The graph of f(x) and table for g(x) = f(kx) are given.

The graph shows an upward opening parabola labeled f of x that passes through a point negative 2 comma 8, a point negative 1 comma 2, a vertex 0 comma 0, a point 1 comma 2, and a point 2 comma 8.


x g(x)
−8 8
−4 2
0 0
4 2
8 8

What is the value of k?
k is equal to one fifth
k = 5
k is equal to one fourth
k = 4

An explicit formula for the given arithmetic sequence is aₙ = 28 - 2n.

Given sequence is,

26, 24, 22, ....

This is clearly an arithmetic sequence, since the consecutive numbers have same difference.

Explicit formulas are used to find the nth term of a sequence.

Here, first term, a = 26

Common difference, = 24 - 26 = -2

nth term of the sequence is,

aₙ = a + (n - 1)d

aₙ = 26 + (n - 1). -2

aₙ = 26 - 2(n - 1)

   = 28 - 2n

Hence the required formula is aₙ = 28 - 2n.

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If 40% of John's sales correspond to 120 bags of potatoes, 300 bags of potatoes correspond to 120%

To solve this problem, we can use a proportion. If 40% of John's sales correspond to 120 bags of potatoes, we can set up the following proportion:

40/100 = 120/x

Here, x represents the number of bags of potatoes that correspond to 120% of John's sales. To solve for x, we can cross-multiply and simplify:

40x = 12000

x = 300

Therefore, 300 bags of potatoes correspond to 120% of John's sales. This means that if John's sales increase by 20% (from 100% to 120%), he would sell 300 bags of potatoes.

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The number of total number of ways a large pizza can be made with e 3 toppings without repetition is 35 , the number of ways a pizza can be made using 3 toppings is 35 , therefore in total there are  70 ways the pizza can be made using 3 toppings and 4 toppings.



In order to evaluate the following we have to relie on the principles of permutation and combination

(a) In case of large pizzas, there are 7 toppings to select from and we have to take 3 toppings without repetition.

This can be done in 7C3 ways

(7!)/(3! x (7-3)!)

= 35 ways.

(b) In case of three-topping pizzas, there are 7 toppings to select from and we have to take 3 toppings without repetition.

This can be done in 7C3 ways

(7!)/(3! x (7-3)!)

= 35 ways.

(c) In case of making 3 toppings and 4 toppings of pizzas, there are two cases:

Case 1: Three-topping pizzas

Number of ways a large pizza can be made with e 3 toppings without repetition is 35

Case 2: Four-topping pizzas

This is accomplished  in 7C4 ways

(7!)/(4! x (7-4)!)

= 35 ways

Therefore, the total number of distinct three or four-topping pizzas is case 1 + case 2

= 35+35

= 70

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The complete question is

A local pizza store offers a choice of seven toppings and three sizes(small, medium, and large).

(a) How many distinct large three-topping pizzas do they offer,assuming that toppings cannot be repeated?

(b) How many distinct three topping pizzas do they offer, assuming that toppings cannot be repeated?

(c) How many distinct three or four-topping pizzas do they offer, assuming that toppings cannot be repeated?

The square's area is increased by 21 square units, it becomes 100 square units and the original area of the square was 79 square units.

To solve this problem, we can use algebra. Let x be the original area of the square. We know that when we increase the area by 21 square units, we get 100 square units. So we can set up an equation:

x + 21 = 100

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 21 from both sides:

x + 21 - 21 = 100 - 21

x = 79

Therefore, the original area of the square was 79 square units. To check our answer, we can plug it back into the original equation:

79 + 21 = 100

This is true, so our answer is correct.

In summary, to find the original area of a square when the area is increased by 21 square units and becomes 100 square units, we can use algebra and set up the equation x + 21 = 100, where x is the original area. Solving for x, we get x = 79. Therefore, the original area of the square was 79 square units.

To find the original area of the square, we need to consider the given information: when the square's area is increased by 21 square units, it becomes 100 square units.

Since the area is increased by 21 square units to reach 100 square units, we can calculate the original area by subtracting 21 from 100:

Original Area = 100 - 21
Original Area = 79 square units

So, the original area of the square was 79 square units.

