The car will travel 800 kilometers in 5 hours.
What is the unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given
1 mile = 1.6 km
100 mile = 1.6 * 100 = 160 km
in 1 hr car travels 160 km
in 5 hrs car travels = 160 * 5 = 800 km
The car will travel 800 kilometers in 5 hours.
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In 5 hours, the car will travel 800 kilometers.
To convert the car's speed from miles per hour to kilometers per hour, you multiply by the conversion factor of 1.6 kilometers per 1 mile. Therefore, a speed of 100 miles per hour is equivalent to 100 × 1.6 = 160 kilometers per hour.
Next, to calculate how many kilometers the car will travel in 5 hours at the speed of 160 kilometers per hour, you simply multiply the speed by the time. The car will travel 160 km/h × 5 h = 800 kilometers in 5 hours.
Megan drove from her house to work at an average speed of 45 miles per hour. The drive took her
20 minutes. If the drive home took her 30 minutes and she used the same route in reverse, what was her average speed going home?
Question 10 options:
30 miles per hour
13.33 miles per hour
26.6 miles per hour
3 miles per hour
Answer:
30 mph
Step-by-step explanation:
The average speed = Total distance / Total Time
Distance at 45 m/hr.
t = 20 minutes = 20/60 = 1/3 hour.
r = rate = 45 miles / hour
d = r * t
d = 45 * 1/3 = 15 miles.
Average Speed going home.
t = 30 minutes
t = 30 min / 60 min // hour = 1/2 hours
r = 15 miles / 1/2 = 15 * 2 = 30 miles / hr.
Please help lol, I have 1 question left after this one
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 9 and d = - 2, hence
[tex]a_{n}[/tex] = 9 -2(n - 1) = 9 - 2n + 2 = - 2n + 11
[tex]a_{n}[/tex] = - 2n + 11 ← n th term formula
A copy machine at your school can print 80 sheets per minute. How long will it take your teacher to print 6,000 pages?
1 hour
1.25 hours
1.5 hours
1.75 hours
Answer: it will take 1.25 hours
Step-by-step explanation:
It
It will take the teacher 1.25 hours to print 6,000 pages.
To calculate how long it will take to print 6,000 pages with a copy machine that can print 80 sheets per minute, we need to divide the total number of pages by the rate of printing per minute to find out the time in minutes, and then convert that time into hours if necessary.
Step 1: Divide the total number of pages by the printing speed to find the time in minutes.
Total pages: 6,000
Printing speed: 80 pages/minute
Time calculation: 6,000 pages divided by 80 pages/minute = 75 minutes
Step 2: Convert minutes into hours by dividing by 60 since there are 60 minutes in an hour.
Conversion to hours: 75 minutes divided by 60 minutes/hour = 1.25 hours
Therefore, it will take the teacher 1.25 hours to print 6,000 pages.
write the quadratic equation whose roots are -4 and 6 and whose leading coefficient is 3
Answer:
y = 3x² - 6x - 72
Step-by-step explanation:
Since the roots are x = - 4 and x = 6 then the factors are
(x + 4) and (x - 6) and the quadratic function is
y = a(x + 4)(x - 6) ← a is a multiplier, in this case 3, so
y = 3(x + 4)(x - 6) ← expand factors and distribute by 3
y = 3(x² - 2x - 24)
y = 3x² - 6x - 72
3x²-6x-72. The quadratic equation whose roots are -4 and 6 with a leading coefficient of 3 is 3x²-6x-72.
The solutions of a quadratic equation are x = -4 and x = 6 with a leading coefficient of 3. The solutions are two real numbers which means that (x + 4) and (x - 6) are the factors of our unknown quadratic equation and the leading coefficient is 3.
[tex]3(x+4)(x-6)=0[/tex]
Expand (x+4)(x-6):
[tex]3(x^{2} -2x-24)=0\\3x^{2} -6x-72=0[/tex] which is our quadratic equation.
Total profit is defined as total revenue, R(x), minus total cost, C(x), and is given by the function P(x) = R(x) - C(x). Given R(x) = 58x -0.4x^2and C(x) = 2x + 14, find each
of the following.
a) P(x)
b) R(80), C(80), and P(80)
P(x)=
(Type in descending powers of x.)
[tex]\bf \begin{cases} R(x)=58x-0.4x^2\\ C(x)=2x+14 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ P(x)\implies \stackrel{revenue}{R(x)}-\stackrel{costs}{C(x)}\implies (58x-0.4x^2)-(2x+14) \\\\\\ (58x-0.4x^2)-2x-14\implies 58x-0.4x^2-2x-14 \\\\\\ 56x-0.4x^2-14\implies \boxed{-0.4x^2+56x-14} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf R(80)\implies 58(80)-0.4(80)^2\implies R(80)=4640-2560\implies \boxed{R(80)=2080} \\\\[-0.35em] ~\dotfill\\\\ C(80)=2(80)+14\implies C(80)=160+14\implies \boxed{C(80)=174} \\\\[-0.35em] ~\dotfill\\\\ P(80)=-0.4(80)^2+56(80)-14 \\\\\\ P(80)=-2560+4480-14\implies \boxed{P(80)=1906}[/tex]
The profit function P(x) is 56x - 0.4x² - 14. When we plug x=80 into the equations, we find that R(80) = 3680, C(80) = 174, and P(80) = 3506.
Explanation:To solve the student's question, firstly we use the provided data. The profit function P(x) can be expressed as the difference between the revenue function R(x) and the cost function C(x).
To find P(x), we subtract the equation for C(x) from the equation for R(x). So, P(x) = R(x) - C(x) = (58x - 0.4x²) - (2x + 14) = 56x - 0.4x² - 14.
To answer the second part of the question, we substitute x=80 into the equations for R, C, and P.
Therefore R(80) = 58×80 - 0.4×80² = 3680, C(80) = 2×80 + 14 = 174, and P(80) = 56×80 - 0.4×80² - 14 = 3506.
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Please someone hurry.
Answer:
b
Step-by-step explanation:
Point O is the center of the circle. What is the value of x?
Hello!
I want to help you but where is the image or answer choices? Thanks for asking— I’ll help if a I have the answer options or a photo because the question can’t be answered as there would be an infinite possible choices. It’d be great help! Thanks!
Have a great day!
~ Destiny ^_^
Answer:
24
Step-by-step explanation:
If its the figure shown, the answer is 24.
A cube with side lengths measuring 4 inches. The cube was sliced parallel to the base. Identify the cross-section and calculate its area.
Answer:
The resulting cross section is a square an the area is [tex]A=16\ in^{2}[/tex]
Step-by-step explanation:
we know that
All the faces of the cube are square with side lengths measuring 4 inches
If the cube was sliced parallel to the base
then
the cross section is a square with side lengths measuring 4 inches
so
The area of a square is
[tex]A=b^{2}[/tex]
we have
[tex]b=4\ in[/tex]
substitute
[tex]A=4^{2}[/tex]
[tex]A=16\ in^{2}[/tex]
what is the independent variable?
a. bike A
b. bike B
c. time
d. distance
Answer:
c. time
Step-by-step explanation:
time is always the independent variable because you can't control it
The independent variable among the option is time.
What is an independent variables?An independent variable is defines as the variable that is changed or controlled in a scientific experiment.
Independent variables are stand alone variables. They are not dependent on any other variables.
Therefore, time is usually controlled in any experiment. Therefore, time is the independent variables among the option.
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Complete the synthetic division problem below.
Answer:
B is the correct answer.
Step-by-step explanation:
Apex
Answer:
Quotient: [tex]2x^2-2x+2[/tex]
B is correct
Step-by-step explanation:
Given: The format of synthetic division.
We take first number at bottom row and multiply with -3, write the result below second number (4) and then simplify (4-6=-2)
Repeat the process at end.
At last we get 0 (Remainder)
Last number of last row shows remainder and rest are coefficient of quotient.
Synthetic Division: Please find attachment.
-3 | 2 4 -4 6 |
-6 6 -6
2 -2 2 0
last row : 2 -2 2
Initially we had 4 terms ( three degree polynomial)
Quotient must have two degree polynomial.
Quotient: [tex]2x^2-2x+2[/tex]
Find the reciprocal of 5/7
Answer:
7/5
Step-by-step explanation:
reciprocal means flip the equation
The answer is 7/5.
Hope this helps!
What is the interquartile range of the following data set? 5, 6, 7, 3, 4, 5, 6, 8, 7
Answer:
2.5
Step-by-step explanation:
lower quartile.
3, 4, 5, 5, 6, 6, 7, 7, 8
median = 6
lower quartile 1/4th position
(4+5)/2 = 4.5
Upper quartile 3/4th position
(7+7)/2 = 7
Interquartile range = upper quartile - lower quartile
= 7 - 4.5
= 2.5
Answer:
Interquartile range = Q3 - Q1 = 7 - 4.5 = 2.5
Step-by-step explanation:
Before we calculate interquartile range, you should understand that:
Interquartile range is the range between Q3 and Q1 of a dataset i.e Q3 - Q1
Where,
Q1 is the middle value in the first half of the data set and
Q3 is the middle value in the second half of the data set.
So to calculate the interquartile range we find the Q3 and Q1
5, 6, 7, 3, 4, 5, 6, 8, 7
So in the data set to find Q1 and Q3, we rearrange the dataset and divide it into First half and second half.
3, 4, 5, 5, 6, 6, 7, 7, 8
First half = 3, 4, 5, 5
Second half = 6, 7, 7, 8
So
Q1 = (4+5)/2 = 4.5
Q3 = (7+7)/2 = 7
Interquartile range = Q3 - Q1 = 7 - 4.5 = 2.5
simplify with foil (w + x )(w + x )
Foil is an acronym that stands for:
First
Outside
Inside
Last
First:
(w + x )(w + x ) = [tex]w^{2}[/tex]
Outside:
(w + x )(w + x ) = wx
Inside:
(w + x )(w + x ) = wx
Last:
(w + x )(w + x ) = [tex]x^{2}[/tex]
so...
[tex]w^{2}[/tex] + wx + wx + [tex]x^{2}[/tex]
[tex]w^{2} +x^{2} + 2xw[/tex]
Hope this helped!
Answer: [tex]x^2+2wx+w^2[/tex]
Step-by-step explanation:
Given the expression [tex](w + x )(w + x )[/tex] , which indicates the multiplication of two binomials, you can simplify it with FOIL:
Multiply:
The first terms (w by w).
The outside terms (w by x).
The inside terms together (x by w).
The last terms together (x by x).
Then, you get:
[tex](w + x )(w + x )=(w)(w)+(w)(x)+(x)(w)+(x)(x)=w^2+wx+wx+x^2[/tex]
Adding like terms, you get:
[tex]x^2+2wx+w^2[/tex]
Please help me with the process to find the answer for #15, #16, #17 and #18
Thank you it’s very much appreciated! :)
Well I wanna do you want us to pick you guys up tomorrow at night to
Annette has a credit card that uses the previous balance method. The
opening balance of one of her 30-day billing cycles was $2990, but that was
her balance for only the first 7 days of the billing cycle, because she then paid
off her entire balance and didn't make any new purchases. If her credit card's
APR is 31%, which of these expressions could be used to calculate the
amount Annette was charged in interest for the billing cycle?
Answer:
Option D is correct.
Step-by-step explanation:
Previous Balance Method uses the "previous" balance, that is, the balance from the month before.
Here, it is given that the opening balance of one of her 30-day billing cycles was $2990. This means this was previous month amount or previous balance.
So, Annette will be charged the interest on $2990.
Hence, option D is correct.
Answer:
D.
Step-by-step explanation:
20 POINTS What are the x-intercepts of the graph? A) x = -5 B) x = 1 and 5 C) x = 0 and 4 D) x = -1 and 5
Answer:
B) x = 1 and 5Step-by-step explanation:
x-intercept: the intersection point of the graph with the x axis.
Therefore, the x-intercepts are x = 1 and x = 5 (look at the picture).
The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary.
legs: 10 in. and 30 in.
34 in.
31.6 in.
37.2 in.
28.3 in.
Answer:
The third side is approximately 31.6 inches long.
Step-by-step explanation:
When given the lengths of two sides of a right triangle, you can easily use Pythagorean Theorem (a2+b2=c2; a or b being the legs, c being the hypotenuse) to find the length of the third side. Since the legs (10 in. and 30 in.) are already given to us, we can simply insert the numbers into Pythagorean Theorem and solve for the third side! It should look a little something like this: 102+302=c2, then solve for the squares to get 100+900=c2, then add the two side lengths to get to 1,000=c2, then find the square root of both sides (now, since the c is already being squared, they will cancel out to just c, but you will get the actual square root of 1,000). Should all go well, you should get an answer of 31.6227766017, which just so happens to round out to 31.6. And with that, we have our final no-longer-missing side length of 31.6 inches.
Hope this helped!
A tree casts a shadow 15 feet long. At the same time, an 18-foot flag pole casts a shadow 10 feet long. How tall is the tree?
The tree is 27 feet tall. In order to find that out you know that because it is occurring at the same time of day, the two shadows are proportional to each other. Then set up two fractions like I did in the image and cross multiply to find x. Hope this helps!
The following table shows the number of police calls that were made last year in each of the cities in Hogdon County. If the mean of the data set is 273 calls, find the number of police calls in Thornbury.
Answer:
222 Calls
Step-by-step explanation:
We are given four values and the mean of the given data, so in order to find the fifth value, we will use the formula for mean. The formula for mean is:
Mean=(∑x)/n
Here n is the total number of values which is 5
Let x_5 be the number of calls for Thornbury
Putting the values of mean and the data given
273=(244+353+235+311+x_5)/5
273*5=1143+x_5
1365=1143+x_5
x_5=1365-1143
x_5=222 Calls
So the number of police calls in Thornbury is 222 ..
Answer:
[tex]222[/tex] - written in [tex]2/24/2021[/tex]
Step-by-step explanation:
The answer is [tex]222[/tex] because...
First Step:
Multiply the mean by how many numbers in total there are, including the [tex]?[/tex] mark: [tex]273[/tex] * [tex]5=1365[/tex]
Second Step:
Add up all the numbers, not including the [tex]?[/tex] mark: [tex]244+353+235+311=1143[/tex]
Third Step:
Now subtract those numbers: [tex]1365-1143=222[/tex]
Fourth Step/Final answer:
Now we know that the answer is [tex]222[/tex]
7x+4+x=20 what is x? plz help
7x+4+x=20
8x+4=20
8x+4-4=20-4
8x=16
Divide by 8 for 8x and 16
8x/8=16/8
x=2
Check answer by using substitution method
7(2)+4+2=20
14+6=20
20=20
Answer is x=2
Answer:
x=2
Step-by-step explanation:
7x+4+x=20
Combine like terms
8x +4 = 20
Subtract 4 from each side
8x+4-4 =20-4
8x = 16
Divide each side by 8
8x/8 = 16/8
x = 2
At the football game, 4 hamburgers and 5 soft drinks cost $27, and 3 hamburgers and 3 soft drinks cost 18$. Which system of equations below can be used to determine the price of a hamburger and the price of the soft drink
The system of equations that can be used to determine the price of the hamburger and the soft drink is 4H + 5S = $27 (H = hamburger cost, S = soft drink cost) and 3H + 3S = $18.
