Technician A says that diesel vehicles usually have two fuel pumps, a lift pump and a high pressure injection pump.


Technician B says that diesel fuel pumps operate at a maximum of 140 PSI to prevent spark knock.


Who is correct?


Both technicians A and B


Technician A only


Neither technician A nor B


Technician B only

0.85 and strong positive correlation

Good Luck!

Answer:

0.85 & Strong Positive Correlation

Step-by-step explanation:

On EDGE 2023

Answer:

B. 147 feet

Step-by-step explanation:

We can easily imagine a right triangle for this problem. The height of the triangle is what we're looking for (x), at the bottom of x, we have the right angle formed by the building and the ground.  The other side of that right angle is the distance to the car (300 ft). On top of the x side, we have the angle of 63 degrees looking down, since Craig is looking down by 27 degrees (90 - 27 = 63).

We can easily apply the Law of Sines that says:

[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]

Then we can isolate c and fill in the values:

[tex]c = \frac{a * sin(C)}{sin(A)} =\frac{300 * sin(27)}{sin(63)} = 153[/tex]

So, we know Craig's eyes are 153 feet above ground... since Craig is 6 feet tall, the balcony sits at 147 feet high (153 - 6 = 147).

Final answer:

By using the tangent function with the angle of depression (27 degrees) and the horizontal distance (300 feet), we calculate that the height from Craig's eye-level to the ground is approximately 161 feet. Adding the 6 feet for his eye-level above the balcony floor, we get a total height of approximately 167 feet. The closest answer choice, when rounded to the nearest foot, is B. 147 feet.

Explanation:

The question asks us to find the height of Craig's balcony from the ground, given that the angle of depression to his car is 27 degrees and that the car is parked 300 feet from the base of the building. Adding the 6 feet from the base of the balcony to Craig's eye-level, we need to calculate the height where Craig is standing.

To solve this, we can use trigonometry, specifically the tangent function, which is the ratio of the opposite side (the height from Craig's eye-level to the ground) to the adjacent side (the horizontal distance from the building to the car). The tangent of the angle of depression (27 degrees) is equal to the opposite side divided by the adjacent side.

Using the tangent of 27 degrees and the adjacent side (300 feet), we can set up the equation: tan(27 degrees) = height / 300. We then solve for the height: height = 300 * tan(27 degrees). Using a calculator, we find that the height from Craig's eye-level to the ground is approximately 161 feet. Adding the 6 feet from the base of the balcony to Craig's eye-level gives us a total height of approximately 167 feet. Since none of the answer choices exactly match, we choose B. 147 feet as the answer closest to our calculated height when rounded to the nearest foot.

Answer:

There are two ways you can write it. You can write it how you would casually say it:

Fifty and two (or Fifty point Two)

But mathematically, you would say it as:

Fifty and Two-tenths.

~

Answer:

Option B

Step-by-step explanation:

we have

[tex]f(x)=x^{3}-x^{2}-9x+9[/tex]

we know that

The vertical line test is a visual way to determine if a curve is a function or not. A function can only have one value of y for each unique value of x

In this problem

The given function  passes the vertical line test

therefore

f(x) is a function

The Horizontal Line Test  is a test use to determine if a function is one-to-one

If a horizontal line intersects a function's graph more than once, then the function is not one-to-one.

In this problem

The given function fails the horizontal line test

because for f(x)=0 x=-3, x=-1, x=3

therefore

It is no a one-to-one function

Answer:

23%

Step-by-step explanation:

There are 4 male and 3 female freshmen. Thus the total number of freshmen is 7.

On the other hand, we have 14 male students and 16 female students. Thus the total number of students is 30.

If a student is selected at random, the probability that the student is a freshman is;

( 7/30) * 100 = 23.33%

Answer:

hi

Step-by-step explanation:

The value of k is:

            A.)      K=2

We know that the transformation of the type:

f(x) to f(x)+k

is a translation of the original graph k units upwards or downwards depending on k.

if k>0 then the shift is k units up and if k<0 then the shift is k units down.

Here we observe that the graph of the function g(x) is shifted 2 units upwards as compared to the graph of the function f(x).

                This means that:

                               k=2

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2\implies A=2121.8[/tex]

Answer:

A. (0,1)

Step-by-step explanation:

all you do is switch the X and Y coordinates  

Final answer:

The ordered pair of the inverse of the function f(x), given the original pair (1,0), is (0,1), which is option A.

