Steve and Brian are both avid bicyclists. Each week, Steve rides for a total of 2x hours at an average speed of x miles per hour.
sBrian rides 6 more hours a week than Steve, but at an average speed that is 4 miles per hour less than Steve's average speed.
Which of the following functions will give the total distance that Brian rides each week, in miles?

The following are the measures of angles and sides using the sine and cosine rules:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

The sine rule is a relationship between the size of an angle in a triangle and the opposing side. While the cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

1). Using the sine rule:

19/sin85 = 13/sunQ

Q = sin⁻¹[(13 × sin85)/19] {cross multiplication}

Q = 43

m∠P = 180° - (85 + 43) = 52°

QR = sin⁻¹[(19 × sin52)/sin85]

QR = 15.

2). m∠C = 180 + (19 + 139) = 22°

Using the sine rule:

BC = (12 × sin139)/sin22

BC = 21.

DC = (12 × sin19)/sin22

DC = 10.4

3). m∠V = 180 - (41 + 100) = 39°

Using the sine rule:

VX = (16 × sin41)/sin100

VX = 10.7

WX = (16 × sin39)/sin100

WX = 10.2

4). Using the cosine rule:

HF² = 7² + 13² - 2(7)(13)cos136°

HF = √338.8491

HF = 18.4

applying sine rule;

F = sin⁻¹[(7 × sin136)/18.4]

F = 15.3

m∠H = 180 - (15.3 + 136) = 28.7

Therefore, the measures of angles and sides using the sine and cosine rules are:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

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(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

Answer:

\(648\sqrt{6}\)π

Step-by-step explanation:

\(\frac{4}{3}\)π(9√6)³

=\(\frac{4}{3}\)π81*6*√6

=(486*\(\frac{4}{3}\))√6π

=648√6π

False. The weight of a variable in a standardized predictor environment does not necessarily indicate that the variable has a higher discriminating power.

Discriminating power is determined by the correlation of a predictor variable with the outcome variable. We can calculate the correlation between a predictor variable and an outcome variable using Pearson's correlation coefficient, which is represented by the formula:

r = (NΣXY - (ΣX)(ΣY)) / √[(NΣX2 - (ΣX)2)(NΣY2 - (ΣY)2)].

In this formula, N is the sample size, ΣX is the sum of the predictor variable, ΣY is the sum of the outcome variable, ΣXY is the sum of the products of the predictor and outcome variables, and ΣX2 and ΣY2 are the sums of the squares of the predictor and outcome variables, respectively. The Pearson's correlation coefficient ranges from -1 to +1, with +1 indicating perfect positive correlation, 0 indicating no correlation, and -1 indicating perfect negative correlation. A higher correlation coefficient indicates a higher discriminating power.

Therefore, the weight of a variable in a standardized predictor environment does not indicate whether or not the variable has a higher discriminating power; this is determined by the correlation between the predictor and outcome variables.

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Answer:

Step-by-step explanation:

Given question is incomplete; here is the complete question.

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.

The volume of pyramid A is ____ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ______the volume of pyramid A.

Since, volume of pyramid = \(\frac{1}{3}(\text{Area of the base})(\text{Height})\)

Volume of the pyramid A = \(\frac{1}{3}(\text{length}\times \text{Width})(\text{height})\)

                                          = \(\frac{1}{3}(10\times 20)(h)\)

                                          = \(\frac{200h}{3}\)

Volume of pyramid B = \(\frac{1}{3}(10)^2(h)\)

                                    = \(\frac{100h}{3}\)

Ratio of the volumes of the pyramids = \(\frac{\text{Volume of pyramid A}}{\text{Volume of pyramid B}}\)

                                                              = \(\frac{\frac{200h}{3}}{\frac{100h}{3} }\)

                                                              = 2

Therefore, volume of pyramid A is TWICE the volume of pyramid B.

If If height of the pyramid B increases twice of pyramid A,

Then the volume of pyramid B = \(\frac{1}{3}(100)(2h)\)

                                                   = \(\frac{200h}{3}\)

Ratio of volumes of pyramid B and pyramid A = \(\frac{\text{Volume of pyramid B}}{\text{Volume of pyramid A}}\)

                                                                            = \(\frac{\frac{200h}{3}}{\frac{200h}{3}}\)

                                                                            = 1

Therefore, new volume of pyramid B is EQUAL to the volume of pyramid A.  

Answer: The first or the second point (- 2, - 3) or (- 2, 1)

Step-by-step explanation:

Ok, a relation (x, y) is a function only if, for each value x in the domain, we have only one value y in the range such that:

f(x) = y.

Here we have the pairs:

(- 2, - 3), (- 2, 1), (- 4, 3), (0, 4), (1, 1), and (2, 3).

Here, for the value x = -2, we have two different values of y.

y = 1 and y = 3.

So this is not a function, then if we want that this relation becomes a function, we must remove the first or the second point.

Answer:

I think B

Step-by-step explanation:

Answer:

Answer choices?

Step-by-step explanation:

For the function f(x) = ⌊x²/3⌋, the values of f(s) for different sets s are as follows: a) f(s) = {1, 0, 0, 0, 1, 3}, b) f(s) = {0, 0, 1, 3, 5, 8}, c) f(s) = {0, 8, 16, 40}, d) f(s) = {1, 12, 33, 77}

The function f(x) = ⌊x²/3⌋ represents the floor of x²/3. To find f(s) for different sets s, let's evaluate it for each case:

a) For s = {-2, -1, 0, 1, 2, 3}:

  - For -2, (-2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For -1, (-1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 0, (0)²/3 = 0/3 = 0.

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 3, (3)²/3 = 9/3 = 3.

  Therefore, f(s) = {1, 0, 0, 0, 1, 3}.

b) For s = {0, 1, 2, 3, 4, 5}:

  - For 0, (0)²/3 = 0/3 = 0.

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 3, (3)²/3 = 9/3 = 3.

  - For 4, (4)²/3 = 16/3, and ⌊16/3⌋ = 5.

  - For 5, (5)²/3 = 25/3, and ⌊25/3⌋ = 8.

  Therefore, f(s) = {0, 0, 1, 3, 5, 8}.

c) For s = {1, 5, 7, 11}:

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 5, (5)²/3 = 25/3, and ⌊25/3⌋ = 8.

  - For 7, (7)²/3 = 49/3, and ⌊49/3⌋ = 16.

  - For 11, (11)²/3 = 121/3, and ⌊121/3⌋ = 40.

  Therefore, f(s) = {0, 8, 16, 40}.

d) For s = {2, 6, 10, 14}:

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 6, (6)²/3 = 36/3 = 12.

  - For 10, (10)²/3 = 100/3, and ⌊100/3⌋ = 33.

  - For 14, (14)²/3 = 196

The values of f(s) for the given sets show how the function ⌊x²/3⌋, which represents the floor of x²/3, behaves for different inputs.

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False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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Given:

The radius of the cylinder = 2 cm

Height of the cylinder = 5 cm

To find:

The volume of the cylinder.

Solution:

We know that, the volume of a cylinder is:

\(V=\pi r^2h\)

Where, r is the radius and h is the height of the cylinder.

Putting \(r=2,h=5\) in the above formula, we get

\(V=\pi (2)^2(5)\)

\(V=\pi (4)(5)\)

\(V=20\pi \)

Therefore, the volume of the cylinder is \(20\pi \) cubic cm and its approximate value is 62.832 cubic cm.

Answer:

$27.5

Step-by-step explanation:

Other solution

38.2 X 0.8 = 30.56 (20% off)

30.56 X 0.9 = 27.504 (Another 10% off)

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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Answer:

125 / 8 centimeters

Step-by-step explanation:

Given:

V = s³

Where,

V = volume of the cube

s = side length of the cube

if marie's cube has a side length of 2 1/2 centimerters

That is,

s = 2 1/2 cm

V = s³

= (2 1/2)³

= (5/2)³

= 125 / 8 centimeters

NOTE:

(5/2)³ = 5³ / 2³

= 5*5*5 / 2*2*2

= 125 / 8

Answer:

y = - 2x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y =mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (- 4, 3 ) into the partial equation

3 = 8 + c ⇒ c = 3 - 8 = - 5

y = - 2x - 5 ← equation of line

Answer:

i think its a mirror

Step-by-step explanation:

mark as brainliest if its crct

Using the formula of the combination and for the values of 'p' and 'q'. The statement is false.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

The formula is:

\(C(p,q) = \frac{p!}{q!(p-q)!}\)

p=4 and put q=0 to 4

C(4,2) > C(4,0),C(4,1),C(4,3),C(4,4)

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Answer:

Step-by-step explanation:

The sequence of arc lengths is a geometric sequence with first term 14 ft and common ratio 0.8. The general (n-th) term of such a sequence is given by ...

  an = a1 · r^(n-1) . . . . . . . first term a1, common ratio r

For this scenario, the n-th term is ...

  an = 14·0.8^(n-1)

__

The 5th term is ...

  a5 = 14·0.8^(5-1) ≈ 5.734 . . . . feet

__

For the arc length to be less than 1 ft, we require ...

  14·0.8^(n-1) < 1

  0.8^(n-1) < 1/14

  (n -1)log(0.8) < log(1/14) . . . . . . note that these log values are negative

  n -1 > log(1/14)/log(0.8)

  n > 1 +log(1/14)/log(0.8) ≈ 12.8

The 13th swing will have an arc length less than 1 ft.

__

The sum of n terms of a geometric sequence is given by ...

  Sn = a1 · (1 -r^n)/(1 -r)

13 terms of our sequence will total ...

  S13 = 14 · (1 -0.8^(13))/(1 -0.8) ≈ 66.152 . . . feet

The total distance traveled in 13 swings is about 66.152 feet.

To determine the number of different orders of top-three finishers that include all seniors, we need to calculate the combinations of selecting three players from the eight seniors.

The probability of the top-three finishers all being seniors can be calculated by dividing the number of different orders of top-three finishers that include all seniors by the total number of different orders of top-three finishers.

In this scenario, we have 14 players, consisting of six juniors and eight seniors. To find the number of different orders of top-three finishers that include all seniors, we need to calculate the combinations of selecting three players from the eight seniors, which is denoted as C(8, 3). Using the combination formula, we can determine this value.

The probability of the top-three finishers all being seniors is obtained by dividing the number of different orders of top-three finishers that include all seniors by the total number of different orders of top-three finishers, which can be calculated by dividing C(8, 3) by the total number of different orders of selecting three players from the entire team, denoted as C(14, 3).

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The degree measure of the missing angle is `1619.49°`.

Given that the sum of the degree measures of the interior angles of a convex polygon is `1620°`.

It is given that Claire forgot to include one angle.

We have to find the degree measure of the forgotten angle.

To solve this problem, let's first find out the total number of angles present in the polygon.

The formula to find the sum of the degree measures of the interior angles of a polygon is given by:

\(S = (n - 2) \times 180°\)

where S is the sum of the degree measures of the interior angles and n is the total number of sides of the polygon.

Using the formula mentioned above, we can find the value of n as follows:

\($\begin{aligned}(n - 2) \times 180 &= 1620\\n - 2 &= 9\\n &= 11\end{aligned}$\)

Hence, the polygon has 11 sides.

As we know that a polygon with n sides has n angles,

Therefore, the number of angles present in the polygon is 11.

Now, let's find the degree measure of the forgotten angle.

We know that the sum of the degree measures of the interior angles of a polygon is equal to `1620°`.

Since one angle is missing, the sum of the remaining angles should be `1620° - x`,

where x is the degree measure of the missing angle.

Since the polygon has 11 sides, it has 11 angles.

Therefore, \($S = (n - 2) \times 180= (11 - 2) \times 180= 1620$\)

Let the degree measure of the missing angle be x.

Then, the sum of the remaining angles = \($(S - x)$\)

Therefore, the sum of all angles in the polygon is,\($(S - x) + x

= 1620$$(S - x)

= 1620 - x$$\begin{aligned}&

= 1619 + 59/121\\&

= 1619.49\end{aligned}$\)

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Answer:70/100

Step-by-step explanation: 100/100 is 100% so with that logic 70/100 would mean 70%

Answer:

two blocks east

Step-by-step explanation:

the north and south cancel out and then 3 blocks east - 1 block west = 2 blocks east

The cylindrical shell is subjected to an internal pressure of 70MPa. The shell's inner radius is 10 cm, and the outer radius is 16 cm. The maximum and minimum hoop stresses in the cylindrical shell are determined below.

For an element of thickness dr at a distance r from the center, the hoop stress is given by equation i:

σθ = pdθ...[i]Where, p is the internal pressure.

The thickness of the shell is drThe circumference of the shell is 2πr.

Therefore, the force acting on the element is given by:F = σθ(2πrdr)....[ii]

Let σmax be the maximum stress in the shell. The stress at radius r = a, which is at the maximum stress, is given by:σmax = pa/b....[iii]

Here a = radius of the shell, and b = thickness of the shell.

According to equation [i], the hoop stress at radius r = a is given by:σmax = pa/b....[iii].

Substitute the given values:σmax = 70 × 10^6 × (16 - 10)/(2 × 10) = 56 × 10^6 Pa.

The minimum hoop stress in the shell occurs at the inner surface of the shell. Let σmin be the minimum stress in the shell.σmin = pi/b....[iv].

According to equation [i], the hoop stress at radius r = b is given by:σmin = pi/b....[iv]Substitute the given values:

σmin = 70 × 10^6 × 10/(2 × 10) = 35 × 10^6 Pa.

Therefore, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa.

A thick cylindrical shell with an inner radius of 10 cm and an outer radius of 16 cm is subjected to an internal pressure of 70MPa. Maximum and minimum hoop stresses in the cylindrical shell can be determined using equations and the given data. σθ = pdθ is the formula for hoop stress in the cylindrical shell.

This formula calculates the hoop stress for an element of thickness dr at a distance r from the center.

For the cylindrical shell in question, the force acting on the element is F = σθ(2πrdr).

Let σmax be the maximum stress in the shell. According to equation [iii], the stress at the radius r = a, which is the maximum stress, is σmax = pa/b.σmax is calculated by substituting the given values.

The maximum hoop stress in the shell is 56 × 10^6 Pa according to this equation.

Similarly, σmin = pi/b is the formula for minimum hoop stress in the shell, which occurs at the inner surface of the shell.

The minimum hoop stress is obtained by substituting the given values into equation [iv].

The minimum hoop stress in the shell is 35 × 10^6 Pa.As a result, the maximum and minimum hoop stresses in the cylindrical shell are 56 × 10^6 Pa and 35 × 10^6 Pa, respectively.

Thus, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa. These results are obtained using equations and given data.

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Answer:

k = -6

w = 9 or -9   (see explanation below)

f = -7

Step-by-step explanation:

The entities on the left and right of the = sign are matrices

Matrix elements are referred to using row and column numbers as indexes

The size of the matrix is number of rows x number of columns

In this problem, both matrices are of size 2 x 2 = 4

The first entry of the matrix on the left ie the top left is referred to as entry 11 where 1 is the row and 1 is also the column

Using this notation, the matrix entries for the matrix on the LHS are

a₁₁ = -12     (first row, first  column)
a₁₂ = - w²   (first row, second column)

a₂₁ = 2f       (second row, first column)

a₂₂ = 3         (second row, second column)

These values  should correspond to the exact same elements for the matrix on the RHS which has elements
a₁₁ = 2k
a₁₂ = - 81
a₂₁ = -14
a₂₂ = 3

Equating the elements in LHS matrix to the corresponding RHS matrix elements gives us

-12 = 2k ⇒ k = -6

- w² = -81
⇒ w² = 81    (by dividing both sides by -1)
⇒ w = ±9  
( we can't be sure whether it is +9 or -9 since 9² = (-9)² = 81

2f = -14
⇒ f = -7 (by dividing both sides by 2)

Answer:

18.1

Step-by-step explanation:

All radii of a circle are congruent (same length), which means if we draw in a radius from the center to the end of the 16.3, it would be the same length of x.

Now we can use sa very simple theorem.... the pythagorean therom!

\(7.9^{2} + 16.3^{2} = x^{2} \\62.41 + 265.69 = x^{2} \\328.1 = x^{2} \\18.1 = x\)(rounded)

I hope this helps you.

Answer:

new

words

to cause to be

one who

Step-by-step explanation:

neo means new

lex means to speak (words)

ize means to make (to cause to be)

er means the one (one who)

Answer:

\( V = \pi r^2 h\)

And for this case the value for the height is \( h = 10.7 in\) the diameter is provided \( D = 2r = 8.1 in\) so then the radius is given by:

\( r = \frac{D}{2}=\frac{8.1 in}{2}= 4.05 in\)

Then we can find the volume with the first formula and replacing we got:

\( V = \pi (4.05in)^2 (10.7 in)= 551.4 in ^3\)

The final answer for this case would be 551.4 cubic inches

Step-by-step explanation:

The volume for a right circular cone is given by this formula:

\( V = \pi r^2 h\)

And for this case the value for the height is \( h = 10.7 in\) the diameter is provided \( D = 2r = 8.1 in\) so then the radius is given by:

\( r = \frac{D}{2}=\frac{8.1 in}{2}= 4.05 in\)

Then we can find the volume with the first formula and replacing we got:

\( V = \pi (4.05in)^2 (10.7 in)= 551.4 in ^3\)

The final answer for this case would be 551.4 cubic inches

Answer V:183.8^3 previous answer is wrong

to get the equation of any straight line, we only need two points off of it, hmmm let's use the points in the picture below.

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{-7}{1}\implies -7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-7}(x-\stackrel{x_1}{0}) \\\\\\ y-5=-7x\implies y=-7x+5\)

The greatest of the 4 consecutive integers with a sum of -278 is -68

Let n, n + 1, n + 2 and n + 3 be four consecutive integers.

The sum of four consecutive integers is -278.

⇒ n + (n + 1) + (n + 2) + (n + 3) = -278

⇒ n + n + n + n + 1 + 2 + 3 = -278

⇒ 4n + 6 = -278

⇒ 4n = -278 - 6

⇒ 4n = -284

⇒ n = -284/4

⇒ n = -71

So, the consecutive integers would would be:

n = -71

n + 1 = -70

n + 2 = -69

n + 3 = -68

here, the greatest of the 4 integers is -68

Therefore, the greatest of the 4 consecutive integers with a sum of -278 is -68

Learn more about the consecutive integers here:

https://brainly.com/question/24600756

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