2. Marshall wants to save at least $175
for a new video game system and
some games. So far, he has saved
$68.50.
Part A
Write an inequality to represent the
amount of money, a, that Marshall still
needs to save.

Answer:1.33333333333 hamburgers every minute

Step-by-step explanation:40 burgers ÷ 30minutes = 1.333333 burgers every minute

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

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Answer:

1st one is (0.03)(250)

2nd one is $7.50

3rd one is $30.00

Step-by-step explanation:

Answer:

1st one is (0.03)(250)

2nd one is $7.50

3rd one is $30.00

Step-by-step explanation:

edgenutiy sucks

btw the dude above me got it right

The average rate of change between 1991 and 1996 is 40 million

The given parameters are:

Population in 1991 = 1.5 billion

Population in 1996 = 1.7 billion

The average rate of change between 1991 and 1996 is calculated as:

Rate = (1.7 billion -1.5 billion)/(1996 - 1991)

Evaluate

Rate = 40 million

Hence, the average rate of change between 1991 and 1996 is 40 million

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Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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The graph of the new function will be a line that is steeper than the original line and slopes upward from left to right.

Since, A slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

The slope of the function y = -3.5x + 12.8 is -3.5. If the slope is changed to 1.5, the graph of the new function will be steeper than the original function.

When the slope of a linear function is positive, the line slopes upward from left to right. When the slope is negative, the line slopes downward from left to right. The greater the absolute value of the slope, the steeper the line.

Since the new slope is positive and greater than 1, the graph of the new function will be a line that is steeper than the original line and slopes upward from left to right.

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A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.

In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.

Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).

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Answer:

it’s D dotted line with shading below

Step-by-step explanation:

i got it on my quiz

Answer:

Assuming you meant 19 1/2 then the answer would be 9.

Step-by-step explanation:

Answer:

x=23

Step-by-step explanation:

6(x+2)=5(x+7)

6x+12=5x+35

6x-5x=35-12

x=23

Answer:

The calculated χ² = 21.455       falls in the critical region χ² ≥  7.815  so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the type of hard drive and the store where the computers were bought are dependent

against the claim

Ha: the type of hard drive and the store where the computers were bought are independent

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( 4-1) (2-1)=  3 d.f

4) Computations:

Using the calculator we summarize the results as

Under H0 , the observed frequencies are :

Observed         Expected  E        χ²= (O-E)²/E

13                          (23.58)            [4.75]                

11                           (10.63)             [0.013]                  

19                          (14.69)              [1.264]

9                            (3.09)              [11.282]

109                       (98.42)              [1.138]

44                          (44.37)            [0.003]

57                           (61.31)               [0.303]

7                             (12.91)               [2.703]                            

∑                                                            21.455        

5) Conclusion:

The calculated χ² = 21.455       falls in the critical region χ² ≥  7.815  so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.

The p-value is .000085.

The result is significant at p < .05 meaning the claim is accepted.

Answer:

23pupils

Step-by-step explanation:

Given parameters:

Number of 18th grade boys this year = 18

Percentage decrease  = 28%

Unknown:

How many 8th grade teams were there last year  = ?

Solution:

Since this is a percentage decrease, ;

     Number of pupils this year  = Number of pupils last year - (28% x 18 )

                  18 + (28% x 18 ) = Number of pupils last year

         Number of pupils last year = 23pupils

The shortest distance between point P and Q is 9.4.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point P (-4,-2)

x₁ = -4

y₁ = -2

Point Q ( 4,3)

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 4 - (-4) )² + ( 3 - (-2) )² )

D = √( ( 4 + 4 )² + ( 3 + 2 )² )

D = √( 8² + 5² )

D = √( 64 + 25 )

D = √89

D = 9.4

Therefore, the distance is 9.4.

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Answer:

This problem is easier than it appears to be at first glance! If we assume the ground is located at y = 0, then we only use the following equation to solve:

y = -9t + 18

0 = -9t + 18

-18 = -9t

t = 2

Therefore, it takes 2 units of time (whatever units the problem specifically states) for the rocket to hit the ground.

The time will be equal to t = 2 units for the parametric equations x=3t² and y=−4t+16.

A parametric equation in mathematics describes a collection of numbers as functions of one or more independent variables known as parameters.

This issue is simpler than it first appears to be! We can only use the following equation to solve it if we assume that the ground is at y = 0.

y = -9t + 18

0 = -9t + 18

-18 = -9t

t = 2

Therefore, it takes 2 units of time (whatever units the problem specifically states) for the rocket to hit the ground.

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Answer:

y"-6y'+18y=0

Second order

Step-by-step explanation:

Since there are 2 constants, the order of the differential equation will be 2. This means we will need to differentiate twice.

y = e^(3x) (acos3x +bsin3x)​

y'=3e^(3x) (acos3x+bsin3x)

+e^(3x) (-3asin3x+3bcos3x)

Simplifying a bit by reordering and regrouping:

y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)

y"=

3e^(3x) cos3x (3a+3b)+-3e^(3x) sin(3x) (3a+3b)

+3e^(3x) sin3x (3b-3a)+3e^(3x) cos(3x) (3b-3a)

Simplifying a bit by reordering and regrouping:

y"=

e^(3x) cos3x (9a+9b+9b-9a)

+e^(3x) sin3x (-9a-9b+9b-9a)

Combining like terms:

y"=

e^(3x) cos3x (18b)

+e^(3x) sin3x (-18a)

Let's reorder y like we did y' and y".

y = e^(3x) (acos3x +bsin3x)

y=e^(3x) cos3x (a) + e^(3x) sin3x (b)

Objective is to find a way to combine or combine constant multiples of y, y', and y" so that a and b are not appearing.

Let's start with the highest order derivative and work down

y"=

e^(3x) cos3x (18b)

+e^(3x) sin3x (-18a)

We need to get rid of the 18b and 18a.

This is what we had for y':

y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)

Multiplying this by -6 would get rid of the 18b and 18a in y" if we add them.

So we have y"-6y'=

e^(3x) cos3x (-18a)+e^(3x) sin3x (-18b)

Now multiplying

y=e^(3x) cos3x (a) + e^(3x) sin3x (b)

by 18 and then adding that result to the y"-6y' will eliminate the -18a and -18b

y"-6y'+18y=0

Also the characteristic equation is:

r^2-6r+18=0

This can be solved with completing square or quadratic formula.

I will do completing the square:

r^2-6r+18=0

Subtract 9 on both sides:

r^2-6r+9=-9

Factor left side:

(r-3)^2=-9

Take square root of both sides:

r-3=-3i or r-3=3i

Add 3 on both sides for each:

r=3-3i or r=3+3i

This confirms our solution.

Another way to think about the problem:

Any differential equation whose solution winds up in the form y=e^(px) (acos(qx)+bsin(qx)) will be second order and you can go to trying to figure out the quadratic to solve that leads to solution r=p +/- qi

Note: +/- means plus or minus

So we would be looking for a quadratic equation whose solution was r=3 ×/- 3i

Subtracting 3 on both sides gives:

r-3= +/- 3i

Squaring both sides gives:

(r-3)^2=-9

Applying the exponent on the binomial gives:

r^2-6r+9=-9

Adding 9 on both sides gives:

r^2-6r+18=0

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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According to the information we can infer that the change between 11 and 12 is 1.3 m/hr

To establish the value of the change in height between 11 and 12 we must look at the values of the y axis. According to this information we can establish that 11 o'clock coincides with 5.2 and 12 o'clock coincides with 3.9. So we must subtract these two values:

According to the above, we can infer that the change between these two hours is 1.3 m/hr.

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a = uk/b

u = ab/k

uk = ab

a = uk/b

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

The given equation is x²+24x=33.

We need to factorise the equation using completing the square method.

Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.

Now, x²+24x-33=0

Add and subtract (b/2)²=144 to the equation.

x²+24x-33+144-144=0

⇒x²+24x+144-33-144=0

⇒(x+12)²-177=0

⇒(x+12)²=177

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

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Answer:

5

Step-by-step explanation:

-9 + x = -4

( move +x to right and -4 to left)

-9 +4= -x

[sign changes when number is moved]

-5= -x

[negative signs cancel out each other/ divide both sides by negative sign]

x = 5

Answer:

thirty-five and seven tenths

Answer:

(3 x 10)+(5 x 1)+(7 x 0.1)

or

30+5+.7

Step-by-step explanation:

Answer:

Either (c) or (a), (B also looks like a good answer, but I'd go for c)

Step-by-step explanation:

If I'm inincorrect, I apologize!

Answer:

\(4n+5\)

So, the position vector of a point r is (1-1/3)p + (1/3)q.

The position vector of a point can be found using the following formula:

r = (1-λ)p + λq

where λ is the scalar value that represents the ratio in which the point divides the line segment.

In this case, the ratio of the point dividing the line segment is 1:2. So, λ = 1/3.

Substituting the values of p and q, we get:

r = (1-1/3)p + (1/3)q

To show that point p is the midpoint of the line segment rq, we can use the following property of midpoints:

The position vector of the midpoint of a line segment with endpoints p and q is given by (p+q)/2.

In this case, the position vector of point p is (1-1/3)p + (1/3)q, and the position vector of point q is (2/3)p + (2-2/3)q = (2/3)p + (4/3)q

So, the midpoint of the line segment rq is given by:

((1-1/3)p + (1/3)q + (2/3)p + (4/3)q)/2 = (3/3)p + (5/3)q

which is (p+q)/2, so p is the midpoint of the line segment rq

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The conic section that is formed inside the image that we have here is the Hyperbola.

This is also referred to a a quadratic curve. This type of curve is one that occurs due to the fact that there is an intersection of the surface of a particular cone.

This is a pair of shapes that are formed at the intersection of a particular plane. These two shapes would have two equal cones which appear on the opposite  sides of the plane but they have the same vertex.

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Answer: hyperbola

Step-by-step explanation:

Answer:

Minimum = 8

Maximum = 28

Median = 22

First Quartile = 12

Third Quartile = 26

Step-by-step explanation:

✔️Minimum value = the value at the beginning of the whisker from your left = 8

✔️Maximum value = the value at the end of the whisker to your right = 28

✔️Median = the value at the vertical line that divides the box into two = 22

✔️First Quartile = the value at the beginning of the edge of the box = 12

✔️Third Quartile = the value at end of the edge of the box = 26

Answer:

Step-by-step explanation:

Toni didn’t add it up correctly, so the real answer is 151

Answer:

1/4 is the clope of the line

Step-by-step explanation:

a slope is just a rise ofver run from one dot to anothor so you go up 1 and over 4 and if you dont do the 2 dots that are closest to each other you have to simplify you r exspresion you will always get 1/4 on this graph

Answer: I'm pretty sure it is D. intervalled

explanation: Because it can never be exact each and every time