The number of hours she was driving = 5.7 hours or in fraction 57/10 hours.
What is fraction?
A fraction is a number that represents a part of a whole.
Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.
Given, a total gallons is in mixed fraction 4 3/4
can be written as
16+3/4 = 19/4
Let x be the hours she was driving.
The she used 5/6 gallons.
x (5/6) = 19/4
x = 19/4(6/5)
x = 5.7 hours
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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.
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.
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
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.
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
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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Use the Law of Cosines to determine the indicated angle 0. (Assume a = 65.01, b = 36.38, and c = 42.05. Round your answer to two decimal places.)
a = 65.01, b = 36.38, and c = 42.05.
And it is required to find the measure of angle 0 which will be the angle B
Using the law of cosine
[tex]\begin{gathered} b^2=a^2+c^2-2\cdot a\cdot c\cdot\cos B \\ \cos B=\frac{a^2+c^2-b^2}{2\cdot a\cdot c}=\frac{65.01^2+42.05^2-36.38^2}{2\cdot65.01\cdot42.05}=0.854 \\ \end{gathered}[/tex][tex]\angle\emptyset=\angle B=\cos ^{-1}0.854=31.31[/tex]the answer is rounded to two decimals
options 1. a (-3,50) b (-2,0) c (0,-4) d (1,-6) 2. a (-3,50) b (0,-4) c (-1,-6) d (2,0)3. a (-3,50) b (-2,0) c (0,-4) d (2,0)
Answer:
The x-intercepts shown in the table are (-2, 0) and (2, 0).
The y-intercept shown in the table is (0, -4)
Explanation:
The x-intercepts are the points where the value of f(x) is 0. Then, these points are (-2, 0) and (2, 0)
Additionally, the y-intercept is the point where the value of x is 0, so the y-intercept is (0, -4).
Then, the answers are:
The x-intercepts shown in the table are (-2, 0) and (2, 0).
The y-intercept shown in the table is (0, -4)
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:
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
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]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]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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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
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.
Suppose that a regression line for some data transformed with logarithmspredicts that when y equals 8, log(%) will equal 1.603. What does theregression line predict y will equal when y equals 8? Round your answer to thenearest whole number.
Given the relationship between y and x to be
[tex]y=a^x\text{ ------ equation 1}[/tex]Take the logarithm of both sides,
[tex]\begin{gathered} \log y=\log ^{}_{}a^x \\ \Rightarrow\log \text{ y = x }\times\text{ log a ---- equation 2} \end{gathered}[/tex]But when x = 8, log y = 1.603.
Thus, substituting the above values into equation 2, we have
[tex]\begin{gathered} 1.603\text{ = 8 }\times\text{ log a} \\ \text{divide both sides by 8} \\ \log \text{ a= }\frac{1.603}{8} \\ \Rightarrow\log \text{ a =0.2}004 \\ \text{Thus, } \\ a=1.586 \end{gathered}[/tex]From equation 1,
[tex]\begin{gathered} y=a^x \\ \Rightarrow y=1.586^x\text{ ----- equation 3} \end{gathered}[/tex]Thus, when x = 8
[tex]\begin{gathered} y=1.586^x \\ y=1.586^8 \\ \Rightarrow y=40.03 \end{gathered}[/tex]Thus, the value of y will be 40 (to the nearest whole number)
The correct option is D
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.
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
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
Can someone please help me solve this problem number 9
The perimeter of the room was calculated in question 6, and it is 54 feet.
Since the borders come in 5-yard rolls, let's first convert 54 feet to yards.
Each yard has 3 feet, so we can divide the amount of feet by 3 to get it converted to yards:
[tex]\frac{54}{3}=18[/tex]Thus, the perimeter of the room is 18 yards. Since each roll has 5 yards,we will need:
[tex]\frac{18}{5}=3.6[/tex]Abou 3.6 rolls, but since we can only have whole rolls, we will have to approximate it to 4 rolls.
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)
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:
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]
At an amusement park, the two most popular rollercoasters are the Python and the Vortex. The Python is 212 feet long and the Vortex is 210 feet long. How many times as long is the Python as the Vortex?
Answer:
About 1.01 times longer
Step-by-step explanation:
we have to divide 212 by 210 since these are the lengths to get about 1.01.
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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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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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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.
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $15. For one performance,there were 50 tickets sold in all, and the total amount paid for them was $1275. How many tickets of each type were sold?
Given:
there are two types of tickets to a show: advance and same-day
Let the number of tickets from the type of Advance = x
And the number of tickets from the type of Same-day = y
there were 50 tickets sold in all
So,
[tex]x+y=50\rightarrow(1)[/tex]Advance tickets cost $30 and same-day tickets cost $15.
the total amount paid for them was $1275
So,
[tex]30x+15y=1275\rightarrow(2)[/tex]Solve the equations (1) and (2) to find (x) and (y)
[tex]\begin{gathered} x+y=50\rightarrow(\times-15) \\ 30x+15y=1275 \\ ============= \\ -15x-15y=-750 \\ 30x+15y=1275 \\ ============= \\ 15x=525 \\ x=\frac{525}{15}=35 \\ y=50-x=50-35=15 \end{gathered}[/tex]So, The answer will be:
The number of tickets from the type of Advance = x = 35
And the number of tickets from the type of Same-day = y = 15
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
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.