Substitute a for x
[tex]-f\text{ (x ) = - f (a) = - }\frac{2a}{a-1}[/tex]Determine - f(a) for f(x) =2x/x-1 and simplify.
Thus, the solution becomes:
[tex]-\frac{2a}{a-1}\text{ or }\frac{2a}{1-a}[/tex]GIVEN: P(N) = 0.25 and P(R) = 0.6If the probability of P(N R) = 0.15, are N and Rindependent events?a) Yes, because P(N) + P(R) +0.15b) No, because P(N).P(R) +0.15c) Yes, because P(N) X P(R) = 0.15d) Not enough information
P(N∩R) represents the probability of A and B.
When two events are independent events, the joint probability is calculated by multiplying their individual probabilities.
P(N∩R) For independent events:
[tex]P\mleft(N\cap R\mright)=P(N)\times P(R)[/tex]Substituting the known values for P(N) and P(R):
[tex]\begin{gathered} P(N\cap R)=0.25\times0.6 \\ P(N\cap R)=0.15 \end{gathered}[/tex]0.15 is the value of P(N∩R) given by the problem, and since we get the same result using the formula for independent events, we can affirm that N and R independent events.
Answer:
c) Yes, because P(N) X P(R) = 0.15
nine cubes are glued together to form the solid shown in the digram .
ANSWER
D. 272.25 mm²
EXPLANATION
First we have to find the area of one face of one cube:
[tex]A=2.75^2=7.5625\operatorname{mm}^2[/tex]Now we have to count how many faces of the squares are in the surface of the solid. Or a faster way is to multiply the total number of faces of the 9 cubes: 6*9=54 and subtract the number of faces that are not on the surface:
There are 18 faces of the cubes that are not on the surface of the solid. The number of faces from the 9 cubes that are on the surface of the solid is:
[tex]54-18=36[/tex]The surface area of the solid is the area of a face of one cube multiplied by the number of faces on the surface of the solid:
[tex]SA=36\cdot A=36\cdot7.5625=272.25\operatorname{mm}^2[/tex]Answer:
D. 272.25 mm²
Step-by-step explanation:
the sum of three consecutive integers is 267.what is that largest interger
The sum of three consecutive integers is 267. If the first one is a, then the second would be a + 1, while the third would be a + 2. Therefore, you would have;
[tex]\begin{gathered} a+(a+1)+(a+2)=267 \\ a+a+1+a+2=267 \\ 3a+3=267 \\ \text{Subtract 3 from both sides} \\ 3a=264 \\ \text{Divide both sides by 3} \\ a=88 \end{gathered}[/tex]The largest (third) integer is a + 2, therefore
[tex]\begin{gathered} a+2=88+2 \\ a+2=90 \end{gathered}[/tex]The largest integer therefore is 90.
Equivalent Linear Expressions MC 2.02
Which expression is equivalent to (-3 1/3d + 3/4) - (3 5/6d + 7/8)
A: 1/2d-1/8
B: 1/2d-1 5/8
C: 43/6d-1/8
D: -43/6d-1/8
The expression is equivalent to the given expression is -43/6d-1/8.
What is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given an expression [tex]-3\frac{1}{3d} +\frac{3}{4} - (3\frac{5}{6d}+\frac{7}{8} )[/tex]
= -10/3d +3/4 - 23/6d - 7/8
= -10/3d - 23/6d + 3/4 - 7/8
= -43/6d - 1/8
Hence, The expression is equivalent to the given expression is -43/6d-1/8.
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Answer:
- 4/15x + 4
Step-by-step explanation:
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Which expression represents the simplest factorization of 56st – 21t?
The expression which represents the simplest factorization of 56st – 21t is 7t(8s - 3).
How to factorise an expression?Factorization is the process of creating a list of factors. It is also an expression listing items that when multiplied together will produce a desired quantity.
Greatest common factor is the largest positive integer or polynomial that is a divisor of several different numbers.
56st - 21t
Factors of
56st = 1, 2, 4, 7, 8, 14, 28,:56, t, s
21t = 1, 3, 7, 21
The common factors of 56st and 21t is 7 and t
56st - 21t
= 7t(8s - 3)
Check:
7t(8s - 3)
= 56st - 21t
In conclusion, the simplest factorization of the expression 56st - 21t is 7t(8s - 3).
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Not homework just review for test not worth any points
Recall that:
Interest is the monetary gain for lending money to a third party.
Simple interest is applying the interest to the original amount without considering the extra flow of money each time the interest is applied.
Compounded interest is applying the interest to the total amount including the extra flow of money each time the interest is applied.
1) Plan A. From the given information, in 12 months Ari will earn:
[tex]I=500\cdot0.065\cdot12=390.[/tex]dollars, therefore she will have a total of $890.00.
2) Plan B. Now we use the formula for compounded interest to compute the total amount that Ari will have after one year:
[tex]A=500(1+0.065)^{12}=500\cdot2.129096\approx1064.55.[/tex]3) From the above calculations, we conclude that Ari will make more money if she invests in plan B.
4) Ari has to leave the money for another:
Using plan B. Let t be the number of extra months Ari needs to leave the money in the fund, then:
[tex]1100=500\cdot(1.065)^{12+t}\text{.}[/tex]Solving for t, we get:
[tex]\begin{gathered} 1.065^{12+t}=2.2, \\ (12+t)ln(1.065)=\ln (2.2), \\ 12+t=\frac{\ln (2.2)}{\ln (1.065)}=12.52, \\ t=12.52-12=0.52. \end{gathered}[/tex]Then, Ari needs to leave the money for another half a month but since the interest is applied each month she needs to leave the money for another whole month.
Using Plan A: Let t be the number of extra months Ari needs to leave the money in the fund, then:
[tex]1100=500\cdot0.065\cdot(12+t)\text{ +500.}[/tex]Solving for t we get:
[tex]\begin{gathered} \frac{1100-500}{500\cdot0.065}=12+t, \\ t=\frac{600}{32.5}-12, \\ t=6.46. \end{gathered}[/tex]Then, Ari needs to leave the money for another 6.46 months but since the interest is applied monthly she needs to leave the money for another 7 months.
Jane has a pre-paid cell phone with A Fee and Fee. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 430 minutes and the cost was $227.50. In July she used 780 minutes and the cost was $385.00.
Given:
the plan of the pre-paid cell phone
The plan has a monthly fee and a charge for each minute
Let the monthly cost = C
and the number of minutes = x
the general equation will be:
C = ax + b
Where (b) is the monthly fee, and (a) is the charge per minute
We will find the values of (a) and (b) using the following:
1) 430 minutes cost $227.50
2) 780 minutes cost $385.00.
So, we have the following equations:
[tex]\begin{gathered} 430a+b=227.5\rightarrow(1) \\ 780a+b=385\rightarrow(2) \end{gathered}[/tex]Solve the equations, subtract equation (1) from (2) to eliminate (b), and solve for (a):
[tex]\begin{gathered} 780a-430a=385-227.5 \\ 350a=157.5 \\ a=\frac{157.5}{350}=0.45 \end{gathered}[/tex]Substitute with (a) into equation (1) to find the value of (b)
[tex]\begin{gathered} 430\cdot0.45+b=227.5 \\ 193.5+b=227.5 \\ b=227.5-193.5=34 \end{gathered}[/tex]So, the equation of the monthly cost will be:
[tex]C=0.45x+34[/tex]Part (b): When x = 484 minutes, we will find C
so, substitute with (x) into the equation of C
[tex]\begin{gathered} C=0.45\times484+34 \\ C=217.8+34 \\ C=251.8 \end{gathered}[/tex]So, the answer will be:
A) C = 0.45x + 34
B) $251.8
Solve the equation involving absolute value. Type you answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. |x^2+2x-36|=12 x=Answer, Answer, Answer and Answer
Given:
The euqation is,
[tex]|x^2+2x-36|=12[/tex]Explanation:
Simplify the equation.
[tex]\begin{gathered} |x^2+2x-36|=12 \\ x^2+2x-36=\pm12 \end{gathered}[/tex]Solve the x^2 + 2x - 36 = 12 for x.
[tex]\begin{gathered} x^2+2x-36=12 \\ x^2+2x-36-12=0 \\ x^2+8x-6x-48=0 \\ x(x+8)-6(x-8)=0 \\ (x+8)(x-6)=0 \\ x=-8,6 \end{gathered}[/tex]Solve the equation x^2 + 2x - 36 = -12 for x.
[tex]\begin{gathered} x^2+2x-36+12=0 \\ x^2+2x-24=0 \\ x^2+6x-4x-24=0 \\ x(x+6)-4(x+6)=0 \\ (x+6)(x-4)=0 \\ x=-6,4 \end{gathered}[/tex]Thus solution of the equation is x = -8, -6, 4, and 6
help!!! thanks :))))))
The length of given sides BC = 38 and EF = 38.
Given:
ΔABC ≅ ΔDEF
BC = x + 30 , EF = 4x + 6
we know that
BC = EF
x + 30 = 4x + 6
30 - 6 = 4x - x
24 = 3x
divide by 3 on both sides
3x/3 = 24/3
x = 8
BC = x + 30
= 8 + 30
= 38
EF = 4x + 6
= 4*8 + 6
= 32+6
= 38
Therefore the length of given sides BC = 38 and EF = 38.
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Write an equation in slope-intercept form for the line that is parallel to y = 3x + 7 and passes through the point (-4, -8).
The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
What is a slope-intercept form?It gives the graph of a straight line and it is represented in the form
y= mx +c. It is one of the form used to calculate the equation of a straight line. We have to calculate the slope of the line from the equation. The slope calculated can be used in the slope-intercept form. It is the most popular form of a straight line.
We need to find the slope to the line y = 3x +7.
The slope of a line is m
Here, from the equation y=3x+7, m=3
So, m=3
The slope-intercept form is,
y= mx +c
-8 = 3(-4)+c
-8=-12+c
c=4 and m=3
Now, the above equation equation becomes,
y=3x+4
The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
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11. Determine if the following sequence is arithmetic or geometric. Then, find the 12th term. 2, 6, 18, 54, ... a. arithmetic: 35 b. arithmetic: 354,294 c. geometric: 35 d. geometric: 354,294
We have the sequence: 2, 6, 18, 54...
If the sequence is arithmetic, there must be a common difference between the terms that remains constant.
This is not the case for this sequence.
We can try by seeing if there is a common factor k such that:
[tex]a_n=k\cdot a_{n-1}[/tex]We can do it by:
[tex]\frac{a_2}{a_1}=\frac{6}{2}=3[/tex][tex]\frac{a_3}{a_2}=\frac{18}{6}=3[/tex][tex]\frac{a_4}{a_3}=\frac{54}{18}=3[/tex]There, we have a geometric sequence, with factor k=3:
[tex]a_n=3\cdot a_{n-1}[/tex]We can relate it to the first term as:
[tex]\begin{gathered} a_2=3\cdot a_1 \\ a_3=3\cdot a_2=3\cdot3\cdot a_1=3^2\cdot a_1 \\ a_4=3\cdot a_3=3\cdot3^2\cdot a_1=3^3\cdot a_1 \\ a_n=3^{n-1}\cdot a_1=3^{n-1}_{}\cdot2 \end{gathered}[/tex]For n=12, we have:
[tex]a_{12}=3^{12-1}\cdot2=3^{11}\cdot2=177,147\cdot2=354,294[/tex]The value of a12 is 354,294.
The answer is d) Geometric, 354,294.
Find the missing side. Round to the nearest tenth.
1)
X
1.
2.
21°
16
2)
12
40°
The sides of a triangle can be determined if the trigonometric ratios and angles are given. The missing sides of the given triangle are 6 and 8 respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The diagram for the given triangle is given below,
Since, sin(x) = (The side opposite to angle x) / Hypotenuse
Apply the above trigonometric ratio in triangle 1 to get,
Sin(21°) = x / 16
=> x = 16 × Sin(21°)
=> x = 16 × 0.36
=> x = 5.76
Which is approximately 6 when taken as nearest to tenth.
Similarly for triangle 2, it can be written as,
Sin(40°) = x / 12
=> x = 12 × Sin(40°)
=> x = 12 × 0.64
=> x = 7.68
Which is approximately 8 when taken as nearest to tenth.
Hence, the missing sides for the given triangles are 6 and 8 approximately.
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What is the connection between side ratios and angle in a right triangle
Trigonometric ratios are ratios between any two sides of a right triangle that can then be used to determine the measure of an angle between those two sides. Primary trigonometric ratios (in a right triangle trigonometry) are: sin (x), cos (x) and tan (x)
On the basis of any two side lengths, we may even determine the acute angle measurements in a right triangle. We may get the ratios of the lengths of the triangle's sides to an acute angle in a right triangle by knowing the acute angle's measurement.
What relationship exists between a triangle's side ratios and angle?In a triangle, the longest side is located across from the largest angle, while the shortest side is located across from the smallest angle.
Triangle Unfairness: The lengths of any two sides added together in a triangle always exceed the length of the third side.
Pythagoras Theorem, a²+b²=c² in a right triangle with hypotenuse c.
A triangle is a right triangle if its sides conform to the relationship a²+b²=c²
The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.
Remember that the Pythagorean theorem only holds true for right triangles, in which case the converse of the theorem also holds true. In other words, if a triangle's sides satisfy the connection, then it must be a right triangle.
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Which is the best estimate of 162% of 79?
We have to multiply 79 by the percentage in decimal form ( divided by 100)
79 x (162/100) = 79 x 1.62 = 127.98
rounded: 128
The best estimate is 128
Find the maximum value of the objective function and the values of x and y for which it occurs. F= 2x+y3x+5y ≤45 x ≥0 and y ≥02x+4y ≤32The maximum value of the objective function is ______.
The objective function is:
[tex]F=2x+y[/tex]We need to find the shaded region where 4 inequalities overlap, then we need to graph the given inequalities:
[tex]\begin{gathered} 3x+5y\leq45 \\ 5y\leq-3x+45 \\ y\leq\frac{-3}{5}x+\frac{45}{5} \\ y\leq-\frac{3}{5}x+9 \end{gathered}[/tex]And the other one:
[tex]\begin{gathered} 2x+4y\leq32 \\ 4y\leq-2x+32 \\ y\leq\frac{-2x}{4}+\frac{32}{4} \\ y\leq-\frac{1}{2}x+8 \end{gathered}[/tex]And x>=0, y>=0
The graph is:
The coordinates of the shaded region are then:
(0,0), (0,8), (10,3) and (15,0)
To obtain the maximum value, let's evaluate the objective function in all the coordinates:
[tex]\begin{gathered} F(0,0)=2\times0+0=0+0=0 \\ F(0,8)=2\times0+8=0+8=8 \\ F(10,3)=2\times10+3=20+3=23 \\ F(15,0)=2\times15+0=30+0=30 \end{gathered}[/tex]Then, the maximum value is the largest value obtained, then it's 30 and it occurs at x=15 and y=0.
I will show you the pic
If it rotates clockwise around the origin. It will be in the following quadrant
[tex]\begin{gathered} 90^{\circ}\rightarrow quadrant\text{ 1} \\ 180^{\circ}\rightarrow quadrant\text{ 4} \\ 270^{\circ}\rightarrow quadrant\text{ 3} \\ 360^{\circ^{\prime}^{\prime}}\rightarrow quadrant\text{ 2} \end{gathered}[/tex]A full one- gallon container can beused to fill the one-liter containers, as shownbelow. Write a unit rate that estimates thenumber of liters per gallons.
Explanation
Step 1
as we can see in the picture
[tex]1\text{ gallons}\rightarrow3\text{ liters}[/tex]so, to find the unit rate make
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of liters}}{Number\text{ of gallons}} \\ \text{replace} \\ \text{Unit rate=}\frac{3\text{ liters}}{1\text{ gallon}}=\text{ 3 liters per gallon} \end{gathered}[/tex]I hope this helps you
pan made a scale drawing of a swimming pool. The diving board is 2 inches long in the drawing. The actual diving board is 18 feet long. What scale did Pam use for the drawing?
Divide the length of the object on the drawing by its actual size to find the scale:
[tex]\frac{2\text{ inches}}{18\text{ feet}}[/tex]Since each feet has 12 inches:
[tex]\frac{2\text{ inches}}{18\text{ feet}}=\frac{2\text{ inches}}{18\cdot12\text{ inches}}=\frac{2}{216}=\frac{1}{108}[/tex]Therefore, the scale used in the drawing is 1:108 (one inch in the paper equals 108 inches in real life).
What is the solution to the inequality x(x – 3) > 0?Question 8 options:A) x ≤ 0 or x ≥ 3B) x < 0 or x > 3C) x ≤ 0 and x ≥ 3D) 0 < x < 3
,Inequalities
It's given the inequality:
x(x - 3) > 0
Note the left side is the product of two expressions: x and x-3.
That product must be greater than zero, or positive.
Recall that the product of two numbers is positive in two different cases:
Both are positive, for example 5*4=20
Both are negative, for example (-5)*(-4) = 20
This means that we can provide two different answers to the inequality, both valid:
1. When x >0 AND x - 3 >0 (both positive), or
2. When x <0 AND x - 3 < 0 (both negative).
The first condition leads to:
x>0 AND x>3. If we intersect these conditions, the solution for this part is x>3.
The second condition gives us:
x<0 AND x<3. The intersection of these conditions gives x<0.
Thus, the final solution is the union (OR) both partial intervals above, i.e.
x>3 OR x<0 --> Option B)
Answer:
X < 0 and x > 3.
Step-by-step explanation:
chatgpt.
Find the following values of the function6(-7+8f(x) = 75 - 2.c12-2 < -2– 2 4f(-4)=f(-2) =f(-1) =f(9) =91)Answers in progress)
Find the following values of the function
6
(-7+8
f(x) = 7
5 - 2.c
12
-
2 < -2
– 2a> 4
f(-4)=
f(-2) =
f(-1) =
f(9) =
9
1)
2cuestionAngelique is buying towels for her apartment. She finds some green towels, x, that cost $5 each and bluetowels, y, that cost $9 each. She wants to buy at least 4 towels, but does not want to spend more than$38. How many of each towel can she purchase?Enter the system of inequalities that represents the situation. Then select the graph of the system andselect one possible solution.The system of inequalities
x: green towels (each one cost $5)
y: blue towels (each one cost $9)
She wants to buy at least 4 towels:
[tex]x+y\ge4[/tex]She does not want to spend more than $38:
[tex]5x+9y\leq38[/tex]The sytem of inequalitites is:
[tex]\begin{gathered} x+y\ge4 \\ 5x+9y\leq38 \end{gathered}[/tex]Graph: First inequality in red, second inequality in blue
Solution: Area shaded of both colours
[tex]undefined[/tex]Find f in:f ÷ -2/3 = -1/3
ANSWER
[tex]f\text{ = }\frac{2}{9}[/tex]EXPLANATION
We want to find f in:
[tex]f\text{ }\div\text{ -}\frac{2}{3}\text{ = -}\frac{1}{3}[/tex]To do that, we multiply both sides by -2/3.
That way, it cancels out the -2/3 on the left hand side and isolates f.
So we have:
[tex]\begin{gathered} f\text{ }\div(-\frac{2}{3})\cdot\text{ (-}\frac{2}{3})\text{ = -}\frac{1}{3}\cdot\text{ -}\frac{2}{3} \\ f\text{ = }\frac{2}{9} \end{gathered}[/tex]That is the answer.
Find the length of x.43a. 2.5b. 3C. 4d. 5e. 656
the given triangle is a right angle triangle.
by Pythagoras theorem.
4^2 + 3^2 = x^2
16 + 9 = X^2
25 = x^2
[tex]\begin{gathered} x^2=25 \\ x=5 \end{gathered}[/tex]so, the answer is x = 5.
Write an equation for each scenario, then find the solution.5. You're making a Wawa run for snacks and energy drinks on your bike. It takes you0.4 hours at x miles per hour to make it to Wawa. On your way back you have toride 3 miles per hour slower (you're weighed down by your Wawa goodies) and ittakes you 0.5 hours. How far is it from your house to Wawa?6. Laura retired from her job recently, and she has saved about $500,000 over the
Let y represent the distance from your house to wawa. This means that the distance from wawa to your house is also y miles.
It takes you 0.4 hours at x miles per hour to make it to Wawa.
Distance = speed * time
Therefore, on your way to wawa, the expression would be
y = 0.4 * x = 0.4x
On your way back you have to ride 3 miles per hour slower. This means that your speed was (x - 3) miles per hour. Since it took you 0.5 hours, the expression for distance would be
y = 0.5(x - 3)
Since the distance is the same, it means that
0.4x = 0.5(x - 3)
0.4x = 0.5x - 1.5
0.5x - 0.4x = 1.5
0.1x = 1.5
x = 1.5/0.1
x = 15
Therefore,
y = 0.4x = 0.4 * 15
y = 6
The distance from your house to wawa is 6 miles
What is (6/7)/(2/7)?
To find the value of;
[tex]\frac{(\frac{6}{7})}{(\frac{2}{7})}[/tex]When dividing fractions, for example a divided by b is equals a times 1/b;
[tex]a\text{ divided by b = a }\times\frac{1}{b}[/tex]note that the divisor which is b is inversed and multiplied.
So, let us apply the same rule to the given question.
The divisor which is the second fraction for the question is 2/7, we need to inverse 2/7 and multiply it by the first fraction.
The inverse of 2/7 is 7/2, So;
[tex]\frac{(\frac{6}{7})}{(\frac{2}{7})}=\text{ }\frac{6}{7}\times\frac{7}{2}=\frac{(6\times7)}{(7\times2)}=\frac{42}{14}[/tex]And finally;
[tex]\frac{42}{14}=3[/tex]Therefore the final answer is 3.
[tex]\frac{(\frac{6}{7})}{(\frac{2}{7})}=\text{ 3}[/tex]
Fourteen more than 4 times a number is 42what is equation?what is solution?
We have to express this phrase in mathematical terms.
We call the number x.
Then, four times a number is "4x".
Fourtenn more than 4x is "4x+14", and this is equal to 42.
Then, we can write:
[tex]4x+14=42[/tex]And solve as:
[tex]\begin{gathered} 4x+14=42 \\ 4x=42-14 \\ 4x=28 \\ x=\frac{28}{4} \\ x=7 \end{gathered}[/tex]Answer: the equation is 4x+14=42 and the solution is x=7
y=x-8 how would I do it
to find two points that satisfy the function, you need to give one value and calculate the other one, for example.
I will use x=4 and x=8
when x=4
y=4-8=-4
so one point is (4,-4)
and when x=8
y=8-8=0
so the other point is (8,0)
so you need to graph these points and then plot the line, like this:
I really don't understand this lesson can you help me please
Data:
M = Math books
E = Englisg books
TB = Total books
The total of the books is the addition of the math and english books
[tex]TB\text{ = M+ E}[/tex]The Math books are: M= E-9 (Nine less that English books (E))
So replacing this in the expression for Total Books:
[tex]TB=(E-9)+E\text{ }\Rightarrow TB=E-9+E[/tex]The final expression is:[tex]TB=2E-9[/tex]which line is steeper y=+2 or y= -7/3x -5
The inclination of the lines in the coordinate system is given by their slopes, so to determine which line is steeper you have to compare the absolute values of both slopes.
The first equation y=2 has no slope, if you draw it you will see that for any value of x, y doesn't change, it is always 2.
You can also say that the slope of this equation is equal to zero.
For the second equation y=-7/3x-5, the slope is equal to -7/3.
The second equation is steeper than the first one since the absolute value of its slope is greater.
The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 19 21What ACT score is the mode for the class?
Recall that in statistics, the mode is the value that appears most frequently in a set of data. You may find it useful to represent the data in statistical graphs such as dot plots or bar charts. In this case, we will use the following chart
As we can see from the image, The most frequently used numbers are 19 and 21. We are dealing with a bimodal data set. The mode is given by 19 and 21.