Please answer question 14. A and B.

We can answer the two questions by relying on our knowledge of how to solve equations, showing how both strategies are efficient, and finding x.

a. Both strategies will work and lead to the same solution. It's just a matter of personal preference which one to use. However, subtracting 7 from both sides may be more efficient in this case because it eliminates the need for an extra step of adding 5 to both sides.

b. TStarting with 7 = 3x - 5, we can add 5 to both sides to get:

7 + 5 = 3x - 5 + 5

12 = 3x

12/3 = 3x/3

4 = x

To solve an equation, you need to find the value of the variable that makes the equation true. The following steps can be used to solve most equations:

It's important to remember that whatever you do to one side of the equation, you must also do to the other side to maintain the equality. Additionally, if the equation has parentheses, use the distributive property to simplify the expression inside the parentheses.

Some equations may have special cases, such as quadratic equations or equations with absolute values. These types of equations may require additional steps and methods to solve.

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Answer:

the answer is d

Step-by-step explanation:

just see the matching coordinates

Answer:

In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term. To Factor the form :ax 2 + bx + c. Factor : 6x 2 + 19x + 10. 1) Find the product of 1st and last term( a x c).

Step-by-step explanation:

I hope that helped you!! sorry if not!!

1.904 mcg/kg/min is what the client receives.

The number of mcg/kg/minute = flow rate × concentration ÷ mass of client

Flow rate = 12 ml/ hour = 12 /60 = 1/5 = 0.2 ml/min

Formula:

Concentration = mass of dopamine/volume

mass of dopamine = 800mg

volume = 500ml

Concentration = 800/ 500

= 1.6 mg/ml

= 1.6 × 1000 mcg/mg

= 1600 mcg/mg

Here the mass of the client = 70kg

Now calculating mcg/kg/minute = flow rate× concentration÷ mass of client

= 0.08 ml/min × 1600mcg/ml ÷70 kg

= 320/70

= 1.904 mcg/kg/min

Therefore mcg/kg/min is 1.904.

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Answer:

17x^2-5x-17

Step-by-step explanation:

(8x^2-6x-8)-(-9x^2-x+9)

8x^2-6x-8+9x^2+x-9

17x^2-5x-17

Answer:

I want to say A)

Step-by-step explanation:

Answer: 31.39%

Step-by-step explanation:

Given: The ages of rocks in an isolated area are known to be approximately normally distributed with a mean of 7 years and a standard deviation of 1.8 years.

i.e. \(\mu = 7 \ \ \ \ \sigma= 1.8\)

Let X be the age of rocks in an isolated area .

Then, the probability that rocks are between 5.8 and 7.3 years old :

\(P(5.8<X<7.3)=P(\dfrac{5.8-7}{1.8}<\dfrac{X-\mu}{\sigma}<\dfrac{7.3-7}{1.8})\\\\=P(-0.667<Z<0.167)\ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<0.167)-P(z<-0.667)\\\\=P(Z<0.167)-(1-P(z<0.667))\\\\=0.5663-(1-0.7476)\\\\=0.3139\)

\(=31.39\%\)

Hence, the percent of rocks are between 5.8 and 7.3 years old = 31.39%

Answer:

Here are the answers, in order:

dependent, the same amount, independent

dependent, a different amount, independent

For the first loan, the final payment is $1,576.25. For the second loan, the final payment is $0. The calculations consider the given interest rates and compounding periods.



To determine the final payment for the first loan, we need to calculate the accumulated value of the loan after six years. For the first year, interest is compounded quarterly at a rate of 10% per annum. The accumulated value after one year is $10,000 * (1 + 0.10/4)^(4*1) = $10,000 * (1 + 0.025)^4 = $10,000 * 1.1038125.For the next three years, interest is compounded semi-annually at a rate of 8% per annum. The accumulated value after four years is $10,000 * (1 + 0.08/2)^(2*4) = $10,000 * (1 + 0.04)^8 = $10,000 * 1.3604877.

Finally, for the remaining two years, interest is compounded annually at a rate of 7.5% per annum. The accumulated value after six years is $10,000 * (1 + 0.075)^2 = $10,000 * 1.157625.To find the final payment, we subtract the payments made so far ($5,000 and $6,000) from the accumulated value after six years: $10,000 * 1.157625 - $5,000 - $6,000 = $1,576.25.For the second loan, we calculate the accumulated value after six years using the given interest rates and compounding periods for each period. The accumulated value after two years is $5,000 * (1 + 0.09/4)^(4*2) = $5,000 * (1 + 0.0225)^8 = $5,000 * 1.208646.

The accumulated value after four years is $5,000 * (1 + 0.10/12)^(12*2) = $5,000 * (1 + 0.0083333)^24 = $5,000 * 1.221494.Finally, the accumulated value after six years is $5,000 * (1 + 0.10)^2 = $5,000 * 1.21.To find the final payment, we subtract the payments made so far ($2,500 and $2,500) from the accumulated value after six years: $5,000 * 1.21 - $2,500 - $2,500 = $0.

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Answer:

120 minutes

Step-by-step explanation:

the total bill was $58 so we have to subtract the $40 monthly bill part to find how much extra money she paid because her call was over 200 minutes

58-40=18

Then divide the $18 by $0.15 since the $18 is the total amount of each time she was charged $0.15 for going 1 minute over 200 minutes

18÷0.15 = 120

120 is te Amount Of minutes she went over her 200 minute limit

120 minutes

Taylor's total bill was $58 so then i had to subtract the $40 monthly bill part to find how much extra money she paid because her call was over 200 minutes

58-40=18

Then I divide the $18 by $0.15 since the $18 is the total amount of each time she was charged $0.15 for going  over 200 minutes

18÷0.15 = 120

120 is the amount of minutes she went over her 200 minute limit

-Millie

The set of points at which the function f(x, y) = xy/(8ex − y) is continuous is the set of all points (x, y) such that 8ex ≠ y.

To determine the set of points at which the function is continuous, we need to check if the limit of the function exists and is equal to the value of the function at that point.

Taking the limit of the function as (x,y) approaches (a,b) gives:

lim_(x,y)→(a,b) f(x,y) = lim_(x,y)→(a,b) xy/8ex-y

Using L'Hopital's rule, we can find that the limit is equal to \(ab/8e^(b-a)\).

The function is continuous for all points (a,b) in \(R^2\).

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Answer:

A Yes, because every x value corresponds to exactly one y value

Step-by-step explanation:

A function has a one to one correspondence, or every x goes to only one y value

Since each x goes to only 1 y value this is a function

Answer: It is a function

Step-by-step explanation:

One way to tell if it is a function or not, is to look at the X and Y. While 2 different X values can get the same Y value, one X value should not have 2 different Y values. In the table you can see, there are no repeating X values that have different Y values.

EXAMPLES:

(14, 15)

(13,15)

If these two showed up in a table, it could still be a function

(14, 15)

(14, 16)

If these pairs showed up in a table, than it would not be considered a function

Based on the given pictures:

Angle ∠1 has a more than 90° angle, means that it is classified as obtuse angle.

Angle ∠2 has a less than 90° angle, means that it is classified as an acute angle.

∠ABC is a straight angle because it creates a straight line with 180°.

Angle ∠2 can be named as ∠EBD because it was created by lines EB and ED.

∠WXY = 88°

∠WXZ = 4x - 3

∠ZXY = 2x + 1

∠WXY = ∠WXZ + ∠ZXY

88 = (4x - 3) + (2x + 1)

88 = 6x - 2

6x = 90

x = 15

∠HIJ = 108°

IK bisects ∠HIJ

∠HIK = 4x + 2

∠HIJ = 2∠HIK

108 = 2(4x + 2)

108 = 8x + 4

8x = 104

x = 13

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Answer:

3/2

Step-by-step explanation:

when you plot it time is x and distance is y so go up 3 right 2

Answer:

y=x-5

Step-by-step explanation:

For this, use point-slope formula, which is (y-y1)=k(x-x1), in which k is slope.

Now, substitute in your values. (y-2)=1(x-7)

Then, since you got y-2=x-7, add 2 to both sides.

You get y=x-5

y = x +5  is the equation of the line that passes through the point (7,2) and has a slope of 1.

The equation of a straight line is y=mx+c where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y-intercept. There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

given, a line that passes through the point (7,2) and has a slope of 1

Since the Slope of the line = 1

From the slope-intercept form of the line

y = mx + c

thus, the Equation of the line

y = 1 * x + c

y = x + c

Since this line passes through coordinates (7, 2 ) this point will satisfy the equation

7 = 2 + c

c = 5

hence, the equation of a line

y = x +5

therefore, the equation of the line that passes through the point (7,2) and has a slope of 1 is y = x +5.

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The value of x from the given diagram is approximately 17.7

Applying this theorem to the given triangle, we will have:

x/x+14.2  = 13.3/13.3+10.7

x/x+14.2 = 13.3/24

x/x+14.2 =0.55416

x = 0.55416(x+14.2)

x - 0.55416x = 7.8692

0.44584x = 7.8692

x = 17.7

Hence the value of x from the given diagram is approximately 17.7

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The bookstore sold a total of 150 chemistry textbooks and 225 sociology textbooks.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Let C be the number of chemistry textbooks sold and S be the number of sociology textbooks sold. We can write the following system of equations to represent the given information:

C + S = 375

C = 2S

To solve this system of equations, we can substitute the second equation into the first equation to get C + 2S = 375. Then we can solve for S by subtracting C from both sides to get 3S = 375 - C. Dividing both sides by 3 gives us S = (375 - C) / 3.

Substituting this expression for S back into the second equation, we get C = 2((375 - C) / 3). Multiplying both sides by 3 and simplifying gives us 3C = 750 - 2C, or C = 750 / 5 = 150.

Substituting this value for C back into the first equation, we get 150 + S = 375, so S = 375 - 150 = 225.

Hence, the bookstore sold a total of 150 chemistry textbooks and 225 sociology textbooks.

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The otiginal price will be the 100% and the sale price will be the 100% minus the 30% so will be the 70%, so with this information we can use a rule of 3 to solve the problem so:

so the equation will be:

In order to reflect a point over the y-axis, we just need to change the signal of its x-coordinate.

So for the point (3, 7), the reflection over the y-axis would be (-3, 7).

Therefore we have:

Blank 1: -3

Blank 2: 7

The vector A is (49.9m) x and vector B is (1.5m) x.

In the given question, A − B = (−51.4m)x, C =(62.2m)x, and A +B +C =(13.8m)x.

Find the vector A. Find the vector B.

We may disregard the vector x and treat the issue as an arithmetic one since all of the measurements are in the same direction (simultaneous equations).

A − B = −51.4.............................(1)

C = 62.2.............................(2)

A + B + C = 13.8.............................(3)

Now putting the value of C from Equation (2) in Equation (3)

A + B + C = 13.8

A + B + 62.2 = 13.8

Subtract 62.2 on both side, we get

A + B = 13.8 - 62.2

A + B = - 48.4.....................(4)

Adding the equation (1) and (4), we get

2A = - 99.8

Divide by 2 on both side, we get

A = - 49.9

Now subtracting the equation (1) and (4), we get

2B = -48.4 - ( -51.4)

2B = 3

Divide by 2 on both side, we get

B = 1.5

Since all of the calculations are done in terms of the unit vector x.

So the answer is vector B = (1.5m) x and vector A = (49.9m) x.

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The total revenue from adult ticket sales (10a) must be greater than or equal to $1200.

Let's represent the number of student tickets sold as 's' and the number of adult tickets sold as 'a'.

The revenue from student ticket sales can be calculated as 7.50s, and the revenue from adult ticket sales can be calculated as 10a.

To satisfy the constraint that the drama club must make no less than $1200, we can write the following inequality:

7.50s + 10a ≥ 1200

This inequality states that the total revenue from student ticket sales (7.50s) plus the total revenue from adult ticket sales (10a) must be greater than or equal to $1200.

This inequality ensures that the ticket sales generate enough revenue to cover the show's costs. The drama club needs to sell enough tickets, both student and adult, to meet or exceed the minimum revenue requirement of $1200.

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Answer:K= -4

Step-by-step explanation:

The Laplace Transform of f(t) is F(s) = (3 + 5/s) + (1 - 5e^(-s)) / s.

The given function is:

f(t) = 3u(0 - t) + 5u(t - 0)u(1 - t) + u(t - 1)Step 1:To convert f(t) into a unit step function, use the following steps:

For t < 0, the function is zero, so no unit step function is required.

For 0 ≤ t < 1, f(t) = 5. Thus, for this interval, the unit step function is u(t - 0).For t ≥ 1, f(t) = 1.

Thus, for this interval, the unit step function is u(t - 1).

Therefore, f(t) = 3u(0 - t) + 5u(t - 0)u(1 - t) + u(t - 1) = 3u(-t) + 5u(t)u(1 - t) + u(t - 1) Step 2: The Laplace Transform of f(t) is: F(s) = L {f(t)} = L {3u(-t) + 5u(t)u(1 - t) + u(t - 1)} = 3L {u(-t)} + 5L {u(t)u(1 - t)} + L {u(t - 1)}Here, L{u(-t)} = 1/s and L{u(t - 1)} = e^(-s) / s.L {u(t)u(1 - t)} = L {u(t) - u(t - 1)} = L {u(t)} - L {u(t - 1)} = 1/s - e^(-s) / s

Therefore, F(s) = 3L {u(-t)} + 5L {u(t)u(1 - t)} + L {u(t - 1)} = 3 × 1/s + 5 × [1/s - e^(-s) / s] + [e^(-s) / s] = (3 + 5/s) + (1 - 5e^(-s)) / s

Therefore, the Laplace Transform of f(t) is F(s) = (3 + 5/s) + (1 - 5e^(-s)) / s.

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The Laplace transform of F(s) - f(t) is given function by \(F(s) - (3 + 5e^{(-s)}) / s = 1 / s^2 - 6 / s^4\).

Writing the function in terms of the unit step function:

f(t) = 3u(t) + 5u(t-1)

The unit step function u(t) is 1 for t ≥ 0 and 0 for t < 0.

The function f(t) is equal to 3 for t ≥ 0 and 5 for 0 ≤ t < 1.

So, we can express f(t) in terms of the unit step function as:

f(t) = 3u(t) + 5u(t-1)

Finding the Laplace transform of f(t):

Using the linearity property of the Laplace transform, we can find the transform of each term separately.

L{3u(t)} = 3 / s (by the Laplace transform property of u(t))

\(L\ {5u(t-1)} = 5e^{(-s)} / s\) (by the Laplace transform property of u(t-a))

Therefore, the Laplace transform of f(t) is given by:

\(F(s) = L{f(t)} = 3 / s + 5e^{(-s)} / s\)

Alternatively, we can combine the terms:

\(F(s) = 3 / s + 5e^{(-s)} / s\)

\(= (3 + 5e^{(-s)}) / s\)

So, the Laplace transform of f(t) is \(F(s) = (3 + 5e^{(-s)}) / s\).

Finding the Laplace transform of F(s) - f(t):

We are given F(s) - f(t) = t < 5 (t - 5)³, t > 5.

Using the Laplace transform properties, we can find the transform of each term.

L{t} = 1 / s² (by the Laplace transform property of t^n)

L{(t - 5)³} = 6 / s⁴ (by the Laplace transform property of (t-a)ⁿ)

Therefore, the Laplace transform of F(s) - f(t) is given by:

L{F(s) - f(t)} = L{(t < 5) (t - 5)³, (t > 5)}

= 1 / s² - 6 / s⁴

So, the Laplace transform of F(s) - f(t) is given by \(F(s) - (3 + 5e^{(-s)}) / s\) = 1 / s² - 6 / s⁴.

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Answer:

1. A - \(y\leq \frac{3}{2} x+3\)

2. D - (1,5)

Step-by-step explanation:

The equation \(y\leq \frac{3}{2} x+3\) fits this graph.

y has to be less than x due to the shaded part of the graph being on the underside of the line

To confirm this we can plug in a value to see if the inequality is true

I will use the origin as an example:

\(0\leq \frac{3}{2} (0)+3\)

\(0\leq 3\)

This inequality is true meaning this point is in the shaded region of the graph

Also the equation has to have an equal to because it has a solid line and not a dotted line

The point that isn't a solution is (1,5) due to the fact it isn't in the shaded region and when plugged into the equation gives a false inequality

\(5\leq \frac{3}{2} (1)+3\)

\(5\leq \frac{3}{2}+3\)

\(\frac{10}{2} \leq \frac{9}{2}\)

This inequality is false which means the point (1,5) isn't a solution to this equation.

Answer:

1.) A

2.) D

Step-by-step explanation:

1.) find equation of line:

    b=3,   m=1.5

y=1.5x+3

shaded is below therefore

y\(\leq\)1.5x+3

*line under inequality because line is solid

2.) (1,5) is not a solution because it is above shaded figure

a. To find the 30th percentile for the standard normal distribution, we first need to locate the z-score that corresponds to this percentile. We can use a standard normal distribution table or a calculator to find this value. From the table, we can see that the z-score that corresponds to the 30th percentile is approximately -0.524. Therefore, the 30th percentile for the standard normal distribution is z = -0.524.

b. To find the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5, we can use the formula for transforming a standard normal distribution to a normal distribution with a given mean and standard deviation. This formula is:
z = (x - μ) / σ
where z is the standard normal score, x is the raw score, μ is the mean, and σ is the standard deviation.
To find the 30th percentile for this distribution, we first need to find the corresponding z-score using the formula above:
-0.524 = (x - 10) / 1.5
Multiplying both sides by 1.5, we get:
-0.786 = x - 10
Adding 10 to both sides, we get:
x = 9.214
Therefore, the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5 is x = 9.214. This means that 30% of the observations in this distribution are below 9.214.

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The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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Answer:

  8 5 5

Step-by-step explanation:

Line 3 sets t = 5

Line 5 sets n = t = 5

Line 6 sets c = n+3 = 8

The displayed values for c, n, are

  8 5 5

Answer:

x

x

are the same

Step-by-step explanation:

when you plug in g(x) into f(x)

f(x)=16((1/4)(x)^.5)==x

then vice versa

g(x)=(1/4)((16x^2)^.5)==x

They are the same and, therefore, inverses of each other.

Answer:

yayz fwee pwoints thwank ywuo

Step-by-step explanation: