7(3+6x)>147
Solving inequalities

The linear function is y = (-1/2)x + 4.

What is a linear function?

A linear function whose graph is a straight line and which is represented by an equation of the form y = ax + b where a and b are constants, a does not equal zero, and x is any real number.

Here, we have

Given,

A linear function has an x-intercept of 8 and a y-intercept of 4.

So, The two points on the line are (8, 0) and (0, 4).

Now, slope(m) = (4 - 0)/(0 - 8).

slope(m) = -4/8.

slope(m) = -1/2.

As it has a y-intercept of 4 it is the value of b, In y = mx + b.

Hence, the linear function is y = (-1/2)x + 4.

To learn more about the linear function from the given link

https://brainly.com/question/28033207

#SPJ4

The area under the curve is \(\frac{6 \sqrt{3}}{5}\).

Consider the following parametric equations:\($$x=t^2-3 t \text { and } y=\sqrt{t} \text { and the } y \text {-axis. }$$\)

The objective is to find area enclosed by the curve using the formula.

The area under the curve is given by parametric equations x=f(t), y=g(t),  and is traversed once as t increases from α to β, then the formula for calculating the area under the curve:

\($$A=\int_\alpha^\beta g(t) f^{\prime}(t) d t$$\)

The curve has intersects with y-axis. so x=0

\($$\begin{aligned}t^2-3 t & =0 \\t(t-3) & =0 \\t & =0 \text { or } t=3\end{aligned}$$\)

Now we have to draw the graph,

Let f(t)=\(t^2-3 t, g(t)=\sqrt{t}$\)

Differentiate the curve f(t) with respect to t.

\(f^{\prime}(t)=2 t-3\)

Now, find the area under the curve use the above formula.

\(\begin{aligned}A & =\int_0^3(\sqrt{t})(2 t-3) d t \\& =\int_0^3(2 t \sqrt{t}-3 \sqrt{t}) d t \\& =\int_0^3\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t \\& =\left[2 \frac{t^{\frac{5}{2}}}{\frac{5}{2}}-3 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^3 \\& \left.\left.=\left[\frac{4 t^{\frac{5}{2}}}{5}-2 t^{\frac{3}{2}}\right]_0^3\right]^{\frac{5}{2}}\right] \\\\\end{aligned}$$\)

\(& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right]\)

\($\begin{aligned}& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right] \\& =\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}-0 \\& =\frac{6 \sqrt{3}}{5}\end{aligned}\)

Therefore,  the area of the curve is \(\frac{6 \sqrt{3}}{5}\).

For more question such on parametric equations

https://brainly.com/question/28537985

#SPJ4

The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

More can be learned about the perimeter of a shape at https://brainly.com/question/24571594

#SPJ1

Answer:

x+6

Step-by-step explanation:

to find f(-x) plug in -x for all the values of x in the equation

since the absolute value of -x is x you get x+6

3x+2y+1=0

hopefully this helps

Answer: y = -(2/3)x + 0.5

Step-by-step explanation:

The form of a straight line in slope-intercept form is y=mx+b.  m is the slope an b is the y intercept.  

We can calculate m, the slope, from the two points given.  From that we can calculate b by using one of the two points in the equation.

Slope (m) is the change in y divided by the change in x.  For these two points we can find the x change (3 -(-1)) = 4 (the distance between -1 and 3).  The change in y is (-4-2) = -6.  The slope is therefore (-6/4), or  -3/2.

y = (-3/2)x + b

No enter either point for x and y and calculate b.

2 = -(3/2)*(-1) + b

2 = +(3/2) + b

b = 0.5

y = -(2/3)x + 0.5

Answer:

\(x = \sqrt{ {17}^{2} - {15}^{2} } = \sqrt{289 - 225} = \sqrt{64} = 8\)

So x = 8 = 8.0

The answer is 1. The ΣX for a sample of n=12 scores with M=8 is 96, 2. The mean for combined samples of n=15 (mean=10) and n=10 (mean=8) is 9.33, 3a. The original mean before adding 6 points is 8, 3b. The original mean before multiplying scores by 4 is 8, 4. The new sample means after removing X=18 is 22.5, and 5. The score added to a population with μ=24 to achieve μ=34 is 34.

1. For any sample, we can find the sum of the scores (ΣX) by multiplying the mean by the number of scores. So in this case:ΣX = M * nΣX = 8 * 12ΣX = 96Therefore, the ΣX value for this sample is 96.

2. To find the mean of the combined samples, we can use the formula: Mean of combined samples = (n1 * mean1 + n2 * mean2) / (n1 + n2) = Mean of combined samples = (15 * 10 + 10 * 8) / (15 + 10) = Mean of combined samples = 9.33. Therefore, the mean for the combined samples is 9.33.

3. a: We can use the formula for shifting the mean to find the original mean: M1 = M2 - kM1 = 14 - 6M1 = 8. Therefore, the value for the mean before 3 points were added to each score is 8. b. The researcher then realizes that she instead needs to multiply each score by 4. Using the original scores, she multiplies each by 4 and finds the mean to be M=32. We can again use the formula for shifting the mean to find the original mean: M1 = M2 / kM1 = 32 / 4M1 = 8. Therefore, the value of the mean prior to multiplying each score by 4 points is 8.

4. To find the new sample mean, we need to remove the score and adjust the mean accordingly. We can use the formula: New mean = (ΣX - X) / (n - 1)New mean = (ΣX - 18) / 10. Given that the original mean is 22, we can solve for ΣX:22 = ΣX / 1122 * 11 = ΣX243 = ΣX. Now we can plug in to find the new mean: New mean = (243 - 18) / 10 = New mean = 22.5. Therefore, the value of the new sample mean is 22.5.

5. We can use the formula for adding a score to a population to find the value of the added score: N μ = ΣX / NN * μ = ΣX / N + 1. Given that N = 10 and μ = 24 for the original population, we can solve for ΣX:10 * 24 = ΣX240 = ΣX. Now we can use the new mean and the formula to solve for the added score:11 * 34 = 240 + X / 11274 = 240 + XX = 34. Therefore, the value of the score that was added is 34.

For more questions on mean

https://brainly.com/question/1136789

#SPJ8

The answer provides solutions to the various statistical maths problems that involve calculations of mean and sum of scores. These problems explore the understanding of the concept of mean, summation and basic operations.

To answer these questions, you'll need to understand basic concepts of statistics, specifically the calculation of means, and summation of scores (ΣX). So, let's break them down one by one:

https://brainly.com/question/31538429

#SPJ12

Answer:

3) = C (0.505)

4) = B (4.32 kilograms)

Step-by-step explanation:

0.505 is in-between 0.482 and 0.51

1.08 X 4 = 4.32

Answer:

3. C. 0.505 gram

4. B. 4.32 kilograms

$1075 is the total cost of the dinners she served if she earned $275 on Friday

percentage, a relative value indicating hundredth parts of any quantity.

Given that Lisa  earns a daily wage of $60,

Tips that are equal to 20% of the total cost of the dinners she serves

We can write this as 60+20/100x.

The total cost of the dinners she served if she earned $275 on Friday

is given by

275=60+0.2x

Subtract 60 on both sides

275-60=0.2x

215=0.2x

Divide both sides by 0.2

215/0.2=x

1075=x

Hence, $1075 is the total cost of the dinners she served if she earned $275 on Friday

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

What is Distance?

Distance is defined as the space between two points in space.

To find out how far Jake will have traveled after 3 hours, we can use the formula:

distance = speed x time

where speed is the rate at which Jake is traveling and time is the duration of the travel. In this case, the speed is 12 mph and the time is 3 hours.

So, the distance traveled after 3 hours is:

distance = 12 mph x 3 hours = 36 miles

Therefore, Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

To know more about Distance visit,

https://brainly.com/question/26550516

#SPJ4

Answer:

Angles of:

1 = 87 degree, 2= 62 degree

Step-by-step explanation:

Here, we have a Vertically opposite angle so equate both the equations and get the value of x. then substitute the value of x in both equations.

hope it helps!

Answer:5/8

Step-by-step explanation:

\(\begin{gathered} \boxed{ \sf \frac{3}{4} - \frac{1}{8}} = \\ \\ \sf \frac{8 \div 4 \times 3 - 8 \div 8 \times 1}{8} = \\ \\ \sf\frac{6 - 1}{8} = \\ \\ \sf \boxed{ \sf\frac{5}{8}} \end{gathered}\)

Therefore, the result of this subtraction of fractions is five eighths.

