If x and y are in direct proportion and y is 2 when x is 4 and y is 6 when x is 12.
By definition of proportionality,
If y is directly proportional to x,
y α x
i,e y = k(x)
K is the constant of proportionality
when x = 4, y =2
2 = k(4) --> k = 1/2
Now y = k.x
y = 1/2 (12)
y = 6
What is the Constant of Proportionality?
The proportional constant is a ratio that connects two given values in a so-called proportional relationship. Other names for the constant of proportionality are constant ratio, constant rate, unit rate, constant of variation, or even rate of change.
To find the constant of proportionality, first identify the variables x and y. To find out the relationship between weight and number of sticks, x is the weight and y is the number of butter sticks. Use the equation k = y÷ x to find the constant of proportionality.
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help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answer:
a) 1835 feet.
b) 1323 feet.
Step-by-step explanation:
Substitute each value of t into the equation to find the height at that particular time.
When t = 2, P(t) = -16(2)^2 + 1899 ⇒ P(t) = -64 + 1899 ⇒ P(t) = 1835.
When t = 6, P(t) = -16(6)^2 + 1899 ⇒ P(t) = -576 + 1899 ⇒ P(t) = 1323.
list the transformations
Answer:
on what?
Step-by-step explanation:
Solve quadratic equations -x^2 +3x < 3
The given quadratic inequation,
[tex]-x^2+3x<3[/tex]Subtract 3 on both sides,
[tex]\begin{gathered} -x^2+3x-3<3-3 \\ -x^2+3x-3<0 \end{gathered}[/tex]Multiply both sides by -1 that results in a change of symbol of the inequality,
[tex]\begin{gathered} (-1)\cdot(-x^2+3x-3)>(-1)\cdot0 \\ x^2-3x+3>0 \end{gathered}[/tex]Use the method of completing squares,
[tex]\begin{gathered} (x)^2-2(x)(\frac{3}{2})+(\frac{3}{2})^2-(\frac{3}{2})^2+3>0 \\ (x-\frac{3}{2})^2-\frac{9}{4}+3>0 \\ (x-\frac{3}{2})^2+\frac{3}{4}>0 \\ (x-\frac{3}{2})^2^{}>-\frac{3}{4} \end{gathered}[/tex]Consider that the square of any real number is always positive, and hence greater than a negative number.
So we can observe that the result obtained above is valid for all real number values of 'x'.
Thus, the solution of the given inequality is the set of all real numbers,
[tex]x=(-\infty,\infty)[/tex]The probability the Shane will sink a foul shot is 80%. If Shane attempts 40 foul shots, what is the probability that he sinks at least 28 shots? Round your answer to the nearest whole percenta-96%b-90%c-95%d-80%
For this problem we have to calculate the probability that x is greater or larger than 28
[tex]\begin{gathered} P(x\ge28)=\Sigma P(x=i) \\ i\text{ goes from 28 to }40 \end{gathered}[/tex]For each i, the probability
[tex]P(x=i)=\frac{40!}{28!\cdot12!}\cdot0.8^i\cdot0.2^{40-i}[/tex]Now computing the sum:
[tex]P(x\ge28)=96[/tex]The answer is 96%
Will you help me find the Exact value of sec pi/3 and help me under stand how to
To find the exact value of sec π/3, use a sp cial triangle with an angle
π/3 radians=60º.
Consider an equilateral triangle with each side length of 1 unit.
Recall that each angle in an equilateral triangle is 60º.
Draw the altitude of the triangle. Note that the altitude of an equilateral triangle is an angle bisector of the vertical angle and also a perpendicular bisector of its base:
Recall that the Secant Ratio in a right triangle is given as:
[tex]\sec\theta=\frac{\text{ Hypotenuse}}{\text{ Adjacent}}[/tex]Substitute θ=60º, hypotenuse=1, and adjacent=1/2 into the equation:
[tex]\begin{gathered} \sec60^{\circ}=\frac{1}{\frac{1}{2}}=\frac{2}{1}=2 \\ \Rightarrow\sec60^{\circ}=2 \\ \Rightarrow\sec\frac{\pi}{3}=2 \end{gathered}[/tex]The exact value of sec π/3 is 2.
Write a quadratic function in standard form whose graph passes through the given points1. (-1,5), (0,3), (3,9)
The Standard Form of a Quadratic Function:
[tex]\text{ y = ax}^2\text{ + }bx\text{ + c}[/tex]Using the given points (-1,5), (0,3), and (3,9), let's substitute each point to the equation.
At (-1,5):
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow5=a(-1)^2\text{ + b(-1) + c}[/tex][tex]\text{ 5 = a - b + c}[/tex]At (0,3):
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow3=a(0)^2\text{ + b(0) + c}[/tex][tex]\text{ 3 = c}[/tex]At (3,9):
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow9=a(3)^2\text{ + b(3) + c}[/tex][tex]\text{ 9 = 9a + 3b + c}[/tex]We now get these equations:
5 = a - b + c ; 3 =c; 9 = 9a + 3b + c
Let's determine the value of a, b and c. We get,
Substituting 3 = c to 5 = a - b + c,
[tex]\text{ 5 = a - b + c }\rightarrow\text{ 5 = a - b + 3 }\rightarrow\text{ a - b = 2}[/tex][tex]\text{ b = a - 2}[/tex]Let's substitute 3 = c and b = a - 2 to 9 = 9a + 3b + c,
[tex]\text{ 9 = 9a + 3b + c }\rightarrow\text{ 9 = 9a + 3(a-2) + 3}[/tex][tex]\text{ 9 = 9a + 3a - 6 + 3 }\rightarrow\text{ 12a = 9 + 6 - 3 }\rightarrow\text{ 12a = 12}[/tex][tex]\text{ a = }\frac{12}{12}\text{ = 1}[/tex]Since a = 1, let's solve for the value of b which is b = a - 2.
[tex]\text{ b = a - 2 }\rightarrow\text{ b = 1 - 2}[/tex][tex]\text{ b = -1}[/tex]Since we've identified that a = 1, b = -1 and c = 3, let's substitute the values to the standard form of a quadratic function to be able to make the equation.
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow y=(1)x^2\text{ + (-1)x + (3)}[/tex][tex]\text{ y = x}^2\text{ - x + 3}[/tex]Therefore, the quadratic function in a standard form whose graph passes through the given points (-1,5), (0,3), (3,9) is y = x^2 - x + 3.
An astronomical unit is about 92,955,807 miles. Use a single digit times a power of ten to estimate this value to the nearest ten million miles.
9 10 million miles or [tex]9*10^7[/tex] miles is the estimated value of an astronomical unit to the nearest ten million miles.
Given that:-
1 astronomical unit = 92,955,807 miles
We have to estimate its value to the nearest ten million miles.
We know that,
10 million miles = 10,000,000 miles
Hence,
1 mile = (10/10000000) million miles
92955807 miles = 929558070/10000000 million miles
92955807 miles = 92.955807 million miles
For 10 million miles, we can write,
92955807 miles = 9.2955807 10 million miles
We can estimate 9.2955807 10 million miles to 9 10 million miles
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(b) You need to raise a total of $600 for your trip. There are 10 days before you leave. You estimate that youwill be able to sell 15 cans of soda per day. How much should you charge for each can?Set up the problem:Ix 1Answer:$per can
The Solution:
To raise a total $600 in 10 days with an estimate of selling 15 cans of soda per day.
To find the amount you should charge for each can is:
[tex]\frac{\text{ \$600}}{\text{ 10 days}}\times\frac{\text{ 1 day}}{\text{ 15 cans per day}}=\frac{600}{150}=\text{ \$4}[/tex]Therefore, the correct answer is $4 for each can of soda.
Write an equation of the circle with center (6,8) and radius 7
Let’s find the equation of a circle with
radius r = 7 and center (h,k) =(6,8).
By definition, an equation of the circle with center (h,k) and radius r is
[tex](x-h)^2\text{ }+\text{ (}y-k)^2\text{ = }r^2[/tex]This is called the standard form for the equation of the circle. Then, in our case, replacing the data we have, we should have:
[tex](x-6)^2\text{ }+\text{ (}y-8)^2\text{ = 7}^2\text{ = 49}[/tex]so, we can conclude that the equation of the circle with center (6,8) and radius 7 is :
[tex](x-6)^2\text{ }+\text{ (}y-8)^2\text{ }^{}\text{ = 49}[/tex]I can find percentages and values using the 68-95-99.7 rule, z-scores, and the standard normal distribution.answer the questions only if you know the answer please
ANSWER and EXPLANATION
1) We want to find the z score for a student who had a GPA of 3.8.
To do this, we have to apply the formula for z score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where:
x = score/GPA
μ = mean
σ = standard deviation
Therefore, the z score for the student with a GPA of 3.8 is:
[tex]\begin{gathered} z=\frac{3.8-3}{0.6} \\ z=\frac{0.8}{0.6} \\ z=\text{1}.33 \end{gathered}[/tex]2) The z score is a measure of how far away a data point is from the mean, in other words, it is a measure of how many standard deviations a data point is above or below a mean.
We can find how many standard deviations there are in a z score of -2.4 by dividing -2.4 by the standard deviation (0.6):
[tex]\begin{gathered} \frac{-2.4}{0.6} \\ -4 \end{gathered}[/tex]Therefore, since the z score is negative, we can conclude that the student's GPA is 4 standard deviations below the mean value.
Raffi has forgotten to multiply numbers that contain decimals. To multiply 0.4 x 1.34, he ignores the decimals
and multiples 4 x 134 = 536. Explain how Raffi could use estimation to determine where the decimal
point should be placed.
Answer:
.536 would be the correct answer. You could estimate by rounding 1.34 to 1 and 0.4 is close to .5 or 1/2. What is 1/2 of 1 1/2 or .5. This would lead me to place the decimal before the 5.
Step-by-step explanation:
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If cost of 15 eggs is ? 75, then find out the cost of 4 frozen eggs
Problem:
If the cost of 15 eggs is $75, then find out the cost of 4 eggs?
Solution:
If the cost of 15 eggs is $75, then each egg cost:
[tex]\frac{\text{\$75}}{15}=\text{ \$5 for each egg}[/tex]thus, 4 eggs cost :
$5 x 4 = $20
then, the correct answer is $20
try to write an equation to describe the relationship between the stage number N and the number of squares S.
Let's first identify the number of squares in each stage:
Stage 1: 7 squares.
Stage 2: 14 squares.
Stage 3: 21 squares.
If we notice the sequence, we notice that it increases by 7 per stage, therefore:
Stage N: N*S
Where S is always equal to 7.
Foe example, in the stage 4:
Stage 4: 4*7 = 28 squares.
The equation is:
7*N
The equation y=4.9x represents a proportional relationship. what is the constant proportionately?
Given that angle ABC and EBF form a right angle, if measurement of ABC = 30° and EBF
= 6x° what is the value of x?
We know that ABC and EBF are complementary, or add up to 90°. So:
ABC + EBF = 90°
ABC = 30°
EBF = 6x°
6x° + 30° = 90°
6x° + 30 - 30 = 90 - 30
6x° = 60°
6x°/6 = 60°/6
x° = 10°
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Answer:
Top Left: -6
Top Right: -x
Bottom Left: 12x
Bottom Right: 2x^2
Trinomial: 2x^2 + 11x - 6
Step-by-step explanation:
Hello! Let's help you with your question here!
So, box method. From your question, the process is pretty easy. It would require a bit more work when factoring a trinomial.
The equation in question is already factored which is very useful, now it's a matter of the values in the box. I am on the assumption that the two top boxes and the two left boxes are filled in for you and you just need to fill the middle (if that isn't the case, do let me know). To just fill the boxes in the middle, evaluate it like you would multiplying rows and columns. So, it would be as such:
6 x
-1 -6 -x
2x 12x 2x^2
In terms of simplifying, we use FOIL to expand it out into a trinomial and collect like terms. Therefore, it becomes:
[tex](x+6)(2x-1) = (x*2x)+(x*(-1))+(6*2x)+(6*(-1))[/tex]
[tex]= 2x^2 + (-x) + (12x) + (-6)[/tex]
[tex]=2x^2+11x-6[/tex]
Let me know if there are any questions and if it is wrong, do let me know!
Solve this system by substitution: y = 5x - 15 y = 2x - 6 Remember to write your answer as a coordinate point (x,y)
Given the following System of equations:
[tex]\begin{cases}y=5x-15 \\ y=2x-6\end{cases}[/tex]You can use the Substitution method to solve it, as following:
1. Solve for "x" from the first equation:
[tex]\begin{gathered} y=5x-15 \\ y+15=5x \\ \\ x=\frac{y+15}{5} \end{gathered}[/tex]2. Now you must substitute this equation into the second original equation:
[tex]\begin{gathered} y=2(\frac{y+15}{5})-6 \\ \end{gathered}[/tex]3. Solve for "y":
[tex]\begin{gathered} y=\frac{2y+30}{5}-6 \\ \\ y+6=\frac{2y+30}{5} \\ \\ (5)(y+6)=2y+30 \\ 5y+30=2y+30 \\ 3y-2y=30-30 \\ y=0 \end{gathered}[/tex]4. Knowing the value of "y"; you can substitute it into this equation:
[tex]x=\frac{y+15}{5}[/tex]Then:
[tex]x=\frac{(0)+15}{5}[/tex]5. Evaluating, you get that the value of "x" is:
[tex]\begin{gathered} x=\frac{15}{5} \\ \\ x=3 \end{gathered}[/tex]Then, the answer is:
[tex](3,0)[/tex]A new energy drink advertises 177 calories in for 12 ounces. How many calories are in 20 ounces of the drink? _ calories
We can use the rule of three to solve this question, first, we need to build our relation, remeber that we need to put calories on one side and ounces on the other:
[tex]\begin{gathered} 177\rightarrow12 \\ x\rightarrow20 \end{gathered}[/tex]Now we need to solve it for x, we can build it as a fraction
[tex]\frac{177}{x}=\frac{12}{20}[/tex]Now we can solve it for "x", let's do a cross multiplication:
Therefore
[tex]12x=177\cdot20[/tex]We can divide by 12
[tex]x=\frac{177\cdot20}{12}[/tex]Now we can just to the calculus and we will have the value of x, if we do it we get
[tex]x=295\text{ calories}[/tex]Therefore, there are 295 calories in 20 ounces of drink
Connect the points to form a rectangle. What is the perimeter of the rectangle
The answer is option A 34 units.
We need to count the distance between the points and then add them to get the perimeter.
L and M are 5 units away, as well as X from J
L and X are 12 units away, as well as M from J
Now we can add the distances:
5 + 5 + 12 + 12 = 34
THen the perimeter is 34 units
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Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
Given the speeds of each runner below, determine who runs the fastest.
Ron runs 12 feet per second.
Brooke runs 329 feet in 24 seconds.
Jessica runs 1 mile in 591 seconds.
Tony runs 645 feet in 1 minute.
Answer:
Brooke with 13 ft/sec
Step-by-step explanation:
Ron is (12 ft/second)
To figure out Brooke we have to divide 329 by 24 to figure out her feet per second.
329/24 = 13.7083 so already is ahead of Ron.
To figure out Jessica we must first figure out the length of a mile in feet to keep the feet per second denominator going.
1 mile= 5280 ft
so now we divide
5280/591 = 8.9340
So Jessica is not the fastest so Brooke still stands number 1.
For Tony we divide 645 by the number of seconds in one minute
there are 60 seconds in a minute so
645/60= 10.75
So the fastest is brooke.
Ron = 12 ft/sec
Brooke = 13 ft / sec
Jessica = 8 ft / sec
Tony = 10 ft/ sec
find the image of P(7,7) under a dilation with scale factor 1/2 and center of dilation (1,3)
Given,
The coodinates of the points are P(7,7).
The scale factor is 1/2.
The coordinates of center of dilation is (1,3).
In the operation described here, it is the vector (center of dilation→ similar point) that will get multiplied by a factor 1/2.
The vector from the centre (1,3) to point (7,7) has coordinates (7,7) - (1,3)
[tex]((7-1),(7-3))=(6,3)[/tex]Now, dilated the coordinates by the scale factor of 1/2 then,
[tex]\frac{1}{2}(6,3)=(3,\frac{3}{2})[/tex]Image of the point is at,
[tex]\begin{gathered} (3,\frac{3}{2})=(3+1,\frac{3}{2}+3) \\ =(4,\frac{9}{2}) \end{gathered}[/tex]Hence, the coordinates of the image is (4,9/2).
A Web music store offers two versions of a popular song. The size of the standard version is 2.3 megabytes (MB). The size of the high-quality version is 4.1 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 3796 MB. How many downloads of the standard version were there?
The number of downloads of the standard version is 949.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Two versions of a song.
S = Standard version size = 2.3 MB
H = High-quality size = 4.1 MB
Hgh quality size = 3 x Standard quality size
H = 3 x S
H = 3S ____(1)
The total size downloaded for the two versions was 3796 MB.
This can be written as:
H + S = 3796 ______(2)
From (1) and (2) we get,
3S + S = 3796
4S = 3796
S = 3796/4
S = 949
Now,
From (1),
H = 3S = 3 x 949 = 2847
The number of downloads of the standard version is 949
The number of downloads of the High-quality version is 2847
Thus,
The number of downloads of the standard version is 949.
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there are 60 seventh graders in the school. This make up 15% of the student in the school. How many students are in the school,total?
60 seventh graders make up 15% of the students in the school.
The procedure to solve this problem will be to first, divide 60 by 15 to find how much people make up 1%, and then multiply that number of people by 100% to find the total of students.
Step 1. Divide 60 people by 15% to find how many people are 1% of the students:
[tex]\frac{60}{15}=4[/tex]4 students are 1% of the total students.
Step 2. Now, we multiply the number we just find in step 1 by 100% to find the total amount of students in the school:
[tex]4\times100=400[/tex]There are 400 students in the school.
Answer: 400
Find the standard form of the equation of the circle having the following properties:
Center at the origin
Containing the point (-3,8)
Answer: x^2 + y^2 = 73
Step-by-step explanation:
H, K would be the center
R would be the radius
H, K= 0,0
(x-0)^2 + (y-0)^2= r^2
x^2 + y^2= r ^2
To Find Radius, you find distance between Origin, and Point
[tex]D=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
X2, Y2= (-3, 8)
X1, Y1= (0,0)
[tex]D= \sqrt{((-3)-(0))^{2} + ((8-0))^2} \\D= \sqrt{(-3)^2 + (8)^2} \\D= \sqrt{9+ 64} \\D=\sqrt{73} \\D= 6\sqrt{2}[/tex]
R= 6[tex]\sqrt{2}[/tex]
x^2+y^2= (6[tex]\sqrt{2}[/tex])
or x^2+y^2= 73
What is a unit rate?
we have that
A unit rate is a ratio between two numbers, where the second quantity is one unit
Example
5/1 m/sec is the same that 5 m/sec
that means
speed is 5 meters per one second
2 example
$6 per oz
that means -----> the cost is $6 per one ounce
the cost of manufacturing and selling x units of a product is c-7x+11 and the corresponding revenue R is R - x^2 - 15 find the number of the units needed to earn below and above the btrak even value
We know:
Profit = Revenue - Cost
When Revenue is equal to Cost, we have the break-even point.
Let's equate revenue and cost:
[tex]\begin{gathered} R=C \\ x^2-15=7x+11 \end{gathered}[/tex]To find the value of x, we can take all terms to LHS (Left-Hand-Side) and use the quadratic formula. The process of finding x is shown below:
[tex]\begin{gathered} x^2-15=7x+11 \\ x^2-15-7x-11=0 \\ x^2-7x-26=0 \\ u\sin g\text{ quadratic formula,} \\ x=-2.7,9.7 \end{gathered}[/tex]We can't have a negative value, so we disregard x = -2.7
What we have is
x = 9.7
So,
For 10 units (and above) sold, we will have a profit.
For 9 units (and below) sold, we will incur a loss.
A three-dimensional figure has the following properties:* It has a circular base.* It has a second, circular base parallel to the first, with a round smooth face between them.What kind of solid is it?sphererectangular prismconecylinder
With the information provided we will have that the solid is:
*A Cylinder.
If a die is rolled one time, find these probabilities
c) Getting a number greater than 3 and an even number.
P(a number greater than 3 and an even number
4/6 = 2/3
The probability of receiving a number greater than 3 and an even number is 2/3.
What is probability?The likelihood or chance that an event will occur is referred to as probability.When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are. Statistics is the study of events governed by probability.P(E) = (Number of positive outcomes) / (Sample space)
Here,
When a die is rolled once, the sample space is
S = {1, 2, 3, 4, 5, 6}. The total score is 6.
The events will be E ={ 4, 5, 6, 2}
if a number greater than 3 and an even number are rolled. The expected result is 4.
The likelihood of receiving a number greater than 3 and an even number is 4/6 = 2/3
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