So, the number of students in Band, Art, Music and Journalism are 2n, 7n+6, 4n-2 and 2(4n+6) respectively.
Since the number of students enrolled in Art and Music is equal to the number of students enrolled in Band and Journalism, we have the equation
7n + 6 + (4n-2) = 2n + 2(4n+6).
We now expand the brackets :
7n + 6 + 4n - 2 = 2n + 8n + 12
-> 11n + 4 = 10n + 12
-> 11n + 4 - 10n - 12 = 0
-> n - 8 = 0
-> n = 8.
Therefore, the number of students that enrolled in :
Band : 2n = 16 students.
Art : 7n + 6 = 62 students.
Music : 4n - 2 = 30 students.
Journalism : 8n + 12 = 76 students.
76 = 16 = 62 + 30 = 92, satisfying the requirement.
-5 / 3 + 4k / = -115
Answer:
[tex]\frac{11}{2} ,-\frac{13}{2}[/tex]
Step-by-step explanation:
we know That l [tex]x[/tex] l = x when x > 0 and l x l = - x when x <0
for the given equation - 5|3 + 4k| = - 115
when 3 + 4k > 0 the equation becomes
-5(3+4k) = - 115
→ -5 · 3 - 5 · 4k = - 115
→- 20k = - 115 + 15 = - 110
→ k = -[tex]\frac{110}{-20}[/tex] = [tex]\frac{11}{2}[/tex]
Again when 3 + 4k <0 the equation becomes
-5(-(3+ 4k )) = - 115
→15 + 20k = - 115
→ 20k = - 115 - 15
→ 20k = - 130
⇒ k = -[tex]\frac{130}{20}[/tex] = -[tex]\frac{13}{2}[/tex]
find the weighted mean for three exams if the first one was worth 75 points and the student received a score of 70%, the second was worth 50 points and the student received a score of 80% and the third was worth 30 points and the student received a score of 95%?
The weighted mean for three exams is 78.1%.
Define weighted mean.The weighted mean is a form of mean that is computed by averaging all the products after multiplying the weight (or probability) connected to a specific event or result by its connected quantitative outcome. The difference between the weighted arithmetic mean and a regular arithmetic mean is that certain data points contribute more to the final average than others, as opposed to all data points contributing equally. In mathematics, the average value of the data is determined using the weighted mean. When calculating the weighted mean, the average value can be determined by giving various weights to some of the individual variables.
Given,
Weighted mean for student:
Weights = 155
∈x₁ w₁/∈w₁
121/155 × 100%
78.045%
78.1%
The weighted mean for three exams is 78.1%.
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Find the remainder for the quotient using either substitution or synthetic division.
x - 5 is a factor of the polynomial
f(x) = x^3 - x^2 - 17x - 15)
(The answer must include what the remainder value is and what it indicates.)
(x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15 as there is no remaider.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given a polynomial function f(x) = x³ - x² - 17x -15.
If (x - 5) is it's factor then f(5) = 0.
∴ f(x) = x³ - x² - 17x -15.
f(5) = 5³ - 5² - 17(5) - 15.
f(5) = 125 - 25 - 85 - 15.
f(5) = 0.
So, the remainder is zero hence (x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15.
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If a body is moving in the horizontal axis with a velocity Vx= 6m/s and in the vertical axis Vy=8m/s
What is the magnitude of the velocity of the body V?
1. V= 12.1
2. V= 8.67
3. V= 11
4. V= 10
If a body is moving in the horizontal axis with a velocity Vx= 6m/s and in the vertical axis Vy=8m/s, the magnitude of the velocity of the body V is 10
The given parameters are;
The velocity of the body relative to the horizontal axis, vₓ = 6 m/s
The velocity of the body relative to the vertical axis, = 8 m/s
Required;
The measure of the magnitude of the velocity of the moving body, v
The velocity of the body can be represented vectorially as follows;
v = 6·i + 8·j
|V| = [tex]\sqrt{Vx^{2} + Vy^{2} }[/tex]
|V| = [tex]\sqrt{6^{2} + 8^{2} }[/tex]
= [tex]\sqrt{64 + 36}[/tex]
= √100
|V| = 10
Therefore if a body is moving in the horizontal axis with a velocity Vx= 6m/s and in the vertical axis Vy=8m/s, the magnitude of the velocity of the body V is 10
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(5x10^3) (9x10^7) in standard form
Answer:
4.5 times 10^11
Step-by-step explanation:
From 450000000000 as the solution to 4.5 times 10^11
Substitute the length of the sides (10 m, 26 m, n) into the Pythagorean Theorem. Then, find the length of the missing siden.
Answer:
n = 24 m
Step-by-step explanation:
n² + 10² = 26²
n² + 100 = 676
n² = 576
n = 24 m
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
always :)
Step-by-step explanation:
got it right
The perimeter is 20ft. Write an equation and use it to find the value of X.
To calculate the value of x in the diagram below:
The perimeter of a a square =
[tex]\begin{gathered} P\text{ = }4l \\ \text{Where P = perimet}er \\ l\text{ = length} \end{gathered}[/tex][tex]\begin{gathered} \text{Length = x ft} \\ P\text{erimeter = 20 ft} \\ P=\text{ 4l} \\ P=4x \\ 20\text{ = 4x} \\ x=\frac{20}{4} \\ x=5ft \end{gathered}[/tex]Hence the value of x = 5ft
Answer the questions to compare 3/12 and 2/9 by using their decimal forms.
1. How can you find the decimal forms of 3/12 and 2/9?
2. Find the decimal form of 3/12. Show your work.
3. Find the decimal form of 2/9. Show your work.
4. Classify the decimal forms of 3/12 and 2/9 as repeating or terminating.
5. Which of the numbers, 3/12 or 2/9, is greater? How do you know?
You can find the decimal forms of 3/12 and 2/9 by dividing the numerators of each of the fraction by its denominator.
The decimal form of 3/12 is 0.25.
The decimal form of 2/9 is 0.222.
The decimal form of 3/12 is a terminating decimal.
The decimal form of 2/9 is a repeating decimal.
The greater fraction is 3/12. This is because the hundredth value of 3/12 in decimal form is greater than that of 2/9.
What are the decimal forms?A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above and the denominator is the number below.
A decimal is a number that is made up of integers and non-integers that are separated by a decimal point. The integers are before the decimal point. The non-integers are after the decimal point. In order to convert a fraction to a decimal, divide the numerator by the denominator.
3 / 12 = 0.25
2 / 9 = 0.22
A terminating decimal is a decimal that ends. A repeating decimal is a number that does not end. An example of a terminating decimal is 0.25, 0.1. An example of a repeating decimal is 0.33, 0.222.
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If you pay $50 for 2.5 kg of cashews, how much do they cost per kg?
What is f(–1) for the function shown?
Answer:
f(-1) = 3
Step-by-step explanation:
This line has function f(x) = 2x - 1, so
f(-1) = 3.
Answer:
f(-1) = 3
Step-by-step explanation:
See attached. For some reason Brainly thinks my explanation has links or swear words. It does not.
URGENT DUE IN 5 MINS
Find the total earnings based on the given information.
Base Salary: $76,000
Total Sales: $238,000
Commission: 4.5%
Enter the correct answer in the box.
Step-by-step explanation:
I guess we earn 4.5% of total sales.
100% = 238,000
1% = 100%/100 = 238000/100 = $2,380
4.5% = 1% × 4.5 = 2380×4.5 = $10,710
total earnings : base salary + commission =
= 76000 + 10710 = $86,710
You want to buy some beans. A 6-ounce package costs $1.98. A 15-ounce package costs $.4.80 26-ounce package costs $.8.84 Which package is the best buy?
The best package of beans to buy is 26 ounce costs $8.84
How to calculate the best package ?
The first step is to find the unit rate for each packages
package a
6= 1.96
1= x
cross multiply both sides
6x= 1.96
x= 1.96/6
x= 0.326
package b
15= 4.80
1= x
cross multiply both sides
15x= 4.80
x= 4.80/15
x= 0.32
package c
26= 8.84
1= x
cross multiply both sides
26x= 8.84
x= 8.84/26
x= 0.34
Hence the best package that should be purchased is the 26 ounce package that costs $8.84
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The coordinates of the endpoints of
PQ
are P(3,5) and Q(18,15). Point R is on
PQ
and divides it such that PR:QR is 1:4.
What are the coordinates of R?
The coordinates of point R on PQ that divides the line segment PR : QR is 1 : 4 is (6, 7).
The given information are :
coordinates of P ( 3, 5)
coordinates of Q ( 18, 15 )
where,
x₁ = 3
x₂ = 18
y₁ = 5
y₂ = 15
The formula to calculate the coordinates of point R is:
Coordinates of R = ( mx₂+nx₁ / m+n , my₂+ny₁ /m+n )
here m= 1, n=4
Coordinates of R = ( [tex]\frac{1*18+4*3}{1+4}[/tex] , [tex]\frac{1*15+4*5}{1+4}[/tex] )
Coordinates of R = ( [tex]\frac{18+12}{5}[/tex] , [tex]\frac{15+20}{5}[/tex] )
Coordinates of R = ( [tex]\frac{30}{5}[/tex] , [tex]\frac{35}{5}[/tex] )
Coordinates of R = ( 6, 7 )
Therefore, the coordinates of point R are (6, 7).
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What is the linear function has the same slope in the graph?
The linear function that has the same slope is y = x
Equation of LineTo solve this question, we have to determine the slope and y-intercept for this graph.
We would need two coordinate points in order to do this;
A = (6, 6)B = (1, 1)The slope of a line is given as
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]
Let's substitute the values into the equation and solve.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{1 - 6}{1- 6}\\m = \frac{-5}{-5} \\m = 1[/tex]
The slope of the line is equal to 1
The y-intercept is the point at which the line touches the y-axis and in this graph, the y-intercept is at 0.
The equation of this line is equal to y = x
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Please it’s argent!
What type of transformation is used when moving a knight in a game of chess? Meaning which direction clockwise or counterclockwise? 90, 180, or 270 degrees?
Answer:The knight moves multiple squares each move. It either moves up or down one square vertically and over two squares horizontally OR up or down two squares vertically and over one square horizontally. This movement can be remembered as an "L-shape" because it looks like a capital "L".
Step-by-step explanation:
this is all i got as a experienced player of chess. hope i helped some:).
Are any of the figures B, C, Or D scales copies for figure A. Explain how you know
Answer:
C
Step-by-step explanation:
twice as bigger than A
Hello can you help please
Answer:
The measure of angle BOC is 45°
Step-by-step explanation:
If you need to show your work tell me please!
2. The ratio of creamy to crunchy peanut
butter jars on a grocery store shelf is 5 to 3
There are 18 jars of crunchy peanut butter.
What is the total number of jars of peanut
butter on the shelf?
Using ratio, the total number of peanut butter on the shelf is 144.
What is the ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, the ratio of creamy to crunchy peanut butter:
5:3If there are 18 jars of crunchy peanut butter, the total number of peanut butter will be:
5(18):3(18)90:54Total ⇒ 90 + 54 = 144
Therefore, using ratio, the total number of peanut butter on the shelf is 144.
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[tex]\sqrt{x} 320-\sqrt{x} 125+\sqrt{x} 200+3\sqrt{x} 32+2\sqrt{x} 50[/tex]
[tex]\sqrt{320x}-\sqrt{125x}+\sqrt{200x}+3\sqrt{32x}+2\sqrt{50x}[/tex]. The root equation we got [tex]3\sqrt{ 5x}+32\sqrt{2x}[/tex].
Given that,
[tex]\sqrt{320x}-\sqrt{125x}+\sqrt{200x}+3\sqrt{32x}+2\sqrt{50x}[/tex]
We have to solve the roots equation.
The factor of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9. This can be expressed as either 3² or 3×3. We refer to this as a square because there is a 2 exponent. When the exponent is now 1/2, the square root of the integer is being discussed.
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolized by the character "[tex]\sqrt{.}[/tex]" The number underneath the square root symbol is referred to as the radicand, whereas the square root symbol itself is known as a radical.
[tex]\sqrt{320x}-\sqrt{125x}+\sqrt{200x}+3\sqrt{32x}+2\sqrt{50x}[/tex]
[tex]\sqrt{64\times 5x}-\sqrt{25\times 5x}+\sqrt{100\times 2x}+3\sqrt{16\times 2x}+2\sqrt{25\times 2x}[/tex]
[tex]8\sqrt{5x}-5\sqrt{ 5x}+10\sqrt{2x}+3\times 4 \sqrt{2x}+2\times 5\sqrt{ 2x}[/tex]
[tex](8-5)\sqrt{ 5x}+10\sqrt{2x}+12 \sqrt{2x}+10\sqrt{ 2x}[/tex]
[tex]3\sqrt{ 5x}+(10+12+10)\sqrt{2x}[/tex]
[tex]3\sqrt{ 5x}+32\sqrt{2x}[/tex]
Therefore, The root equation we got [tex]3\sqrt{ 5x}+32\sqrt{2x}[/tex].
Complete question: Find the root equation in [tex]\sqrt{320x}-\sqrt{125x}+\sqrt{200x}+3\sqrt{32x}+2\sqrt{50x}[/tex].
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Nathan is going to invest $80,000 and leave it in an account for 16 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Nathan to end up with $160,000?
Answer: ≈4.33%
Step-by-step explanation:
i need help with finding the value for the ratio find how many cats to dogs and the ratio is 4:5 d you think you can help me please.
There are exactly 30 more cats than dogs and 5/9 of the pets at the farm are cats. Therefore, options C and E are correct answers.
Given that, the ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, 4+5=9
Number of dogs = 4/9 × 270
= 120
So, number of cats = 270 - 120 =150
Now, difference in number of dogs to cats = 150-120
=30
There are exactly 30 more cats than dogs and 5/9 of the pets at the farm are cats. Therefore, options C and E are correct answers.
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"Your question is incomplete, probably the complete question/missing part is:"
The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:
a. The number of dogs is 4/5 the number of cats
b. 4/5 of the pets at the farm are dogs
c. There are exactly 30 more cats than dogs
d. There are exactly 30 dogs at the farm
e. 5/9 of the pets at the farm are cats
Find the total fees:
Applications: 64
Fee: $5.10/application
Enter the correct answer in the box.
Step-by-step explanation:
since the fee is $5.10 for each and every application, the result is simply taking the fee of one application 64 times.
that means multiplication.
so, the result is
64×5.10 = $326.40
explain how to get the answer
For the first values of x, the values of 1/x are given below:
0.500.830.400.070.20For the second value of x, the values of 1/x are given below:
0.050.080.040.0070.02For the third value of 1/x, the values of x is given below:
5.08.34.07.142.0Calculations and ParametersIn order to find 1/x, we would have to put the value of x as the denominator and 1 as the numerator.
For x= 2
The value of 1/x would be 1/2 = 0.50
For x= 1.2
The value of 1/x would be 1/1.2= 0.83
Follow the same sequence to get the other answers.
For 1/x= 0.2
The value of x would be 1/0.2= 5.0
This is because
For 1/x= 0.2,
You would cross multiply and then find the value of x
Apply the same method to the other values.
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Write the equation of the line graphed below.
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
In this case, our slope is undefined. We know this because the slope never changes in the x direction:
[tex]m=\frac{x}{0}[/tex]
Thus, we can only conclude that the equation is simply [tex]x=-2[/tex] since a y component is not possible.
Question, Frank is wanting to create a scale model of the Eiffel Tower. the real Eiffel Tower is 984 feet tall and 328 feet wide at its base. If Frank's model is 15 inches tall, how wide (in inches) must his scale model be?
Answer:
5
Step-by-step explanation:
ƒ(x) = −x² + 10x − 20; Find ƒ(4)
59/60 converted to a fraction
Answer:
Step-by-step explanation:
As a decimal it is 0,98333........ (the 3 is recurring)
10. Higher Order Thinking Winston compares the heights of two plants
to see which plant grows more per day. The table shows the height
of Plant 1, in centimeters, over 5 days. The graph shows the height
of Plant 2, in centimeters, over 10 days. Winston says that since
Plant 1 grows 6 cm per day and Plant 2 grows 4 cm per day,
Plant 1 grows more per day.
Plant 1
Days
2 3 4 5
Height (cm) 6 9 12 15
a. Do you agree with Winston? Explain your response.
b. What error might Winston have made?
Height (cm)
Answer:
b what error Winston have made in height
793 one digit is right and in the right place.
725
one digit is right but in the wrong place.
317
two digits are right but both in the wrong place.
849
491
all digits are wrong.
one digit is right but in the wrong place?
Answer:
153
Step-by-step explanation:
Hello! Unsure if this is a proper question but I can sure try!
Let's start with the logic of it:
793:
To start with this one, one digit is right and is in the right place. From this step, we can't really infer anything.
725:
One digit is right but in the wrong place. Now we can do something here. There is another digit here that's correct but in the wrong place. We can eliminate 7 entirely from both 725 and 793 as they are in the same position and cannot be in the right and wrong place at the same time.
317:
Two digits are right but in the wrong places. Since we eliminated 7, the two right digits are 3 and 1, just in the wrong spots. At this point, we still need to figure out one more digit so we can't infer their positions just yet.
849:
All digits are wrong. This only affects 793, which removes 9. From here on out, 3 is the correct digit in the right place.
491:
One digit right but in the wrong place. From here, the rule from 849 applies here, meaning we can rule out 9 and 4, leaving us with 1.
From here, it gets a bit tricky. Since 3 is in the correct place. From 725, we have already ruled 7 out, leaving us with 2 and 5. But since we already know 3 is in the last place, it means 5 must be moved to the middle digit in order for 725's statement to be true. Meaning 2 is ruled out.
Finally, the only digit we are left with is 1 as for the rule of 317 and 491.
Making the answer 153.
Let me know if that is correct or wrong and do help me understand if it was wrong!
