PLEASE HELP THIS IS URGENT!
The engine torque y (in foot-pounds) of one model of car is given by y=−3.75x^2+23.2x+38.8, where x is the speed (in thousands of revolutions per minute) of the engine.
a. To the nearest ten, what is the engine speed that maximizes torque? ------____ revolutions per minute
To the nearest hundredth, what is the maximum torque?
____ ft-lbs
Question 2
b. Explain what happens to the engine torque as the speed of the engine increases.
As the engine speed increases, the torque _____ until the engine speed reaches
_____ thousand revolutions per minute and then the torque ______

Answer:

The factor form of given expression is (x-4)(x-2i)(x+2i).

Step-by-step explanation:

The given expression is

[tex]x^3-4x^2+4x-16[/tex]

It can be written as

[tex]f(x)=x^3-4x^2+4x-16[/tex]

According to the rational root theorem, all possible rational roots are in the form of

[tex]\frac{a_0}{a_n}[/tex]

Where, a₀ is constant term and [tex]a_n[/tex] is leading coefficient.

[tex]f(4)=4^3-4(4)^2+4(4)-16=0[/tex]

Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.

Use synthetic method to find the remaining factors.

[tex](x^3-4x^2+4x-16)=(x-4)(x^2+4)[/tex]

[tex](x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)[/tex]

[tex](x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)[/tex]

Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).

Answer:

(x-4)  (x-2i) (x+2i)

Step-by-step explanation:

x^3−4x^2+4x−16

I will factor by grouping

x^3−4x^2+  4x−16

The first group is the first 2 terms.  I can factor out an x^2

x^2 (x-4) + 4x-16

The second group I can factor out a 4

x^2 (x-4) + 4(x-4)

Now I can factor out (x-4)

(x-4)  (x^2 +4)

We know that x^2 + 4 factors into +2i and -2i  because

(a^2 -b^2) = (a-b) (a+b)  but  we have (a^2 + b^2)  = (a-bi)  (a+bi)

(x-4) (x-2i) (x+2i)

Answer:

$25.96

Step-by-step explanation:

We have been given that Ming took a cab across town. His fare was $22, and he leaves an 18% tip.

To find the total amount by Ming for cab ride will be equal to 22 plus 18% of 22.

[tex]\text{Total amount paid by Ming for the cab ride}=22+(\frac{18}{100}*22)[/tex]

[tex]\text{Total amount paid by Ming for the cab ride}=22+(0.18*22)[/tex]

[tex]\text{Total amount paid by Ming for the cab ride}=22+3.96[/tex]

[tex]\text{Total amount paid by Ming for the cab ride}=25.96[/tex]

Therefore, Ming paid a total amount of $25.96 to the cab driver.

Answer:

All options are wrong.

Step-by-step explanation:

We have y > –3x + 3 and y > 2x – 2

Option A - (1,0)

          y > –3 x 1 + 3 = 0

         We have y = 0, which is not greater than 0.

         Option A is not correct.        

Option B - (–1,1)

          y > –3 x -1 + 3 = 6

         We have y = 1, which is not greater than 6.

         Option B is not correct.

Option C - (2,2)

          y > –3 x 2 + 3 = -3

         We have y = 2, which is greater than -3.

          y > 2 x 2 – 2  = 2

         We have y = 2, which is not greater than 2.

         Option C is not correct.  

Option D - (0,3)

          y > –3 x 0 + 3 = 3

         We have y = 3, which is not greater than 3.

         Option D is not correct.    

All options are wrong.

Answer:

C. |-9| = 9

Step-by-step explanation:

Distance is always non-negative. Distances in a negative direction are made positive by the use of the absolute value function. The distance from 0 to -9 is one such distance.

Given that Mary has 2 bags of sweets. each of which contains same number of sweets.

Let us assume each bag contains x  number of sweets.

After eating 4 sweets, total number of sweets left in two bags = x+x-4=2x-4

But given 2x-4 = 30

                2x-4+4 = 30+4

                 2x=34

                [tex]x=\frac{34}{2} = 17[/tex]

Hence there are 17 sweets in each bag at starting.

Mary had two bags with an equal number of sweets. After eating 4 sweets, she had 30 left, which means each bag originally contained 17 sweets.

To solve the problem of determining how many sweets were in each bag to start with, we must consider that Mary had two bags with an equal number of sweets and ended up with 30 sweets after eating 4 sweets. We can represent the initial number of sweets in each bag as 'x'. So the equation for the total number of sweets after she eats 4 is 2x - 4 = 30.

Let's solve this equation step by step:

Add 4 to both sides: 2x = 30 + 4

Simplify: 2x = 34

Divide both sides by 2 to solve for x: x = 34 / 2

Therefore, x = 17

This means that initially, there were 17 sweets in each bag.

Area of a triangle is 1/2 x base x height.

base = 12

Height = x+6

Area = 1/2 * 12 * x+6

Area = 1/2 * 12x * 72

Area = 6x + 36

Perimeter is the sum of the 3 sides:

x-7 + 12 + 2x+5

3x -2 + 12

3x+10

The last choice is the correct answer.

Answer:

[tex]a_5=-4[/tex]

Step-by-step explanation:

[tex]a_n=a_{n-1}-3\\\\a_1=8\\\\a_2=a_1-3\to a_2=8-3=5\\\\a_3=a_2-3\to a_3=5-3=2\\\\a_4=a_3-3\to a_4=2-3=-1\\\\a_5=a_4-3\to a_5=-1-3=-4[/tex]

To find the value of a5, we subtract 3 repeatedly from the previous value starting with a1=8. After iterating this process four times, we find that a5 equals -4.

The sequence given is defined by a1 = 8 and an = an-1 - 3. To find a5, we need to apply the formula recursively starting from a1:

a2 = a1 - 3 = 8 - 3 = 5

a3 = a2 - 3 = 5 - 3 = 2

a4 = a3 - 3 = 2 - 3 = -1

a5 = a4 - 3 = -1 - 3 = -4

So, the value of a5 is -4.

Answer:

0.375 is answer

Step-by-step explanation:

Given that the  math teacher gave her students two tests. On the first test, 80% of the class passed the test.  But only 30% of the class passed both tests.

Let A - the students pass I test

B = students pass second test

Then P(A) = 80%=0.8 and P(AB) = 30% =0.30

Required probability =probability that a student passes the second test, given that they passed the first one

= P(B/A) = P(AB)/P(A)

= 0.30/0.80

=3/8

=0.375

Right answer is 0.375

The probability that a student passes the second test, given that they passed the first one, is 0.375.

The subject of this question is Mathematics, specifically focusing on the concept of conditional probability. The question asks about the probability that a student passes the second test, given that they passed the first one. Given that 80% of the class passed the first test and 30% passed both tests, we can use the formula for conditional probability P(B|A) = P(A and B) / P(A). Here, A represents passing the first test, and B represents passing the second test.

P(B|A) = P(A and B) / P(A) = 0.30 / 0.80 = 0.375.

Therefore, the probability that a student passes the second test, given that they passed the first one is 0.375.

A constant is a number that stays the same no matter what any outside variables are.  In this case, the variables are the number of hours of the event and the number of attendees.  However, it states in the problem that the event will be 5 hours so that becomes known; the only thing that might change is the number of attendees so you can eliminate any cost that will be affected by that.  You are left with Facility Rental, Musical Entertainment, and Cleaning Fee.  Furthermore, you can be sure that Musical Entertainment and Cleaning Fee must be included in the constant because they are described as "flat rates", which means they do not change.

The answer is D) It is the total cost for entertainment, facility rental, and cleaning.

Hope this helps!

The statement that best describes the constant in the expression

25n + 2,800 is:

It is the cost per person for food, linens, and food decorations.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Facility Rental = $150 per hour of the event

Linens = $2 per attendee

Food = $20 per attendee

Table Decorations = $3 per attendee

Musical Entertainment = $1,800

Cleaning Fee = $250

The total cost of the event.

= 25n + 2,800

Where n is the number of attendees.

Now,

25 is the total cost per attendee for food, linens, and table decorations.

Thus,

The constant in the expression is 25 which is the cost per attendee for food, linens, and table decorations.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ3

Final answer:

The divisibility rule for 7 is more complex than the rules for 2, 3, 5, and 10 due to the lack of a simple pattern or quick digit check, requiring multiple steps and manipulations of the number.

Explanation:

The divisibility rule for 7 is more complicated than the rules for 2, 3, 5, and 10 because it does not follow a simple pattern or involve a quick check of a number's last digit or sum. The rules for divisibility by 2, 3, 5, and 10 are straightforward: a number is divisible by 2 if its last digit is even, by 3 if the sum of its digits is divisible by 3, by 5 if its last digit is 0 or 5, and by 10 if it ends in 0.

The rule for divisibility by 7 requires more steps and cannot be easily performed in one's head. The process typically involves subtracting or adding multiples of 7 from different segments of the number, which often makes it more difficult for students to use effectively without practice or further understanding of the method. Complicated rules for divisibility by 7 prove the point that while mathematical rules are universally valid, some rules are inherently more complex than others.

A small company plans to invest in a new advertising campaign.

There is a 20% chance that the company will lose $5,000 ,

50% chance of a break even, and a 30% chance of a $10,000 profit

So the expected value from the advertisement campaign is calculated as - 20% of 5000 + 0% of 5000 + 30% of 10,000

= -1000 + 0 + 3000

= 2000

The expected value from the advertisement campaign is $2000.

So the Company must go ahead with the campaign.

Answer : Option A

Hope it helps.

Thank you ..!!

The fraction equivalent to -84/-90 in the least common terms is 14/15, as both the numerator and the denominator can be divided by the common factor 6, resulting in a simplified positive fraction.

To find which fraction is equivalent to -84/-90 in the least common terms, we need to simplify the fraction by canceling out any common factors in the numerator and the denominator. We observe that both numbers are divisible by 6. When we divide the numerator and the denominator by 6, we get:

-84 / -90 = (-84 / 6) \/ (-90 / 6) = 14 / 15

Since a negative divided by a negative results in a positive number, we eliminate the negative signs and get the fraction in its least common terms as 14/15.

Answer is 6 kg:

Given that Adam was asked to post a parcel.  The weight of the parcel was 12 lbs and 8 oz.

To convert the weight in kgs:

Let us convert oz into pounds first to make it uniform.

We have 16 0z. = 1 lb

Hence 8 oz. = 8/16 = 0.5 lbs

Weight of the parcel = 12.5 lbs.

We have the converting factor as

2.2 pounds make 1 kg.

Hence 12.5 pounds = 12.5/2.2 = 5.6818

So weight of the parcel in kg= 6. (after rounding off)

Odd numbers are those numbers that gives a fraction when divided by 2

Prime numbers are those that can be divided only by 1 and the number itself.

Odd numbers are therefore : 23, 25, 31 and 45

Prime numbers are therefore: 2, 23 and 31

The midpoint between -4 and 8 is answer B) 2

The correct logical order for the statements I, II, and III in the proof is: I. Definition of a Straight Angle, III. Angle Addition Postulate, and II. Substitution Property of Equality. This order supports the conclusion that corresponding angles, created by the transversal intersecting parallel lines, are congruent.

To complete the two-column proof that demonstrates the congruence of the corresponding angles when segments UV and WZ are parallel and line ST intersects both at points Q and R respectively, we need to place statements and reasons I, II, and III in the most logical order. This should allow us to show

corresponding angles are congruent, which is the ultimate aim of the proof.

The correct order of statements and reasons to complete the proof is:

Definition of a Straight Angle (I): We know that the angle measure of a straight line is 180°, hence m∠SQT = 180°.

Angle Addition Postulate (III): Based on the postulate, we can express m∠SQV + m∠VQT as equal to the measure of angle SQT because the two angles combine to form the straight angle, therefore m∠SQV + m∠VQT = m∠SQT.

Substitution Property of Equality (II): By substituting the equal values established in statements I and III, we get m∠SQV + m∠VQT = 180°.

After arranging the statements and their corresponding reasons, the proof logically demonstrates that the congruent angle pairs are a result of transversal ST intersecting parallel lines UV and WZ.

answer is equal to 2X44/5mile=17.6mile

Each section of a race is 25 mile.

The race has 4 sections.

Which expression tells how many miles long the entire race is?

Answer:

4×2/5

ANSWER

[tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]

EXPLANATION

Given;

[tex]4x-12y=1[/tex]

and

[tex]6x+4y=4[/tex]

The augmented matrix of the two linear equation is given by;

[tex]\left[\begin{array}{ccc}4&-12|&-1\\6\:&\:\:\:4|&4\end{array}\right][/tex]

We now perform row operations;

[tex]\frac{1}{4}\times R_1 \rightarrow R_1 [/tex].

This gives us

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\6\:&\:\:\:4|&4\end{array}\right][/tex]

[tex]R_2-6R_1 \rightarrow R_2[/tex]

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:22|&\frac{11}{2}\end{array}\right][/tex]

[tex]\frac{1}{22}R _2 \rightarrow R_2[/tex]

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]

[tex]R_1+3R_2 \rightarrow R_1[/tex]

[tex]\left[\begin{array}{ccc}1&0|&\frac{1}{2}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]

Hence [tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]

Answer:

Total temperature change 104.25 f.

Step-by-step explanation:

Average temperature change is calculated by dividing total temperature change by the total hours it took for the change.

We have been given the average temperature change.

We have to multiply average temperature change by the total number of hours it took for the temperature to change we get the total temperature change.

⇒ Total temperature change =  Average temperature change * total hours

                                                = [tex]-4.17*25[/tex]

                                                 =104.25 f

Lets say Alexis received 85, 89, 92, and x points in her four tests.

Average of a data set or the mean of a data set, we need to add all the values together and divide by the number of values in the set.

So here 85, 89, 92, and x are the values of the data set and the number of values are 4 (since there are 4 tests).

[tex]Avg=\frac{sum}{n}[/tex]

where 'n' represents the number of values and sum represents the total sum of the values.

Here we need to know how much Alexis need to score in her next test so that she can have an average of 90.

So we know the value of average that is 90.

Now,

[tex]90 = \frac{85+89+92+x}{4}[/tex]

Solving for 'x' we get:

[tex]90=\frac{266+x}{4}[/tex]

[tex]266+x=90 \times 4[/tex]

[tex]266+x=360[/tex]

Therefore,

[tex]x=360-266=94[/tex]

So, Alexis need to score at least 94 on her next test in order to have an average of at least 90.

Remark

You could convert base two to base 10 and then convert base 10 to base 8. That's the long way. The procedure below is the short way.

Step One

Write the base 2 number in groups of 3 starting from the right and going left

11 100 111

Step Two

Convert the base 2 numbers in groups of 3 to base 8. The largest result will be a 7

11 = 2*1 + 1 = 2 + 1 = 3

100 = 1*2^2 = 4

111 = 1*2^2 + 1*2 + 1 = 7

Step Three

Read the answer going down.

347 is the answer

Answer

347(8) = C

Answer:

Option C)347(8) is correct. Below is the explanation for changing the base 2 number to the base 8

Step-by-step explanation:

Given:

      11100111(2)

To find:

      Number with base 8.

Let's convert the given base 2 number to a base 10 number or an integer. Then convert it to a base 8 number.

11100111(2) = 1* [tex]2^{7}[/tex]+1* [tex]2^{6}[/tex]+1*[tex]2^{5}[/tex] + 0*[tex]2^{4}[/tex] +0*[tex]2^{3}[/tex] +1* [tex]2^{2}[/tex]+1*[tex]2^{1}[/tex] +1*[tex]2^{0}[/tex]

Simplify it

                 =128 +64+32 +0+0+4+1+1

                 =231

Now, change this integer 231 to a base 8 number ( I have attached a file for this)

We get an answer of 347(8). Option C is correct!

You can learn more:

https://brainly.com/question/11454182.

First, let's simplify the expression: 7 - 5 + 3x - 1  ⇒   3x + 1  (slope=3, y-intercept = 1)

Next, let's understand what they are asking for:

no solutions means same slope but different y-intercepts

Answer: 3x + _______ (the blank can be anything except 1)

one solution means different slopes

Answer: ________x + _______ (the first blank can be anything except 3, the second blank can be anything)

infinitely many solutions means same slope and same y-intercept

Answer: 3x + 1

Answer:

1.3x+9

2.1x+4

3.3x+1

Step-by-step explanation:

To express the ratio of flour to butter from a recipe as a fraction in simplest form, start by setting it up as a fraction and then multiply by the reciprocal of the denominator. In this case, a recipe with 6 cups of flour and three-fourths cup of butter simplifies to a ratio of 8:1.

To find the ratio of the amount of flour to the amount of butter as a fraction in simplest form, we start by writing the amounts given in the recipe as a fraction. There are 6 cups of flour and three-fourths (3/4) cup of butter. The initial ratio is therefore:

6 cups of flour / (3/4) cup of butter

To simplify, we can multiply both the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) by the reciprocal of the denominator:

6 / (3/4) = 6 × (4/3) = 24/3 = 8

So, the simplest form of the ratio of flour to butter is 8:1.

Answer:

At least 6907 people.

Step-by-step explanation:

Population std deviation = sigma= 10.6

Since population std deviation is known, we can use normal probability table to get sample size from confidence interval.

The sample mean weight loss is within 0.25 lb of the true population mean.

Hence  margin of error < 0.25

Margin of error = z critical (std dev/n) where n = sample size

Z critical for 95% = 1.96

Hence 0.25 >1.96(10.6)/sq rt n

Simplify to get

sq rt n > 1.96(10.6)/0.25 = 83.104

Square both the sides to get

n > 83.104 square = 6906.27

i.e. sample size should be atleast 6907.

x = 2 ± [tex]\frac{1}{2}[/tex]√10

express the equation in standard form : ax² + bx + c = 0 ( a ≠ 0 )

then x = ( - b ±√( b² - 4ac) ) / 2a

given 2x² = 8x - 3, then

2x² - 8x + 3 = 0 ( in standard form )

with a = 2, b = - 8, c = 3

x = (8 ±√(64 - 24) )/4 = (8 ±√40) / 4 = (8 ± 2√10) / 4

x = 2 ± [tex]\frac{1}{2}[/tex]√10

The answer is B (-6,5) becuase C is located at (-3,4). -3 - 3 is -6... and 4 + 1 is 5

Final answer:

To calculate the average monthly weight loss of the black bear, divide the total weight loss by the number of hibernation months. The bear lost 0.1 pound per month during its 712 months of hibernation.

Explanation:

To find the average weight loss per month of the black bear, you need to divide the total weight loss by the number of months of hibernation. The black bear lost 64.4 pounds over 712 months.

First, we write out the calculation needed:
64.4 pounds ÷ 712 months.

When you perform the division, you get approximately 0.0904494382 pounds per month. Rounding to the nearest tenth gives us 0.1 pounds per month.

Therefore, the bear experienced an average weight change of 0.1 pound per month during hibernation.

Air bag manufactured by Aces(A)=57%

So, Probability [tex]P(A)=\frac{57}{100}[/tex]

Air bag manufactured by Best (B) =26%

So, Probability [tex]P(B)=\frac{26}{100}[/tex]

Airbag manufactured by Cool(C)=17%

So, Probability [tex]P(C)=\frac{17}{100}[/tex]

Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively.

Let K be the event which kill people.

Probability of Air bag made by A which kill people [tex]P(K/A)=\frac{1}{100}[/tex]

Probability of Air bag made by B which kill people [tex]P(K/B)=\frac{4}{100}[/tex]

Probability of Air bag made by C which kill people [tex]P(K/A)=\frac{13}{100}[/tex]

If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool

Using Baye's theorem:

[tex]P(C/K)=\frac{P(K/C)P(C)}{P(K/A)P(A)+P(K/B)P(B)+P(K/C)P(C)}[/tex]

Substitute the values of probabilities into formula

We get,

[tex]P(C/K)=\frac{0.17\times 0.13}{0.57\times 0.01+0.26\times 0.04+0.17\times 0.13}[/tex]

Now we calculate it and get probability

So, [tex]P(C/K)=0.5785[/tex]

So, 57.85% of passenger kills if the airbag was manufactured by Cool.