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The equation of the straight line passing through the point (3, 3) and perpendicular to the line y = -¹/₂x - 4 is y = 2x - 3.

The slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points on the line. The given line is y = -1/2x - 4. We can rewrite this equation in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Comparing the given equation with the slope-intercept form, we get:

m = -1/2

Therefore, the slope of the given line is -1/2

The point-slope form of the equation of a straight line is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. We know that the line passes through the point (3, 3) and has a slope of 2 (perpendicular to the slope of the given line).

Substituting these values in the point-slope form, we get:

y - 3 = 2(x - 3)

Expanding and simplifying this equation, we get:

y = 2x - 3

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Complete Question:

Find the equation of the straight line passing through the point (3, 3) which is perpendicular to the line y=-1/2x-4

Answer:

False

Step-by-step explanation:

Trailing zeros after the decimal point are not always significant. The number of significant figures after the decimal point is determined by the measurement instrument used to obtain the value.

The x values of 2x²+4x+10 =0, in this case the square root of a negative number is not a real number, so this equation has no real solutions, and the x values of 4x²-5x-6=0 are x₁ = 1.5 and x₂ = -0.75.

To find the x values of each quadratic equation, we can use the quadratic formula;

For the equation 2x² + 4x + 10 = 0

a = 2, b = 4, c = 10

x = (-b ± √(b² - 4ac))/2a

x = (-4 ± √(4² - 4(2)(10) / 2(2)

x = (-4 ± √(-24)) / 4

The square root of a negative number is not a real number, so this equation has no real solutions.

For the equation 4x² - 5x - 6 = 0

a = 4, b = -5, c = -6

x = (-b ± √(b² - 4ac)/2a

x = (5 ± √(5² - 4(4)(-6) / 2(4)

x = (5 ± √(121)) / 8

x = (5 ± 11) / 8

x₁ = (5 + 11) / 8 = 1.5

x₂ = (5 - 11) / 8 = -0.75

Therefore, the solutions to 4x² - 5x - 6 = 0 are x₁ = 1.5 and x₂ = -0.75.

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Answer:

The rate of change is 2 feet per second.

The probability of guessing the 4-digit code correctly on the first try is 1/24.

Since there are 4 unique digits (1, 3, 5, and 7) and the code has 4 digits, there are a total of 4! (4 factorial) possible sequences for the code.

The calculation for 4! is 4 x 3 x 2 x 1 = 24.

Therefore, there are 24 different sequences.

Since you are trying to guess the code correctly on the first try, there is only one correct sequence out of the 24 possible sequences.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes), the number of favorable outcomes is 1 (correct sequence), and the total number of possible outcomes is 24.

So, the probability is 1/24.

Hence, Given the 4 unique digits 1, 3, 5, and 7 in a 4-digit code, there are 24 possible sequences for the code. The probability of guessing the code correctly on the first try is 1/24.

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The simplified exponential notation of the given expression is x⁸.

Given that, simplified exponential notation, x³·x⁵,

x³·x⁵ we need to simplify it,

We know that,

mᵃ × mᵇ = mᵃ⁺ᵇ

x³·x⁵ = x³⁺⁵

x³·x⁵ = x⁸

Hence, the simplified exponential notation of the given expression is x⁸.

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The value of the unknown number is 10.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given that; twice the sum of a number and 2 is 14 more than the number.

Let's call the number we're trying to find "x".

According to the problem, "Twice the sum of a number and 2 is 14 more than the number." In equation form, this is:

2(x + 2) = x + 14

Now we can solve for x:

Apply distributive property

2×x + 2×2 = x + 14

2x + 4 = x + 14

Subtract x from both sides

2x - x = 14 - 4

x = 14 - 4

x = 10

Therefore, the number we're looking for is 10.

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The value of the different trigonometric ratios given are:

sin θ  = 0.923

tan θ = 2.4

sec θ = 2.6

There are different trigonometric ratios such as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are given:

cos(θ) = 10/26, 0 ≤ θ ≤ π/2

Thus, sin θ and cos θ will be in the first quadrant based on the interval given. Thus:

cos⁻¹(10/26) = 1.176

sin 1.176 in radians  = 0.923

tan 1.176 in radians = 2.4

sec 1.176 = 1/cos 1.176 = 2.6

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By using identities, we get [tex](n^2-1)(n^2+1)=n^4-1[/tex]

The given equation is:

[tex](n -1)(n+1)(n^2+1)[/tex]

To find the given equation, by using appropriate identities

We use the identity is:

[tex](a-b)(a+b)=(a^2-b^2)[/tex]

Hence, [tex](n-1)(n+1)=(n^2-1)[/tex]

Then, [tex](n^2-1)(n^2+1)[/tex]

To solve by multiplication, we get:

[tex](n^2-1)(n^2+1)=(n^2)^2-(1)^2\\\\(n^2-1)(n^2+1)=n^4-1[/tex]

Hence, By using identities, we get [tex](n^2-1)(n^2+1)=n^4-1[/tex]

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Answer:

The value of the x-coordinate of point A is cos 0 = 1.

The probability of a bulb lasting for between 557 and 561 hours is roughly 0.0382 or 3.82%

Able to utilize the standard ordinary dissemination to discover the likelihood of a bulb enduring for between 557 and 561 hours. To do this, we ought to standardize the values utilizing the equation:

z = (x - μ) / σ

where x is the bulb lifetime we're fascinated by

, μ is the cruel(mean) lifetime,

and σ is the standard deviation.

For 557 hours:

z1 = (557 - 530) / 15 = 1.8

For 561 hours:

z2 = (561 - 530) / 15 = 2.07

Employing a standard ordinary conveyance table or a calculator with a typical dissemination work, we are able to discover the probabilities corresponding to these z-scores:

P(z1 < Z < z2) = P(1.8 < Z < 2.07)

This speaks to the likelihood of a bulb enduring between 557 and 561 hours, where Z could be a standard ordinary variable.

Employing a standard ordinary dispersion table or a calculator, we discover:

P(1.8 < Z < 2.07) ≈ 0.0382

Therefore, the likelihood of a bulb enduring for between 557 and 561 hours is roughly 0.0382 or 3.82% (adjusted to four decimal places). 

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The maximum area of a rectangle that is above the x-axis and below the graph of a parabola can be determined using calculus. The parabola is given by the equation y = ax^2 + bx + c, and the rectangle's dimensions are x (width) and y (height).

The area of the rectangle is given by A = xy. To find the maximum area, we need to find the maximum value of A. To do this, we can substitute the parabola equation for y in the area equation:
A = x(ax^2 + bx + c)
Next, we take the derivative of A with respect to x:
dA/dx = a(3x^2) + b(2x) + c
To find the critical points, we set dA/dx to zero:
0 = 3ax^2 + 2bx + c
Now, we solve for x to find the critical points. These points will help us determine where the maximum area occurs. After identifying the maximum point, we can substitute the x-value back into the parabola equation to find the corresponding y-value. Finally, the maximum area can be calculated by multiplying the obtained x and y values:
Max Area = x_max * y_max.

Hence, The maximum area of a rectangle that is above the x-axis and below the graph of a parabola can be determined using calculus. The parabola is given by the equation y = ax^2 + bx + c, and the rectangle's dimensions are x (width) and y (height).

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The length of the arc on a circle of radius r of 33 cm intercepted by a central angle 1.5 radians is 49.5 cm.

the measure of θ in radians given that s (arc length) is 14 and the radius is 11 is 1.3 radians.

We know that from trigonometric formula, if the arc length of 's' subtends an angle of θ in radian at the center of a circle with radius of 'r' units then the relation between then is given by,

s = rθ

For the first case:

Radius of the circle is (r) = 33 cm.

Central angle is (θ) = 1.5 radian

Then the length of the arc (s) is given by = 33*1.5 = 49.5 cm.

For the second case:

Radius of the circle is (r) = 11 units.

and the arc length of the circle is (s) = 14 units.

So the measure of the central angle (θ) = s/r = 14/11 = 1.3 radians (round to nearest tenth).

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Answer:

  A.  {x | 1 ≤ x ≤ 3 }

Step-by-step explanation:

You want the domain of the graph shown.

The domain is the horizontal extent of the graph. The left graph (for part a. shown) extends from x=1 to x=3. The domain is ...

  {x | 1 ≤ x ≤ 3 }

The sale price of the pens would be P^(150) x 1.08 .

We are given that Jane bought pens at $ 150 a dozen and sold them after a markup of 8%.

The markup price can be written as 0.08

To find the sale price of the pen, we need to multiply the sale price per by 12.

1 dozen  = 12 units.

Therefore, we have;

Sale prize per dozen = P^(150)/12 x 1.08 x 12

Sale prize per dozen = P^(150) x 1.08

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The probability of drawing a 5 from a randomly chosen card from the set of cards with numbers 2, 3, 4, 5, and 6 is 20%.

This is because there is only one card with a 5 out of a total of five cards, so the probability of selecting the 5 card is 1/5, or 0.2, which is equivalent to 20%.

The formula for calculating probability is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is drawing the 5 card, and the total number of possible outcomes is the number of cards in the set, which is 5. Therefore, the probability of drawing a 5 is 1/5 or 0.2 or 20%.

The probability of drawing a 5 is independent of any previous draws or future draws, assuming the cards are being drawn randomly and with replacement.

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Isolate the variable by dividing each side by factors that don't contain the variable.

w = a/5

According to unitary method, a package of tissues should contain at least 152,500 tissues to meet the needs of 2500 people during a cold.

To determine the number of tissues required in a package, we need to use a unitary method. A unitary method is a mathematical method used to find the value of a single unit when the value of a known number of units is given. In this case, we know that an average person uses 61 tissues during a cold. Therefore, we can use this information to find the number of tissues required in a package.

Suppose we want to find the number of tissues required for 2500 people during a cold. We can use the unitary method as follows:

Number of tissues required for 1 person = 61

Number of people = 2500

To find the number of tissues required for 2500 people, we need to multiply the number of tissues required for one person by the number of people. Therefore,

Number of tissues required for 2500 people = Number of tissues required for 1 person × Number of people

= 61 × 2500

= 152,500

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As a result, the painting's proportions are 14 meters by 10 meters.

Let's use "w" to denote the painting's breadth in metres.

The length of the picture, according to the problem, is 6 metres less than double its breadth, which can be written as:

2w - 6 = length

The painting has a surface area of 140 m2, which means:

140 = (2w - 6) x w area = length x width

By expanding and simplifying the right side of the equation, we get:

140 = 2w² - 6w

2w² - 6w - 140 = 0

When we divide both sides by 2, we get:

w² - 3w - 70 = 0

We can factor this quadratic equation to answer it:

(w - 10)(w + 7) = 0

This offers us two alternatives for w:

w = 10 or w = -7

We can discard the artwork because its breadth cannot be negative.

w = -7 is the solution.

As a result, the painting's breadth is 10 meters.

We can use the length equation we discovered earlier to calculate the length of the painting:

2w - 6 = 2(10) - 6 = 14 metres length

As a result, the painting's proportions are 14 meters by 10 meters.

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Answer:

I think in this case, the triangles are similar based on the Side-Angle-Side rule.

Step-by-step explanation:

Sides:

9:3 = 12:4

Angle:

C : C'

There are 18 frogs in the pond.

Yes, a ratio is a type of relation between two or more quantities that indicates how many times one quantity is contained within another. In mathematics, a relation is a set of ordered pairs that describes the relationship between two or more variables. Ratios are often used to express the relative size or amount of two quantities, and they can be written in several ways, such as using a colon, a slash, or as a fraction.

Let's assume the initial number of frogs and snails in the pond were 3x and 10x, respectively.

After 6 more snails entered the pond, the number of snails became 10x + 6.

Now the ratio of frogs to snails is 3:11. We can write this as:

3x / (10x + 6) = 3/11

Cross-multiplying, we get:

33x = 3(10x + 6)

Simplifying, we get:

33x = 30x + 18

3x = 18

x = 6

Therefore, the initial number of snails was 10x = 60, and the initial number of frogs was 3x = 18.

