Instructions: Find the surface area of
each figure. Round your answers to the
nearest tenth, if necessary.
Surface Area:
5.2 cm.
cm²

Answer:

11x9=99 16x9=144=243 144+99

The cost of the carpet required for the given rectangular floor is $1584.

A rectangle is a quadrilateral with equal pairs of sides.

Given that:

The shape of the floor is a rectangle.

The length of the floor is 16 feet.

The width of the floor is 11 feet.

So,

The area of the floor = length × breadth

                                   = 16 × 11

                                   = 176 sq feet

The area of the floor is 176 sq feet.

The cost of the carpet for a 1 sq foot floor = $9

The cost of the carpet for a 176 sq feet floor = $9 × 176

                                                                          = $1584

Thus, the cost of the carpet for a 176 sq feet floor is $1584.

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The expected payoff from rolling the die is 0 usd.

According to the given question.

A die is rolled.

So, the possiblbe outcomes for a dice = {1, 2, 3, 4, 5, 6}

⇒ Total number of outcomes = 6

Also, it is given that

If a die is roll to a 1 or 2, we win 2usd and if it rolls to 3, 4, 5, or 6 we lose 1 usd.

As, we know that "Probability denotes the possibility of the outcome of any random event". And probability of any event can be calculated as

P(E) = total number of favorable outcomes/ Total number of outcomes

So,

The probability that die rolls 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3

And, the probability thet die rolls 3, 4, 5, or 6

= 1/6 +  1/6 + 1/6 + 1/6

= 4/6

= 2/3

Therefore, the excepted payoff from rolling this die

= [tex]2\times\frac{1}{3} - 1\times\frac{2}{3}[/tex]

[tex]= \frac{2}{3} - \frac{2}{3}[/tex]

= 0 usd

Hence, the expected payoff from rolling the die is 0 usd.

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Answer:

Option A is correct.

3x^2+6

Step-by-step explanation:

We have to find (f-g)(x):

We can write it f(x)-g(x), so substitute the values:

f(x)-g(x)=(4x^2+1)-(x^2-5)

=4x^2+1-x^2+5

=3x^2+6

Answer:

10,000

Step-by-step explanation:

Tbh this was pretty simple. If he makes twice the money as you, he pays twice as much too. Meaning he makes 40k a year and pays 10k for taxes

Answer: 1208.96

Step-by-step explanation:

The volume of the cylinder is [tex](\pi)(4^2)(4)=64\pi[/tex]

The volume of the prism is [tex](6)(12)(14)=1008[/tex]

So, the total volume is [tex]1008+64\pi=\boxed{1208.96}[/tex]

Length of the line

= [tex]\sqrt{((-2)-(-8))^{2}+(10-2)^{2} }[/tex]

= [tex]\sqrt{36+64}[/tex]

=[tex]\sqrt{100}[/tex]

= 10

The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.

In this question we must find the vertex coefficient of the equation of the parabola, which is the vertex form of the quadratic equation:

y - k = C · (x - h)²

If we know that (h, k) = (- 5, - 2) and (x, y) = (- 4, 2), then the vertex coefficient is:

2 - (- 2) = C · [- 4 - (- 2)]²

4 = C · (- 2)²

C = 1

The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.

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Step-by-step explanation:

180(n-2)/n=90 ( this is the solution for the 90)

cross multiplying

180n-360=90n

180n-90n=360

90n=360

90n/90=360/90

n=4, the number of sides for the polygon with 90° is 4 sides

Solution for 100°

180(n-2)/n=100

180n-360=100n

180n-100n=360

80n=360

80n/80=360/80

n=4.5

Same applies to the rest 110°,125° ,150°,175°

given,

wagon weight with sand = 100 pounds

wangon weight = 80 ounces ÷ 16 = 5 pounds

sand weight = 100 - 5 = 95 pounds//

Matt's BAC the equation for is  mathematically given as

X= 4 standard drinks

This is further explained below.

Blood Alcohol Content, sometimes known as BAC, is a measurement that expresses the amount of alcohol present in the blood as a percentage. Because it is measured in grams per 100 milliliters of blood, a blood alcohol concentration (BAC) of 0.08 indicates that your blood contains 0.08 percent alcohol by volume.

Generally, One standard drink is equal to twelve ounces of beer.

He drank a total of 48 ounces of beer since he had three cups of beer that were each 16 ounces.

In conclusion, the number of standard drinks that Matt consumed

X= 48/12

X= 4 standard drinks

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The equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form is,

[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]

Given:  [tex](-1,2)[/tex] and [tex](6,3).[/tex]

The slope of the line passing through[tex](x1,y1)[/tex] [tex](x2,y2)[/tex] is [tex]\frac{y^{2} }{x^{2} } -\frac{y^{1} }{x^{1} }[/tex]

The slope of our line[tex]=\frac{(3-2)}{(6+1)} =\frac{1}{7}[/tex]

Slope intercept from the equation would be [tex]y= 1/7 x +C[/tex]

Find C:

Since [tex](-1,2)[/tex] lies on the line, substitute these in the line equation

[tex]2 = \frac{1}{7(-1)} +c[/tex]

[tex]C=2+\frac{1}{7} =\frac{15}{7}[/tex]

Therefore, the equation in slope intercept form is[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]

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Answer:

Let , the constant factor be x so 3 X + 5 x + 7 x = 180

Step-by-step explanation:

Find out the value of x

7x+3x+5x=180

15x=180

x=180/15

x=12

now,

     x=3 multiplied by 12=36

     x=7 multiplied by 12=84

      x=5 multiplied by 12=60

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Answer:

2.571428

Step-by-step explanation:

The mean absolute deviation of a dataset is the average distance between each data point and the mean.

Answer: 380 ft and 780 ft

Step-by-step explanation:

We can assume that the flag is a rectangle. If the width of the flag is w, then the length is w + 400.

The formula for the perimeter of a rectangle is [tex]2(l+w)[/tex]. Let's plug in the values we know.

[tex]P=2(l+w)\\2320=2(w+400+w)\\1160=2w+400\\760=2w\\w=380[/tex]

We know that the length is 400 more than the width, so let's find the length.

[tex]l=w+400\\l=380+400=780[/tex]

Hence, the flag's width is 380 ft and the length is 780 ft.

Answer:

5/52

Step-by-step explanation:

There are 52 cards in a deck, with 26 red and 26 black cards. There are 2 red ones, 2 black threes, and 1 six of hearts. The # of favorable outcomes is 2 + 2 + 1 = 5, so the answer is 5/52.

32 bottles are needed to poured 4 gallons of chocolate milk.

The correct option is D.

A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.

Pints to Gallons Ratio: 1:8

Permit x bottles to be present.

There are x bottles required for 4 gallons of chocolate milk.

Because of the direct proportion

4/x = 1/8

x = 4 x 8

x = 32

As a result, 32 bottles are required.

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The length of line segment AB by observation if the diagram in the task content is; 14.

It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.

Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.

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the surface area of the sphere is π/4 cm^3

It is important to know the formula for surface area and volume of a sphere

Surface area = [tex]\frac{4\pi }{r^2}[/tex]

Volume = [tex]\frac{4}{3} \pi r^3[/tex]

First, let's determine the value of radius, r

The value for volume was given as  256/3π cm3.

[tex]\frac{256}{3} \pi = \frac{4}{3} \pi r^3[/tex]

Pi cancels out and we have cross multiply to get the radius

[tex]256 * 3 = 4 * 3 r^3[/tex]

[tex]12r^3 = 768[/tex]

Make r the subject of the formula

[tex]r = \sqrt[3]{\frac{768}{12} }[/tex]

[tex]r = \sqrt[3]{64}[/tex]

r = 4

Let's substitute to find the surface area

Surface area = [tex]\frac{4\pi }{4^2}[/tex]

Surface area = π/4

Surface area = π/4 cm^3

Thus, the surface area of the sphere is π/4 cm^3

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Answer:

480

Step-by-step explanation:

Answer:

[tex]e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...[/tex]

[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]

Step-by-step explanation:

Taylor series expansions of f(x) at the point x = a

[tex]\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...[/tex]

This expansion is valid only if [tex]\text{f}\:^{(n)}(a)[/tex] exists and is finite for all [tex]n \in \mathbb{N}[/tex], and for values of x for which the infinite series converges.

[tex]\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1[/tex]

[tex]\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]

[tex]\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4[/tex]

[tex]\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4[/tex]

[tex]\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4[/tex]

Substituting the values in the series expansion gives:

[tex]e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...[/tex]

Factoring out e⁴:

[tex]e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right][/tex]

Taylor Series summation notation:

[tex]\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n[/tex]

Therefore:

[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]

Answer:

8km  5mi

Step-by-step explanation:

20x400=8000meters a km = to 1000meters

8000/1000=8km

A mile is a kilometer/ 1.6  8/1.6=5 miles

Sanford ran approximately 8 kilometers and about 4.97 miles.

Given that a coach made someone run 20 laps on a 400 m track.

We need to find the number of mile he ran as well as number of kilometers he ran.

To find out how many kilometers Sanford ran, we can use the fact that 1 kilometer is equal to 1000 meters.

Similarly, to find out how many miles he ran, we'll use the conversion factor of 1 mile being equal to approximately 1609.34 meters.

Let's calculate it:

1 lap = 400 meters

20 laps = 20 x 400 = 8000 meters

Kilometers:

8000 meters ÷ 1000 meters/kilometer = 8 kilometers

Miles:

8000 meters ÷ 1609.34 meters/mile ≈ 4.97 miles

So, Sanford ran approximately 8 kilometers and about 4.97 miles.

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We can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

Given the following data:

Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured in kilometer per hour (kph).

Mathematically, speed can be calculated by using this formula;

Speed = distance/time

In order to calculate the airplane’s ground speed, we would apply the law of cosine:

C² = A² + D² - 2(A)(D)cosθ

Substituting the given parameters into the formula, we have;

C² = 700² + 60² - 2(700)(60)cos45

C² = 434,203.03

C = √434,203.03

C = 658.94 kph.

In conclusion, we can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

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Answer:

See below.

Step-by-step explanation:

Converse

The converse of a statement is formed by switching the hypothesis and the conclusion.

Given statement:  If n is an even integer, then 2n + 1 is an odd integer.

Converse:  If 2n + 1 is an odd integer, then n is an even integer.

Given statement:  If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

Converse:  If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.

Given statement:  If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.

Converse:  If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.

Given statement:  If the decimal expansion of a real number is terminating, then the number is rational.

Converse:  If a real number is rational, then the decimal expansion of the number is terminating.

The surface area of the cone exists as πr² + πrl

= (3.14)(6)² + (3.14)(6)(3)

= 169.56 cm²

Therefore, the surface area of the cone exists at 169.56 cm².

The surface of the cone consists of the lateral surface and the base area. So,

1. the lateral surface exists equal to πrs, where r exists the radius of the base and s exists the slant height of the cone.

2. the base area exists πr² (since the base exists a circle with radius r).

Then the surface area exists SA = πrs + πr²

The surface area of the cone exists as πr² + πrl

where "r" exists the radius, "l" exists the slant height

The radius of the cone exists at 6 cm

The slant height of the cone exists at 3 cm

To find the surface area of a cone

The surface area of a cone = πr² + πrl

= (3.14)(6)² + (3.14)(6)(3)

= 169.56 cm²

Therefore, the surface area of the cone exists at 169.56 cm².

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The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

A circle is shown in the picture.

PTR is the tangent of a circle.

AT=PT

Angle APT=20°

Let O is the center of the circle:

Angle BOT = 2 Angle PAT = 40 degrees

BO = TO = r

Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees

RTP is the tangent

OT ⊥ PTR

Angle OTA = 90 - Angle ATR = 50 degrees

Angle ABT = 180 - Angle PAT - Angle BTA

= 180 - 20 -  (170 + 50)

= 40 degrees

Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.

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The correct option regarding the outliers of the data-set is given by:

The greatest value, 78, is the only outlier.

The IQR for this problem is:

IQR = 37 - 13 = 24.

Hence the bounds for outliers are:

The options are:

Hence the correct option is that only 78 is an outlier.

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Answer:

12.8 km

Step-by-step explanation:

each mile has 1.6 km in it so in order to find the total distance in km we need to multiply the miles by 1.6= 8 miles x 1.6 =12.8 km

Answer:

Step-by-step explanation:

x=100 bc like 180-80=100

y=80 bc vertical angles

Answer:

y = 80*

x = 100*

Step-by-step explanation:

y is the same to the 80* angle and therefore x is 100*

180* - 80 = 100*

Answer:

x - 4

Step-by-step explanation:

monomial is one term

-11x is only one term

x-4 isn't

3 is one term

22xy is only one term

only x-4 isn't a monomial