How to subtract unlike fractions:

Heterogeneous fractions are fractions that have different denominators.

To subtract heterogeneous fractions we follow these steps:

The probability that the weight of a randomly selected newborn baby boy born at the local hospital will be greater than 2620 grams is 0.9099 (rounded to four decimal places).

The probability can be calculated using the standard normal distribution as follows:

P(Z > (2620 - 3245) / 625) = P(Z > -1.335)

Using a standard normal distribution table, we find that the probability of Z being greater than -1.335 is 0.9099.

We use the standard normal distribution because we know the mean and standard deviation of the population of newborn baby boys' weights. We convert the raw score of 2620 grams to a z-score, which tells us how many standard deviations the raw score is away from the mean.

Learn more about probability

https://brainly.com/question/24756209

#SPJ4

Answer:

D

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = - 3 , then

\(a_{n}\) = 8 - 3(n - 1) = 8 - 3n + 3 = - 3n + 11 → D

Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.

The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.

So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:

(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)

= (1/4) × 8x − (1/3) × 12y

= 2x − 3y

Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.

To learn more about distributive property here:

https://brainly.com/question/29048637

#SPJ1

Answer:

The answer is "The product is greater than 3/8 and less than 7/2"

Step-by-step explanation:

This is because the product of 3/8 and 7/2 is 21/16.

When you simplify 21/16, you get 1 and 5/16 which is greater than 3/8 but less than 7/2, which simplified is 3 and 1/2.

Answer:

The product is greater than 3/8 and less than 7/2

Step-by-step explanation:

The number is greater than 3/8

It is greater than 1/8 but not less than 1/2

This number is less than 7/2

Answer:

36

Step-by-step explanation:

90÷5=18

18×2=36

We multiply two because the ration for adults is 2

Answer:

ran throught a cal is

Step-by-step explanation:

Slope (m) =  

ΔY /ΔX =1/3 =0.33333333333333

Answer:

y=6x

Step-by-step explanation:

if u times x by 6 you get the y number underneath

for example:

x=1

y=6

so 1×6=6

x=2

y=12

so 2×6=12

Answer:

Distributive property.

Step-by-step explanation:

A distributive property is a rule that states that, multiplying two factors such as a binomial and trinomial would give the same result as multiplying the sum of two addends by the other factor.

Hence, the distributive property is used to simplify the product of a binomial and trinomial.

For example, let's find the product of (2x + 4)(5x² + 3x + 10)

First of all, we would distribute trinomial into each of the term in the binomial.

2x(5x² + 3x + 10) + 4(5x² + 3x + 10)

Distributing the monomial into the trinomial, we have;

2x(5x²) + 2x(3x) + 2(10) + 4(5x²) + 4x(3x) + 4(10)

Expanding the bracket, we have;

10x³ + 6x² + 10 + 20x² + 12x² + 40

Collecting like terms, we have;

10x³ + (6x² + 20x² + 12x²) + 10 + 40

10x³ + 38x² + 50

Therefore, (2x + 4)(5x² + 3x + 10) = 10x³ + 38x² + 50

Expressions that are tested by the 'if' statement is called conditions.

A condition is an expression that evaluates to either 'True' or 'False', and it determines whether the code block within the 'if' statement is executed. The 'if' statement allows the program to make decisions and execute different codes based on whether the condition is 'true' or 'false'. For example, in Python, an 'if' statement might look like this:

if x > 10:

   print("x is greater than 10")

In this example, the condition being tested is 'x > 10', which will evaluate as 'True' or 'False' depending on the value of x. If the condition is 'True', then the code block within the 'if' statement (in this case, the print statement) will be executed. If the condition is 'False', then the code block within the 'if' statement will be skipped.

To learn more about python, refer:-

https://brainly.com/question/30427047

#SPJ4

Answer:

x = 10

Step-by-step explanation:

21 = 4x - 9 - x

21 = 3x - 9

30 = 3x

10 = x

Answer:

x = 10

Step-by-step explanation:

Given

21 = 4x - 9 - x, that is

21 = 3x - 9 ( add 9 to both sides )

30 = 3x ( divide both sides by 3 )

10 = x

Answer: Its not possible.

