Answer:
10 rows with 6 passengers per row
Step-by-step explanation:
Let x be the number of rows and y the number of passengers per row.
Then we can interpret the story as the following two equations:
xy=60
(x+2)(y-1)=60
Solving these two equations:
y=60/x
(x+2)(60/x-1)=60 (substitute y)
60 - x + 120/x - 2 = 60 (multiply by -x)
x² + 2x - 120 = 0 (factor)
(x-10)(x+12) = 0
x = 10
y = 60/10 = 6
and indeed 10 * 6 = 60 and also 12 * 5 = 60
Stuck on this one .......
Answer:
Exponent Product Rule
Step-by-step explanation:
Exponent multiplication: (a^b)(a^c)= a^(b+c)
t^3=(t^2)t
Because t=t^1, we have
t^2+t^1=t^3
This can be shown by the Exponent Product Rule
Answer: t²⁺¹
Step-by-step explanation:
The law of exponents states that when multiplying terms with the same base, you ADD the exponents. Note that "t" has an exponent of 1.
t³ = (t²)t¹ = t²⁺¹
I hope this is what you were looking for.
Select the correct answer. If g = 8, what is the value of the expression g/2+3 ? A. 8/5 B.11/2 C. 7 D. 19
Answer:
7Option C is the correct option
Step-by-step explanation:
g = 8 ( given )
Now,
[tex] \frac{g}{2} + 3[/tex]
Plugging the value of g
[tex] \frac{8}{2} + 3[/tex]
[tex] \frac{8 + 3 \times 2}{2} [/tex]
[tex] \frac{8 + 6}{2} [/tex]
[tex] \frac{14}{2} [/tex]
[tex]7[/tex]
Hope this helps...
Good luck on your assignment...
-5 x = 4 what property of equality was use to solve this equation
Answer:
Division property of equality.
simplify the expression into form a+bi, where rational numbers
(4-i)(-3+7i) - 7i(8+2i)
Answer:
-12+28i+3i-7i-65i+28
14 -41i
The organization that Jones works for is running for a father son dinner for those employees is invited to attend along with his youngest son. If Jones is known to have two children, what is the condition probability that they are both boys given that he is invited to the dinner?
Answer:
25%
Step-by-step explanation:
The probability of having a boy is 50%
To calculate the probability of him having 2 boys, multiply the probabilities together
0.5(0.5) = 0.25
will give brainliest help plz i can't get back on the password won't go to my email and my little brother changed the password I am scared I lost everything PLZ HELP ME
Need Help!!!! What is 1495486+73940426 Thanks!
Answer:
75435912
Step-by-step explanation:
1495486+73940426
= 75435912
Answer:
75,435,912
Step-by-step explanation:
=> 1495486 + 73940426
Using Calculator
=> 75,435,912
In the figure, a//b, and both lines are intersected by transversal t. Complete the statements to prove that m<1=m<5.
Answer:
Transitive Property of EqualityAlternate Interior Angles TheoremStep-by-step explanation:
a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.
__
b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.
Answer:
Step-by-step explanation:
which of the following descriptions represent the transformation shown in the image? Part 3c
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
I need help in this page
Step-by-step explanation:
a. 3.14 * 4² = 50.24 cm²
b. 16 cm
c. V = B * h = 50.24 * 16 = 803.84 cm²
How much time will it take Jenny to bike 15 miles if she bikes at a speed of 6 mph?
Answer:
this lesson, we will investigate the relationship between the distance traveled, the rate or speed or travel, and the time that it takes to travel that distance at that rate. We will also look at a few other related products.
Distance = (Rate)(Time)
The equation that relates distance, rate, and time is
d = rt
Where d is the distance traveled, r is the rate, and t is the time. On the CAHSEE exam, you will be given two of these and will be asked to use the above equation to find
took Markus half an hour to drive home from work. He averaged 34 miles per hour. How far does Markus live from his work?SolutionWe are given that it takes 1/2 an hour for the trip. This is a time: t = 1/2We are given that he averages 34 miles per hour. This is a rate: r = 34We are asked how few he has traveled. This is a distance. We use the d=rt equation: d = rt = (34)(1/2) = 17Answer:
2.5 hours
Step-by-step explanation:
First, try rewriting Jenny's speed in it's fraction form: 6 mi/hr
Next, use the units to set up an equation that relates Jenny's speed to the distance they want to travel. Let's call the unknown time t:
6mi/hr=15mi/t
1/t=6/15 (mi/hr•1/mi)
t=15/6 (hrs/mi•mi)= 15/6 (hrs•mi/mi)= 15/6 hrs
t=2.5hrs
So it'd take Jenny 2.5hrs at 6mph to go 15 miles. The key here is to keep track of the units. You can treat them like fractions and reduce them away as if they were numbers or variables.
Describe fully the single transformation that’s maps triangle A onto triangle B.
Answer:
reflection of the axis y=4
Step-by-step explanation:
becuase it is reflected on itself
Answer:
Reflect Triangle A by the line y = 4
Step-by-step explanation:
The answer is reflect Triangle A by y = 4 because the two triangles are symmetric.
The table represents an exponential function.
What is the multiplicative rate of change of the
function?
x
1
0 1 / 3
2
3
0 2 3
y
6
4
8
3
16
9
O 2
09
4.
Question Correction
The table represents an exponential function. What is the multiplicative rate of change of the function?
(A)1/3 (B)2/3 (C)2 (D)9
[tex]\left|\begin{array}{c|c}x&y\\--&--\\1&9\\2&6\\3&4\\4&\dfrac83\\\\5&\dfrac{16}{9}\end{array}\right|[/tex]
Answer:
(B) [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
An exponential function is a function of the form
[tex]y= a (b)^{x}[/tex]
where a is the initial value and b is the multiplicative rate of change
When x=2, y=6, we have:
[tex]6= a (b)^{2}[/tex]
When x=3, y=4, we have:
[tex]4= a (b)^{3}[/tex]
Dividing the two equations:
[tex]\dfrac{a (b)^{3}}{a (b)^{2}} =\dfrac{6}{9} \\b=\dfrac{6}{9}\\b=\dfrac{2}{3}[/tex]
The multiplicative rate of change, b is [tex]\dfrac{2}{3}[/tex].
The correct option is B.
Answer: It's B) 2/3
Hope it helps :3
Find the value of x
Answer:
8
Step-by-step explanation:
the value of x is 8 because the sides are the same
Val's whole-house central air conditioner uses 3,500 watts when running. Val runs the AC 6 hours per summer day. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
[You've posted your question under the wrong subject. Please try your best to post your questions under the right subject so that you get the required answer to your question.]
Answer:
11,340 cents
Step-by-step explanation:
• Step I)
Power of the air conditioning = 3500 W
Our first step to calculating energy consumption is:
Converting it into kilowatts:
1000 W = 1 kW
3500 W = 3.5 kW
• Step II)
Take the time the appliance was used, in hours:
Time is taken = 6 hours per day
For 30 days,
Time = 6 × 30
= 180 h
• Step III)
Calculate the energy consumption by multiplying the power rating of the appliance with the time it was used (in hours).
E = 3.5 kW × 180 h
= 630 kWh
• Step IV)
For billing the amount:
Multiply the energy consumed by the cost per kWh (often written as "unit")
Cost = 18 cents per kWh
Total cost = 18 × 630
= 11, 340 cents
Thus, his AC costs him 11, 340 cents.
A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: Aequals=4, Bequals=3, Cequals=2, Dequals=1, and Fequals=0. Compute the grade point average (GPA) and round the result to two decimal places.
Answer:
1.69Step-by-step explanation:
Let the five courses with their corresponding credit hours be represented as shown;
FST 201 = 4
FST 203 = 5
FST 112 = 1
FST 219 = 5
FST 223 = 4
If a student earned grades of B, B, A, C, and D respectively in those courses with the following grading system A =4, B =3, C =2, D =1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.
Credit point for each course = Number of credit hour * point for each grade
FST 201 = 4 * 4 = 16points (A)
FST 203 = 5 * 4 = 20points (A)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 4 = 20points (A)
FST 223 = 4 * 4 = 16points (A)
Total credit point = 16+20+4+20+16 = 76points
Total credit point gotten by the student is calculated as thus;
FST 201 = 4 * 3 = 12points (B)
FST 203 = 5 * 3 = 15points (B)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 2 = 10points (C)
FST 223 = 4 * 1 = 4points (D)
Total credit point gotten by the student = 45points.
student's Grade Point Average (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)
T or F? Is 3y=5x If x is 3 and y is 5?
Answer:
True
Step-by-step explanation:
3y=5x
Put x as 3 and y as 5.
3(5) = 5(3)
15 = 15
Hence, true.
Answer:
trueX=3
y=15
[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]
Proved.
Hope it helps..
The marketing research department of a computer company used a large city to test market the firm's new laptop. The department found the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by the following equation.
p= 1275 = 0.17x^2 0 < x < 80
So, weekly revenue can be approximated by the following equation.
R(x)= rp = 1275x- 0.17x^3 0 < x <80
Required:
a. Find the local extrema for the revenue function. What is/are the local maximum/a?
b. On which intervals is the graph of the revenue function concave upward?
c. On which intervals is the graph of the revenue function concave downward?
Answer:
a. Local maximum = 50 units per week.
b. The graph is never concave upward.
c. (0, 80)
Step-by-step explanation:
a. The revenue function is:
[tex]R(x) = 1275x-0.17x^3[/tex]
The derivate of the revenue function for which R'(x) = 0 gives us the local extrema:
[tex]R'(x) =0= 1275-0.51x^2\\x=\sqrt{2,500}\\x=50[/tex]
The second derivate of the revenue function determines if x =50 is local maximum or minimum:
[tex]R''(x) = -1.02x\\R''(50) = -1.02*50=-51\\[/tex]
Since the second derivate yields a negative value, x = 50 units per week is a local maximum.
b. Since there are no local minimums in the range of 0 < x < 80, the graph is never concave upward.
c. Since there is only one local maximum in the range of 0 < x < 80, the graph is concave downward from x>0 to x<80 or (0, 80)
Kajol has $75. This is 3/8 of the amount she earned. How much did she earn?
Answer:
$200
I hope this helps!
Answer:
200rupees
Step-by-step explanation:
according to the question ,kajol has 75 rupees
amount earned=3/8* amount earned
=75/3*8
=200 rupees
Which parent function is f(x) = x^2?
O A. An exponential parent function
OB. The linear parent function
C. The absolute value parent function
D. The quadratic parent function
Answer:
D. Quadratic parent function.
Step-by-step explanation:
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answer:
Answer is Y
Step-by-step explanation:
Write 6 17/20 as a decimal
Answer:
6.85
Step-by-step explanation:
6 17/20
Convert to improper fraction.
137/20
Divide.
= 6.85
Answer:
6.85
Step-by-step explanation:
17/20 = 85/100
17 x 5 = 85
20 x 5 = 100
so,
6 + 85/100 = 6.85
A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves.
One of the friends used the equation One-fourth (t + 34) = StartFraction 40 over 4 EndFraction to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?
Answer:
The individually paid $1.5 for the tip and $8.5 for the food
Step-by-step explanation:
Total money spent = $40
Food bill = $34
if the situation is represented by the equation [tex]\frac{1}{4}(t+34) = \frac{40}{4}[/tex] where t is the amount of the tip, the amount for the tip can be calculated as shown;
[tex]\frac{1}{4}(t+34) = \frac{40}{4}\\ t+34 = 40\\t = 40-34\\t = 6[/tex]
Amount of the tip = $6
If they decided to split the bill and tip evenly among themselves, amount paid by each friend for the food and the tip can be gotten using the equation representing the situation where t = $6 as shown;
[tex]= \frac{1}{4}(t+34) \\= \frac{1}{4}(6+34)\\= \frac{1}{4}(6)+\frac{1}{4}(34)\\= 1.5+8.5\\[/tex]
From the result above, it can be seen that each friend paid $1.5 for their tip and $8.5 for their food
Answer:
A) Each friend paid $8.50 for the food and $1.50 for the tip.
The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 95 grams of this substance. Construct an exponential model for the amount of the substance remaining on a given day. Use your model to determine how much of the substance will be left after 4 days
Answer:
Exponential model
Y = y0e-0.693(t½)
Amount remaining after 4 days
5.9413 grams
Step-by-step explanation:
The formula will he given by
Y = y0e-k(t½)
The half life t½ for this radioactive substance is a day.
Initial mass y0 = 95 grams
Mass after one day = 95/2
Mass after one day = 47.5
.
Value of the decay constant k is not given, let's look for k.
Y = y0e-k(t½)
47.5= 95e-k(1)
47.5/95= e-k(1)
0.5= e-k(1)
In 0.5 = -k
-0.693= -k
0.693 = k
Y = y0e-0.693(t½)
Amount remaining after 4 days
Y = y0e-0.693(t½)
Y = 95e-0.693(4)
Y= 95e-2.772
Y= 95(0.06254)
Y= 5.9413 grams
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
4) →BRAINLIEST & 10+ POINTS! ← A wheel with diameter 44 cm completes four revolutions in 0.5 seconds. Find the linear speed of the edge of the wheel in cm per second. ⇒Round to the nearest whole number. Linear speed = ____ cm/s
Answer:
352 cm/s
Step-by-step explanation:
circ = 44pi
speed = distance * time
distance = circ * 4 = 176pi
speed = 176pi/0.5
Answer:
≈ 1106 cm/s
Step-by-step explanation:
linear speed = angular speed x radius of the rotation
v = ωr
v = linear speed (m/s)
ω = angular speed (radians/s)
r = radius of the rotation (m)
------------
Given:
d= 44 cm ⇒ r= 44/2 cm= 22 cmω= 4 rev/0.5 s= 8 rev/s= 8*2π/s= 16π/s (converted rev to radians)Linear speed is:
v= 22*16π cm/s ≈ 1106 cm/s (rounded to full number)5x is equal to 8X raise to power - 1/3
Answer:
No solutions.
Step-by-step explanation:
5x = 8x^-1/3
Divide 8 into both sides.
5/8x = x^-1/3
Divide both sides by x.
5/8 = x^-4/3
Multiply both sides by the exponent -3/4.
5/8^-3/4 = x
1.422624 = x
Plug in 1.422624 for x to check.
It does not work. There are no real solutions.
1. How many mL of 70% and 40% alcohol elixirs
should be mixed to prepare 300 mL of 60%
alcohol?
Answer:
that they are 200 mL of 70% and 100 mL of 40%
Step-by-step explanation:
We have to build a 2x2 system of equations with the information from the statement as follows:
0.70 * x + 0.4 * y = 300 * 0.6
x + y = 300 => x = 300 - y
where x is elixir 1 (70%) and y elixir 2 (40%).
replacing we have:
0.70 * (300 - y) + 0.4 * y = 300 * 0.6
210 * - 0.7 * y + 0.4 * y = 180
-0.3 * y = 180 - 210
y = -30 / -0.3
y = 100
now for x:
x = 300 - 100
x = 200
Which means that they are 200 mL of 70% and 100 mL of 40%
How many gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze? Use the six step method.
Answer:
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
Step-by-step explanation:
Let x represent the number of gallons of the 50% antifreeze solution.
The volume of the 10% antifreeze is = 90 gallons
The volume of the mixture that is 40% antifreeze = 90+x
The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;
50% of x + 10% of 90 = 40% of (90+x)
0.50(x) + 0.10(90) = 0.40(90+x)
0.50x + 9 = 36 + 0.40x
Collecting the like terms;
0.50x - 0.40x = 36-9
0.10x = 27
x = 27/0.10
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
There are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answer: a. 1320
b.495
Step-by-step explanation:
Complete question is provided in the attachment.
Total members on the board = 12
a. Persons to chose : chairperson, first vice chairperson, second vice chairperson, and secretary
i.e. Total 3 posts in an order.
Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex] [By permutation]
[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]
hence, 1320 different slates of candidates are possible .
b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]
[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]
Hence, the number of different subcommittees are possible =495