A recycling plant recycled 4.9 kg of paper and cardboard the first hour and 7.8 kg/h
afterwards. The plant runs for 8 hours. What is the range of the function?

The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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If the weekly salary is reduced by 9.5% for CCSS and the salary is 50000, then they would pay $45250.

The percent reduction in the weekly salary is = 9.5% = 0.095,

So, the amount of the reduction is;

⇒ reduction = 9.5% of 50,000

⇒ reduction = 0.095 x 50,000

⇒ reduction = 4750

So, the reduction in the weekly salary is 4750,

Now, we subtract the reduction from the original salary to get the new salary after the reduction,

⇒ new salary = 50000 - 4750

⇒ new salary = 45250

Therefore, the new salary after the 9.5% reduction for CCSS is $45250.

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Answer: g = 2

Step-by-step explanation:

Because 6 = 1 and  12 = g so g would have to be two

The original dimensions of the metal piece are:

Let's say the length of the original metal piece is L and the width is W. The squares that are cut from the corners have sides of x. After the flaps are folded upward, the resulting dimensions of the box are L - 2x and W - 2x. The volume of the box is given as:

       (L - 2x) * (W - 2x) * x = x³

        LWx - 2Lx² - 2Wx² + 4x³ = x³

        LWx - 2Lx² - 2Wx² = 0

        LW = 2(L + W)x²

       LW / x² = 2(L + W)

       LW / V^(2/3) = 2(L + W)

        LW = 2(L + W) * V^(2/3)

        LW = 2V^(2/3) (L + W)

        LW = 2 * V^(2/3) * (L + W)

        L = W + t for some t > 0.

        W (W + t) = 2 * V^(2/3) * (W + t + t)

        W² + Wt = 2 * V^(2/3) * (2t + W)

        W² = 2 * V^(2/3) * 2t + 2 * V^(2/3) * W

        W² = 4 * V^(2/3) * t + 2 * V^(2/3) * W

        W^2 / (2 * V^(2/3) + 1) = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + 2 * V^(2/3)

        * W / (2 * V^(2/3) + 1)

        W * (2 * V^(2/3) + 1) = 4 * V^(2/3) * t + 2 * V^(2/3) * W

        W = 4 * V^(2/3) * t / (2 * V^(2/3) + 1)

        L = W + t = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + t

        L = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + t

        W = 4 * V^(2/3) * t / (2 * V^(2/3) + 1)

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Using statistical concepts, it is found that the standard deviation of the probability distribution is of

\(s = 1.5(1.9) = 2.85\)

When a constant is multiplied to each data in a variable, both the mean and the standard deviation are multiplied by the constant.

In this problem, the standard deviation, which is the square root of the variance, is of:

\(\sigma = \sqrt{\sigma^2} = \sqrt{3.6} = 1.9\)

The price of each is of $1.5, hence:

\(s = 1.5(1.9) = 2.85\)

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Answer:

the answer is the D(-1,-3)

Answer:

For 7 houses you will need 5.83 acres of land and the builder will have 4.16 acres of land unused 

Step-by-step explanation:

Answer:

The focus would lie at (-8,16)

Step-by-step explanation:

Answer: 4-4z

Step-by-step explanation: Coming the like terms in order to simplify the equation. There are four z's and they combine as they are like terms. Since we don't know the value of z, thats the most simplified form.

To calculate (f-g)(x) we simply subtract g from f and the organize the powers in descending order

we get

So (f-g)(x) = x^2-14x+33

Answer:

Step-by-step explanation:

When you multiply radicals together, the only rule that needs to be followed is that the index is the same on both. These are both square roots (so the index is a 2 on each radical) so we can multiply the radicals together to get 5√66.  That does not simplify at all and is irrational (since the decimal goes on without repeating)

Answer:

34

Step-by-step explanation:

every time it goes up it goes little higher each and every time till it reaches a limit

The true statements about the dilation are as follows;

The scale factor is One-eighth

The coordinates of the C prime are (0.75, 0.5).

The coordinates of B prime are (–0.25, 1).

Given

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4).

If A prime has coordinates of (–0. 25, 0. 5) after the triangle has been dilated with a center of dilation about the origin.

Transformation is the movement of a point from its initial location to a new location. If an object is transformed then all its points are also transformed. Types of transformation are reflection, dilation, rotation, and translation.

Dilation is the enlargement or reduction in the size of an object. If a point X(x, y)  is dilated about the origin by a factor k, its new location is X'(kx, ky).

Triangle ABC with vertices at A(–2, 4), B(–2, 8), and C(6, 4) is dilated to give A'(-0.25, 0.5)

kA = A'

(-2k, 4k) = (-0.25, 0.5)

-2k = -0.25, hence k = 1/8

Therefore the scale factor is 1/8 (one- eight)

The new location of the vertices is B'(-0.25, 1), C'(0.75, 0.5)

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Therefore , the solution of the given problem of function comes out to be Nolan dropped the ball from a height of 12 units at the beginning.

The study of mathematics includes numbers, symbols, and their parts, as well as anatomy, building, and both actual and hypothetical geographic locations. The relationships between different components, each of which has a corresponding result, are described by a function. A function is made up of a variable of distinct components that, when put together, produce specific results for each input.

Here,

Assume that h represents the original height at which Nolan threw the ball. The object bounces once and rises to a height of 4, so after the bounce it has a height of h + 4.

=> h = k f(1) (1)

where k is a constant that denotes how much energy the object retains after each bounce.

=> h = k(4) (4)

The knowledge that the ball returns to a height of 4 on the first bounce must be used to determine the value of k:

=> 4 = k f(1) (1)

=> 4 = k (4/3)

=> k = 3

When we put this number of k back into the equation as a replacement for h, we get:

=> h = k(4) = 3(4) = 12

Nolan dropped the ball from a height of 12 units at the beginning.

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Answer:

Step-by-step explanation:

The scale factor is 2

If the line y = 3x + 7 endures a dilation with center (0,7) and scale factor 10 as a result, the image's inclination is 30.

The slope of a line serves as a gauge for its steepness. The ratio of something like the vertical change (emergence) to the parallel change (run) either between two locations on the line is what is referred to as the slope. In other terms, slope is the amount of rise or fall that a line experiences for each unit of distance away. The slope method can be used to determine a line's slope: slope equals (y2 + y1)/. (x2 - x1) where any two locations on the line (x1, y1) and (x2, y2) are. The line moves up from left to right if the slope is positive (i.e., it has a positive inclination), but if the slope is negligible, the line decreases gradually from left to right (i.e., it has a negative inclination).

given

Any point's distance from the center must be multiplied by 10 in order to execute a dilation with a center (0,7) and scale factor of 10.

For instance, the initial line's point (1, 10) is on it, and its distance from the center is 10 - 7 = 3.

In the image, the equivalent point will be 10 times farther from the center, which (1, 37). Also on the initial line, the point (2, 13) is situated at a distance from the center of 6 - (7, 13). In the image, the equivalent point will be 10 times farther from the center, which (2, 67).

By calculating the slope of the line connecting these two locations, we can determine the slope of the image. The slope method is used to:

slope equals (y2 + y1)/. (x2 - x1)

where (1, 37) for (x1, y1) and (2, 67) for (x2, y2), we obtain:

slope = (67 - 37) / (2 - 1) = 30

As a result, the image's inclination is 30.

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Answer:

y = \(\frac{x+1}{2}\)

Step-by-step explanation:

y = 2x - 1

switch the x and y variables

x = 2y - 1

solve for y

x + 1 = 2y

\(\frac{x+1}{2}\) = y

The volume of the cone is 37.68 centimetres cube.

The volume of cone can be described as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore, we were given the radius of the cone and the slant height. We will use Pythagoras's theorem to find the height of the cone.

Hence,

c² = a² + b²

where

Therefore,

5² - 3² = h²

25 - 9 = h²

h = √16

h = 4 cm

Hence,

volume of a cone = 1 / 3 πr²h

r = 3 cm

h = 4 cm

volume of a cone = 1 / 3 × 3.14 × 3² × 4

volume of a cone = 1 / 3 × 3.14 × 9 × 4

volume of a cone =  113.04 / 3

volume of a cone =  37.68 cm³

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Answer:

\(\sqrt{97}\) units

Step-by-step explanation:

Calculate the distance using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = A(- 5, 3) and (x₂, y₂ ) = B(4, - 1)

d= \(\sqrt{(4+5)^2+(-1-3)^2}\)

  = \(\sqrt{9^2+(-4)^2}\)

   = \(\sqrt{81+16}\)

    = \(\sqrt{97}\) ≈ 9.85 ( to 2 dec. places )

Answer: 1.50

Step-by-step explanation: 1 wing = 0.75 2 wings= 1.50

0.75 times 2 because there are 2 wings

Answer:

41.41

Step-by-step explanation:

cosA=6/8=3/4

I used a calculator

The answer is 4/8 or 1/2 or 0.5 or 50%

Step-by-step explanation:

A nickel has two faces, heads and tails
Equation of probability = Number of chances/Total Numbers of chances

So, 4 chances of heads / 8 chances of heads or tails, thus, there is a chance of 50% if Harry tosses the coin 4 times to get a head

Since the total probability of the sample space S must be equal to 1, it is not possible for three events with probabilities that add up to more than 1 to form the sample space.

9. If S={a,b,c,d,e,f} with P(a)=P(b)=P(c) and P(d)=P(e)=P(f)=0.1, find P(a).

Since P(a), P(b), and P(c) are equal, we can let P(a) = P(b) = P(c) = x.

Then, we know that P(d) = P(e) = P(f) = 0.1.

The total probability of the sample space S is equal to 1. So, we can write the equation:
P(a) + P(b) + P(c) + P(d) + P(e) + P(f) = 1

Substituting the given values, we get:
3x + 0.1 + 0.1 + 0.1 = 1
3x + 0.3 = 1
3x = 1 - 0.3
3x = 0.7

Dividing both sides by 3, we find:
x = 0.7/3
So, P(a) = 0.233.

10. If S={a,b,c,d,e,f} with P(a)=P(b)=P(c), P(d)=P(e)=P(f), and P(d)=2P(a), find P(a).

Let P(a) = P(b) = P(c) = x. And let P(d) = P(e) = P(f) = y.

We also know that P(d) = 2P(a).

Using the equation for the total probability:
P(a) + P(b) + P(c) + P(d) + P(e) + P(f) = 1

We can substitute the given values:
3x + 3y = 1
We also know that P(d) = 2P(a):
y = 2x

Substituting this into the previous equation:
3x + 3(2x) = 1
3x + 6x = 1
9x = 1

Dividing both sides by 9, we find:
x = 1/9
So, P(a) = P(b) = P(c) = 1/9.

11. If E and F are two disjoint events in S with P(E)=0.2 and P(F)=0.4, find P(E∪F), P(Ec), and P(E∩F).

Since E and F are disjoint, their intersection, E∩F, is empty.

The probability of the union of two disjoint events is the sum of their individual probabilities:
P(E∪F) = P(E) + P(F) = 0.2 + 0.4 = 0.6

The complement of E, Ec, is the event that consists of all outcomes in S that are not in E.

The complement of an event has a probability equal to 1 minus the probability of the event:
P(Ec) = 1 - P(E) = 1 - 0.2 = 0.8

Since E and F are disjoint, their intersection, E∩F, is empty, so its probability is 0:
P(E∩F) = 0

12. It is not possible for E and F to be two disjoint events in S with P(E)=0.5 and P(F)=0.7 because the sum of their probabilities would exceed 1.

Since the total probability of the sample space S must be equal to 1, it is not possible for two events with probabilities that add up to more than 1 to be disjoint.

13. If E and F are two disjoint events in S with P(E)=0.4 and P(F)=0.3, find P(E∪F), P(Fc), P(E∩F), P((E∪F)c), and P((E∩F)c).
Since E and F are disjoint, their intersection, E∩F, is empty.

The probability of the union of two disjoint events is the sum of their individual probabilities:
P(E∪F) = P(E) + P(F) = 0.4 + 0.3 = 0.7

The complement of F, Fc, is the event that consists of all outcomes in S that are not in F.

The complement of an event has a probability equal to 1 minus the probability of the event:
P(Fc) = 1 - P(F)

= 1 - 0.3

= 0.7
Since E and F are disjoint, their intersection, E∩F, is empty, so its probability is 0:
P(E∩F) = 0

The complement of the union of two events, (E∪F)c, is the event that consists of all outcomes in S that are not in the union of E and F.

The complement of an event has a probability equal to 1 minus the probability of the event:

P((E∪F)c) = 1 - P(E∪F) = 1 - 0.7 = 0.3
The complement of the intersection of two events, (E∩F)c, is the event that consists of all outcomes in S that are not in the intersection of E and F.

The complement of an event has a probability equal to 1 minus the probability of the event:
P((E∩F)c) = 1 - P(E∩F) = 1 - 0 = 1

14. It is not possible for S={a,b,c} with P(a)=0.3, P(b)=0.4, and P(c)=0.5 because the sum of their probabilities exceeds 1.

Since the total probability of the sample space S must be equal to 1, it is not possible for three events with probabilities that add up to more than 1 to form the sample space.

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Answer:

AC is 6.5 cm

Step-by-step explanation:

From trigonometric ratios:

\( \sin( \theta) = \frac{opposite}{hypotenuse} \\ \)

opposite » 3 cm

hypotenuse » AC

angle » 28°

\( \sin(28 \degree) = \frac{3}{AC} \\ \\ AC = \frac{3}{ \sin(28 \degree) } \\ \\ AC = \frac{3}{0.46} \\ \\ AC = 6.5 \: cm\)

Answer:

Here sin28 = perpendicular/hypotenuse

AC = sin28 * 3

AC = 0.46*3

AC = 1.38

Answer:

Step-by-step explanation:

( - ∞, - 7), (-3, 5)

By looking at the data under PURCHASE BEHAVIOR, we can see that the consumers in this segment purchase a backpack at a range of purchase every five years. The Option E is correct.

We have several factors that can determine a consumer's purchase interval, including:

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Answer:

Step-by-step explanation:

answer is c. once every year

Answer:

x = 121°

Step-by-step explanation:

The lower left interior angle of the triangle is adjacent to 115° and are supplementary, thus

interior angle = 180° - 115° = 65°

The angle round a point is 360°

The vertex interior angle = 360° - 304° = 56°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle, thus

x = 65° + 56° = 121°