Using a system of equations, the expression, in terms of x, for the total number of students at the college is:
T = 11x.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem
For this problem, considering the Venn diagram, we have that:
A + x students play the Piano.B + x students play the Guitar.Thus the total number of students in the college is given by:
T = A + B + x.
1/2 of the students who learn the piano also learn the guitar, hence:
A = x.
Thus the number of students who play the piano is:
A + x = x + x = 2x.
5 times as many students learn the guitar as learn the piano, hence:
B + x = 5(2x)
B + x = 10x
B = 9x.
Hence:
T = A + B + x
T = x + 9x + x
T = 11x.
The expression, in terms of x, for the total number of students at the college is:
T = 11x.
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can someone please help me?
Answer:
x=3
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
45x = 25x+57+x
Combine like terms
45x = 26x+57
Subtract 26x from each side
45x-26x = 26x+57-26x
19x = 57
Divide by 19
19x/19 = 57/19
x = 3
I’ll give you brainlest if you answer this question correctly it goes to the first person!
Answer:
It would be -4 for "x" and -6 for "y"
Step-by-step explanation:
x+z=-4+-6=-10
x-y=-4--6=2
What is the area, in square centimeters, of the parallelogram
below?
12 cm
8 cm
A.48
B.84
C.96
D.108
Answer: 96cm² or C
Step-by-step explanation:
Area of parallelogram = b × h
b = 12
h = 8
12 × 8 = 96
The area of this parallelogram is 96cm²
Help me please!!!!!!!!!!!!!
9514 1404 393
Answer:
$6.50/lb
Step-by-step explanation:
To find price per pound, divide price by pounds.
$35.75/(5.5 lb) = $6.50/lb
what is the product of the rational expression 2/x+1 • 5/3x
\(\left(\dfrac{2}{x+1}\right)\cdot\left(\dfrac{5}{3x}\right) = \dfrac{10}{3x^2+3x}\)
B is right
What is the greatest three-digit number that is a multiple of three and eight?
"984" will be the biggest three-digit number that is a multiple of three and eight.
What is the number line?A horizontal line with evenly spaced numerical increments is called a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
To find the greatest three-digit number that is a multiple of three and eight.
Multiple of 3 and 8 will have to be the multiple of 24.
Since the maximum three-digit number is 999.
We will divide 999 by 24 and the remainder:
Remainder = 15
Thus,
The Greatest three-digit number will be = 999-15
The greatest three-digit number will be = 984
therefore, the Greatest three-digit number that is a multiple of three and eight will be "984".
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What is joule per meter second?
Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.
Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.
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Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-axis?V=2Π∫ xf(x)dxV=Π∫ xf(x)dxV=2Πx2f(x)dxV=Π2∫ xf(x)dx
The volume of the solid created by revolving a curve f(x) around the y-axis is 2π \(\int\limits^a_b {xf(x)} \, dx\)
What is the cylindrical shell?
A region enclosed by two identically sized cylinders with the same central axis is known as a cylindrical shell. We often denote the height of the cylinders by H, the inner cylinder's radius by r, and the thickness of the shell by t, resulting in a larger cylinder's radius equal to r + t.
Here,
We consider a strip of height y = f(x), and width dx; it is x units away from the axis of rotation.
Now, we rotate this strip about the y-axis; we obtain a cylindrical shell with
radius = x
height = f(x)
thickness = dx
The volume of cylindrical shell = (circumference)×(height)×thickness
= (2πx)×(f(x))×dx
The volume of revolution = 2π \(\int\limits^a_b {xf(x)} \, dx\)
Hence, the volume of the solid created by revolving a curve f(x) around the y-axis is 2π \(\int\limits^a_b {xf(x)} \, dx\)
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14 = 2y/5 what is the solution?
Answer:
y=35
Step-by-step explanation:
y in (-oo:+oo)
14 = (2*y)/5 // - (2*y)/5
14-((2*y)/5) = 0
(-2/5)*y+14 = 0
14-2/5*y = 0 // - 14
-2/5*y = -14 // : -2/5
y = -14/(-2/5)
y = 35
y = 35
if the positive integer x leaves a remainder of 2 when divided by 8, what will the remainder be when x 9 is divided by 8?
The remainder when a positive integer x leaves a remainder of 2 when divided by 8 and x+9 is divided by 8 is 5.
If the positive integer x leaves a remainder of 2 when divided by 8, then we can say that x = 8k + 2, where k is an integer.
Now, if we divide x+9 by 8, we get:
(x+9)/8 = (8k + 2 + 9)/8
= (8k + 11)/8
= k + (11/8)
So, the remainder when x+9 is divided by 8 is 11/8. However, since we are dealing with integers, the remainder can only be a whole number between 0 and 7.
Therefore, we need to subtract the quotient (k) from the expression above and multiply the resulting decimal by 8 to get the remainder:
Remainder = (11/8 - k) x 8
Since k is an integer, the only possible values for (11/8 - k) are -3/8, 5/8, 13/8, etc. The closest whole number to 5/8 is 1, so we can say that:
Remainder = (11/8 - k) x 8 ≈ (5/8) x 8 = 5
Therefore, the remainder when x+9 is divided by 8 is 5.
If a positive integer x leaves a remainder of 2 when divided by 8, then x can be expressed as 8k + 2, where k is an integer. To find the remainder when x+9 is divided by 8, we divide x+9 by 8 and subtract the quotient from the decimal part. The resulting decimal multiplied by 8 gives us the remainder. In this case, the decimal is 11/8, which is closest to 1. Thus, we subtract the quotient k from 11/8 and multiply the result by 8 to get the remainder of 5.
The remainder when a positive integer x leaves a remainder of 2 when divided by 8 and x+9 is divided by 8 is 5.
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Charmaine made 8 stacks with her coins.
Every stack had 6 coins.
How many coins did she have altogether?
If Charmaine made 8 stacks with her coins and every stack had 6 coins, then the number of coins that she has all together is 48 coins
The number of coins that she has made = 8 stacks
The number of coins in each stack = 6 coins
To find the number of coins that she has, we have to multiply the number of stack and number of coins in each stack
Then the number of coins that she has all together = The number of coins that she has made × The number of coins in each stack
Substitute the values in the equation
= 8 × 6
= 48 coins
Hence, if Charmaine made 8 stacks with her coins and every stack had 6 coins, then the number of coins that she has all together is 48 coins
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Anthony's Ice Cream Shop sold 18 sundaes. 8 of the sundaes had nuts on top. What is the ratio of the number of sundaes without nuts to the number of sundaes with nuts?
A cylinder made of lead has a height of 4 inches and a diameter of 2 inches how heavy is a cylinder if lead weighs. 04 pound per cubic inch?
To calculate the weight of the lead cylinder, we need to determine its volume first. The volume of a cylinder can be calculated using the formula: Volume = π * r^2 * h
Given that the diameter of the cylinder is 2 inches, the radius (r) is 1 inch. The height (h) is 4 inches.
Substituting these values into the formula, we get:
Volume = 3.14159 * 1^2 * 4
Volume = 12.56636 cubic inches
Now, to calculate the weight, we multiply the volume by the weight per cubic inch of lead:
Weight = Volume * Weight per cubic inch
Weight = 12.56636 * 0.04
Weight = 0.5026544 pounds
Therefore, the weight of the lead cylinder is approximately 0.5027 pounds.
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Jane spent 3 hours exploring a mountain with a dirt bike. First, she rode 48 miles uphill. After she reached the peak she rode for 15 miles along the summit. While going uphill, she went 5 mph slower than when she was on the summit. What was her rate along the summit?
Answer: \(25\ mph\)
Step-by-step explanation:
Given
Jane took 3 hours
First she rode 48 miles with let say with \(x\) mph
then she rode 15 miles with speed \((x+5)\) mph
Equate the time in each ride and equate it to total time
\(\Rightarrow 3=\dfrac{48}{x}+\dfrac{15}{x+5}\\\\\Rightarrow 3x(x+5)=48(x+5)+15x\\\\\Rightarrow 3x^2+15x=48x+48\times 5+15x\\\\\Rightarrow 3x^2-48x-240=0\\\\\Rightarrow (x-20)(x+4)=0\\\\\text{Neglecting the negative value as speed cannot be negative}\\\\\Rightarrow x=20\ mph\)
So, her along the summit is \(x+5=25\ mph\)
How do you do this ??????????????????????
Answer:
b
Step-by-step explanation:
you can take the rectagel and you x the rectagel
evaluate g(r)=-5r+13 g(3)
Answer:
r57
Step-by-step explanation:
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Evaluate the expression for the given value of the variable.
Answer:
-11
Step-by-step explanation:
Insert the value of b: |(-4 * -2) - 8| + |-1 - (-2)²| + 2(-2)³
Simplify & solve: |8 - 8| + |-1 - 4| + 2 * -8
|0| + |-5| + -16
0 + 5 - 16
-11
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. He believes that the mean income is $28.4, and the standard deviation is known to be $6.6. How large of a sample would be required in order to estimate the mean per capita income at the 85% level of confidence with an error of at most $0.56
To estimate the mean per capita income for a major city in California with an error of at most $0.56 at the 85% confidence level, the economist needs to determine the required sample size.
To calculate the required sample size, we can use the formula: \(n = \left(\frac{{Z \cdot \sigma}}{{E}}\right)^2\), where \(n\) is the sample size, \(Z\) is the Z-score corresponding to the desired confidence level (in this case, for 85% confidence level, \(Z \approx 1.44\)), \(\sigma\) is the known standard deviation (\$6.6), and \(E\) is the desired margin of error (\$0.56). Plugging in the values, we have \(n = \left(\frac{{1.44 \cdot 6.6}}{{0.56}}\right)^2 \approx 52\). Therefore, a sample size of approximately 52 would be required to estimate the mean per capita income with an error of at most $0.56 at the 85% confidence level.
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Gaseous butane CH3CH22CH3 will react with gaseous oxygen O2 to produce gaseous carbon dioxide CO2 and gaseous water H2O. Suppose 1.2 g of butane is mixed with 2.75 g of oxygen. Calculate the maximum mass of carbon dioxide that could be produced by the chemical reaction. Be sure your answer has the correct number of significant digits.
The maximum mass of carbon dioxide that could be produced by the chemical reaction between 1.2 g of butane and 2.75 g of oxygen is 4.40 g.
To calculate the maximum mass of carbon dioxide produced, we first need to determine the limiting reactant. We compare the number of moles of butane and oxygen by dividing their respective masses by their molar masses. The molar mass of butane (C4H10) is 58.12 g/mol, and the molar mass of oxygen (O2) is 32.00 g/mol.
Using these values, we find that the number of moles of butane is 1.2 g / 58.12 g/mol = 0.0206 mol, and the number of moles of oxygen is 2.75 g / 32.00 g/mol = 0.0859 mol. Since butane has fewer moles than oxygen, it is the limiting reactant.
Next, we need to determine the molar ratio of carbon dioxide to butane using the balanced chemical equation. The balanced equation is:
2 C4H10 + 13 O2 -> 8 CO2 + 10 H2O
From this equation, we can see that for every 2 moles of butane, 8 moles of carbon dioxide are produced. Therefore, for the 0.0206 mol of butane, we can calculate the corresponding mass of carbon dioxide as follows:
0.0206 mol butane * (8 mol CO2 / 2 mol butane) * (44.01 g/mol CO2) = 0.361 g CO2
Thus, the maximum mass of carbon dioxide that could be produced is 0.361 g. However, it is important to note that this assumes ideal conditions and complete conversion, so in reality, the actual yield may be lower due to factors like incomplete reactions or side reactions.
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The box-and-whisker plot below represents some data set. What percentage of the
data values are between 16 and 72?
20
40
60
80
100
Considering the given box-and-whisker plot, it is found that 50% of the data values are between 16 and 72.
What does a box-and-whisker plot shows?A box and whisker plot shows five things:
The minimum value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum value.From this plot, we have that:
The 25th percentile is of 16.The 75th percentile is of 72.Hence, 50% of the data values are between 16 and 72.
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can you help me with the question pls it's about standard form/scientific notation.
I'm confused with the minuses on the indices.
Answer:
-3 squared means it is 0.1 for each -1, so it would be 0.001
Step-by-step explanation:
it is 0.003 for a and the rest you can figure out
Dante watched a video for 3/8 minutes. He watched another video for 1/8 minutes.
For how long did he watch videos in all?
Write your answer as a fraction in simplest form.
Answer:4/8 are u in pre?
Step-by-step explanation:
4. Answer the following questions. 1) The mathematical statement of the second law of thermodynamics. 2) The mathematical statement of the second law of thermodynamics for a noncyclic process. 3) The
If α and β are the zeroes of the polynomial 6y 2 − 7y + 2, find a quadratic polynomial whose zeroes are 1 α and 1 β .
Answer:
\(2y^2-7y+6=0\)
Step-by-step explanation:
We are given that \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(6y^2-7y+2\)
\(y^2-\frac{7}{6}y+\frac{1}{3}\)
We have to find a quadratic polynomial whose zeroes are \(1/\alpha\) and \(1/\beta\).
General quadratic equation
\(x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes\)
We get
\(\alpha+\beta=\frac{7}{6}\)
\(\alpha \beta=\frac{1}{3}\)
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}\)
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}\)
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2\)
\(\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}\)
\(\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3\)
Substitute the values
\(y^2-(7/2)y+3=0\)
\(2y^2-7y+6=0\)
Hence, the quadratic polynomial whose zeroes are \(1/\alpha\) and \(1/\beta\) is given by
\(2y^2-7y+6=0\)
Lora's phone records data for screen time each week. last week, she used 920 minutes. this week, lora used 690 screen time minutes on the phone. calculate the percent decrease in screen time this week. 25% 33% 40% 75%
The percentage decrease in Lora's screen time on phone is 25% this week.
Percentage related problems work around a certain reference value. This reference value is what the output percentage refers to when showing any growth or decay in the other value.
For this problem, last week's screen time is that reference value i.e. 920 minutes per week.
Now, current week's usage is 690 minutes per week. For calculating percentage decrease, we first find our the difference (in minutes).
\(Decrease=S_{1}- S_{2}=920-690=230\)
Now, for its percentage we compare this value to our reference value i.e. last week's screen time. This will tell us about the decrease in screen time with reference to last week. This is what percentage does i.e. compares two sets of data.
\(Decrease=\frac{difference}{S_{1}}*100= \frac{230}{920}*100\)
\(Decrease=25\)%
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Answer:25
Step-by-step explanation:
Alia bought a home for her pet turtle. The rectangular tank is 3 feet long, 1 foot wide, and 2 feet high. What is the volume of the tank?
The volume of the tank is Blank
cubic feet
Answer:
6 ft^3 or cubic ft
Step-by-step explanation:
Volume = B x H or L x W x H
Base = L x W
Length: 3 ft
Width: 1 ft
Height: 2 ft
3 x 1 x 2 = 6
6 ft^3
A random experiment consists of tossing a fair six-sided die repeatedly. How many tosses are required to be certain that the probability that at least one '6' appears is greater than or equal to 1/2?
I keep getting 3 from 1/6+1/6+1/6=1/2, it says the correct answer is 4.
We need at least 5 tosses to be certain that the probability of getting at least one 6 is greater than or equal to 1/2.
The probability of not getting a 6 on a solitary throw of a fair six-sided kick the bucket is 5/6. Subsequently, the probability of not getting a 6 on n throws is \((5/6)^n\). The probability of getting somewhere around one 6 in n throws is 1 - \((5/6)^n\).
To view the quantity of throws expected as sure that the probability of getting somewhere around one 6 is more prominent than or equivalent to 1/2, we can set the probability equivalent to 1/2 and address for n:
1 - \((5/6)^n\) = 1/2
\((5/6)^n\) = 1/2
Taking the normal logarithm of the two sides, we get:
n ln(5/6) = ln(1/2)
n = ln(1/2)/ln(5/6) ≈ 4.807
Hence, we really want something like 5 throws to be sure that the probability of getting no less than one 6 is more prominent than or equivalent to 1/2.
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If the area of a square is 16 square feet, how long are the sides?
Answer:
4 square feet each.
Step-by-step explanation:
A square is 4 times 4 so if you divide 16 divided by 4 it is 4.
Answer:
The sides are going to 4 square feet long.
Step-by-step explanation:
This is true because since a square has equal length sides. And there are 4 sides. So divided 4 by 16 to get 4. So, the answer is 4 square feet long.
Mark brainliest if ya don't mind!
In the figure below, AE | BD. What is the value of x?
Answer:
The value of x=3
Step-by-step explanation:
We are given that
AE is parallel to BD.
BC=12 units
CD=16 units
DE=4 units
AB=x
We have to find the value of x.
Triangle proportionality theorem:
When a line is parallel to one side of a triangle and intersect the other two sides of triangle, then the line divides the sides proportionally.
Using triangle proportionality theorem
\(\frac{BC}{AB}=\frac{CD}{DE}\)
\(\frac{12}{x}=\frac{16}{4}\)
\(x=\frac{12\times 4}{16}\)
\(x=3\)units
Hence, the value of x=3
scores on the wechsler adult intelligence scale for the 20 to 34 age group are approximately normally distributed with mean 110 and standard deviation 15. how high must a person score to be in the top 5% of all scores? enter your answer as a whole number.
The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
What is defined as the normal distribution?A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.A histogram inside a normal distribution curve is sometimes used to design the curve.The formula for the normal distribution is;
z = (x - μ)/σ
where,
z = z- score, taken fro tableMean μ = 110Standard deviation σ = 15Sample mean x.If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.
In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.
z = 1.7
Put the value in formula ad find x.
1. 7 = (x - 110)/15
x = 25.5 + 110
x = 135.5
x = 136 (whole number)
Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
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