Find the value of x:
X
4
10

Answer:

375

Step-by-step explanation:

Since they started at the same point and went in opposite directions, add the 2 distances.

162.5 + 212.5 = 375

Using the binomial distribution, we have that:

A. The salesperson should expect 1.54 customers until he finds a customer that makes a purchase.

B. There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The expected number of trials until q successes are found is:

[tex]E(X) = \frac{q}{p}[/tex]

In this problem, the probability of a success is of p = 0.65, hence:

[tex]E(X) = \frac{1}{0.65} = 1.54[/tex]

The salesperson should expect 1.54 customers until he finds a customer that makes a purchase.

The probability is p = 0.65 multiplied by P(X = 0) when n = 3, hence:

0.65 x (0.35)³ = 0.0279.

There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

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Answer:

y + 1/2 = 3(x - 2)

Step-by-step explanation:

We have to think about this question in point-slope form, which is a form that explicitly gives us the slope of the line and a single point that it passes through. Point-slope form looks like this: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point that the line goes through. We are given that the line goes through (2, -1/2) which means x1 = 2 and y1 = (-1/2). We are also given that the slope is 3. We can plug these quantities into the equation to solve:

y - (-1/2) = 3(x - 2) OR y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

The correct option is (3).

The slope of a line indicates its direction and steepness. Finding the slope of lines in a coordinate plane can help predict whether the lines are parallel, perpendicular, or have no relationship at all without actually using a compass.

As per the given data:

We have to find out the equation of the line that passes through (2, -1/2) and has a slope of 3.

As we know a point at the slope of the line, we can use the point slope form:

[tex]y - y_1 = m(x-x_1)[/tex] , where m is the slope and [tex](x_1, y_1)[/tex] is the point through which the line passes.

y - (-1/2) = 3(x - 2)

y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

Hence, The equation of the line is y + 1/2 = 3(x - 2).

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Answer:

The product is the difference of squares is [tex]$$\left(c-5\right)\left(c+5\right)={{c}^2}-25$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(c-5)(c+5)=(c)^{2}-(5)^{2} \\&(c-5)(c+5)=c^{2}-25\end{aligned}$$[/tex]

Answer:

the Slope: 11

the y-intercept: (0, - 8) x        y

                                     0       -8

                                     1         3

Step-by-step explanation:

Answer:

[tex]y=\frac{11}{8}x+\frac{1}{2}[/tex]

The final amount of the compound interest after 6 years would be $ 294, 122, 500

The formula for the final amount is given as;

[tex]A = P( 1 + \frac{r}{n}) ^n^t[/tex]

Where

A = final amount

P = principal interest

r = interest rate

n = number of times

t = time of periods

We have,

A = [tex]2500[/tex] [tex]( 1 + \frac{6}{1}) ^1^*^6[/tex]

A = [tex]2500 ( 7)^6[/tex]

A = [tex]2500[/tex] × [tex]117, 649[/tex]

A =$ [tex]294, 122, 500[/tex]

Thus, the final amount of the compound interest after 6 years would be $ 294, 122, 500

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Answer:

Vertex: (-2, 0)

Axis of symmetry: x = -2

Direction of opening: Upwards

Min: 0

Y-intercept: 4

Step-by-step explanation:

    Let us graph this line, and then pull out the details we need. See attached.

    What do all of these different things mean?

Vertex: This is where the graph intercepts the axis of symmetry (x = -2, see below) and is at point (-2, 0) for this graph.

Axis of Symmetry: This is the line that the graph is symmetrical across. The "center" of the graph. Here, it is x = -2.

Direction of Opening: The direction that the graph is going/opening towards. In this case, it is upwards.

Min: The minimum (in this case) value, the lowest y-coordinate. This is 0 here.

Y-intercept: The point at which the line intercepts the y-axis. This is 4 here.

Answer:

See Below

Step-by-step explanation:

Since they are lines, and if two lines have angles that are congruent, then it has to be perpendicular. Angles sum up to 180, and since they are equal, it is 90.

The game is profitable since the payout is always less than what you earn.

Given that a fair game with 4 or more outcomes using a binomial situation presented in this lesson (simulated with a spinner or random number) and adjust the point values the  so cost of the 10 points will make the game profitable.

Let's discuss the Lucky 7 game

The game is played with the two fair dice rolls.

You put your money on either of 3 things: Above 7, Lucky 7 or below 7

The game below is designed in Excel:

Each cell formula to generate the game:

They are 36 possible outcomes.

7 is the most likely number coming up

6/36=1/6

of the time.

Thus the expected value of the bet is:

(5/12)x₂+(5/12)x₂+(1/6)x₃=26/12

Which, of course, can not make any sense. so, the good idea from the standpoint of the bank is to pay two times on only one of the two possibilities, not a seven, and to give the bet back on the 7. This then gives:

(5/12)x₂+(5/12)x₀+(1/6)x₁=12/12=1

Which is a perfectly fair game.

Of course, the bank wouldn't approve either, so we probably need more restrictions. The way 7 comes out is: 2 ways for each case, (1,5), (2,5), (3,4), then a constraint like not to pay on (5,1) would be added.

Then the 7 returns the money

4/36 = 1/9.

The new case then yields:

(5/12)x₂+(5/12)x₀+(1/9)x₁=34/36=17/18

This says that for every $18 handled in bets the bank expects to pay out $17.

Hence we can say that the game is profitable since the payout is always less than what you earn.

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Option (A) :  least: 10 hours; greatest: 14 hours

The function f(x) = sin x has all real numbers in its domain, but its range is

−1 ≤ sin x ≤ 1.

How to solve such range questions?

Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question

Given: d(t) = 2sin(xt) + 12

=  −1 ≤ sin (xt) ≤ 1.

=  −2≤ 2 sin (xt) ≤ 2.

=  10 ≤ 2sin (xt) + 12 ≤ 14

=   10 ≤d(t) ≤ 14

Thus  least: 10 hours; greatest: 14 hours

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The data is modeling a geometric sequence because they have a common ratio of 2.

The recursive formula to determine the time she will complete station 5

Part C:

The explicit formula to find the time she will complete the 9th station.

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Answer:

OC

Step-by-step explanation:

4×3=12m

5+1=6n

4÷1=4

Hence, the area of base is [tex]x^2 - 2x - 9[/tex]

Division in maths is breaking a number into equal parts and finding out how many equal parts can be made.

The volume of a rectangular prism is,

        Volume = Area x Height

Substituting the given expressions,

[tex]x^3 + 2x^2 - 17x - 36 = Area x (x + 4)[/tex]

Area = [tex](x^3 + 2x^2 - 17x - 36) / (x + 4)[/tex]

Now, let's use synthetic division,

-4 |    1    2    -17   -36

----    __-4___8___36

        1    -2     -9     0

The expression for the area is [tex]x^2 - 2x - 9[/tex]

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Answer:

QR=17

Step-by-step explanation:

[tex](12)(x-2)=(3)(3x-1)\\12x-24=9x-3\\3x-24=-3\\3x=21\\x=7[/tex]                

 [tex]x=7\\\\QR=12+x-2\\=12+(7)-2\\QR=17[/tex]

The probability of not winning of united is [tex]\frac{2}{5}[/tex] .

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that the probability of winning of united is [tex]P(A)=\frac{3}{5}[/tex] .

Usually, we take the total probability is 1

So, the probability of not winning of united is [tex]1-\frac{3}{5}[/tex]

                                                                        [tex]=\frac{5-3}{5}\\=\frac{2}{5}[/tex]

Therefore, the probability of not winning of united is [tex]\frac{2}{5}[/tex] .

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Answer:

-4

Step-by-step explanation:

Work Shown:

| x-1 | < 2

-2 < x-1 < 2 ... see note1 below

-2+1 < x-1+1 < 2+1 ... see note2

-1 < x < 3

A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.

In this question we have two rigid transformations to be defined: (i) Rotation, (ii) Translation. Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. Herein we must describe the characteristic of a rotation and a translation.

A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.

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Answer:

A rotation is a transformation where an object-

moves in a circular arc around a point

A translation is a transformation where an object-

moves a specified distance along a line parallel to a specified line

Step-by-step explanation:

Plato answer

You can by 42 combinations of items from the store

The given parameters are:

Envelop = 7

Stamp = 6

The number of combination is:

Combination = Envelop * Stamp

So, we have:

Combination = 7 * 6

Evaluate

Combination = 42

Hence, you can by 42 combinations of items from the store

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Hello,

[tex]Speed = \frac{Distance}{Time} = \frac{15 km}{3 h} = \boxed{5 km/h}[/tex]

Stan walked at 5 km/h

The total interest for 4 years with a principal amount of $500 and a rate of 2% is $40.

The formula for the simple interest is,

I = PTR

where

I is the interest, P is the principal amount, T is the period, and R is the rate of interest.

The given data is,

Kaitlin wants to save $500 in her savings account. I.e., P = $500

For 4 years i.e., T = 4 years and the rate R = 2%  i.e., R = 0.02

Then,

the total interest for 4 years with no more deposits is

I = PTR

 = $500 × 4 × 0.02

 = $40

Therefore, the total interest that Kaitlin will earn for 4 years is $40.

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Answer:

Step-by-step explanation:

Hi!

A is congruent to angle C. Because angle FCE is on the other side of the angle C which is equal to A, angle FCE has to equal A

Based on the calculations, the scale factor for this dilation is equal to 1/3.

First of all, we would use the distance formula to find the length of side QR and Q'R' as follows:

Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]

Substituting the given points into the formula, we have;

Distance QR = √[(5 - (-1))² + (0 - 0)²]

Distance QR = √[(5 + 1)² + (0)²]

Distance QR = √[6² + 0]

Distance QR = √36

Distance QR = 6 units.

For side Q'R', we have:

Distance Q'R' = √[(1 - (-1))² + (2 - 2)²]

Distance Q'R' = √[(1 + 1)² + (0)²]

Distance Q'R' = √[2² + 0]

Distance Q'R' = √4

Distance Q'R' = 2 units.

Now, the scale factor for this dilation is given by:

Scale factor = Q'R'/QR

Scale factor = 2/6

Scale factor = 1/3.

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Answer:

Step-by-step explanation:

its 1/3

a. x = 120°

b. x = 88°

c. x = 146°

Determining the value of x

A. We have that x and angle 80° as shown in the diagram is on a straight

Angles on a straight line = 180°

Then,

x + 80° = 180°

Make 'x' subject

x = 180° -  80°

x = 100°

B. From the diagram, we can see that 'x' at ∠BCD is alternate to ∠EDC which is 88°

It is important to note that alternate angles are equal

Then,

x =  88°

C. From the diagram, we can see that 'x' at CDE is on a straight line with ABC

Angles on a straight line are equal

Then,

x + 34° = 180°

Make 'x' subject of formula

x = 180° - 34°

x = 146°

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Answer:

Step-by-step explanation:

I'm going to assume you want it to be a perfect triangle, so then we would have the equation 4x=24. So we can divide each side by 4 to get rid of the 4 and get x by itself. So 24/4= 5. So x=5

The system of inequalities represents the number of color copies, x, and grayscale copies, y, that julissa can print to meet her goal is;

x + y ≥ 8

x + y ≥ 84x + 2y ≤ 25

let

x + y ≥ 8

4x + 2y ≤ 25

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The expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

Given the expression below;

-0.5 (1.7 + 1.7)

According to the distributive law;

A(B+C) = AB + AC

Expand

-0.5(1.7) + (-0.5)(1.7)

-0.5(1.7) - 0.5(1.7)

2(-0.5(1.7))

Hence the expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

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Answer:

Step-by-step explanation:

Since the sum of all exterior angles in a polygon is 360°, we have to divide 360 by 6 to find the number of sides.

360/6 = 60.

So, the polygon has 60 sides.

Hope this helps! (:

Answer:

14

Step-by-step explanation:

because it is a small angle that will indooor more sides