a researcher is performing an analysis on a 2x2x4 research design. how many independent variables are there in the design?

The total bill of the dinner to celebrate birthday including sales tax and tip to the nearest cent is $202.01

Cost of the meal = $168.34

Sales tax = 5% of $168.34

= 0.05 × 168.34

= $8.417

Tip = 15% of $168.34

= 0.15 × 168.34

= $25.251

Total bill = Cost of the meal + Sales tax + Tip

= $168.34 + $8.417 + $25.251

= $202.008

Hence, the total bill is $202.01 to the nearest cent.

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Answer:

Max at t=2, 128 m/s

Min at t=6, 0 m/s

Step-by-step explanation:

Given the position function of a particle with respect to time, find the minimum and maximum velocity the particle travels over the interval [1,7].

[tex]s(t)=t^4-16t^3+72t^2+5[/tex]

(1) - Find the velocity function of the particle

The velocity function is a derivative of the position function.

[tex]s'(t)=v(t)\\\\s(t)=t^4-16t^3+72t^2+5\\\\\Longrightarrow s'(t)=\frac{d}{dx}[t^4-16t^3+72t^2+5] \\\\\text{Use the derivative rules.}\\\\\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Constant Rule:}}\\\\\frac{d}{dx}[k]=0 \end{array}\right} \\\\\\\Longrightarrow s'(t)=(4)t^{4-1}-16(3)t^{3-1}+72(2)t^{2-1}+0\\\\\Longrightarrow s'(t)=4t^{3}-48t^{2}+144t\\\\[/tex]

[tex]\therefore \boxed{v(t)=4t^{3}-48t^{2}+144t}[/tex]

(3) - Take the derivative of v(t)

[tex]v(t)=4t^{3}-48t^{2}+144t\\\\\Longrightarrow v'(t)=12t^2-96t+144[/tex]

(4) - Let v'(t)=0 and solve for "t," these are the critical points

[tex]v'(t)=12t^2-96t+144\\\\\Longrightarrow 0=12t^2-96t+144\\\\\Longrightarrow 0=12[t^2-8t+12]\\\\\Longrightarrow 0=t^2-8t+12\\\\\Longrightarrow (t-6)(t-2)=0\\\\\therefore \text{The critical points are} \ \boxed{t=6 \ \text{and} \ t=2}[/tex]

(5) - Find the max/min values (in this case these values represent the particle's velocity) by plugging the critical points into v(t)

[tex]\text{Recall that} \ v(t)=4t^{3}-48t^{2}+144t \ \text{and} \ t=6, \ t=2\\\\\text{\underline{When t=6:}}\\\\\Longrightarrow v(6)=4(6)^{3}-48(6)^{2}+144(6)\\\\\Longrightarrow \boxed{v(6)=0 \ m/s}\\\\\text{\underline{When t=2:}}\\\\\Longrightarrow v(2)=4(2)^{3}-48(2)^{2}+144(2)\\\\\Longrightarrow \boxed{v(6)=128 \ m/s}[/tex]

Thus, at time, t=6, the particle's velocity is smallest, 0 m/s. And at time, t=2, the particle's velocity is greatest, 128 m/s.

The correct matching of the items of math in the columns is:

A composite number is a number that possesses additional factors besides 1 and its own value. The smallest number that can be divided evenly by all the denominators given is known as the least common denominator.

Non-numeric criteria are used to group data in categorical data. Fractions that have identical numerical values are referred to as equivalent fractions. When a line segment passes through the center of a circle and joins two points on its circumference, it is known as the circle's diameter.

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Answer:

2.02

Explanation:

Each pail of plaster covers 97 Square feet of ceiling

The ceiling of the room is 14 ft long

= 14×14

= 196

Therefore the pail of plaster that will be needed to cover the rooms can be calculated as follows

= 196/97

= 2.02

The length of y of the triangle is y = 9√2 units

Given data ,

Let the Triangle be ΔABC , such that

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

On simplifying , we get

From the trigonometric relations , we get

sin θ = opposite / hypotenuse

sin 45° = 9 / y

Multiply by y on both sides , we get

y = 9 / sin 45°

On simplifying , we get

y = 9√2 units

Hence , the length is y = 9√2 units

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Answer:

x = 2, 6

Step-by-step explanation:

differentiate f(x) using the power rule

f'(a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and f'( constant) = 0

given

f(x) = x³ - 12x² + 6x - 8

f'(x) = 3x² - 24x + 6

equate f'(x) to - 30

3x² - 24x + 6 = - 30 ( add 30 to both sides )

3x² - 24x + 36 = 0 ( divide through by 3 )

x² - 8x + 12 = 0 ← in standard form

(x - 2)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 6 = 0 ⇒ x = 6

solution is x = 2, 6

There are 98,087,770 cubic feet inside the Great Pyramid.

To calculate the approximate volume of the Great Pyramid in Giza, we can use the formula for the volume of a pyramid:

Volume = (1/3) × base area × height

Since the Great Pyramid is square-based, the base area is equal to the length of one side squared. Given that the length of one side of the base is 755 feet, the base area is [tex]755^2[/tex] square feet.

Using the given height of 481 feet, we can substitute these values into the formula:

Volume = (1/3) × [tex]755^2[/tex] × 481

Calculating this expression, we find that the approximate volume of the Great Pyramid is:

Volume ≈ 98,087,770 cubic feet

There are approximately 98,087,770 cubic feet inside the Great Pyramid.

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Answer:

17 and 35

Step-by-step explanation:

x + y = 52

x − y = 18

Add the equations together:

2x = 70

x = 35

Substitute into either equation:

y = 17

The value of the standardized test statistic for this significance test is -1.3

For the standardized test statistic for this significance test, we need to compare the sample proportion to the hypothesized population proportion.

The null hypothesis (H₀)  

H₀: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is equal to 30%.

The alternative hypothesis (H₁)

H₁: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is different from 30%.

The sample size is 25 and 5 of those files are missing a medical,

The sample proportion (p) can be calculated as

(p) hat = (Number of files missing justification) / (Total number of files)

(p) hat = 5 / 25

(p) hat = 0.2

The standard error is given by

SE = √[((p) hat × (1 - (p) hat)) / n]

SE = √[(0.2 × (1 - 0.2)) / 25] = √(0.16 / 25) = 0.08

For the standardized test statistic, we use the formula:

z = ((p) hat - p₀) / SE

where p₀ is the hypothesized population proportion.

p₀ = 30% = 0.3

z = (0.2 - 0.3) / 0.08 = -0.1 / 0.08 = -1.25 = -1.3

The value of the standardized test statistic for this significance test is approximately -1.3

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The set of numerical values that represents the minimum, lower quartile, median, upper quartile, and maximum, in that order, is:

51, 53, 55, 58, 60

To determine the minimum, lower quartile, median, upper quartile, and maximum of the given data set, we can arrange the values in ascending order:

51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60

Arranging the values in ascending order gives us:

51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60

The minimum value is 51.

The lower quartile (Q1) is the median of the lower half of the data, which is 53.

The median (Q2) is the middle value of the data set, which is 55.

The upper quartile (Q3) is the median of the upper half of the data, which is 58.

The maximum value is 60.

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Answer:

Therefore, the coordinates of the midpoint M are (1, 8).

Step-by-step explanation:

The midpoint formula is:

M = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

Using this formula, we have:

M = ((1 + 1)/2, (7 + 9)/2) = (1, 8)

Therefore, the coordinates of the midpoint M are (1, 8).

Kyra will receive $125 USD when she converts £67.50 to USD.

Given that, Kyra wants to convert some Australian dollars to pounds she received £67.50.

Exchange rate =

Exchange rates are typically quoted as currency pairs, where one currency is the base currency and the other is the counter currency.

To convert £67.50 into USD using the exchange rate of $1 = £0.54, you can multiply the amount in pounds by the exchange rate.

Here's the calculation:

£67.50 x $1/£0.54 = $125

Therefore, Kyra will receive $125 USD when she converts £67.50 to USD.

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Answer:

y = (1/3)x - 5

Step-by-step explanation:

x - 3y = 15

x - 15 = 3y

3y = x -15

y = (1/3)x - 5

Hello !

Answer:

[tex]\boxed{y=\frac{1}{3}x-5}[/tex]

Step-by-step explanation:

An equation in slope-intercept form is [tex]y=mx+b[/tex].

Let's isolate y in our equation :

[tex]x-3y=15\\-3y=-x+15\\3y=x-15\\y=\frac{1}{3}x-5[/tex]

Our equation is in the form [tex]y=mx+b[/tex] with [tex]m=\frac{1}{3}[/tex] and [tex]b=-5[/tex].

Have a nice day

It will take approximately 35 years for the population of San Diego to double if it grows at a rate of 2.0% per year.

