using the graph in the picture:
1. PQ is a line which is parallel to the y-axis. Find the length of PQ

The exponential function that could be represented by the graph is given as follows:

[tex]y = 10^x[/tex]

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:

a = 1.

When x is increased by one, y is multiplied by 10, as we have that when x = 1, y = 5 and when x = 2, y = 50, hence the parameter b is given as follows:

b = 10.

Hence the function is given as follows:

[tex]y = 10^x[/tex]

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The expression [2 x (5 + 1)] ÷ 2 evaluates to 6 when applying the appropriate order of operations

When evaluating the expression [2 x (5 + 1)] ÷ 2, the true statement is that the expression simplifies to 6. The order of operations, also known as the PEMDAS rule, guides us in performing the calculations correctly.

According to the PEMDAS rule, we start by evaluating the expression inside the parentheses, which is (5 + 1), resulting in 6. Next, we multiply 2 by the result of the parentheses, giving us 12. Finally, we divide 12 by 2, which yields the final answer of 6.

This process ensures that we follow a consistent and agreed-upon method for evaluating mathematical expressions. By adhering to the PEMDAS rule, we maintain clarity and precision in our calculations, allowing us to obtain the correct result.

In conclusion, the expression [2 x (5 + 1)] ÷ 2 evaluates to 6 when applying the appropriate order of operations.

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Answer:

The deck will cover 153.86 square feet of Nicole's yard

Step-by-step explanation:

We want to find the area of the deck as the area is "the total space taken up by a flat (2-D) surface".  Furthermore, the mention of square feet also indicates that we want to find area since the area is always in square units.

The formula for the area of a circle is given by:

A = πr^2, where

Thus, we can plug in 3.14 for π and 7 for r, allowing us to solve for A, the area of the circular deck in square feet:

A = 3.14(7)^2

A = 3.14(49)

A = 153.86

Thus, the deck will cover 153.86 square feet of Nicole's yard.

Probability of selecting an athlete that stretches = 7/16

Percentage of athlete that do not stretch and got injured = 51.33%

a)

From table,

Athletes that stretch = Athletes that got injured while stretching + Athletes that do not got injured while stretching

Athletes that stretch = 55 + 295

Athletes that stretch = 350

Total number of athletes = stretch + does not stretch

total number of athletes = 350 + 450 = 800

Probability of an event to occur = Number of favourable outcomes / Total number of outcomes.

Probability of selecting an athlete that stretches = 350/ 800

Probability of selecting an athlete that stretches = 7/16

b)

Given

Athlete that do not stretch = 450

Athlete that got injured that do not stretch = 231

Now,

Percentage of athlete that do not stretch and got injured = 231/450 × 100

Percentage of athlete that do not stretch and got injured = 51.33%

Hence from the data given in table the required values can be found out.

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The value of x using the theorem of intersecting secants is 10

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

intersecting secants

Using the intersecting secants equation, we have

8 * (8 + x) = 6 * (6 + 18)

Evaluate the like terms

So, we have

8 * (8 + x) = 6 * 24

Divide both sides by 8

8 + x = 6 * 3

So, we have

8 + x = 18

Subtract 8 from both sides

x = 10

Hence, the value of x is 10

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Answer:

Minimum value = -6

Step-by-step explanation:

The minimum value is the y-coordinate of the minimum on the parabola.

Currently 3/4x^2 + 6x + 6 is in standard form, whose general equation is:

ax^2 + bx + c

Step 1:  We can first find the x-coordinate of the maximum using the following formula:

-b / 2a

From the function, we see that 6 is b and 3/4 is a.  Now, we plug these values into the formula and simplify:

-6 / (2 * 3/4)

-6 / (6/4)

-6 / (3/2)

-6 * 2/3

-12/3

-4

Step 2:  Now we can plug in -4 for x in the function to find the minimum value:

y = 3/4(-4)^2 + 6(-4) + 6

y = 3/4(16) -24 + 6

y = 48/4 - 24 + 6

y = 12 - 24 + 6

y = -12 + 6

y = -6

Thus, the minimum value of the function y = 3/4x^2 + 6x + 6 is -6

Answer:

a) 30 people , b) C

Step-by-step explanation:

for a), 40 % answered yes. so 60% answered no.

