It is not sensible to measure a football pitch in nanometres because they are extremely small units of length which are typically used to measure particles or atomic structures.
Why would measuring a football pitch in nanometres be impractical?Nanometres are a billion times smaller than a meter making them unsuitable for measuring macroscopic objects like a football pitch. Football pitches are typically measured in meters or yards which provide a more appropriate scale for their size.
Nanometres are better suited for measuring things on a molecular or atomic level such as the size of nanoparticles or the spacing between atoms. Attempting to measure a football pitch in nanometres would not only be impractical but also misleading as it would not accurately reflect the dimensions of the pitch in a meaningful way.
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Side two of triangle is for more units inside won the third triangle is three times the length of side one is the perimeter of a triangle is 39 units right and solve the equation to find the length of all three sides of the triangle
the lengths of the three sides of the triangle are approximately:
Side one: 4.875 units
Side two: 19.5 units
Side three: 14.625 units
Let's denote the lengths of the sides of the triangle as follows:
Side one: x
Side two: 4x (since it is four times the length of side one)
Side three: 3x (since it is three times the length of side one)
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the perimeter is given as 39 units. We can set up an equation to solve for x:
x + 4x + 3x = 39
Combining like terms:
8x = 39
Dividing both sides by 8:
x = 39/8
Simplifying the fraction:
x = 4.875
Now, we can find the lengths of all three sides by substituting this value of x back into our expressions for each side:
Side one: x = 4.875 units
Side two: 4x = 4.875 * 4 = 19.5 units
Side three: 3x = 4.875 * 3 = 14.625 units
Therefore, the lengths of the three sides of the triangle are approximately:
Side one: 4.875 units
Side two: 19.5 units
Side three: 14.625 units
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The dimensions of a room are 16 x 14 x 10 meters.
There are 4 windows of 1. 3 m x 1. 4 m and 2 doors of
2 m x 1 m. What will be the cost of white washingthe walls, if the rate of white washing is Rs 5 per m
2
?
Therefore, the cost of white washing the walls will be Rs 5 × 588.72 = Rs 2943.60.
The total surface area of the four walls can be calculated by multiplying the perimeter of the room (2 × (length + width)) by the height of the room. In this case, the total surface area of the four walls is 2 × (16 + 14) × 10 = 600 square meters.
Next, we need to subtract the areas of the windows and doors from the total surface area of the walls. There are four windows with dimensions of 1.3 meters in height and 1.4 meters in width, so the total area of the windows is 4 × (1.3 × 1.4) = 7.28 square meters. There are also two doors with dimensions of 2 meters in height and 1 meter in width, so the total area of the doors is 2 × (2 × 1) = 4 square meters.
Subtracting the areas of the windows and doors from the total surface area of the walls, we get 600 square meters - (7.28 square meters + 4 square meters) = 588.72 square meters.
Finally, we can calculate the cost of white washing the walls by multiplying the rate per square meter (Rs 5) by the total surface area of the walls (588.72 square meters). Therefore, the cost of white washing the walls will be Rs 5 × 588.72 = Rs 2943.60.
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The size of a computer monitor is given as the length of the screens diagonal d in inches.The equation d=5/6
Therefore, the size of a computer monitor whose diagonal measures d = 5/6 inches is 5/6 inches.
Most computer monitors range from 19 to 34 inches, measured diagonally from corner to corner. The average user will be happy with 22-24" screens. This range provides enough screen real estate for general productivity tasks and even light multitasking without overcrowding your desktop.
Full HD (1080p) stays fairly sharp on monitors of this size. As they're not too big, you can easily place them in a setup with 2 screens. A 24-inch monitor is also suitab
The size of a computer monitor is given as the length of the screens diagonal d in inches.
The equation d=5/6.
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Please Help You have accepted a job from a company that will pay you $38,900 in the first year of employment and will give you a 3% raise for each year thereafter. How much will you earn if you work for that company for 5 years? Round to the nearest dollar as needed.
[tex]S_5=78,967\\S_5=206,525\\S_5=162,743\\S_5=40,067[/tex]
To calculate your earnings for 5 years, we can use the given information that you will receive a 3% raise each year.
In the first year, your earnings are $38,900. For the subsequent years, we can calculate the raise amount and add it to the previous year's earnings. Year 2: $38,900 + 3% of $38,900, Year 3: (Year 2 earnings) + 3% of (Year 2 earnings), Year 4: (Year 3 earnings) + 3% of (Year 3 earnings), Year 5: (Year 4 earnings) + 3% of (Year 4 earnings). Calculating each year's earnings: Year 2: $38,900 + 0.03 * $38,900, Year 3: (Year 2 earnings) + 0.03 * (Year 2 earnings), Year 4: (Year 3 earnings) + 0.03 * (Year 3 earnings), Year 5: (Year 4 earnings) + 0.03 * (Year 4 earnings).
Using these calculations, we find the earnings for each year: Year 1: $38,900, Year 2: $40,067, Year 3: $41,240, Year 4: $42,422, Year 5: $43,613.
Therefore, if you work for the company for 5 years, you will earn approximately $43,613.
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AD≅AE, \overline{BA} \parallel \overline{CE},BA∥CE, \overline{CB} \parallel \overline{DA}CB∥DAand \text{m}\angle DAE = 52^{\circ}.m∠DAE=52∘. Find \text{m}\angle BAD.m∠BAD.A
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
We are given that ,
[tex]$AD \cong AE$, $BA || CE$, $CB || DA$, and $m\angle DAE = 52^\circ$.[/tex]
To find [tex]$m\angle BAD$[/tex], we need to use the fact that
[tex]$BA || CE$ and that $AD \cong AE$.[/tex]
Statement: Given
[tex]$AD \cong AE$, $BA || CE$, $CB || DA$ and $\angle DAE = 52^\circ$.[/tex]
To find: [tex]$\angle BAD$.[/tex]
Solution:
Here is the figure that represents the given statements:
As we know that [tex]$BA || CE$[/tex],
so we can say that [tex]$\angle DAE$[/tex] and [tex]$\angle ECD$[/tex] are corresponding angles.
Thus, [tex]$\angle ECD = 52^\circ$.[/tex]
In [tex]$\triangle ACE$[/tex] , we have [tex]$\angle ACE + \angle ECD + \angle AEC = 180^\circ$[/tex].
As [tex]$CE || BA$, $\angle AEC = \angle BAD$[/tex]
So, we have [tex]$\angle ACE + \angle ECD + \angle BAD = 180^\circ$[/tex]
Putting values of [tex]$\angle ECD$ and $\angle ACE$[/tex] in the above equation,
we get
[tex]\begin{align*}\angle BAD + \angle ACB + 52^\circ &= 180^\circ \\ \Rightarrow \angle BAD &= 180^\circ - 52^\circ - 80^\circ \\ \Rightarrow \angle BAD &= 48^\circ\end{align*}Thus, the measure of $\angle BAD$[/tex] is [tex]$48^\circ$[/tex].
Hence, option (B) is correct.
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During a gift exchange ten
different board games are
in a pile. Each person takes
a turn selecting a gift
without replacing it. What
is the probability that the
first gift chosen is
Monopoly and the second is
Scrabble?
To find the probability of selecting Monopoly as the first gift and Scrabble as the second gift without replacement, we need to consider the total number of board games and the number of favorable outcomes. Hence, the probability that the first gift chosen is Monopoly and the second gift is Scrabble is 1/90.
Let's assume there are 10 different board games in the pile. The first person chooses a gift, and since they want to select Monopoly, there is 1 favorable outcome out of the 10 board games. After the first gift is chosen, there are now 9 board games remaining, with 1 of them being Scrabble, which is the desired outcome for the second gift.
The probability of the first gift being Monopoly and the second gift being Scrabble without replacement can be calculated as the product of the probabilities of each event. The probability of choosing Monopoly as the first gift is 1/10, and the probability of choosing Scrabble as the second gift is 1/9.
Therefore, the overall probability can be calculated as (1/10) * (1/9) = 1/90.
Hence, the probability that the first gift chosen is Monopoly and the second gift is Scrabble is 1/90.
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A woman bought some large frames for $19 each and some small frames for $9 each at a closeout sale. If she bought 27 frames for $343, find how many of each type she bought.
Let x be the number of large frames and y be the number of small frames that a woman bought from the closeout sale.Therefore, the two equations that we can use to solve the problem are:
x + y = 27 ...(1)and19x + 9y = 343 ...(2)Multiplying equation (1) by 9 and subtracting it from equation (2), we get:19x + 9y = 343 ...(2)- (9x + 9y = 243) ...(3)10x = 100x = 10Thus, the woman bought 10 large frames
.Substituting x = 10 in equation (1), we get:10 + y = 27y = 27 - 10y = 17Thus, the woman bought 17 small frames. Therefore, the woman bought 10 large frames and 17 small frames.
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80% of 120 is what value?
A worker takes 5 hours to make 300 deyasHow much hours will a worker take to make 45 deyas
We can use a proportion to determine how long it would take a worker to make 45 days.
Let's set up the proportion:
(5 hours) / (300 deyas) = (x hours) / (45 deyas)
To solve for x, we can cross-multiply and then divide:
5 hours * 45 deyas = 300 deyas * x hours
225 hours = 300 deyas * x hours
Now, divide both sides by 300 days to isolate x:
x hours = 225 hours / 300 deyas
Simplifying the right side:
x hours = 0.75 hours
Therefore, a worker would take approximately 0.75 hours (or 45 minutes) to make 45 days.
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Calculate the trimmed mean for each sample by deleting the smallest and largest observation.What are the corresponding trimming percentages?
To calculate the trimmed mean for each sample by deleting the smallest and largest observation, we remove the extreme values and find the mean of the remaining data. The corresponding trimming percentage is the percentage of observations excluded from the calculation.
The trimmed mean is a way to reduce the influence of outliers or extreme values in a data set by excluding them from the calculation. By deleting the smallest and largest observations, we remove the outliers and focus on the central tendency of the data.
To find the trimming percentage, we need to determine the number of observations excluded relative to the total number of observations in the sample. Suppose the sample has "n" observations.
When we remove the smallest and largest values, we eliminate 2 observations. Therefore, the trimming percentage can be calculated as (2 / n) * 100.
For example, if the sample has 10 observations, the trimming percentage would be (2 / 10) * 100 = 20%. This means that the smallest and largest values are excluded, representing a trimming of 20% of the data.
In summary, the trimmed mean is calculated by removing the smallest and largest observations and finding the mean of the remaining values. The corresponding trimming percentage is determined by dividing the number of observations excluded by the total number of observations in the sample and multiplying by 100.
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y=1/2x^3
A patch in the shape of the region shown above is to be sewn onto a flag. If each unit in the coordinate system represents one foot, how much material is required for the patch?
a.
15.525 ft²
c.
10.525 ft²
b.
15.125 ft²
d.
10.125 ft²
The correct answer is option (b) 15.125 ft², representing the amount of material required for the patch.
The amount of material required for the patch, which is in the shape of the region defined by the equation y = (1/2)x^3, can be determined by calculating the area under the curve.
The patch's shape is defined by the equation y = (1/2)x^3. To find the area under the curve, we need to integrate the equation with respect to x over the appropriate interval. In this case, we are not given specific limits of integration, so we assume the interval is from x = 0 to x = 3 (based on the curve's shape shown in the equation).
The integral for finding the area under the curve is: A = ∫[0 to 3] (1/2)x^3 dx.
Evaluating the integral, we get: A = [(1/2) * (1/4)x^4] evaluated from 0 to 3.
Plugging in the limits, we have: A = (1/2) * (1/4) * (3^4 - 0^4) = (1/2) * (1/4) * (81 - 0) = (1/2) * (1/4) * 81 = 15.125 ft².
Therefore, the correct answer is option (b) 15.125 ft², representing the amount of material required for the patch.
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3) Helena has x dollars in her checking account. On July 8, she deposited
$1,870, k dollars, and $469.30. She also cashed a check fort dollars and one
for $91.40. Write an algebraic expression that represents the amount of
money in her account after the transactions.
O X + 2,247.90 +k-t
O x-k-t+1,870
O x + k + t + 469.30
O x + 1,788.20 +kt
The algebraic expression that represents the amount of money in Helena's account after the transactions is "x + 1,788.20 + k - t". Hence, the correct option is O x + 1,788.20 +kt.
Helena had x dollars in her account.
On July 8, she deposited $1,870, k dollars, and $469.30.
Therefore, the amount deposited by Helena is "1,870 + k + 469.30".
She also cashed a check for t dollars and one for $91.40.
Therefore, the amount she cashed is "t + 91.40".
To find the algebraic expression that represents the amount of money in her account after the transactions, we have to add the deposited amount and subtract the cashed amount from her initial balance.
x + 1,870 + k + 469.30 - t - 91.40x + 1,788.20 + k - t
Therefore, the algebraic expression that represents the amount of money in Helena's account after the transactions is "x + 1,788.20 + k - t".Hence, the correct option is O x + 1,788.20 +kt.
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Mis Strickland bought 4 spools of thread. Each spool of Indigo thread is 7 meters long and each spool of orange thread is 5 meters long. It was Strickland bought 28 meters of thread in total, how many rolls of each color did she buy?
Let's denote the number of spools of Indigo thread as 'x' and the number of spools of orange thread as 'y'. The given information tells us that each Indigo spool is 7 meters long and each orange spool is 5 meters long.
We can set up a system of equations based on the given information:Equation 1: x + y = 4 (since she bought 4 spools in total)Equation 2: 7x + 5y = 28 (since the total length of thread is 28 meters) To solve this system of equations, we can use various methods, such as substitution or elimination. Let's solve it using the substitution method:From Equation 1, we can express x in terms of y as x = 4 - y.Substituting x = 4 - y into Equation 2, we get:
[tex]7(4 - y) + 5y = 28\\28 - 7y + 5y = 28\\-2y = 0\\y = 0[/tex]
Substituting y = 0 back into Equation 1, we find:
[tex]x + 0 = 4\\x = 4[/tex]
Therefore, Strickland bought 4 spools of Indigo thread and 0 spools of orange thread.In summary, Strickland bought 4 rolls of Indigo thread and 0 rolls of orange thread to have a total length of 28 meters
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Last week, the price, in dollars, of a gallon of gasoline was g. This week, the price of gasoline per gallon increased by 5%. Which expressions represent this week's price, in dollars, of a gallon of gasoline?
The expression that represents this week's price, in dollars, of a gallon of gasoline is 1.05g.
Given that last week, the price, in dollars, of a gallon of gasoline was g. This week, the price of gasoline per gallon increased by 5%.We are to find which expressions represent this week's price, in dollars, of a gallon of gasoline.
If the price of gasoline per gallon last week was g, and it has increased by 5% this week, then this week's price of gasoline per gallon will be 5% greater than last week's price, which is equal to 1.05 times the price of last week's gasoline per gallon.Therefore, this week's price, in dollars, of a gallon of gasoline is given by the expression 1.05g.
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To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.
x2 + x + ≥
The desired revenue for the buffet can be represented by the inequality (P + x) * C ≥ R, where P is the initial price, x represents $1 increases, C is the average number of customers per hour, and R is the desired revenue.
To represent the restaurant owner's desired revenue, we need to create an inequality in standard form based on the given information. Let's assume the initial price of the buffet is $P, and x represents the number of $1 increases. The new price of the buffet would be P + x.The average number of customers per hour is represented by the variable C. The revenue generated per hour can be calculated by multiplying the price paid by each customer (P + x) and the average number of customers per hour (C). Hence, the hourly revenue can be expressed as (P + x) * C.
To create an inequality representing the desired revenue, we need to set a specific target revenue level. Let's assume the owner desires a minimum revenue of R dollars per hour. The inequality representing the desired revenue can be expressed as:
(P + x) * C ≥ R
This inequality states that the product of the new buffet price (P + x) and the average number of customers per hour (C) must be greater than or equal to the desired revenue (R) to meet the owner's expectations.
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Who did nehemiah leave in charge of jerusalem while he traveled.
According to the Bible, Nehemiah left Hanani, along with Hananiah the commander of the citadel, in charge of Jerusalem while he traveled. This is mentioned in Nehemiah 7:2, which states:
"Then I put Hanani my brother and Hananiah the commander of the citadel in charge of Jerusalem, for he was a faithful man and feared God more than many."
Nehemiah, a cupbearer to the Persian king Jerusalem, was granted permission to return to Jerusalem to rebuild its walls. During his absence, he entrusted the responsibility of overseeing Jerusalem to Hanani and Hananiah. Hanani is described as Nehemiah's brother and Hananiah as the commander of the citadel, indicating their positions of authority and trustworthiness.
Nehemiah's decision to leave Hanani and Hananiah in charge highlights his confidence in their faithfulness and fear of God, indicating that he believed they would fulfill their duties responsibly during his absence.
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If 8-i is the sum of two complex numbers, and one of the binomials is 7 - 2i, which represents
the other binomial?
the other binomial is 1 + i.
We are given that 8-i is the sum of two complex numbers and one of the binomials is 7 - 2i. We are to find the other binomial.Let the other binomial be x + yi where x and y are real numbers. Then, 7 - 2i + x + yi = 8 - i => (7 + x) + (y - 2)i = 8 - iComparing real and imaginary parts on both sides, we get:7 + x = 8 => x = 1y - 2 = -1 => y = 1Hence, the other binomial is 1 + i.More than 100 words:The sum of two complex numbers is a complex number that is the result of adding two complex numbers. In mathematical notation, we write this as (a + bi) + (c + di) = (a + c) + (b + d)i. In this question, we are given that 8-i is the sum of two complex numbers. Let these two complex numbers be (x + yi) and (7 - 2i).Then, we have (x + yi) + (7 - 2i) = 8 - iExpanding the left-hand side, we get:x + yi + 7 - 2i = 8 - iRearranging the terms, we get:x + 7 + yi - 2i = 8 - iGrouping the real and imaginary parts, we get:x + 7 = 8 (real part)yi - 2i = -1 (imaginary part)Simplifying the first equation, we get:x = 1Substituting x = 1 into the second equation and solving for y, we get:y - 2 = -1y = 1
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A swimming pool has a length of 50 meters, a width of 30 meters and a depth of 1. 75 meter. What is the volume?
To calculate the volume of a rectangular prism such as a swimming pool, you need to multiply the length, width, and depth of the pool.
Therefore, we can calculate the volume of the swimming pool as follows:
Volume of the swimming pool= Length × Width × Depth
Given that, The length of the swimming pool is 50 meters, the width of the swimming pool is 30 meters, the depth of the swimming pool is 1.75 meters.
Therefore, Volume of the swimming pool= Length × Width × Depth
= 50 × 30 × 1.75
= 2625 cubic meters.
The volume of the swimming pool is 2625 cubic meters. To find out the volume of a swimming pool with a length of 50 meters, a width of 30 meters and a depth of 1.75 meters, we will use the formula for the volume of a rectangular prism which is V = l × w × h.
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Polygon JKLMNP represents a bus route with vertices
J (2, 4), K (2, 7), L (7, 7), M (7, 2), N (5, 2), and P (5, 4).
Each grid square represents 16 square miles.
The area of the polygon JKLMNP, representing the bus route, is 6400 square miles based on the given scale of 16 square miles per grid square.
In the given information, the polygon JKLMNP represents a bus route with specific vertices, and each grid square represents 16 square miles.
The vertices of the polygon are given as:
J (2, 4)
K (2, 7)
L (7, 7)
M (7, 2)
N (5, 2)
P (5, 4)
To determine the area of the polygon in terms of square miles, we need to calculate the area of the shape enclosed by the given vertices.
The distance between the vertices on the x-axis represents the width of the polygon, and the distance between the vertices on the y-axis represents the height.
Calculating the width:
KJ = 7 - 2 = 5 units
Calculating the height:
ML = 7 - 2 = 5 units
To convert these units to miles, we multiply by the given scale of 16 square miles per grid square:
Width = 5 * 16 = 80 square miles
Height = 5 * 16 = 80 square miles
Finally, to find the area of the polygon, we multiply the width by the height:
Area = Width * Height = 80 * 80 = 6400 square miles
Therefore, the area of the polygon JKLMNP, representing the bus route, is 6400 square miles based on the given scale of 16 square miles per grid square.
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At El Toro Mexican Restaurant you can order a burrito, a taco or an enchilada. Any of these can be filled with either beef or chicken and topped with one of three salsas: mild, medium or hot.
How many different combinations of meals can you order if you pick one of each option?
There are a total of 18 different combinations of meals you can order at El Toro Mexican Restaurant by choosing one option each for the main dish (burrito, taco, or enchilada), filling (beef or chicken), and salsa (mild, medium, or hot).
To find the number of combinations, we multiply the number of options for each choice. There are 3 options for the main dish (burrito, taco, or enchilada), 2 options for the filling (beef or chicken), and 3 options for the salsa (mild, medium, or hot).
Thus, the total number of combinations is obtained by multiplying these options together: 3 (main dish) * 2 (filling) * 3 (salsa) = 18. Therefore, there are 18 different combinations of meals you can order at El Toro Mexican Restaurant by selecting one option each for the main dish, filling, and salsa.
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Darryl wants to add enough water to 8 gallons of a 10% bleach solution to make a 5% bleach solution. Which equation can he use to find x, the number of gallons of water he should add? Original (Gallons) Added (Gallons) New (Gallons) Amount of Bleach 0. 8 0 0. 8 Amount of Solution 8 x 8 x StartFraction 0. 8 Over 8 x EndFraction times StartFraction 5 Over 100 EndFraction = 1 StartFraction 0. 8 Over 8 x EndFraction times = StartFraction 5 Over 100 EndFraction StartFraction 0. 8 Over 8 x EndFraction = StartFraction 100 Over 5 EndFraction StartFraction 0. 8 Over 8 x EndFraction divided by StartFraction 5 Over 100 EndFraction = 1.
Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution.
Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution .The correct equation that Darryl can use to find x, the number of gallons of water he should add, is:
0.8 / (8 + x) = 5/100
Let's break down the equation and explain each part:
The numerator 0.8 represents the amount of bleach in the original 8-gallon solution.
The denominator (8 + x) represents the total volume of the new solution after adding x gallons of water.
5/100 represents the desired concentration of the new solution, which is 5% bleach.
By setting up this equation, we equate the amount of bleach in the original solution (0.8 gallons) to the amount of bleach in the new solution (5% of the total volume, which is (8 + x) gallons).
Simplifying the equation:
0.8 / (8 + x) = 5/100
To solve for x, we can cross-multiply:
0.8 * 100 = 5 * (8 + x)
80 = 40 + 5x
Subtracting 40 from both sides:
80 - 40 = 5x
40 = 5x
Dividing both sides by 5:
40 / 5 = x
8 = x
Therefore, Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution.
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a clown needed 275 balloons for a party he was going to but the balloons only came in packs of 2 how many packs wouls he need to bye
the clown would need to buy 138 packs of balloons to have a total of 275 balloons for the party.
IfIf the balloons only come in packs of 2, we need to determine how many packs the clown would need to buy in order to have a total of 275 balloons.
To find the number of packs needed, we divide the total number of balloons (275) by the number of balloons in each pack (2).
275 balloons ÷ 2 balloons per pack = 137.5 packs
Since we cannot have a fraction of a pack, we round up to the nearest whole number.
Therefore, the clown would need to buy 138 packs of balloons to have a total of 275 balloons for the party.
Note: Rounding up to the nearest whole number ensures that the clown has enough balloons and avoids having a fractional number of packs.
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A sample of n = 5 scores has a mean of M = 12. If one person with a score of X = 18 is added to the sample, what is the value for the new mean?.
A sample of n = 5 scores has a mean of M = 12. If one person with a score of X = 18 is added to the sample, the new mean, can be calculated as 14.
The initial sample of n = 5 scores has a mean of M = 12. To find the new mean after adding a score of X = 18 to the sample, we can use the formula for the mean: M = (sum of scores) / (number of scores).
The sum of the original scores is 5 * 12 = 60. When we add the score of 18, the new sum becomes 60 + 18 = 78. Since the total number of scores is now 6, the new mean is calculated as 78 / 6 = 13.
Therefore, the new mean after adding a score of 18 to the sample is 14.
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Dilate HAT if H(-1,-1), A(1,0), T(-1,2) by a scale factor of 2 from the point (-1,2). help it’s due in a few hours
To dilate the points H(-1, -1), A(1, 0), and T(-1, 2) by a scale factor of 2 from the point (-1, 2), So the answer is: the dilated points are H(-3, 3), A(-1, 4), and T(-3, 6) when dilated by a scale factor of 2 from the point (-1, 2).
The following steps are:
1. Calculate the translation vector from (-1, 2) to the origin (0, 0). Subtract the coordinates of the origin from the coordinates of the point (-1, 2):
Translation vector = (-1 - 0, 2 - 0) = (-1, 2).
2. Apply the dilation to each point using the scale factor of 2. Multiply the translation vector by the scale factor:
Dilation vector = Scale factor * Translation vector
= 2 * (-1, 2)
= (-2, 4).
3. Translate the points back to their original position by adding the dilation vector to each point:
Dilated point H: (-1, -1) + (-2, 4) = (-3, 3)
Dilated point A: (1, 0) + (-2, 4) = (-1, 4)
Dilated point T: (-1, 2) + (-2, 4) = (-3, 6)
So, the dilated points are H(-3, 3), A(-1, 4), and T(-3, 6) when dilated by a scale factor of 2 from the point (-1, 2).
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!! WILL GIVE A BRAINILIST
A box contains 6 yellow 3 red 5 green colored pencils. A colored pencil is chosen at random it is not replaced then another is chosen. What is the probability of choosing a red followed by a YELLOW?
The probability of selecting a red pencil followed by a yellow pencil is 3/182. The probability of choosing a red pencil followed by a yellow pencil is obtained by multiplying the probability of choosing a red pencil and the probability of choosing a yellow pencil without replacing the red pencil.
It is expressed as a fraction, decimal, or percentage. It is computed by dividing the number of possible successful outcomes by the number of total outcomes. The number of pencils in the box is 14.
The probability of choosing a red pencil is 3/14 because there are three red pencils in the box. The likelihood of selecting a red pencil followed by a yellow pencil is the product of these two probabilities:
3/14 × 1/13
= 3/182.
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The energy magnitude M of an earthquake can be modeled by the equation
M=(2/3)log E - 9. 9, where E is the amount of energy released. What is the magnitude of an earthquake with an energy release of 7. 079 X 10^26? Round your answer to the nearest whole number
The magnitude of an earthquake with an energy release of 7.079 × 10^26 is approximately 8.
To find the magnitude (M) of an earthquake with an energy release of 7.079 × 10^26, we can substitute this value into the given equation:
M = (2/3)log(E) - 9.9
where E is the amount of energy released.
Substituting E = 7.079 × 10^26 into the equation:
M = (2/3)log(7.079 × 10^26) - 9.9
Now, let's calculate the magnitude:
M = (2/3)log(7.079) + (2/3)log(10^26) - 9.9
Using the properties of logarithms:
M = (2/3)log(7.079) + (2/3)(26) - 9.9
M = (2/3)log(7.079) + 17.33 - 9.9
M = (2/3)log(7.079) + 7.43
Now, we can evaluate the logarithm:
M = (2/3)(0.850) + 7.43
M = 0.567 + 7.43
M ≈ 7.997
Rounding to the nearest whole number, the magnitude of the earthquake is 8.
Therefore, the magnitude of an earthquake with an energy release of 7.079 × 10^26 is approximately 8.
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Juan tiene manzanas que cuestan 4 euros al kilo y su amigo Fran tiene plátanos que cuestan 2 euros más que las manzanas. ¿Cuánto cuestan las manzanas? ¿Y los plátanos?
The cost of the apples is 4 euros per kilo and the cost of the bananas is 6 euros per kilo.
How to find the cost of the bananas?We know that Juan has apples that cost 4 euros per kilo, and Fran has banans that cost 2 more euros than tha apples.
Then if the cost of the apples is A, and the cost of the bananas is B, we can write the linear equation:
B = A + 2
We know that A = 4, replacing that we will get:
B = 4 + 2
B = 6
The bananas cost 6 euros per kilo.
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State what additional information is required in order to know that the triangles are congruent for the reason given.
SAS
a) OP=OV
b) RO=TO or OP=OV
c) RO=TO
d) angle R=angle T
additional information to prove that the two triangles have all three corresponding sides and angles congruent. Hence option d is correct.
When we sa that two triangles are congruent, it means that they have all three pairs of corresponding sides and angles that are congruent
t. So, in order to know that the triangles are congruent using the SAS (Side-Angle-Side) method, we need to have additional information to prove that the two triangles have all three corresponding sides and angles congruent.
Option a): OP = OV. This is not sufficient to show congruence between the triangles using the SAS method. The given reason does not provide any angle information.
Option b): RO = TO or OP = OV. This is also not sufficient to show congruence using the SAS method. The given reason provides only two corresponding sides and no angle information.
Option c): RO = TO. This is not sufficient to show congruence using the SAS method. The given reason provides only one pair of corresponding sides and no angle information.
Option d): Angle R = Angle T. This is sufficient to show congruence using the SAS method. This given reason provides one pair of corresponding sides and an included angle that is congruent in both triangles. Thus, the two triangles have two pairs of congruent sides and a congruent angle between them, which satisfies the SAS condition.
From the above analysis, we can conclude that option (d) is the correct answer. To know whether two triangles are congruent using the SAS method, we need to have additional information to prove that the two triangles have all three corresponding sides and angles congruent
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The garden's length is 40.8 feet. it will be divided into 12 sections across. how long is each section? show your work.
Each section of the garden will be 3.4 feet long.
To find the length of each section, we can divide the total length of the garden by the number of sections.
Length of the garden: 40.8 feet
Number of sections: 12
Length of each section = Total length of the garden / Number of sections
Length of each section = 40.8 feet / 12
Length of each section = 3.4 feet
Therefore, each section of the garden will be 3.4 feet long.
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