find x
100 = (5x+8)+(4x+2)

Answer:

to go from y=x² which has a minimum vertex at (0,0), you must shift the vertex one unit to the left and then one unit up to get a maximum vertex at (-1,1)

you can then plot points that can be created from an x-y table; such as (1,-7), (-1,1), (2,17), (-2,-1), etc

Step-by-step explanation:

First tranfer x to 1 units left .

Multiply by 2

Flip the parabola (turn a negative)

Transfer y 1 units up

The interquartile range of the set 14, 13, 13.5, 16, 14, 15.5. 14.5 is 2 second.

The middle half of your data set, or the second and third quartiles, is represented by the interquartile range (IQR). The interquartile range provides the spread of the middle half of a data set, whereas the range provides the spread of the entire data set.

Given that,

Jacob participates in 100 meter dash.

The data that shows time in seconds,

14, 13, 13.5, 16, 14, 15.5. 14.5

To find the interquartile range, first find median of the given set,

Arrange from lower to higher value of data,

13, 13.5, 14, 14, 14.5, 15.5, 16.

Median of the data= 14

The lower half of the set = 13, 13.5, 14

The upper half of the set = 14.5, 15.5, 16

Q₁ = Middle term of the lower half = 13.5

Q₂ = Middle term of the upper half = 15.5

The interquartile range = 15.5 - 13.5 = 2 second

The required interquartile range of the set is 2 seconds.

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Answer: answer b

Step-by-step explanation:

Answer:

28 are red

Step-by-step explanation:

(1/5) are blue.  The rest are red, which would be 4/5 of the total.  (1/5)+(4/5) = 1 or 100%

(1/5)*(35) = 7 are blue

(4/5)*(35 = 28 are red

--------------------

Total = 35 cars

Answer:

Step-by-step explanation:

The strategy to determine the boundary line is that we need to remove the inequality sign and replace it with and equal to sign and then sketch the equation of the function which is

\(4x+3y=12\)

to sketch the function we need the function's x-intercept which means the graphs crosses the x-axis at that specific point (x , 0) and y-intercept which means the graph crosses the y-axis at that specific point (0 , y).

Since both these points lie on line we can substitute it into the equation to find the x-y intercepts and hence sketch the line so here goes.

For x-intercept:

\(4x+3y=12\\4(x)+3(0)=12\\4x=12\\x=12/4\\x=3\)

so the x-intercept is (3 , 0)

For y-intercept:

\(4x+3y=12\\4(0)+3(y)=12\\3y=12\\y=12/3\\y=4\)

so the y-intercept is (0 , 4)

now we sketch these 2 points and draw a straight line joining both the points as shown in the image below.

Answer:

c ≤ 6

Step-by-step explanation:

Lets make our equation!

2.5 per chore thats our slope

+3 she starts with 3 dollars

y = 2.50x +3

Substitute y for 17!

17 = 2.5x +3

Subtract 3!

14 = 2.5x

Divide both sides by 2.5!

x = 5.6

5.6 --> 6

x = 6

Turn it into an inequality!

c ≤ 6

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Answer:

a y intercept (0,8)

Flat rate 8

b  slope is 4

c  3.5 hours

Step-by-step explanation:

The y intercept is where it crosses the y axis, which is (0,8)

The flat rate is the y intercept which is 8

The rate per hour is the slope

m = ( y2-y1)/(x2 -x1)

Using 2 point ( 1,12) and ( 2,16)

    = (16 -12)/(2-1)

     = 4/1

    = 4

The equation is

y = mx+b

y = 4x+8

Let y = 22

22 = 4x+8

Subtract 8 from each side

22-8 = 4x+8-8

14 = 4x

Divide by 4

14/4 = 4x/4

3.5 = x

3.5 hours

(0,8) is the y intercept because it crosses the y axis.

We can see that the flat rate is 8, which is the y intercept.

\( \quad\quad\quad\boxed{ \tt{m = \frac{rise}{run} = \frac{ y \tiny{2} \: \small{ - } \: y \tiny{1}}{x \tiny{2} \: \small{ - } \: x \tiny{1}} }}\)

\(\quad\quad\quad\boxed{ \tt{m = \frac{16 - 12}{2 - 1} }}\)

\(\quad\quad\quad\boxed{ \tt{m = \frac{4}{1} }}\)

\( \quad\quad\quad\boxed{ \color{green}\tt{m = 4}}\)

\( \quad \quad \quad \boxed{ \tt{y = mx + b}}\)

\( \quad \quad \quad \boxed{ \tt{y = mx + b}}\)

\( \quad \quad \quad \boxed{ \tt{22 =4x + 8}}\)

\( \quad \quad \quad \boxed{ \tt{22 - 8 = 4x + 8 - 8}}\)

\( \quad \quad \quad \boxed{ \tt{14 = 4x \: \:\cancel{ \color{red}+ 8 - 8}}}\)

\(\quad \quad \quad \boxed{ \tt{ \frac{14 = \cancel4x}{ \cancel{4} }}}\)

\(\quad \quad \quad \boxed{ \color{green} \tt{3.5 = x}}\)

_________

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Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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Answer:

x=number of miles driven on that day 258-13x=x

Step-by-step explanation:

I am not sure if this is correct because it's been a while since I have done this type of math but the reasoning for this is if we take 258 dollars and subtract that by the amount of money spent for an hourly wage (which is 13x), we have a specific number left over, and since driving has an expense of 1 dollar, whatever number left over would be the number of miles driven in that one day. If you would want to find the value for x, it would be an infinite number but rounded down, it would be 18 (this is a whole nother math topic that I won't explain because it would be too long). Also please don't use this as a reliable answer because I am PRETTY sure this is incorrect but hopefully I could help :)

Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?

Step-by-step explanation:

EDGE2021

Answer:

y = -2/9 |X| - 8

Step-by-step explanation:

I'm not certain whether the -7 is part of the |X| or it's just out of the equation. But shifting an equation up or down is very intuitive.

If you want to move an equation up a certain unit, you just add that many units (positive) onto the end of an equation. The same goes for moving a unit down, where you subtract that many units you want to go down.

Answer:

y=-2/9 |x| -8

Step-by-step explanation:

y = f(x) + C  C < 0 moves it down

y=-2/9 |x| -7 Shift down 1 by subtracting 1

y=-2/9 |x| -7-1

y=-2/9 |x| -8

By using the cross multiplication, we can determine the solutions to the equation  w=2 , w=6.

By multiplying the numerator of one side by the denominator of other side and equating the resulting two products, cross multiplying can be used to solve a fractional equation when each side has a fraction with a single denominator.

Given the expression \(\frac{w}{2w-4} = \frac{4}{w}\)

By using cross multiplication, we have

\(w^{2} = 4(2w-3)\\ w^{2} = 8w-12\\w^{2}-8w+12=0\\(w-2)(w-6)=0\\w=2 and w=6\)

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Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

The mean of the fitted exponential distribution is 66.67.

To find the mean of the fitted exponential distribution, we first need to estimate the parameter lambda using maximum likelihood estimation.

The probability density function of the exponential distribution is given by

f(x; lambda) = lambda * exp(-lambda * x)

where x is the claim size and lambda is the parameter to be estimated.

The likelihood function for the observed data is the product of the individual probabilities of each claim

L(lambda) = lambda^n * exp(-lambda * sum(x_i))

where n is the number of observed claims and x_i is the i-th claim size.

The log-likelihood function is given by:

ln L(lambda) = n * ln(lambda) - lambda * sum(x_i)

To estimate the parameter lambda, we need to maximize the log-likelihood function with respect to lambda:

d/d(lambda) ln L(lambda) = n/lambda - sum(x_i) = 0

Solving for lambda, we get

lambda = n / sum(x_i)

Substituting the observed values, we get

lambda = 6 / (20 + 45 + 50 + 80 + 100 + 2*100) = 0.015

Therefore, the estimated parameter of the fitted exponential distribution is lambda = 0.015.

The mean of the exponential distribution is given by

E(X) = 1/lambda

Substituting the estimated value of lambda, we get

E(X) = 1/0.015 = 66.67

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Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

Answer:

its 918 people

Step-by-step explanation:

Answer:

its 918 people

Step-by-step explanation:

The values for which the function fail to exist be x = 1/3, 4.

Given, a function f(x)

f(x) = (x - 3)/((3x - 1)(x - 4))

we have to find the values of x for which the function fail to exist

as, we know the function can not have zero in the denominator

so, the given function f(x) = (x - 3)/((3x - 1)(x - 4))

will have zero denominator for,

(3x - 1)(x - 4) = 0

(3x - 1) = 0 or (x - 4) = 0

3x = 1 or x = 4

x = 1/3 or x = 4

The given function f(x) = (x - 3)/((3x - 1)(x - 4)) will have zero denominator for x = 1/3 or x = 4.

So, the values for which the function fail to exist be x = 1/3, 4

Hence, the values for which the function fail to exist be x = 1/3, 4

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The set {(x, y) | y = λx + μ, where x, y ∈ R} is a subspace of R^2 if and only if μ = 0.

To determine the values of μ for which the set {(x, y) | y = λx + μ, where x, y ∈ R} is a subspace of R^2, we need to check if the set satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector.

1. Closure under addition:
Let (x₁, y₁) and (x₂, y₂) be two arbitrary elements in the set. Their sum is given by (x₁ + x₂, y₁ + y₂). Substituting the values of y₁ and y₂, we have (x₁ + x₂, λx₁ + μ + λx₂ + μ).

For the sum to be in the set, we require (λx₁ + μ + λx₂ + μ) = λ(x₁ + x₂) + 2μ. Therefore, the set is closed under addition if and only if 2μ = 0, or μ = 0.

2. Closure under scalar multiplication:
Let (x, y) be an arbitrary element in the set and let c be a scalar. The scalar multiplication c(x, y) is given by (cx, cy). Substituting the value of y, we have (cx, c(λx + μ)).

For the scalar multiplication to be in the set, we require c(λx + μ) = λ(cx) + cμ. Therefore, the set is closed under scalar multiplication for all values of μ.

3. Contains the zero vector:
The zero vector is given by (0, 0). Substituting the value of y, we have (0, λ(0) + μ) = (0, μ).

Since μ can be any real number, the set contains the zero vector for all values of μ.

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Answer:

h(-9)=27

Step-by-step explanation:

find the absolute value of |-3(-9)|, simplifies to |27|, which is just 27. hope it helps

Answer:

-3

Step-by-step explanation:

The k value represents when the function moves up or down.

Since there are no vertical compressions or shifts, we can just focus on how much the graph went down. The function g(x) went down 3 units.

Therefore, k would equal -3.

Both of them have to do with adding to the number

Srry Im not a math wizard like most people

Answer: Because the fraction will increase instead of decrease

Step-by-step explanation:

63. "Adrenopathy" is the correct term for any disease of the adrenal gland.

64. Corporeal. 65. Thyropathy 66. Isletoma 67. Adrenergic 68.  Islet-related 69. Goiter 70. Thyrotropic 71. Somatic 72. Gonadotropic

63. Adrenopathy: The correct word parts to form the term that describes any disease of the adrenal gland are "adreno-" and "-pathy." The prefix "adreno-" refers to the adrenal gland, and the suffix "-pathy" indicates a disease or disorder.

64. Corporeal: To describe something pertaining to the body, the correct word part is "corpor-" which means body. By adding the suffix "-eal" meaning pertaining to, we form the term "corporeal" which means relating to the body.

65. Thyropathy: When combining the word parts for a disease of the thyroid gland, we use "thyro-" to refer to the thyroid gland and "-pathy" to indicate a disease or disorder. Thus, "thyropathy" is the term that describes any disease of the thyroid gland.

66. Isletoma: A tumor of the pancreatic islets can be described using the word parts "islet-" referring to the pancreatic islets and "-oma" which signifies a tumor. Therefore, "isletoma" is the appropriate term for a tumor of the pancreatic islets.

67. Adrenergic: To indicate something that is activated by epinephrine, the correct word part is "adreno-" referring to the adrenal gland, and the suffix "-ergic" indicating activation or stimulation by a substance. Thus, "adrenergic" describes something that is activated by epinephrine.

68. Islet-related: The word part "islet-" refers to the pancreatic islets. To describe something pertaining to the pancreatic islets, we can use the suffix "-related." Therefore, "islet-related" is the correct term for something pertaining to the pancreatic islets.

69. Goiter: Enlargement of the thyroid is commonly referred to as a "goiter." In this case, the specific word parts from the bank are not used to form the term.

70. Thyrotropic: When we want to describe something that acts on the thyroid, the appropriate word parts are "thyro-" for the thyroid gland and the suffix "-tropic" indicating an agent that acts upon or influences something. Thus, "thyrotropic" is the correct term for something acting on the thyroid.

71. Somatic: To describe something that acts on the body, the word part "somato-" is used, which refers to the body. Therefore, "somatic" is the term that describes something acting on the body.

72. Gonadotropic: The word part "gonado-" is used to refer to the reproductive organs. When we want to describe something that acts on the reproductive organs, the suffix "-tropic" is used, indicating an agent that acts upon or influences something. Therefore, "gonadotropic" is the correct term for something acting on the reproductive organs.

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Answer:

5.4 units

Step-by-step explanation:

From the figure ,it's clear that   sin(50) = PQ/7

Then

PQ = 7×sin(50) = 5.362311101833

Therefore the approximate length of PQ I saw 5.4

Translations, reflections, and rotations produce a figure that is congruent to the original figure.

When we perform translations, reflections, and rotations on a figure, the resulting figure maintains the same size, shape, and orientation as the original figure. In other words, the transformed figure is congruent to the original figure.

Here's a brief explanation of each transformation:

1. Translations: A translation involves sliding a figure in a particular direction without changing its orientation or shape. Every point of the figure moves the same distance and direction. The resulting figure is congruent to the original because all corresponding sides and angles remain the same length and measure.

2. Reflections: A reflection involves flipping a figure over a line, called the line of reflection. Each point of the figure is mirrored across the line, creating a symmetrical image. The resulting figure is congruent to the original because the distance between corresponding points remains the same, and the angles formed between intersecting lines are preserved.

3. Rotations: A rotation involves turning a figure around a fixed point, known as the center of rotation. The figure is rotated by a specific angle in a clockwise or counter clockwise direction. The resulting figure is congruent to the original because all corresponding angles and side lengths remain unchanged.

In each of these transformations, the congruency of the resulting figure to the original figure is a fundamental property. Congruent figures have the same shape and size, even though they may be positioned differently in space. This property allows us to apply the concept of congruence in geometry to establish relationships, prove theorems, and solve geometric problems.

Therefore, when we perform translations, reflections, and rotations on a figure, we produce a transformed figure that is congruent to the original figure.

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The labor productivity of this manufacturing process in terms of dollars per labor hour is $73.47.

To find the labor productivity of this manufacturing process in terms of dollars per labor hour, we need to calculate the total revenue from the tuxedos and divide it by the total number of labor hours.

Total revenue from tuxedos = 96 tuxedos * $225 per tuxedo

                                               = $21,600

Total number of labor hours = 7 employees * 42 hours per employee

                                               = 294 labor hours

Labor productivity = Total revenue / Total number of labor hours

                               = $21,600 / 294 labor hours

                               = $73.47 per labor hour

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Answer:

Step-by-step explanation:

1)  12

The mean of any number series is all of them added together and divided by the amount of numbers there are, when you add all the numbers together you get 96, and you divide it by 8 because that's how many numbers there are.

2)  5

Range is the distance between the smallest and largest number in the series, there is a difference of 5 between 10 and 15.

3) mean: 12  mode: 13, the mode is larger

The median is found by writing the numbers down in order and ticking off the number on each side back and forth until you come to the middle, if the number sequence has an even amount of values like it is here, you split the difference of the two middle numbers. The two middle numbers this time are 11 and 13 so you find the middle which is 12. The mode is the number that appears most frequently, which is 13, which means that the mode is greater than the mean.

4) Joanne's dance class' youngest student(s) are 13 years old, but the difference between the youngest and the oldest student will still be 5 so the oldest member(s) of the dance class are 18.

hope this helped

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The solution for definite integral ∫2^x dx from [−1,1] is

 3/ 2 ln2

Definite Integral:

A definite integral is defined as the exact limit and summation examined in the previous section to find the net area between the function and the x axis. Also note that the definite integral notation is very similar to the indefinite integral notation. The reason for this will become clear in due course.

There are a few terms that should be left out along the way. The number "a" below the integral sign is called the lower integral limit, and the number "b" above the integral sign is called the upper integral limit. Even if the intervals a and b are specified, the lower bound is not necessarily less than the upper bound. Collectively, a and b are often referred to as the interval of integration.

Given a function :

f(x) that is continuous function on the interval [a , b]

we divide the interval into n subintervals of equal breadth, Δx, and from each interval choose a point, x i. Then the definite integral of f(x) from a to b is

\(\int\limits^b_a f(x) \, dx = \lim_{n \to \infty} f(xi)\) Δx.

According to the question:

let's start by differentiating 2ˣ.

   y = 2ˣ

⇒ ln y = x ln 2

⇒ 1/y dy/dx = ln2

⇒ d /dx = y ln 2 = 2ˣ ln2

So remembering integration is the reverse of differentiating.

  y = 2ˣ

⇒ dy/dx = 2ˣ ln 2

⇒ ∫2ˣ dx = 2ˣ / ln 2 + C

2ˣ > 0, ∀ x ∈ R, there is no negative area so we can

Insert the limits and evaluate immediately.

= 1/ ln2 [2x]\(\left \{ {{y= -1} \atop {x=1}} \right.\)

= 1/ln 2  (2¹ - 2⁻¹)

= 3/ 2ln 2

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Answer:

arc length ≈ 23.6 cm

Step-by-step explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × \(\frac{1.25\pi }{2\pi }\) ( r is the radius ) ( cancel 2π on numerator/denominator )

    = 2 × 3 × 1.25π

    = 7.5π

    ≈ 23,6 cm ( to the nearest tenth )

To simplify the radical expression -√32, break it down into its prime factors, rewrite as -√(2^5), and then simplify as -2^(5/2). Multiplying the coefficient (-2) with the exponent (5/2) gives -2 * 2^(1/2), resulting in a simplified radical expression of -2√2.

To simplify the radical expression -√32, we can break down the number 32 into its prime factors.
The prime factorization of 32 is 2 * 2 * 2 * 2 * 2 = 2^5.

Next, we can rewrite the radical expression as -√(2^5).

Since the square root of a number is equal to the number raised to the power of 1/2, we can rewrite -√(2^5) as -2^(5/2).

Finally, we can simplify -2^(5/2) by multiplying the coefficient (-2) with the exponent (5/2). This gives us -2 * 2^(1/2).

Therefore, the simplified radical expression for -√32 is -2√2.

In summary, to simplify the radical expression -√32, we break down 32 into its prime factors, rewrite it as -2^(5/2), and then simplify it to -2√2.

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