After 6 more snails entered the pond, the new number of snails became 60 + 6 = 66.

Since the ratio of frogs to snails is still 3:11, the number of frogs in the pond is:

(3/11) * 66 = 18

So, there are 18 frogs in the pond.

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The weight of the Avery's lunch box using given weights is equal to 0.92 pounds (rounded to two decimal places).

Total weight of the backpack= 2 2/3 pounds

                                                = 8/3 pounds

The weight of the each book =7/8 pounds.

Let x be the weight of the lunch box in pounds.

An equation that represents the total weight in Avery's backpack,

2(7/8) + x = 8/3

To solve for x, simplify and solve for x,

⇒14/8 + x = 8/3

Multiplying both sides by 24 the least common multiple of 8 and 3 to clear the fractions,

⇒42 + 24x = 64

Subtracting 42 from both sides,

⇒24x = 22

Dividing both sides by 24,

⇒x = 22/24

Simplifying the fraction,

⇒x = 11/12

     =  0.92 pounds (rounded to two decimal places).

Therefore, the  weight of the lunch box is equal to 0.92 pounds (rounded to two decimal places).

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Answer:

  8 inches

Step-by-step explanation:

You want the diameter of a circle that has a circumference between 20 and 27 inches, expressed as an integer number of inches near the high end without going over.

The relationship between diameter and circumference of a circle is ...

  C = πd

  d = C/π

For the given circumference range, the diameter range is ...

  20 ≤ πd ≤ 27

  20/π ≤ d ≤ 27/π

   6.4 ≤ d ≤ 8.5

Integers in this range are 7 and 8. The largest one is 8.

8 inches is the most reasonable diameter of the circular cardboard model.

A toy passed the strength test then the probability that is without finishing defects is 0.938

Given that Factory of wooden toys checks the quality of production before its commercial date.

F: is the toy is w/o finishing defects

S: the toy passes the strength test

P(S(bar)/F(bar)) = P(S(bar)∩F(bar)) / P(F(bar))

= P(F(bar)/S(bar)) × P(S(bar)) / P(F(bar)/S(bar)) × P(S(bar)) + P(F(bar)/S)×P(S)

= (1-0.95) ×0.08 / (1-0.95)× 0.08 + (1-0.92) × 0.92

= 0.02 / 0.098

= 1/4

P(S) = P(S/F)× P(F) + P(S/F') × P(F')

= 0.95 × 0.92 + 0.08 × 0.08

= 0.934

b) P(F/S) = P(S/F)× P(F) / P(S)

= 0.95 × 0.92 / 0.934

= 0.938

Hence, a toy passed the strength test then the probability that is without finishing defects is 0.938

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Answer:

Dylan's grocery bill was $41.25.

Step-by-step explanation:

Let's call the cost of the grapes "g".

We know that the grapes cost $1.25 more than the apples, so we can write:

g = 3.50 + 1.25 = 4.75

The combined cost of the grapes and apples is 20% of Dylan's total grocery bill, so we can write:

3.50 + 4.75 = 0.20x

where x is the total grocery bill.

We can solve for x by simplifying the equation:

8.25 = 0.20x

x = 8.25 / 0.20

x = 41.25

Therefore, the total amount of Dylan's grocery bill was $41.25.

Answer:  

Dylan's total grocery bill was $41.25

Step-by-step explanation:

Let the cost of the apples be a. Then, the cost of the grapes is a + 1.25, since the grapes cost $1.25 more than the apples.

The combined cost of the apples and grapes is a + (a + 1.25) = 2a + 1.25.

We know that the combined cost of the apples and grapes is 20% of Dylan's total grocery bill, so we can set up the following equation:

2a + 1.25 = 0.2x

where x is the total cost of Dylan's grocery bill.

To solve for x, we can isolate x on one side of the equation:

2a + 1.25 = 0.2x

2a = 0.2x - 1.25

a = 0.1x - 0.625

We also know that the cost of the apples is $3.50, so we can set up another equation:

a = 3.5

Substituting this into the equation we just found:

3.5 = 0.1x - 0.625

4.125 = 0.1x

x = 41.25

Therefore, Dylan's total grocery bill was $41.25.