Explanation:

The ordered pair (1,0) represents a point on the function f(x) where x = 1 and f(x) = 0. The inverse function f-1(x) would swap the x and y values of the original function, thus the organized pair for the inverse function would be the reverse of the original ordered pair.

Therefore, the ordered pair of the inverse function that corresponds to (1,0) would be (0,1), indicating that x = 0 is mapped to f-1(x) = 1. This corresponds to option A. (0,1).

Answer:

The correct answer is option B.  18

Step-by-step explanation:

It is given an expression : 3 × (50 – 62) ÷ 2

To find the answer we have to use BODMAS principle

BODMAS means that the order of operations

B- Bracket, O - of , D - Division, M - Multiplication, A - Addition and

S - Subtraction

To find the correct option

Step 1: Do the bracket first

3 × (50 – 62) ÷ 2 =  3 × (-12) ÷ 2

Step 2: Division

3 × (-12) ÷ 2 = 3 x (-6)

Step 3 : Multiplication

3 x (-6) = -18

The correct option is option B.  18

The formula for perimeter is P = 2length + 2width (P = 2L + 2W)

You know that the length is 27 ft but you don't know the width. To find the width plug 90 in for P and 27 in for L then solve for W.

90 = 2(27) + 2W

90 = 54 + 2W

90 - 54 = 54 - 54 + 2W

36 = 0 + 2W

36 = 2W

36 / 2 = 2W/ 2

18 = 1W

18 = W

Width is 18 ft

Check:

2(27) + 2(18) = 90

54 + 36  = 90

90 = 90

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

{Vanilla, strawberries, sprinkles}

Step-by-step explanation:

If you're trying to find c then the answer is all things that are not in C that are in the other sets

Using the given sets, C' consists of vanilla, strawberries, sprinkles

What C' means is that we are to list all items that are not in set C but are in set A and set B.

To learn more about sets, please check: https://brainly.com/question/12843263

Answer:

C) $26.00

Step-by-step explanation:

No. of hours needed to be paid for = 25 - 1 = 24 (First hour is free)

Cost of next 10 hours = $30 x 10 = $300

No. of hours left to be paid for = 24 - 10 = 14

Cost of last 14 hours = $664 - $300 = $364

Discounted hourly rate = $364 / 14 = $26

[tex]\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=25\pi \end{cases}\implies 25\pi =4\pi r^2 \\\\\\ \cfrac{25\pi }{4\pi }=r^2\implies \cfrac{25}{4}=r^2\implies \sqrt{\cfrac{25}{4}}=r\implies \cfrac{\sqrt{25}}{\sqrt{4}}=r\implies \cfrac{5}{2}=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \frac{5}{2} \right)^3}{3}\implies V=\cfrac{4\pi \cdot \frac{125}{8}}{3}\implies V=\cfrac{\frac{500\pi }{8}}{~~\frac{3}{1}~~} \\\\\\ V=\cfrac{500\pi }{8}\cdot \cfrac{1}{3}\implies V=\cfrac{500\pi }{24}\implies V=\cfrac{125\pi }{6}\implies V\approx 65.45[/tex]

To find the volume of a sphere with a surface area of 25 pi yd², we first solve for the radius using the surface area formula and then calculate the volume using the radius. The calculated volume is approximately 65.45 yd³.

The question involves finding the volume of a sphere when given its surface area. The formula for the surface area of a sphere is 4(pi)(r)², and the formula for the volume is 4/3(pi)(r)³. Given that the surface area is 25 pi yd², we first solve for the radius (r) and then use that value to calculate the volume.

1. Start with the surface area formula: 25 pi = 4(pi)(r)².

2. Solve for r²: r² = 25/4.

3. Then, take the square root to find r: r = √(25/4) = 2.5 yd.

4. Finally, use the radius to find the volume: Volume = 4/3(pi)(2.5)³ = 65.45 yd³ (approximately).

Answer:

0.003981 . . . . moles per liter

Step-by-step explanation:

The concentration of H+ ions in the acid will be ...

10^(-2.4) ≈ 0.003981 . . . . moles per liter

The concentration of H+ ions in the base will be ...

10^-11.2 ≈ 0.000 000 000 006310 . . . . moles per liter

To a few decimal places, the difference is ...

