The equation shown is used to find the force of gravity, F = G(m₁m₂)/R², between two objects.
What is gravitational force?All physical things with mass are drawn to the gravitational force, which can be thought of as an attractive force. The strongest known natural force is actually this one.
The attracting force F has a magnitude equal to G. (the gravitational constant, a number the size of which depends on the system of units used and which is a universal constant) multiplied by the product of the masses (m₁ and m₂) and divided by the square of the distance R:
F = G(m₁m₂)/R².
Newton’s Law would imply an infinite gravitational force when two very small objects touch, that is, when their centers of mass are so close that "r" is effectively zero.
In reality, this would only take place at the subatomic scale, but at the time of Newton, they were unaware of subatomic particles, the Quantum Theory, or Einstein's reinterpretation of gravity, which would have allowed them to rule out infinite or extremely strong gravitational forces. The least powerful force is gravity.
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Outliers are points that
Answer:
Outliers are points that are on the very edge of a scatter plot, separated from the other points.
Step-by-step explanation:
find the conditional expectation of alpha x poisson and gamma distribution law of iterated expectation
The conditional expectation of αX given Y=y is (αλy / β + αλ)^α * e^(-(β+αλ)/βy) and the Law of Iterated Expectation gives E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β).
Let X be a Poisson random variable with parameter λ and Y be a Gamma random variable with parameters α and β. We want to find the conditional expectation of αX given Y=y and then apply the Law of Iterated Expectation to find E[αX].
The conditional probability density function of αX given Y=y is:
fX|Y(x|y) = P(X=x|Y=y) = P(X=x,Y=y) / P(Y=y)
Since X and Y are independent, we have:
P(X=x,Y=y) = P(X=x)P(Y=y)
Therefore, the conditional probability density function of αX given Y=y is:
fX|Y(x|y) = (λ^x/x!) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) / (λ^y * e^(-λ) * β^α / Γ(α))
fX|Y(x|y) = (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)
Now we can calculate the conditional expectation of αX given Y=y:
E[αX|Y=y] = ∑ x=0^∞ αx * fX|Y(x|y)
E[αX|Y=y] = ∑ x=0^∞ αx * (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)
E[αX|Y=y] = (αλy / β + αλ)^α * e^(-(β+αλ)/βy)
Now we can apply the Law of Iterated Expectation to find E[αX]:
E[αX] = E[E[αX|Y]]
E[αX] = E[(αλY / β + αλ)^α * e^(-(β+αλ)/βY)]
Since Y is a continuous random variable, we need to integrate over all possible values of Y:
E[αX] = ∫ 0^∞ (αλy / β + αλ)^α * e^(-(β+αλ)/βy) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) dy
E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β)
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The set of whole numbers is equal to the set of natural numbers.
• A. True
B. False
Answer:
False
Step-by-step explanation:
This statement is false.
The set of whole numbers include the set of Natural numbers "N" = {1, 2, 3, 4, 5, 6, ...}, the set of the negatives of the natural numbers: {-1, -2, -3, -4,...}, and the zero: {0}
We see then that the set of Natural numbers is a subset of the set of whole numbers Z = {... -4,-3,-2,-1, 0,1, 2, 3, 4, 5, ...}
Answer: i think False
Step-by-step explanation: why not pick false…..
Hope this helps^^
What’s the answer for these questions
The difference in the production levels will be 3x + 8.
The amount that Jackson spent more will be 5.20 - p.
How to calculate the valueAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Based on the information, a company has two manufacturing plants that had levels of 5x + 11 and 2x - 4.
The difference in the production levels will be:
= 5x + 11 - 2x - 3
= 3x + 8
The amount that Jackson spent more will be:
= 7.65 + 5p - 2.45 - 4p
= 5.20 - p.
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a distribution table for the scores on an exam is shown below. the second row says that 10% of the students scored between 60 and 70. fill in the blanks in the height column. do not include units.
The median for the distribution table is falls within the range of 60-70 points.
Understanding the concept of median is crucial in analyzing data and making statistical inferences.
From the given distribution table, we can see that the percentage of students scoring between 0-60 points is 15%, between 60-70 points is 10%, between 70-80 points is 25%, between 80-90 points is 30%, and between 90-100 points is 20%. To calculate the cumulative percentage, we can add up the percentages from left to right.
For instance, the cumulative percentage of students scoring between 0-70 points is
=> 15% + 10% = 25%.
Similarly, the cumulative percentage of students scoring between 0-80 points is
=> 15% + 10% + 25% = 50%.
We can repeat this process to find the cumulative percentage for each score range.
Once we have the cumulative percentages, we can find the median score. In this case, since the total percentage is 100%, the median score would be the point at which the cumulative percentage reaches 50%. We can use the height column to calculate this value.
Starting from the lowest score range, we can add the heights until the cumulative percentage exceeds 50%. The point where this happens is the median score.
Moving on to the next score range, the cumulative percentage for scores between 0-70 points is 25%, which is greater than 50%. Therefore, the median score falls within the range of 60-70 points.
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Complete Question:
A distribution table for the scores on an exam is shown below. The second row says that 10% of the students scored between 60 and 70. Fill in the blanks in the height column. Do not include units.
Points (Width) % 0-60 60-70 70-80 80-90 90-100
(Area) Height=Area/Width (% per point) 15 10 25 30 20
What is the median score?
You have $4,500 to invest. Which plan would generate the most interest after three years?
A. 5.0% compounded semi-annually
B. 4.9% compounded quarterly
C. 4.8% compounded monthly
D. 5.1% compounded yearly
The plan which generate the most interest after three years is 5.0% compounded semi-annually, the correct option is A
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]
Given that;
The amount of investment= $4,500
Now,
The amount with rate of 5.0% compounded semi-annually;
The final balance is ₹5,218.62.
The total compound interest is ₹718.62.
The amount with rate of 4.9% compounded quarterly;
The final balance is ₹5,207.94.
The total compound interest is ₹707.94.
The amount with rate of 4.8% compounded monthly;
The final balance is ₹5,195.49.
The total compound interest is ₹695.49.
The amount with rate of 5.1% compounded yearly;
The final balance is ₹5,209.31.
The total compound interest is ₹709.31.
Therefore, maximum compound interest will be of 5% semi annually.
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what’s the volume of each rectangular prism
1. 4 yd 7 yd 2 yd
Answer: volume would be 56
Step-by-step explanation:
Volume = length X width X height
Determine whether the scenario involves independent or dependent events. Then find the probability.
Your sock drawer has two white socks, six brown socks, and four black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right. P (white, brown WITHOUT replacing)
-Independent; 1/11
-Dependent; 1/12
-Dependent; 1/11
-Independent; 1/12
The second sock picked is dependent on the first. The probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock is 1/12.
To calculate the probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock, we first need to count the total number of possible outcomes. There are 8 socks in the drawer: 2 white, 6 brown, and 4 black. Since we are picking two socks without replacing the first, the total number of possible outcomes is 8C2 = 28.
Next, we need to count the number of favourable outcomes. In this case, there is only one favourable outcome: picking a white sock for the left foot and a brown sock for the right foot.
Therefore, the probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock is 1/28.
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in your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. there are 100 points available for each score. however, the lab score is worth 17% of your total grade, each major test is worth 25%, and the final exam is worth 33%. compute the weighted average for the following scores: 95 on the lab, 68 on the first major test, 95 on the second major test, and 81 on the final exam. enter your answer as a whole number.
The weighted average is 86. To calculate the weighted average, we first need to find the contribution of each score to the total grade based on their weightage.
Lab score contribution = 0.17 x 95 = 16.15
First major test contribution = 0.25 x 68 = 17
Second major test contribution = 0.25 x 95 = 23.75
Final exam contribution = 0.33 x 81 = 26.73
Total contribution = 16.15 + 17 + 23.75 + 26.73 = 83.63
Therefore, the weighted average is 83.63/0.8 = 86.
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Ravi collected 3 parcels, A, B and C. Parcel A is the heaviest and Parcel B is the lightest. The mass of Parcel B is 3/8kg. The difference in the mass between Parcel A and Parcel C is 1/5kg. Find the total mass of the 3 parcels.
Answer:
2 5/8 kg
Step-by-step explanation:
To find the total mass of the 3 parcels, we need to determine the mass of Parcel A and Parcel C.Since Parcel B is the lightest, with a mass of 3/8 kg, and the difference in mass between Parcel A and Parcel C is 1/5 kg, we can say that Parcel A weighs 3/8 + 1/5 = 4/8 = 1/2 kg more than Parcel C.Let's call the mass of Parcel C "x". Then, Parcel A weighs x + 1/2 kg.The total mass of the 3 parcels can be found by adding the masses of all 3 parcels:x + x + 1/2 + 3/8 = 3x + 9/83x = 3 - 9/83x = 27/8 - 9/83x = 18/8x = 6/8 = 3/4 kgSo, the mass of Parcel C is 3/4 kg, the mass of Parcel A is 3/4 + 1/2 = 1 1/4 kg, and the total mass of the 3 parcels is 3/4 + 1 1/4 + 3/8 = 2 5/8 kg.In conclusion, the total mass of the 3 parcels is 2 5/8 kg.
Here's a box plot that summarizes the number of history questions on Ms. Jones's homework
assignments.
–
|||||||||
+H
024 6 8 10 12 14 16 18 20
Number of questions
Find the median of the data.
questions
Answer:
I will tell you the answer
Step-by-step explanation:
Answer:
the median is 11 questions.
Step-by-step explanation:
khan academy :)
square root of 12 simplifying radicals
What are the Variable, coefficients, and constant terms for 4x+15x, 6n+25+7n+4, 3a+4a+17+a+1 ?
In the expression, 4x+15x, variable: x; coeficient: 4, 15; constant: 0
In the expression 6n+25+7n+4, variable: n, coeficient: 6, 7; constant: 25, 4
In the expression 3a+4a+17+a+1, variable: a, coeficient: 3, 4, 1; constant: 17, 1
What are the parts of an algebraic expression?Generally, in an algebraic expression terms, variables, coefficients, and constants are seen. The parts of an expression that are added by either an addition or a subtraction notation are called the terms. The letter of a term is called a variable, the numerical value written along the variable of a term is called a coefficient, and the term contains only the numerical value called a constant.
Take the expression 4x+15x. The terms are 4x and 15x.
Clearly, the variables of the terms are x, the coefficients of the terms are 4 and 15, and the constant is 0. So, the required answers are obtained.
Take the expression 6n+25+7n+4. The terms are 6n, 25, 7n, and 4.
Clearly, the variables of the terms are n, the coefficients of the terms are 6 and 7, and the constants are 25 and 4. So, the required answers are obtained.
Take the expression 3a+4a+17+a+1. The terms are 3a, 4a, 17, a, and 1.
Clearly, the variables of the terms are a, the coefficients of the terms are 3, 4, and 1, and the constants are 17 and 1. So, the required answers are obtained.
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A bag contains 6 black marbles, 14 white marbles, and 5 grey marbles.
You pick one without looking. What is the probability that the marble will be
either white OR black? Answer as a fraction or whole number in lowest
form.
Frank currently rents an apartment for $ 700 per month. He is considering purchasing a $125,000 condominium. He has been approved for a 30-year term mortgage with a 5.25% interest rate. Use technology to create a loan amortization model.
What is Frank's monthly mortgage payment? What is the total interest he will pay on the loan? What is the total of all loan payments he will make? What is the difference between Frank's monthly loan payment and his monthly rent? Match the amount to the statement.
- $ 690.25
- $ 123,492
- $ 700
- $ 205,125
- $ 9.75
- $ 248,492
- $ 275,684
- $ 12.75
- $ 165,875
- $ 725,75
A. His monthly mortgage payment is $690.25.
B. He will pay a total of $123,492 in interest over the life of the loan
C. He will make a total of $248,490 in loan payments over the life of the loan.
D. The difference between his monthly loan payment and his monthly rent is $9.75.
How did we get these values?Here are the calculations based on the given information:
Loan amount = $125,000
Interest rate = 5.25%
Loan term = 30 years (360 months)
Monthly mortgage payment = $690.25
To calculate the monthly mortgage payment, we can use the following formula:
P = L[c(1 + c)^n]/[(1 + c)^n - 1]
Where:
P = monthly mortgage payment
L = loan amount
c = monthly interest rate (5.25% / 12)
n = loan term in months (30 years x 12 months)
Plugging in the numbers, we get:
P = 125000[(0.0525/12)(1 + 0.0525/12)^360]/[(1 + 0.0525/12)^360 - 1]
P = $690.25
Therefore, Frank's monthly mortgage payment is $690.25.
B. To calculate the total interest he will pay on the loan, we can multiply the monthly mortgage payment by the total number of payments (360) and subtract the loan amount:
Total interest = Pn - L
Total interest = $690.25 x 360 - $125,000
Total interest = $123,492
Therefore, Frank will pay a total of $123,492 in interest over the life of the loan.
C. To calculate the total of all loan payments he will make, we can multiply the monthly mortgage payment by the total number of payments:
Total loan payments = P n
Total loan payments = $690.25 x 360
Total loan payments = $248,490
Therefore, Frank will make a total of $248,490 in loan payments over the life of the loan.
D. To calculate the difference between Frank's monthly loan payment and his monthly rent, we can subtract his monthly rent ($700) from his monthly mortgage payment ($690.25):
Monthly difference = $700 - $690.25
Monthly difference = $9.75
Therefore, the difference between Frank's monthly loan payment and his monthly rent is $9.75.
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a chef used 1/4 cup of milk for one recipe. Then she used 2 cups of milk for 5 recipes. The total number of cups of milk the chef used can be found by expression.
1/4+(2x5)
Answer:
Step-by-step explanation:
Answer:
The chef used a total of 10.25 cups of milk.Step-by-step explanation:
By adding together the specific amounts the chef used in each recipe, one can determine the total number of cups of milk she consumed. In order to achieve this, we can condense the phrase:
1/4 + (2 x 5) = 1/4 + 10
The two amounts on the right side of the equation can then be added:
1/4 + 10 = 10.25
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find the missing length, round to the nearest tenth if necessary
It is less than 21 so it has to be 19.4.
6. The velocity of a cruise ship is equal to
the square root of the rate of fuel
consumption minus 3 units.
Write the velocity function of a cruise ship
as a function of the fuel consumption and
graph the function.
The velocity function is written as v(x) = sqrt(x - 3)
The graph is attached
How to write the function of the fuel consumptionIf the velocity of a cruise ship is equal to the square root of the rate of fuel consumption minus 3 units,
Then we can write the velocity function as:
v(x) = sqrt(x - 3),
where
x represents the rate of fuel consumption.
The graph is plotted and attached
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The image of triangle ABC after a 180° rotation around
the origin is:
A'(-1, 2)
B'(-4, 2)
C'
Answer:If A is at point (x,y), then A' would be at point (-x,-y). Same goes for points B and C.
Step-by-step explanation:
(Order statistics and independence) Let X be the minimum and Y the maximum of two independent, nonnegative random variables S and T with common continuous density f. Let Z denote the indicator function of the event (S > 2T). Vhat is the distribution of Z? b) Are X and Z independent? Are Y and Z independent? Are (X, Y) and Z independent? c) Is X independent of Y?
a. P(Z = 1) = ∫G(s)f(s)ds is the distribution of Z.
b. X and Z are independent.
c. X and Y are not independent.
a) We have Z = I(S > 2T), where I is the indicator function. Then,
P(Z = 1) = P(S > 2T) = ∫∫(s > 2t) f(s) f(t) ds dt
Using the fact that S and T are independent, we get
∫∫(s > 2t) f(s) f(t) ds dt = ∫∫f(s)ds ∫∫f(t)I(s > 2t)dt ds
Letting G(s) = ∫f(t)I(s > 2t)dt, we get
P(Z = 1) = ∫G(s)f(s)ds
b) We have X = min(S,T) and Z = I(S > 2T). To check whether X and Z are independent, we compute their joint distribution:
P(X > x, Z = 1) = P(S > 2T, S > x, T > x) = ∫∫(s > 2t) f(s) f(t) ds dt ∫[tex]x^\infty[/tex]f(u)du
= ∫[tex]x^\infty[/tex]f(u)du ∫[tex](u/2)^x[/tex] f(t) dt ∫[tex]t^\infty[/tex] f(s) ds
= 1/2 ∫[tex]x^\infty[/tex]f(u) ∫[tex]t^\infty[/tex] f(s) ds dt
= 1/2 ∫[tex]x^\infty[/tex]f(u) G(t) dt
= 1/2 ∫[tex]x^\infty[/tex]f(u) ∫f(t)I(u > 2t)dt du
= ∫[tex]x/2^\infty[/tex] f(u) ∫f(t)I(u > 2t)dt du
= P(X > x)P(Z = 1), using the fact that S and T are independent.
Therefore, X and Z are independent. Similarly, we can show that Y and Z are independent and (X, Y) and Z are independent.
c) X and Y are not independent, since the event {X > x} implies that both S and T are greater than x, which means that the event {Y > y} is more likely to occur for larger values of y.
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How do we prove by contrapositive that if n is an integer and n^3+5 is odd, then n is even?
To prove by contrapositive, we need to show that if n is odd, then n^3+5 is even.
The contrapositive of the original statement is logically equivalent to the original statement. if we can prove the contrapositive, then we have also proven the original statement.
Proof by contrapositive:
Assume that n is an odd integer, which means that n can be written in the form n = 2k + 1, where k is an integer.
Then, n^3+5 = (2k+1)^3 + 5
= 8k^3 + 12k^2 + 6k + 1 + 5
= 8k^3 + 12k^2 + 6k + 6
We can factor out a 2 from the last two terms of this expression:
n³ + 5 = 2(4k³ + 6k²)
Since 4k³ + 6k² + 3k + 3 is an integer, we can see that n³ + 5 is an even integer, which means that n is even by definition.
we have proven that if n is an integer and n³ + 5 is odd, then n is even by contrapositive.
n^3+5 = 2(4k^3 + 6k^2 + 3k + 3)
Since 4k^3 + 6k^2 + 3k + 3 is an integer, n^3+5 is even.
we have shown that if n is odd, then n^3+5 is even, which is the contrapositive of the statement we were asked to prove.
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calculate the herfindahl-hirschman index for two scenarios. initially, there are four teams, and they compete for 10 years. team a wins 8 championships and team b wins 2. the other teams win none. now suppose there are eight teams. two teams win 4 championships, two win one each, and the others all win zero
The HHI is less than 1,800, which is considered a low level of market concentration. Therefore, we can conclude that both scenarios represent relatively competitive markets.
The Herfindahl-Hirschman Index (HHI) is a measure of market concentration that is commonly used to assess the degree of competition in a market. The index is calculated as the sum of the squared market shares of all the firms in the market. The HHI can range from 0 to 10,000, with higher values indicating greater market concentration.
To calculate the HHI for the two scenarios given, we need to first calculate the market shares of the teams in each scenario. In the first scenario, there are four teams with the following market shares:
Team A: 8/10 = 0.8
Team B: 2/10 = 0.2
Teams C and D: 0/10 = 0
The HHI for this scenario is calculated as:
HHI = [tex](0.8^2 + 0.2^2 + 0^2 + 0^2) \times10,000[/tex]
= 68,000
In the second scenario, there are eight teams with the following market shares:
Teams A and B: 4/10 = 0.4 each
Teams C and D: 1/10 = 0.1 each
Teams E, F, G, and H: 0/10 = 0 each
The HHI for this scenario is calculated as:
HHI = [tex](0.4^2 + 0.4^2 + 0.1^2 + 0.1^2 + 0^2 + 0^2 + 0^2 + 0^2) \times 10,000[/tex]
= 16,000
In both scenarios, the HHI is less than 1,800, which is considered a low level of market concentration. Therefore, we can conclude that both scenarios represent relatively competitive markets.
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Suppose you have a bag with 10 black and 10 red balls, with the balls of each color numbered 1 to 10 . Suppose you pick two balls (without replacement) uniformly at random from the bag. (i) Show that the probability that you pick a ball of each color is 10/19. (ii) Show that the probability that you pick a ball of each color, with the number on the red ball being one less than the number on the black ball, is 9/190.
The probability of picking one ball of each color is 10/19. The probability of picking a red ball with a number one less than the number on the black ball is 9/190.
(I) To figure the probability of picking one repudiate and one red ball, we can separate it into two cases: first, picking a debase and afterward a red ball, and second, picking a red ball and afterward a renounce.
The probability of picking a torpedo on the principal draw is 10/20 (since there are 10 renounces and 20 all out balls), and the probability of then picking a red ball on the subsequent draw is 10/19 (since there are currently 9 red balls avoided with regards to a sum of 19 balls). So the probability of picking a repudiate first and afterward a red ball is (10/20) * (10/19) = 1/19.
Essentially, the probability of picking a red ball first and afterward a torpedo is (10/20) * (10/19) = 1/19.
Hence, the probability of picking one chunk of each tone is the amount of these two probabilities: 1/19 + 1/19 = 2/19.
Notwithstanding, we want to isolate by 2 to represent the way that we might have picked the balls in the contrary request nevertheless have one chunk of each tone. So the last probability is (2/19)/2 = 10/19.
Consequently, the probability of picking one wad of each tone is 10/19.
(ii) To figure the probability of picking a red ball with a main not exactly the number on the debase, we can initially fix the renounce that we pick. There are 10 decisions for the renounce. The main red ball with a main not exactly the torpedo is the red ball with the following most minimal number, so there is just a single decision for the red ball.
In this manner, the probability of picking a debase and afterward a red ball with the number on the red ball one not exactly the number on the repudiate is (10/20) * (1/19) = 1/190.
We really want to duplicate this by 9, since there are 9 sets of contiguous numbers (1 and 2, 2 and 3, ..., 9 and 10) for which the condition is fulfilled. So the last likelihood is 9/190.
Thusly, the probability of picking one chunk of each tone, with the number on the red ball being one not exactly the number on the debase, is 9/190.
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In the following system, what is the x-value of the solution?
y = 4
y = 2x - 5
Answer:
x = 9/2
Step-by-step explanation:
As both equations are set equal to "y", we can set the equations equal to each other and solve for the x-value:
[tex]4=2x-5\\9=2x\\x=\frac{9}{2}[/tex]
jina wants to pour 81.76 grams if salt into a container. So far, she poured 15.2 grams. How much more salt should jina pour?
37. The profit P of a small business (in thousands
of dollars) since it was founded can be
by the function below, where tis
the years since 1990. Use the Remainder
Theorem to find the company's profit in 2017.
modeled
P(t) = 0.5tª − 3t³ +t² +25
The company's profit in 2017, modeled by the given function, was $193651949.5
How to find the company's profit in 2017The equation of the function is given as
P(t) = 0.5t^6 − 3t³ +t² +25
First, we calculate the value of t in 2017
t = 2017 - 1990
t = 27
Using the Remainder theorem
To find the company's profit in 2017, we need to substitute t = 27 in the given function P(t):
P(27) = 0.5(27)^6 - 3(27)^3 + (27)^2 + 25
Evaluate
P(27) = 193651949.5
Therefore, the company's profit is $193651949.5
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Determine whether the lines intersect, and if so, find the point of intersection and the cosine of the angle of intersection. (If an answer does not exist, enter DNE.)
x = 6t + 2, y = 3, z = −t + 1
x = 2s + 2, y = 2s + 3, z = s + 1
P(x, y, z) =
cos(θ) =
The lines intersect, and the point of intersection and the cosine of the angle of intersection cosθ is 52.9°.
6t + 2 = 2s + 2; 7 = 2s + 7;
- t + 1 = s + 1
6t = 2s; 2s = 0 - t = s;
s = 0, t = 0.
So, (x, y, z) = (2, 7, 1) is intersection point
Direction vector of 1st line u = <6, 0, -1>; direction vector of 2nd line: v = <2, 2, 1>
cosθ = (6·2 + 0·2 - 1·1>/(√37·√9)
= 11/(3√37); θ
= cos-1(11/(3√37)
= 52.9°
Therefore, the value of cosθ is 52.9°
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the environment of a right triangle for the specified angle, its sine is the rate of the length of the side that's contrary that angle to the length of the longest side of the triangle( the hypotenuse), and the cosine is the rate of the length of the conterminous length to that of the hypotenuse.
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You are going to use an incline plane to lift a heavy object to the top of a shelving unit with a height of 7 ft. The base of the incline plane is 12 ft from the shelving unit. What is the length of the incline plane?
The length of the incline plane is equivalent to 13.9ft
Application of Pythagoras theorem
According to the theorem, the square of the hypotenuse is equal to the sum of the square of the adjacent and opposite
c^2 = a^2 + b^2
From the given question, the length of the incline is the hypotenuse 'c' where:
a = 7ft
b = 12ft
Substitute
c^2 = 7^2 + 12^2
c^2 = 49 + 144
c^2 = 193
x = 13.9ft
Therefore the length of the inclined plane is 13.9ft
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4 A shop sells large and small bags of rice. On Monday 57 large bags and 132 small bags were sold. a What percentage of the bags sold were large? b What percentage of the bags sold were small? On Tuesday 73 large bags and 81 small bags were sold. c What percentage of the bags sold on the two days combined was large?
Step-by-step explanation:
a. On Monday, the percentage of large bags sold was 57/(57 + 132) x 100 = 30.22%.
b. On Monday, the percentage of small bags sold was 132/(57 + 132) x 100 = 69.78%.
c. The total number of large and small bags sold on the two days combined was 130/(130 + 154) x 100 = 45.45%.
Listed below are the balances and annual percentage rates for Jimmy's credit cards. If Jimmy makes the same payment each month to pay off his entire credit card debt in the next 12 months, how much will he have paid in interest in the 12 month period?(Hint, find out how much interest Jimmy pays to each card over the 12 months seperately, and then add them together.)
A, B, and C's interest rates are 49.96, 296.32 and 102.96, respectively. Since the total interest is $449.24.
What is meant by APR?The annual percentage rate (APR) on a credit card indicates that the interest you pay over a year is generally equivalent to your balance.
The balances and annual percentage rates for Jimmy's credit cards are shown below.
If Jimmy pays the same amount each month, he will be free of his credit card debt in a year.
We know that the formula
[tex]$P V=\frac{P M T\left[1-\left(1+\frac{r}{12}\right)^{12 n}\right]}{\frac{r}{12}}$[/tex]
Where, PV be present value
PMT be monthly payment
r be interest rate
n be time
For credit card A, we have
[tex]$\begin{aligned} 563 & =\frac{{PMT}\left[1-\left(1+\frac{0.16}{12}\right)^{12}\right]}{\frac{0.16}{12}} \\ \text { PMT } & =51.08\end{aligned}$[/tex]
Total payment will be, 51.08 × 12 = 612.96
The interest charge will be, 612.96 − 563 = 49.96
For credit card B, we have
[tex]$\begin{aligned} & 2525=\frac{{PMT}\left[1-\left(1+\frac{0.21}{12}\right)^{12}\right]}{\frac{0.21}{12}} \\ & \mathrm{PMT}=235.11\end{aligned}$[/tex]
Total payment will be, 235.11 × 12 = 2821.32
The interest charge will be, 2821.32 − 2525 = 296.32
For credit card C, we have
[tex]$\begin{aligned} 972 & =\frac{\text { PMT }\left[1-\left(1+\frac{0.19}{12}\right)^{12}\right]}{\frac{0.19}{12}} \\ \text { PMT } & =89.58\end{aligned}$[/tex]
Total payment will be, 89.58 × 12 = 1074.96
The interest charge will be, 1075.96 − 972 = 102.96
Total interest = 102.96 + 296.32 + 49.96
Total interest = 449.24
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