But 20 people answered yes so 20/x = 0.4 which gives, x = 20/0.4

so x = total number of people = 50

the rest answered no so 50 - 20 = y

30 people answered no

b) C is the correct chart

The amount invested is $2500.

Simple interest is the amount that a customer earns for making an investment. It is usually a linear function of the amount invested, the interest rate and the duration of the investment.

Simple interest = amount invested x time x interest rate

Amount invested = simple interest / (time x interest rate)

=$100 / (0.02 x 2)

= $2,500

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The trigonometric ratio include the following:

In order to determine each of the trigonometric ratios, we would apply each of the trigonometric ratios because the given side lengths represent the adjacent side, opposite side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp, sin(θ) = Opp/Hyp, tan(θ) = Opp/Adj

Where:

sin(θ) = Opp/Hyp

sin B = b/c

sin(θ) = Opp/Hyp

sin A = a/c

tan(θ) = Opp/Adj

tan A = a/b

cos(θ) = Adj/Hyp

cos B = a/c

cos(θ) = Adj/Hyp

cos A = b/c

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Complete Question:

Use the right triangle to determine the each of the trigonometric ratio.

Answer:

11.8 cm²

Step-by-step explanation:

Cosine rule: a ² = b ² + c ²  - 2bc COS A

COS A = (b ²  +  c ²   -  a ²) / (2bc)

Area of triangle = ½ ab sin C

name the angle that joins the '3' side to either of the '8' sides. label that angle as A.

now, Cos A = (8² + 3² - 8²) / [(2)(3)(8)]

= 3/16.

A = inverse Cos (3/16)

= 79.193°.

Area of triangle = 1/2 ab Sin C (we'll just use letter A instead of C)

= 1/2 (3)(8) sin (3/16)

= 11.8 cm².

another way you can find it is by this simpler method:

think of one side of 8, the side of 3 and the height that you do not know by using Pythagoras' Theorem for right-angled triangle. (a² + b² = c²). go halfway up the '3' side, then cut across straight to where the '8' sides meet. we now have right-angled triangle. let's call the height you don't know h.

we have 1.5² + h² = 8²

h² = 8² - 1.5²

h² = 61.75

h = √61.75

so area = 1/2 X 1.5 X √61.75

= 11.8 cm²

Answer:

y= 3x^2-7x+16= -11.917

y=3x^2+2x-2= -11.917

Step-by-step explanation:

Find the Vertex of   y = -3x2-7x-16

1. Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens down and accordingly has a highest point (AKA absolute maximum) .    We know this even before plotting  "y"  because the coefficient of the first term, -3 , is negative (smaller than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -1.1667  

Plugging into the parabola formula  -1.1667  for  x  we can calculate the  y -coordinate :

 y = -3.0 * -1.17 * -1.17 - 7.0 * -1.17 - 16.0

or   y = -11.917

Find the Vertex of   y = -3x2-7x-16

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens down and accordingly has a highest point (AKA absolute maximum) .    We know this even before plotting  "y"  because the coefficient of the first term, -3 , is negative (smaller than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -1.1667  

Plugging into the parabola formula  -1.1667  for  x  we can calculate the  y -coordinate :

 y = -3.0 * -1.17 * -1.17 - 7.0 * -1.17 - 16.0

or   y = -11.917

Answer: B, or 320 in cubed

Step-by-step explanation:

From the given system of linear equations there are no solutions.

The given system of equations are 5x+y=3 and 10x+2y=-6.

Here, 5x+y=3 -----(i) and 10x+2y=-6 ⇒ 5x+y=-3 --------(ii)

Subtract equation (i) from equation (ii), we get

5x+y-(5x+y)=-3-3

5x+y-5x-y=-6

0≠ -6

There are no solutions

Hence, from the given system of linear equations there are no solutions.

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The solution of the equation 2|2x - 1| - 8 = 18 is x = 7 or x = -6.

The solution of the equation 2|2x - 1| - 8 = 18 can be obtained as follows:

Step 1: Add 8 to both sides of the equation2|2x - 1| = 26

Step 2: Divide both sides of the equation by 2|2x - 1| / 2 = 26 / 2|2x - 1| = 13

Step 3: The absolute value of a number is always positive, so we can divide the equation into two separate equations.|2x - 1| = 13 or -|2x - 1| = 13

Step 4: Solve for x in each equation.

Solution for the first equation:|2x - 1| = 132x - 1 = 13 or 2x - 1 = -13 2x = 14 or 2x = -12 x = 7 or x = -6

Solution for the second equation:-|2x - 1| = 13|2x - 1| = -13

There is no solution to this equation because the absolute value of a number cannot be negative.

Therefore, the solution of the equation 2|2x - 1| - 8 = 18 is x = 7 or x = -6.

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Answer:

a. 12. 56m

b. 25.12cm

Step-by-step explanation:

a. Circle with radius (r) = 2m:

The circumference of a circle is the distance around its outer edge. To find the circumference, we use the formula: Circumference = 2 * π * r, where π (pi) is approximately 3.14 and r is the radius of the circle.

In this case, the radius (r) is given as 2m. Plugging in this value into the formula, we have:

Circumference = 2 * 3.14 * 2

= 12.56 meters

Therefore, the circumference of the circle with a radius of 2m is 12.56 meters.

b. Circle with diameter (d) = 8cm:

The diameter of a circle is the distance across the circle, passing through the center. To find the circumference, we use the formula: Circumference = π * d, where π (pi) is approximately 3.14 and d is the diameter of the circle.

In this case, the diameter (d) is given as 8cm. Plugging in this value into the formula, we have:

Circumference = 3.14 * 8

= 25.12 centimeters

Therefore, the circumference of the circle with a diameter of 8cm is 25.12 centimeters.

Hope this helps!

Answer:

[tex]C = \pi d[/tex]

[tex]C=2\pi r[/tex]

Formula [tex]C[/tex] = [tex]2\pi r[/tex]

[tex]a.~r=2~m[/tex]

[tex]2(3.14)(2)[/tex]

[tex]12.56~m[/tex]

Formula [tex]C[/tex] = [tex]\pi d[/tex]

[tex]b.~ d = 8~cm[/tex]

[tex]3.14*8[/tex]

[tex]25.12~ cm[/tex]

Answer:

1048 student tickets were sold and 1452 adult tickets were sold

Step-by-step explanation:

We can use a system of equations to find the quantity of both the adult and student tickets.  We can allow A to represent the quantity of adult tickets and S to represent the quantity of student tickets.

First equation:  (For the context of my explanation, revenue is defined as the product of price of an item and the quantity) We know that the sum of the revenues earned from the adult tickets equals the total revenue as

(price of adult tickets * quantity of adult tickets) + (price of student tickets * quantity of student tickets) = total revenue

Since we know that the adult tickets cost $3, the student tickets cost $2, and the total revenue earned was $6452, our first equation is:

3A + 2S = 6452

Second Equation:  We further know that the sum of the quantities of adult and student tickets equals the total amount of tickets sold as

quantity of adult tickets + quantity of student tickets = total amount of tickets sold

Since we know that there were 2500 fans in the gym, our second equation is:

A + S = 2500

Method to solve:  We can isolate A in the second equation by subtracting S from both sides.  This will allow us to substitute it in the first equation to first solve for S , the quantity of student tickets sold:

Step 1:  Isolating S in second equation:

(A + S = 2500) - S

A = -S + 2500

Step 2:  Plugging in (substituting) A = -S + 2500 for A in 3A + 2S = 6452:

3(-S + 2500) + 2S = 6452

-3S + 7500 + 2S = 6452

-S + 7500 = 6452

-S = -1048

S = 1048

Now that we know the quantity of student tickets sold was 1048, we can plug in 1048 for S in any of the two equations in our system to solve for A, the quantity of adult tickets sold.  Let's use the first equation:

Step 3:  Plugging in 1048 for S in 3A + 2S = 6452

3A + 2(1048) = 6452

3A + 2096 = 6452

3A = 4356

A = 1452

Thus, the quantity of adult tickets sold was 1452.

