The integral 7√1 - 4x² dx is to be evaluated directly and using a series approximation. (Give all your answers rounded to 3 significant figures.) a) Evaluate the integral exactly, using a substitut

Answer:

volume of a cylinder = 536.9 cm³

Step-by-step explanation:

volume of a cylinder, V = πr²h

where π = 3.14

h = 19 cm

r = ?

given is diameter = 6 cm

as we know, r = d/2 = 6/2 = 3 cm

by substituting the values in the formula,

V = 3.14 * 3² * 19

= 536.94 cm³

by rounding off to the nearest tenth place,

volume of a cylinder = 536.9 cm³

Answer:

v = 537.2 cm3

Step-by-step explanation:

volume:

\(v=\pi r^{2} h\)

\(r=d/2=6/2=3cm\)

\(h=19cm\)

\(v=\pi (3)^{2} (19)=171\pi\)

\(v=537.21\)

Rounded nearest tenth:

\(v=537.2cm^{3}\)

Hope this helps

Answer:

For 2 its 5, and for 6 its 5

Step-by-step explanation:

6x5=30 there are six sides so divide by 6, and there you get 5.

2=5

6=5

Answer:

c = 3/5

Step-by-step explanation:

5c+16.5=13.5+10c

Subtract 5c from both sides:

13.5+5c=16.5

5c=3

c = 3/5

Company B charges $25 x miles than company A.

Let x = Number of miles.

Total charge = Flat charge + (charge per mile) x  (Number of miles)

For Company A ,

Flat charge= $30.50

Charge per mile = 9 cents

For Company B,

Flat charge= $55.50

Charge per mile =  13 cents

Cost from company A = $30.50 + 9c x

Cost from company B = $55.50 + 13c x

Company B cost - Company A cost = $55.50 + 13c x - ($30.50 + 9c x) = $25 x miles.

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Answer:

26

Step-by-step explanation:

This is what I got! I hope this helps!

Answer:

A. SSS

Step-by-step explanation:

Triangle ADT and triangle TDE are congruent triangles by SSS postulate.

Sides DE and DA, sides TE and TA are congruent (DT is common side).

So the answer is A. SSS

Answer:

- 2.5y + 1.6

Step-by-step explanation:

- 2.2y + 0.6 - 0.3y + 1 ← collect like terms

= (- 2.2 - 0.3)y + (0.6 + 1)

= - 2.5y + 1.6

Answer:

step: 1 collect like terms.

(-2.2y-0.3y) +(0.6+1)

setp:2 simplify

-2.5y+1.6

Step-by-step explanation:

Answer:

The equation that could be used to find \(x\), the number of cantaloupes Courtney had originally is \(x-40=23\) and the original number of cantaloupes are \(63\).

Step-by-step explanation:

Number of cantaloupes sold \(=40\).

Number of cantaloupes left \(=23\).

Let Courtney had \(x\) cantaloupes originally.

After selling \(40\) cantaloupes out of the total number of cantaloupes, Courtney is left with \(23\) cantaloupes.

So, the equation is \(x-40=23\).

\(\Rightarrow x=23+40\)

\(\Rightarrow x=63\)

Hence, the equation that could be used to find \(x\), the number of cantaloupes Courtney had originally is \(x-40=23\) and the original number of cantaloupes are \(63\).

a. The probability of exactly 4 successes is approximately 0.2967.

b. The probability of 5 or more successes is approximately 0.5332.

c. The probability of exactly 6 successes is approximately 0.1399.

d. The expected value of the random variable is 3.96

To solve these problems, we'll use the binomial probability formula:

P(X = k) = C(n, k)× \(p^{k}\)× \((1-p)^{(n-k)}\)

where:

P(X = k) is the probability of getting exactly k successes,

n is the sample size,

p is the probability of success,

C(n, k) is the number of combinations of n items taken k at a time.

Now let's solve each part of the problem:

a. The probability of exactly 4 successes:

P(X = 4) = C(6, 4) × (0.66)⁴ × (1 - 0.66)⁽⁶⁻⁴⁾

C(6, 4) = 6! / (4! × (6 - 4)!) = 6! / (4! × 2!) = (6 × 5) / (2 × 1) = 15

P(X = 4) = 15 × (0.66)⁴ × (0.34)² ≈ 0.2967 (rounded to four decimal places)

b. The probability of 5 or more successes:

P(X ≥ 5) = P(X = 5) + P(X = 6)

P(X = 5) = C(6, 5) × (0.66)⁵ × (1 - 0.66)⁽⁶⁻⁵⁾ = 6 × (0.66)⁵ × (0.34)¹ ≈ 0.3933

P(X = 6) = C(6, 6) × (0.66)⁶ × (1 - 0.66)⁽⁶⁻⁶⁾ = 1 × (0.66)⁶× (0.34)⁰ = 0.1399

P(X ≥ 5) = P(X = 5) + P(X = 6) = 0.3933 + 0.1399 ≈ 0.5332 (rounded to four decimal places)

c. The probability of exactly 6 successes:

P(X = 6) = C(6, 6) × (0.66)⁶ × (1 - 0.66)⁽⁶⁻⁶⁾ = 1 × (0.66)⁶ × (0.34)⁰= 0.1399

d. The expected value of the random variable:

The expected value (mean) of a binomial distribution is given by:

E(X) = n × p

E(X) = 6 × 0.66 = 3.96

Therefore:

a. The probability of exactly 4 successes is approximately 0.2967.

b. The probability of 5 or more successes is approximately 0.5332.

c. The probability of exactly 6 successes is approximately 0.1399.

d. The expected value of the random variable is 3.96

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The correct option is option (A) . Using Scatter plots,

Visulazation by scatter plots show the association and the distribution of Y changes as X changes.

Scatter plots:

A scatterplot plots pairs of numeric data using one variable on each axis to explore the relationship between them. If the variables are correlated, the points are along a straight line or curve.

A correlation exists between two variables if one of them is related to the other in some way. A scatterplot is a great place to start. A scatterplot (or scatterplot) is a graph of paired (x,y) sample data with a horizontal x-axis and a vertical y-axis. Each unique (x,y) pair is represented as one point.

Thus, the Visual examination of a scattergram indicates the existence of an association between variables and change in Y with change in X .

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To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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The equation of line is y = 3

Given the points:

(x₁, y₁) = (-1, 3)

(x₂, y₂) = (7, 3)

The slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

The formula for slope is,

m = (y₂ – y₁) / (x₂ – x₁)

We have given,

x₁ = -1

x₂ = 7

y₁ = 3

y₂ = 3

So,

m = (3 – 3) / ( 7-(-1)) = 0/8 = 0

Slope intercept form,

y = mx + b

Considering y as 3, then

3 = 0(x) + b

3 = 0 + b

b = 3

Therefore, the equation of line is

y = 3

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The coordinates of the meeting place are approximately (-4.3, -4.3).

Option D is the correct answer.

We have,

Now,

Midpoint between cities A and B:

(((-16+1)/2), ((-1+6)/2)) = (-7.5, 2.5)

Midpoint between cities A and C:

(((-16+1)/2), ((-1-18)/2)) = (-7.5, -9.5)

Midpoint between cities B and C:

(((1+1)/2), ((6-18)/2)) = (1, -6)

Now we can find the intersection of the three lines formed by these midpoints.

One way to do this is to use the point-slope form of the equation of a line.

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

The line passing through (-7.5, 2.5) and (-7.5, -9.5):

x = -7.5

The line passing through (-7.5, 2.5) and (1, -6):

y = (-8/9)x + 35/9

The line passing through (-7.5, -9.5) and (1, -6):

y = (3/5)x - 33/5

Solving for the intersection of these lines.

x = -4.3

y = -4.3

Therefore,

The coordinates of the meeting place are approximately (-4.3, -4.3).

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Answer:

Below

Step-by-step explanation:

Rank in order of SHORTEST time to LONGEST time ....

  shorter times mean the runner was faster to the finish line.

Answer:

50%

Step-by-step explanation:

Only 4 and 5 can be considered because 6 is not included, so the probability would be 2/4, or 50%.

Answer: 50%

Step-by-step explanation: It says if you pick a random card that is less than 6 or 4. That means that 4 and 5 are the ones you hope to get. 2/4 = 50%.

The surface area of the portion S of the cone z^2 = x^2 + y^2 where z>/ 0 contained within the cylinder y^2 + z^2 < 1 is 8π.

