Caroline is taking a multiple choice test with a total of 40 points available. Each question is worth exactly 5 points. What would be Caroline's test score (out of 40) if she got 2 questions wrong? What would be her score if she got xx questions wrong?

The correct answer is d. 8, as it represents the greatest possible value for the integral of f(x) over the interval [0, 2].

Given that 2 ≤ f(x) ≤ 4 for all x in the interval [0, 2], we know that the function f(x) is bounded between 2 and 4 throughout the interval. To find the greatest possible value of the integral of f(x) over the interval [0, 2], we want to maximize the area bounded by the function and the x-axis.

Since the function is continuous and bounded, we can use the Fundamental Theorem of Calculus to find the integral. The integral of f(x) over the interval [0, 2] represents the area under the curve of f(x) between x = 0 and x = 2.

The maximum possible value of this integral occurs when the function is at its upper bound of 4 throughout the interval. Therefore, the greatest possible value of the integral is the area of the rectangle with a base of 2 (the width of the interval) and a height of 4, which is 2 * 4 = 8.

Hence, the correct answer is d. 8, as it represents the greatest possible value for the integral of f(x) over the interval [0, 2].

To know more about integral refer here:

https://brainly.com/question/31433890

#SPJ11

A) Jo Wexham and Oswestry is 27

B) 32 is the biggest number. So the distance between Wexham and Oswestry is the furthest.

C)  Jo wants to drive from penton to Saxby and then from Saxby to Trafford. Then,  the total distance she will drive is 50 miles.

Distance:

Distance is a numerical or sometimes qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may represent an estimate based on physical length or some other criterion. Most of these concepts of physical and metaphorical distance are formulated in mathematics using the concept of metric space.

Now,

A) Jo Wexham and Oswestry is 27

B) 32 is the biggest number. So the distance between Wexham and Oswestry is the furthest.

C)  Jo wants to drive from penton to Saxby and then from Saxby to Trafford. Then,  

The total distance she will drive is 18 + 32 = 50 miles.

Complete Question:

The chart shows the distances, in miles, between some towns and cities.

Toby lives in Wexham and works in Oswestry.

Wrexham1 8 Ruthin

a) Use the chart to find the road distance between Wexham and Oswestry.

15

21

12

Curwen

15

33

23

Oswestry

Sarah lives in Ruthin and works in Oswestry for

5 days a week. Each day she travels to and

from work using the route shown on the map.

MOLD ROTHEN WRESTHAM

b) How many miles, in total, does she travel to and from work each week? 231 miles

CORNEN

OSWESTRY

Learn more about Distance:

https://brainly.com/question/15172156

#SPJ4

Answer:

1.367431640625 i think

Step-by-step explanation:

You enter the number: 1.5e1016 in Hexadecimal number system and want to translate it into Decimal.

To do this, at first translate it to decimal here so :

1.5e1016 = 1∙160+5∙16-1+14∙16-2+1∙16-3+0∙16-4 = 1+0.3125+0.0546875+0.000244140625+0 = 1.36743164062510

Happened: 1.36743164062510

Result of converting:

1.5e1016 = 1.36743164062510

Answer: 13.12 x 10^147 e

Step-by-step explanation: ( i dont know if thats a multiply but oh well )

1.92e10^75 x 8.2e10^84 / 1.2.e10^12

= 1.92 x 10^75 x 8.2e10^84 / 1.2 x 10^12

= 1.6 x 10^75 x 8.2e10^84 / 1.2 x 10^12

= 1.6 x 10^63 x 8.2e x 10^84

= 13.12 x 10^147 e

please give brainliest! / im still not sure of the answer tho :/

Answer:

x² – x – 12 = (x – 4)(x + 3)

Step-by-step explanation:

Identify two numbers that add to -1 and multiply to -12, let's call them p and q.

So ax² + bx + c = (x + p)(x + q)

pq = c

p + q = b.

It is easier to find these numbers by finding factors of -12.

This can be done by splitting the number up until all the numbers are prime.

-12 → 6 × -2 or -6 × 2 → -(3 × 2 × 2)

There can only be two numbers so the only options we have are 6 and -2, -6 and 2, 3, and -4, or -3 and 4.

We can eliminate them by adding them up.

6 + -2 = 4 ≠ -1 so that can't be it.

-6 + 2 = -4 ≠ -1 so that can't be it either.

-3 + 4 = 1 ≠ -1

therefore p and q are 3 and -4 because 3 + -4 = -1.

so x² – x – 12 = (x – 4)(x + 3)

p = -4, and q = 3.

(x – 4)(x + 3) = x(x + 3) – 4(x + 3) = x² + 3x – 4x + 12 = x² – x – 12

Step-by-step explanation:

\( \frac{4}{8} = \frac{5}{10} = \frac{6}{12} \\ \)

Answer:

(0,5)

Step-by-step explanation:

x + 4y = 20

4y = -x + 20

y = -1/4x + 5

The y - intercept of the line is 5

(0,5)

-Chetan K

For the binomial distribution, √npq formula finds the standard deviation.

See the image below for the complete solution to the question:

Find more on the binomial distribution at: brainly.com/question/15278907

#SPJ4

Answer:

7529536\(m^{36}\)

a. Because the longest side can only be the sum of the other two sides, only (i) and (ii) are feasible (but not equal to the sum). b. Swap the pipe with length 3 and the pipe with length 4 as necessary.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

a. Because the longest side can only be the sum of the other two sides, only (i) and (ii) are feasible (but not equal to the sum).

b. Swap the pipe with length 3 and the pipe with length 4 as necessary.

c. Always place the biggest angle across from the longest side.

Learn more about triangle here:

https://brainly.com/question/2773823

#SPJ1

In school suspension

Answer:

20+20+20=60

20+5+5=30

5-2=3

1+(20*5)=100+1=101

Step-by-step explanation:

Hope it helps :)

Answer:

you do order of operations

Step-by-step explanation:

Answer: - 10

Step-by-step explanation:

The missing word is "modulus". The statement should read: Twelve is congruent to 60 (modulus 8) because both 12 and 60 have 4 as a remainder when divided by 8.

The modulus function, also known as the modulo operation or mod function, is a mathematical operation that returns the remainder when one integer is divided by another. The modulo operation is a quick and efficient way to find the remainder of a division. For example, if we want to know the remainder when 23 is divided by 5, we can simply compute 23 % 5, which equals 3. The symbol "%" is often used to represent the modulo operation in computer programming, while "mod" is used in mathematical notation to indicate congruence. In either case, the statement means that 12 and 60 leave the same remainder when divided by 8.

Learn more about modulus here, https://brainly.com/question/23450491

#SPJ11

Answer:

46

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

First get x

x= (20/10) * 100

x=200

23% of 200 = (23*200)/100 = 46

The null hypothesis would state that the population mean number of cups of coffee that women would drink 32% the population mean number cups of coffee than men drink.

The term "percentage" comes from the Latin phrase "per centum," which means "by the hundred." With 100 as the denominator, percentages are fractions. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam received 30% on his math test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

A certain number or quantity in every hundred is referred to as a percentage. It is a fraction, and the denominator is 100.

In order to learn more about percentage, visit:

https://brainly.com/question/29306119

#SPJ4

Answer:

P:(1,-2) Q: (4, -2) S:(1, 8) R:(4, -6)

Reflect over y axis, so you multiply the x coordinate of each point by -1.

P:(-1,-2) Q: (-4, -2) S:(-1, -8) R:(-4, -6)

Rotate 180 degrees about the origin, so multiply both x and y coordinate of each point by -1.

P:(1,2) Q: (4, 2) S:(1, 8) R:(4, 6)

Translate each point by 0 units on the x axis, and -8 units by the y axis. Apply that arithmetic to the x and y coordinates of the points.

P:(1,-6) Q: (4, -6) S:(1, 0) R:(4, -2)

The derivative of the function \(g(x) = ∫[1, x^3] t^3 dt is g'(x) = (3/4) x^11.\)

To find the derivative of the function \(g(x) = ∫[1, x^3] t^3\)dt using the Fundamental Theorem of Calculus, we can apply Part 1 of the theorem, which states that if the function g(x) is defined as the integral of a function f(t), then its derivative g'(x) can be found by evaluating f(x) at the upper limit of integration and multiplying it by the derivative of the upper limit.

In this case, the upper limit of integration is\(x^3\), so we have:

\(g'(x) = d/dx ∫[1, x^3] t^3 dt\)

Using the power rule for integration, we can integrate \(t^3\) to obtain (1/4) \(t^4\). Applying the Fundamental Theorem of Calculus, we have:

\(g'(x) = d/dx [(1/4) (x^3)^4]\)

Simplifying, we get:

\(g'(x) = d/dx [(1/4) x^12]\)

Taking the derivative using the power rule, we have:

\(g'(x) = (1/4) * 12x^(12-1)g'(x) = (3/4) x^11\)

Therefore, the derivative of the function \(g(x) = ∫[1, x^3] t^3 dt is g'(x) = (3/4) x^11.\)

To know more about derivative refer to-

https://brainly.com/question/30365299

#SPJ11

The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

Learn more about pyramid

brainly.com/question/13057463

#SPJ11

we need to buy at least 694 tickets to have a probability of winning at least 50%.

We can use the binomial distribution formula to solve this problem. Let X be the number of tickets we need to buy to have a probability of winning at least 50%. Then:

P(X ≥ 1) ≥ 0.5

This means that the probability of winning with at least one ticket is at least 50%. We can find this probability using the complement rule:

P(X ≥ 1) = 1 - P(X = 0)

The probability of not winning with any ticket is:

P(X = 0) = (999/1000)^n

where n is the number of tickets we buy. Therefore:

1 - (999/1000)^n ≥ 0.5

Simplifying this inequality, we get:

(999/1000)^n ≤ 0.5

Taking the logarithm of both sides, we get:

n log(999/1000) ≤ log(0.5)

n ≥ log(0.5) / log(999/1000)

n ≥ 693.15

Therefore, we need to buy at least 694 tickets to have a probability of winning at least 50%.

Learn more about Probability

brainly.com/question/30034780

#SPJ11

Answer:

let

s = the number of stools bought, s is integer

c = the number of chairs bought, c is integer

they need to buy 25 more chairs than stools

c = s + 25 => s = c - 25

the chairs cost $32 each and the stools cast $28 each and the budget is $2,620

32c + 28s <= 2620

if i plug s = c - 25 in the above inequality i get

32c + 28(c - 25) <= 2620

by solving the inequality we find

c <= 55.33

since c is integer we can write c<=55

they can buy 55 chairs the most.

Answer:

60°

Step-by-step explanation:

ST = SW, since both are radii of the circle.

SW = WT, given.

STW is an equilateral triangle.

RED is an equilateral triangle.

Therefore, the measure of DE is 60°.

Answer:

Because people fight over the best deals that the store would have to offer... hell with it i chose violence when there were 3 black shirts just because i run a designer company.

Step-by-step explanation:

The orthogonal polynomials with respect to the weight function (a) w(x) = log(x) on the interval (0, 1) are given by the Legendre polynomials. The orthogonal polynomials with respect to the weight function (b) w(x) = p^1 on the interval (0, 1) are the monomials.

(a) For the weight function w(x) = log(x), the orthogonal polynomials on the interval (0, 1) are defined by the Legendre polynomials. The Legendre polynomials are a set of orthogonal polynomials that satisfy a specific recurrence relation. The Legendre polynomial of degree 0 is simply a constant, denoted as P_0(x) = 1. The Legendre polynomial of degree 1 is P_1(x) = x. The Legendre polynomial of degree 2 is P_2(x) = (3x^2 - 1)/2. These polynomials are orthogonal with respect to the weight function w(x) = log(x) on the interval (0, 1).

(b) For the weight function w(x) = p^1, where p is a constant, the orthogonal polynomials on the interval (0, 1) are the monomials. Since the weight function is a constant, the inner product of two different monomials will be zero, making them orthogonal. The monomials are polynomials of the form x^n, where n is a non-negative integer. For example, the monomial of degree 0 is simply 1, the monomial of degree 1 is x, and the monomial of degree 2 is x^2. These monomials are orthogonal with respect to the weight function w(x) = p^1 on the interval (0, 1).

Learn more about orthogonal polynomials  here:

https://brainly.com/question/29734385

#SPJ11

Answer:

0.4

Step-by-step explanation:

divide simply the given problem by using calculator

Answer:

0.4

Step-by-step explanation:

2/5 turned into a decimal is simply 0.4! Hope it helps :)

Answer:

t2 = 52.8 hours

it will take 52.8 hours if its flow is reduced to 5 litres per minute.

Step-by-step explanation:

The volume of the swimming pool can be written as;

Volume V = flow rate × time

V = R×t

V = R1×t1 = R2×t2

R1×t1 = R2×t2

t2 = R1×t1/R2 ........1

Given;

Flow rate R1 = 12 litres per minute

Flow rate R2 = 5 litres per minute

time t1 = 22 hours

Substituting the given values into equation 1;

t2 = R1×t1/R2 = 12×22/5

t2 = 52.8 hours

it will take 52.8 hours if its flow is reduced to 5 litres per minute.

Answer:

Anthony mother's has enough flour for each of Anthony's friends to get a cupcake.

Step-by-step explanation:

Let suppose that Anthony and his friend will receive at least one cupcake, which means that Anthony's mother should make at least 9 cupcakes (\(\frac{3}{4}\) dozens).

From statement we notice that quantity of cupcakes is directly proportional to the quantity of flour.

According to the recipe, the required amount of flour and cupcakes are, respectively:

Flour

\(3\,\frac{1}{3}\,cups = 3 \,cups +\frac{1}{3}\,cups = \frac{10}{3}\,cups\)

Cupcakes

\(2\,\frac{1}{2}\,dozens = 2\,dozens +\frac{1}{2}\,dozens = \frac{5}{2}\,dozens\)

If Anthony's mother has 1 cup of flour at her disposal, the amount of cupcakes is obtained by simple rule of three:

\(x = \frac{5}{2}\,dozen\times\frac{1\,cup}{\frac{10}{3}\,cups }\)

\(x = \frac{3}{4}\,dozen\)

In a nutshell, Anthony mother's has enough flour for each of Anthony's friends to get a cupcake.

The solution of equation x² -14x- 12 is x= 7±√61.

To factorize the expression, we need to use Discriminant Method as

So, x² -14x- 12= 0

a= 1, b= -14, c= -12

So, D = b²- 4ac

D= 196 - 4(1)(-12)

D = 196 + 48

D = 244

So, x= (-b±√D)/2a

x= 14±√244 / 2

x = 14±2√61/2

x= 7±√61

Learn more about Quadratic Equation here:

https://brainly.com/question/22364785

#SPJ1

The expression in simplest radical form is 2.2360x

Simplest Radical Form means simplifying such that there is no square root or cubic root left to be simplified.

The given expression is

\(\rm \sqrt{5}x\)

value of \(\rm \sqrt{5}\) = 2.2360

Therefore the expression in simplest radical form is 2.2360x .

To known more about Simplest Radical form

https://brainly.com/question/12966955

#SPJ1

The minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The minimum and maximum mass measurement is determined from the uncertainty in the measurement.

For a given uncertainty of 2.2%, the minimum and maximum mass measurement is calculated as follows;

2.2% of 1.5 kg = 0.022 x 1.5 kg = 0.033 kg

minimum mass = 1.5 kg - 0.033 kg = 1.467 kg

maximum mass = 1.5 kg + 0.033 kg = 1.533 kg

Thus, the minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The complete question is below:

what is the minimum and maximum mass of 1.5 kg if the uncertainty in measurement is 2.2%?

Learn more about uncertainty in measurement here: https://brainly.com/question/1577893

#SPJ1