A class votes for their class president. Candidate A receives 21 votes, which is 60% of the vote. What is the total number of students who voted?
Answer:
35 total students voted
Step-by-step explanation:
The total number of students who voted is 35
What is percentage?
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
we have,
Candidate A receives = 21 votes which is 60% of the vote
According to the question,
Based on the given conditions, formulate:: 21 ÷ 60%
Multiply both the numerator and denominator with the same integer: 210/6
Cross out the common factor: 35
hence, total number of students who voted is 35
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How many three-eighths are in three and three-fourths
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\( \frac{3 \frac{3}{4} }{ \frac{3}{8} } = \frac{ \frac{12 + 3}{4} }{ \frac{3}{8} } = \frac{ \frac{15}{4} }{ \frac{3}{8} } = \frac{ \frac{15 \times 2}{4 \times 2} }{ \frac{3}{8} } = \\ \)
\( \frac{ \frac{30}{8} }{ \frac{3}{8} } = \frac{30}{8} \div \frac{3}{8} = \frac{30}{8} \times \frac{8}{3} = \frac{30}{3} = \\ \)
\(10\)
Thus there are (( 10 )) 3/8 in 3 3/4 .
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Answer:
\(\frac{3}{8}\) can go into \(3\frac{3}{4}\) exactly 10 times.
Step-by-step explanation:
Convert the mixed number to an improper fraction: \(3\frac{3}{4}=\frac{15}{4}\) (found by multiplying the denominator by the coefficient and adding the numerator)Divide (multiply by the reciprocal): \(\frac{15}{4}*\frac{8}{3}=\frac{120}{12}\)Simplify: \(\frac{120}{12}=10\)Done!Hope this helps!
I NEED HELP AGAINNNNN
1) Are the triangles ABC and PQR in the diagram congruent? GIVE REASONS for your answer.
2) In a piggy bank, there are x numbers of one dollar bills and 2x number of 50 dollar bills. Find the total amount of money in the piggy bank, in terms of x.
Answer:
no they are not equal just look at the picture carefully and you will realise it's not equal
The equations of four lines are given. Identfy which lines are parallel. Line 1: y = -9x + 6 Line 2: x + (1/3)y = -6 Line 3: y = -3x - 8 Line 4: y + 7 = (-1/9)(x + 4)
Answer:
line 2 and line 3
Step-by-step explanation:
line1=y=-9x+6. gradient 1= -9
line2=x+⅓y=-6
⅓y=-6-x. gradient2= -3
y=-18-3x
line3=y=-3x-8. gradient3= -3
line4=y+7=-1/9x-4/9
y=-1/9x-4/9-7. gradient4= -1/9
y=-1/9x-7⁴/9
parallel lines have the same gradient
Use the figure to find the measure of angle 2.
Answer:
∠ 2 = 70°
Step-by-step explanation:
110° and ∠ 1 are corresponding angles and congruent, thus
∠ 1 = 110°
∠ 1 and ∠ 2 are adjacent angles and are supplementary, thus
∠ 2 = 180° - ∠ 1 = 180° - 110° = 70°
-) A floor plan shows that a tiny house has a length of 30 feet and a width of 20 feet.
1) Which expression represents the area
of the tiny house?
30. 20
30 – 20
30 : 20
30 + 20
Answer:30*20
Step-by-step explanation:
The table gives the average number of days of rain in each month of the year. Find the mode of the given data. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Days of Rain 6 7 10 10 11 12 10 10 9 7 7 6 A. 7 B. 7 and 10 C. 9.5 D. 10
The mοde value fοr the table οf data given is οptiοn D. 10.
What is mοde?A mοde is described as the value in a grοup οf values that οccurs mοre frequently. The value that appears the mοst frequently is this οne.
The mοde is nοt necessarily unique tο a given discrete distributiοn, since the prοbability mass functiοn may take the same maximum value at several pοints x1, x2, etc. The mοst extreme case οccurs in unifοrm distributiοns, where all values οccur equally frequently.
The data is given fοr the average number οf days οf rain in each mοnth οf the year.
The mοde will the number οf days repeating itself mοre number οf times.
It can be seen that 10 is repeated 4 times amοng the data given.
Therefοre, the mοde value is 10.
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How many solutions does this equation have? 13b + 7 = 10b - 9
Answer:
b= -16/3
Step-by-step explanation:
an hyperboloid is a 3d shape whose cross sections are hyperbolas. a nuclear cooling tower is in the shape of a portion of a hyperboloid. a cross section of the cooling tower can be modeled by the hyperbola shown below, centered at the origin and opening left/right. if the smallest diameter of the cooling tower is 180 m and the diameter is 195 m at its highest point, 80 m above, write the equation of the hyperbola.
The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.
We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.
Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).
The left/right opening of the hyperbola indicates that the primary axis is horizontal.
The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.
The primary axis' 195 m length and the diameter at its highest point are matched.
The hyperbola's highest point is 80 metres above the centre.
These characteristics allow us to write the hyperbola's equation in standard form:
(x - h)²/a² - (y - k)²/b² = 1
Where (h, k) represents the center of the hyperbola.
Substituting the given values:
Center: (h, k) = (0, 0)
Minor axis: 2a = 180 m, so a = 90 m
Major axis: 2b = 195 m, so b = 97.5 m
Vertical shift: c = 80 m
Now we can write the equation of the hyperbola:
x²/90² - y²/97.5² = 1
Simplifying, we have:
x²/8100 - y²/9506.25 = 1
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For question #3:A) Express the general solution of the given system of equations in terms of real-valued functions.B) Also, draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as t approachs infinity.
The solutions of the system tend towards zero, as the exponential term dominates the other terms.
The general solution of the given system of equations can be expressed as:
x(t) = c1e^(-t) + c2te^(-t)
y(t) = c3e^(-t) + c4te^(-t)
where c1, c2, c3 and c4 are constants of integration.
The direction field of the system can be drawn by plotting the slopes of the two equations at each point. The trajectories of the solutions can be sketched by plotting the solutions of the system at different points in time. As t approaches infinity, the solutions of the system tend towards zero, as the exponential term dominates the other terms.
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Brent leaves school to go home. He walks 10 blocks north and then 6 blocks west. If Brent could walk in a straight line to the school, what is the exact distance between Brent and school
Answer:
11.66 units
Step-by-step explanation:
Given that he walks 10 blocks north and then 6 blocks west..
When combined with the straight line to the school, this forms a right angled triangle with the straight line as the hypotenuse.
Hence, let the straight line be h
h^2 = 10^2 + 6^2 (using Pythagoras theorem)
h^2 = 100 + 36
h^2 = 136
h = √ 136
h = 11.66 units
Compare A and B, if 120 % of A is equal to 150 and 105 % of B is equal to 165.
A....B
The comparison between A and B is as follows:A < B.
We are given that:120 % of A is equal to 150 => (120/100)A = 150
Divide both sides by 120/100: A = 150 × 100/120 = 125
And, 105 % of B is equal to 165 => (105/100)B = 165
Divide both sides by 105/100: B = 165 × 100/105 = 157.14
Therefore, A = 125 and B = 157.14
Compare A and B:It can be seen that B is greater than A. Therefore, B > A. Hence, the comparison between A and B is as follows:A < B.
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the f-test for anova in a regression model with 4 predictors and 47 observations would have how many degrees of freedom?
The degree of freedom for the f-test for anova in a regression model with 4 predictors and 47 observations is (4,42)
degree of freedom = (k, n - k - 1)
= (4, 47 - 4 - 1)
= (4, 42).
Any statistical test with an F-distribution for the test statistic under the null hypothesis is known as an F-test. In order to determine which statistical model better represents the population from which the data were sampled, it is most frequently applied when contrasting models that have been fitted to data sets.
Exact "F-tests" are typically required after least squares fitting of the models to the data. In honor of Ronald Fisher, George W. Snedecor came up with the name. In the 1920s, Fisher created the statistic as the variance ratio.
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1 define and give an example for: rate:
2 define and give an example for unit rate
pls help I'm struggling
Step-by-step explanation:
1. quantity, amount, or degree of something measured per unit of something else her typing rate was 80 words per minute. b : an amount of payment or charge based on another amount specifically : the amount of premium per unit of insurance.
2.A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate
Match each pair of polynomials to their sum. 12x2 3x 6 and −7x2 − 4x − 2 −2x − 2 2x2 − x and −x − 2x2 − 2 2x2 x x2 2 and x2 − 2 − x 2x2 9x − 2 x2 x and x2 8x − 2 5x2 − x 4.
To match each pair of polynomials to their sum, we need to perform the addition operation for each pair of polynomials. Pair 1: 5x^2 - x + 4 ,Pair 2: 2x^2 - 3x , Pair 3: -x^2 - x, Pair 4: 3x^2 + 9x - 2 ,Pair 5: 5x^2 - x + 4.
Let's go through each pair of polynomials and find their sum:
Pair 1:
12x^2 + 3x + 6
-7x^2 - 4x - 2
Sum: (12x^2 - 7x^2) + (3x - 4x) + (6 - 2) = 5x^2 - x + 4
Pair 2:
-2x - 2
2x^2 - x
Sum: -2x + 2x^2 - x = 2x^2 - 3x
Pair 3:
x^2 + 2
-x - 2x^2 - 2
Sum: (x^2 - 2x^2) + (-x) + (2 - 2) = -x^2 - x
Pair 4:
2x^2 + x
x^2 + 8x - 2
Sum: (2x^2 + x^2) + (x + 8x) + (0 - 2) = 3x^2 + 9x - 2
Pair 5:
5x^2 - x
4
Sum: 5x^2 - x + 4
In summary, the matches of the pairs of polynomials to their sums are:
Pair 1: 5x^2 - x + 4
Pair 2: 2x^2 - 3x
Pair 3: -x^2 - x
Pair 4: 3x^2 + 9x - 2
Pair 5: 5x^2 - x + 4
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Shirley is building a shed. The length is 2x + 3 feet long and the width is x + 1 feet long
1) what is the perimeter of the shed
2) what is the area of the shed
Please help I really want to go to sleep please I can’t handle it anymore
The perimeter of shed is, (6x+ 4)
The area of the shed is, (2x² + 5x + 3)
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Shirley is building a shed. The length is 2x + 3 feet long and the width is
x + 1 feet long.
Now, We know that;
The perimeter of rectangle = 2 (Length + Width)
Substitute all the values, we get;
⇒ Perimeter = 2 (2x + 1 + x + 1)
⇒ Perimeter = 2 (3x + 2)
⇒ Perimeter = (6x + 4)
And, Area of rectangle = Length × Width
Substitute all the values , we get;
⇒ Area = (2x + 3) × (x + 1)
⇒ Area = (2x² + 2x + 3x + 3)
⇒ Area = (2x² + 5x + 3)
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-7x + 17 > 115 solution
Answer:
x<-14
Step-by-step explanation:
Isolate x
-7x>98
x<-14
(can I get brainliest please)
what is 8y-2x=-40 in slope-intercept form?
Answer:
y=2/8x-5
Step-by-step explanation:
y=mx+b is slope intercept form
8y=2x-40
y=2/8x-5
Ms. Trimmer paid $65 last year for her subscription to Drama Teachers Monthly. This year the fee is $78. What rate of increase is this?
Answer:
20%
Step-by-step explanation:
an inverse relationship in which one factor increases as another factor decreases represents?
A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).
suppose you have a random 500-digit prime p. suppose some people want to store passwords, written as numbers. if x is the password, then the number 2x (mod p) is stored in a file. when y is given as a password, the number 2y (mod p) is compared with the entry for the user in the file. suppose someone gains access to the file. why is it hard to deduce the passwords?
The reason it's hard to deduce the passwords in this system is due to the properties of prime numbers and modular arithmetic.
The reasoning is as follows:1. A prime number p is a number greater than 1 that has no positive divisors other than 1 and itself. In your case, p is a 500-digit prime number.
2. When a password x is given, 2x (mod p) is stored in a file. This operation uses modular arithmetic, which helps maintain the security of the password storage system.
3. When someone provides a password y, the system computes 2y (mod p) and compares it with the stored value. If the values match, the password is considered correct.
4. If an attacker gains access to the file, they only have the values of 2x (mod p) for different users. To deduce the original passwords x, they would need to solve the equation 2x ≡ 2y (mod p) for x, given the known values of 2y (mod p).
5. Solving this equation is equivalent to finding the discrete logarithm, which is a hard problem in number theory, especially when dealing with large prime numbers like a 500-digit prime.
6. Due to the difficulty of solving the discrete logarithm problem, it is computationally infeasible for an attacker to deduce the original passwords x, given the stored values 2x (mod p).
In conclusion, the difficulty of deducing the passwords in this system comes from the properties of prime numbers and the complexity of the discrete logarithm problem, making it a secure method for storing passwords.
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5. If -5(-2x + 10) is equivalent to 10x + b, what
is the value of b?
Answer:
b = - 50
Step-by-step explanation:
Using F.O.I.L (First Outer Inner Last)
-5 × - 2x = 10x
-5 × 10 = - 50
10x - 50
10x - 50 = 10x + b
10x - 10x - 50 = b
b = - 50
there are women and men signed up to join a ballroom dance class. in how many ways can the instructor choose of the people to join if or fewer must be men?
There are 210 ways in which the instructor can choose the people to join if or fewer must be men.
Using the combination formula: C(n,r)= n! / r!(n - r)! where:n = 5r = 2C(n,r)= 5! / 2!(5 - 2)! C(n,r) = 5! / 2!3!C(n,r) = (5 * 4) / (2 * 1)(3 * 2 * 1)C(n,r) = 10
Therefore, the possible combination of selecting 2 objects from a set of 5 objects is 10. In the context of the question, if the instructor wants to choose a certain number of people to join a ballroom dance class if at most, "n" people must be men, we can use the combination formula to calculate the total possible combinations.
Let's say the instructor wants to choose "k" people to join a ballroom dance class, "n" of whom must be men. If there are "m" men and "w" women signed up to join the class, then the total possible combinations are given by: C(m,n) * C(w,k-n)
The number of ways in which an instructor can choose of the people to join if or fewer must be men is given by the sum of possible combinations of choosing 0 men, 1 man, 2 men, 3 men, .... up to "n" men. Calculate the possible combinations using the combination formula as shown above for each value of "n" and then sum them up.
C(3,0)C(7,4) + C(3,1)C(7,3) + C(3,2)C(7,2) + C(3,3)C(7,1) + C(3,4)C(7,0)= 1(35) + 3(35) + 3(21) + 1(7) + 0= 35 + 105 + 63 + 7= 210
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A DVD has a diameter of 14 centimeters. What is the area of the DVD? Round your answer to the nearest
hundredth. Use 3.14 for it.
The area of the DVD is about
1 cm?
Which division problem does the model below show?
1
1
1
1
1
1
1
1
1
8
1
8
1
6
5
1
1
1
1
1
1
1
1
6
ö
1
6
fo
-lo
1
6
Ok
Answer:
4÷1/6=24
Step-by-step explanation:
What are the only two values such that the Fn=n
4. Which statement is true?
A. The value of the 7 in 17,265 is 20 times the value of the 7 in 26,173.
B. The value of the 7 in 17,265 is 10 times the value of the 7 in 26,173.
C. The value of the 7 in 17,265 is 100 times the value of the 7 in 26,173.
D. The value of the 7 in 17,265 is to times the value of the 7 in 26,173.
A store marks up its notebook computers by 22%. What price does the store charge
its customers for a $600 notebook computer?
Simplify -4x-3+6x-2 simplify
Answer:
2x-5
Step-by-step explanation:
Answer:
2x - 5
Step-by-step explanation:
combine like terms
-4x and + 6x = 2x
-3 and -2 = -5
2x - 5
fabiana opened a savings account with $14,200 that earns 1.2% simple interest annually. after how many years will the balance of the account be $15,478 ? round to the nearest tenth if necessary.
After 7.5 years will the balance of the account be $15,478.
Given:
fabiana opened a savings account with $14,200 that earns 1.2% simple interest annually.
here A = 15478 , p = 14,200 , r = 1.2%
Simple interest formula:
A = p(1 + rt)
15478 = 14,200(1 + 1.2%t)
15478 = 14,200 + 14,200(0.012t)
1278 = 170.4t
t = 1278/170.4
t = 7.5 years
Therefore after 7.5 years will the balance of the account be $15,478.
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