How do I solve for the minimum and maximum of the function y=-1/2x^2 -5x+2

Answer:

Part A ⇒ n>-140/p and p≠0  

Part B. ⇒ d=-30-2a/5

Step-by-step explanation:

Part A. -np-80<60

First, add by 80 both sides of equation.

-np-80+80<60+80

Simplify.

60+80=140

-np<140

Then, multiply by -1 both sides of equation.

(-np)(-1)>140(-1)

Simplify.

np>-140

Divide by p both sides of equation.

np/p>-140/p; p≠0

Simplify to find the answer.

n>-140/p; p≠0 is the correct answer from part a.

___________________________________

Part B. 2a-5d=30

First add by 2a from both sides of equation.

2a-5d+2a=30+2a

Then, simplify.

-5d=30-2a

Divide by -5 from both sides of equation.

-5d/-5=30/-5-2a/5

Simplify, to find the answer.

d=-30-2a/5 is the correct answer from part b.

Part A:

For this case we have the following inequality:

[tex]-np-80 <60[/tex]

We add 80 to both sides of the inequality:

[tex]-np <60+80\\-np <140[/tex]

Dividing between -p on both sides, having to change the inequality sign:

[tex]n> - \frac {140} {p}[/tex]

Part B:

For this case we have the following equation:

[tex]2a-5d = 30[/tex]

Subtracting 2a on both sides:

[tex]-5d = 30-2a[/tex]

Dividing between -5 on both sides:

[tex]d = \frac {30-2a} {- 5}\\d = \frac {-30+2a} {5}\\d = - \frac {30} {5} +\frac {2a} {5}\\d = -6+ \frac {2a} {5}[/tex]

Answer:

[tex]n> - \frac {140} {p}\\d = -6+\frac {2a} {5}[/tex]

Answer: $5,224.74

Step-by-step explanation:

You need to calculate the 6% of  $4,929.00.

Convert the percentage to decimal form:

[tex]\frac{6}{100}=0.06[/tex]

Now multiply  $4,929.00 by 0.06:

[tex](\$4,929.00)(0.06)=\$295.74[/tex] (This is the 6% of $4,929.00)

Finally, you need to add $295.74 to $4,929.00. Then you get:

[tex]\$4,929.00+\$295.74=\$5,224.74[/tex]

Therefore, the 6% sales tax on $4,929.00 is: $5,224.74

Final answer:

To calculate the probability of a shopper spending less than 20 minutes in the store, the Z-score is found using the formula Z = (X - μ) / σ, resulting in a Z-score of -0.25, which corresponds to a probability of approximately 0.40.

Explanation:

The question asks for the probability that a randomly selected shopper will spend less than 20 minutes in a store, given that the average time spent is 22 minutes with a standard deviation of 8 minutes, and that these times are normally distributed. To find this probability, we use the Z-score formula:

Z = (X - μ) / σ

Where X is the value we are checking (20 minutes), μ is the mean (22 minutes), and σ is the standard deviation (8 minutes). Plugging in the numbers, we get:

Z = (20 - 22) / 8 = -0.25

Next, we look up the Z-score in a standard normal distribution table, or use a calculator with normal distribution functions, to find the probability that a Z-score is less than -0.25. This probability is approximately 0.40.

Final answer:

Stephanie cuts the rope into five 1-meter-long pieces by dividing the total length (5 meters) by the number of pieces (5).

Explanation:

If Stephanie cuts a five-meter-long piece of rope into five equal parts, we would divide the total length of the rope by the number of parts to find the length of each piece. In this case, the calculation would be:

So, the length of each part would be 5 meters ÷ 5, which equals 1 meter. Therefore, each piece of rope would be 1 meter long.

Answer:

-∞ < x < ∞

Explanation:

x³ is the inverse of ∛x and x³ has range of all real numbers and is one to one function, so its inverse will have domain of all real numbers.

Answer:

Option 1 negative (-) infinity < X < infinity

Step-by-step explanation:

Answer:

The percentage of the distribution is less than 75 is 97.72%.

Step-by-step explanation:

Given,

Mean of the distribution,

[tex]\mu=67[/tex]

Standard deviation,

[tex]\sigma = 4[/tex]

Thus, the z-score of the score 75,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]=\frac{75-67}{4}[/tex]

[tex]=\frac{8}{4}[/tex]

[tex]=2[/tex]

With the help of z-score table,

[tex]P(x<75)=0.9772=97.72\%[/tex]

Hence, the percentage of the distribution is less than 75 is 97.72%.

Answer:

Step-by-step explanation:

For equations like these, where the coefficient of one of the variables is 1, it is convenient to choose values for the other variable. Values of 0 and 1 are usually easy to work with.

In the first equation, ...

  for x=0, y = 2 . . . . . . . . . point (0, 2)

  for x=1, y = -2+2 = 0 . . . point (1, 0)

In the second equation, ...

  for y=0, x = -4 . . . . . . . . . point (-4, 0)

  for y=1, x +3 = -4, so x = -7 . . . . point (-7, 1)

Answer:  B) 67%

Step-by-step explanation:

Find the Area of the Bullseye and Middle ring

A = π r²

A (inside) = π(8)² = 64π

Find the Area of the entire Target

A (target) = π (14)² = 196π

Find the Area of the Outer ring

A (outer ring) = A (target) - A(inside)

                      =   196 π    -    64π

                      =    132 π

The last step is to find the probability of landing on the outer ring:

[tex]P=\dfrac{success (area\ of\ outer\ ring)}{total\ possible\ outcomes(area\ of\ target)}=\dfrac{132\pi}{196\pi}=0.673=\large\boxed{67\%}[/tex]

Answer:

67%

Step-by-step explanation:

Answer:

53.27

Step-by-step explanation:

To begin, we want to figure out what percent of products are defective and non defective, and of which type, so we can figure out probabilities. So, we start with that 5% of chairs are defective. We know that 35% of product sales are chairs, so 5% of 35% is 35%*0.05 (a percent can be divided by 100 to convert to decimals)= 1.75%. For tables, 12% of 55 is 55*0.12=6.6 percent. For beds, we first must figure out what percent of sales are beds. For this, we must take our total (100%) and subtract everything that is not beds, which is tables and chairs. This, 100-35-55=10, which is our percent of beds. Then, 8% of that is 0.8%. So, we know that the probability that an item is defective is 0.8+6.6+1.75=9.15%. The item pulled was not defective, so we want to figure out the probability of that, which would be the total-defective=100-9.15=90.85%. We then need to figure out which of that 90.85 is divided by tables, as we want to figure out what the probability of a table is. We know that 12% of tables are defective, so 100-12=88% are not. 88% of 55% is 55*0.88=48.4, so there is a 48.4% chance that if you picked out anything, it would be a non defective table. However, we are only picking things out from nondefective items, or the 90.85%. We know that 48.4 is 48.4% of 100, but we want to figure out what percent 48.4 is of 90.85. To find this, we do (48.4/90.85) * 100, which is 53.27 rounded. Feel free to ask further questions!

Answer:

The second choice is correct.

Step-by-step explanation:

    These are triangles, so the interior angles have to add up to 180 degrees. Since 45 degrees and m<1 are vertical angles, they will have the same measure. So right off the back we know that m<1 =45. To find the measure<2 all you need to do is add 45 and 59, then subtract that answer from 180. M<2= 76. That leaves only one option. The second  one.

The measurements of the angles are Angle 1 = 45 degrees, Angle 2 = 76 degrees, Angle 3 = 80 degrees. The correct option is b) 1 = 45, 2 = 76, 3 = 80.

Let's solve this step by step to find the measurements of angles 1, 2, and 3.

We named the two triangles as OAB and OCD, with a common vertex O. angle O makes vertically opposite angle 45 degree in triangle OAB and angle 1 in OCD, angle A makes angle 2, angle B makes angle 59 degree, angle C makes 55 degree and angle D makes angle 3.Given the information:

In triangle OAB:

Angle OAB (angle 2) = 59 degrees

Angle O = 45 degrees (vertically opposite to angle 1)

In triangle OCD:

Angle O = 45 degrees (again, vertically opposite to angle 1)

Angle OCD (angle 3) = ?

First, let's find angle 2 in triangle OAB:

In triangle OAB, the sum of angles in a triangle is 180 degrees.

So, angle 2 + angle O + angle OAB = 180 degrees.

59 + 45 + angle OAB = 180 degrees.

Now, solve for angle OAB:

angle OAB = 180 degrees - 59 degrees - 45 degrees

angle OAB = 76 degrees

Now, let's find angle 3 in triangle OCD:

In triangle OCD, the sum of angles in a triangle is also 180 degrees.

So, angle O + angle OCD + angle C = 180 degrees.

45 + angle 3 + 55 = 180 degrees.

Now, solve for angle 3:

angle 3 = 180 degrees - 45 degrees - 55 degrees

angle 3 = 80 degrees

So, the measurements of angles 1, 2, and 3 are as follows:

Angle 1 = 45 degrees

Angle 2 = 76 degrees

Angle 3 = 80 degrees

The correct option is:

b) 1 = 45, 2 = 76, 3 = 80

To know more about angle:

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Answer: 11

Step-by-step explanation:

5% × 220 =

(5 ÷ 100) × 220 =

(5 × 220) ÷ 100 =

1,100 ÷ 100 =

11;

5% of 220 = 11

Answer:

44% is your answer.

Step-by-step explanation:

So, 220/5= 44/1= 44%

Because if you divide 220 by 5 you'll get 44 and 5 divided by 5 ofcourse is 1.

(I'm doing these also in my class, so hopefully i helped you.)

Answer: There is probability of 96.4% that  a day in March will be foggy if it is a cloudy.

Step-by-step explanation:

Since we have given that

Probability of the days in March are cloudy = 57%

Probability of the cloudy days in March are foggy = 55%

Let A be the event of cloudy days in March.

Let B be the event of foggy days in March.

So, here,

P(A) = 0.57

P(A∩B) = 0.55

We need to find the probability that days are foggy given that it is cloudy.

We would use "Conditional probability":

[tex]P(B\mid A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.55}{0.57}=0.964=96.4\%[/tex]

Hence, There is probability of 96.4% that  a day in March will be foggy if it is a cloudy.

Answer Do it

Step-by-step explanation 165 divided by 100 =x times 43

Answer: a) 0.7814

b) False

Step-by-step explanation:

To find : The p-value of z , where

[tex]-1.23<z< +1.23[/tex]

[tex]P(-1.23<z< +1.23)=1-P(z<-1.23)\\\\=1-0.1093=0.7814[/tex]

Hence, the standard normal probability [tex]P(-1.23<z< +1.23)=0.7814[/tex]

In the formula used to convert "real-world" data values into z numbers, the standard deviation of the data is considered.

The formula to calculate the z score is [tex]z=\dfrac{x-\mu}{\sigma}[/tex].

If sample size (n) is given then , the [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

Hence, the statement is false.

The problem is to calculate the number of additional men needed to build an airstrip in less time given two men already took five hours. The additional man required is one after solving the equation, but this is not an option provided, indicating a potential error in the question.

The question involves calculating the number of additional men required to build an airstrip in less time. If it took 2 men 5 hours to build an airstrip, we can say they have a combined work rate of 1 airstrip per 5 hours, or ​​(1/5) airstrip per hour. To finish the job in 4 hours, which is 1 hour less than the original time, we would need a work rate of 1 airstrip per 4 hours.

So, if we let the number of additional men be X, we can set up the equation as follows:

Since we cannot hire half a person, we round up to the nearest whole number. Hence, one additional man would be sufficient to complete the work in 1 hour less time. However, none of the options given (A) Two, (B) Three, (C) Four, or (D) Six, are correct. Therefore, the answer is not provided in the given options and this represents a possible error in the question itself.

Answer:

gragh

Step-by-step explanation:

its one of the few ways to analyze data and compare it to find the best choice

Answer with explanation:

The Inequality should be:

   [tex](1+x)^n\geq 1+n x[/tex]

Where, n and x are any integers.

⇒For, x= -1

L HS

 [tex]=[1+(-1)]^n\\\\=(0)^n\\\\=0[/tex]

R HS

→1+n × (-1)

=1-n

If, n is any Integer, then for, n=1

1-1=0

For, n=2

1-2= -1

....

So,   [tex](1+x)^n\geq 1+n x[/tex]

for, x=-1.

⇒For, x=1

L HS

 [tex]=[1+(1)]^n\\\\=(2)^n[/tex]

For, n=1

L H S=1

For, =2

L H S=4

R HS

→1+n × (1)

=1+n

If, n is any Integer, then for, n=1

1+1=2

For, n=2

1+2= 3

....

So,    [tex](1+x)^n\geq 1+n x[/tex]

for, x=1.

Answer:

Step-by-step explanation:

You can't simplify the sum, but you can factor it.

t^2 + 2t - 3

(t  + 3)(t - 1 )

That's about all you can do.

Answer:

It is already in simplest form.

Step-by-step explanation:

It cannot be further simplified because it does not have any like terms.

Answer:

Step-by-step explanation:

I'm making the assumption you are looking for a graph of y=log_3(x)

So 3^0=1          which means log_3(1)=0              graph (1,0)

     3^1=3          which means log_3(3)=1              graph (3,1)

     3^2=9         which means log_3(9)=2             graph (9,2)

     3^3=27       which means log_3(27)=3           graph (27,3)

Can you find a graph that fits these points?

Answer:

honesty you cant realy use a calculator because you need to meadian mode and range them first

Step-by-step explanation:

Answer:

The correct answer is option C.  1/12

Step-by-step explanation:

It is given that, two dies are rolled.

The outcomes of tossing two dies are,

(1,1), (1,2), (1,3), (1,4), (15), (1,6)

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

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

Number of possible outcomes = 36

To find the probability

The possible outcomes are getting sum 10 which are,

(4,6), (5, 5) and (6,4)

Number of possible outcomes = 3

Therefore probability of getting sum 10 = 3/36 = 1/12

The correct answer is option C.  1/12

Answer:

x = -5 sin (2t)

Step-by-step explanation:

k is the spring stiffness.  The unstretched length of the spring is L.

When the mass is added, the spring stretches to an equilibrium position of L+s, where mg = ks.  When the mass is displaced a distance x (where x is positive if the displacement is down and negative if it's up), the spring is stretched a total distance s + x.

There are two forces on the mass: weight and force from the spring.  Sum of the forces in the downward direction:

∑F = ma

mg − k(s + x) = ma

mg − ks − kx = ma

Since mg = ks:

-kx = ma

Acceleration is second derivative of position, so:

-kx = m d²x/dt²

Let's find k:

F = kx

400 = 2k

k = 200

We know that m = 50.  Substituting:

-200x = 50 d²x/dt²

-4x = d²x/dt²

d²x/dt² + 4x = 0

This is a linear second order differential equation of the form:

x" + ω² x = 0

The solution to this is:

x = A cos (ωt) + B sin (ωt)

Here, ω² = 4, so ω = 2.

x = A cos (2t) + B sin (2t)

We're given initial conditions that x(0) = 0 and x'(0) = -10 (remember that down is positive and up is negative).

Finding x'(t):

x' = -2A sin (2t) + 2B cos (2t)

Plugging in the initial conditions:

0 = A

-10 = 2B

Therefore:

x = -5 sin (2t)

Answer: The value of n is  374. The value of p is 0.21. The value of q is 0.79.

Step-by-step explanation:

Given : In a clinical trial of a cholesterol drug, 374 subjects were given a placebo, and 21% of them developed headaches.

∴ Sample size : [tex]n=374[/tex]

The probability that cholesterol drug developed headaches :[tex]p=0.21[/tex]

Then , the probability that cholesterol drug did not develop headaches :[tex]q=1-p=1-0.21=0.79[/tex]

Hence, The value of n is  374.

The value of p is 0.21.

The value of q is 0.79.

[tex]h(x)=(5-2x^6)^3+\dfrac1{5-2x^6}[/tex]

Let [tex]g(x)=5-2x^6[/tex] and [tex]f(x)=x^3+\dfrac1x[/tex]. Then [tex]h(x)=f(g(x))[/tex].

Set [tex]u=5-2x^6[/tex]. By the chain rule,

[tex]\dfrac{\mathrm dh}{\mathrm dx}=\dfrac{\mathrm dh}{\mathrm du}\cdot\dfrac{\mathrm du}{\mathrm dx}[/tex]

Since [tex]h(u)=u^3+\dfrac1u[/tex] and [tex]u(x)=5-2x^6[/tex], we have

[tex]\dfrac{\mathrm dh}{\mathrm du}=3u^2-\dfrac1{u^2}[/tex]

[tex]\dfrac{\mathrm du}{\mathrm dx}=-12x^5[/tex]

Then

[tex]\dfrac{\mathrm dh}{\mathrm dx}=\left(3u^2-\dfrac1{u^2}\right)(-12x^5)=\boxed{-12x^5\left(3(5-2x^6)^2-\dfrac1{(5-2x^6)^2}\right)}[/tex]

which we could rewrite slightly as

[tex]\dfrac{\mathrm dh}{\mathrm dx}=-\dfrac{12x^5(3(5-2x^6)^4-1)}{(5-2x^6)^2}[/tex]

To differentiate the given function using the chain rule, we need to identify the functions f(x) and g(x), then calculate their derivatives. Once we have the derivatives, we can apply the chain rule to find the derivative of the composite function h(x).

Chain Rule

To differentiate the function h(x) = (5 - 2x^6)³ + 1/(5 - 2x^6) using the chain rule, we can write it as the composite function h(x) = f(g(x)).

Let's identify the functions f(x) and g(x):

f(x) = x³, g(x) = (5 - 2x^6)

Next, let's calculate the derivatives of f(x) and g(x):

f'(x) = 3x², g'(x) = -12x^5

Finally, we can apply the chain rule to differentiate h(x):

h'(x) = f'(g(x)) * g'(x) = (3(5 - 2x^6)²) * (-12x^5)

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The probability that a defective component came from shipment II is:

                   [tex]0.7143\ or\ 71.43\%[/tex]

Let A denote the event that the defective component was from shipment I

Also, P(A)=2%=0.02

and B denote the event that the defective component was from shipment II.

i.e. P(B)=5%=0.05

Also, P(shipment I is chosen)=1/2=0.5

and P(shipment II is chosen)=1/2=0.5

The  probability that a defective component came from shipment II is calculated by Baye's rule as follows:

[tex]=\dfrac{\dfrac{1}{2}\times 0.05}{\dfrac{1}{2}\times 0.02+\dfrac{1}{2}\times 0.05}}\\\\\\=\dfrac{0.05}{0.07}\\\\=\dfrac{5}{7}\\\\=0.7143\ or\ 71.43\%[/tex]

Hence, the answer is:

                        [tex]0.7143\ or\ 71.43\%[/tex]

By applying Bayes' Rule, we can compute the probability that a defective component came from shipment II as approximately 71.4%.

Given that there are two shipments of components both containing defective parts, we can apply the Bayes' Rule to answer your question.

Let's assume that D is the event that a component is defective and I and II are events that the component came from shipment I and shipment II respectively. Since the defective component can come from either shipment with equal probability, P(I) = P(II) = 0.5. Also, it's given that the component is defective, so P(D) = 1.

The probability that a component from shipment I is defective, P(D/I), is 2% or 0.02 and from shipment II is 5% or 0.05. We want to find the probability that a defective component came from shipment II, or P(II/D).

To do this, we use Bayes' Rule: P(II/D) = [P(D/II) * P(II)] / P(D).

Substituting the values in, we get: P(II/D) = [0.05 * 0.5] / [0.5 * (0.02 + 0.05)] = 0.0625 / 0.035 = ~0.714. So the probability that a defective component came from shipment II is approximately 0.714 or 71.4%.

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Answer:

  11

Step-by-step explanation:

Suitable software can generate these collections. They are ...

{13,1,1,1,1,1}, {11,3,1,1,1,1}, {9,5,1,1,1,1}, {9,3,3,1,1,1},

{7,7,1,1,1,1}, {7,5,3,1,1,1}, {7,3,3,3,1,1}, {5,5,5,1,1,1},

{5,5,3,3,1,1}, {5,3,3,3,3,1}, {3,3,3,3,3,3}}

The number of distinct collections of six positive odd integers that sum to 18 is indeed:[tex]\[\boxed{11}\][/tex]

[tex]\[2(k_1 + k_2 + k_3 + k_4 + k_5 + k_6) + 6 = 18\]\[k_1 + k_2 + k_3 + k_4 + k_5 + k_6 = 6\][/tex]

Here are the possible combinations of non-negative integers (up to permutations) that sum to 6:

[tex]1. \( (6, 0, 0, 0, 0, 0) \)2. \( (5, 1, 0, 0, 0, 0) \)3. \( (4, 2, 0, 0, 0, 0) \)4. \( (4, 1, 1, 0, 0, 0) \)5. \( (3, 3, 0, 0, 0, 0) \)6. \( (3, 2, 1, 0, 0, 0) \)7. \( (3, 1, 1, 1, 0, 0) \)8. \( (2, 2, 2, 0, 0, 0) \)9. \( (2, 2, 1, 1, 0, 0) \)10. \( (2, 1, 1, 1, 1, 0) \)11. \( (1, 1, 1, 1, 1, 1) \)[/tex]

Now let's map these back to the odd integers using [tex]\(a_i = 2k_i + 1\):[/tex]

[tex]1. \( (13, 1, 1, 1, 1, 1) \)2. \( (11, 3, 1, 1, 1, 1) \)3. \( (9, 5, 1, 1, 1, 1) \)4. \( (9, 3, 3, 1, 1, 1) \)5. \( (7, 7, 1, 1, 1, 1) \)6. \( (7, 5, 3, 1, 1, 1) \)7. \( (7, 3, 3, 3, 1, 1) \)8. \( (5, 5, 5, 1, 1, 1) \)9. \( (5, 5, 3, 3, 1, 1) \)10. \( (5, 3, 3, 3, 3, 1) \)11. \( (3, 3, 3, 3, 3, 3) \)[/tex]

These are all distinct collections (up to permutations) of positive odd integers that sum to 18.

Thus, the number of distinct collections of six positive odd integers that sum to 18 is indeed:[tex]\[\boxed{11}\][/tex]

1 pencil and 4 pens = 5 total

Picking the pencil would be 1/5 ( 1 pencil out of 5 total items)

5 color pencils  + 5 crayons = 10 total items.

Picking a color pencil would be 5/10 which reduces to 1/2

To find the probability of both happening, multiply them together:

1/5 x 1/2 = 1/10

The probability is 1/10

Answer:

  the graph is shown below

Step-by-step explanation:

The solution region is that quadruply-shaded area above the line y=-2 and to the left of the line x=1. It is further bounded above by the line y = -1/2x +3.5.

Answer: The cost of child's ticket = $10

The cost of adult ticket = $ 13

Step-by-step explanation:

Let x be the cost of a child ticket and y be the cost of an adult ticket.

Then According to the question, we have

[tex]6x+2y=86..........................(1)\\\\10x+3y=139.......................(2)[/tex]

Multiply equation (1) by 3 and equation (2) by 2, then we have

[tex]18x+6y=258.......................(1)\\\\20x+6y=278...........................(2)[/tex]

Subtract equation (1) from equation (2), we have

[tex]2x=20\\\\\Rightarrow\ x=10[/tex]

Substitute the value of x in equation (1), we get

[tex]60+2y=86\\\\\Rightarrow\ 2y=26\\\\\Rightarrow\ y=13[/tex]

Hence, the cost of child's ticket = $10

The cost of adult ticket = $ 13

Answer:

C.94

Step-by-step explanation:

The alternate interior angle of angle c is angle 6. So from there you just subtract the 84 from the 180 to get the 94 degrees.