The length of a telephone call made to a company is denoted by the continuous random variable T. It is modelled by the probability density function f(t) = 1/50t, 0

Given that the equation of the line in the diagram is `y = 5 - x`. The line cuts the y-axis at P. So, the coordinates of point P are (0,5) and the gradient of the line is `-1`.

The equation of the line can be written as `y = -1x + 5`.Therefore, the y-intercept of the line is 5. Therefore, the coordinates of point P are (0,5).

To find the gradient of the line, we have to write the equation of the line in the form of `y = mx + c`.

We can rewrite `y = -1x + 5` as `y = (-1)x + 5`.From the above form of the equation, we can see that the gradient `m` is `-1`.Therefore, the gradient of line 1 is `-1`.Hence, the required answer is: Coordinates of point P is `(0,5)`.The gradient of the line is `-1`.

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Answer: d = 3.162278

Step-by-step explanation:

Answer:

3.162278

Step-by-step explanation:

Answer: No

Step-by-step explanation:

Because Mode is not the best centre of tendency use for statistical data. And mode cannot be used for average.

Mean should be used for average values

Answer:

da ba dee da ba doo im blue

Step-by-step explanation:

Grace made a dot plot showing the distances she ran each day for two weeks.

She says that she usually runs 7 miles each day because that is the distance that occurs most often.

Do you agree with Grace’s reasoning?

Use the drop-down menus to explain and show your answer.

Dot plot named as ALTDCDistances RunALTDC has number line from 1 to 7. 1 dot on 1, 3 dots on 2, 3 dots on 3, 3 dots on 4 and 4 dots on 7 are given.

The mode, which is (3,4, or 7) ,(is or is not) a typical distance for the data. The median, which is (3.5,4, or 7),(is or is not) a typical distance for the data. The mean, which is (3,4, or 7) ,(is or is not) a typical distance for the data. So, Grace’s reasoning(is or is not ) correct.

Answer:

f(-8)= -7660

Step-by-step explanation:

f(-8)= 3(-8)^2·5(-8)+20

The story based on the distance-time graph is given below:

Once upon a time, there was a daring bird named Ziggy. Ziggy loved to soar high in the sky, feeling the wind rush beneath her wings.

One day, as she flew higher and higher, she spotted a berry bush on the ground below. Without thinking twice, she dove down to snatch a berry.

But as she got closer, she realized the bush was a trap set by a mischievous fox. Ziggy narrowly escaped the trap and soared back into the sky, but not before losing some altitude.

Determined to keep flying, Ziggy flapped her wings with all her might, gradually ascending back up to her previous height. And as she flew onward, she couldn't help but wonder what other surprises lay ahead.

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Step-by-step explanation:

C + 1 = 2(L-1)

C +1= 2L -2

C- 2L = -3 ......(eq.1)

L+1 = C-1

C- L = 2 .....(eq.2)

by elimination :

C - 2L = -3

C - L = 2

________-

- L = -5

L = 5

C = 2+5 = 7

so, Leo has 5 cars and Charlie has 7 cars

Answer:

Charlie=7, Leo=5

Step-by-step explanation:

cant explain

Answer:  If T is the midpoint, then ST = TU. 8x + 11 = 12x - 1.

Step-by-step explanation:

Answer:

SU is x² + 4x + 32

Step-by-step explanation:

That means T is a point between SU. Therefore;

SU = ST + TU

\(SU = ( {x}^{2} ) + (4x + 32) \\ SU = {x}^{2} + 4x + 32\)

Answer:

\(\dashrightarrow \: { \tt{3.{ \bar{42}, \: \: 0, \: \: \frac{17}{9}, \: \: \frac{7}{3} , \: \: - 6, \: \: 8 }}}\)

Step-by-step explanation:

• A rational number is a number which can have a denominator i.e fraction, integers [ have denominator of 1 ]

Answer:

A,C,D,E,F,G

Step-by-step explanation:

...............hope it helps

On a linear graph, the unit rate is obtained by calculating the slope of the line.

Answer:

x = -3

Step-by-step explanation:

Solution

Area of the rectangle = length x breadth

A. Write an equation to showing relationship between x and y:

The equation for the relationship between x and y is

3x + 2y = 30

Answer:

working on it

Step-by-step explanation:

It is not necessarily true that either [a] = [0] or [b] = [0] when [a],[b] ∈ z6 and [a]·[b] = [0].

This is because in z6, there are other pairs of elements that multiply to [0] besides [0] and any other element. For example, [2]·[3] = [6] = [0] in z6, but neither [2] nor [3] are equal to [0].

However, if [a],[b] ∈ z7 and [a]·[b] = [0], then it is necessarily true that either [a] = [0] or [b] = [0]. This is because z7 is a field, meaning that it has no zero divisors (elements that multiply to [0] besides [0] itself). Therefore, the only way for [a]·[b] = [0] in z7 is if either [a] or [b] are equal to [0].

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a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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Answer:

We conclude that

\(a\times \left(b-c\right)=\:a\times b-a\times c\)

           \(-\frac{7}{3}=-\frac{7}{3}\)

        L.H.S = R.H.S    

Step-by-step explanation:

Given the property expression

\(a\times \left(b-c\right)=\:a\times b-a\times c\)

Given that:

Determining the LEFT-HAND SIDE

\(a\times \left(b-c\right)\)

substituting a= -3/5, b= 5/9 and c= -10/3​

\(a\times \left(b-c\right)\:=\:\:-\frac{3}{5}\times \left(\frac{5}{9}-\left(-\frac{10}{3}\right)\right)\:\:\:\:\:\:\:\:\:\:\:\:\)

                  \(=-\frac{3}{5}\times \:\left(\frac{5}{9}+\frac{10}{3}\right)\:\:\:\)

                  \(=-\frac{3}{5}\times \frac{35}{9}\)

                   \(=-\frac{7}{3}\)

Determining the RIGHT-HAND SIDE              

\(\:a\times \:b-a\times \:c\)

substituting a= -3/5, b= 5/9 and c= -10/3​

\(\:a\times \:b-a\times \:c=ab-ac\)

                      \(=-\frac{3}{5}\left(\frac{5}{9}\right)-\left(-\frac{3}{5}\right)\left(-\frac{10}{3}\right)\)

                      \(=-\frac{3}{5}\cdot \frac{5}{9}-\frac{3}{5}\cdot \frac{10}{3}\)

                      \(=-\frac{15}{45}-\frac{30}{15}\)

                      \(=-\frac{1}{3}-2\)

                      \(=\frac{-7}{3}\)

Apply the fraction rule:  \(\frac{-a}{b}=-\frac{a}{b}\)

                      \(=-\frac{7}{3}\)

Therefore, we conclude that

\(a\times \left(b-c\right)=\:a\times b-a\times c\)

           \(-\frac{7}{3}=-\frac{7}{3}\)

        L.H.S = R.H.S                                          

Answer:

y = - \(\frac{5}{2}\) x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = \(\frac{-2-3}{0-(-2)}\) = \(\frac{-5}{0+2}\) = - \(\frac{5}{2}\)

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - \(\frac{5}{2}\) x - 2 ← equation of line

1. The area of shaded portion is 75m².

2. The area of shaded portion is 104 m².

3. The area of shaded portion is 284 m²

Area of the square = 10 × 10 = 100m²

Area of unshaded portion= 5 × 5 = 25 m²

therefore, area of shaded portion = 100- 25 = 75m²

2. Area of rectangle = 30 × 19= 480m²

area of unshaded portion= 28 × 17 = 376m²

therefore, area of shaded portion= 480 - 376 = 104 m²

3. Area of rectangle= 60 × 40 = 2400m²

area of unshaded portion= 56 × 36 = 2016m²

therefore, area of shaded portion= 2400- 2016 = 284 m²

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Based on the given t-value of 0.35, it's unlikely that there's a difference between the arms and legs data in terms of the maximum weight students can lift.

If the t-value of the lab group investigating the maximum weight students can lift with their arms compared to their legs is 0.35, the conclusion that would be justified is that it's unlikely there's a significant difference between the arms and legs data. A t-value is used to determine if there is a significant difference between two sets of data. In this case, the t-value is 0.35, which is a relatively small value. When the t-value is small, it indicates that the difference between the two sets of data is not significant. Therefore, it is unlikely that there is a significant difference between the maximum weight students can lift with their arms compared to their legs. However, it's important to note that this conclusion is based solely on the t-value and does not take into account any other factors that may affect the results, such as sample size or individual variability.

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Answer:

you could make this really simple by dividing 300 by 4 to see how much 1/4 of that is and then subtracting 1/4 from 300 to see how much dashawn's water bottle holds,

Step-by-step explanation:

300/4 =75 so 1/4 is equal to 75 mL

300-75=225mL

Dashawn's water bottle holds 225mL

In both cases, the logic used is deductive reasoning. In the first question (a), the logic follows the form of a deductive syllogism. In the second question (b), the logic follows a deductive pattern.

In the first question (a), the logic follows the form of a deductive syllogism. It starts with a general premise that everyone in the Family Madrigal has a special gift. The second premise states that Luisa is in the Family Madrigal. From these two premises, the conclusion is drawn that Luisa has a special gift. This deductive reasoning relies on the truth of the premises and the logical structure of the argument.

Similarly, in the second question (b), the logic follows a deductive pattern. The first premise states that every dog the person has seen is covered in fur. The second premise states that Barky is a dog. From these premises, the conclusion is drawn that Barky is covered in fur. This deductive reasoning relies on the assumption that the person's observations are representative and that Barky fits the category of dogs.

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Answer:

Step-by-step explanation:

I'm going to assume that the car goes 50-x mph uphill and 50+x mph downhill.

x ≅ 24 miles per hour

26 mph uphill and 74 mph downhill

Answer:

252 m^2

Step-by-step explanation:

The equation for surface area in a rectangular prism is SA = 2 (lh +wh + lw ).

So when we plug in the numbers inti the equation we do SA = 2(12×3 + 6×3 + 12×6)

FOLLOW P.E.M.D.A.S (parentheses, exponents, multiplication, division, addition, subtraction)

we get SA = 2(36 + 18 + 72)

then we multiply 2, by each of the numbers.

SA = (72 + 36 + 144)

Add them together and you get

SA = 252

Answer: -3/16

Step-by-step explanation:

When there is a negative exponent like x^-2 it equals 1/(x^2) the negative puts the number as a fraction so continuing...

-12(x^-2) (y^-2) can be rewritten as

-12 (1/x^2) (1/y^2) now we plug in x = -2 and y = 4

-12 (1/(-2^2) (1/(4^2)); -2^2 = 4 , 4^2 = 16

-12 (1/4) (1/16)

-3 (1/16)

= -3/16

We can convert that 30% into a decimal, as: 0.3 (That's 30/100)

Now, we can multiply this 0.3 by any quantity that we want to calculate 30% from.

For example, let's take Justin's commission:

Adding this to his base salary,

We can conclude that Justin's paycheck for the week would be $1,117.5

Similarly, the expression for Justin's paycheck in a week were he made x dollars in sales is:

Answer:

No Solution.

Step-by-step explanation:

3x-8=3(x-4)+1

3x-8=3x-12+1

3x-3x-8=-12+1

-8=-11

no solution.

Answer:

5016 feet

Step-by-step explanation:

Answer:

Answer is in attached photo. (B)

Step-by-step explanation:

The solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:

1) Substitution Method

2) Elimination Method

Answer:

a) growth

Step-by-step explanation:

f(t) = 1/4 × 4^t

let t = 2

f(2) = 1/4 × 4²

f(2) = 4

let t = 3

f(3) = 1/4 × 4³

f(3) = 16

As the value of t increases, the output increases, so the answer is a) growth.