Which ratio is equivalent to 4/7 with greater terms?
Let g(x) = 2x and h(x) = x2 + 4. Evaluate (g ∘ h)(3).
A. 16
B. 40
C. 26
D. 36
The value of (goh)(3) is 26.
What is composition of function?The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).
given:
g(x) = 2x , h(x) = x²+4
Now,
(goh)(3)
=g(h(3))
=g(9+4)
=g(13)
=2*13
=26
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Each pair of points lies on a line with the given slope. Find y. (2,2), (5,y); slope: 2
What is the transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the center of dilation?
The transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the center of dilation is:
C'(27,9)
Step-by-step explanation:Dilation transformation--
A dilation transformation is a transformation which changes the size of the original figure but the shape remain unchanged.
i.e. if any figure is dilated by a scale factor k with the center of dilation as origin.
Then the change pr transformation in each of the vertices of the figure is given by:
(x,y) → (kx,ky)
We are given a point C which is located at C(9,3)
Hence, here k=3
Hence, we get:
C(9,3) → C'(9×3,3×3)
i.e. C(9,3) → C'(27,9)
HELP PLEASE SOMEONE ASAP
Some steps to construct an angle MNT congruent to angle PQR are listed below. Step 3 is not listed: Step 1: Use a compass to draw an arc from point Q which intersects the side PQ at point A and the side QR at point B. Step 2: Draw a segment NT and use the same width of the compass to draw an arc from point N which intersects the segment NT at a point X. Step 3: Step 4: Join points N and Y using a straightedge. Which statement describes step 3 correctly?
A.  Maintaining the same width of the compass as BQ, draw an arc from point X such that it intersects the arc drawn from N in a point Y. 
B. Use the same width of the compass as the width of NX, and draw an arc from point X such that it intersects the arc drawn from N in a point Y.
C.  Use the same width of the compass as AQ, and draw an arc from point X which intersects the arc drawn from N in a point Y. 
D. Maintaining the same width of the compass as AB, draw an arc from point X such that it
The total amount of money in a savings account after t years is given by the function A=1000(1.023)^t .
How could this function be rewritten to identify the monthly interest rate?
What is the approximate monthly interest rate?
Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table.
Function Monthly interest rate
A = 1000(1 + 0.023)^12t
A = 1000(1.023^12)^t/12
A = 1000(1.023^t/12)^12t
0.23%
0.19%
0.31%
Answer:
[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]
Rate of interest (r) = 0.19% monthly
Step-by-step explanation:
Given: The total amount of money in a saving account after t years.
[tex]A=1000(1.023)^t[/tex]
Formula:
[tex]A=P(1+r)^t[/tex]
Now we compare this formula with with given model.
P=1000
Rate of interest annually (r) = 0.023
Time = t
We need to change into monthly interest
New rate will divide by 12
New time will multiply by 12
[tex]r=\frac{0.023}{12}=0.0019[/tex]
[tex]t=12\times t =12t[/tex]
Function for monthly rate
[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]
Rate of interest (r) = 0.19% monthly
[tex]\text{Thus, Function Monthly interest rate: }A=1000(1+\frac{0.023}{12})^{12t}\text{ and Monthly Interest rate }= 0.19\%[/tex]
Find the greatest possible enclosed area of a rectangular corral given 400 feet of fencing
Answer:
Maximum area = 10000 square units.
Step-by-step explanation:
We are given the following information:
Rectangular perimeter of coral = 400 units.
Let length of the coral be x. Then,
Perimeter = 400 = 2(Length +Breadth)
[tex]400 = 2(x + Breadth)\\Breadth = 200 - x[/tex]
Thus, the area of rectangle is given by,
[tex]Area = Length\times Breadth = x\times (200-x) = 200x - x^2[/tex]
Thus, we have to maximize the function:
[tex]f(x) = 200x - x^2[/tex]
We will use double derivative test.
First we differentiate with respect to x.
[tex]\displaystyle\frac{d(f(x))}{dx} = \displaystyle\frac{d(200x - x^2)}{dx} = 200 - 2x[/tex]
Equating this to zero to obtain critical points,
[tex]200 - 2x = 0\\200 = 2x\\x = 100[/tex]
Now, again differentiating with respect to x.
[tex]\displaystyle\frac{d^2(f(x))}{dx^2} = -2 < 0[/tex]
Thus, by double derivative test, local maxima occurs for this function at x = 100
So, Length = x = 100 units
Breadth = 200 - x = 100 units
Maximum area = 10000 square units.
Can somebody tell me if this is factorable? I've been trying this with a friend and we can't come up with any numbers. x^2 + 9x - 4
A bell tolls every 10 minutes. Another bell tolls every 15 minutes. Both bells toll at 6:00 PM. They will toll together again at??
A cylindrical chemical storage tank mush have a height 4 meters greater than the radius of the top of the tank. determine the radius of the top and the height of the tank if the tank must have a volume of 15.71 cubic meters
Final answer:
To determine the radius and height of the cylindrical tank with a given volume of 15.71 cubic meters, where height is 4 meters greater than the radius, we use the volume formula for a cylinder, resulting in a cubic equation that must be solved.
Explanation:
The question asks for the radius of the top and the height of a cylindrical tank with a volume of 15.71 cubic meters, where the height is 4 meters greater than the radius. The formula for the volume of a cylinder is V = πr²h, where V is volume, r is radius, and h is height. Since h = r + 4, we can write the equation in terms of r as V = πr²(r + 4).
To find the radius, we substitute the given volume, 15.71 m³, into the equation:
15.71 = πr²(r + 4)
This results in a cubic equation which we need to solve to find the value of r. After solving (which may require numerical methods or approximations due to the complexity of cubic equations), we find the value of the radius and can then determine the height by adding 4 meters to the radius.
F 100 tires are randomly selected for shipment to an outlet what is the probability that they are all good?
Four hundred people were asked whether gun laws should be more stringent. three hundred said "yes," and 100 said "no." the point estimate of the proportion in the population who will respond "no" is
a. 75
b. 0.75
c. 0.5
d. 0.25
The proportion in the population who will respond "no" is 0.25
what is probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Given:
Total people surveyed= 400
people say 'yes'= 300
people say 'no' = 100
Now, proportion in the population who will respond "no" is
= 100/400
=1/40
= 0.25
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The price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $5.00
In 1994, it will the price reach $5.00.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We are given with the equation as,
⇒ [tex]p(t) = 1.1 e^{0.047t}[/tex]
where p represents the price, t represents the time in years. price varies exponentially with time.
Now, If p is 5 dollars in the future,
Then, We can formulate;
5 = [tex]1.1 e^{0.047t}[/tex]
ln 4.54 = 0.047 t
0.657 = 0.047 t
t = 13.97
t = 14 years
t = 14 years or year 1994.
Thus, In 1994, it will the price reach $5.00.
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A 6foot tree casts a 3.25 ft shadow. How tall is a tree that casts a 10 ft shadow?
The height of the tree is 18.46 feet.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A 6 foot tree casts a 3.25 ft shadow.
let the height of the tree who cast shadow 10 ft.
So, Using Proportion
6 / 3.25 = x / 10
60 = 3.25 x
x= 60/ 3.25
x= 18.46 feet
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Final answer:
To determine the height of a tree that casts a 10 ft shadow, using the ratio from a 6 ft tree that casts a 3.25 ft shadow, we find the tree is approximately 18.46 feet tall through the concept of similar triangles.
Explanation:
The question asks how tall a tree is that casts a 10 ft shadow, given that a 6 ft tree casts a 3.25 ft shadow. This problem can be solved using the concept of similar triangles, where the ratio of the heights of the trees is equal to the ratio of the lengths of their shadows.
To find the height of the tree that casts a 10 ft shadow, we set up the proportion as follows:
Height of first tree / Shadow of first tree = Height of unknown tree / Shadow of unknown tree
Substituting the given values:
6 ft / 3.25 ft = Height of unknown tree / 10 ft
By cross-multiplying and solving for the height of the unknown tree, we get:
(6 ft × 10 ft) / 3.25 ft = 18.46 ft
Therefore, a tree that casts a 10 ft shadow is approximately 18.46 feet tall.
Jessica is filling glasses with water. Each glass holds 3/5 cup of water. She pours 4 1/5 cups of water into the glasses. How many glasses does she fill with water? Enter your answer in the box.
Answer:
7 glasses
Step-by-step explanation:
Given: Jessica is filling glasses with water. Each glass holds [tex]\frac{3}{5}[/tex] cup of water. She pours [tex]4\frac{1}{5}[/tex] cups of water into the glasses.
To find: The number of glasses she fill with water.
Solution:
Each glass holds [tex]\frac{3}{5}[/tex] cup of water.
She pours [tex]4\frac{1}{5}[/tex] cups of water into the glasses.
To find the number of glasses she fill with water, we need to divide the total volume of water with the volume in each glass.
So, the number of glasses she fill with water can be calculated as
[tex]=\frac{4\frac{1}{5}}{\frac{3}{5}}[/tex]
[tex]= \frac{\frac{21}{5}}{\frac{3}{5} }[/tex]
[tex]=\frac{21}{5}\times\frac{5}{3}[/tex]
[tex]=\frac{21}{3}[/tex]
[tex]=7[/tex]
So, she can fill 7 such glasses with water.
Expand
2y (2y + 8 )
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\boxed{\mathsf{2y(2y + 8)}}\\\\\large\text{DISTRIBUTE \boxed{\text{2y}} WITHIN the PARENTHESES}\\\\\large\boxed{\mathsf{= 2y(2y) + 2y(8)}}\\\\\large\boxed{\mathsf{= 4y^2+ 16y}}\\\\\large\text{You DON'T have any like terms so we cannot do anything to this}\\\large\text{equation.}\\\\\\\huge\boxed{\rm{Therefore, your\ answer \ is: \mathsf{4y^2 +16y}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
which of the following is a solution of x^2+6x=-22
What is the value of x?
A. 56
B. 78
C. 12
D. 24
If the balance is $1020, the payment is $100, and the interest is 1.5% per month, how much is the unpaid balance?
A) $920.00
B) $933.80
C) $13.80
D) $1,020.00
Use this graph of g to find g(7)
Simplify sec(arcsec 1/2).
A. undefined
B. -1/2
C. 1/2
D. 2
The population for a city is 39194 and grows continuously at the rate of 6.9% each year. What is the approximate population in 17 years?
Answer:
121,854
Step-by-step explanation:
Initial population of the town A= 39194
rate growth of population R= 6.9%= 0.069
we need to find the population after n = 17 years
we can find that easily using growth rate formula
A= P(1+R/100)^n
A= 39194(1+0.069)^17
= 121,854
therefore population at the end of 17 years= 121,854
Factor the expression completely over the complex numbers.
y4−16
Which table represents a linear function?
Answer:
C: 1 -2
2 -10
3 -18
4 -26
Step-by-step explanation:
how because its me i'm always right
Determine the correct equation for the following verbal sentence: The total distance traveled, d, at a constant speed of 45 miles per hour is the product of the speed and the number of hours traveled, h. a. d = h + 45 c. 4072-01-01-03-00_files/i0210000.jpg b. d = 45h d. d = 45 - h Please select the best answer from the choices provided A B C D
Your answer is B..........
PLEASE HELP ASAP WILL GIVE 30 POINT FOR WHOEVER ANSWER IT AND WILL MARK BRAINIEST
Look at the cups shown below (images are not drawn to scale):
A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
Write 247.903 in expanded form
Answer:
The answer is
247.903=200.000+47.000+7.000+0.900+0.003
Step-by-step explanation:
In order to determine the expanded form, we have to know about the rule. The expanded form is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression.
For example:
6.432 in expanded notation form is 6.000 + 0.400 + 0.030 + 0.002
In this case:
247.903=200.000+47.000+7.000+0.900+0.003
How do I write and graph an inequality in two variables and use them to solve a real-world problem?
Jill Hartman earns $750 per week plus 3% of sales in excess of $6,500. If Jill sells $25,000 in the first week, her earnings are:
The earnings of Jill Hartman for the week is A = $1,305
Given data ,
To calculate Jill's earnings for the first week, we need to determine the amount of sales in excess of $6,500 and then calculate her additional earnings based on that amount.
Sales in excess of $6,500 = Total sales - $6,500 = $25,000 - $6,500 = $18,500
Now we can calculate Jill's additional earnings based on the sales in excess of $6,500:
Additional earnings = 3% of sales in excess of $6,500 = 0.03 * $18,500
Additional earnings = $555
Finally, we can calculate Jill's total earnings for the first week by adding her base salary to her additional earnings:
Total earnings = Base salary + Additional earnings = $750 + $555
Total earnings = $1,305
Hence , Jill's earnings for the first week, with sales of $25,000, are $1,305
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Solve for n: 21k − 3n + 9p > 3p + 12
Answer: n<7k+2p-4
Step-by-step explanation: