A Pringles chip can has a diameter of 8 cm and a height of 30 cm. Determine the volume of the cylindrical can.
The area of a circle is shown below.
A = πr²

What happens when the slope of a line is undefined is that, the line is a vertical line that crosses the x-axis.

The points could be (1, 5) and (1, 10)

It is known that linear equations have slopes

These slopes are the average rate of change of the function

The values of these slopes can be

When the slope is undefined, it means that the line is a vertical line

An example of the vertices on such line is (x, y) and (x, y + n)

See that the x coordinate remains constant, while the y coordinate changed

Take for instance, a line that passes through (1, 5) and (1, 10) would have an undefined slope

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The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.

This is a plane figure which is referred to as a quadrilateral and has four right angles. The area is calculated by the following below:

Area = Length × breadth.

In cases where the algebra tile rectangles is used , it is ideal to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 7cm and the breadth is 6cm then the area will be  7cm × 6cm = 42cm²

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The 6th term is -487 i.e, option(a)

What is a Sequence ?

A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence.

There are 4 types of sequence, arithmetic sequences, geometric sequences, quadratic sequences and special sequences.

Given, the 1st term = -3

According to question, we get the term by multiplying the previous term by 3 and then adding 2.

Now, calculate the other terms.

so, the 2nd term will be

-3 * 3 + 2 = -7

3rd term

-7 * 3 + 2 = -19

4th term

-19 * 3 + 2 = - 55

5th term

-55 * 3 + 2 =  -163

6th term

-163 * 3 + 2 = -487

Hence, the 6th term is -487 i.e, option(a)

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The probability that a randomly selected student likes neither rock nor country is taken as;

P(R' ∩ C') = 0.326

Let us denote them as follows;

Number that like to be rock music be - R

Number that like to be Country music be - C

Number that like to be Jazz music be - J

Thus, as we are given and we have;

R is equal to 206

C is equal to 161

J is equal to  118

P(R') =206

P(C') =161

P(R' ∩ C') = 0.326

So, now P is removed  

R ∩ C = 30 - 11 = 1

Hence the answer is none of the above

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The little monsters solved 15 problems in March's Math meet

Given, that in November's math meet, the little monsters of beast academy solved 1/5 of the problems.

In March's math meet, they solved 2/3 of the problems.

In total, the little monsters solved 13 of 30 problems over both math meets.

Let, the number of problems in November be n,

and  the number of problems in March be m

According to the question,

n + m = 30 as, the total problems be 30

Now, (1/5)n + (2/3)m = 13 as, they solved total 13 problems

n + m = 30 ... (1)

n/5 + 2m/3 = 13 ... (2)

On simplifying Eq (2) becomes

3n + 10m = 195 ... (2)

On multiplying Eq (1) by 3, we get

3n + 3m = 90

3n + 10m = 195

On subtracting, we get

- 7m = - 105

m = 105/7

m = 15

So, the problems asked in March's Math meet be 15.

Hence, 15 problems were asked at March's Math meet.

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Answer:

Step-by-step explanation:

Given:

Binomial: x² + 10x

To Find:

Solution:

To find the constant we would compare the binomial with (a + b)² i.e. a² + 2ab + b² as it is the formula for perfect square.

By comparing we get:

a² = x²

2ab = 10x

b² = constant (To find out)

From this we can make out:

a = x

[tex] \therefore[/tex]

[tex] \rm \implies 2 \times x \times b = 10x \\ \\ \rm \implies b = \frac{10x}{2x} \\ \\ \rm \implies b = 5 \\ \\ \therefore \\ \\ \rm \implies {b}^{2} = 25[/tex]

So, constant that should be added to the binomial so that it becomes a perfect square trinomial is [tex] \boxed{\rm 25} [/tex].

Perfect square trinomial is x² + 10x + 25

Factorisation of the trinomial:

[tex] \rm \implies {x}^{2} + 10x + 25 \\ \\ \rm \implies {x}^{2} + 10x + {5}^{2} \\ \\ \rm \implies {x}^{2} + 5x + 5x + {5}^{2} \\ \\ \rm \implies x(x + 5) + 5(x + 5) \\ \\ \rm \implies (x + 5)(x + 5) \\ \\ \rm \implies {(x + 5)}^{2} [/tex]

The maximum number of deaths could be 5840000.

acc to our question-

hence,The maximum number of deaths could be 5840000.

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Answer:

55 L

Step-by-step explanation:

The value of vehicle after 15 years is $12,846.98 when purchased at $32500 and with rate of depreciation 6%.

The depreciation rate is the percentage at which an asset depreciates over its anticipated useful life. It can also be described as the portion of an organization's long-term investment in an asset that the organization claims as a tax-deductible expense over the course of the asset's useful life.

Here,

The value of vehicle=$32500

rate of depreciation=6% per year

time period=15 years

The percent value of vehicle=100-6=94%

Therefore to find the value in 15 years we multiply 32500 by 0.94 raised to the 15th power.

The value of vehicle after 15 years=$12,846.98

After 15 years, a vehicle that cost $32,500 and had a 6% depreciation rate is worth $12,846.98.

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Answer: What??

Step-by-step explanation:

Use parentheses that may or may not contain parameters directly after the function name to invoke the function.

As part of GAIA, the AI created for Project Zero Dawn in reaction to the Faro Plague, the subordinate functions are a part. The Faro Swarm's deactivation and the planet's terraforming are all objectives of Project Zero Dawn, and they are all accomplished through their extensive suite of subfunctions, each of which is dedicated to a particular purpose.

There are nine supporting roles.

A top engineer on the Zero Dawn project known as an Alpha created each of the nine subordinate functions. They were supported by a project development team made up of professionals in their industry who were well-known throughout the world.

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Now we have to,

→ find the required value of b.

Formula we use,

→ (AC)² = (BC)² + (AB)²

Then the value of b will be,

→ (10)² = b² + (6)²

→ 100 = b² + 36

→ b² = 100 - 36

→ b = √64

→ [ b = 8 ft ]

Hence, value of b is 8 ft.

use desmos graphing calcu

The distance covered by second cyclist is, 9 + (3/4)b miles.

What is speed?

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).

Given: Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions.

The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.

Speed of first cyclist = 12 miles per hour.

Speed of second cyclist = 12 + b miles per hour.

Since, distance = speed x time

The distance covered by the second cyclist in 45 minutes is,

45 minutes = 45/60 = 3/4 hour.

Therefore, distance covered by second cyclist is,

=  (12 + b) x 3/4 = 9 + 3b/4 miles.

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The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

[tex]\pi[/tex] ± z[tex]\sqrt{\frac{\pi \p(1-\pi )}{n} }[/tex]

z is the z-score that has a pvalue of [tex]1-\frac{\alpha }{2}[/tex]

Since, the coin is fair, so [tex]\pi =0.5[/tex].

The margin of error is:

[tex]M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}[/tex]

99% confidence level:

So [tex]\alpha =0.01[/tex] ,z is the value of Z that has a p value of 1-[tex]\frac{0.01}{2}[/tex]=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=[tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

[tex]0.18=2.575\sqrt{\frac{0.5*0.5}{n} }[/tex]

[tex]0.18\sqrt{n} =2.575*0.5[/tex]

[tex]\sqrt{n}=\frac{2.575*0.5}{0.18}[/tex]

[tex]\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}[/tex]

n = 51.16

Thus, we have to flip the coin at least 52 times.

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The function of the graph is f(x) = |x - 3| + 5

From the question, we have the graph that can be used in our computation:

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the minimum point on the graph is located at the point (3, 5)

This means that

Vertex = (3, 5) i.e.  (h, k) = (3, 5)

Recall that the general form of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

On the graph, we have

(x, f(x)) = (2, 6)

So, we have

6 = a|2 - 3| + 5

This gives

a = 1

So, we have

f(x) = 1 * |x - 3| + 5

Evaluate

f(x) = |x - 3| + 5

Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5

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Multiplication of  2.9x and 5x gives 14.5x²

The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants

Given: 2.9x and 5x

To multiply 2.9x and 5x, multiply the numbers and multiply the letters:

2.9x × 5x = 2.9 × 5 × x × x = 14.5x²

Therefore,   2.9x multiplied by 5x is 14.5x²

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The height of the TV is 31 inches . This can be calculated using Pythagoras theorem.

What is Pythagoras theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

Main Body:

according to the question --

hypotenuse = 52 in

base = 42 in

height =?

Pythagoras theorem = [tex]{P^{2} +B^{2} }[/tex] = [tex]H^{2}[/tex]

inserting the values --

52² = 42² +H²

H² = 2704- 1764

H² = 940

H≈31 inches

Hence the height of TV is 31 inches

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The average skid mark for the car is 98.5 feet.

The average skid mark can be calculated by the formula -

S = ✓30Dfn, where s is speed of car, D is skid distance, f is drag factor and n is braking efficiency. Keep the values in formula to calculate the value of D.

57 = ✓30 × D × 1.1 × 1

Performing multiplication on Right Hand Side of the equation

57 = ✓D × 33

Taking square on both sides of the equation

D = 57² ÷ 33

Taking square on numerator on Right Hand Side of the equation

D = 3249 ÷ 33

Performing division on Right Hand Side of the equation

D = 98.45 feet

Rounding to the nearest tenth of a foot

D = 98.5 feet

Hence, the average skid mark is 98.5 feet.

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The probability that x < y is 1/8 or 0.25 .

What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .

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x = -1 is the solution to the given inequality |x| - 2 ≤ -3.

The five steps to resolving inequalities are as follows?

When addressing an inequality, we can:

Isolate the variable on one side of the inequality and place all other constants on the other. To achieve this, alter the inequality by performing opposing procedures. First, multiply each side by two to isolate the x. Any action you take toward one side must also be taken toward the other.

C) If x = -1,

|x| - 2 ≤ -3

|-1| - 2 ≤ -3.

1 - 2 ≤ -3.

-1 ≤ -3 which is true.

Hence, x = -1 is the solution to the given inequality |x| - 2 ≤ -3.

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pizzeria will not deliver to mikayla as distance is out of radius.

According to question, as the reference with the origin of the circle, it can deliver pizzeria in the radius of 6 miles

mikayla lives 4 miles north and 6 miles west,

So, distance of mikayla from company,

By using Pythagoras theorem

Distance = √(4)^2 + (6)^2 = √52 miles

As distance is greater than radius, pizzeria will not deliver to mikayla.

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The location of the points A and B on side PQ and PR, and the information that segment AB is parallel to QR indicates;

Part A: Triangle ΔPQR is similar to ΔPAB by AA similarity postulate

Part B: The line segment on triangle ΔPAB that corresponds to line segment QR is segment AB

Part C: The angle on triangle ΔPAB that corresponds to angle ∠Q is angle ∠A

Please find attached the drawing of triangles ΔPQR and ΔPAB created with MS Word

The in formation in the question are;

Line [tex]\overline{AB}{[/tex] is parallel to [tex]\overline{QR}[/tex], [tex]\left(\overline{AB} \parallel \overline{QR}\right)[/tex]

ΔPQR and ΔPAB overlap

Part A: Angle ∠PQR is congruent to angle ∠PAB (corresponding angles to parallel lines having a common transversal)

∠PRQ is congruent to ∠PBA (Corresponding angles formed by a common transversal to parallel lines)

ΔPQA is similar to ΔPAB (Angle-Angle, AA similarity postulate)

Part B: Corresponding sides of triangles are located on the same relative position within the triangle

Segment QR is the included segment to ∠PQR and ∠PRQ, which are each congruent to ∠PAB and ∠PBA, respectively in ΔPAB and segment AB is the included side to ∠PAB and ∠PBA, therefore, the line segment on triangle ΔPAB that corresponds to line segment QR is segment AB

Part C: Angle ∠Q on triangle ΔPQR is adjacent to segment QR on the right and angle ∠P on the left, while angle ∠A is adjacent segment AB on the right and ∠P on the right, segment AB in ΔPAB corresponds to segment QR on triangle ΔPQR, therefore, by the relative position of angle ∠A on triangle ΔPAB, it is the angle that corresponds to angle ∠Q

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The interval of the cost of the car is [5600, ∞).

Here we have to find the cost of the car.

Let x be the cost of the car.

So from the question, we have that the cost of the repair is 25% or more of the car's value.

So we have to find the interval notation of the cost of the car.

x ×25% ≥ 1400

x × 25/100 ≥ 1400

x ≥ 1400× 100/25

x≥ 5600

So we get that the cost of the car is greater than $5600.

Therefore the cost of the car in an interval is [5600, ∞)

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Lauren got 5 votes in class president election.

Number of votes Lisa got = 36

Let the number of votes of Lauren be x. So, forming the equation between the number of votes of Lisa and Lauren.

36 = x + 6x

Calculating the value of x from mentioned equation

36 = 7x

Rewriting the equation with 7 as denominator

x = 36/7

Performing division on Right Hand Side of the equation

x = 5.14

Rounding off the digits as number of votes will be whole number

x = 5

Based on the mentioned information, Lauren got 5 votes.

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Answer: B. ≤

Step-by-step explanation:

≤

Answer:  The correct answer is x=−3 or x=5

Step-by-step explanation:

Solve for x^2−2x=15 using the quadratic equation

Step 1) Subtract 15 from both sides

x2−2x−15=15−15

x2−2x−15=0

For this equation: a=1, b=-2, c=-15

1x2+−2x+−15=0

Step 2) Use quadratic formula with a=1, b=-2, c=-15

x= (−b±√b2−4ac)/2a

x= (−(−2)±√(−2)2−4(1)(−15))/2(1)

x= (2±√64)/2

x=5 or x=−3

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The weight of the U.S. flag in pounds is 2,998.44 pounds.

The dimension of the U.S. flag is in feet. The dimensions have to be converted to yards.

1 foot = 1/3 yards

225 / 3 = 75 yards

505 / 3=  168.33 yards

The next step is to determine the area of the U.S. flag.

Area = length x width

75 x 168.33 = 12,625 yards²

Weight of the U.S. flag in ounces = 12,625 yards² x 3.8 = 47,975 ounces

1 ounce = 1/16 pounds

Weight of the U.S. flag in pounds = 47,975 / 16 = 2,998.44 pounds

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The required measure of the angle is m∠A=64°.

orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

,

Here,
Angles are represented by an algebraic expression, and the sum of the angle is 180°.
According to the question,
m∠A+m∠B+m∠C=180°
Substitute the value in the equation,
4x+90°+x+10=180°
5x = 180 - 100
5x = 80
x = 16°

Thus, the required measure of the angle is m∠A=64°.

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a. The equation that represents the given data is y = 700x + 2,000.

b. The average daily attendance at Disneyland on its 80th anniversary is 58,000.

We are given the data about average daily attendance at Disneyland's anniversary celebrations. At Disneyland's 40th anniversary, the average daily attendance was 30,000 people. On the 60th anniversary, the average daily attendance was 44,000 people. We need to create an equation that would represent y, the average daily attendance, based on x, the number of years after Disneyland opened.

We can write the data in the form of points on the coordinate axes. The coordinates of the points are (40, 30,000) and (60, 44,000). We can use the two-point form to write an equation.

(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)

(y - 30,000) = [(44,000 - 30,000)/(60 - 40)]*(x - 40)

(y - 30,000) = [(14,000)/(20)]*(x - 40)

(y - 30,000) = (700)*(x - 40)

y = 700x - 28,000 + 30,000

y = 700x + 2,000

Now, we need to find out the average daily attendance at Disneyland on its 80th anniversary.

y = 700*80 + 2,000

y = 56,000 + 2,000

y = 58,000

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