Optional Step 4:  We can check that we've found the correct answers by plugging in 1048 for S and 1452 for A in both equations in our system and checking that we get 6452 for the first equation and 2500 for the second equation:

Plugging in 1048 for S and 1452 for A in 3A + 2S = 6452 (i.e., the first equation in our system):

3(1452) + 2(1048) = 6452

4356 + 2096 = 6452

6452

Plugging in 1048 for S and 1452 for a in A + S = 2500 (i.e., the second equation in our system):

1048 + 1452 = 2500

2500 = 2500

The equation for the water level, L, after d days can be written as:

L = 340 - 0.5d

To find in how many days the water level will be 260m, we can substitute L = 260 into the equation and solve for d:

260 = 340 - 0.5d

0.5d = 340 - 260

0.5d = 80

d = 80 / 0.5

d = 160

Therefore, the water level will be 260m after 160 days.

From the circle the value of angle x is 90 degrees

We have to find the value of x

The radius of the circle is 18.5

As we observe the figure the angle x is opposite to the 90 degrees

The angle x and angle 90 degrees are vertical angles

We know that the vertical angles are equal or same

∠x = 90 degrees

Hence, the value of angle x is 90 degrees from the circle

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Answer:

56.55km^3

and

6385.03in^3

Step-by-step explanation:

The volume of a sphere is:

Vol = 4/3•pi•r^3

We're going to do 1/2 of that for the hemisphere shape you have in these questions.

Vol = 1/2•4/3•pi•r^3

= 4/6•pi•3^3

= 2/3•pi•27

= 18pi

~= 56.54866776

~= 56.55km^3

One more time for #6.

Vol = 1/2•4/3pi•r^3

= 4/6pi(29/2)^3

= 2/3pi(29/2)^3

not as much stuff cancelling, so we just toss it all into the calculator.

~= 6385.025269033

~= 6385.03in^3

The probability that the newspaper Mario buys has reviewed both performances, given that he buys the first newspaper, is 0.72 or 72%.

a) Let's assume the probability of the first newspaper reviewing his performance is 2/7 and the probability of the second newspaper reviewing his performance is 5/7. The probability of both papers reviewing his performance is (2/7) * (5/7) = 10/49.

b)Since Clarissa buys both newspapers, there are two scenarios: either the first newspaper reviews her performance and the second one doesn't, or the second newspaper reviews her performance and the first one doesn't. The probability of only one paper reviewing her performance is 2 * (3/7) * (4/7) = 24/49.

c) If Mario buys one newspaper at random, there is a 2/7 chance that he buys the first newspaper and a 5/7 chance that he buys the second newspaper. Since each newspaper has reviewed one performance, the probability that the newspaper he buys has reviewed both performances is (2/7) * (5/7) = 10/49.

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The factorization of the given expression is 2x⁵(x²-9).

The given expression is 2x⁷ - 18x⁵.

The factors are the polynomials which are multiplied to produce the original polynomial.

Here, 2x⁵(x²-9)

Therefore, the factorization of the given expression is 2x⁵(x²-9).

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Step-by-step explanation:

1/2×13×12= 78

12×14= 132

13×14= 182

total surface area

= (78×2)+(132×2)+182

= 602 ft^2

The fraction 3/7 will not make the equation true.

so the answer is No.

In mathematics, a fraction is a representation of a part of a whole or a division of one quantity by another. It is expressed in the form of a ratio of two integers, where the number on the top is called the numerator and the number at the bottom is called the denominator.

The fraction 3/7 will not make each equation true.

To see why, we can simply substitute 3/7 into each equation and check if it makes the equation true.

For the equation, we have:

[tex]\sf 18 \times \huge \text (\dfrac{3}{7}\huge \text) = (2 \times 3 \times 3) \times \huge \text (\dfrac{3}{7}\huge \text) = \dfrac{54}{7}[/tex]

So the left-hand side simplifies to 54/7, which is not the same as the right-hand side of 42. Therefore, the fraction 3/7 does not make the second equation true.

Therefore, The fraction 3/7 will not make the equation true.

so the answer is No.

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The universal class is considered a proper class because it contains all sets but cannot itself be treated as a set due to the limitations imposed by set theory. Recognizing it as a proper class ensures the consistency and avoids the paradoxes that would arise if it were treated as a set.

In set theory, classes are collections of objects that share a common property or satisfy a specific condition. A proper class is a class that is not a set, meaning it cannot be treated as an object within the theory of sets. One example of a proper class is the universal class, denoted as "V" in Von Neumann–Bernays–Gödel set theory (NBG) or "U" in Morse–Kelley set theory (MK).