Explanation:The question you're asking involves setting up a system of equations to solve for the cost of a hamburger and a soft drink based on the given information. Since two different meals with different quantities of hamburgers and soft drinks have specific costs, we can make the following two equations where H represents the cost of a hamburger and S represents the cost of a soft drink: 4H + 5S = $27 and 3H + 3S = $18. This system of equations can be solved using various methods like substitution or elimination to determine the individual costs of a hamburger and a soft drink.
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Which graph represents the absolute value of -3?
Answer:
The third graphStep-by-step explanation:
|a| = a for a ≥ 0
|a| = -a for a < 0
therefore
|3| = 3 and |-3| = -(-3) = 3
Answer:
Graph 1 is the correct representation of absolute value of -3.
Step-by-step explanation:
Absolute value of a number is the measure of positive distance on a number line from zero to that number.
It is denoted by:
[tex]\mid c \mid = c, \text{if c} > 0\\ ~~~~~ = -c, \text{if c} < 0[/tex]
So, the absolute value of -3 =
[tex]\mid -3 \mid = 3[/tex]
The correct representation of the absolute value option 1.
As the graph in option 1 represents the positive distance between zero and -3.
A company conducted a survey to see wether its new toothpaste was more popular with children or adults. Of the children surveyed 28% use the toothpaste. Compare this what is the percent of adults who use toothpaste.
Answer:
C
Step-by-step explanation:
To find the percent of adults who use toothpaste, we divide the number of adults who use toothpaste by the total adults.
0.08/0.75
The answer is about 11 percent, so C is the true statement.
Answer:
C is right on Ap ex!
Step-by-step explanation:
That answer is right, I don't know why that person commented wrong, but they must have been doing a different question!
y Probability 10 0.10 20 0.25 30 0.05 40 0.30 50 0.20 60 0.10 The probability distribution of y, a discrete random variable, is given in the table. What is the expected value of y? A. 25.0 B. 26.5 C. 35.0 D. 35.5
Answer:
The answer is D.35.5 got it right on plato
Step-by-step explanation:
The expected value of the random variable y found from its given probability distribution is given by: Option D: 35.5
How to find the mean (expectation) and variance of a random variable?Supposing that the considered random variable is discrete, we get:
[tex]\text{Mean} = E(X) = \sum_{\forall x_i} f(x_i)x_i[/tex]
where [tex]x_i; \: \: i = 1,2, ... ,n[/tex] is its n data values
and [tex]f(x_i)[/tex] is the probability of [tex]X = x_i[/tex]
The probability distribution of Y is given as:
Y = y f(y) = P(Y = y)
10 0.10
20 0.25
30 0.05
40 0.30
50 0.20
60 0.10
Thus, the expectation (also called expected value) of y is calculated as:
[tex]E(Y) = \sum_{\forall y_i} f(y_i)y_i \\\\E(Y) = 10 \times 0.1 + 20\times 0.25 + 30 \times 0.05 + 40 \times 0.3 + 50 \times 0.2 + 60 \times 0.1\\\\E(Y) = 1 + 5 + 1.5 + 12 + 10 + 6 = 35.5[/tex]
Thus, the expected value of the random variable y found from its given probability distribution is given by: Option D: 35.5
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PLEASE HELP I AM DESPERATELY LOOKING FOR GOOD ANSWERS
Which question ? Are you looking for?
4. Point A=-1.5 Point B =-.2. Point c= 1.2
5.8x 4=32. 32+21=53
Please find which quadratic equation matches the graph with work attached
Answer:
C
Step-by-step explanation:
Firstly, we know that the function must be negative due to its shape. This means that the answer cannot be B
Next we can use the equation [tex]x=\frac{-b}{2a}[/tex] that is used in order to find the vertex of the parabola.
A)
[tex]f(x)=-x^2+6x+7\\a=-1,b=6,c=7\\\\x=\frac{-6}{-2} \\x=3[/tex]
As the vertex is at x=3 on the graph, this one could be a contender.
C)
[tex]f(x)=-x^2+6x-7\\a=-1,b=6, c=-7\\\\x=\frac{-6}{-2} \\\\x=3[/tex]
This also could be the equation
D)
[tex]f(x)=-x^2-6x-7\\\\a=-1, b=-6, c=-7\\\\x=\frac{6}{-2} \\\\x=-3[/tex]
This rules option D out.
For this last step, we can look at where the zeroes would be for each equation. (These values are irrational, so we cannot look at specific number)
A)
[tex]f(x)=-(x^2-6x-7)[/tex]
As this equation has a negative value for c, this means that one zero must be positive and the other must be negative.
This means that option A can be ruled out
C)
[tex]f(x)=-(x^2-6x+7)[/tex]
As this equation has a positive value for c, this means that both of the zeroes must be positive. This means that it is the only one that fits all of the criteria.
Un rombo tiene un ángulo de 22 grados. Cuanto vale la suma de sus ángulos que no midan 22 grados?
Answer:
The sum of the angles that do not measure 22 degrees is equal to 316°
Step-by-step explanation:
The question in English is
A rhombus has a 22-degree angle. How much is the sum of its angles that do not measure 22 degrees worth?
we know that
The opposite internal angles of a rhombus are equal and the adjacent internal angles are supplementary
so
Let
x -----> the measure of an adjacent angle to 22 degrees in the rhombus
x+22°=180°
x=180°-22°=158°
therefore
The sum of the angles that do not measure 22 degrees is equal to
158°+158°=316°
Which linear inequality is represented by the graph?
Answer:
the answer is b
Step-by-step explanation:
Answer:
The linear inequality is [tex]y > \cfrac 23 x+3[/tex], which is the third option.
Step-by-step explanation:
In order to determine the inequality, we need to first identify the line equation associated to it, to do that we can identify a couple of points and get the slope then the line equation.
Identifying points and finding slope.
From the segmented line we can tell that it crosses the points (0,3) and (3, 5), thus we can find the slope using
[tex]m = \cfrac{y_2-y_1}{x_2-x_1}[/tex]
Replacing the points we get
[tex]m= \cfrac{5-3}{3-0}[/tex]
[tex]m = \cfrac 23[/tex]
Writing the line equation.
Now that we have the slope m, and a point (0,3) we can find the line equation using,
[tex]y-y_1 = m(x-x_1)[/tex]
Replacing the point and slope we get
[tex]y-3 = \cfrac 23 (x-0)[/tex]
Simplifying and solving for y we get
[tex]y = \cfrac 23 x+3[/tex]
Writing the inequality.
Notice that the associated line is a segmented line, so the linear inequality does not contain it that is why we only need to use greater than or less symbols.
Then we can tell that the shaded area is above the segmented line so we can conclude that the linear inequality is
[tex]y > \cfrac 23 x+3[/tex],
And that is the third option.
what is the product of (3 squared 8)(4 squared 3)? Simplify your answer.
Answer:
3456
Step-by-step explanation:
the given equation is: [tex](3^{2} 8) (4^{2} 3)[/tex]
= (9 × 8) (16 × 3)
= (72) (48)
= 3456
Describe the end behavior of the function below f(x)=4(2)^(-x)-3
Final answer:
The function f(x) = 4(2)^(-x) - 3 approaches -3 as x approaches infinity and decreases without bound as x approaches negative infinity, with a horizontal asymptote at y = -3.
Explanation:
The end behavior of a function describes what happens to the function's values as x approaches infinity or negative infinity. For the function f(x) = 4(2)^(-x) - 3, as x approaches infinity, the term 2^(-x) approaches zero, because any non-zero base raised to the power of negative infinity is zero. Thus, the function approaches -3. Conversely, as x approaches negative infinity, the term 2^(-x) grows exponentially, and the function's values decrease without bound, heading towards negative infinity. However, since f(x) involves a negative exponential function, the graph ultimately will approach the horizontal asymptote y = -3.