Step-by-step explanation:There aer two vairables. Whats the value of N

Hey there!

n = 4/5(m + 7)

n = 4/5(1m + 7)

n = 4/5(1m) + 4/5(7)

n = 4/5m + 28/5

n = 4/5m + 5.6

Thus, your answer is probably:

n = 4/5m + 5.6 or n = 4/5m + 28/5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The smallest value of prime number, p used as counterexample to the statement p² + p + 1 is p = 7

Counterexample refers to instance that will make a statement false hence we look for values that will not hold true with the statement:

p² + p + 1

Where p = 2

2² + 2 + 1 = 7

Where p = 3

3² + 3 + 1 = 13

Where p = 5

5² + 5 + 1 = 31

Where p = 7

7² + 7 + 1 = 57

57 is not a prime number and hence the counterexample

Learn more about counterexample  here:

https://brainly.com/question/28924130

#SPJ1

Gerald is scheduled to be in class for 45/93 of the time from 8:00 a.m. to 2:15 p.m. on Thursday.

To determine the fraction of time Gerald is scheduled to be in class, calculation of the duration of his class and divide it by the total duration from 8:00 a.m. to 2:15 p.m.

Step 1: Calculate the duration of Gerald's class:

The class starts at 8:30 a.m. and ends at 12:00 p.m. To find the duration, we subtract the start time from the end time:

12:00 p.m. - 8:30 a.m. = 3 hours and 30 minutes.

Step 2: Calculate the total duration from 8:00 a.m. to 2:15 p.m.:

To find the duration, we subtract the start time from the end time:

2:15 p.m. - 8:00 a.m. = 6 hours and 15 minutes.

Step 3: Calculate the fraction of time Gerald is scheduled to be in class:

To find the fraction, we divide the duration of Gerald's class by the total duration:

3 hours and 30 minutes / 6 hours and 15 minutes = 210 minutes / 375 minutes.

To simplify the fraction,  divide both the numerator and denominator by their greatest common divisor, which is 15:

210 minutes ÷ 15 / 375 minutes ÷ 15 = 14 / 25.

Therefore, Gerald is scheduled to be in class for 14/25 of the time from 8:00 a.m. to 2:15 p.m. on Thursday.

To know more about fraction of time, visit;
https://brainly.com/question/26468354
#SPJ11

Answer:

Step-by-step explanation:

hello :

r+b=7... (*)

3.75r+2.75b=22.25.... (**)

use (*) :  r = 7 - b

put this value in (**) :

3.75(7 - b)+2.75b =  22.25

26.25 -375b +2.75b = 22.5

-375b +2.75b = 22.5 - 26.25

- b = -3.75

so : b  = 3.75

but : r = 7 - b

r = 7 - 3.75

r = 3.25

The finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is given by

\(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\),

where \(f_{n-2}\), \(f_{n-1}\), and \(f_n\) represent the function values at nodes \(n-2\), \(n-1\), and \(n\) respectively, and \(h\) represents the spacing between the nodes.

To derive this approximation, we start with the Taylor series expansion of \(f_{n-1}\) and \(f_n\) around \(x_n\):

\(f_{n-1} = f_n - hf'_n + \frac{h^2}{2}f''_n - \frac{h^3}{6}f'''_n + \mathcal{O}(h^4)\),

\(f_{n-2} = f_n - 2hf'_n + 2h^2f''_n - \frac{4h^3}{3}f'''_n + \mathcal{O}(h^4)\).

By subtracting \(4f_{n-1}\) and adding \(3f_n\) from the second equation, we eliminate the first-order derivative term and retain the second-order derivative term. Dividing the result by \(2h\) gives us the desired finite difference approximation to \(O(h^2)\).

In conclusion, the finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is \(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\). This approximation is obtained by manipulating the Taylor series expansion of \(f_{n-1}\) and \(f_n\) to eliminate the first-order derivative term and retain the second-order derivative term, resulting in a second-order accurate approximation.

Learn more about function here:

https://brainly.com/question/31062578

#SPJ11