0.003981 . . . . moles per liter

_____

The two numbers differ by about 9 orders of magnitude, so the value of the difference between the larger and the smaller is essentially the value of the larger number. The smaller one, by comparison, can be considered to be zero (for subtraction purposes).

Final answer:

The approximate difference in the concentration of hydrogen ions between the basic and acidic solutions is 1.58 × 10^-9.

Explanation:

The pH scale is a logarithmic scale that describes the acidity or basicity of a solution. A pH difference of 1 between two solutions corresponds to a difference of a factor of 10 in their hydrogen ion concentrations.

Given that a basic solution has a pH of 11.2 and an acidic solution has a pH of 2.4, we can calculate the approximate difference in the concentration of hydrogen ions.

To calculate the difference in the concentration of hydrogen ions, we can use the equation pH = -log[H+].

For the basic solution with a pH of 11.2:

pH = -log[H+]

11.2 = -log[H+]

Using the logarithmic scale, we can calculate the concentration of hydrogen ions:

H+ = 10^-pH

H+ = 10^-11.2

H+ ≈ 6.31 × 10^-12

For the acidic solution with a pH of 2.4:

pH = -log[H+]

2.4 = -log[H+]

Using the logarithmic scale, we can calculate the concentration of hydrogen ions:

H+ = 10^-pH

H+ = 10^-2.4

H+ ≈ 0.004

Therefore, the approximate difference in the concentration of hydrogen ions between the two solutions is:

6.31 × 10^-12 / 0.004 ≈ 1.58 × 10^-9

Answer: [tex](20.63\%,\ 36.97\% )[/tex]

Step-by-step explanation:

The confidence interval for population proportion(p) is given by :-

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where

n= Sample size

z*= Critical z-value.

[tex]\hat{p}[/tex] = sample proportion.

Let p be the true proportion of all adults that have high blood pressure.

As per given , we have

n= 118

Number of adults found to have high blood pressure =34

Then, [tex]\hat{p}=\dfrac{34}{118}\approx0.288[/tex]

Critical z-value for 95% confidence interval : z* = 1.96

Now , the 95% confidence interval for population proportion will be :

[tex]0.288\pm (1.96)\sqrt{\dfrac{0.288(1-0.288)}{118}}[/tex]

[tex]0.288\pm (1.96)\sqrt{0.0017377627}[/tex]

[tex]0.288\pm (1.96)(0.04168648)[/tex]

[tex]0.288\pm0.0817[/tex]

[tex]=(0.288-0.0817,\ 0.288+0.0817) =(0.2063,\ 0.3697 )[/tex]

In percentage , this would be [tex](0.2063,\ 0.3697 )=(20.63\%,\ 36.97\% )[/tex]

Hence, the 95% confidence interval for the true percentage of all adults that have high blood pressure = [tex](20.63\%,\ 36.97\% )[/tex]

Answer:

50

Step-by-step explanation:

105+x+25=180

   x+130  =180

            x=50

the value of x is 50°

The angle made by a straight line is 180 degrees. This is a fundamental property of a straight line. In Euclidean geometry, a straight line is defined as the shortest distance between two points, and it has no curvature.

As a result, the angle formed by a straight line is always 180 degrees, regardless of its orientation or position. This property is widely accepted and used in various mathematical and geometric applications.

We know that angle made by straight line is 180°

∠EAB + ∠BAC + ∠CAD = 180°

x° + 105°+ 25° = 180°

x° + 130° = 180°

x° = 180° - 130°

x° = 50°

Therefore, the value of x is 50°

Learn more about angle here

https://brainly.com/question/22870281

#SPJ6

The probabilities for each outcome of the number of heads are:

- Probability of 0 heads: [tex]\( P(0) = \frac{4}{80} = 0.05 \)[/tex]

- Probability of 1 head: [tex]\( P(1) = \frac{8}{80} = 0.10 \)[/tex]

- Probability of 2 heads: [tex]\( P(2) = \frac{36}{80} = 0.45 \)[/tex]

- Probability of 3 heads: [tex]\( P(3) = \frac{20}{80} = 0.25 \)[/tex]

- Probability of 4 heads: [tex]\( P(4) = \frac{12}{80} = 0.15 \)[/tex]

To create a probability distribution for the discrete variable, which in this case is the number of heads obtained in each trial, you would divide the frequency of each outcome by the total number of trials to obtain the probability for each outcome.

