The ratio of green balloons to the total number of balloons is 3 to 8.
What is Ratio?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.
Given, the number of red balloons = 22
the number of blue balloons = 18
the number of green balloons = 24
Total number of balloons = 22 + 18 + 24 = 64
Now,
the ratio of green balloons to the total number of balloons =
= (the number of green balloons)/(Total number of balloons)
= 24/64
= 3/8
= 3:8
Hence, the required ratio is 3 to 8.
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is going to invest $820 and leave it in an account for 19 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for John to end up with $1,830?
The rate of interest for an amount which is compounded quarterly is 4.25%
Given,
The principal amount invested by Oliver, P = $820
The time period of the investment, t = 19 years
The interest is compounded quarterly, n = 4
The amount after 19 years, A = $1830
The compound interest formula;
A = [tex]P (1+\frac{r}{n} )^{nt}[/tex]
We have to find the rate of interest;
For that;
A = [tex]P (1+\frac{r}{n} )^{nt}[/tex]
1830 = 820 [tex](1+\frac{r}{4} )^{76}[/tex]
1830/820 = [tex](1+\frac{r}{4} )^{76}[/tex]
₇₆√1830/820 = 1 + r/4
₇₆√1830/820 - 1 = r/4
r = 4 (₇₆√1830/820 - 1)
r = 0.042 x 100
r = 4.25%
That is,
The rate of interest for an amount which is compounded quarterly is 4.25%
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a plant is already 11 centimeters tall, and it will grow one centimeter ever month.Let H be thed plants height(in centimeters) after M months. Write an equation realted H to M
The growth follows a linear equation, for that we need
y = mx + c
The number of months would be the x axis as that is the thing changing, and the height would be the y axis as that is the thing being measured to change.
That now gives us
H = mM + c
m is the gradient and c is the y intercept
We can figure out the gradient because after 1 month the height increases by 1 so the change in y vs the change in x is 1 so the gradient must be 1.
The y intercept in this case is the initial condition and therefore is 11cm.
The final answer being
H = M + 11
an underwater drone is located 9 3/5 meters below sea level. the drone is moved to a location that is 15 1/2 meters below sea level. which measure best describes the change in the location of the drone? 26 1/10m 5 9/10m -5 9/10m -26 1/10m
The measure that best describes the change in the location of the drone is D. -26 1/10m
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the underwater drone is located 9 3/5 meters below sea level and the drone is moved to a location that is 15 1/2 meters below sea level
The change will be:
= - 9 3/5 - 15 1/2
= - 9 6/10 - 15 5/10
= - 25 1/10
The change is - 25 1/10m.
The options are incorrect.
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Choose the correct answer below.
A. The statement is true because the definition of the instantaneous rate of change for a function f at x is the same as the definition of the derivative of a function f at x
B. The statement is false because the derivative is the average rate of change of x with respect to y=f(x).
C. The statement is false because the derivative is the average rate of change of y=f(x)with respect to x
D. The statement is false because the derivative is the instantaneous rate of change of x with respect to y=f(x)
The correct answer to this question is A.
Hardest thing ever. Please help! I will give branliest answer
Answer:
This is commutative property of supplements
what is the slope of a line perpendicular to the line whose equation is 2x+2y=-12
Answer:
The slope of a line perpendicular to m=2 is m= 1.
Step-by-step explanation:
2x+2y=-12
2y=-2x-12
y= -x-6.
The equation is in slope-intercept form now, so it is easy to tell what the slope is.
The slope of y= -x-6 is m = -x. Technically, -x = -1x, so now make the -1 positive and find the reciprocal, which is still 1.
All you need to do to find the perpendicular slope of any line is simply to find the reciprocal of the number and make the positive/negative number the opposite. I hope this helps, have a good day/night! :)
PLEASE HELP
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 50 degrees at midnight and the high and low temperature during the day are 58 and 42 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
The equation for temperature 67, gives the time as 4.8 hours.
What is amplitude?
A sound is a type of energy that is created when objects vibrate. For it to spread, a medium is needed. As a result, sound cannot travel in a vacuum because there is nothing for the sound waves to travel through. The object's back-and-forth movement creates the sound. Sound vibration is the name for this. Additionally called oscillatory motion. Oscillation describes the regular rhythmic back-and-forth movement.
We know that the general equation of a sine wave is:
[tex]$$y(t)=A \{Sin}(W(t-C))+D$$[/tex]
where,
A- Amplitude
D = Average of Max(y) and Min(y);
[tex]W=\frac{2 \pi}{\text { Period }}[/tex]
C - Phase shift on y(axis)
Part a)
Given Max T= 94 and Min T = 66
Hence,
D = (Max+Min)/2 = 80
A = Max - D = 94-80= 14
Since period is 24 hours, so W = 2\pi/24 = \pi/12
Thus the function till now is:
[tex]T(t)=14Sin(\frac{\pi}{12}(t-C))+80[/tex]
Given low temperature occurs at 3 AM so,
T(3)=66
Solving this we get C = 9
Hence,
[tex]T(t)=14Sin(\frac{\pi}{12}(t-9))+80[/tex]
Part b)
Given Max T= 58 and Average = 45
Hence,
D = 45
A = Max - D = 58-45= 13
Since the period is 24 hours, so W = [tex]2\pi/24 = \pi/12[/tex]
Thus the function till now is:
[tex]T(t)=13Sin(\frac{\pi}{12}(t-C))+45[/tex]
Given high temperature occurs at 5 PM so,
T(17)=58
Solving this we get C = 11
Hence,
[tex]T(t)=13Sin(\frac{\pi}{12}(t-11))+45[/tex]
The temperature at 4 AM is:
[tex]T(4)=13Sin(\frac{\pi}{12}(4-11))+45 = 32.44[/tex]
Part c)
Given Max T= 86 and Min T = 64
Hence,
D = (Max+Min)/2 = 75
A = Max - D = 86-75= 11
Since period is 24 hours, so W = 2\pi/24 = \pi/12
Thus the function till now is:
[tex]T(t)=11Sin(\frac{\pi}{12}(t-C))+75[/tex]
Given average temperature occurs at 8 AM so,
T(8)=75
Solving this we get C = 8
Hence,
[tex]T(t)=11Sin(\frac{\pi}{12}(t-8))+75[/tex]
Now,
We need to find t such that T(t) = 67.
[tex]67=11Sin(\frac{\pi}{12}(t-8))+75[/tex]
[tex]\Rightarrow t=4.88945 \approx 4.89 hours[/tex]
Hence, The equation for temperature 67, gives the time as 4.8 hours.
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12456 round to the nearest ten thousand
Answer:
12000 is the correct answer.
Step-by-step explanation:
Hope this helps you :)
Mark has brainiest please
Milos makes a diagram of an upcoming trip to his grandparents' house using what he recalls about the time and mileage from past trips.
Miles
Using Milos's diagram, find the constant of proportionality in miles per hour.
Answer:
6261
Step-by-step explanation:
it was 6261 because I have to do a i test at
How do you change a fraction to a decimal?
Group of answer choices
Divide the numerator by the denominator
Move the decimal over 2 places
Change the denominator to 100
Divide the denominator by the numerator
Answer:
it is the answer number 1
Solve the exponential equation 31^d = 38
Solve the inequality. Write the solution set in interval notation.
11 ≤ 6(n + 4) - 4n
Take a look at the attachments...
Hope this helps! :)
Using the distributive property, an expression is equivalent to 20+30
Which of the following tables represents the proportional relationship for 3 cups of grape juice for every one fourth cup of rainbow sherbet?
Grape Juice (cups) 0.25 1 1.5
Rainbow Sherbet (cups) 3 6 9
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 0.25 0.5 0.75
Rainbow Sherbet (cups) 0.25 1 1.5
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 3 6 9
Grape Juice (cups) 0.25 0.5 0.75
The table that represents the proportional relationship for 3 cups of grape juice for every one fourth cup of rainbow sherbet is:
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 0.25 0.5 0.75
What table represents the proportional relationship?The table that represents the proportional relationship would have a constant ratio of grape juice to rainbow sherbet of 3 cups to one fourth constantly.
One-fourth is equivalent to 1 / 4 when written as a fraction and 0.25 when written as a decimal.
In the second table, when 3 and 0.25, 6 and 0.5, 9 and 0.75 cups of grape juice and rainbow sherbet are expressed in it simplest form, they are all equivalent to 3 and 1/4.
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Answer:
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 0.25 0.5 0.75
Step-by-step explanation:
I took the exam and got it right
When the mortgage is completely paid off for Mark and Lynne’s house, it will be 4 times as old as it is now. If they have 15 years left on the mortgage, how old is the house right now?
Mrs. Croaker’s class calculated that their class frog, named Fred, jumped 23 times every day, for 14 days in a row. Write an equation the students could use to find the total number of jumps Fred took. Discuss how you know this equation will solve the problem, and then solve it.
The required equation is y = 23x - 9 which represents the total number of jumps.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Mrs. Croaker’s class calculated that their class frog, named Fred, jumped 23 times every day, for 14 days in a row.
the total number of jumps = total days × number of jumps per day
the total number of jumps = 14 × 23
the total number of jumps = 322
We can see that two points are (1, 23) and (14, 322)
y - 14 = (322-23/14-1)(x - 1)
y - 14 = 23(x - 1)
y = 23x - 23 + 14
y = 23x - 9
Therefore, the required equation is y = 23x - 9 which represents the total number of jumps.
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Sam was injured in an accident, and the insurance company has offered him the choice of $45,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?
Answer:
Step-by-step explanation:
$427,011.92
Distribute 28(x + 0.7)
28x + 19.6
28x + 28.07
28x + 0.7
(x+0.7)/28
Answer:
just multiply 28 and (28x), then 28 and 0.7 (19.6) and then put them into the correct answer (28x+19.6)
Employees wage please help me!
You are a new loan officer with Alpha Mortgage, and the manager of the loan department has just presented a problem to you. He is unable to complete the APR calculation on an adjustable rate mortgage that a borrower applied for yesterday. The loan features initial payments based on a 5 percent rate of interest at loan closing. The current composite rate on the loan is 7 percent. Two discount points have been paid by the borrower. Any difference between borrower payments and the interest payment required at the composite rate will be accrued in the mortgage balance in the form of negative amortization. The mortgage amount desired by the borrower is $74,500 for a 30-year term.
Required:
Determine the APR, assuming that the ARM is made with a 2 percent annual and 5 percent over-the-life interest rate cap. (Do not round intermediate calculations.)
Answer:
Step-by-step explanation:
Apr is 248 the customer has to pay 248 dollars every month for 30 years he has to pay 7,440 dollars to the bank or he will lose the house.
Find the equation of a line that passes through the point (2,-4) and has a gradient of -5. Leave your answer in the form y = m x + c
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 5}(x-\stackrel{x_1}{2}) \implies y +4= -5 (x -2) \\\\\\ y+4=-5x+10\implies {\Large \begin{array}{llll} y=-5x+6 \end{array}}[/tex]
If cos 0 = 4/√27 and angle is in Quadrant I, what is the exact value of tan 20
in simplest radical form?
Answer:
See below
Step-by-step explanation:
In Q I cos sin and thus tan are all positive
tan = sin / cos so you need to find sin
TRIG identity:
cos^2 + sin^2 =1
16/27 + sin^2 =1
sin^2 = 1 - 16/27 = 11/27
sin = sqrt (11/27)
tan = sqrt (11/27) / ( 4/sqrt27) =+ sqrt (11) /4
What is a graph theory in math?
Answer:
Graph theory is used in dealing with problems that have a reasonably natural graph/network structure.
Explanation:
For example,
road networks - nodes = towns
road junctions, arcs = roads
Communication networks - telephone systems
'Computer systems'
Foreign exchange/multinational tax planning (network of fiscal flows).
Hope it helped! :)
Graph theory is applied to problems that have a fairly natural graph/network structure.
What is graph theory?Graph theory is the study of graphs in mathematics, which are mathematical structures used to model pairwise relationships between objects. In this context, a graph is made up of vertices (also known as nodes or points) connected by edges (also called links or lines).
Graph Theory is the study of relationships. Graph theory, given a set of nodes and connections that can abstract anything from city layouts to computer data, provides a useful tool for quantifying and simplifying the many moving parts of dynamic systems.
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At the Fidelity Credit Union, a mean of 7.3 customers arrives hourly at the drive-through window. What is the probability that, in any hour, less than 1 customer will arrive? Round your answer to four decimal places.
The probability that the customer would come in that time is 0.0007
How to solve for the probabilityThe question puts the mean u = 7.3
We are required to get the probability of less than 1 customer in one hour. The poisson probability formula is what would be used to solve this problem
the formula is given as
[tex]P(X=x) = e^-^u*^u^x[/tex]/X!
where x = 1
p(X=x) = P(X = 0)
P(X < 1) = P(X = 0)
e⁻⁷.³ x 7.30 / 0!
= 0.0007
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can you help me with this question
The graph that represents the solution of the inequality is
What is a system of inequality?
An inequality is known as an expression in which two value do not have an equal sign. they have either >, <,≥,≤. And to compute the solution
We plot the inequality and find the common region between them.
We are given a system of inequalities
Which are
y > x-1 and y< -x-2
We plot the graphs of the inequalities
Now we have plotted the graph the red one represents inequality y> x-1
and blue one represents inequality y< -x-2
And the intersection of the two is known as the solution of the system of inequality
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Bilquis has x dimes and y nickels. She has at least 15 coins worth no more than $1 combined. Solve this system of inequalities graphically and determine one possible solution.
One of the possible solutions to this system of linear inequation is
(10, 5).
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Bilquis has x dimes and y nickels.
We know a nickel is 5 cents and a dime is 10 cents.
She has at least 15 coins,
∴ x + y ≥ 15...(i)
She has no more than $1 combined.
0.05x + 0.1y ≤ 1...(ii)
The possible solution of these two inequalities by the graphing method we get (10, 5)
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1. If the ice skates are on sale for 30% off, how much money
would you save?
Answer:
14.40 rounded, 14.3999 whole number
Step-by-step explanation:
hope this helps :)
16 miles = how much kilometers?
Answer:
25.749504 kilometers
Step-by-step explanation:
16miles x 1.609(constant) = 25.749504
riangle ABCis transformed with the center of dilation at the origin.
Pre-image: △ABC with vertices A(−5, −4), B(−7, 3), C(3, −2)
Image: △A′B′C′with vertices A′(−3.75, −3), B′(−5.25, 2.25), C′(2.25, −1.5)
What is the scale factor of the dilation that maps the pre-image to the image?
Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 3x²
Also, we have
Vertex = (5, 9)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (5, 9)
Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 5)² + 9
This also means that
f(x) = -3(x - 5)² + 9
The -3 is gotten from f(x) = -3x²
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
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