Charli,
First find what 1/4 of 2/3 is.
1/4 of 2/3 = 1/6
(That is 1/4 times 2/3 = 1/6)
So, the bottle was 2/3 full, it is now ...
2/3 - 1/6
=4/6 - 1/6
= 3/6 or 1/2 full.
We know that the bottle of soft drink has a remaining volume which is 2 / 3 of the original.
Since Jack drank 1 / 4 of the remaining volume, hence only 3 / 4 now finally remains, the total is:
(2 / 3) * (3 / 4) = 6 / 12 = 1 / 2
Hence the bottle is now one half full
How long will it take for $2800 to grow to $24,900 at an interest rate of 5.6% if the interest is compounded continuously? round the number of years to the nearest hundredth?
Find y to the nearest tenth.
2.7
2.9
7.5
y = 8 x cos(20)
y = 7.517
y = 7.5
The initial balance of a mutual fund is $1800. The fund is expected to grow in value at an annual rate of 5%.
Let x represent the number of years since the fund was started. Let y represent the value of the fund x years later.
What equation models the value of the mutual fund x years after it was started?
Functions f(x) and g(x) are shown below:
f(x) = -4(x - 6)^2 + 3
g(x) = 2 • cos(2 • x - pi) + 4
Using COMPLETE SENTENCES, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.
Write the equation of the function whose graph is shown.
Answer:
[tex]y=1(x-5)^2 + 3[/tex]
Step-by-step explanation:
Given : from the graph vertex is (5,3)
Also graph passes through point (8,12)
We use vertex form of quadratic equation
General vertex form is
[tex]y=a(x-h)^2 + k[/tex]
vertex is (5,3)
h= 5 and k =3
So equation becomes [tex]y=a(x-5)^2 + 3[/tex]
Now we need to find out 'a'
We use (8,12) to find out 'a'
Plug in x=8 and y = 12
[tex]12=a(8-5)^2 + 3[/tex]
[tex]12=a(3)^2 + 3[/tex]
12= 9a + 3
subtract 3 on both sides
9 = 9a
divide both sides by 9
so a=1
Final equation is
[tex]y=1(x-5)^2 + 3[/tex]
An equation of the function of this graph is equal to [tex]y=1(x-5)^2 + 3[/tex]
Given the following data:
Points on the x and y-axis = (8, 12).Vertex (h, k)= (5, 3).How to write a function.The vertex form of a quadratic equation can be used to write an equation of the function of a graph.
Mathematically, the vertex form of a quadratic equation is given by this formula:
[tex]y=a(x-h)^2 + k[/tex]
Substituting the given parameters into the formula, we have;
[tex]12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1[/tex]
a = 1.
For the equation:
[tex]y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3[/tex]
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"you buy a baseball bat and a ball for $1.10. the baseball bat costs $1.00 more than the ball. how much did the ball cost?"
after 5 years what is the total amount of a compound interest investment of 32,000 at 3% interest, compounded quarterly
A.57.795.56
B.32,426.67
C.43,099.36
D.37,157.89
If (1, 2) and (3, 4) lie on the same line, give the slope-intercept equation of the line.
Final answer:
The slope-intercept equation of the line that passes through (1, 2) and (3, 4) is y = x + 1, with a slope of 1 and a y-intercept of 1.
Explanation:
To find the slope-intercept equation of a line that passes through the points (1, 2) and (3, 4), we first need to determine the slope of the line. We use the formula for the slope (m) given by the change in y over the change in x, or Δy/Δx. Calculating the slope, we get:
m = (4 - 2) / (3 - 1) = 2 / 2 = 1.
Now we have the slope, we can use the slope-intercept form of the line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in one of the points, say (1, 2), into this equation gives us:
2 = (1)(1) + b
Which simplifies to:
b = 2 - 1 = 1
So the y-intercept (b) is 1. Therefore, the slope-intercept equation of the line is:
y = x + 1
Which step should be used to prove that point a is equidistant from points c and b? (1 point)?
Which of the following statements describes the process for solving 4x ≥ -24?
Divide both sides of the inequality by -24 and flip the symbol.
Divide both sides of the inequality by -24 but don't flip the symbol.
Divide both sides of the inequality by 4 and flip the symbol.
Divide both sides of the inequality by 4 but don't flip the symbol.
Answer:
Your answer would be D.
Step-by-step explanation:
The m6 = (11x + 8)° and m7 = (12x – 4)° What is the measure of 4? m4 = 40° m4 = 48° m4 = 132° m4 = 140°
The measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
From the diagram, we can observe that angles 6 and 7 are vertically opposite angles.
From one of the angle theorems, we have that vertically opposite angles are equal
That means,
measure of ∠ 6 = measure of ∠ 7
From the question,
we have that, m6 = (11x + 8)° and m7 = (12x – 4)°
Since, the measures of angles 6 and 7 are equal, then we can write that
(11x + 8)° = (12x – 4)°
Now, determine the value of x, we will solve the equation
11x + 8 = 12x – 4
First, subtract 11x from both sides
11x - 11x + 8 = 12x - 11x - 4
8 = x - 4
Now, add 4 to both sides
8 + 4 = x -4 +4
12 = x
∴ x = 12
Now, we will determine the measure of ∠6
m ∠6 = (11x + 8)°
Put x = 12
∴ m ∠6 = (11(12) + 8)°
m ∠6 = (132 + 8)°
m ∠6 = 140°
To determine the measure of ∠4, m4, we will first determine the measure of ∠8.
From the diagram,
m ∠6 + m ∠8 = 180° (Sum of angles on a straight line)
∴ 140° + m ∠8 = 180°
Then,
m ∠8 = 180° - 140°
m ∠8 = 40°
From the diagram, we can observe that angles 4 and 8 are corresponding angles.
Also, from one of the angle theorems, we have that corresponding angles are equal.
Hence, the measure of ∠ 4 equals the measure of ∠ 8.
From above, m ∠8 = 40°
∴ m ∠4 = 40°
Hence, the measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
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Find the quotient and remainder using long division. x6 + 4x4 + 4x2 + 16 x2 + 4
What are the names of the eight line section and the six line section that combine to form the 14 lines of a petrarchan sonnet?
The answer is an octave and a sestet. A sestet is the title specified to the second split of an Italian sonnet (as contrasting to an English or Spenserian sonnet), which must contain of an octave, of eight lines and must be followed by a sestet, of six lines. The first recognized user of this poetical type was the Italian poet named Petrarch.
Use two or three unit fractions to convert. 1515 daysdaysequals=_______ secondsseconds
It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We need to find the unit fractions to convert 15 days into seconds.
1 day = 24 hour
1 hour = 60 minutes.
1 minutes = 60 seconds
Therefore, 24 hours = 24 x 60 x 60 = 86400 seconds
There are 86400 seconds in one day.
Then 15 days = 15 x 86400 = 1,296,000
Hence, It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
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Pleaseeee help!!!!!!!!!
suppose the correlation coefficient between the number of the college students in a city and the number of city buses is 0.89. which statement must be true?
Answer:
Step-by-step explanation:
Given that the correlation coefficient between the number of college students in a city and the number of city buses is 0.89.
We find that correlation coefficient is a measure of linear association between two variables.
When the absolute value of correlation coefficient is near 1, there is strong correlation. If correlation has a positive sign, there is a posiitive association between the two variables.
Here the correlation coefficient is positive and also near 1. Thus there is a strong linear correlation between the two variables.
Or whenever there is an increase in one variable there will be an increase in other variable also.
Determine whether 2y=3x-1 represents a direct variation. if it does, find the constant of variation.
The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.
The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:
Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.
Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.
However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.
please help and explain to me!
Describe which of the two points lies on the graph of the line
Y-x=4
A. 9,5
B. 5,9
Joe walked of a mile in of an hour. what is his unit rate in miles per hour? (1 point) = mile per hour = miles per hour = miles per hour = mile per hour
if f(x)=2x-4 find f(q+1)
The value of f(q+1) is 2(q-1).
What is a function?A relation or expression involving one or more variables.
Given that, f(x) = 2x - 4
When x = q+1
f(q+1) = 2(q+1) - 4
f(q+1) = 2q + 2 - 4
f(q+1) = 2q - 2
f(q+1) = 2(q-1)
Hence, the value of f(x) when x = (q+1) is 2(q-1)
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Helpppppppppppppppppp
Which property can be used to remove the parentheses in the expression 1.7(x+9)
Can you help me solve #s 43 an 44 pleeeease
PLEASE HELP ASAP!!!!!
Carl, Brian, Dave, and Ashley want to attend the same university. Unfortunately only two spots remain and these four friends have the same GPA, as well as virtually identical community service and leadership experiences. Therefore, the two spots will be determined by their SAT and ACT scores. Carl scored 1,280 on the SAT, while Brian scored 1,325. Dave scored 28 on the ACT, while Ashley scored 30. Use z-scores to determine which two students should be admitted. The mean SAT score was 1,000 with a standard deviation of 175 and the mean ACT score was 20.6 with a standard deviation of 5.2 Both tests are normally distributed.
A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?
The interval notation is:
0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;
The second and third car seats are suitable.
The number lines shows the weights of the car seats which is designed for in comparison the weight of the 32lb child.
Three car seats are designed as follows:
The car seat made for children upto 30lb. The seat for children between 15lbs and 40lbs andThe seat designed for a child between 30 lb and 85 lbAs the seat designed for a child upto and including 30 lb would not be suitable for 32 lb child. Because 32lb is more than the 30 lb.
Now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 32lb.
The interval notation is:
0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;
The second and third car seats are suitable.
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Which irrational number can be multiplied by negative square root of 41 to get a product that equals 1?
For this case we define the following variable:
x: unknown number
We then have the following equation:
[tex]- \sqrt {41} x = 1[/tex]
From here, we clear the value of x.
We have then:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
Answer:
An irrational number that can be multiplied by negative square root of 41 to get a product that equals 1 is:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
2x to the fourth power + 5x squared + 3, factored
Jasmine is 23 years old. jasmine is 3 years less than half of george's age. write and solve an equation to find george's age.
take 23 and multiply by 3 then divide by 2 and your answer should be x34
Circle J and circle K are shown in the diagram below.
What is the total number of lines of tangency that are common to circle J and circle K?
3
2
4
1
Thank you!