Based on the number of students at Roxas Middle School and the number of students studying Chinese and Spanish, the number of students who study Spanish is 182 students.
What number of students study Spanish?The first thing to do is to find out the number of students who are studying either Spanish or Chinese:
= Total number of students - Students studying both Spanish and Chinese
= 374 - 100
= 274 students
Then, assuming the number of students studying Chinese alone is x, the expression to find them would be:
274 = 2x + x
Solving gives:
2x + x = 274
3x = 274
x = 274 / 3
x = 91 students
The number studying Spanish is twice this number so will be:
= 91 x 2
= 182 students
In conclusion, there are 182 student studying Spanish.
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A
a = 10
C = 15
B
b
Find the length of b using
the Pythagorean Theorem.
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.
What is the Pythagorean Theorem?The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is: 11.2.
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Find one possible missing coordinate so that the point becomes a solution to the given inequality. (x, 8) is a solution to 3x - 4 < y. X =
Answer:
x = 0
Step-by-step explanation:
Substituting the given "point" into the equation gives the possibilities for x.
SubstitutionUsing (x, y) = (x, 8), the inequality becomes ...
3x -4 < 8
Solving for x gives ...
3x < 12 . . . . . . . add 4
x < 4 . . . . . . . divide by 3
Any value of x less than 4 will make (x, 8) a solution to the inequality. For example, ...
x = 0 . . . . . . (0, 8) is a solution to the inequality
SOLVE THE FOLLOWING PROBLEMS.
A) IN HOW MANY WAYS CAN THE LETTERS OF THE WORD “TRACK” BE ARRANGED?
B) A STUDENT MUST SELECT AND ANSWER SIX OUT OF TEN QUESTIONS ON AN EXAM. IN HOW MANY WAYS CAN THIS BE DONE?
C) A TEACHER DECIDES TO GIVE SIX IDENTICAL PRIZES TO 6 OF THE 20 STUDENTS IN HIS CLASS. IN HOW MANY WAYS CAN THIS BE DONE
The answers to the question are:
12021038760How to solve for permutations and combinations1. The letters of the word track can be arranged in 5! ways
These are 5 x 4 x 3 x 2 x1
= 120
2. The way that the student would be able to select 6 out of 10 questions would be by 10C6
= 210 ways
C)This teacher would be able to make the decision of the prices to the students using =20C6= n!(n-r!r!)
= 38760
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For the function f(x)=3x²-7, find the value of f(x) when x=3.
Answer:
Step-by-step explanation:
Simply plug in a 3 where you see an x in the function:
[tex]f(3)=3(3)^2-7[/tex] so
f(3) = 3(9) - 7 and
f(3) = 27 - 7 so
f(3) = 20
Factorise: a8 - b8
please solve this
Answer:
(a - b)(a + b)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )
Step-by-step explanation:
by repeated use of the difference of squares factorising method, that is
a² - b² = (a - b)(a + b)
given
[tex]a^{8}[/tex] - [tex]b^{8}[/tex]
= ([tex]a^{4}[/tex] )² - ([tex]b^{4}[/tex] )²
= ([tex]a^{4}[/tex] - [tex]b^{4}[/tex] )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis using difference of squares
= ( a² - b²)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis by difference of squares
= (a - b)(a + b)(a² + b² )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )
Heyy I just need some help with question 13,17,19 if anyone could help me and show the work that would be amazing thank you!!
Answer:
13. Answer: 0
17. Answer: 3
19. Answer: 2
Step-by-step explanation:
13. f(g(3))
First find g(3) on the right graph.
We see that at x = 3, g(x) = 4
So g(3) = 4
Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer
17.f(f(5))
f(5) = 1
f(f(5)) = f(1) = 3 answer
19. g(g(2))
g(2) = 0
g(g(2)) = g(0) = 2 answer
Dividends Per Share Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 60,000 shares of cumulative preferred 3% stock, $20 par and 400,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $32,000; second year, $72,000; third year, $80,000; fourth year, $100,000. Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00".
The dividends per share on each class of stock for each of the four years for Seventy-Two Inc. are as follows:
Cumulative Preferred Stock:Year 1 Year 2 Year 3 Year 4
Distributed Dividends $32,000 $40,000 $36,000 $36,000
Outstanding shares 60,000 60,000 60,000 60,000
Dividend per share $0.53 $0.67 $0.60 $0.60
Common Stock:Year 1 Year 2 Year 3 Year 4
Distributed Dividends $0 $32,000 $44,000 $64,000
Outstanding shares 400,000 400,000 400,000 400,000
Dividend per share $0 $0.08 $0.11 $0.16
Data and Calculations:3% Cumulative Preferred Common Stock
Outstanding shares 60,000 400,000
Par Value $20 $25
Total value $1,200,000 $10,000,000
Annual dividend $36,000 ($1,200,000 x 3%)
Year 1 Year 2 Year 3 Year 4
Distributed Dividends $32,000 $72,000 $80,000 $100,000
Cumulative Preferred $32,000 $40,000 $36,000 $36,000
Common Stock $0 $32,000 $44,000 $64,000
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The coefficient of 8 • 2N is
Answer:
16
Step-by-step explanation:
when we multiply we have 16n so thats is d coefficient
X
Erica works 30 hours/week for
$10/hour, but she must pay $30 in
taxes. What is her take-home income?
Answer:
$270
Step-by-step explanation:
Find her gross income....then subtract taxes:
30 hr/week * $10/hr - $ 30 = $270
One number is six more than three times another. If their sum is decreased by four, the result is twenty-two. Find
the numbers.
The smaller of the numbers is
Due Wed 08/10/
and the larger is
Answer: 5 is the smaller number and 21 is the larger number
Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.
Let f(r) = 6,
find f-¹(r)
There is no answer because there cannot be one to one function inverse.
A shark begins 172.5 meters below sea level and then swam up 137.1 meters,. Where is the sharks location now in relation to sea level
Answer:
35.4m below sea level
Step-by-step explanation:
172.5 - 137.1 = 35.4
The shark's location is now 35.4m below sea level.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 4 -2 = 2
Using the arithmetic operations of addition and subtraction, the shark's location is now in relation to sea level if the shark begins 172.5 meters below sea level and then swam up 137.1 meters.
Assume that distance below sea level is positive,
⇒ 172.5 - 137.1 = 35.4
Hence, the shark's location is now 35.4m below sea level.
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question:
|x-2|, if x > 5
simplify without the absolute value sign
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its positive numerical value.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
Find the area of circle Y. The image is represented by circle Y with a sector XYZ that has an area of 85.5 square meters. That sector has an arc that measures 117 degrees. The radius of the circle is unknown.
Answer:
263.08 m²
Step-by-step explanation:
The fraction of circle area that a sector represents is proportional to the central angle.
Proportioncircle area/circle angle = sector area/sector angle
circle area / 360° = 85.5 m² / 117°
Multiplying by 360°, we have ...
circle area = (360/117)(85.5 m²) = 263.08 m²
The area of the circle is about 263.08 m².
What is the solution to x2 – 9x < –8? x < 1 or x > 8 x < –8 or x > 1 1 < x < 8 –8 < x < 1
In mathematics a linear inequality is an inequality involving a linear function. A linear inequality contains one of the inequality symbols.< is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to.
x²− 9x < − 8Let's find the critical points of the inequality.
x² − 9x = − 8x² − 9x −(−8) = − 8 −(−8) (Subtract -8 from both sides)
x² − 9x + 8 = 0(x − 1)(x − 8) = 0 (Factor left side of equation)
x − 1 = 0 or x − 8 = 0 (Set factors equal to 0)
x=1 or x=8Check intervals in between critical points. (Test values in the intervals to see if they work.)x < 1 (Doesn't work in original inequality)
1 < x < 8 (Works in original inequality)
x > 8 (Doesn't work in original inequality)
Answer:1 < x < 8
The third option is the correct one.
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Question 3 of 10
If a circle has a diameter of 24 inches, which expression gives its area in
square inches?
OA. 12. T
OB. 242. T
O C. 122. T
OD. 24. T
SUBMIT
Answer:
OB:.242.T gives it's area in square inches
Question
Which of the following equations is equivalent to 8x - 6y = 12?
y = ³x - 1²/2 3
y=x-2
y = 2x - 12
y = 8x - 6
The equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
What are Equivalent Equations?Equations that are equivalent to each other have the same value when evaluated or simplified.
Given the equation, 8x - 6y = 12, to determine which of the given equations in the options is equivalent to, rewrite the equation in slope-intercept form, as y = mx + b.
8x - 6y = 12
Subtract 8x from both sides of the equation
8x - 8x - 6y = -8x + 12
-6y = -8x + 12
Divide both sides of the equation by -6
-6y/-6 = -8x/-6 + 12/-6
y = 4x/3 + (-2)
y = 4x/3 - 2
Therefore, the equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
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Composition of two functions:Basic
The functions, q(x) and r(x) are defined as 2•x + 1, and -5•x - 3, respectively, therefore;
[tex] \: (q \: \circ \: r) (1)= - 15[/tex]
[tex] \: (r \: \circ \: q) (1)= -18[/tex]
Which method can be used to evaluate the given composite functions?The given functions are;
q(x) = 2•x + 1
r(x) = -5•x - 3
The evaluation of the composite functions can be presented as follows;
[tex](q \: \circ \: r) (x)= q(r(x))[/tex]
Therefore;
[tex](q \: \circ \: r) (1)= q(r(1))[/tex]
r(1) = -5×1 - 3 = -8Which gives;
[tex](q \: \circ \: r) (1)= q( - 8)[/tex]
q(-8) = 2×(-8) + 1 = -15
Therefore;
[tex](q \: \circ \: r) (1)= - 15[/tex]
Similarly, we have;
[tex](r \: \circ \: q) (1)= r(q(1))[/tex]
q(1) = 2×1 + 1 = 3
r(3) = -5×3 - 3 = -18
Which gives;
[tex](r \: \circ \: q) (1)= -18[/tex]
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Armando tiene 25 chocolates en una caja y caja y cada chocolate tiene un relleno de 4 posibles fresa, mora y piña. De los 25 chocolates de la caja de armando sabes que tiene 8 tienen relleno de mora y 5 de piña si una persona torna al azar un chocolate de la caja
cuales de la posibles posibilidades se puede calcular
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
¿Como encontrar las probabilidades?
Sabemos que hay 25 chocolates en total en la caja, tal que:
8 son de mora.5 son de piñalos 12 restantes son de fresa o cereza.La probabilidad de obtener un tipo particular de sabor se obtiene como el cociente entre el número de chocolates de ese sabor y el total de chocolates.
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
Sabemos que 5 chocolates tienen relleno de piña, entonces 20 no tienen relleno de piña. es decir, la probabilidad es:
P = 20/25 = 4/5
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Michael Wittry has been investing in his Roth IRA retirement account for 20 years. Two years ago, his account was worth $215,658. After losing of its original value, it then gained of its new value back. What is the current value of his Roth IRA?
The current value of his Roth IRA is $215,658.00
What is Roth IRA retirement account?
Roth IRA retirement account is a retirement account where the contributions to the account are invested after taxes after have been deducted.
In other words, when the individual make contributions, taxes are first of all, deducted so as to invest the after-tax contribution into the Roth IRA account
The account lost 1/3 of its original value of $215,658
balance after the loss=$215,658-(1/3*$215,658)
balance after the loss=$ 143,772.00
Now the account regained 1/2 of its new balance of $ 143,772.00
balance now=$143,772.00+(1/2*$143,772.00)
balance now=$215,658.00
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Complete with the missing fractions:
michael wittry has been investing in his roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origiInal value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?
I need help ASAP PLS HELP MEE I'll mark brainlist if correct and ill add 50 points I NeED The answer 5 mins AFTER PLS DO IT BEFORE 5 MIn (with explanation)
On which number line do the points represent negative seven and one over two and +1?
Answer list (below)
Answer:
Second number line
Step-by-step explanation:
This second line is the only line on which
[tex]-7\frac{1}{2} \text{ appears to the left of } 0 \text{ on the line (Point R)}\\+1 \text{ appears to the right of } 0 \text{ on this number line (Point T) }\\[/tex]
Answer:
○B (second option)
Step-by-step explanation:
In the second option, we can see that the point T is at +1. The point R is between -7 and -8, therefore we understand that it is at a value of [tex]\bf -7\frac{1}{2}[/tex].
All the other options have the points R and T at values not asked for in the question.
3a²+ab²-b² x a²-2ab²-3b²
/a+b
Answer:
It might be - c² or b³ *SORRY IF IM WRONG HAVE A GOOD DAY :D)
Step-by-step explanation:
I agree with the person above ^^^
Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.
A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.
The graph g(x) is the graph of f(x) translated units , and g(x) =
g(x) is a translation of 6 units downwards.
How to identify the translation that generates g(x)?
Here we have the function:
y = f(x) = 3x + 1
Notice that the y-intercept of f(x) is:
f(0) = 3*0 + 1 = 1
The y-intercept of f(x) is y = 1.
Now, we know that the y-intercept of g(x) is -5. then:
g(x) = 3x - 5 = f(x) - 6
Meaning that g(x) is a translation of 6 units downwards.
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Answer:
translated 2
units up
g(x)= f(x-2)
Step-by-step explanation:
You purchase a very basic cell phone plan that charges $24.99 a month. This plan allows for data usage but that will cost you $5 for every GB you use in a month. Write an equation below in slope-intercept form that models this situation.
The equation of this given condition in the intercept form would be
y = 5x + 24.99
The slope-intercept is the most “popular” form of a straight line. Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified or read off from this form.
The linear equation written in the form
y = mx + b
is in slope-intercept form where: m is the slope, and b is the y-intercept.
In the given question the slope of the equation is 5 as $5 is charged for every GB used while $24.99 would be the intercept.
Thus the equation of this given condition in the intercept form would be
y = 5x + 24.99
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A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Find the area of the sector formed by the 60 degree central angle.
503π in2503π in2
103π in2103π in2
100π in2100π in2
None of the Above
The area of the sector of the circle is: A. 50/3π in.².
What is the Area of a Sector of a Circle?The area of a sector that is bounded by two radii of a circle is calculated using the formula, ∅/360 × πr², where we have the following parameters:
r = radius of the circle∅ = central angle formed by the sector.Thus, we are given the following regarding the sector of the circle:
Central angle (∅) = 60 degrees
Radius (r) = 10 inches.
Plug in the values into ∅/360 × πr²:
Area of sector = 60/360 × π(10²)
Area of sector = 1/6 × π(100)
Area of sector = 100/6 × π
Area of sector = 50/3 × π
Area of sector = 50/3π in.²
Thus, the area of the sector of the circle is: A. 50/3π in.².
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I hope you could get this answer
Answer: -12
Step-by-step explanation: x is -4 so -(-4) is positive 4. d = 3 so -3 = -3. -3x4 = -12.
Devon is young and has just graduated college with her associate’s degree. She plans to start saving money for retirement as soon as she starts her new job. By taking 10% of her monthly gross income, Devon is able
to contribute (a) $__________ each month to a retirement plan. The account is expected to earn interest with an APR of 5.25% compounded monthly. Round answers to two decimal places.
a. How much money will be in Devon’s retirement account if she continues to make the same monthly
.
investment for 40 years?
b. Overall, Devon contributed how much of her own money into the retirement account?
c. What percent of the final balance in Devon’s retirement account was interest?
You may not ask for help from others or give help to others on specific project questions.
Part 1: Continued
2. Later in life, Devon convinces her friend Taylor to start saving for retirement as well. Even though Taylor is the same age as Devon, she hasn’t started saving for retirement yet. With only 20 years left until they both plan to retire, Taylor decides she needs to invest at least twice as much as Devon each month to try to catch up to Devon’s retirement plan. Taylor opens a similar retirement account to Devon’s that also has an APR
5.25% compounded monthly. She will invest (b) $__________ per month. Round answers to two decimal places.
a. How much money will be in Taylor’s retirement account if she continues to make the same monthly
investment for 20 years?
b. By the time she retires, Taylor will have contributed how much of her own money overall?
c. What percent of the final balance in Taylor’s retirement account will be interest?
3. Write complete sentences that identify which person had the higher amount and by how much. Round answers to two decimal places.
a. Who had more money in their retirement account when they planned to retire? How much more?
b. Who contributed more to their retirement account? How much more?
Part 1: Devon is able to contribute (a) $450 each month to a retirement plan.
a. The amount in Devon's retirement account if she makes the same monthly investment for 40 years is $733,253.26.
b. Overall, Devon's total contribution of her own money into the retirement account is $216,000.
c. The percent of the final balance in Devon's retirement account that was interest was 70.5%.
Part 2: Taylor will invest (b) $1,733.00 per month.
a. The amount that will be in Taylor's retirement account if she makes the same monthly investment for 20 years is $733,253.26.
b. By the time that Taylor retires, she will have contributed $415,920 of her own money into the account.
c. The percent of the final balance in Taylor's retirement account that will be interest is 43.3%.
3. Both Devon and Taylor had the same amount, $733,253.26, in their retirement accounts when they planned to retire.
a. None had more money at their retirement.
b. Taylor contributed more to her retirement account by $199,920 ($414,920 - $216,000).
Data and Calculations:Devon's Investments:Gross monthly income = $4,500
APR = 5.25% compounded monthly
N (# of periods) = 480 months (12 x 40 years)
I/Y (Interest per year) = 5.25%
PV (Present Value) = $0
PMT (Periodic Payment) = $450 ($4,500 x 10%)
Results:
FV = $733,253.26 ($517,253.26 + $216,000)
Sum of all periodic payments = $216,000 ($450 x 480)
Total Interest = $517,253.26
Percentage of interest out of the FV = 70.5% ($517,253.26/$733,253.26 x 100)
Taylor's Investment:N (# of periods) = 240 months (12 x 20 years)
I/Y (Interest per year) = 5.25%
PV (Present Value) = $0
FV (Future Value) = $733,253.26
Results:
PMT = $1,733.00
Sum of all periodic payments = $415,920 ($1,733 x 240
Total Interest = $317,333.26
Percentage of interest out of the FV = 43.3% ($317,333.26/$733,253.26 x 100)
Thus, based on the time value of money of investments, it is more profitable to start investing early.
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A college class is made up of f freshman and s sophomores. If 5 freshmen drop this class would be 3 times the number of freshman. Which of the following equations represents a in terms of f ?
Answer:
The answer is G.
f-5 drop the class while s class is 3(f-5)
therefore, s=3(f-5)
In a certain school 70% of the students in first-year chemistry have had algebra. If there are 290 students in first-year chemistry, how many of them have had algebra?
The number of the students in the school that have had algebra is 203
How to determine the number of students?The given parameters in the question are
Proportion of students taking algebra, p = 70%Number of students in the school, n = 290The number of students that had algebra in the school is calculated as:
Algebra = Proportion of students taking algebra * Number of students in the school
The above equation can be represented as:
Algebra = np
Substitute values for n and p in the above equation
So, we have
Algebra = 290 * 70%
Express 70% as decimal i.e. 0.70
So, we have
Algebra = 290 * 0.70
Evaluate the product i.e. multiply 290 and 0.70
So, we have
Algebra = 203
Hence, the number of the students in the school that have had algebra is 203
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