The number of small rooms reserved is 13 and the number of large rooms reserved is 12.
Given, Nolan is blocking off rooms for the guests. We will solve the problem using the linear equation. The number of small rooms is x and number of large rooms is y.
There are total of 25 rooms, which can be written as,
x+y=25 ------(1)
Small room can accommodate 3 people and large room 5 people, which can be written as follows,
3x+5y=99 --------(2)
Multiplying the equation 1 by 3, we get
3x+3y=75
Substracting equation 1 and 2, we get
3x+5y=99
3x+3y=75
- - -
---------------
0x+2y=24
2y=24
y=12
x+12=25
x=25-12
x=13
Therefore, the number of small rooms is 13 and large rooms is 12.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line in the graph is -3/4
Slope of a LineThe slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.
Taking two points from the line;
Point A = (0, 3)Point B = (4, 0)The slope of a line is given as
m = y₂ - y₁ / x₂ - x₁
Substituting the values into the formula;
m = 0 - 3 / 4 - 0
Slope = -3/4
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Help please get it right you will get branly
40 ahletes are surveyed it is found that 30 athletes play tennis and 10 play gold 5 play both. what is the probability an athlete plays golf or tennis but not both?
The probability an athlete plays golf or tennis but not both = 0.75
Probability:The ratio of favorable outcomes to all possible outcomes of an event is known as probability.
The formula to calculate the probability of an event is given by
Probability(E) = Favorable Outcomes/Total Outcomes
Here we have 40 athletes,
Number of athletes who plays both tennis and golf = 5
Number of athletes who plays tennis = 30
=> Number of athletes who plays only tennis = 30 - 5 = 25
Number of athletes who plays golf = 10
Number of athletes who plays only golf = 10 - 5 = 5
From the above calculations,
Number of athletes who plays tennis or golf but not both = 25 + 5 = 30
Probability that athletes play golf or tennis but not both = 30/40 = 0.75
Therefore,
The probability an athlete plays golf or tennis but not both = 0.75
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The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and Plan 2 charges $14 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
Help ASAP!
Inequality which shows the number of phone calls in order to make Plan 1 more economical is, x> 375.
It means if customer calls for more than 375 times Plan 1 is more economical for him/her.
Given that Plan 1 offers unlimited calls against $29 per month.
and Plan 2 offers each call against $0.04 and with an adiditional charge $14 per month.
Let if there are x calls in a month then Plan 1 is more economical.
Plan 1 is more economical means Plan 1 costs the customer less than the Plan 2.
So for x calls the bill according to Plan 2 = 14 +0.04x
And the charge $29 fixed for Plan 1.
So the required inequality is,
14+0.04x > 29
Solving the inequality we get,
0.04x > 15
.x > 375
So the calls should be more than 375.
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45= |b-12| Solve for all values of b in simplest form.
The value of b after solving the expression 45= |b-12| is 57 or -33
Given,
The algebraic expression; 45= |b-12|
Algebraic expression;
An algebraic expression is an equation made up of variables and arithmetic operations like multiplication and division.
We are aware that the encoding of a modulus sign as a rand absolute value with two values a value, either positive or negative.
Here,
45= |b-12|
45 = ± (b - 12)
Solve for;
b = 45 + 12
b = 57
Solve for;
b = - 45 + 12
b = - 33
Therefore,
The value of b after solving the expression 45= |b-12| is 57 or -33
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A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1700. The law firm assigned a total of 14 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.
The Number of Associates and Number of Partners assigned to the case by the law firm is 5 and 9 respectively. We can solve this by using the concept of Linear Equation.
Given that,
Daily rate charged to the client for each Associate = $ 800
Daily rate charged to the client for each Partner = $ 1700
Let number of Associates assigned to case = X
And number of Partners assigned to case = Y
So, According to Question
X + Y = 14 ----(1)
800X + 1700Y = 19300 ---(2)
From the equation (1) , Y = 14 – X
Substituting the value of Y into equation (2) we get,
800X + 1700(14-X) = 19300
800X + 23800 – 1700X = 19300
23800 – 900X = 19300
23800 – 19300 = 900X
4500=900X
4500/900 = X
X = 5
Put the value of X into equation (1),
5 + Y = 14
Y = 14 -5
Y = 9
So we let the number of Associates assigned to case X and number of partners assigned to case Y and the value of X is 5 and Y is 9 .
Hence the number of Associates assigned to the case is 5 and the number of Partners assigned to the case is 9.
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PLEASE HELP I WILL GIVE OUT BRAINLIST!!!!!
We list the operations done between two functions below:
g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3) h(x) - g(x) = - 4 · x² - 2 h(f (x)) = 6 · x² + 1 f(x) + g(x) = 7 · x² + 2 · x + 1 h(f(2)) = 25 f(h(3)) = 29 g(2) + h(2) = 2 2 · f(0) - g(2) = - 15How to make operations between two functions
In this problem we find three functions, two of them defined by quadratic equations (f(x), g(x)) and the other defined by a linear equation (h(x)). There are five operations that can be used b two functions:
Addition: (f + g) (x) = f(x) + g(x)Subtraction: (f - g) (x) = f(x) - g(x)Multiplication: (f · g) (x) = f(x) · g(x)Division: (f / g) (x) = f(x) / g(x)Composition: (f ° g) (x) = f (g (x))Now we proceed to determine the result of each operation:
Case 1:
g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3)
Case 2:
h(x) - g(x) = (2 · x - 3) - (4 · x² + 2 · x - 1)
h(x) - g(x) = - 4 · x² - 2
Case 3:
h(f (x)) = 2 · (3 · x² + 2) - 3
h(f (x)) = 6 · x² + 1
Case 4:
f(x) + g(x) = (3 · x² + 2) + (4 · x² + 2 · x - 1)
f(x) + g(x) = 7 · x² + 2 · x + 1
Case 5:
h(f(x)) = 6 · x² + 1
h(f(2)) = 6 · 2² + 1
h(f(2)) = 25
Case 6:
f(h(x)) = 3 · (2 · x - 3)² + 2
f(h(x)) = 3 · (4 · x² - 12 · x + 9) + 2
f(h(x)) = 12 · x² - 36 · x + 29
f(h(3)) = 12 · 3² - 36 · 3 + 29
f(h(3)) = 29
Case 7:
g(x) + h(x) = (4 · x² - 12 · x + 9) + (2 · x - 3)
g(x) + h(x) = 4 · x² - 10 · x + 6
g(2) + h(2) = 4 · 2² - 10 · 2 + 6
g(2) + h(2) = 2
Case 8:
2 · f(x) - g(x) = 2 · (3 · x² + 2) - (4 · x² + 2 · x - 1)
2 · f(0) - g(2) = 2 · (3 · 0² + 2) - (4 · 2² + 2 · 2 - 1)
2 · f(0) - g(2) = 4 - 19
2 · f(0) - g(2) = - 15
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PLEASE help, I've been trying to get this for like an hour.
The solution of the equation is (-2, 3) and to eliminate x we have to multiply equation(i) by 3 and multiply equation(ii) by 4.
How to solve system of equation by elimination method?System of equation can be solved using different method such as elimination method, substitution method and graphical method,
Let's use elimination method to solve the system of equation.
Therefore,
4x + 5y = 7
3x - 2y = - 12
Multiply equation(i) by 3 and equation(ii) by 4 to eliminate x.
Hence,
12x + 15y = 21
12x - 8y = - 48
Subtract the equations
23y = 69
y = 69 / 23
y = 3
Hence,
4x = 7 - 5y
4x = 7 - 5(3)
4x = 7 - 15
4x = -8
x = -8 / 4
x = -2
Therefore, the solution is (-2, 3)
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Find the area of a rectangle whose side lengths are 8x² feet and 8x³ feet.
A.The area of the rectangle is 16x² feet squared.
B. The area of the rectangle is 64x5 feet squared.
C.The area of the rectangle is 16x² + 16x³ feet squared.
D.The area of the rectangle is 16x5 feet squared.
Answer:
ccccccccc
Step-by-step explanation:
How many students catch the train?
Thank you for helping.
Answer:
35
Step-by-step explanation:
18+17=35
What is different about synthesis of lagging strand
compared to synthesis of the leading strand?
A) synthesis of leading strand does not occur in 5*...
The difference between lagging strand and leading strand based on DNA replication is.
What is DNA?
DNA stands for deoxyribonucleic acid.
Main body:
The major difference between a lagging and leading strand is that the lagging strand replicates discontinuously forming short fragments, whereas the leading strand replicates continuously. Find out more such differences between a lagging and leading strand, in the table below.
Lagging Strand
Description:
The strand that opens in the 3’ to 5’ direction towards the replication fork is referred to as the lagging strand.The strand is replicated discontinuously.Short stretches called okazaki fragments are formed during replication.Each fragment requires its own set of primers.It requires DNA ligase enzymes for the joining of short okazaki fragments.It grows away from the replication fork.The synthesis of new strands is slow.Leading Strand
Description:
The strand that runs in the 5’ to 3’ direction in the replication fork is referred to as the leading strand.The strand is replicated continuously.No short fragments are formed.It requires only one primer.It does not require DNA ligase.It grows in the direction of the replication fork.The synthesis of new strands is fast.Therefore the difference between lagging strand and leading strand are as follows.
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Javier is making a recipe that requires 160 milliliters of 40% pure fruit juice. He has a 25% pure fruit juice solution and a 50% pure fruit juice solution.
How many milliliters of each solution should he mix to obtain the needed solution?
Answer:
64 milliliters of 25% juice
96 milliliters of 50% juice.
Step-by-step explanation:
Answer:
96 mL of the 50% juice
64 mL of the 25% juice
Step-by-step explanation:
Declaration
Let the number of mL of 25% juice = x
Let the number of mL of 50% juice = y
Equations
25/100 * x + 50/100 y = 40/100 * 160 Combine
x + y = 160 mL
Solution
0.25x + 0.5y = 0.4 * 160
0.25x +0.5y = 64 Multiply this equation by 4
0.25*4x + 0.5*4y = 64*4 Combine
x + 2y = 256 Put the first equation underneath and subtract
x + 2y = 256
x + y = 160 Subtract
y = 96 mL of 50% fruit juice
x + y = 160
x + 96 = 160 Subtract 96 from both sides.
x + 96 - 96 = 160-96
x = 64 mL of the 25% fruit juice.
(-3,5), (6,5)
what is the point slope form of equation of the line
The equation of the line passing through the points (-3,5) and (6,5) is y = x/9 + 13/3 .
In the question ,
it is given that ,
the required line passes through the points (-3,5) and (6,5) ,
we need to find equation of line ,
to find the equation , we first need to calculate the slope (m) .
slope(m) = (6-5)/(6-(-3))
= 1/9
So , the equation of the line passing through the point (6,5) with slope 1/9 in point slope form is
(y - 5) = 1/9(x - 6)
9(y - 5) = 1(x - 6)
9y - 45 = x - 6
9y = x - 6 + 45
9y = x + 39
y = x/9 + 39/9
y = x/9 + 13/3
Therefore , The equation of the line passing through the points (-3,5) and (6,5) is y = x/9 + 13/3 .
The given question is incomplete , the complete question is
What is the equation of the line in the point slope form passing through the points (-3,5) and (6,5) ?
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f(x) = 0.75(10-x)+1
Someone help please
The solution for f(3) in the function when the function f(x) = 0.75(10 - x) + 1 is 6.25
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = 0.75(10-x)+1
To make the equation legible, we need to rewrite it
So, we have the following representation
f(x) = 0.75(10 - x) + 1
Also from the question, we have
f(3)
This means that the value of x is 3, and we calculate f(x) when x = 3
Substitute the known values in the above equation, so, we have the following representation
f(3) = 0.75(10 - x) + 1
So, we have the following equation
f(3) = 0.75(10 - 3) + 1
There are constants to add or subtract to both sides of the equation
Also, there are factors to multiply or divide from both sides of the equation
So, we have the following representation
f(3) = 0.75 * 7 + 1
Solving further, we have
f(3) = 5.25 + 1
Evaluate the sum
f(3) = 6.25
Hence, the solution is 6.25
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Possible question
Given f(x) = 0.75(10-x)+1, find f(3).
negative 3/4x-1=14 what does x stand for
Answer:
20
Step-by-step explanation:
add 1 to both sides
3/4x=15
multiply both by 4
3x=60
divide by 3
x=20
If A = 2 1 bh, and b=16, A = 40, What is the value of h?
If A = 21 bh, b= 16, and A= 40, then value of h is 0.1190.
∴ A= 21 bh, b = 16, A= 40
Putting the values in A = 21 bh, we get
A= 21 bh
⇒ 40 = 21×16×h
⇒h = 40/21×16
⇒h = 0.1190
So the value of h is 0.1190.
gentle ben is a horse at a colorado dude ranch. over the past 8 weeks, a veterinarian took random weekly glucose readings from gentle ben. the sample mean of the 8 blood tests was we may assume that x has a normal distribution, and the population values are . does the sample data indicate that gentle ben has a glucose rate higher than 85? (use
At the 0.05 level of confidence, there is enough data to say that Gentle Ben's blood glucose is higher than 85 mg/100 ml.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph. Data are symmetrically distributed and skew-free in a normal distribution. As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.
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HELP its growth and decay question
Population in 2011 is 361.606 million, Population in 2025 is 438.094 million, Year when population will be 2 billion is 2136
What is Function?
A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
Solution:
Given the function of the population = P(t) = 3111(1+0.0138)^t
1. Population of Indonesia in 2011
= P(11) = 311 (1.0138)^11
= P(11) = 361.606 million
2. Population of Indonesia in 2025
= P(25) = 311 (1.0138)^25
= P(25) = 438.094 million
3. Year when population is 2 billiion
2000 million= 311(1.0138)^x
x = 136 years approx. i.e. 2136
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Select the correct answer. The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system? x + 3y = 42 2x − y = 14 A. Multiply the second equation by -3. The solution is x = 12, y = 9. B. Multiply the second equation by -2. The solution is x = 12, y = 10. C. Multiply the second equation by 2. The solution is x = 15, y = 9. D. Multiply the second equation by 3. The solution is x = 12, y = 10.
Answer:
x is 13 and y is 10
Step-by-step explanation:
Multiply the second equation by 3
Answer:
D. Multiply the second equation by 3. The solution is x = 12, y = 10.
Step-by-step explanation:
You want the multiplier for the elimination of the y-variable in the system of equations x +3y = 42; 2x -y = 14.
MultiplierThe coefficients of y are +3 and -1, so multiplying the second equation by 3 will make it the opposite of the former. Then their sum is zero, which is what you want when eliminating the y-variable.
ApplicationMultiplying the second equation by 3 and adding the first gives ...
3(2x -y) +(x +3y) = 3(14) +(42)
7x = 84 . . . . . . . . . simplify. Note the y-variable has been eliminated.
x = 12 . . . . . . . . . divide by 7
2(12) -y = 14 . . . . substitute for x in the second equation
24 -14 = y = 10 . . . . add y-14
The solution is (x, y) = (12, 10).
1. For each pair of fractions, decide which fraction is larger. Explain using one of these strategies: common denominator, common numerator, compare to 1, or
compare to 1/2.
a. 5/6 or 5/7
b. 3/4 or 9/10
c. 2/9 or 5/9
d. 2/8 or 5/9
2. A student says, "3/5 is smaller than 1/2 because 3/5 is 2 pieces away from a whole but 1/2 is only 1 piece away." Is the student's reasoning correct? Explain.
Please help me I also upload a picture so you can use that if needed
For each pair of fractions, following fraction is larger
a) 5/6 > 5/7
b) 2/9 < 5/9
c) 3/4 < 9/10
Define fraction.An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given,
Fraction:
a) 5/6 or 5/7
Taking LCM,
LCM = 42
5/6 × 7/7
35/42
5/7 × 6/6
30/42
5/6 > 5/7
b) 2/9 or 5/9
They have same denominator,
So,
2/9 < 5/9
c) 3/4 or 9/10
Taking LCM:
LCM = 20
3/4 ×5/5
15/20
9/10 × 2
18/20
3/4 < 9/10
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Solve inequality 2(5-x)-6<15-4x-9
Answer:
x<1
Step-by-step explanation:
10-2x-6<15-4x-9 (distributive property)
4-2x<6-4x (simplified both sides)
-2x<2-4x (1st step to get x isolated)
2x<2 (2nd step to get x isolated)
x<1 (divide 2 from each side)
and that's how! :)
x-4/5 - x+1/6 = 1/3 ill be very happy if answered
It took an ice cream truck 28 minutes to drive through one neighborhood. The truck stopped
driving through the neighborhood at 2:05 p.m.
What time did the clock show when the truck start driving through the neighborhood?
Answer:
1:38
Step-by-step explanation:
i think that is the answer
Answer: Its started driving through the neighborhood at 1:37
Step-by-step explanation:
Pls help with this question
Answer:
x=-1
Step-by-step explanation:
5x+6=1
5x=-5
x=-1
hopes this helps please mark brainliest
PLEASEE HELP JUST DO 4-9 I REALLY NEED HELP THANKS! FOR 50 POINTS
Answer:
4. d = 4
5. d = 8.8
6. d = 6
7. d = 10
8. d = 3
9. d = 1
Step-by-step explanation:
4. (-5, 2), (-5, 6)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(-5 - (-5))² + (6 - 2)²
d = √(-5 + 5)² + (4)²
d = √(4)²
d = √16
d = 4
5. (4.5, -3.3), (4.5, 5.5)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(4.5 - 4.5)² + (5.5 - (-3.3)²
d = √(0)² + (5.5 + 3.3)²
d = √(8.8)²
d = √77.44
d = 8.8
6. ((5(1/2), (-7(1/2)) and ((5(1/2), (-1(1/2))
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(11/2) - (11/2)² + (-3/2) - (-15/2))²
d = √(d)² + ((-3/2) + (15/2)²
d = √(6)²
d = √36
d = 6
7. (-2(1/4)), -8) and (7(3/4), -8)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(31/4) - (-9/4))² + (-8 - (-8))²
d = √(31/4) + (9/4))² + (-8 + 8)²
d = √(10)²
d = √100
d = 10
8. (5(1/4)), (-3(1/4) and ((5(1/4), (-6(1/4))
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(21/4) - (21/4))² + (-25/4) - (-13/4))²
d = √(-25/4) + (13/4))²
d = √(-3)²
d = √9
d = 3
9. (-1(1/2)), (-6(1/2) and ((-2(1/2), (-6(1/2))
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(-5/2) - (-3/2))² + (-13/2) - (-13/2))²
d = √(-5/2) + (3/2))²
d = √(-1)²
d = √1
d = 1
I hope this helps!
How do I solve this problem 4i)(-8i)(5 + 5i)
Answer:
Step-by-step explanation:
(4i)·(-8i)·(5+5i) = 160+ 160i
We take into account that (i)² = -1
1)
(4i)·(-8i) = (-32)·i² = (-32)·(-1) = 32
2)
32·(5 + 5i) = 32·5 + 32·(5i) = 160 + 160 i
Find the sum of these polynomials (x^2-x+8)+(10x^2+7)
Answer:
11x^2 - x + 15
Step-by-step explanation:
x^2-x+8+10x^2+7 =
= 11x^2 - x + 15
What is the domain of F(x) = 1 ?
O A. x = 0
O B. F(x) *0
C. all real numbers
D. all real numbers except 0
Answer:
C. all real numbers
Step-by-step explanation:
You want the domain of the function F(x) = 1.
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. The function F(x) is defined for all possible values of x, so its domain is all real numbers.
Clarence' Ice Cream Shop old 6 undae. 4 of the undae had nut on top. What i the ratio of the number of undae with nut to the total number of undae? Write your anwer a two number eparated by a colon (for example, 2:3)
Ratio of the sundae with nut to total number is 2:3.
The ratio will be written as numerator and denominator seperated by colon. The numerator will be number of sundae with nut and denominator will be total number of sundae. So, writing the numbers in mentioned description of ratio.
Ratio of the number of sundae with nut to the total number of sundae = 4 : 6
The ratio can be further simplified by dividing both numerator and denominator by 2.
Ratio of the number of sundae with nut to the total number of sundae = 2 : 3
Thus, the required ratio fo sundae is 2:3.
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there is a 40% chance of getting stuck in traffic when leaving the city. on two separate days, what is the probability that you get stuck in traffic both days? a. 0.16 b. 0.40 c. 0.20 d. 0.80
Answer:
A
Step-by-step explanation:
40% = 40/100 = 4/10 = 2/5
2/5 * 2/5 = 4/25 = 0.16
