An inequality is shown.
Select the statement(s) and number line(s) that can represent the inequality. Click all that apply.

The equation of exponential function=y = 0.054 × [tex]1.028^{x}[/tex]

As the name implies, exponents are utilised in exponential functions. But remember that a variable serves as the exponent instead of a constant as the basis of an exponential function.

A function is a power function rather than an exponential function if its base is a variable and its exponent is a constant.

If the graph of exponential function passes through the points (1960,19.005) and (2010,19.548), then the coordinates of these points satisfy the equation, y = [tex]ab^{x}[/tex]

Now, 19.005 = a × [tex]b^{1960}[/tex]

⇒  [tex]b^{1960}[/tex] = 19.005/a

Similarly, 19.548 = a × [tex]b^{2010}[/tex]

⇒ [tex]b^{2010}[/tex] = 19.548/a

⇒  [tex]b^{1960}[/tex] × [tex]b^{50}[/tex] = 19.548/a

⇒ [tex]b^{50}[/tex] = 19.548/a × a/19.005

         = 1.028

Putting this value to find a,

we get a = 0.054

So, the equation of exponential function=

y = 0.054 × [tex]1.028^{x}[/tex]

To know more about exponential function, visit:

https://brainly.com/question/14355665

#SPJ1

0.142857.

To convert the rational number 1/7 to its decimal form and round to the nearest thousandth, let's start by converting the fraction into a long division problem.

Enter the numerator of the fraction, 1, into the division box, and then divide it by the denominator of the fraction, 7.

The result of this long division is 0.142857. Finally, round this decimal to the nearest thousandth, which gives us 0.143.

Learn more about decimal form

brainly.com/question/16361602

#SPJ11

The scale factor of the preimage to image is 3. Then the correct option is C.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The picture rectangle has points on coordinates (0, 0), (0, 8), (9, 8), and (9, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).

The scale factor is given as,

SF = 9 / 3

SF = 3

The scale factor of the preimage to image is 3. Then the correct option is C.

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ1

The complete question is given below.

What is the scale factor in the dilation?

On a coordinate plane, the image rectangle has points (0, 0), (0, 8), (9, 8), and (8, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).

a) One-sixth

b) One-third

c) 3

d) 6

Answer:

Step-by-step explanation: C  !!!!!! / 3

Edge 2023

1/6

1/3

3   <--------------- correct

6

The ordered pair that is a member of both equations is (-27/7, -11/7).

To find the ordered pair that is a member of both equations, we need to solve the system of equations. We can do this by using the elimination method.

First, we will multiply the first equation by 2 and the second equation by -4 to eliminate the x variable:

-4x - 8y = 28
-20y - 8x = 16

Next, we will add the two equations together:

-28y = 44

Now we can solve for y:

y = -44/28
y = -11/7

Now we can plug this value of y back into one of the original equations to solve for x:

-2x - 4(-11/7) = 14
-2x + 44/7 = 14
-2x = 14 - 44/7
-2x = 54/7
x = -27/7

Therefore, the ordered pair that is a member of both equations is (-27/7, -11/7).

Answer: The ordered pair that is a member of both equations is (-27/7, -11/7).

To know more about ordered pairs, refer here:

https://brainly.com/question/30805001#

#SPJ11

Ordered pair (0, 3), (1, 48) and many more lies on the graph of the function.

What are Functions?

A function in math is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. It can be represented using an equation, graph, or table of values.

The exponential function [tex]f(x) = 3(4)^(2x)[/tex] can be evaluated for any value of x to get the corresponding value of y. To find ordered pairs that lie on the graph of this function, we can substitute different values of x into the function and calculate the corresponding values of y.

For example, if we substitute x = 0 into the function, we get:

[tex]f(0) = 3(4)^(2(0)) = 3(4)^0 = 3(1) = 3[/tex]

So the ordered pair (0, 3) lies on the graph of the function.

Similarly, if we substitute x = 1 into the function, we get:

[tex]f(1) = 3(4)^(2(1)) = 3(4)^2 = 3(16) = 48[/tex]

So the ordered pair (1, 48) also lies on the graph of the function.

We can repeat this process for other values of x to find more ordered pairs that lie on the graph of the function.

To learn more about Functions from the given link

https://brainly.com/question/22340031

#SPJ1

Answer:

Step-by-step explanation:

45 points for signing up.

2.5 points for each visit [tex]=2.5v[/tex]

Needs to total 75 points.

So [tex]45+2.5v=75[/tex] is the solution.

This is shown by option [tex](D)[/tex].

The required cost of the cans of weedkiller needed to cover lawn are  £ 47.4.

The formula A = 12 (a Plus b) h is used to calculate the area of a trapezoid, where a and b are the bases (parallel sides) and h is the height (the angle between the bases).

We have;

Dimensions of Trapezoid; a = 20, b = 12, Height = h

So;

[tex]$Area = \frac{(a+b)h}{2}$[/tex]

For h, Using Pythagoras theorem;

17² = 8² + h²

h = 15 m

Then,

[tex]$Area = \frac{(12+20)15}{2}$[/tex]

Area = 240 Sq meter

Then,

100  Sq meter = £19.75

For 240  Sq meter

= £19.75(2.4)

= £ 47.4

Thus, required cost is  £ 47.4.

To know more about Trapezoid visit:

brainly.com/question/8643562

#SPJ1

The first ship sails on a bearing of 83° at 30 knots while the second on a bearing of 173° at 20 knots. After two hours, the distance between the ships is 72 NM

The two ships are travelling on different bearings and at different speeds. To calculate the distance between them after two hours, we need to use the formula:

Distance = Speed x Time

The distance the first ship has travelled after two hours:

Distance 1st ship = 30 knots x 2 hours = 60 nautical miles (NM)

The distance the second ship has travelled after two hours:

Distance 2nd ship = 20 knots x 2 hours = 40 nautical miles (NM)

The angle difference = 173° -  83°  = 90°

Since the port, the first ship, and the second ship form a right triangle, we can find the total distance between the two ships using the Pythagorean Theorem.

Distance² = (60 NM)² + (40 NM)²

Distance = √ (3600 + 1600) = √ 5200 = 72 NM


Therefore, after two hours, the two ships will be 72 NM apart.

Learn more about Pythagorean Theorem here:
https://brainly.com/question/24761611

#SPJ11

The result obtained  when x^(4)-6x^(2)-x-19 is divided by x-3  using long division method is    x3 - 18x2 - 9x - 57 + 19/x-3.

The question is, "Use the long division method to find the result when x^(4)-6x^(2)-x-19 is divided by x-3".

To solve this problem using long division, we need to set up the division like this:

    x4 - 6x2 - x - 19

    ___________________      (x-3)

                      0

                           -3x3 - 18x2 - 9x - 57

Now, divide the first term of the numerator by the first term of the denominator, x4/x = x3, and write it above the division. Next, multiply the result x3 by the denominator (x-3) to get -3x3.

Now subtract -3x3 from the numerator (x4 - 6x2 - x - 19) to get -6x2 - x - 19. Divide this by the denominator (x-3) to get -18x2 - 9x - 57, and write it below the division. Now multiply the result -18x2 by the denominator (x-3) to get -54x2 - 27x - 171.

Finally, subtract -54x2 - 27x - 171 from -6x2 - x - 19 to get the remainder, -19.

To know more about long division click on below link:

https://brainly.com/question/28824872#

#SPJ11

(a) The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

(b) The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

The average rate of change of a function is the slope of the line that passes through two points on the graph of the function. It is calculated by the difference in the y-values of the two points divided by the difference in the x-values of the two points.

The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

Therefore, the average rate of change of f on [x,x+h] is (x^2-5x-8h-11)/(x^2-8x-8h+64).

Learn more about Average rate

brainly.com/question/12395856

#SPJ11

The value of  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given equation is  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex]

[tex]\sum \:a_n+b_n=\sum \:a_n+\sum \:b_n[/tex]

By Applying the sum rule

[tex]=\sum \:_{n=1}^{400}2n-\sum \:_{n=1}^{400}1[/tex]

=2×2(400+1)/2 -400

=2×200×401−400

=16000

Hence, the value of  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

The minimum value of the objective function is 16 and it occurs at x = 1 and y = 5.

The given objective function is 9x+3y. The given constraints are y≥−2x+11, y≤−x+10, y≤−3, x+6y≥−4, and x+4.

To minimize this objective function, we need to set up the Lagrangian function:

L(x,y,λ1,λ2,λ3) = 9x+3y - λ1(y+2x-11) - λ2(y-x+10) - λ3(y+3) - λ4(x+6y-4) - λ5(x+4)

We can then find the critical points of this function by taking the partial derivatives of the Lagrangian with respect to x, y, λ1, λ2, and λ3, and setting them equal to zero:

∂L/∂x = 9 - λ2 + 6λ4 = 0
∂L/∂y = 3 - λ1 - λ2 - λ3 - 6λ4 = 0
∂L/∂λ1 = -(y+2x-11) = 0
∂L/∂λ2 = -(y-x+10) = 0
∂L/∂λ3 = -(y+3) = 0
∂L/∂λ4 = -(x+6y-4) = 0
∂L/∂λ5 = -(x+4) = 0

Solving these equations, we get the solution x = 1, y = 5, λ1 = 4, λ2 = -3, λ3 = 8, λ4 = -3, and λ5 = -1.

To know more about Lagrangian function click on below link:

https://brainly.com/question/30426461#

#SPJ11

Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

First, let's calculate the total amount he will need to finance:

Total amount to finance = R160,000 + 0.15 x R160,000 (VAT at 15%) = R184,000

Next, let's calculate the total interest he will need to pay over the 60 months:

Total interest = (principal x rate x time) / 100

where

Total interest = (R184,000 x 10% x 5) / 100 = R92,000

Therefore, the total amount Michael will need to pay over the 60 months is the sum of the total amount financed and the total interest:

Total amount to pay = Total amount to finance + Total interest = R184,000 + R92,000 = R276,000

So, Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

Learn more about interest here : brainly.com/question/20690803

#SPJ1

Answer:

This is an odd function

Step-by-step explanation:

Given a function f(x),

if f(-x) = f(x) then the f(x) is even
If f(-x) = -f(x0 then the function is odd

If neither of the above is true then the function is neither odd nor even

We are given
[tex]f(x) = 4x^3 - x^5 + 5x\\f(-x) = 4(-x)^3 -(x)^5 + 5(-x)\\\\(-x)^3 = - x^3\\(-x)^5 = -x^5\\\\\\\therefore\\f(-x) = 4(-x^3) - (-x^5) + 5 (-x)\\\\= -4x^3 + x^5 - 5x\\\\= -(4x^3 -x^5 + 5x)\\\\= -f(x)[/tex]

So the function is odd

The expression ((-8x⁵)(x⁻³))/(20x²) when simplified, making all exponents positive, will become -2/5.

To simplify the expression ((-8x⁵)(x⁻³))/(20x²), we need to apply the rules of exponents and simplify the coefficients.

First, let's simplify the coefficients:
-8/20 = -2/5

Next, let's apply the rules of exponents:

Product Rule: When multiplying two exponential expressions with the same base, you can add the exponents. That is, xᵃ · xᵇ = xᵃ⁺ᵇ

Quotient Rule: When dividing two exponential expressions with the same base, you can subtract the exponents. That is, xᵃ / xᵇ = xᵃ⁻ᵇ

(x⁵)(x⁻³) = x⁵⁺⁽⁻³⁾ = x²
x²/x² = x²⁻² = x⁰ = 1

So the expression simplifies to:
(-2/5)(1) = -2/5

Therefore, the simplified expression is -2/5.

Learn more about rules of exponents here: https://brainly.com/question/11975096.

#SPJ11

a) P (20 < or = X) =  0.8617: This is the probability that 20 or more of the 30 patients will be helped by the medicine.

b) P (18 < or = X < 25) = 0.8557: This is the probability that between 18 and 25 of the 30 patients will be helped by the medicine.

c) P ( X < 16) = 0.0266: This is the probability that less than 16 of the 30 patients will be helped by the medicine.

The given situation can be modeled using a binomial distribution, where the number of trials is 30, and the probability of success is 0.75. We can use the binomial probability formula to find the probabilities for each of the given conditions. The binomial probability formula is:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and (n choose x) is the binomial coefficient.

a) P (20 < or = X) = 1 - P (X < or = 19) = 1 - sum_{x=0}^{19} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8617

b) P (18 < or = X < 25) = P (X < or = 24) - P (X < or = 17) = sum_{x=18}^{24} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8557

c) P ( X < 16) = sum_{x=0}^{15} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.0266

Therefore, the probabilities are 0.8617, 0.8557, and 0.0266 for the conditions a), b), and c) respectively.

You can learn more about probability at

brainly.com/question/24756209

#SPJ11

The surface area, in square centimeters, of the toy box is 370 cm²

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. Surface area is measured in cm².

Given, the lengths are 9 cm, 5 cm, and 10 cm.

To calculate the surface area, the formula is2(h × W) + 2(h × L) + 2(W × L)

2 x 9 x 5 + 2 x 9 x 10 + 2 x 5 x 10

90 + 180 + 100

370

Therefore, the surface area of the box is 370 cm²

Learn more about surface area, here:

https://brainly.com/question/29298005

#SPJ1

The question is incomplete, the image of the box is attached below:

Answer:

See image attached for complete answer

Step-by-step explanation:

The attached image shows the calculation of probabilities for each branch

I believe it is self-explanatory

Since P(bus to shops) = 0.4, P(walk to shops ) = 1- 0.4 = 0.6

Since P(bus from shops) = 0.7, P(walk from shops) = 1- 0.7 = 0.3

The probabilities at the leaves of the tree(rightmost entries) show the combined probabilities of to and from

For example if she takes a bus to the shops and takes a bus from the shops, the combined probability = 0.4 x 0.7 = 0.28

If she walks to the shops and takes a bus from the shops the combined probability = 0.6 x 0.7 = 0.42

The other two probabilities can be computed the same way

The probability that she walks at least one way
= P(walking to shop) or P(walking from shop)

= sum of the probabilities in the yellow shaded boxes

= 0.12 + 0.42 + 0.18

= 0.72

The area enclosed is 3 unit²

the line y=0 simply denotes the x axis. Now, the straight line y= (1/2)x+1 can be written as (x/(-2))+(y/1) = 1. So, this line touches x axis at (-2,0) and y axis at (0,1). the other line y= -(1/4)x+1 can be written as (x/4)+(y/1)=1. So, this line touches y axis at (4,0) and y axis at (0,1). so, it is evident that the triangle that got forms have the vertices of (4,0), (-2,0) and (0,1), the line joining (4,0) and (-2,0) being the base of the triangle.

so, the base of the triangle is 4+2= 6 unit and height of the triangle is 1 unit.

area of the triangle is 1/2* base* height= 1/2*6*1 = 3 unit^2.

learn more about equation of straight lines here  https://brainly.in/question/14120580

#SPJ11

Answer:

To simplify the expression, we can combine the like terms.

(3x + 1/2) + (7x - 4 1/2)

= 3x + 7x + 1/2 - 4 1/2 (distributing the addition)

= 10x - 4 (combining the like terms)

Therefore, (3x + 1/2) + (7x - 4 1/2) simplifies to 10x - 4.

The exact values are:
cosα = -√7/3
sin2α = 8√7/9

cos2α = -7/9
tan2αcos2α/sin2α = 1

If sinα = −4/3, π⩽α⩽2π/3, we can find the exact value of cosα, sin2α, cos2α, and tan2αcos2α/sin2α by using the trigonometric identities.

cosα = √(1 - sin²α) = √(1 - (-4/3)²) = √(1 - 16/9) = √(-7/9) = -√7/3

sin2α = 2sinαcosα = 2(-4/3)(-√7/3) = 8√7/9

cos2α = 1 - sin²α = 1 - (-4/3)² = 1 - 16/9 = -7/9

tan2αcos2α/sin2α = (sin2α/cos2α)(cos2α/sin2α) = 1

Therefore, the exact values are:
cosα = -√7/3
sin2α = 8√7/9
cos2α = -7/9
tan2αcos2α/sin2α = 1

Learn more about Trigonometric identities

brainly.com/question/24377281

#SPJ11

The vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c

The space curve given is r(t) = sin t i + e^t j + ln(t+1) k. To find the tangent vector of the curve at a given point, we need to take the derivative of the curve with respect to t. The derivative of the curve is r'(t) = cos t i + e^t j + (1/(t+1)) k.

At the point (0, 1, 0), t = 0. So, the tangent vector at this point is r'(0) = cos 0 i + e^0 j + (1/(0+1)) k = <1, 1, 1>.

Now, we need to find which of the given vectors is perpendicular to the tangent vector. Two vectors are perpendicular if their dot product is equal to 0. So, we need to find the dot product of the tangent vector with each of the given vectors and see which one is equal to 0.

a. <1, 1, 1> • <0, 1, 0> = 0 + 1 + 0 = 1 (not perpendicular)
b. <1, 1, 1> • <-1, 0, -1> = -1 + 0 - 1 = -2 (not perpendicular)
c. <1, 1, 1> • <1, 0, -1> = 1 + 0 - 1 = 0 (perpendicular)
d. <1, 1, 1> • <1, -1, 1> = 1 - 1 + 1 = 1 (not perpendicular)
e. <1, 1, 1> • <1, 0, 1> = 1 + 0 + 1 = 2 (not perpendicular)

Therefore, the vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c.

Learn more about Vector

brainly.com/question/29740341

#SPJ11

This as \( 5.4 \times 10^{-10} \) meters, or \( 5.4 \times 10^{-9} \) centimeters

The diameter of a certain atom is about \( 0.54 \) nanometers, which can be rewritten in scientific notation as \( 5.4 \times 10^{-1} \) nanometers. This is because scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. In this case, we move the decimal point one place to the left and multiply by \( 10^{1} \) to get the number in scientific notation. Since nano- means "billionth," we can also write this as \( 5.4 \times 10^{-10} \) meters, or \( 5.4 \times 10^{-9} \) centimeters.

Learn more about  Diameter

brainly.com/question/5501950

#SPJ11

When we square the two sides, we obtain: Z = square (82) , YZ thus has a length of about 9.06 units.

The connection among all three opposites of a right triangle is a key idea in geometry known as Pythagoras' theorem. According to this rule, the square of the hypotenuse's length—the side that faces the right angle—in a right triangle is the product of the squares of the dimensions of the other two sides. You can write this as follows: [tex]a^2 + b^2 = c^2[/tex] where a and b are the sizes of the other two right triangle sides and c has been the angle of the hypotenuse. The theorem is named after Pythagoras, an ancient Greek mathematician who is credited with finding it and creating its mathematical proof.

given

We may apply the Pythagorean theorem to determine the length of YZ.

Triangle VYZ is a right-angled triangle with the legs VY and VZ and the hypotenuse YZ, as may be seen. From the information provided, we can determine the lengths of VY and VZ.

VY = 35 - 36 = -1 (we can see from the diagram that V is to the left of Y, hence VY is negative) (we can see from the diagram that V is to the left of Y, so VY is negative)

VZ = 44 - 35 = 9 (we can see from the graphic that Z is below V, hence VZ is positive) (we can see from the diagram that Z is below V, so VZ is positive)

Using the Pythagorean theorem, we have the following:

[tex]VY^2 + VZ^2 = YZ^2\\YZ^2 = (-1) (-1)^2 + 9^2 \\YZ^2 = 1 + 81 \\YZ^2 = 82[/tex]

When we square the two sides, we obtain: Z = square (82) , YZ thus has a length of about 9.06 units.

To know more about Pythagoras theorem visit :-

https://brainly.com/question/14461977

#SPJ1

3

x

+

7

(

3

x

+

4

)

3

x

+

7

×

3

x

+

7

×

4

3

x

+

21

x

+

28

24

x

+

28

Option B, On a coordinate plane, the locations of the points (9, -5) and (9, 5) related reflection across the x-axis.

The two locations (9, -5) and (9, 5) have the same x-coordinate, but their y-coordinates are different. We need to see how the coordinates of two points change as they undergo various transformations to understand their relationship.

Learn more about the coordinate plane at

https://brainly.com/question/24134413

#SPJ4

Answer:

$3.30

Step-by-step explanation:

66 times 0.05