Answer:
42 mph
Step-by-step explanation:
If you start with the assumption that the answer is an integer, you can solve a problem like this by looking at the factors of 294.
294 = 2·3·7² = 6·49 = 7·42
At 42 mph, the 294-mile trip took ...
time = distance/speed = 294 mi/(42 mi/h) = 7 h
At a speed 7 mph faster, the 294-mile trip took ...
(294 mi)/(49 mi/h) = 6 h . . . . . 1 hour less
The average speed of Imogene's car for the 294-mile trip was 42 miles per hour.
_____
Alternative solution
If you let s represent Imogene's speed, you can use the above time and distance relationship to write an equation relating the trip times:
294/s = 294/(s+7) +1
Multiplying by s(s+7), we get ...
294(s+7) = 294s +s(s+7)
2058 = s^2 +7s . . . . . . . . . . . subtract 294s
We can complete the square by adding (7/2)^2 = 12.25 to both sides
2070.25 = s^2 +7s +12.25 = (s +3.5)^2
±45.5 = s +3.5 . . . . . take the square root; next subtract 3.5
-3.5 +45.5 = s = 42 . . . . use the positive solution
Imogene's average speed was 42 mph.
Imogene's average speed was 294 mph. We solve this by using the relationship between distance, speed, and time, and applying it to the specific constraints of the problem. By setting s = speed, we use two equations representing each scenario and solve for s.
Explanation:Let's assign 's' to Imogene's average speed for the trip. The time taken at this speed is the distance traveled (294 mi) divided by 's' (speed = distance/time), making the time = 294/s. If the car was faster by 7 mph, the speed would be s+7 mph, and the time taken would then be 294/(s+7). The problem states that the second scenario would take 1 hour less, so 294/s = 294/(s+7) + 1.
Cross-multiplication and simplification of this equation result in (294s + 2058) = 294(s +7) or 294s + 2058 = 294s + 2058, which simplifies to 2058 = 7s, or s = 294 mph. Therefore, Imogene's average speed was 294 mph.
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The Simmons family and the Wright family each used their sprinklers last summer. The water output rate for the Simmons family's sprinkler was 20l per hour. The water output rate for the Wright family's sprinkler was 35l per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output 1475l of . How long was each sprinkler used?
Answer:
y=25 and x=30.
Step-by-step explanation:
See picture
Answer:the number of hours that the Simmons family used their sprinklers last summer is 30
the number of hours that the Wright family used their sprinklers last summer is 25
Step-by-step explanation:
Let x represent the number of hours that the Simmons family used their sprinklers last summer.
Let y represent the number of hours that the Wright family used their sprinklers last summer.
The families used their sprinklers for a combined total of 55 hours, it means that
x + y = 55
The water output rate for the Simmons family's sprinkler was 20l per hour. The water output rate for the Wright family's sprinkler was 35l per hour. The total water output was 1475l. It means that
20x + 35y = 1475 - - - - - - - - - - 1
Substituting x = 55 - y into equation 1, it becomes
20(55 - y) + 35y = 1475
1100 - 20y + 35y = 1475
- 20y + 35y = 1475 - 1100
15y = 375
y = 375/15 = 25
x = 55 - y = 55 - 25
x = 30
If it takes 6 printing presses 4 hours to print 5000 newspapers, how long should it take 3 presses to print 3000 newspapers?
Answer:
4 hrs 48 min
Step-by-step explanation:
It takes 6 presses 4 * 3/5 = 12/5 hours to print 3000 newspapers.
It takes 3 presses 2 * 12/5 = 24/5 hours = 4h48min to print 3000 newpapers
A commercial jet and a private airplane flu from Denver to Phoenix. It takes the commercial jet 1.1 hours for the flight, and it takes the private plane 1.8 hours. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane
Answer: the speed of the commercial jet is 540 mph
the speed of the private airplane is 330 mph
Step-by-step explanation:
Let x represent the speed of the commercial jet and
Let y represent the speed of the private airplane.
It takes the commercial jet 1.1 hours for the flight from Denver to Phoenix.
Distance = speed × time
Therefore, distance covered by the commercial jet from Denver to Phoenix would be
1.1 × x = 1.1x
it takes the private airplane 1.8 hours to cover the same distance. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane. It means that
y = x - 210
Distance covered by the private airplane would be
1.8(x - 210) = 1.8x - 378
Since the distance is the same, then
1.8x - 378 = 1.1x
1.8x - 1.1x = 378
0.7x = 378
x = 378/0.7 = 540
y = x - 210 = 540 - 210
y = 330
To find the speeds of a commercial jet and a private airplane, we can set up and solve an equation using the distance and time information provided in the question.
Explanation:The question is about the speeds of a commercial jet and a private airplane flying from Denver to Phoenix. Let's assume the speed of the private airplane is 'x' miles per hour. According to the question, the commercial jet is 210 miles per hour faster than the private airplane. So, the speed of the commercial jet is 'x + 210' miles per hour.
Now, we have the speeds of both planes. We can use the formula 'speed = distance / time' to calculate the distance. Since the time for the commercial jet is 1.1 hours and the time for the private airplane is 1.8 hours, the distances traveled by the commercial jet and the private airplane are '1.1(x + 210)' and '1.8x' miles, respectively.
Since both planes are traveling the same distance, we can set up the equation '1.1(x + 210) = 1.8x' to find the value of 'x'. Solving this equation will give us the speed of the private airplane. Once we have the speed of the private airplane, we can calculate the speed of the commercial jet by adding 210 to it.
VDG~VNQ what is the value of x?
Answer:
x= 8
Step-by-step explanation:
60/48=1.25
15/1.25= 12
12-4=8
[tex]-1*f(-8)-4*g(4) =?[/tex]
Answer:
-7
Step-by-step explanation:
From the graph (see attached), we can read off the values of f(-8) and f(4)
when x = -8, y = f(-8) = -5
when x = 4, y = g(4) = 3
hence, substituting the above values into the given equation:
-1 * f(-8) - 4 * g(4)
= -1 * (-5) - 4 * 3
= 5 - 12
= -7
Can someone help explain this, please?
OP=
4
6
8
Answer:
6
Step-by-step explanation:
jus did it
If the parent function is y = 1/x, describe the change in the equation y = - 1/x-1 - 10
A. Reflected across the x-axis, moves 1 unit to the right, and 10 units up.
B. Moves 1 unit to the right and 10 units down.
C. Reflected across the x-axis, moves 1 unit to the right, and 10 units down.
D. Reflected across the x-axis, moves 1 unit to the left, and 10 units down.
Answer:
C
Step-by-step explanation:
Firstly, we have 1/x as the parent function. 1/x-1 describes the graph of 1/x to shift 1 unit right. -1/x-1, states that it is reflected across the x-axis. And -1/x-1 -10 states that it is shifted 10 units down.
Fastest answer gets brainlyest!
Which exponential expression represents the numerical expression
3 · 3 · 3 · 3 ?
(112)3
(12)3
(3)4
4
Answer:
(3)4
Step-by-step explanation:
3 x 3 x 3 x 3 can also be written as (3)4 or 3 to the 4th power
4x + y = 3 -2x + 3y = -19 what's the solution plz help
The solution to given system of equations is x = 2 and y = -5
Solution:
Given the system of equations are:
4x + y = 3 ---------- eqn 1
-2x + 3y = -19 ---------- eqn 2
We have to find the solution to above system of equations
We can solve the system by substitution method
From eqn 1,
4x + y = 3
Isolate y to one side
y = 3 - 4x ----------- eqn 3
Substitute eqn 3 in eqn 2
-2x + 3(3 - 4x) = -19
-2x + 9 - 12x = -19
Combine the like terms
-14x = -19 - 9
-14x = -28
Divide both sides of equation by -14
x = 2Substitute x = 2 in eqn 3
y = 3 - 4(2)
y = 3 - 8
y = -5Thus the solution is x = 2 and y = -5
Consider the linearization, L(x) of the curve y = x at (36, 6). What are the least and greatest values of x for which this linearization is within 0.1 of the true value of the curve?
On a certain airline, customers are assigned a row number when they purchase their ticket, but the four seats within the row are first come, first served during boarding. If Karen and Georgia end up with random seats in the same row on a sold-out flight, what is the probability that they sit next to each other?
Answer:
The probability that they sit next to each other is 50%.
Step-by-step explanation:
Consider the provided information.
It is given that there are four seats within the row are first come, first served during boarding.
There are 4 seats and 2 customers (Karen and Georgia)
The total number of ways in which Karen and Georgia can sit is: [tex]^4C_2[/tex]
Now if they will sit together, then consider Karen and Georgia as a single unit.
Thus, the number of ways in which they can sit together is: [tex]^3C_1[/tex]
The required probability is:
[tex]P=\frac{^3C_1}{^4C_2} \\\\P=\frac{3}{6}\\\\P=\frac{1}{2}[/tex]
Hence, the probability that they sit next to each other is 50%.
Ms.Shrewsberry gave out a quiz to all 132 of her students. Of all of the students that took the quiz 3/11 of received an A as a grade. How many students got an A?
Answer:
36 students got an'A' grade in the quiz.
Step-by-step explanation:
Given:
Total number of students taking the quiz = 132
Fraction of students getting an 'A' grade = [tex]\frac{3}{11}[/tex]
To find the number of students getting an 'A' grade.
Solution:
In order to find the number of students who got an 'A' grade in the quiz, we will find the fractional part who got an 'A' of the total students taking the quiz.
The fraction of students getting an 'A' is = [tex]\frac{3}{11}[/tex]
Thus, total number of student getting an 'A' is :
⇒ [tex]\frac{3}{11}[/tex] of [tex]132[/tex]
⇒ [tex]\frac{3}{11}\times 132[/tex]
⇒ [tex]\frac{396}{11}[/tex]
⇒ 36 (Answer)
if u answer i will give u brainliest. :)
Answer:
A
Step-by-step explanation:
Answer:
ima need that brainliest dawg the answer a
Step-by-step explanation:
A chemist has 3 and one half mililiters of ammonia in beaker X 0.2 mililiters of ammonia in beaker Y expressed as a mixed number how many mililiters of ammonia does the chemist have all together
Answer:
Molarity is the concentration of x moles of solute in 1 L of solution. ... have different properties i.e., a low molarity acid and high molarity acid can ... For example, a 0.25 mol/L NaOH solution contains 0.25 mol of sodium hydroxide in every litre of solution ... 15.0 g of NaOH in enough water to make a total of 225 mL of solution
Step-by-step explanation:
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers?
a) 72% is a sample; 56% is a population.b) 72% and 56% are both statistics.c) 72% is a statistic and 56% is a parameter.d) 72% is a parameter and 56% is a statistic.e) 72% and 56% are both parameters.
Answer:
c) 72% is a statistic and 56% is a parameter.
Step-by-step explanation:
Previous concepts
A statistic or sample statistic "is any quantity computed from values in a sample", for example the sample mean, sample proportion and standard deviation
A parameter is "any numerical quantity that characterizes a given population or some aspect of it".
Solution to the problem
For this case we know that they select a sample of 663 registered voters and the sample proportion from these registered voters is:
[tex] \hat p = 0.72[/tex] representing the sample proportion of people who voted in the election
They info that they have is that the true proportion before is [tex] p =0.52[/tex] and that represent a value related to the population.
So on this case the 0.72 represent a statistic since represent the sample and the 0.52 is a value who represent the population for this case is a parameter.
So the correct option is:
c) 72% is a statistic and 56% is a parameter.
Solve the following equation for q. 5q - 4p + 6 = 4q – 8.
Answer:
[tex]q=4p-14[/tex]
Step-by-step explanation:
The first step in solving
[tex]5q-4p+6=4q-8[/tex]
is to bring [tex]4q[/tex] on the right the left side to the right side by subtracting it from both sides:
[tex](5q-4p+6)-4q=(4q-8)-4q\\\\(5q-4q)-4p+6=-8\\q-4p+6=-8[/tex]
and we subtract 6 from both sides and get:
[tex]q-4p=-14[/tex]
finally we add [tex]4p[/tex] to both sides and get:
[tex]q-4p+4p=-14+4p[/tex]
[tex]\boxed{q=4p-14}[/tex]
Mark retired from competitive athletics last year. In his career as a sprinter he had competed in the 100-meters event a total of 328 times. His average time for these 328 races was 10.23 seconds. The value 10.23 in this sentence is a?
Answer:
time
Step-by-step explanation:
A car and truck are 540 miles apart. The two vehicles start driving toward Each other at the same time. The car drives at a speed of 65 miles per hour, and the truck travels at a speed of 55 miles per hour. At which point will they both meet.
Answer:they would meet after 4.5 hours
Step-by-step explanation:
At the point where they will both meet, they would have covered a total distance of 540 miles.
Let t represent the time it will take the car and the truck to meet.
Distance = speed × time
The car drives at a speed of 65 miles per hour. Distance covered by the car in t hours would be
65 × t = 65t
The truck travels at a speed of 55 miles per hour.
Distance covered by the truck in t hours would be
55 × t = 55t
Therefore,. 65t + 55t = 540
120t = 540
t = 540/120 = 4.5 hours
The scatter plot below shows the number of prom tickets sold over a period of 7 days. The line of best fit drawn on the plot shown is used to predict the number of tickets sold on a certain day. Use the two points shown on the line of best fit to calculate its slope to the nearest tenth.
Answer:
The slope is [tex]4.2\ \frac{tickets}{day}[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
Let
x ----> the number of days
y ---> the number of tickets sold
we have the points
(1,30) and (7,55)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the given values in the formula
[tex]m=\frac{55-30}{7-1}[/tex]
[tex]m=\frac{25}{6}[/tex]
[tex]m=4.2\ \frac{tickets}{day}[/tex]
On a number line, Karlie has to divide the space between —5 and —3 into five smaller, equal spaces. On what numbers does Karlie have to place the four marks to create the five spaces?
Answer:
{-4.6, -4.2, -3.8, -3.4}
Step-by-step explanation:
The length of the space Karlie is dividing is -3-(-5) = 2 units. Then the length of each of those equal 5 spaces will be 2/5 units = 0.4 units.
Each mark on the number line is 0.4 units to the right of the previous one. The first (left-most) mark is 0.4 units to the right of -5, so is at -5+0.4 = -4.6.
The marks have to be placed at -4.6, -4.2, -3.8, and -3.4.
You want to buy an item with an original price of $75. If there is a 30% discount, how much can you deduct from the original price?
In order to find 30% of 75, we simply calculate 75 x 0.3.
75 x 0.3 amounts to 22.5, which is the amount we deduct.
This leaves a final price of $52.50.
A 30% discount on an item priced at $75 results in a deduction of $22.5.
Explanation:The student's question is about calculating a discount on an item. Here, the discount is a 30% decrease or reduction off the original price of the item, which is $75. To calculate the discount, you multiply the original price by the percentage discount. Remember, since percentage is a proportion, you'll need to convert the percentage to a decimal first by dividing it by 100. Therefore, the formula will be:
Discount = Original Price x Percentage Discount
Substituting in the given values:
Discount = $75 x 30/100 = $22.5
So, with the 30% discount, you can deduct $22.5 from the original price of the item.
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Which equation represents the graph shown?
y = 2x + 2
y = 2x
y = 2x + 3
y = 2x + 1
8.) Simplify.
cot^2 0 - cot ^2 0 cos ^2 0
A.) tan^2 0
B.) -1
C.) 3
D.) sin ^2 0
E.) cos^2 0
Answer:
The answer to your question is letter E. cos²α
Step-by-step explanation:
cot²Ф - cot²Фcos²Ф
Remember that cot = [tex]\frac{cos \alpha}{sin \alpha }[/tex] ; substitute in the previous equation
[tex]\frac{cos^{2}\alpha }{sin^{2} \alpha} - \frac{cos^{2}\alpha }{sin^{2}\alpha } cos^{2}\alpha[/tex]
[tex]\frac{cos^{2}\alpha - cos^{4}\alpha }{sin^{2}\alpha }[/tex] Factor cos²α
[tex]\frac{cos^{2}\alpha(1 - cos^{2}\alpha }{sin^{2}\alpha }[/tex]
Remember that sin²α = 1 - cos²α
[tex]\frac{cos^{2}\alpha sin^{2}\alpha}{sin^{2} \alpha}[/tex]
Simplify
cos²α
The fish store is filling their 5 1/2 gallon tanks for a speacial fish display.They have filled 4 1/2 tanks so far.How many gallons of water have they used?
Answer:
2 1/4 gallons
Step-by-step explanation:
We assume your problem is intended to say there are five tanks, each having a volume of 1/2 gallon, and that 4.5 of these have been filled so far.
The volume of water used is ...
(4.5 tanks)(0.5 gal/tank) = 2.25 gal
2.25 gallons of water have been used.
A chemist has two brine solutions, one containing 4% salt and the other containing 30% salt. How many gallons of each solution should she mix to obtain 45 gallons of a solution that contains 18.4% salt?
Answer:
Number of gallons of 4% salt solution in the mixture = 20.08
Number of gallons of 30% salt solution in the mixture = 24.92
Step-by-step explanation:
Given:
There are two bottles of brine solution:
1 has 4% salt
2 has 30% salt
The chemist mixes some gallons of each bottle to get a 45 gallons solution containing 18.4% salt.
To find the gallons of each solution taken to make the mixture.
Solution:
Let the number of gallons of 4% salt solution mixed be = [tex]x[/tex]
So, number of gallons of 30% salt solution mixed will be = [tex]45-x[/tex]
Amount of salt in [tex]x[/tex] gallons of 4% salt solution will be :
⇒ Percentage concentration x Gallons of solution
⇒ [tex]0.04\times x[/tex]
⇒ [tex]0.04x[/tex]
Amount of salt in [tex](45-x)[/tex] gallons of 30%% salt solution will be :
⇒ Percentage concentration x Gallons of solution
⇒ [tex]0.3\times (45-x)[/tex]
Using distribution
⇒ [tex]13.5-0.3x[/tex]
Total amount of salt in 45 gallons of solution can be given as:
⇒ [tex]0.04x+13.5-0.3x[/tex]
Combining like terms
⇒ [tex]-0.26x+13.5[/tex]
Amount of salt in 45 gallons of 18.4% solution:
⇒ [tex]0.184\times 45[/tex]
⇒ [tex]8.28[/tex]
Thus, we have:
[tex]-0.26x+13.5=8.28[/tex]
Subtracting both sides by 13.5
[tex]-0.26x+13.5-13.5=8.28-13.5[/tex]
[tex]-0.26x=-5.22[/tex]
Dividing both sides by -0.26.
[tex]\frac{-0.26x}{-0.26}=\frac{-5.22}{-0.26}[/tex]
∴ [tex]x=20.08[/tex]
Number of gallons of 4% salt solution in the mixture = 20.08
Number of gallons of 30% salt solution in the mixture = [tex]45-20.08[/tex] = 24.92
Consider the following conditional statement. Rewrite the statement in if-then form, and then write the converse, inverse Converse contrapositive, and biconditional.
Right angles are 90°
If-then:
Converse:
Inverse:
Contrapositve:
Biconditional:
Final answer:
To rewrite a conditional statement in if-then form, use the example given. The converse, inverse, contrapositive, and biconditional can be formed by changing the order and negating the original statement in different ways.
Explanation:
To rewrite the conditional statement 'Right angles are 90°' in if-then form, we can state: 'If an angle is a right angle, then it measures 90°.'
The converse of the conditional statement is: 'If an angle measures 90°, then it is a right angle.'
The inverse of the conditional statement is: 'If an angle is not a right angle, then it does not measure 90°.'
The contrapositive of the conditional statement is: 'If an angle does not measure 90°, then it is not a right angle.'
The biconditional statement is: 'An angle is a right angle if and only if it measures 90°.'
If 8 identical blackboards are to be divided among 4 schools,how many divisions are possible? How many, if each school mustreceive at least 1 blackboard?
Response:
if8 boards are to be distributed then the number of ways can be8C4=70
and if every school must get atlest one board then it is possiblein 70-14 ways = 56 ways..
let abcd be the schools
a b c d
0 0 0 8 4C1= 4 (three schools dont get even1 board)
0 0 1 7 4C2= 6 (two schools dont get even 1board)
0 1 1 6 4C3 =4
hence 6+4+4=14.
Answer:
There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.
Step-by-step explanation:
Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.
The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is [tex] {11 \choose 3} = 165 . [/tex] As a result, we have 165 ways to distribute the blackboards.
If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is [tex] {7 \choose 3} = 35 [/tex]. Thus, there are only 35 ways to distribute the blackboards in this case.
If 8 identical blackboards are to be divided among 4 schools, there are 70 possible divisions. If each school must receive at least 1 blackboard, there are 56 possible divisions.
Explanation:If 8 identical blackboards are to be divided among 4 schools, the number of ways this can be done is 8C4, which is equal to 70.
If each school must receive at least 1 blackboard, then we need to subtract the cases where one or more schools do not receive a blackboard.
To calculate this, we can subtract the number of ways that three schools do not receive a blackboard (4C1 = 4), the number of ways that two schools do not receive a blackboard (4C2 = 6), and the number of ways that only one school does not receive a blackboard (4C3 = 4).
So, the number of divisions where each school receives at least 1 blackboard is 70 - 4 - 6 - 4 = 56 ways.
You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units. You need to cut a slice off the top of the block to decrease the height by 2 units. Th e new block will have a volume of 480 cubic units. a. What are the dimensions of the new block?
Answer:
[tex]Depth = x= 4 units[/tex]
[tex]length = 5x= 5(4)= 20 \ units[/tex]
[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]
Step-by-step explanation:
You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units.
height is decreased by 2 units , so height becomes 2x-2
Volume of a block is length times width time height
[tex]volume = x \cdot 5x \cdot (2x-2)[/tex]
[tex]480 = 10x^3-10x^2[/tex]
divide whole equation by 10
[tex]48= x^3-x^2[/tex]
Subtract 48 from both sides
[tex]x^3-x^2-48=0[/tex]
[tex]\left(x-4\right)\left(x^2+3x+12\right)=0[/tex]
[tex]x-4=0[/tex], x=4
[tex]Depth = x= 4 units[/tex]
[tex]length = 5x= 5(4)= 20 \ units[/tex]
[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]
bob buys 100 candy bars at the store bob eats 47 of the candy bars
what does bob have left now
Answer:
Bob now has 53 candy bars.
Step-by-step explanation:
: )
Answer:
53 bars
Step-by-step explanation:
100-47=53
The length of a football field is x. The width of the field is 70 yards less than the length. Write an expression that represents the perimeter of the field without parentheses.
Answer: the expression representing the perimeter of the field is 4x + 280
Step-by-step explanation:
The perimeter of a figure is the distance around it.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
The length of a football field is x. The width of the field is 70 yards less than the length. This means that the width of the football field is x - 70 yards.
an expression that represents the perimeter of the field without parentheses would be
Perimeter = 2(x + x- 70) = 2(2x + 70)
= 4x + 280