To determine how long it will take for the population of San Diego to double, we can use the concept of exponential growth.

When a population grows by a fixed percentage, the formula to calculate the doubling time is given by:

Doubling Time = (log(2) / log(1 + growth rate))

In this case, the growth rate is 2.0% or 0.02 (expressed as a decimal). Plugging this value into the formula, we can calculate the doubling time.

Doubling Time = (log(2) / log(1 + 0.02))

Using a calculator, we can evaluate this expression:

Doubling Time ≈ 35 years

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So the cosine of the angle between the two planes is 8sqrt(78) / 78.

To find the cosine of the angle between two planes, we need to find the normal vectors of each plane and then use the dot product formula.

The normal vector of the first plane is <1, 1, 1>, and the normal vector of the second plane is <1, 3, 4>.

The dot product of these two vectors is:

<1, 1, 1> · <1, 3, 4> = 1(1) + 1(3) + 1(4) = 8

The magnitude of the normal vector of the first plane is:

|<1, 1, 1>| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)

The magnitude of the normal vector of the second plane is:

|<1, 3, 4>| = sqrt(1^2 + 3^2 + 4^2) = sqrt(26)

Therefore, the cosine of the angle between the two planes is:

cosθ = (normal vector of plane 1) · (normal vector of plane 2) / (magnitude of normal vector of plane 1) * (magnitude of normal vector of plane 2)

= 8 / (sqrt(3) * sqrt(26))

= 8 / (sqrt(78))

= 8sqrt(78) / 78

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Answer:

If $T=1.65$ seconds, then we can solve the equation for $L$ as follows:

$$

T=1.1\sqrt{L}

$$

$$

\frac{T}{1.1}=\sqrt{L}

$$

$$

\left(\frac{T}{1.1}\right)^2=L

$$

Substituting $T=1.65$, we get:

$$

L=\left(\frac{1.65}{1.1}\right)^2=2.25

$$

Therefore, the length of the pendulum is approximately 2.25 feet.

Answer:

  B, D, F

Step-by-step explanation:

You want the diagrams that show lines through the center of enlargement, where the smaller triangle is enlarged to form the larger triangle.

Each point in an enlarged figure is moved toward or away from the center of enlargement along a line through that center. That is, corresponding vertices of a triangle and its enlargement will lie on a line through the enlargement center.

The diagrams of interest are those that show lines through corresponding vertices of the triangles.

Diagrams B, D, F show lines through the center of enlargement.

__

Additional comment

The center of enlargement is marked in the attachment by a blue dot. Enlargement is by a factor of 3.

Points are moved away if the scale factor is greater than 1; toward the center of enlargement for a scale factor less than 1.

<95141404393>

Answer: 28.8%

Step-by-step explanation:

First, add all the pizzas together. This gives us the total; 125

Next, put 36 over the total. 36/125.

Divide 36/125. Equals .288

When doing percentage, You multiply your decimal by 100, or bounce the decimal twice to the right. This gets you 28.8%

Therefore, the speed of the bird is approximately 1.001 kilometers per hour.

We can start by calculating the total distance the bird flew, which is the distance between the nest and the ditch multiplied by the number of round trips:

total distance = 2 × distance between nest and ditch × number of round trips

total distance = 2 × 200 meters × 15

total distance = 6000 meters

Next, we can calculate the bird's average speed by dividing the total distance by the time it took to make the trips:

average speed = total distance ÷ time

average speed = 6000 meters ÷ (1.5 hours × 3600 seconds/hour)

average speed = 0.278 meters/second

To convert this to kilometers per hour, we can multiply by the conversion factor of 3.6:

average speed = 0.278 meters/second × 3.6 kilometers/meter

average speed = 1.001 kilometers/hour

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Let α be one root of the quadratic equation x² + sx + F = 0. If β is the other root, then we have: Therefore, the condition is that the sum of roots of the quadratic equation x² + sx + F = 0 must be zero.

Let α be one root of the quadratic equation x² + sx + F = 0. If β is the other root, then we have:

α + β = -s (sum of roots)

αβ = F (product of roots)

We are given that α is five times β, i.e., α = 5β. Substituting this in the first equation, we get:

5β + β = -s

6β = -s

β = -s/6

Using this value of β, we can find the corresponding value of α:

α = 5β = -5s/6

So, the condition for one root to be five times the other is:

α = 5β or -5s/6 = 5(-s/6)

s = 0

Therefore, the condition is that the sum of roots of the quadratic equation x² + sx + F = 0 must be zero.

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The general solution to the system x' = Ax, where A is the given matrix, can be expressed as x(t) = Ce^(At), where C is a constant matrix and e^(At) is the matrix exponential of At. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.

To find the general solution to the system x' = Ax, we can express the solution in terms of the matrix exponential. The matrix exponential of At, denoted as e^(At), is defined as the power series expansion of the exponential function applied to the matrix At. It can be computed using various techniques, such as diagonalization, Jordan decomposition, or power series.

The general solution to the system x' = Ax can then be written as x(t) = Ce^(At), where C is a constant matrix. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.

The matrix exponential e^(At) has properties that are analogous to those of the scalar exponential function. It satisfies the initial condition e^(A * 0) = I, where I is the identity matrix, and it can be used to find solutions for different initial conditions by appropriately choosing the constant matrix C.

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Answer:

I think it should be -2.5,-4.5

Answer: Yes the answer is -2.5 , -4.5

Step-by-step explanation:

This is not only because the X axis is always first, but also because the lines are not perfectly centered. Hope this helps! Give the other person brainliest, they answered first and they have never gotten one.

The value of x will be 6.383cm.

Point to note

We can use the Pythagorean theorem to find the length of the diagonal which is same as diameter

diameter² = side² + side²

diameter² = 2 * x²

diameter = √(2 * x²)

Since the diameter is equal to twice the radius, we have:

diameter = 2 * radius

radius = diagonal / 2

radius = √(2 * x²) / 2

Recall that  area of the circle is given by:

area = πr²

where r is the radius

Substituting the expression for the radius, we get:

64 cm² = π * (√(2 * x²) / 2)²

64 cm² = π * (2 * x² / 4)

64 cm² = π * (x² / 2)

128 = π * x²

Solving for x, we get:

x² = 128 / π

x = √(128 / π)

x = 6.383

Therefore, the value of x is approximately 6.383cm.

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Answer: i think

Step-by-step explanation: -9.8 m/s^2 is not the force of gravity, it is the free fall acceleration due to gravity on Earth. According to Newton's second law, F = ma. Which means that Weight = mass * gravitational

The proportion that could be used to find the width of Grace's model car is 1/2 = Model width / 12 inches.

To find the width of Grace's model car, a proportion can be set up using the lengths of the actual car and the desired model:

Proportion: Actual width / Actual length = Model width / Model length

Given values:

Actual length = 8 feet

Actual width = 4 feet

Model length = 12 inches

Converting the units:

12 inches = 1 foot (since 1 foot = 12 inches)

Substituting the values into the proportion:

4 feet / 8 feet = Model width / 12 inches

Simplifying the proportion:

1/2 = Model width / 12 inches

To find the model width, cross-multiply and solve for the unknown:

Model width = (1/2) * 12 inches = 6 inches

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Answer:

Graph D

Step-by-step explanation:

We can look at the number of pounds of pecans and cashews, shown on the x- and y-axis, respectively.

All of the graphs have an x-intercept of (4, 0), meaning that the number of pecans being bought is 4 lbs.

Since pecans cost $6 per lb, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.

$6 · 4 lbs = $24

Let's look at the y-axis to see how many lbs of cashews Malik can buy. The y-intercept is (0, 3) for all graphs, meaning that 3 lbs of cashews are being bought.

Since cashews cost $8 per pound, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.

$8 · 3 lbs = $24  

The shaded area represents the values that can be used in the problem. Since we want $24 or less, the shaded region has to be below the line.

Malik can spend no more than $24, so the line should be solid since this means that the values the line touches are inclusive. 4 lbs of pecans and 3 lbs of cashews should be inclusive.

The graph that has all of these properties is Graph D.

Answer:

parallel

Step-by-step explanation:

all horizontal lines are parallel

Answer:Parallel and all horizontal lines are parallel

Step-by-step explanation:

Answer:

solve for k or x?

because x isnt on the equation.

i solved for k though

k = -1, 5

Step-by-step explanation:

Solved by simplifying both sides of the equation, then isolating the variable.

An ounce of the chemical cost in 2018 is $98.54.

Given:

The function c(x) = 72 ⋅ (1.04)ˣ models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory.

Exponential function, involves exponents. an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.

In mathematics, an exponential function is a function of form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

x represents the number of years since 2010.

An ounce of the chemical cost in 2018 is,

= 72 × (1.04)⁸

= $98.54

Therefore, the cost is $98.54.

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