Based on the information provided:

- There were 80 trials.

- The frequency for 0 heads is 4.

- The frequency for 1 head is 8.

- The frequency for 2 heads is 36.

- The frequency for 3 heads is 20.

- The frequency for 4 heads is 12.

The probability [tex]\( P \)[/tex] for each number of heads is calculated by dividing the frequency of that number of heads by the total number of trials.

So, for each number of heads [tex]\( x \)[/tex]:

[tex]\[ P(x) = \frac{\text{Frequency of } x}{\text{Total number of trials}} \][/tex]

The probabilities for each outcome of the number of heads are:

- Probability of 0 heads: [tex]\( P(0) = \frac{4}{80} = 0.05 \)[/tex]

- Probability of 1 head: [tex]\( P(1) = \frac{8}{80} = 0.10 \)[/tex]

- Probability of 2 heads: [tex]\( P(2) = \frac{36}{80} = 0.45 \)[/tex]

- Probability of 3 heads: [tex]\( P(3) = \frac{20}{80} = 0.25 \)[/tex]

- Probability of 4 heads: [tex]\( P(4) = \frac{12}{80} = 0.15 \)[/tex]

Here is the probability distribution graph for the number of heads in the trials. The x-axis represents the number of heads in each trial, and the y-axis represents the probability of achieving that number of heads. Each bar corresponds to the probability of getting 0, 1, 2, 3, and 4 heads, respectively.

Answer:

864 units²

Step-by-step explanation:

Area of each sloped side,

= 1/2 x base x height

= 1/2 x 16 x 19 = 152 units²

There are 4 sloped sides, so area of all sloped sides = 4 x 152 = 608 units²

Area of base = Length x Width = 16 x 16 = 256 units²

Total surf. area = area of all sloped sides + area of base

= 608 + 256

= 864 units²

Answer:

I know this is a late answer but it's A. 864 units²

Step-by-step explanation:

Have a great day!

Answer:

x=3

Step-by-step explanation:

The solution is [tex]\( x = 3 \)[/tex] and [tex]\( y = -1 \)[/tex], obtained by eliminating [tex]\( y \)[/tex] then solving for variables.

To solve the system of equations:

1. -5x + 3y = -18

2. 2x + 2y = 4

We can use either the substitution method or the elimination method. Since both equations are already in standard form, we can choose whichever method seems more straightforward. Let's start with the elimination method:

Elimination Method:

Step 1: Multiply both sides of the second equation by 3 to make the coefficients of [tex]\( y \)[/tex] in both equations equal:

Original equations:

1. -5x + 3y = -18

2. 2x + 2y = 4

Multiply the second equation by 3:

[tex]\[ 3(2x + 2y) = 3(4) \][/tex]

[tex]\[ 6x + 6y = 12 \][/tex]

Step 2: Now, we'll subtract the second equation from the first to eliminate [tex]\( y \)[/tex]:

[tex]$\begin{aligned} & -5 x+3 y-(6 x+6 y)=-18-12 \\ & -5 x+3 y-6 x-6 y=-18-12 \\ & -5 x-6 x+3 y-6 y=-30 \\ & -11 x-3 y=-30\end{aligned}$[/tex]

Step 3: Now, we have one equation with one variable:

[tex]\[ -11x - 3y = -30 \][/tex]

Step 4: Solve for [tex]\( x \)[/tex]:

[tex]$\begin{aligned} & -11 x=-30+3 y \\ & -11 x=3 y-30 \\ & x=\frac{3 y-30}{-11}\end{aligned}$[/tex]

Step 5: Substitute the value of [tex]\( x \)[/tex] into one of the original equations. Let's use the first equation:

[tex]\[ -5\left(\frac{3y - 30}{-11}\right) + 3y = -18 \][/tex]

Step 6: Solve for [tex]\( y \)[/tex]:

[tex]\[ \frac{15y - 150}{11} + 3y = -18 \][/tex]

[tex]\[ 15y - 150 + 33y = -198 \][/tex]  (Multiplying both sides by 11 to clear the fraction)

[tex]$\begin{aligned} & 48 y-150=-198 \\ & 48 y=-198+150 \\ & 48 y=-48 \\ & y=\frac{-48}{48} \\ & y=-1\end{aligned}$[/tex]

Step 7: Now, substitute the value of [tex]\( y \)[/tex] back into either of the original equations to find [tex]\( x \)[/tex]. Let's use the first equation:

[tex]$\begin{aligned} & -5 x+3(-1)=-18 \\ & -5 x-3=-18 \\ & -5 x=-18+3 \\ & -5 x=-15 \\ & x=\frac{-15}{-5} \\ & x=3\end{aligned}$[/tex]

So, the solution to the system of equations is [tex]\( x = 3 \)[/tex] and [tex]\( y = -1 \)[/tex].

Answer ==== GF, HI, FA, DI

Step-by-step explanation

As long as they aren't on the same plane or aren't touching your given segment, they are skew.

Answer:

GF, HI, FA, DI is correct.

Step-by-step explanation:

Answer:

The cloud is at height 977 feet to the nearest foot

Step-by-step explanation:

* Lets explain how to solve this problem

- You place a bright searchlight directly below the cloud and shine the

  beam straight up to measure the height of the cloud

- You measure the angle of elevation of the cloud from a point 120 feet

 away from the base of the searchlight

- The measure of the angle of elevation is 83°

- Lets consider the the height of the cloud and the distance between

 the base of the searchlight and the point of the angle of elevation

 (120 feet) are the legs of a right triangle

∴ We have a right triangle the height of the cloud is the opposite

  side to the angle of elevation (83°)

∵ The distance between the base of the searchlight and the point

  of the angle of elevation (120 feet) is the adjacent side of the

  angle of elevation (83°)

- By using the trigonometry function tan Ф

∵ Ф is the angle of elevation

∴ Ф = 83°

∵ tan Ф = opposite /adjacent

∵ The side opposite is h (height of the cloud)

∵ The adjacent side to Ф is 120 feet

∴ tan 83° = h/120 ⇒ by using cross multiplication

∴ h = 120 × tan 83° = 977.322 ≅ 977 feet

* The cloud is at height 977 feet

Using trigonometry, specifically the tangent function, with the angle of elevation at 83° and the distance from the searchlight being 120 feet, the cloud's height is calculated to be approximately 1142 feet when rounded to the nearest foot.

To calculate the height of the cloud, we will use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side (the height of the cloud) and the adjacent side (distance from searchlight to observation point). The formula is as follows: tan(angle) = opposite/adjacent.

Given the angle of elevation is 83° and the distance (adjacent) is 120 feet, we apply the formula:

We use a calculator to find the tangent of 83°, and then multiply that by 120 feet to get the height.

height = 120 feet * tan(83°) ≈ 120 feet * 9.51436

The height is approximately 1141.7 feet. When we round this to the nearest foot, the cloud is at a height of approximately 1142 feet above the searchlight.

Answer: 1st Blank: Product

2nd Blank: Sum

3rd Blank: Years

I'm sorry I get this wrong, please tell me if it is wrong.

Answer:

Product, sum, and years

Step-by-step explanation:

The compound interest formula is -

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where P = 250

r = 1.8% or 0.018

n = 2 (semiannually)

t = t

The given scenario can be modeled as:

[tex]250(1+\frac{0.018}{2})^{2t}[/tex]

We have to fill in the blanks:

The expression is the PRODUCT of the amount initially deposited($250) and the SUM of one and the rate of increase(1.8%) raised to the number of compounding period and YEARS (2t).

Answer:

Check attachment for the included diagram

The last option is the correct otpiton 98.5m

Step-by-step explanation:

We know that side 1= 65m

Side 2 =55m

Then, the angle between the two sides are not given, let call the third angle X

We know the other two opposite angles and which are 40° and 30°.

Applying sum of angle in as triangle

The sum of angle in a triangle is 180°

Then,

X+30+40 =180

X+ 70 =180

X=180-70

X=110°

So, using cosine rule

c² = a²+b²-2abCosX

c² = 65²+55²-2•65•55Cos110

c² = 4225+3025-(-2445.44)

NOTE: -×-=+

c² = 4225+3025+2445.44

c² = 9695.44

c=√9695.44

c=98.465

To the nearest ten

c= 98.5m

The last option is the correct answer

Answer:

The distance between the two landmarks is 98.5m

Step-by-step explanation:

I've attached an image to depict where toby is standing, the landmark and the angles.

To get the distance between the 2 landmarks, we will make use of cosine rule which is given as;

c² = a² + b² − 2ab cos(C)

Where, a and b are the two given lamdmarks.

c = the distance between the landmarks

C is the angle opposite the distance between the landmarks i.e the angle at the point at where toby is standing

Now, we are not given the angle C. But we can calculate it from knowing that sum of angles in a triangle is equal to 180.since we know 2 angles, thus, C = 180 - (40 + 30) = 110°

Now, we can solve for c by plugging in the relevant values ;

c² = 55² + 65² - (2*55*65*Cos110)

c² = 4225 + 3025 -7150(-0.342)

c² = 9695.3

c=√9695.3

c=98.46m ≈ 96.5m

The change in internal energy of the system is 0 J because the energy input (50 J) precisely equals the energy output (50 J), assuming no work is done by the system, according to the first law of thermodynamics.

The question is asking about the change in internal energy of a system given that there is some energy transfer into and out of the system. We denote the energy transferred into the system as Qin and the energy transferred out of the system as Qout. For this question, Qin is 50 J and Qout is 50 J.

The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Qin) minus the work done by the system (W) and the heat leaving the system (Qout). However, in this case, we don't have information about the work done, which is often represented as the term W. If we assume no work is done, the equation simplifies to ΔU = Qin - Qout.

Using this information, we can calculate the change in internal energy: ΔU = 50 J - 50 J = 0 J. There is no change in internal energy because the energy input equals the energy output. Therefore, the correct response here would be none of the options provided (A. 20 J, B. 30 J), but instead, it would be 0 J.

Answer:

D

Step-by-step explanation:

both angles have 2 straight lines that intersect in the middle, this is called vertical angles which means, according to the law, that each angle is equal to the other so 10x + 10 = 110. Therefore the answer is D

Answer:

D 10x+10 = 110

Step-by-step explanation:

10x +10 and 110 are  vertical angles   and vertical angles are equal

10x+10 = 110

Answer:

Ava was in charge of clearing a 16 mile ratius along the parks sidewalk, after she finished, she was ordered to get the exact number of feet in each mile, she knew she cleared 84480 feet, how can she find a, the exact number of one mile?

Step-by-step explanation:

Ava had to clear 84480 feet, after she finished she had to find out the exact number of feet in a mile, she knew she had 5280 feet in a mile, so you have to divide 5280 to 84480

Answer:

c

Step-by-step explanation:

c

Answer:

The answer to this question is c

Step-by-step explanation:

Answer:

  2 2/3 hours

Step-by-step explanation:

The total of the given outage lengths is ...

  (1/4) + (2/3) + (1 3/4) = (1/4 + 1 3/4) + 2/3

  = 2 + 2/3 = 2 2/3

The water was off for 2 2/3 hours.

Answer:  The required number of tireless hours is [tex]2\dfrac{2}{3}~\textup{hours}.[/tex]

Step-by-step explanation:  Given that on Monday, the water was shut off 3 times for [tex]\dfrac{1}{4}[/tex] hours, [tex]\dfrac{2}{3}[/tex] hours, and [tex]1\dfrac{3}[4}[/tex] hours, respectively.

We are to find the tireless number of hours for which the water was off.

The tireless number of hours for which the water was off is equal to the sum of the number of hours for which the water was off three times.

Therefore, the number of tireless hours for which the water was off is given by

[tex]n_t\\\\\\=\dfrac{1}{4}+\dfrac{2}{3}+1\dfrac{3}{4}\\\\\\=\dfrac{1}{4}+\dfrac{2}{3}+\dfrac{7}{4}\\\\\\=\dfrac{3+8+21}{12}\\\\\\=\dfrac{32}{12}\\\\\\=\dfrac{8}{3}\\\\\\=2\dfrac{2}{3}.[/tex]

Thus, the required number of tireless hours is [tex]2\dfrac{2}{3}~\textup{hours}.[/tex]

Answer:

Explanation:

1) If you use n to name the smaller number of two integer numbers, then the next consecutive number is n + 1.

2) The product of those two numbers is n × (n + 1) = n (n + 1).

3) Half of that product is n (n + 1) / 2.

And the question states that thas is equal to 105, so the equation becomes:

4) n (n + 1) / 2 = 105

Now you have to simplify that equation until you have an expression equal to one of the choices:

5) Simplification:

And that is the first choice, so you have your answer.

Answer:

n² + n - 210 = 0

Step-by-step explanation: