To solve the formula F=J+Jrt for 't', first, subtract 'J' from both sides to get F-J=Jrt. Then, divide both sides by 'Jr', for the final equation for 't' = (F-J)/Jr.
Explanation:This physics-related mathematics question is asking you to solve the given formula F=J+Jrt for 't'. To isolate 't', we first want to eliminate 'J' from the right side. We do this by subtracting 'J' from both sides of the equation. This gives us F-J=Jrt.
Then, we divide both sides by 'Jr'. When we do this, we are left with t=(F-J)/Jr as the rearranged formula with 't' as the subject. This results in 't' being isolated in the equation, which answers the student's question.
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a law firm charges $100 per hour plus a $300 origination fee for its services find a function notation
The required function notations for the total law firm charges is expressed as f(t) = 100t + 300
Given the following
Law firm charges = $100 per hour
The amount of charge for "t" hours will be 100t hours
Also, the original fee = $300
In other to get the total charge using function notation;
f(t) = Law firm charges for "t" hours + Original fee
f(t) = 100t + 300
The required function notations for the total law firm charges is expressed as f(t) = 100t + 300
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For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≥ −1.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≥ −1.
Answer:
C. The vertex is [tex](-3,-1)[/tex], the domain is all real numbers, and the range is [tex]y\leq -1[/tex].
Step-by-step explanation:
We have been given a function [tex]f(x)=-2(x+3)^2-1[/tex]. We are asked to identify the vertex, domain and range of the given function.
We can see that our given parabola is in vertex form [tex]y=a(x-h)^2+k[/tex], where [tex](h,k)[/tex] represents vertex of parabola.
We can rewrite our given equation as:
[tex]f(x)=-2(x-(-3))^2-1[/tex]
Therefore, the vertex of our given parabola would be [tex](-3,-1)[/tex].
We know that parabola is a quadratic function and the domain of a quadratic function is all real numbers.
We know that range of a quadratic function in form [tex]f(x)=a(x-h)^2+k[/tex] is:
[tex]f(x)\leq k[/tex], when [tex]a<0[/tex] and,
[tex]f(x)\geq k[/tex], when [tex]a>0[/tex]
Upon looking at our given function, we can see that [tex]a=-2[/tex], which is less than 0, therefore, the range of our given function would be [tex]y\leq -1[/tex].
The degree of the Boolean function given by f(x,y,z,w) = xy + yz + zw is........
Read the following statement: Line segment CD is congruent to line segment XY.
Which of the following is an equivalent statement?
-CD overbar is similar to XY overbar
- CD overbar is congruent to XY overbar
-CD overbar equals XY overbar
-CD overbar is an element of XY overbar
SOMEONE PLEASE HELP I HAVE A TEST IN 5 MIN!!
The statement which is equivalent to line segment CD is congruent to line segment XY is CD overbar is congruent to XY overbar.
What is a line?A line is made up of an infinite no. of points it can extend in both directions indefinitely.
We know a line has two subsets they are a ray and a line segment.
A ray is a type of line that has one initial point and the other end can extend indefinitely and a line segment is a type of line which has two endpoints.
Given a line, segment CD is congruent to line segment XY.
∴ [tex]\overline{CD}[/tex] ≅ [tex]\overline{XY}[/tex].
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Which of the following terms, when added to the given polynomial, will change the end behavior?
y = –2x7 + 5x6 – 24
a)–x8
b)–3x5
c)5x7
d)1,000
e)–300
Answer:
1.A
2.C
Step-by-step explanation:
The end behaviour of the polynomial function y = -2x⁷ + 56x⁶ - 24 will change for a) - x⁸ and c) 5x⁷.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
Given, a polynomial function y = -2x⁷ + 56x⁶ - 24.
So, the given polynomial function has a degree of 7 and its end behavior will be changed by adding or subtracting terms that are of degree 7 and higher.
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A store sells toaster ovenstoaster ovens for $4646 each, retail price. The wholesale cost to stock the ovensovens is $ 28$28 each. The fixed cost associated with acquiring the ovensovens, storing them in inventory, using shelf space, and advertising the ovensovens for sale is $25002500. a. Write a function for the total cost of stocking the ovensovens for sale. b. Write a function for the total revenue received from selling the ovensovens. c. Write a system of equations and determine the number of ovensovens that must be sold to break even.
Solve the Pythagorean Theorem for the variable a.
c²=a²+b²
The school cafeteria is baking cookies for lunch. each student gets 3 cookies with their lunch. if there are 231 children buying lunch, how many cookies do they have to make?
tina wants to save money for school. tina invests 1100 in an account that pays an interest of 7.25%. how many years will it take the account to reach 6600?
It would take approximately 19 years for Tina's investment to grow from $1100 to $6600 with an annual interest rate of 7.25% if the interest is compounded annually.
Explanation:This problem deals with the concept of compound interest. To find out how many years it will take for Tina's investment to grow from $1100 to $6600 with an interest rate of 7.25%, we would use the formula for compound interest: A = P(1 + r/n)_(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per time unit (year), t is the time the money is invested for in years.
In Tina's case, she does not make additional contributions, so we assume the interest is compounded once per year (n=1). Our formula becomes A = P*(1 + r)_t. Arranging for t, we get t = log(A/P) / log(1+r).
Using these values: A=$6600, P=$1100, r=7.25/100=0.0725, we can find t = log(6600/1100) / log(1+0.0725). Calculating this, you would get around 19 years.
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Solve for x.
x−1/4=38
Enter your simplified answer in the box.
what is the approximate value of the square root of 8
Answer:
2.828427
Step-by-step explanation:
I looked it up
Mr. Small, the store manager for Jay's Appliance, is having a difficult time placing a selling price on a refrigerator that cost $410. Mr. Small knows his boss would like to have a 45% markup based on cost. The selling price should be
Answer:
$594.50
Step-by-step explanation:
1. Divide markup into decimal form
45/100 = .45
2. multiply by cost of Refrigerator
.45 x 410 = $184.50
3. Add markup cost to original Refrigerator cost.
184.50 + 410 = $594.50
The student body of a large university consists of 60% female students. a random sample of 8 students is selected. what is the probability that among the students in the sample at least 7 are female?
The probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
To solve this problem, we'll use the binomial probability formula, which calculates the probability of a certain number of successes (in this case, selecting female students) in a fixed number of trials (the sample size).
Given:
Probability of selecting a female student (success), ( p = 0.60 )
Probability of selecting a male student (failure), ( q = 1 - p = 0.40 )
Sample size, ( n = 8 )
We need to calculate the probability of selecting at least 7 female students from the sample.
Calculate the probability of selecting exactly 7 female students:
[tex]\[ P(X = 7) = \binom{8}{7} \times (0.60)^7 \times (0.40)^{8-7} \][/tex]
[tex]\[ = \frac{8!}{7!(8-7)!} \times (0.60)^7 \times (0.40)^{1} \][/tex]
[tex]\[ = 8 \times 0.60^7 \times 0.40 \][/tex]
[tex]\[ = 8 \times 0.0279936 \times 0.40 \][/tex]
[tex]\[ = 0.1119744 \][/tex]
Calculate the probability of selecting exactly 8 female students:
[tex]\[ P(X = 8) = \binom{8}{8} \times (0.60)^8 \times (0.40)^{8-8} \][/tex]
[tex]\[ = (0.60)^8 \][/tex]
[tex]\[ = 0.60^8 \][/tex]
[tex]\[ = 0.16777216 \][/tex]
Add the probabilities from Step 1 and Step 2 to get the final probability:
[tex]\[ P(X \geq 7) = P(X = 7) + P(X = 8) \][/tex]
[tex]\[ = 0.1119744 + 0.16777216 \][/tex]
[tex]\[ = 0.27974656 \][/tex]
So, the probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
Find the point in the first octant where the tangent plane to x2+116y2+14z2=1 is parallel to the plane x+y+z=10
Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. assume boys and girls are equally likely. is the result the same as the probability of getting sall boys among four children
The probability of having a baby boy on the fourth child, given that the first three children were all boys, is 0.5. This result is not the same as the probability of getting all boys among four children, which is 0.0625. The conditional probability accounts for the information about the first three births.
To solve this probability problem, let's break it down step by step.
Probability of Having a Boy on the Fourth Child:
Assuming boys and girls are equally likely, the probability of having a boy or a girl is 1/2 or 0.5. When considering each child's gender independently, the probability of having a boy on the fourth child is 0.5, regardless of the genders of the previous children.
However, the question specifies that the first three children were all boys. This information is crucial for the conditional probability calculation.
Conditional Probability:
The probability of having a boy on the fourth child given that the first three children were all boys is denoted as [tex]\( P(B_4 | B_1, B_2, B_3) \)[/tex].
Since the events are assumed to be independent (the gender of one child does not affect the gender of another), the conditional probability is the same as the probability of having a boy on any single birth: 0.5.
Comparison with Getting All Boys:
The probability of getting all boys among four children [tex](\( P(B_1 \cap B_2 \cap B_3 \cap B_4) \))[/tex] is the product of the probabilities of having a boy for each birth.
[tex]\[ P(B_1 \cap B_2 \cap B_3 \cap B_4) = P(B_1) \times P(B_2) \times P(B_3) \times P(B_4) \][/tex]
Given that [tex]\( P(B_4) = 0.5 \)[/tex] and the previous births are all boys, [tex]\( P(B_1 \cap B_2 \cap B_3 \cap B_4) = (0.5)^4 = 0.0625 \)[/tex].
The question probable may be:
Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. Assume boys and girls are equally likely. Is the result the same as the probability of getting all boys among four children?
Complete the square
The formula for any arithmetic sequence is a n = a 1 + d(n - 1), where a n represents the value of the nth term, a 1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the arithmetic sequence -7, -3, 1, 5, ...?
Plz help
Find the slope of a line that passes through the points (-3,-1) and (0,-5)
a jar of jelly beans that weigh 4.25 ounces costs 2.89. what is the cost of one ounce of jelly
A sample of 12 measurements has a mean of 8.5 and a sample of 20 measurements has a mean of 7.5. Find the mean of all 32 measurements.
A girl is now one-third as old as her mother. In three years, she will be two-fifths as old as her mother will be. What are their present ages?
A girl is 9; mom is 27
B girl is 18; mom is 54
C girl is 25; mom is 75
Option: A is the correct answer.
A girl is 9; mom is 27
Step-by-step explanation:A girl is now one-third as old as her mother.
i.e. if x is the present age of girl.
and y is the present age of her mother.
Then,
[tex]x=\dfrac{1}{3}y[/tex]
i.e.
[tex]y=3x-----------(1)[/tex]
In three years, she will be two-fifths as old as her mother will be.
This means after three years.
The age of girl will be: x+3
and the age of her mother will be: y+3
This means that:
[tex](x+3)=\dfrac{2}{5}\times (y+3)[/tex]
[tex]5(x+3)=2(y+3)\\\\i.e.\\\\5x+15=2y+6[/tex]
i.e.
[tex]5x+15=2\times 3x+6[/tex]
( since on using equation (1) )
i.e.
[tex]5x+15=6x+6\\\\i.e.\\\\6x-5x=15-6\\\\i.e.\\\\x=9[/tex]
and the value of y from equation (1) is:
[tex]y=27[/tex]
Three consecutive integers have a sum of 297 . Find the integers.
297 /3 = 99
99-1 = 98
99 +1 = 100
98 + 99 + 100 = 297
the numbers are 98, 99 , 100
A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?
Choose all the doubles facts that can help you solve 8+7
Answer: 7 + 7 = 14
8 + 8 = 16
Step-by-step explanation: doubles facts are simply additions where a number is added to it self. The strategy sums up two consecutive numbers when they are next to each other to give their result as given by the question above (8 + 7). We simply add the smaller number together then add one (double-plus-one) OR add the larger number together then subtract one (double-minus-one)
All doubles that can be used in solving 8 + 7 are:
A) 8 + 7 = 7 + (7 + 1) = (7 + 7) + 1 = 14 + 1 = 15 [double-plus-one]
B) 8 + 7 = (8 + 8) - 1 = 16 - 1 = 15 [double-minus-one]
The doubles fact makes use of the associative property of addition —changing the grouping of addends does not change the sum.
What is the justification for each step in solving the inequality?
−2(x+1)≥3x+8−2(x+1)≥3x+8
Select from the drop-down menus to correctly justify each step.
2nd picture is the dropdown box answers
Look at the triangle what is the value of sin X ?
Find the saving plan balance after 4 years with an apr of 7% and monthly payments of 100
The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 107 kilometers, and the distance of planet Venus from the Sun is 1.1 ⋅ 108 kilometers. About how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun? (1 point)
Select one:
a. 5.2 ⋅ 107 kilometers
b. 4.7 ⋅ 108 kilometers
c. 5.2 ⋅ 108 kilometers
d. 5.7 ⋅ 109 kilometers
Answer:
a) 5.2 *10^7 km
Step-by-step explanation:
If we could describe our Solar System, in order of appearance nearer the Sun, it would be like this:
Sun --- Mercury --- Venus --- Earth
Sun --------------------- Venus
1.1 * 10^8 km
Sun -------Mercury
5.8 * 10^7 Km
To find out how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun, all we have to do is simply subtract the distance Sun ---Venus minus Sun ---Mercury
So,
1.1 * 10^8 - 5.8 * 10^7 =
Adjusting the first distance to the same power
110*10^7- 5.8*10^7 =
Subtracting the factors
5.2 * 10^7
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3427 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 65.75 feet per second and Plane B is gaining altitude at 35.5 feet per second.
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude.
Determine the inverse of f(x) = x^3 - x^2 - 2x show steps
Switch the x and y values to find the inverse.
y=x−3x+2
The inverse is given by
x=y−3y+2
Solve for y now:
x(y+2)=y−3
xy+2x=y−3
2x+3=y−xy
2x+3=y(1−x)
2x+31−x=y
The inverse, f−1(x), is given by f−1(x)=2x+31−x.
The function can be graphed using knowledge of asymptotes, invariant points, and intercepts. Prepare a table of values for f(x). Recall that f−1(x) is simply a transformation of(x) over the line y=x, so f−1(x) has a table of values where X and y are inverted relative to f(x).
For example, if the point (2,3) belongs on the graph of f(x), the point (3,2) belongs on f−1(x).