The cone is defined by the equation z^2 = x^2 + y^2.

The cylinder is defined by the equation y^2 + z^2 < 1.

The intersection of the cone and the cylinder is a surface that is part of a cone and part of a cylinder.

The surface area of the cone is given by the formula A = πr^2h, where r is the radius of the base and h is the height of the cone.

The radius of the base of the cone is equal to 1, and the height of the cone is equal to √2. Therefore, the surface area of the cone is π(1)^2(√2) = √2π.

The surface area of the cylinder is given by the formula A = 2πrh, where r is the radius of the base and h is the height of the cylinder.

The radius of the base of the cylinder is equal to 1, and the height of the cylinder is equal to 1. Therefore, the surface area of the cylinder is 2π(1)(1) = 2π.

The surface area of the intersection of the cone and the cylinder is equal to the surface area of the cone minus the surface area of the cylinder. Therefore, the surface area of the intersection is √2π - 2π = 8π.

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The average rate of change of f(x) over the interval 1 ≤ x ≤ 5 is 3.

To find the average rate of change of f(x) = 3x - 7 over the interval 1 ≤ x ≤ 5, we need to calculate the change in the function value divided by the change in x, which is:

(f(5) - f(1)) / (5 - 1)

Substituting the function values, we get:

[(3(5) - 7) - (3(1) - 7)] / (5 - 1)
= (8 - (-4)) / 4
= 3

Therefore, the average rate of change of f(x) over the interval 1 ≤ x ≤ 5 is 3.

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The value of each variable using trigonometric ratios is:

a = 14.9

b = 11.1

The three main trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Using these trigonometric ratios on the attached figure, we have:

cos 48 = 10/a

a = 10/cos 48

a = 14.9

Similarly:

sin 48 = b/a

sin 48 = b/14.9

b = 14.9 * sin 48

b = 11.1

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Answer: Answer is down below.

Step-by-step explanation: (since I can't type angles on here I'll just name their degree)

Supplementary - 53° and 127°

Complementary - 34° and 56°

Neither - 67° and 67°

Hope this helps!

Answer:

10

Step-by-step explanation:

We cannot use the Pythagorean Theorem here because we only have one side length. However, we can use the fact that \(\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}\)

I decided to make the corner with the 60° as ∠A, the corner with the 30° as ∠B, and the corner with the right angle as ∠C. While then making side a as the unmarked side, side b as the side with 5, and the hypotenuse p as side c.

Since we do not need to solve for a in this equation to solve for p, we can simply use the sides and numbers we are given.

Manipulating two of our equations, preferably the equations with the variables b and c, we can get \(\frac{b}{sin(B)}=\frac{c}{sin(C)}\) and solving for c, which is p in this case, will give us \(c=\frac{bsin(C)}{sin(B)}\)

Plugging in the numbers we have gives us \(c=\frac{5sin(90)}{sin(30)}\) = 10 mi

Answer:

Step-by-step explanation:

There are 10 common trig identities which I am aware of.

Some are in the image attached

The first image is known as b

Basic Identities

The second are known as Trigonometric / Pythagorean Identities .

The third : Co-function identities

and many more.

I'm only allowed to post five images so that's all I have.

Answer: B

Step-by-step explanation: Only 3x and 2x Have the exact same variable

Answer:

-8<7

Step-by-step explanation:

if you did at the number line you'll see that the -8 is at the left

and as you go the left number decreases

as you go to the right number increases

Answer:

{-1, 0, 1, 3}

Step-by-step explanation:

A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.

The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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Answer:

X= -7

Step-by-step explanation:

-25 + 8x +20 = -61

8x  -5 = -61

8x = -56

x = -7

The number given is

It is a real number , irrational number and integer.

The correct options are

Irrational number

Integer

Real number.

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Answer:

Answer is 18!

Step-by-step explanation:

hope this helps

Answer:

1.25 or \(1\frac{1}{4}\) pages per minute

Step-by-step explanation:

We are to determine the speed at which Sydney reads

Speed = total pages red / total minutes

50 / 40

The above fraction can be expressed its simplest form by dividing the numerator and the denominator by 10

5 / 4

the above fraction can be expressed as a mixed fraction as \(1\frac{1}{4}\) or as a decimal as 1.25 pages per minute

Answer:

Step-by-step explanation: