Answer:
y = 2.60 (to 3sf)
Step-by-step explanation:
Since x is directly proportional to y², then x = ky², where k is a constant.
When x = 4, y = 3,
4 = k(3)²
4 = 9k
9k = 4
∴[tex]k =\frac{4}{9}[/tex]
∴ When x = 3,
[tex]\frac{4}{9}y^{2} = 3[/tex]
∴y = 2.60 (to 3sf)
Extra Credit
Where does this function cross the x-axis?
y = 25x² - 49
Answer:
Step-by-step explanation:
45
Which is the order from least to greatest of the following
4/3, 0.8, 1/5, 30%?
A. 4/3, 0.8, 1/5, 30%
B. 30%, 4/3, 0.8, 1/5
C. 1/5, 4/3, 30%, 0.8
D. 1/5, 30%, 0.8, 4/3
Which is the order from least to greatest of the following
A. 4/3, 0.8, 1/5, 30%
1.33 , 0.8 , 0.2 , 0.3
B. 30%, 4/3, 0.8, 1/5
0.3 , 1.33 , 0.8 , 0.2
C. 1/5, 4/3, 30%, 0.8
0.2 , 1.33 , 0.3 , 0.8
D. 1/5, 30%, 0.8, 4/3
0.2 , 0.3 , 0.8 , 1.33 these are listed smallest to largest
A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
The smaller number is 9 and the larger number is 18.
According to the question,
We have the following information:
A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
Now, let's take the larger number to be x and the smaller number to be y.
So, we have the following expressions:
x = 2y ...(1)
x+14 = 4y-4
Putting the values of x from the equation 1:
2y+14 = 4y-4
Adding 4 to both sides of the equation:
2y+14+4 = 4y
2y+18 = 4y
Subtracting 2y from both sides of the equation:
18 = 4y-2y
18 = 2y
Dividing by 2 on both sides:
y = 18/2
y = 9
Now, putting this value in equation 1:
x = 2y
x = 2*9
x = 18
Hence, the smaller number is 9 and the larger number is 18.
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In a recent student government election the ratio of students who voted for the winner to all the students who was 0.70 to the number of students who wrote it was 75 how many votes did the winner get?
The winner received 53 of the 75 votes in the student gov. election according to provided ratio.
What is ratio?
In arithmetic, a magnitude relation shows range times one number contains another.
Main body:
Because the ratio of students who voted for the winner compared to all students who voted is 0.70
we can rewrite this as:
0.70 = 70/100
And, because we know the total number of students who voted is 75 and if we call the number of students who voted for the winner s , we can then write this relationship and solve for s :
[tex]\frac{70}{100} = \frac{s}{75}[/tex]
Multiplying both sides by 75.
75*[tex]\frac{70}{100} = \frac{s}{75}[/tex]*75
s= 75*70/100
s = 5250/100
s = 52.5
s ≈ 53.
Hence ,The winner received 53 of the 75 votes.
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Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.
The equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18.
The equation will be written as,
C = T - 3
18 = T-3
T = 18 + 3
T = 21 years
Therefore, the equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
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Divide £72 into.
Ratio 4:5
Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.
What is meant by Ratio?A ratio is the number of times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six.Similarly, the lemon to orange ratio is 6:8, and the orange to total fruit ratio is 8:14. A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero.A proportion exists as a equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)Given:
The given ratio is 4:5.
To find: We have to divide 72 in this ratio.
To divide 72 in the 4:5 ratio, we must perform the following steps:
The ratio is 4:5.
We can write the number of the ratio as 4x and 5x by multiplying a constant x.
The total ratio is 4x+5x=9x.
So, 9x is equal to 72.
We can write-
9x=72
x=8.
So, putting the value of x we get-
4×8 and 5×8
So, the numbers are 32 and 40.
Thus 72 divides itself as 32 and 40 in 4:5 ratio.
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how would you change the exponential growth model if the per capita death rate increased?group of answer choicesi would not change anything about the exponential growth model.i would decrease the initial population size.i would increase r.i would decrease r.
Using the concepts of statistics, we got that if the per capita death rate increased, then the exponential growth model would decrease the initial population size.
We know very well, the set up of a differential equation relating instantaneous population growth with respect to the time to the per capita population growth rate and the current population size at an arbitrary time is as follows:
dN / dt = rN
Now, we are told that the constant, r, is per capita population growth rate. N is current size of the population at some time. "r" is the "organisms added per reproductive period" divided by total population at that time. For instance, if the 10 rabbits are born per month and the current population is 100 rabbits, then r value = 0.1.
Hence, the exponential growth model would decrease the initial population size if the per capita death rate increased.
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Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Hartford was $220. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percentage increase is 61.36%. If the airline charges an additional $50 baggage fee, the new percentage increase will be 45.68%.
What is the percent increase?A percentage increase denotes how much a percentage has risen over time. To get at this figure, discover the difference between the original and final values, then deduct it to get the actual sum of the decrease.
The idea of Percentage increase is simply the amount of increase from the original(initial) to the final figure expressed in terms of 100 parts of the original. E.g. A 10% increase implies that if the original value is divided into 100 parts, the value has increased by an extra 10 parts. So, if the initial value rose by 16%, the value would rise by 16 for every 100 units, and so on.
The formula for calculating the percentage increase can be expressed as:
[tex]\%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]\%\ increase= \frac{355- 220}{220}\times 100[/tex]
[tex]\%\ increase= \frac{135}{220}\times 100[/tex]
[tex]\mathbf{=61.36\%}[/tex]
[tex]New \ \%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]New \ \%\ increase= \frac{405- 220}{405}\times 100[/tex]
[tex]New \ \%\ increase= \frac{185}{405}\times 100[/tex]
[tex]New \ \%\ increase=\mathbf{45.68\%}[/tex]
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along a river is to be fenced. suppose that no fence is needed along the river, the fence on the side opposite the river costs $40 per foot, and the fence on the other sides costs $10 per foot. if the field must contain 64,800 square feet, what dimensions will minimize costs?
The dimensions required to minimize the cost of fencing is 180ft and 360 ft.
According to question
The cost of fence on opposite side of river is $40.
The cost of fence on other sides of river is $10.
Total yield = 64800 sq. feet
Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.
Area of fence = xy = 64800 sq feet
⇒ [tex]y = \frac{64800}{x}[/tex]
Let C be the cost of making fence.
For cost to be minimum, dC/dx should be equal to zero.
C = 40x + 10y * 2
⇒ C = [tex]40x + 10(\frac{64800}{x})*2[/tex]
⇒ [tex]\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0[/tex]
⇒ [tex]40x^{2} = 20 * 64800[/tex]
⇒ [tex]x^{2} = 32400[/tex]
⇒ [tex]x = 180[/tex]
⇒ [tex]y = \frac{64800}{180} = 360[/tex]
So, the dimensions needed will be 180 ft and 360 ft.
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cómo se saca el porcentaje
Answer:
Step-by-step explanation:
Para determinar el porcentaje, tenemos que dividir el valor por el valor total y luego multiplicar el resultado por 100.
A helicopter leaves A and flies 40 miles due east. Then the helicopter flies
10 miles due south and arrives at B. Work out the bearing of B from A.
The bearing of the helicopter from B to A is 75.96 degrees
How to determine the bearing of the helicopter from B to AInformation from the question
A helicopter leaves A and flies 40 miles due east
the helicopter flies
10 miles due south
Work out the bearing of B from A = ?
The bearing from B to A is worked using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = 40 miles
adjacent = 10 miles
The bearing is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 40 / 10
tan x = 4
x = arc tan 4
x = 75.96 degrees
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Two glasses of milk and 3 snack bars have a total of 67 carbohydrates (carbs), and 4 glasses of milk and 2 snack bars have a total of 74 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
a sample of student opinion at a big ten university selects an srs of 200 of the 30,000 undergraduate students and a separate srs of 100 of the 5,000 graduate students. what is the term for this kind of sample?
The term for this kind of sample is cluster sampling
Given
that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.
What is cluster sampling ?
Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.
Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.
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In Exercises 1-4, graph the equation. Ider
1. y - 2 = 2(x - 2)
y=5/x. Make x the subject of the formula
Solve in terms of x.
[tex]y=\frac{5}{x}[/tex]
Multiply by x on both sides to remove it from the denominator.
xy =5
Divide by y to get x by itself
[tex]x=\frac{5}{y}[/tex]
Answer:
x=5/y
Step-by-step explanation:
y=5/x
cross multiplying
yx=5
x=5/y
Huey lost 80 marbles. He was to find 45% of them. How many marbles did Huey find
Answer:
OK, so we know that 50% of the 80 marbles is 40, but we are supposed to find 45% of it, so basically it is 36 marbles he has found, I hope this is right!
Love from Ella
help meeeeeeeeeeeeeeeeee please
Answer:
x= 3.4
x+2= 5.4
x+3= 6.4
Step-by-step explanation:
Just figured it out :)
rewrite 16r^2s^2 as a power of a product
Answer: 16r²s²=(4rs)²
Step-by-step explanation:
[tex]16r^2s^2=\\\\4^2r^2s^2=\\\\(4rs)^2[/tex]
5. A road has a 6% downgrade (meaning for every 100 feet you could go horizontally, you go down 6
feet). What is the angle the road makes?
The angle the road makes is 3.43°
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
A 6% downgrade means that for every 100 units of horizontal run.
The vertical height decreases by 6 units.
The grade has a downward angle of
tan⁻1(6/100) = 3.43°
Hence, the angle the road makes is 3.43°
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in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal.
a) The Probability density function of given uniform distribution example is
F(x) = 1/3.5 for 8.5 < x< 12
Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where
x ---> minimum value and y---> maximum value
Probability density function is a probability function which defines the density of continuous random variable lying between specified range
values. It is denoted by f( a<X<b)
Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.
We have following informations,
weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.
Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.
this implies a = 8.5 , b = 12
F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12
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#Complete Qestion :
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?
6. The equation S = 50+45w represents the savings, S, after w weeks working and
depositing money into a savings account at the bank.
Determine whether there is a proportional relationship between S and w. Explain or
show your reasoning.
The relationship is not a proportional relationship between S and w.
Saving, S, after w weeks, is represented by the equation
S = 50+45w
If y is proportional to x, then
y ∝ x
y =kx
where k is the constant of proportionality.
Here, no constant term and (0,0) satisfies this equation.
The given equation is
S = 50+45w
Here, we have a constant term.
For S=0 and w=0,
0=50+45×0
0=50
Which is not true as 0 ≠ 50.
Since there is a constant term 50 and the equation is not valid for (0,0), therefore, the given relationship is not a proportional relationship.
I hope this answer helps.
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What is the simplest positive form of
-35(mod 6)?
simplify 8^15 ÷8^-3 math is hard for me
Answer:
8^18
Step-by-step explanation:
8^15
8^−3
=
8^15
8−3
= 8^15− (−3)
= 8^18
Which number is greatest? 24/100 0.3 16%
A number is being multiplied by a power of 10. Find the number.
Enter your answers in the boxes.
___________ × 102 = 700
___________ × 103 = 36,000
___________ × 105 = 400,000
Answer:
When you have the base of 10 and an exponential index of “n”, the powers of 10 says that the resulting number will be 1 followed by “n” number of zeros. So for example, 10 to the 7th represents the same thing as 1 followed by 7 zeros. The result is 10,000,000 (10 million). Multiplying whole numbers by a power of ten would mean that you ...
The 1st term of a certain sequence is -10, and the 2nd term is 1. Each subsequent term is obtained by adding the 2 immediately preceding terms. What Is the 5th term of this sequence?
In a sequence of first term-10 and the 2nd term is 1. the 5th term of this sequence is -17
How to find the fifth term of the sequenceinformation given in the question
The 1st term of a certain sequence is -10
the 2nd term is 1
Each subsequent term is obtained by adding the 2 immediately preceding terms
the 5th term of this sequence = ?
Each subsequent term is obtained by adding the 2 immediately preceding terms. This statement means is applied as below
Therefore:
third term
3rd term
= first term + 2nd term
= -10 + 1
= -9
4th term
= 3rd term + 2nd term
= -9 + 1
= -8
5th term
= 4th term + 3rd term
= -9 + -8
= -9 - 8
= - 17
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passes through T(0, -2), perpendicular to CX with C (0, 3) and X (2, -1)
Answer:
it would be honestly idj
Step-by-step explanation:
im tryin to get point
Find x
80°
x+51
X =
OK
60°
ALGEBRA
For the given triangle and the measures of the given angle the value of x is equal to -11° .
As given in the question,
For the given triangle,
Let us consider the triangle name ABC,
Where, m ∠A = x + 51° ,
m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)
m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)
To get the value of x we have,
Sum of all the interior angles of a triangle is equal to 180°
m ∠A + m ∠B + m ∠C = 180°
⇒ x + 51° + 80° + 60° = 180°
⇒ x + 191° = 180°
⇒ x = 180° - 191°
⇒ x = - 11°
Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .
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Kendrick needed 10 gallons of gas last week. This week, Kendrick ended up needing 40%
less. How much gas is that?
Answer:
6 gallons
Step-by-step explanation:
40% of 10 is 4 gallons less
10 - 4 = 6 gallons
Serena just started working at the local salon. She is paid $9.85 per hour and earns, on
average, $58.50 in tips each day. Roseline just started working at a bank. Since she
does not receive tips, she earns $16.35 an hour. The system of equations
{y=9.85x+58.50 y=16.35x can be used to represent the amount of money earned, y,
each day for working x hours.
Determine the number of hours Serena and Roseline have to work to earn the same
amount of money.
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Serena recently began working at the nearby salon. By and large, $58.50 in tips every day. Roseline recently began working at a bank. Since she doesn't get tips, she procures $16.35 60 minutes. The arrangement of conditions {y = 9.85x + 58.50 and y = 16.35x} can be utilized to address how much cash is procured, y, every day for working x hours.
The number of hours Serena and Roseline have to work to earn the same amount of money will be given as,
16.35x = 9.85x + 58.5
6.5x = 58.5
x = 9 hours
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
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