Answer: [tex]h = \frac{J-2b}{2r}[/tex]
Work Shown:
[tex]J = 2hr + 2b\\\\J - 2b= 2hr\\\\h = \frac{J-2b}{2r}[/tex]
Explanation:
In the 2nd step, we isolate the "2hr" by subtracting both sides by 2b. This is do unto the +2b done to the right side initially. We want 2hr all by itself since it contains h.
Then to fully isolate h, we divide both sides by 2r. It might help to think of 2hr as 2r*h so you can pull out the terms easier. The division is done to undo the multiplication.
If writing out the final step using a keyboard, then you would say (J-2b)/(2r). Use parenthesis to indicate which terms are being divided.
(Histograms and Line Plots LC)
The following is a list of movie tickets sold each day for 10 days.
14, 35, 20, 23, 42, 87, 131, 125, 64, 92
Which of the following intervals are appropriate to use when creating a histogram of the data?
0 – 29, 30 – 59, 60 – 89, 90 – 119, 120 – 149
0 – 30, 30 – 55, 55 – 80, 80 – 105, 105 – 130
0 – 24, 25 – 49, 50 – 74, 75 – 99, 100 – 125
0 – 35, 35 – 70, 70 – 105, 105 – 140
The class intervals appropriate to use in creating a histogram of the data are 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130. The correct option is B.
What are the class intervals?A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The width of the intervals must be equal. This means that the difference between the lower bound and the upper bound must be equal. Also, the upper bound of the preceding interval must be the same as the lower bound of the next interval.
This means that the intervals must be overlapping. Of all the options, it is 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130 that satisfy both conditions.
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Answer:first option
Step-by-step explanation:
- 5/8x+10for x=-8
show work
Answer: To solve the equation "-5/8x + 10" for x when x equals -8, we can first substitute -8 for x in the equation:
-5/8(-8) + 10
Next, we can simplify the expression by performing the calculations within the parentheses:
-5/8(-8) + 10 = 5/8(8) + 10 = 5(8)/8 + 10 = 40/8 + 10 = 5 + 10 = 15
Therefore, the value of "-5/8x + 10" when x equals -8 is 15.
(
Write the equation
of the line in
Slope-Intercept
Form.
Answer: y= -2/3x + 0
Step-by-step explanation: y=mx+b
The Y-intercept is at (0,0), so b is 0
Slope is -2/3
So the equation is y=-2/3x + 0
suppose the continuous random variable, x, is uniformly distributed between 2 and 10. what is the probability that x is either less than 3 or greater than 8?
The probability that x is either less than 3 or greater than 8 is 0.375 .
In the question ,
it is given that ,
a continuous random variable X , is uniformly distributed between 2 and 10 ,
So , alpha(α) = 2 and beta(β) = 10 .
the probability that x is either less than 3 or greater than 8 can be calculated by :
P(X < 3 or X > 8) = 1 - (8 - 3)/(β - α)
= 1 - (8 - 3)/(10 - 2)
= 1 - 5/8
On simplifying further ,
we get ,
= 0.375
Therefore , the probability P(X < 3 or X > 8) is = 0.375 .
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can the median of a set of numbers ever be the greatest number in the set of data? explain.
Answer: It should not be able to
Step-by-step explanation:
It should always be in the middle, aka its name, "Median"
Vincent is completing his math homework about the process of Completing the Square to solve quadratic equations. His work is shown below.
solve: x²-3x+7=0
step 1: x²-3x = -7
step 2: x²-3x+9=-7 +9
step 3: (x-3)² = 2
step 4: X-3= = √2
x=3 = √2
Did Vincent make a mistake as he solved the quadratic using Completing the Square? If so, in what
step did he first make a mistake? (Step numbers are labeled in blue on the left)
Answer:
Step-by-step explanation:
He made a mistake in step one turning the 7 into a -7
[tex]x^{2}[/tex] - 3x + 7 = 0
Solving:
[tex]1x^{2}[/tex] - 3x + 7 = 0 ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.
[tex]1x^{2}[/tex] + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.
a = 1, b = -3, c = 7
x = - (-3) ±√[tex](-3)^{2}[/tex] - 4 x 1 x 7
2 x 1
x = 3 ± √[tex](3)^{2}[/tex] - 4 x 7
2
x = 3 ± √9 - 4 x 7
2
x = 3 ±√9 - 28
2
x = 3 ± √-19
2
The square root of a negative number does not exist in the set of real numbers.
x = ∉ R
Select the correct answer from each drop-down menu. consider this quotient. the simplest form of this quotient has a numerator of and a denominator of _______. the expression does not exist when ______.
The simplified form of the given expression has a numerator of (x + 9)(2x + 1) and the denominator of (x + 7) and the expression does exist when (x = 9) and this can be determined by factorizing the given expression.
What is factorizing?By identifying the biggest factors that the terms in the equation have in common, factoring is a technique used in mathematics to simplify algebraic expressions.
Given :
Expression - [tex]\frac{3x^2 - 27x}{2x^2+13x-7}[/tex] ÷ [tex]\frac{3x}{4x^2-1}[/tex]
First, factorize the expression, [tex]4x^2-1[/tex]
So, [tex]4x^2-1[/tex] = [tex](2x-1) (2x+1)[/tex]
Now, factorize the equation: [tex]2x^2+13x-7[/tex]
[tex]2x^2+13x-7[/tex] = [tex]2x^2+14x -x -7[/tex]
= [tex]2x(x+7) -1(x+7)[/tex]
= [tex](2x-1) (x+7)[/tex]
Now, factorize the equation: [tex]3x^2-27x[/tex]
So, [tex]3x^2-27x[/tex] = [tex]3x(x-9)[/tex]
Now, substitute the factorized terms in the given expression:
= [tex]\frac{3x(x-9)}{(2x-1) (x+7)}[/tex] ÷ [tex]\frac{3x}{(2x-1) (2x+1)}[/tex]
= [tex]\frac{(x+9) (2x+1)}{(x+7)}[/tex]
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The complete question is as follows:
Select the correct answer from each drop down menu. The simplest form of this quotient has a numerator of... and a denominator of.... The expression does exist when x=......
Can anyone explain how to solve this?
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_3(y)=11.03\hspace{5em}\log_3(z)=7.74\hspace{5em}\log_3(t)=5.44 \\\\[-0.35em] ~\dotfill[/tex]
[tex]12\log_3\left( \cfrac{z^7}{y^5 t^2} \right)\qquad \textit{let's nevermind the 12 for now} \\\\\\ \log_3\left( \cfrac{z^7}{y^5 t^2} \right)\implies \log_3(z^7)-\log_3(y^5 t^2)\implies \log_3(z^7)-[\log_3(y^5)+\log_3(t^2)] \\\\\\ \log_3(z^7)-\log_3(y^5)-\log_3(t^2)\implies 7\log_3(z)-5\log_3(y)-2\log_3(t) \\\\\\ 7(7.74)-5(11.03)-2(5.44)\implies \stackrel{\textit{let's put back the 12}}{12 ~~ [7(7.74)-5(11.03)-2(5.44)]} \\\\\\ ~\hfill \text{\LARGE -142.2}~\hfill[/tex]
What is the equation of the blue line
Answer:
[tex]y=\frac{1}{2}x+2[/tex]
Step-by-step explanation:
Using the points [tex](0,2)[/tex] and [tex](2,3)[/tex], the gradient is [tex]\frac{3-2}{2-0}=\frac{1}{2}[/tex].
The [tex]y[/tex]-intercept is [tex](0,2)[/tex], so the equation is [tex]y=\frac{1}{2}x+2[/tex].
Courtney is collecting coins she already has two coins in her collection and plans to add four coins each week after six week she has 26 coins write an equation that can be used to determine the number of coins y Courtney will have after x weeks
Answer:
y = 4x + 2
Step-by-step explanation:
24 coins gained after 6 weeks
24 / 6 = 4 coins a week
y = 4x + 2
Find the indicated real nth root(s) of a. n = 4, a = 625
Answer:
5
Step-by-step explanation:
Diego's high school soccer team started a fundraiser selling treats at their games. They spent $1000 to start and an additional $0.30 on each candy bar and can of soda. They decide to sell both the candy and the soda for $2.00 each to make things simple
How much do they need to sell to break even (where revenue is equal to cost)?
How much do they need to sell to make at least $5,000 in profit?
Do you think it is likely for them to make at least $5,000 in profit? In what situations
would it be possible for them to make at least $5,000 in profit?
The answer to this Question based on Profits is No they cant make 5000$ profit
What is profit?
Profit is simply the extra money we earn on selling good etc things and there are tonnes of different ways of making money and profit
Solution:
Here Diego high school soccer team started a fundraiser selling treats at their games
Initial money spent = 1000$
They decided to make 0.3$ revenue on both candy and soda hence total 0.6$ revenue in one pack
one pack costs for 2$ where 0.6$ is revenue and actual cost is 1.4$
Total packs to sell = 1000/1.4
= 714 packs
hence total profit = 714 * 0.6 = 428$
hence maximum revenue they can make is 428$ and it is maximum
hence they cant make 5000$ profit
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Good points please answer
The values of sin2x, cos2x and tan2x is [tex]-\frac{3\sqrt{13}}{11}[/tex], 2/11 and [tex]-\frac{3\sqrt{13}}{2}[/tex] respectively.
What is tan function?
The tan function, one of the primary six trigonometric functions, is typically expressed as tan x. It is the ratio of the angle's opposite and adjacent sides when a right-angled triangle is being considered.
Tangent is a verb that means "to touch" in Latin, from the root tangere. A circle is precisely the point at which a line tan to it intersects. In trigonometry, the tan function, a periodic function, is crucial. Utilizing the unit circle will make understanding the tangent function the simplest possible.
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If you buy 11 half gallons of milk, how many liters of milk do you have?
Answer: About 20.82 liters.
Step-by-step explanation:
To go from gallons to liters, we will multiply by 3.785. Since we are in half gallons, we will multiply 11 by 0.5 for 5.5 full gallons. Now, we will multiply;
5.5 gallons * 3.785 = 20.8198 ≈ 20.82 liters
Arrange the steps in the correct order to solve the equation,
3(22-5) - 4 = 10
Add 4 to each side of the
equation:
3/22 - 5) = 14
Use the Exponential Property and
write in decimal form:
(2 - 5)log2 = log4. 67
log4. 67
Find the value of Toga
and substitute
2-5 = 2. 23
Simplify
23. 625
Take the log of each side:
log(22+ - 5) = log('9).
2 - 5 - 1034. 87
Divide each side by log 2
Tog?
Add 5 to each side of the
equation
2+ = 2. 23 +5
Divide both sides of the equation
The correct order to solve the equation is given below .
In the question ,
it is given that ,
the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 ,
Step(1) , adding 4 to each side of the equation ,
3*([tex]2^{2 t - 5}[/tex]) = 14
Step(2) , dividing both sides of the equation by 3 ,
we get , ([tex]2^{2 t - 5}[/tex]) = 14/3 .
Step(3) , taking log on each side ,
log([tex]2^{2 t - 5}[/tex]) = log(14/3)
Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,
we get ,
(2t - 5)*log(2) = log(4.67)
Step(5) , Dividing each side by log(2) ,
we get , 2t-5 = log(4.67)/log(2) .
Step(6) , Add 5 to each side of equation
we get , 2t = 2.23 + 5 ;
Step(7) , Simplifying we get ,
we get , t = 3.625 .
Therefore , the the solution of the given equation is t = 3.625 .
The given question is incomplete , the complete question is
Arrange the steps in the correct order to solve the equation,
3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 .
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Kareem makes muffins using a ratio of 3. 5 3. 5 cups of flour for every 1. 75 1. 75 cups of sugar. If he has 3. 5 3. 5 cups of sugar, how much flour does he need to make the muffins?.
If Kareem has 3.5 cups of sugar then the amount of flour that Kareem need to make the muffins is 7 cups .
In the question ,
it is given that ,
the ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .
let the number of cups of flour be "y" and
the number of cups of sugar be "x" .
So , y ∝ x ,
y = k*x , where k is the constant of proportionality .
From the given data ,
3.5 = k*1.75
k = 3.5/1.75
k = 2 .
we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .
the equation becomes ,
y = 2*3.5
y = 7
Therefore , Kareem needs 7 cups of flour .
The given question is incomplete , the complete question is
Kareem makes muffins using a ratio of 3. 5 cups of flour for every 1. 75 cups of sugar. If he has 3. 5 cups of sugar, how much flour does he need to make the muffins ?
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a rumor spreads among a group of 400 people. the number of people who have heard the rumor after t hours is given by:
Time required to spread the rumor so that half of the given heard the rumor is equal to 15 hours (approximately).
As given in the question,
Number of people among whom rumor is spread = 400
Number of people is represented by N(t)
Time is represented by 't' hours
Function representing relation between number of people who heard about the rumor and time
N(t) = 400/ ( 1+ 399 × e^(-0.4t) )
Condition : Half of the given number of people heard the rumor
N(t) = 400/2
= 200
Substitute the value in the function we get,
200 = 400/ ( 1+ 399 × e^(-0.4t) )
⇒ ( 1+ 399 × e^(-0.4t) ) = 400 ÷ 200
⇒ 1 + 399 × e^(-0.4t) = 2
⇒ 399 × e^(-0.4t) = 2 - 1
⇒ e^(-0.4t) = 1 ÷ 399
⇒ e^(-0.4t) = 0.002506
⇒ -0.4t = [tex]log _{e}[/tex] (0.002506)
⇒ t= 14.97 hours
⇒ t= 15 hours (round off)
Therefore, time required to spread the rumor among half of the given number of people is equal to 15hours(approximately).
The complete question is:
A rumor spreads among a group of 400 people. The number of people, N(t), who have heard the rumor by the time t in hours since the rumor started to spread can be approximated by a function of the form
N(t) = 400 / (1+399e^(-0.4t))
Approximately how long will it take until half the people have heard the rumor?
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A polygon has vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0). Which represents a geometric translation of the give
polygon 4 units to the right and 5 units down?
Answer:
(-1, 3), (3, 3), (5, 3), (1, 0)
Step-by-step explanation:
A translation of 4 units to the right means adding 4 to every x-coordinate.
The new coordinates are:
(-1, 3), (3, 3), (5, 3), (1, 0)
PLEASE HELP!!(DUE TMRW)!!!!!
Answer:
Step-by-step explanation:
12
x=12y
2:3
3:14
nope-60/2=30
495/9=55
The Burj Khalifa building in Dubai, United Arab Emirates, is one of the tallest buildings in the world at 2,722 feet tall. An American football field is 360 feet in length.
A photo of the Burj Kalifa building in Dubai, United Arab Emirates is shown. The caption reads the Burj Kalifa is one of the tallest buildings in the world. The bracket from the ground to the top of the building is labeled two thousand seven hundred twenty-two feet.
Approximately how many football fields tall is the Burj Khalifa building? Round to the nearest tenth.
Answer:
7.6
Step-by-step explanation:
You want to know the number of 360 ft football fields tall the 2722 ft Burj Khalifa building is.
Football fieldsThe ratio of height to football field length is ...
(2722 ft)/(360 ft/field) ≈ 7.6 fields
The height of the building is about 7.6 football field lengths.
The function g is defined by g(x) = ( 2x – 3 )( x + k )
Given that g(0) = – 15 find (i) k (ii) x such that g(x) = 0
Answer:
Step-by-step explanation:
(-3)(k) = -15
-3k = -15
k = -15/-3
k = 5
(2x+3)(x+5) = 0
2x + 3 = 0
2x = -3
x = -3/2
x+ 5 = 0
x = -5
a paper company needs to ship paper to a large printing business. the paper will be shipped in small boxes and large boxes. the volume of each small box is 7 cubic feet and the volume of each large box is 14 cubic feet. a total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. define the variables that you use to write the system.
The required system of equations is x+y = 21 and 7x +14y = 252.
Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.There are three methods typically used to solve systems of linear equations: graphing, the substitution method, and the elimination method. These methods can be applied to more complex systems of nonlinear equations as well.
Let the number of small boxes be x.
Let the number of large boxes be y.
The volume of each small box is 7 cubic feet.
The volume of each large box is 14 cubic feet.
The total number of boxes is 21.
Total volume of all boxes is 252 cubic feet.
So, x+y = 21.
This is the first equation.
Also, the total volume is equal to the sum of the volumes of all individual boxes.
So, 7x + 14y = 252
Thus, the required system of equations is x+y = 21 and 7x +14y = 252.
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The required system of equations is x + y = 21 and 7x + 14y = 252 using the concept of equations.
What are system of equations?A system of equations in algebra is made up of two or more equations that are solved together to obtain the solution for a two or more variable problem.
Volume of each small box is 7 cubic feet and volume of each large box is 14 cubic feet. Take the number of small boxes to be x and number of large boxes to be y.
Given total number of boxes shipped is 21. Therefore using the concept of equation,
x + y = 21 --- (1)
Total volume of small box is given by:
Total volume of small box = (Volume of a small box) * (Number of small box)
Total volume of small box = 7x
Similarly the total volume of large box is,
Total volume of small box = 14y
Given the total volume of carried box is 252 cubic feet. Using the concept of equations,
7x + 14y = 252 ---(2)
The equations (1) and (2) gives the required system of equations.
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Khadija has $0.90 worth of nickels and dimes. She has a total of 10 nickels and dimes altogether. By following the steps below, determine the number of nickels, x, and the number of dimes, y, that Khadija has.
Determine three ways to have a total of 10 coins:
Khadija has 8 nickels and 2 quarters
How to determine the number of each coin?From the question, we have the following parameters that can be used in our computation:
Worth of coins = $0.90
Type of coins = Dimes and quarters
Represent the nickels with n and the quarters with q
So, we have the following representation
n + q = 10
0.05n + 0.25q = 0.9
Make n the subject
n = 10 - q
So, we have
0.05(10 - q) + 0.25q = 0.9
Evaluate the products
0.5 - 0.05q + 0.25q = 0.9
This gives
0.2q = 0.4
Divide both sides by 0.2
q = 2
Recall that
n = 10 - q
So, we have
n = 10 - 2
Evaluate
n = 8
Hence, the number of nickels is 8
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pls help due tomorrow !!!
The required quadratic equation is x² - 12x + 36 Or (x - 6)².
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
We know (a - b) = a² - 2ab + b².
Given, An expression 36 - 12x + __
now, here b² = 36 ⇒ b = 6,
∴ - 2ab = - 2(a)(6).
So, a = 1.
∴ The required quadratic equation is x² - 12x + 36 Or (x - 6)².
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in 2016, a 1952 Willie Mays rookie card from Topps sold for $478,000! Currently, a toaster may cost $25. How many toasters could you buy with the money spent on the willie Mays rookie card?
Answer: 19120 Toaster
Step-by-step explanation: We just need to take $478000 divided by 25, equal to 19120 Toaster!
A roller-coaster goes over a 12 m tall hill then approaches a 30 m hill. What is the minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill?
254.8 m/s
15.96 m/s
Not enough information to answer
18.78 m/s
Not enough information to answer
Option C is the correct answer.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
A roller-coaster goes over a 12 m tall hill and then approaches a 30 m hill.
The minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill.
To find the minimum velocity we need to know the acceleration of the roller coaster that comes down the 12 m tall hill.
The value of the acceleration is not given.
So,
We can not find the minimum velocity.
Thus,
Not enough information to answer
Option C is the correct answer.
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please help
some one
If a boy grow 5 inche, he will be one half a tall a hi iter , hi iter i 68 inche tall. How tall i the boy?
If a boy grows 5 inches, he will be one half a tall as his sister , his sister is 68 inches tall. So the height of the boy is 29 inches
What is division?In mathematics, the opposite of multiplication is the process called division. Finding the number of times one quantity is included within another is the procedure. The letters "/" or "" are typically used to denote this. For instance, 8 boys divided by 2 may be expressed as 8/2 or 82. The outcome in this situation would be 4, which is the quantity that 2 may be found in 8 times. The quotient, or outcome of the division, and the remainder, or quantity remaining after dividing, may both be found using division. Calculus, algebra, geometry, and other branches of mathematics all make use of the crucial mathematical notion of division.
How to solve?
If the boy grows 5 inches, he will be 68/2 =34 inches tall
The boy's current height is 34 - 5 = 29 inches
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Figure out what the slope and points from the equation are
y + 9 = 2(x + 5)
y - 4 = -3(x - 3)
Answer:
y + 9 = 2(x + 5): slope is 2
y - 4 = -3(x - 3): slope is -3
(12/5, 29/5)
Step-by-step explanation:
y + 9 = 2(x + 5)
y + 9 - 9 = 2(x + 5) - 9 ==> subtract both sides by 9 to isolate y
y = 2(x + 5) - 9 ==> simplify
y = 2x + 2*5 - 9 ==> distribute x and 5 by multiplying them by 2
y = 2x + 10 - 9
y = 2x + 1 ==> slope is 2
y - 4 = -3(x - 3)
y - 4 + 4 = -3(x - 3) + 4 ==> add both sides by 4 to isolate y
y = -3(x - 3) + 4
y = -3x - 3(-3) + 4 ==> multiply x and -3 by -3 by distributive property
y = -3x - (-9) + 4
y = -3x + 9 + 4 ==> simplify
y = -3x + 13 ==> slope is -3
Since y = -3x + 13 and y = 2x + 1:
2x + 1 = -3x + 13 ==> solve for x
2x + 3x + 1 = -3x + 3x + 13
5x + 1 = 13
5x + 1 - 1 = 13 - 1
5x = 12
x = 12/5
y = 2x + 1
y = 2(12/5) + 1 ==> plug in 12/5 for x
y = 24/5 + 1 ==> solve for y
y = 24/5 + 5/5
y = (24+5)/5 ==> y = 29/5 ==> (x, y) = (12/5, 29/5)
A store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store manager at a selling price of $2. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
The manager's likely error is $20 if a store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
A markup of 11% on all items. An item costing $18 is displayed by the store manager at a selling price of $2.
The manager’s likely error was forgetting to add the $2 back to the $18.
$2= 11% of $18 = 1.98(=2)
For a markup,
= $2 + $18
= $20
Thus, the manager's likely error is $20 if a store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store.
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