies z=58^{\circ}[/tex]

The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A pastry specialist sells boxes of treats for $5 each. She has a sum of 20 boxes of treats to sell, and each crate contains 12 treats.

Let 'x' be the number of boxes of cookies and 'y' be the total cost. Then the equation is given as,

y = 5x

The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

Answer:

Step-by-step explanation:

At a significance level of 0.10, there is enough evidence to conclude that the treatment is dependent to the side effect of Nausea

The observed values are given as;

Result          Drug           Placebo          Total

Nausea          36                 13                 49

No Nausea     254              262              516    

Total              290               275              565      

The expected values are as follows;

EXPECTED    

                              DRUG                    PLACEBO

NAUSEA    (290 * 49/565) = 25.150442         (275*49/565) = 23.849558

NO NAUSEA (290*516/565) = 264.849558   (275*516/565) = 251.150442

Test statistic = ∑((observed - (expected)²)/expected    =  ∑(O - E²)/E

This gives the test statistic as;

                           DRUG            PLACEBO

NAUSEA         4.680351           4.935643

NO NAUSEA     0.444452        0.468695

∑(O - E²)/E = 10.52914

From a chi square calculator, our critical Value = 2.71

The conditions are;

If (calculated value > crit Value), then we reject Null hypothesis and accept the Alternative hypothesis

If (calculated value < critical value) we accept Null hypothesis and reject Alternative hypothesis

We are given;

Null Hypothesis; The two variables are independent

Alternative Hypothesis; The two variables are dependent

Since (10.52914 > 2.71) we reject Null Hypothesis and Accept Alt Hypothesis

Read more about chi square statistics at; https://brainly.com/question/4543358

#SPJ1

Answer:

y+29103.83045673370361328125

The formula for a permutation is: P(n,r) = n! / (n-r)!

What is Permutations ?

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}. As you can see, there are no other ways to arrange the elements of set A. The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

The formula for a permutation is: P(n,r) = n! / (n-r)!

Learn more about Permutations at :

https://brainly.com/question/1216161

#SPJ4

The expression 6x - 2  is equivalent to 5x + 2(3x - 1) - 5x. Option (1) is Correct.

Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

The equality (=) sign is used to denote equivalent phrases. Since the values of both expressions are constant for all values of x, 3(x + 2) and 3x + 6 are equal expressions. 3x + 6 = 3 × 4 + 6 = 18.

Here the expression is : 5x + 2(3x - 1) - 5x ...... (1)

let x=1 put in equation 1

then we get,

=5(1)+2(3(1)-1)-5(1)

=5+6-2-5

=4

now verify with all Options: put x =1

6x - 2 = 6(1) -2

=6-2

=4 (Correct value)

Option 2:

6x + 2

=6(1)+2

=8 (wrong Option)

Option 3:

16x - 2

=16-2

=14  (wrong Option)

Option 4:

=16x + 2

=16+2

=18 (wrong Option)

Learn more about expression visit: brainly.com/question/1859113

#SPJ4

Correct Question:

Which of the following is equivalent to the expression below?

5x + 2(3x - 1) - 5x

1. 6x - 2

2. 6x + 2

3. 16x - 2

4. 16x + 2

Using sum of infinite series in a geometric progression, the total number of jumps is 40 inches

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term.

The jumps are infinite and to find the total distance, we can use the equation given;

S = a(1 / 1 - r)

The first term (a) = 20 in

The common ratio = 10 / 20 = 1/2 = 0.5

Substituting the values into the equation;

S = 20(1 / 1 - 0.5)

S = 20(1 / 0.5)

S = 20 * 2

S = 40 in

The total distance is 40 inches

Learn more on geometric progression here;

https://brainly.com/question/1662572

#SPJ1

Answer: x = 3

Step-by-step explanation:

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.

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

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

Answer:

r=8, r=9, r=10

Step-by-step explanation:

5(7)≤6(7)-8

35≤42-8

35≤34

not true.

5(8)≤6(8)-8

40≤48-8

40≤40

true.

5(9)≤6(9)-8

45≤54-8

45≤46

true.

5(10)≤6(10)-8

50≤60-8

50≤52

true.

have a great day!

Answer:

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

We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS.

SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.

The missing bit is the other side of the marked angle B and D:

The probabilities for each case in this problem are given as follows:

a) A and B disjoint -> P(B and not A) = 1/2.

b) A is contained in B -> P(B and not A) = 1/6.

c) P(A and B) = 1/8 ->  P(B and not A) = 3/8.

The probability that we want to obtain in this problem is given as follows:

P(B ∩ Ac).

Which is the probability of B and the complement of A, that is:

P(B and not A).

If A and B are disjoint, it means that their intersection is of 0, hence:

P(B and not A) = P(B) = 1/2.

If A is contained in B, all elements of A are contained in B, hence the proportion of elements that are in B but not A is given as follows:

P(B and not A) = 1/2 - 1/3 = 1/6.

If the probability of the intersection is of 1/8, the proportion of elements that are in B but not A is given as follows:

P(B and not A) = 1/2 - 1/8 = 4/8 - 1/8 = 3/8.

(as 1/8 of them belong to both B and A, hence they do not belong to the complement of A).

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The length of the sides of EFG are 144 cm, 128 cm and 112 cm. And length of the longest side of QRS is 360 cm.

A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is represented as ΔABC.

In Euclidean geometry, any three points, if not collinear, define a unique triangle and, at the same time, a unique plane (that is, two-dimensional Euclidean space). That is, there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it. But this is not the case in high dimensional Euclidean space. This article is about triangles in Euclidean geometry, specifically the Euclidean plane, unless otherwise stated.

According to the question:

Triangles EFG and QRS are similar

So EF/QR = FG/RS = EG/QS

Therefore,

The length of the sides of EFG are 144 cm, 128 cm and 112 cm.

Here, 112 is smallest side of triangle EFG  

Let, the smallest side of EFG  be EF so QR is also the smallest side of triangle QRS i.e. QR = 280 cm & other sides be assumed "x" & "y"

Now,

   112/280 = 144/x = 128/y

⇒ 2/5 = 144/x = 128/y

Taking first two, we get

x = 360 cm

Now,

Taking first and third , we get ,

y = 320 cm

So others two sides of triangle QRS are 320 cm & 360 cm.

And length of the longest side of QRS is 360 cm.

Learn more about Triangle:

https://brainly.com/question/2773823

#SPJ4

Jane's share in the profit as per the amount invested by her is $39,375.

A ratio shows us the number of times a number contains another number.

Given that Capital balances were $100,000 for John, $75,000 for Sally and $225,000 for Jane. Therefore, the ratio of the capital invested by three can be written as,

John : Sally : Jane = $100,000 : $75,000 : $225,000

John : Sally : Jane = 4 : 3 : 9

Now, the profit will be shared as per the capital invested, therefore, as per the capital invested. Thus, we can write,

4x + 3x + 9x = $70,000

16x = $70,000

x = $70,000 / 16

x = $4,375

Further, Jane's share can be written as,

Jane's share = 9x

                     = 9 × $4,375

                     = $39,375

Hence, Jane's share is $39,375.

Learn more about Ratios here:

https://brainly.com/question/1504221

#SPJ1

(a) The expected value is 48 and the standard deviation is 5.366  .

(b) The probability that this year's class will beat the record is 0.0250  .

In the question ,

it is given that ,

the number of students is (n) = 120

40% of graduates will go on to college , that means (p) = 0.4

Part(a)

the expected value is E(x) is

E(x) = n*p = 120*0.4 = 48 .

the standard deviation is √np(1-q) = √120*0.4*0.6 = √28.8 ≈ 5.366

Part(b)

Using normal distribution for approximation ,

μ = 48 , σ = √28.8 and z = (x - 48)/√28.8   .

P(class will beat the record) = P(x>58)

= P(x>58.5)    continuity correlation

= P(Z > (58.5 - 48)/√28.8) = P(Z > 1.96) that is

= 0.0250 .

Therefore , (a) expected value = 48 , standard deviation = 5.366

(b) the required probability is 0.0250  .

Learn more about Standard Deviation here

https://brainly.com/question/14788733

#SPJ4

Validity is the extent to which findings may be generalized, while Internal validity validity refers to the ability to infer that there is a causal relationship between variables.

"Information available from the question",

In the question:

Validity is the extent to which findings may be generalized, while___ validity refers to the ability to infer that there is a causal relationship between variables.

To fill up the blank space:

Now, According to the question:

Let's Know:

Internal and external validity are two ways of testing cause-and-effect relationships.

Internal validity refers to the degree of confidence that the causal relationship being tested is trustworthy and not influenced by other factors or variables.

External validity refers to the extent to which results from a study can be applied (generalized) to other situations, groups, or events.

Now, According to the above statement is:

Hence, Validity is the extent to which findings may be generalized, while Internal validity validity refers to the ability to infer that there is a causal relationship between variables.

Learn more about Internal Validity at:

https://brainly.com/question/9292757

#SPJ4

Answer:

Below

Step-by-step explanation:

y =  100 - ( x-250)/20  *8      for every 20 above 250 eight fewer students from the 100 who would enroll at 250 level   ( this is for x >= 250...the question says nothing about enrollment change from lowering the price BELOW 250)

Answer:

103

Step-by-step explanation:

2018-2014=4

1023-611=412

4x=412

x=103

The amount of the investment at a rate of 7% for 6 months will be $2200.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Harriett Weiss procured $77 in straightforward premium in a half year at a yearly loan fee of 7%.

Then the amount of the investment is given as,

$77 = [P x 7 x (6/12)]/100

$7700 = P x 7 x 1/2

7P = $15400

P = $2200

The amount of the investment at a rate of 7% for 6 months will be $2200.

More about the simple interest link is given below.

https://brainly.com/question/2793278

#SPJ1

On solving the provide question, we got to know that volume of cube is [tex]343 cm^3[/tex] and volume of cuboid is [tex]224 cm^3[/tex], so volume cube is greater.

We are aware that a rectangle has four corners and is a two-dimensional form. Think of the form as a collection of parallel rectangles. The resultant form is known as a cube. Take a look at the following three-dimensional cube. Height, Width, and Length

The volume of the cube = [tex]a^3[/tex]

Where a is the length of the side = 7cm

volume of cube = [tex]7 X 7 X 7= 343 cm^3[/tex]                  

volume of the cuboid = l*b*h

[tex]7 X 8 x 4 = 224 cm^3[/tex]

To know more about cuboid visit:

https://brainly.com/question/29568631

#SPJ1

The solutions of the systems of equations are x = 3 and y =  − 4.

The substitution technique is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions.

This method entails determining the value of the x-variable in terms of the y-variable from the first equation and then replacing the value of the x-variable in the second equation.

Here we have

−7x − 2y = −13 ----- (1)

   x − 2y = 11 ----- (2)

Do (2) - (1)

=> −7x − 2y − (x − 2y)  = −13 − 11

=> −7x − 2y − x + 2y = − 24

=>  −8x =  − 24  

=>   8x = 24

=>   x = 3

Now substitute x = 3 in (2)

=>   3 − 2y = 11  

=>  − 2y = 8

=>  y = − 4

Therefore,

The solutions of the systems of equations are x = 3 and y =  − 4.

Learn more about Systems of equations at

https://brainly.com/question/12895249

#SPJ1

Answer:

The steps are listed below.

The proportion is 135 : 5 : : A : 8 and the value of A is 216 minutes

The time required for Erica to cook her 8 pound roast is 216 minutes

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the time required by Erica to roast 8 pound be = A

Now , the equation will be

Total amount of roast = 5 pound

The time required for Erica to roast 5 pound = 135 minutes

So , the proportion will be

Time required for Erica to roast 5 pound : 5 = Time required by Erica to roast 8 pound : 8

Substituting the values in the equation , we get

135 / 5 = A / 8

Multiply by 8 on both sides of the equation , we get

The value of A = ( 135 x 8 ) / 5

The value of A = 27 x 8

The value of A = 216 minutes

Therefore , the value of A is 216 minutes

Hence , The proportion is 135 : 5 : : A : 8 and the value of A is 216 minutes

The time required for Erica to cook her 8 pound roast is 216 minutes

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ1

The output variable of interest from a simulation model will be a Discrete variable

Discrete variables can be counted in a finite amount of time. You can count the change in your pocket, for example.

You have access to the funds in your bank account. You could also count the money in each person's bank account. It may take you a while to count that last item, but the point is that it is still countable or  number of students present. The quantity of red marbles in a jar.

According to the question,

The output variable of interest from a simulation model will be a discrete variable.

As output variable will take a counted value.

Hence , option (c) discrete is correct

To know more about Discrete variable here

https://brainly.com/question/13339063

#SPJ4

Answer:

D

Step-by-step explanation:

i did this before trust me

The answer of this question is found to be 0.0012.

The mean total service time is 10 minutes times lambda (the average number to turn up during the hour)

Lambda is 7, since the average rate is 7 per hour and your time window is 1 hour.

mean service time = 7 × 10 = 70 minutes.

For a poisson process, lambda is both the mean and variance of the arrivals.

So the variance = 10² × lambda = 700, since we want the variance of the service time, rather than the variance of the arrival rate.

This is because:

σ(aX) = a × σ(X).

and σ = sqrt(variance)

σ(service time) = 10 σ(arrival time)

variance(service time) = (10 × σ(arrival time))²

variance(service time) = 100 × variance(arrival time) = 100 × lambda =    100 × 7

mean(servicetime) = 70

variance(servicetime) = 700

2.5 hour = 150 min

Z = [tex]\frac{(S - 70)}{\sqrt{700} }[/tex]  follow N(0,1)

P(S > 150) = P(  [tex]\frac{(S - 70)}{\sqrt{700} }[/tex]>  [tex]\frac{(150 - 70)}{\sqrt{700} }[/tex])

=P(Z > -2.5512)

=0.0012

Learn more about probability here ;

https://brainly.com/question/13604758

#SPJ4

By using the concept of discount, it can be calculated that
a) Original cost of earrings is $20

b) Discount = $30

c) 30% discount has been given.

What is discount?

Discount is the price that is reduced from the original price of an article to sell that article at a cheaper cost during a sale.

a) Let the original cost of earrings be $x

Rate of discount = 15%

Discount given = $ [tex]\frac{15}{100}\times x[/tex] = $[tex]\frac{3x}{20}[/tex]

By the problem,

[tex]\frac{3x}{20} = 3\\x = \frac{3 \times 20}{3}\\[/tex]

x = $20

Original cost of earrings is $20

b) Cost of mom jeans = $50

Rate of discount  = 60%

Discount = [tex]\frac{60}{100}\times 50 =[/tex] $30

c) Cost of Vintage rock t-shirt = $40

Let the percentage discount be x%

Discount = [tex]\frac{x}{100} \times 40[/tex]

By the problem,

[tex]\frac{x}{100}\times 40 = 12\\x = \frac{12 \times 100}{40}\\[/tex]

x = 30%

To learn more about discount, refer to the link-

https://brainly.com/question/1548141

#SPJ1

the actual velocity of the plane is 380 mph [14.6° east of south], and the actual speed and direction of the plane are 380 mph and 14.6° east of south respectively.

Actual velocity vector = 380 mph [14.6° east of south]

Actual speed = 380 mph

Actual direction = 14.6° east of south

The actual velocity of the plane can be determined by subtracting the velocity of the tail wind (80 mph) from the initial velocity of the plane (460 mph). This gives us a result of 380 mph. To calculate the direction of the actual velocity, we need to subtract the direction of the tail wind (20 degrees west of south) from the direction of the initial velocity of the plane (10 degrees east of south). This gives us a result of 14.6° east of south. Therefore, the actual velocity of the plane is 380 mph [14.6° east of south], and the actual speed and direction of the plane are 380 mph and 14.6° east of south respectively.

Learn more about velocity here

https://brainly.com/question/29253175

#SPJ4

The value of the y such that the slope associated with both points is 2/7 will be 6.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The slope could be positive or negative.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

As per the given points,(10, y) and (3,4) and slope m = 2/7

2/7 = (4 - y)/(3 - 10)

4 - y = -7(2/7)

4 - y = -2

y = 4 + 2 = 6

Hence "The value of the y such that the slope associated with both points is 2/7 will be 6".

To learn more about slopes,

https://brainly.com/question/3605446

#SPJ1