Which statement about the following graph is correct?
O
The graph is symmetric about the line x = -1.
The graph is symmetric about the line y = -1.
The graph is not symmetric.
The graph is symmetric about the line x-1.

The probability that there will be no customers arriving at a checkout counter in the next minute is 0.16530.

The number of customers arriving per minute at the checkout counter of a grocery store is following Poisson Distribution.

A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as [tex]P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}[/tex] .

In the question, we are asked to find the probability that no customer arrives at the checkout, hence we put x = 0, and the mean number of customers per minute (λ) = 1.8.

Substituting the values of x and λ in the equation, we get:

[tex]P(X = 0) = e^{-1.8} \frac{1.8^{0}}{0!}[/tex] ,

or, [tex]P(0) = e^{-1.8} = 0.16530[/tex] .

Therefore, the probability that there will be no customers arriving at a checkout counter in the next minute is 0.16530.

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Using the given information, length of QR = 16.6 cm

The area of the trapezium is 304.5 cm²

From the question we are to calculate the length of QR and the area of trapezium PQRS

In the given diagram,

Let the midpoint of PS be T

Then, we can write that

|OP|² = |OT|² + |PT|²  (Pythagorean theorem)

|OP| = radius = 13 cm

|PT| = 1/2 × PS = 1/2 × 24 cm = 12 cm

∴ 13² = |OT|² + 12²

169 = |OT|² + 144

|OT|² = 169 -144

|OT|² = 25

|OT| = √25

|OT| = 5 cm

Also, let the midpoint of QR be U

Then, we can write that

|OQ|² = |OU|² + |QU|² (Pythagorean theorem)

|OQ| = radius = 13 cm

From the given information,

The distance of QR from O is twice the distance of PS from O

∴ |OU| = 2 × |OT|= 2 × 5 cm = 10cm

Thus,

13² = ||² + 12²

169 = 10² + |QU|²

|QU|² = 169 -100

|QU|² = 69

|QU| = √69

|QU| = 8.3 cm

Now,

Length of QR = 2 × |QU| = 2 × 8.3 cm

Length of QR = 16.6 cm

b)

Area of the trapezium = 1/2(|QR| + |PS|) × |TU|

Area of the trapezium = 1/2(16.6 + 24) × 15

NOTE: |TU| = |OT| + |OU|

Area of the trapezium = 1/2(40.6) × 15

Area of the trapezium = 20.3 × 15

Area of the trapezium = 304.5 cm²

Hence, the area of the trapezium is 304.5 cm²

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Answer: f(2)=g(2)

Step-by-step explanation:

The graphs intersect at x=2.

The correct statement which is true regarding the functions on the graph is,

f (2) = g (2)

We have to given that,

Graph of functions f (x) and g (x) are shown in figure.

Now, From the graph,

At x = 2;

f (2) = 0

And, At x = 2;

g (2) = 0

Therefore, At x = 2,

f (2) = g (2) = 0

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Answer:

  (c)  y < x^2 -5x

Step-by-step explanation:

A quadratic inequality is one that involves a quadratic polynomial.

The degree of a polynomial is the value of the largest exponent of the variable. When the degree of a polynomial is 2, we call it a quadratic.

For the following inequalities, the degree of the polynomial in x is shown:

We see that the degree of the polynomial in x is 2 in ...

   y < x^2 -5x

so that is the quadratic inequality you're looking for.

__

Additional comment

When a term involves only one variable, its degree is the exponent of that variable: 5x^3 has degree 3. When a term involves more than one variable, the degree of the term is the sum of the exponents of the variables: 8x^4y3 has degree 4+3=7.

It would be take upto 999 revolutions.

Let try to solve it,

Let n represent number of revolutions.

We are asked to find the number of revolutions it will take for a car wheel of diameter 30 in. to travel a distance of one mile.

1 mile = 63360 inches.

We will use circumference of circle formula to solve our given problem.

Circumference = pi*d , where, D represents diameter of circle.

Now, we will set the product of n and circumference of circle equal to 63360 inches as:

pi*22*n= 63360

n= 63360*7/ 22*22

n= 443520/444

n= 998.91

Therefore It would be take upto 999 revolutions.

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The correct statement is [tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]

The proper form of the question is added as an attachment

The expressions are given as:

[tex](2.06 * 10^{-2})(1.88 * 10^{-1})[/tex]

[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]

Evaluate both expressions

[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) = 2.06 * 1.88 * 10^{-2-1}[/tex]

[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) = 3.87 * 10^{-3[/tex]

[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}} = \frac{7.69}{1.88} * 10^{5-2[/tex]

[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}} = 4.09 * 10^3[/tex]

By comparing both expressions, we have:

[tex]3.87 * 10^{-3} < 4.09 * 10^3[/tex]

This means that:

[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]

Hence, the correct statement is [tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]

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Answer:

64/7

Step-by-step explanation:

Each term is multiplied by -4 (a number not a fraction as the denominator stays the same each time).

[tex]\frac{-16}{7} *\frac{-4}{1}= \frac{64}{7}[/tex]

Answer

64/7

Step-by-step explanation:

Khan <3

The number, which on divided by 7 gives a quotient of 247 and a remainder of 3 is 1732. Computed using linear equations.

In the question, we are informed that a number when divided by 7, gives a quotient of 247 and a remainder of 3.

Assuming the number to be x.

We can say that x is our dividend, 7 is the divisor, 247 is the quotient, and 3 is the remainder.

The division algorithm equation is:

Dividend = Divisor*Quotient + Remainder,

Substituting values in this equation, we get a linear equation:

x = 7*247 + 3.

To solve for the unknown number x, we solve the equation as follows:

x = 7*247 + 3,

or, x = 1729 + 3,

or, x = 1732.

Thus, the number, which on divided by 7 gives a quotient of 247 and a remainder of 3 is 1732. Computed using linear equations.

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Answer: tan x

Step-by-step explanation: An angle determines if a side is opposite the angle, or adjacent the angle. Since p/a is something to do with the tangent, as it is not using the hypotenuse (the longest side.) Tangent is Opposite/Adjacent, while Sine is Opposite/Hypotenuse and Cosine is Adjacent/Hypotenuse. The only thing that makes sense is tangent.

So, that leaves us with either tan y or tan x. Well, with x, the angle that x points to (which is the opposite side) is p, and the adjacent is a, so p/a must be Tangent(x) since it is Opposite/Adjacent sides.

Only if it was r/p would it be tan y, since r becomes the opposite and p becomes the adjacent.

Answer:

Step-by-step explanation:

First bullet is called Perfect Square Trinomial (PST), the first and last is a perfect square and the middle is twice the product of the squared first and last term.  To factor, just copy the middle sign and square the first and last term.

---

2nd bullet is also a PST with a value on a. Likewise you just need to square the first and last term. Then, copy the middle sign.

--

3rd bullet is a trinomial. To get the factor, get the prime factor of the value of a. Then, find the factors of 8 that when add up results to the value of b.

-

4th bullet is a special case. First get the square root of the first and last term, and copy the sign, Then, copy the factors and change it to the opposite sign.

Answer:

24

Step-by-step explanation:

If x were to be 2, then we need to substitute the 2 in for x

So, it would be 6(2)^2

2 times 2 is 4 and 4 times 6 is 24

Hope this helped! :)

Answer:

A. 13 < X < 14

Step-by-step explanation:

Because x is square rooted, that means the other values inside the equation will also be square rooted. If we square root 169, that would be 13 & since there is only one option with 13, the answer will be A.

Answer:

For question 3, the slope would be -5

Step-by-step explanation:

If you wanted to graph this you would have to plot one of the points that is already given. Then from that point, you would move 5 units down and 1 unit to the right. If you run out of space, you can go to the other direction by going 5 units up and 1 to the left.

Hope this helps :)

Answer:

578 sq ft

Step-by-step explanation:

he length of a rectangular garden is twice its width and its area is 578 square feet.

Answer:

60 or 60:1 (Depending on the answer choices)

Step-by-step explanation:

160 feet = 1920 inches (160 * 12)

[tex]\frac{1920}{32} = \frac{60}{1}[/tex]

The scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).

The scale factor is the simplest ratio between the actual and the model's size of the same object.

In the question, we are informed that in a movie, a child who was 32 inches tall was ''blown up'' to be 160 feet tall.

We are asked to determine the scale factor needed for the props in the movie.

To find the scale factor, we first find the size of the child in the movie in inches.

Size = 160 feet = 160*12 inches = 1920 inches.

Now, the scale factor is calculated as the ratio of the actual size to the size in the movie, that is,

Scale factor = 32:1920 = 32/1920 = 1:60.

Therefore, the scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).

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Answer:

26. y= 3/1 x + c

27. m = 1 so eqn will be y = 1x + c

Step-by-step explanation:

find the slope if not given and then use the eqn,

y= mx + c

where m is slope and c is y intercept

Hello and Welcome to Brainly!

Let's take this problem step-by-step:

The problem wants the final answer to be in the form ⇒ y = mx + b

Let's find both of these values first

            (x₁,y₁), (x₂,y₂) are any two points on the line

                 ⇒ let's use (-4,0) and (0,-4)

                      [tex]Slope = \frac{-4-0}{0--4} =\frac{-4}{4} =-1[/tex]

           ⇒, therefore, the y-intercept is -4

Our equation as of now: y __ -x - 4

Now let's use some points to test:

  ⇒ what way inequality should face:

       [tex]0 _._._. -(0) - 4\\0 _._._. -4\\0 \geq -4[/tex]

Therefore our equation is [tex]y\geq -x-4[/tex]

  * we use '≤' since the line is solid

        ⇒ if the line were dotted, we would use '>'

Answer: y ≥ -x - 4

Hope that helps!

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Answer:

y ≥ -x − 4.

Step-by-step explanation:

a. Find the graph of their common region in the attachment

b. The area of the common region of the graphs is 8 units²

Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.

So, the graph of x + y ≤ 6 is the region below the line y = - x + 6

From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)

Find the graph of their common region in the attachment

From the graph, we see that the common region is a right angled triangle with

So, its area = 1/2 × height × base

= 1/2 × 4 units × 4 units

= 1/2 × 16 units²

= 8 units²

So, the area of the common region of the graphs is 8 units²

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Answer:

A' = (3, 6)

B' = (9, -3)

C' = (-12, -6)

Step-by-step explanation:

you can mulitply both the x and y coordinates of each point by the scale factor (3)

point (1, 2) becomes point (3, 6)

(3, -1) becomes (9, -3)

(-4, -2) becomes (-12, -6)

hope this helps!! have a lovely day :)

{this is why whoever wrote the problem gave that hint--you can follow through on that logic, but just remember that it has to be a scaled version of the original figure--so the ratios between points (and x/y values) must be consistent}

Answer:

40%

Step-by-step explanation:

The function represented by f(x) = (1/2)(3)ˣ is an exponential growth

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

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The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

If b > 1, it is an exponential growth but if b < 1, it is an exponential decay.

Given the function:

f(x) = (1/2)(3)ˣ

since 3 > 1, it is an exponential growth.

The function represented by f(x) = (1/2)(3)ˣ is an exponential growth

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Jun Wei has a total of 40 coins. An algebraic expression or equation with the given information is formed to calculate the total number of coins.

An algebraic expression is the combination of one or more variables, coefficients, and constants separated by operators. Each of them is called terms of the expression.

Eg: a + 6x + 5y + 2

Here there are 4 terms with 3 variables, 3 coefficients, and one constant.

Given that,

Jun Wei has 12 more 10 cents coins than 20 cents coins.

So,

Consider the number of 20-cent coins = x

Then, the number of 10 cent coins = x + 12

It is given that the total value of all the coins is $5.40.

Where 1 $ = 100 cents. That implies, $5.40 = 540 cents

So,

the total value of the coins = 540 cents

⇒ 20(x) + 10(x + 12) = 540

⇒ 30x = 540 - 120

⇒ 30x = 420

∴ x = 40

Hence, there are 40 coins with Jun Wei.

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Answer:

C

Step-by-step explanation:

please mark brainliest

Answer:

the 3rd answer option

Step-by-step explanation:

why ?

similar to the other questions.

we know the total number of coins, which is a sum of quarters and dimes. nothing else is in there.

so,

16 = q + d

and each type of coin has a defined value : a quarter is $0.25, a fine is $0.10.

and so, when you add up the value of all quarters and all dimes you get $3.10.

Effect of multiplying the parent function f(x) = x ^ 2 by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.

Therefore, the effect of multiplying the parent function f(x) = x ^ 2 by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.

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Colorado and Boston have 263 and 219 days of sunshine respectively.

Let the number of days of sunshine in Colorado is x and the number of days of sunshine in Boston is y.

Total number of days of sunshine=482

Also, the number of days of sunshine in Colorado is 1.2 times the number of days of sunshine in Boston.

So, the equation is formed as follows:

x+y=482  -(1)

The other equation is formed as:

x=1.2y  -(2)

Substitute the value x from equation (2) in (1),

1.2y+y=482

2.2y=482

y=482/2.2

y=219

Substitute the value of y in equation (1),

x+219=482

x=482-219

x=263

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The length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

Jurgen cuts 5 meter-long timber beam into 3 pieces, first piece 2.34metres second piece 1.85.

Let the length of the third piece is x m.

2.34 + 1.85 + x = 5

4.19 + x = 5

x =  0.81 m

Thus, the length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.

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