The universal class is defined as the class that contains all sets. It encompasses every possible set that can be constructed within the theory of sets. It is important to note that the universal class itself is not considered a set because it would lead to logical inconsistencies and paradoxes, such as Russell's paradox.

To understand why the universal class is considered a proper class, we need to delve into the foundations of set theory. In most set theories, including Zermelo-Fraenkel set theory (ZF), which is the most commonly used, there is a principle called the limitation of size. This principle ensures that only sets of a certain size can be considered objects within the theory.

The limitation of size prevents the universal class from being considered a set because it would violate the size restrictions. If the universal class were a set, it would contain itself as an element, leading to the well-known Russell's paradox. Russell's paradox arises from the assumption that there exists a set of all sets that do not contain themselves as elements. If the universal class were a set, it would both contain and not contain itself, creating a contradiction.

To avoid such paradoxes and maintain consistency within set theory, the universal class is treated as a proper class. This means that it is not regarded as an object that can be manipulated or operated upon like a set. Instead, it serves as a collection that encompasses all sets, acting as a foundational concept within set theory.

In summary, the universal class is considered a proper class because it contains all sets but cannot itself be treated as a set due to the limitations imposed by set theory. Recognizing it as a proper class ensures the consistency and avoids the paradoxes that would arise if it were treated as a set.

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Answer:

-3125

Step-by-step explanation:

To find the value of a₆, we can use the given recursive formula and substitute the values for a₁ and the preceding terms until we reach the desired term.

Given:

a₁ = 1

aₙ = -5aₙ₋₁

Let's calculate the values step by step:

a₂ = -5a₁ = -5(1) = -5

a₃ = -5a₂ = -5(-5) = 25

a₄ = -5a₃ = -5(25) = -125

a₅ = -5a₄ = -5(-125) = 625

a₆ = -5a₅ = -5(625) = -3125

Therefore, the value of a₆ is -3125.

Hope this helps!

Answer:

the cost to rent one water tank is $226.08.

Step-by-step explanation:

Given:

Radius (r) = 3 feet

Height (h) = 2 feet

Cost per cubic foot = $4

The volume of a cylinder is given by the formula:

Volume = π * r^2 * h

Substituting the given values:

Volume = 3.14 * (3 feet)^2 * 2 feet

Volume = 3.14 * 9 square feet * 2 feet

Volume = 56.52 cubic feet

The cost to rent one water tank is calculated by multiplying the volume by the cost per cubic foot:

Cost = Volume * Cost per cubic foot

Cost = 56.52 cubic feet * $4

Cost = $226.08

Step-by-step explanation:

To find the cost to rent one water tank, we need to calculate its volume and then multiply it by the rental cost per cubic foot.

The formula for the volume of a cylinder is given by:

V = πr²h

where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

In this case, the radius (r) is 3 feet, and the height (h) is 2 feet. Plugging these values into the formula, we get:

V = 3.14 * (3^2) * 2

V = 3.14 * 9 * 2

V = 56.52 cubic feet

Now, we can multiply the volume by the rental cost per cubic foot:

Cost = V * $4

Cost = 56.52 * $4

Cost = $226.08

Therefore, the cost to rent one water tank is $226.08.

Answer:

All of the above are true.

Step-by-step explanation:

It is given that:

[tex]Q=\{x|x~\text{is an odd integer greater than 5}\}[/tex]

So, the set Q is written in the set builder notation.

In the roster form, the set Q would be as follows:

[tex]Q=\{7,9,11,13,\cdots\}[/tex]

From the roster form, we observe that 5 is not an element of Q while 7 is an element of Q.

So, the first three statements are true.

The numerical expression (45 - 28) - |15 - 21| after simplification gives the value 11.

Given a numerical expression,

(45 - 28) - |15 - 21|

We have to find the value of the expression.

We find the difference of the numbers in the bracket and inside the absolute symbol.

45 - 28 = 17

15- 21 = -6

Absolute value of this is,

|15- 21| = |-6| = 6

So the expression is,

(45 - 28) - |15 - 21| = 17 - 6 = 11

Hence the value is 11.

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The complete question is as given below.

Simplify (45 - 28) - |15 - 21|

A) 11

B) 17

C) 23

D) 29​

Answer:

Step-by-step explanation: