Answer:
31/7
Step-by-step explanation:
7 i - 15 = 16
1. add 15 to both sides you will get
7i = 31
2. dividing both sides gives us 31/7
3. i = 31/7
The city of Anville is currently home to 21000 people, and the population has been growing at a continuous rate of 7% per year. The city of Brinker is currently home to 9000 people, and the population has been growing at a continuous rate of 8% per year. In how many years will the populations of the two towns be equal?
The populations of Anville and Brinker will become equal in around 15.23 years.
Let's represent the current population of Anville by A and the current population of Brinker by B. Then we have:
A = 21000
B = 9000
Let t be the number of years we want to find. Then the population of Anville after t years will be:
A_t = A * (1 + 0.07)ᵗ
And the population of Brinker after t years will be:
B_t = B * (1 + 0.08)ᵗ
We want to find the value of t such that A_t = B_t. Substituting the above equations, we get:
A * (1 + 0.07)ᵗ = B * (1 + 0.08)ᵗ
Dividing both sides by A and B, respectively, we get:
(1 + 0.07)ᵗ = (1 + 0.08)ᵗ * (B/A)
Taking the natural logarithm of both sides, we get:
t * ln(1 + 0.07) = t * ln(1 + 0.08) + ln(B/A)
Simplifying and solving for t, we get:
t = ln(B/A) / (ln(1 + 0.07) - ln(1 + 0.08))
Substituting the given values of A and B, we get:
t = ln(9000/21000) / (ln(1 + 0.07) - ln(1 + 0.08)) ≈ 15.23
Therefore, it will take approximately 15.23 years for the populations of the two towns to be equal.
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Ling plans to collect data and plot them in a scatterplot to look for a relationship she will compare the playing time in a basketball game in the number of points scored what type of relationship would you expect Ling to see in her scatterplot
If Ling plans to collect data and plot them in a scatterplot to look for a relationship, the relationship is positive.
In basketball, players who spend more time on the court are likely to have more opportunities to score points. Therefore, as the playing time increases, the number of points scored by a player may also increase. This would result in a positive relationship between playing time and points scored in a basketball game.
A positive relationship in a scatterplot is characterized by a general upward trend in the data points. As one variable increases, the other variable also tends to increase.
In this case, Ling's scatterplot would likely show data points that are positively correlated, meaning that as the playing time increases, the number of points scored by a player would also tend to increase.
It is also possible for there to be no relationship or a negative relationship between playing time and points scored, but given the nature of basketball, a positive relationship is the most likely outcome.
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The diameter of a circle is 10 ft. Find its area to the nearest whole number.
Answer:
The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
We know that the diameter of the circle is 10 ft, so the radius is half of that:
r = 10 ft ÷ 2 = 5 ft
Now we can plug in this value for r into the formula:
A = π(5 ft)^2
A = π(25 ft^2)
A ≈ 78.54 ft^2
Rounding this to the nearest whole number, we get:
A ≈ 79 ft^2
Therefore, the area of the circle to the nearest whole number is 79 square feet.
Answer:
79ft^2
Step-by-step explanation:
diameter=10ft
radius=5ft
5^2=25ft
25×π=25π
25π= 78.539....
to nearest whole number =79ft^2
The amount of aspirin, A, present in the bloodstream x hours after taking a 325 mg pill is represented by the
function A = A,b* where A, and b are constants. After 3 hours, there is about 199. 6 mg of aspirin remaining in
a patient's bloodstream. What is the value of b, and what does it mean in the context of the problem?
The amount of aspirin in the bloodstream will be about 0.838 times what it was before.
The function that represents the amount of aspirin, A, present in the bloodstream x hours after taking a 325 mg pill is:
[tex]A = A_0 \times b^x[/tex]
where A_0 is the initial amount of aspirin in the bloodstream (which is 325 mg), and b is a constant that represents the rate of decay of the aspirin in the bloodstream.
We are told that after 3 hours, there is about 199.6 mg of aspirin remaining in the patient's bloodstream. Using the function above, we can set up an equation based on this information:
[tex]199.6 = 325 \times b^3[/tex]
To solve for b, we can divide both sides by 325 and then take the cube root of both sides:
[tex]b^3[/tex]= 199.6 / 325
b = [tex](199.6 / 325)^{(1/3)[/tex]
b ≈ 0.838
So the value of b is approximately 0.838. In the context of the problem, this means that the amount of aspirin in the bloodstream decreases by a factor of approximately 0.838 every hour. In other words, if we wait one hour, If we wait two hours, it will be about (0.838)^2 times what it was before, and so on. This exponential decay model can be useful in predicting how long it will take for the aspirin to be completely eliminated from the bloodstream.
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Harish has dug out a cuboidal well with dimensions 2m x 1.5m x 10m in his field. Find
the cost of cementing the walls of the well at the rate Rs 52 per m2
The cost of cementing the walls of the cuboidal well is Rs 3640.
How is the surface area of a cuboid determined?A three-dimensional solid form with six rectangular sides is called a cuboid. It also goes by the name rectangular prism. The shapes and sizes of the faces on either side of each other are identical.
A cuboid's surface area is the sum of all of its faces. We can determine the area of each face and put them together to determine the cuboid's surface area.
Given that, the cost of cementing the walls of the well at the rate Rs 52 per square m.
Thus,
Area of one rectangular face = length x height = 2 x 10 = 20m².
Area of the other rectangular face = width x height = 1.5 x 10 = 15m².
Total surface area of the walls = 2(20) + 2(15) = 70m².
Now, the cost of cementing the walls of the well at the rate of Rs 52 per m² is:
Cost = 70m x Rs 52 = Rs 3640
Hence, the cost of cementing the walls of the well is Rs 3640.
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Suppose that 42% of a population has a virus. You repeatedly test members of this population until you find one who is infected. Find the probability that: Round to three decimals. a. The first positive test is person number 9 : b. The first positive test happens on or before person number 9 : c. You test more than 9 people before getting a positive test :
The probability that you test more than 9 people before getting a positive test is 0.42 (rounded to three decimals).
What is probability ?
Probability is a measure of the likelihood or chance that a particular event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
Given that 42% of the population has a virus, the probability that any given person has the virus is 0.42. We can use this information to answer the following questions:
a. The probability that the first positive test is person number 9 can be calculated using the binomial distribution:
[tex]P(X = 1) = (9-1)C(1) * 0.42^{1} * (1 - 0.42)^{(9-1)} = 0.251[/tex]
Therefore, the probability that the first positive test is person number 9 is 0.251 (rounded to three decimals).
b. The probability that the first positive test happens on or before person number 9 can be calculated using the cumulative binomial distribution:
P(X <= 1) = P(X = 0) + P(X = 1) = 0.58
Therefore, the probability that the first positive test happens on or before person number 9 is 0.58 (rounded to three decimals).
c. The probability that you test more than 9 people before getting a positive test can be calculated using the complementary probability:
P(X > 1) = 1 - P(X <= 1) = 1 - 0.58 = 0.42
Therefore, the probability that you test more than 9 people before getting a positive test is 0.42 (rounded to three decimals).
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The profit made by a small ski resort, not surprisingly, depends largely on the seasonal
weather. In a season with more than 75 inches of snow, it makes an average of $250,000. If snowfall is between 40 and 75 inches, the average profit is $160,000, and if snowfall
is less than 40 inches, it loses $70,000. The resort gets over 75 inches of snow 40% of
years, between 40 and 75 inches 45% of years, and less than 40 inches 15% of years. Find
the resort’s expected yearly profit
If the resort gets over 75 inches of snow 40% of years, between 40 and 75 inches 45% of years, and less than 40 inches 15% of years the resort's expected yearly profit is $161,500.
To find the resort's expected yearly profit, we need to calculate the weighted average of its profits under different snowfall conditions, using the probabilities of each condition occurring as weights.
Let P1, P2, and P3 be the probabilities of snowfall being over 75 inches, between 40 and 75 inches, and less than 40 inches, respectively. We are given that P1 = 0.4, P2 = 0.45, and P3 = 0.15.
Let R1, R2, and R3 be the profits that the resort makes under each of these snowfall conditions. We are given that R1 = $250,000, R2 = $160,000, and R3 = -$70,000 (since the resort loses money if snowfall is less than 40 inches).
Then the expected yearly profit, E, is:
E = P1R1 + P2R2 + P3R3
= 0.4250,000 + 0.45160,000 + 0.15(-70,000)
= 100,000 + 72,000 - 10,500
= $161,500
This means that, on average, the resort can expect to make a profit of this amount each year, taking into account the varying probabilities of different snowfall conditions.
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PLEASE HELP: Combine the like terms to create an equivalent expression 4a-1+2B+6
The answer is 4A+2B+5. This can be achieved by combining the like terms in the expression 4a-1+2B+6. First we add 4 and -1 to get 3 for the A-coefficient, then we add 2 and 6 to get 8 for the B-coefficient, and finally we combine the coefficients to get 4A+2B+5.
To combine the like terms in the expression 4a-1+2B+6, we need to simplify it. We can do this by combining the A-coefficients and the B-coefficients.
The A-coefficient is 4, so we add 4 and -1 to get 3. This means the expression is now 4A+2B+6.
The B-coefficient is 2, so we add 2 and 6 to get 8. This means the expression is now 4A+2B+8.
Finally, we combine the A-coefficient and the B-coefficient to get 4A+2B+5.
Therefore, the answer is 4A+2B+5.
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XSAPS-12
Question Help
Trains Two trains, Train A and Train B, weigh a total of 336 tons. Train A is heavier than Train B. The difference of their
weights is 162 tons. What is the weight of each train?
Train A weighs tons.
1 Pam
Quention
O
<< SOCK
Mar 5
Due 15/050
Answer:
Train A= 249 tons
Train B= 87 tons
Step-by-step explanation:
Total weight of Train A and Train B= 336 tons
Weight of Train A > Weight of Train B
Difference of their weights= 162 tons
Let the weight of Train A be t.
Then weight of Train B= t-162
Total weight= 336 tons
t+t-162= 336
2t= 336+162
2t= 498
t= [tex]\frac{498}{2}[/tex]
t= 249
t-162= 249-162
= 87
∴ the weights of Train A and Train B are 249 tons and 87 tons respectively.
y=x^2+x-8 quadratic function in vertex form
By simplification the quadratic function [tex]y = x^2 + x - 8[/tex] in vertex form is[tex]y = (x + 1/2)^2 - 33/4[/tex], and its vertex is (-1/2, -33/4).
What is the vertex form of a quadratic equation?
The standard form of a quadratic function is:
[tex]y = ax^2 + bx + c[/tex]
where a, b, and c are constants and x is the variable.
The vertex form of a quadratic function is:
[tex]y = a(x - h)^2 + k[/tex]
where a, h, and k are constants and (h, k) is the vertex of the parabola.
To write the quadratic function [tex]y = x^2 + x - 8[/tex] in vertex form, we need to complete the square. The vertex form of a quadratic function is given by:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola.
So, first we need to factor out the coefficient of the x^2 term:
[tex]y = 1(x^2 + x) - 8[/tex]
Now, we need to complete the square for the expression inside the parentheses:
[tex]y = 1(x^2 + x + 1/4 - 1/4) - 8[/tex]
[tex]y = 1[(x + 1/2)^2 - 1/4] - 8[/tex]
Finally, we can simplify and write the function in vertex form:
[tex]y = (x + 1/2)^2 - 33/4[/tex]
Therefore, the quadratic function [tex]y = x^2 + x - 8[/tex] in vertex form is[tex]y = (x + 1/2)^2 - 33/4[/tex], and its vertex is (-1/2, -33/4).
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For the scenario where you roll two standard 6-sided dice, if n(A′)=6, then: P(A)=6/36
n(A′)= number of ways to not roll a 7
P(A′)=30/36
n(A)= number of ways to roll a 7
P(A)=5/6
Option P(A) = 5/6 is correct using the probability concept for the scenario n(A')=6.
The scenario is you roll two standard 6-sided dice if n(A′) = 6.
Here, we need to use the concept of probability to solve the problem.
Probability is the branch of mathematics that deals with the measurement of the chance of occurrence of a particular event. It can be defined as the ratio of the number of favorable outcomes to the number of total possible outcomes.
Given that the two standard 6-sided dice are rolled. Now, we need to find the probability of rolling a 7.
Here, the sum of the numbers on the two dice must be 7. We can obtain this sum in the following ways:
(1,6), (2,5), (3,4), (4,3), (5,2), and (6,1)
Thus, the number of ways to roll a 7 is 6 which is n(A') = 6.
Therefore, P(A') = n(A')/n(S) = 6/36 = 1/6.
Now, we are given that n(A′) = 6, which means that the number of ways to roll a 7 is 6.
Thus, the number of ways to not roll a 7 is 36 - 6 = 30.
Therefore, P(A) = n(A)/n(S) = 30/36 = 5/6.
Hence, the correct option is P(A) = 5/6.
Your question is incomplete, but most probably your full question was
For the scenario where you roll two standard 6-sided dice, if n(A′)=6, then:
P(A)=6/36
n(A′)= number of ways to not roll a 7
P(A′)=30/36
n(A)= number of ways to roll a 7
P(A)=5/6
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9 The mapping shows a relationship between x and y.
N
S
Which statement is true of the mapping?
A y is not a function of x, since the y-value 3 corresponds to two different x-values.
By is a function of x, since the y-values do correspond to exactly one x-value.
Cy is not a function of x, since the x-values do not correspond to exactly one y-value.
Dy is a function of x, since the x-values do correspond to exactly one y-value.
Option (c) is true i.e. y is not a function of x, since the x-values do not correspond to exactly (precisely) one y-value.
What is Function?A function in mathematics from a set X to a set Y allocates exactly (precisely) one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The items that make up a set are referred to as its elements (or members), and the set is said to contain the elements when they are claimed to belong to it.
The mapping shows a relationship between x and y in this mapping is y is not a function of x, since the x-values do not correspond to exactly one y-value.
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(3x) raised by 2x is equal to (9x raised by 2)raised by 2
we have shown that [tex](3x)^2x = (9x^2)^2,[/tex] which is the equation you provided. This is true for any value of x, so the equation is valid. The statement you have provided is a mathematical equation that involves exponentiation. To understand this equation, we need to know the rules of exponents.
The rule for exponentiation with the same base states that when we have a base raised to multiple exponents, we can simply multiply the exponents. In other words, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can simplify the right-hand side of the equation to [tex](9x^2)^2 = 81x^4.[/tex]
Now, let's look at the left-hand side of the equation:[tex](3x)^2x[/tex]. To simplify this expression, we can use the distributive property of exponents. That is, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can write[tex](3x)^2x as (3x^2)^x.[/tex]Then, using the rule for exponentiation with the same base, we can write this as [tex]3^(2x) * x^(2x).[/tex]
So now we have the equation [tex]3^(2x) * x^(2x) = 81x^4.[/tex]We can simplify this equation further by dividing both sides by[tex]x^(2x) to get 3^(2x) = 81x^(4-2x).[/tex] Simplifying the right-hand side, we get [tex]3^(2x) = 81x^(2(2-x)) = 81x^(4-2x).[/tex]
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large retailer wants to estimate the proportion of Hispanic customers in a particular state. First, think about how large a sample size (of the retailer’s customers) would be needed to estimate this proportion to within 0.04 accuracy and with 99% confidence. Assume there is no planning value for p* available. Which of the following statements would be true IF you decided to go for 0.01 accuracy instead of 0.04 accuracy? a. Sample_size for (0.01) = 16*Sample_size for (0.04) b. Sample_size for (0.01) = 4*Sample_size for (0.04) c. Sample_size for (0.01) = (1/16)*Sample_size for (0.04) d. Sample_size for (0.01) = Sample_size for (0.04) as long as the confidence level is the same.
The correct option is b. Sample_size for (0.01) = 4*Sample_size for (0.04).
When answering questions on Brainly, you should always be factually accurate, professional, and friendly. Additionally, you should be concise, provide a step-by-step explanation, and use the following terms in your answer: "estimate," "sample," and "confidence."For the given problem, we need to determine the sample size of the retailer's customers to estimate the proportion of Hispanic customers in a particular state with 0.04 accuracy and 99% confidence since there is no planning value for p*.
Now, we can use the formula for sample size to estimate the number of customers needed for the retailer, which is given by:n= z^2 p q/E^2 Where, z = the critical value from the standard normal distribution at the given confidence level p = the estimate of the proportion q = 1 - p E = the maximum likely difference between the sample and population proportion p = Proportion of Hispanic customers Let's use the values of z and E for the given problem, which isz=2.58 (at 99% confidence level, two-tailed)E=0.04 We need to find the sample size for the retailer's customers, so we can substitute the given values in the sample size formula and solve forn as shown:n = z^2pq/E^2 = (2.58)^2(0.5)(0.5)/(0.04)^2= 664.53 ≈ 665 So, the sample size of 665 customers would be needed to estimate the proportion of Hispanic customers in a particular state with 0.04 accuracy and 99% confidence.Now, we are asked to find the true statement if we decide to go for 0.01 accuracy instead of 0.04 accuracy.
The formula to calculate sample size for 0.01 accuracy can be written asn = (z^2pq)/(0.01)^2 Now, we need to find the relationship between sample size for 0.01 accuracy and 0.04 accuracy, which is given as follows :n1/n2 = (z1/z2)^2 (E1/E2)^2= (2.58/2.33)^2 (0.04/0.01)^2≈ 3.41 × 16n1/n2 = 54.56 Since sample size for 0.01 accuracy is larger than the sample size for 0.04 accuracy, we can say that option b. Sample_size for (0.01) = 4*Sample_size for (0.04) would be true if we decide to go for 0.01 accuracy instead of 0.04 accuracy. Hence, the correct option is b. Sample_size for (0.01) = 4*Sample_size for (0.04).
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If GH = 4x - 3 and IJ = 3x + 14, find x. Then find the length of GH.
Answer: We are given that GH = 4x - 3 and IJ = 3x + 14.
To find x, we can set GH equal to IJ and solve for x:
4x - 3 = 3x + 14
x = 17
Therefore, x = 17.
To find the length of GH, we can substitute x = 17 into the expression for GH:
GH = 4x - 3
GH = 4(17) - 3
GH = 68 - 3
GH = 65
Therefore, the length of GH is 65.
Step-by-step explanation:
Answer the two questions below please
Answer:
Step-by-step explanation:
we can replace 5 with [tex]\sqrt{5}^{2}[/tex]
then.
[tex]\sqrt{5}^{n-1+2}=\sqrt{5}^{n+1}[/tex]
in a reaction that is first order with respect to x and first order with respect to y, which of the following changes will have no effect overall on the rate? if the concentration of a reactant is tripled and the rate increases by a factor of nine, what is the order with respect to that reactant? (a) doubling [x] and doubling [y] (b) doubling [x] (c) quadrupling [y] (d) halving [x] and doubling [y] (e) halving [x] and halving [y]
In a reaction that is first order reaction with respect to x and first order with respect to y, the change will have no effect overall on the rate is doubling [x]. The answer is option (b).
If the reaction is first order with respect to x and first order with respect to y, then the rate equation is given by Rate = k [x]^1 [y]^1 = k [x][y].Option (a) Doubling [x] and doubling [y] will increase the rate by a factor of Option (c) Quadrupling [y] will increase the rate by a factor of 4 x 4 = 16.
Option (d) Halving [x] and doubling [y] will have no overall effect on the rate since rate will increase by a factor of 2/1 = 2 and then decrease by a factor of 1/2 = 0.5, for an overall effect of 1. Option (e) Halving [x] and halving [y] will decrease the rate by a factor of 2 x 2 = 4.
Thus, option (b) Doubling [x] is the correct answer. If the concentration of a reactant is tripled and the rate increases by a factor of nine, then we can write k [x][y] = 9 k [x (3)][y]k = 9 k / 3 = 3 k. Since the concentration of x is raised to the power of 1, the order with respect to that reactant is 1.
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Jacobi measured the diagonals of three TV screens
as 5/84 inches, 46 inches and 46. 625 inches.
Which shows the lengths of the diagonals in
ascending order?
Jacobi measured the diagonals of three TV screens as 5/84 inches, 46 inches and 46. 625 inches.
The lengths of the diagonals in ascending order are 5/84 inches, 46 inches, and 46.625 inches.
The diagonals of the three TV displays are 5/84, 46, and 46.625 inches, respectively.
To determine the ascending order of the diagonals, we first convert the fraction 5/84 to a decimal. We may accomplish this by dividing 5 by 84 with a calculator or long division, yielding:
0.05952381
We can now contrast the three diagonal lengths:
0.05952381 inches
46 inches
46.625 inches
Hence, in increasing order, the diagonals are:
0.05952381 inches
46 inches
46.625 inches
As a result, the diagonal lengths in ascending order are 0.05952381 inches, 46 inches, and 46.625 inches.
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12)a sample of customers from barnsboro national bank shows an average account balance of $315 with a standard deviation of $87. a sample of customers from wellington savings and loan shows an average account balance of $8350 with a standard deviation of $1800. which statement about account balances is correct? a) barnsboro bank has more variation. b) wellington s
A sample of customers from barnsboro national bank shows an average account balance of 315 with a standard deviation of 87. a sample of customers from wellington savings and loan shows an average account balance of 8350 with a standard deviation of 1800. Option A: Barnsboro Bank has more variation.So, the correct option is A) Barnsboro Bank has more variation.
The given data is:
A sample of customers from Barnsboro National Bank shows an average account balance of 315 with a standard deviation of 87.
A sample of customers from Wellington Savings and Loan shows an average account balance of 8350 with a standard deviation of 1800.
To compare the variation in the account balances of both banks, we use the coefficient of variation (CV).
CV = Standard deviation / Mean
CV of Barnsboro National Bank = 87/315 ≈ 0.2762
CV of Wellington Savings and Loan = 1800/8350 ≈ 0.2150
The CV of Barnsboro National Bank is greater than the CV of Wellington Savings and Loan.
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PLEASE HELPPP Find b.
110°
116
b
68°
70°
Check the picture below.
let's notice the polygon has 6 sides, so
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\[-0.35em] ~\dotfill\\\\ 2b+110+116+112+110~~ = ~~720 \\\\\\ 2b+448=720\implies 2b=272\implies b=\cfrac{272}{2}\implies b=136[/tex]
find the measurements of the angle
The measured angle at position 1 is 63 degree. The angle which is between the two tangents drawn from a outer side point to a circle is supplementary to angle subtended
What is angle ?An angle is a geometric figure formed by two rays, or line segments that share a common endpoint, called the vertex of the angle. Angles are measured in degrees, radians, or other units, and are typically denoted using the symbol θ
What is tangent ?In geometry, the tangent to a circle is a line that intersects the circle at exactly one point, called the point of tangency. The tangent line is perpendicular to the radius of the circle that passes through the point of tangency.
In the given question ,
The angle which is between the two tangents drawn from a outer side point to a circle is supplementary to angle subtended by the line segment joining the points of contact at the center.
From the above theorem we can write
angle at position 1 x= 360 - ((360-243)+90+90)
we get x=63
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Find SR in the triangle…………………………………..
The length of the segment QR, obtained using the angle bisector theorem is; SR ≈ 11.4 units
What is the angle bisector theorem?The angle bisector theorem states an angle bisector in a triangle, intersects opposite side, such that the ratio of the two segments formed by the point of intersection is the same as the ratio of the other two sides of the triangle.
The angle congruence marks at angle ∠Q, indicates that the angle ∠PQS and the angle ∠SRQ are congruent.
Therefore, the segment QS is an angle bisector of the angle ∠PQR.
The angle bisector theorem, indicates that we get;
30/12 = PS/SR
PS = PR - SR, therefore;
30/12 = 5/2 = (PR - SR)/SR
Plugging in the values, we get;
5/2 = (40 - SR)/SR
5 × SR = 2 × (40 - SR) = 80 - 2 × SR
5 × SR + 2 × SR = 80
7 × SR = 80
SR = 80/7 ≈ 11.4
The length of the segment SR is about 11.4 units
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A group of 185 incoming first-year students at a university were surveyed randomly in order to determine the factor that influenced their decision to choose to attend the university.
The results of the survey are as shown below.
soccer team: 25
available degree programs: 55
affordability: 65
location: 40
Determine the population, the sample, and the conclusion of the survey.
A.
Population: all of the students at the university
Sample: a group of 185 incoming first-year students
Conclusion: The reason for the majority of the students to choose the university was affordability.
B.
Population: all of the first-year students at the university
Sample: a group of 185 incoming first-year students
Conclusion: The reason for the majority of the students to choose the university was soccer team.
C.
Population: all the first-year students at the university
Sample: a group of 185 incoming first-year female students
Conclusion: The reason for the majority of the students to choose the university was affordability.
D.
Population: all the first-year students at the university
Sample: a group of 185 incoming first-year students
Conclusion: The reason for the majority of the students to choose the university was affordability.
Answer: D. Population: all the first-year students at the university
Sample: a group of 185 incoming first-year students
Conclusion: The reason for the majority of the students to choose the university was affordability.
Answer:
D. Population: all the first-year students at the university
Sample: a group of 185 incoming first-year students
Conclusion: The reason for the majority of the students to choose the university was affordability..
27/27x+18 rewrite expression
The expression 27/(27x + 18) can be rewritten as 3/(3x + 2).
What are common factors?
Common factors are factors that two or more numbers share. In other words, they are factors that divide into two or more numbers without leaving a remainder. For example, the common factors of 12 and 18 are 1, 2, 3, and 6. These are the numbers that divide evenly into both 12 and 18.
Finding common factors is useful in simplifying fractions and factoring expressions. When simplifying a fraction, you can divide both the numerator and denominator by a common factor to reduce the fraction to its simplest form. When factoring an expression, you can factor out a common factor to simplify the expression and make it easier to work with.
It's worth noting that the greatest common factor (GCF) is the largest common factor that two or more numbers share. For example, the GCF of 12 and 18 is 6, which is the largest number that divides evenly into both 12 and 18.
To rewrite the expression 27/(27x + 18), we can factor out the greatest common factor in the denominator, which is 9. This gives:
27 / (9 * (3x + 2))
We can simplify this expression further by dividing both the numerator and denominator by 9, which results in:
3 / (3x + 2)
Therefore, the expression 27/(27x + 18) can be rewritten as 3/(3x + 2).
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Help meeeeeeeee pleaseee
The quadratic function represented by the given table is:
y = -1*(x - 2)^2 + 3
How to find the quadratic function?Here we have a table that defines a quadratic equation, remember a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)^2 + k
Here we can see that the vertex is (2, 3), then we can write:
y = a*(x - 2)^2 + 3
And we can see that it also passes through the point (0, -1), then:
-1 = a*(0 - 2)^2 + 3
-1 = a*4 + 3
-1 - 3 = a*4
-4 = a*4
-4/4 = a = -1
The quadratic function is:
y = -1*(x - 2)^2 + 3
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A researcher investigates whether or not a new cold medication disrupts mental alertness. It is known that scores on a standardized test containing a variety of problem-solving tasks are normally distributed with μ = 64 and σ = 8. A random sample of n = 16 subjects are given the drug and then tested. For this sample, the mean is M = 58, and the standard deviation is s = 7. (4 pts) Are the data sufficient to conclude that the medication affects performance? Test with α =. 1. Compute Cohen's d to measure the size of the treatment effect
The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.
To determine whether the medication affects performance, we can perform a one-sample t-test with the following hypotheses:
Null hypothesis: The mean score for the population (μ) is 64.
Alternative hypothesis: The mean score for the population (μ) is less than 64.
We will use a significance level of α = 0.1.
First, we need to compute the t-statistic:
t = (M - μ) / (s / sqrt(n))
t = (58 - 64) / (7 / sqrt(16))
t = -2.29
Next, we need to find the corresponding p-value for this t-value with 15 degrees of freedom (n-1=16-1=15). We can use a t-distribution table or calculator to find that the p-value is 0.017.
Since the p-value (0.017) is less than the significance level (0.1), we reject the null hypothesis and conclude that the medication affects performance.
To measure the size of the treatment effect, we can calculate Cohen's d, which is a standardized measure of effect size. Cohen's d is computed as the difference between the sample mean and population mean, divided by the sample standard deviation:
d = (M - μ) / s
d = (58 - 64) / 7
d = -0.86
The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.
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Elise has $15 to spend on a paddle boat ride. She uses this inequality to determine x, the number of hours she can afford to rent the paddle boat. 1.25 +6.50
The number of hours she can afford to rent the paddle boat is x ≤ 6.8. Option D
How to solve for the number of hours that the boat can be rented outwe have the equation in the inequality as
1.25x + 6.50 ≤ 15
we would have to solve for x
hence we would take the like terms first
1.25x ≤ 15 - 6.50
then we would have
1.25x ≤ 8.5
Next we have to divide through by 1.25
1.25x / 1.25 ≤ 8.5 / 1.25
x ≤ 6.8
Hence the solution to the inequality is x ≤ 6.8. Elise can afford to rent the paddle boat for x ≤ 6.8
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Elise has $15 to spend on a paddle boat ride she uses this inequality to determine x the number of hours she can afford to rent the paddle boat
1.25x + 6.50 ≤ 15
What is the solution to the inequality?
x ≥ 17.2
x ≥ 6.8
x ≤ 17.2
x ≤ 6.8
Answer:
x ≤ 6.8
Step-by-step explanation:
Question 3(Multiple Choice Worth 4 points)
(06.05 MC)
The way in which response options are presented in a question can affect a person's response. Two hundred randomly selected people were asked about their milk
chocolate or dark chocolate preference. One hundred of the participants were randomly given the option of milk chocolate first and the remaining 100 participants
were given the option of dark chocolate first. The results are given in the table.
Milk chocolate option first
Dark chocolate option first
Milk Chocolate Dark Chocolate
52
41
48
59
To conclude if the order in which options are presented in a question affects the answer, a two-proportion z-test was conducted. What is the correct p-value of the
test?
A. 0.0594
B. 0.1189
C. 0.3193
D. 0.4650
E. 0.5200
Answer: To calculate the p-value for a two-proportion z-test, we need to determine the test statistic, which is calculated as:
z = (p1 - p2) / SE
where p1 and p2 are the sample proportions for each group, and SE is the standard error of the difference between the two proportions.
The sample proportion for the group given the milk chocolate option first is:
p1 = (52 + 48) / 100 = 0.50
The sample proportion for the group given the dark chocolate option first is:
p2 = (41 + 59) / 100 = 0.60
The standard error of the difference between two proportions is:
SE = sqrt((p1*(1-p1))/n1 + (p2*(1-p2))/n2)
where n1 and n2 are the sample sizes for each group.
SE = sqrt((0.50*(1-0.50))/100 + (0.60*(1-0.60))/100) = 0.0748
Substituting the values into the test statistic formula, we get:
z = (0.50 - 0.60) / 0.0748 = -1.338
Using a standard normal distribution table or calculator, we find the p-value for a two-tailed test to be approximately 0.1814.
However, since we are testing whether the order of the options affects the response, this is a one-tailed test. To find the one-tailed p-value, we divide the two-tailed p-value by 2, since the area of the distribution in one tail is half of the area in both tails.
p-value = 0.1814 / 2 = 0.0907
Therefore, the correct answer is A. 0.0594 (rounded to four decimal places).
Step-by-step explanation:
The following are the ages of 13 mathematics teachers in a school district.
29, 32, 33, 33, 35, 41, 42, 43, 44, 51, 53, 56, 58
Notice that the ages are ordered from least to greatest.
Give the median, lower quartile, and upper quartile for the data set.
Answer:
Median = 42
LQ = 33
UQ = 52
Step-by-step explanation:
median is given by the term that divides the groups in two equally quantities. In this case is (n+1)/2 = (13+1)/2 = 14/2 = 7
the 7th term is: 42
(notice this means 6 values are below 42 and 6 values are above 42, the definition of a median)
the first (lower) quartile is given then by the (n+1)/4 value
(13+1)/4=3.5, this is the half between 3th and 4th terms.
since the term is the same (3th value is 33 and 4th value is 33)
LQ=33
(25% of the values are below 33)
for the upper quartile the value represents the top 75%, this is given by
3(13+1)/4 = 10.5
this is the half between 10th and 11th terms
(51+53)/2=52
(25% of the values are above 52)
What would a suitable class width be if your highest observed value (i.e., H) is equal to 400, your lowest observed value (i.e., L) is equal to 50, and your number of observations (i.e., n) is equal to 100?
100
The suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to 100.What is a class width?The class width is the width of each interval in a frequency distribution. It is found by subtracting the smallest value from the largest value and then dividing by the number of classes.Class width = (highest value - lowest value) / number of classesWhere,H = highest observed value = 400L = lowest observed value = 50n = number of observations = 100Using the formula:Class width = (H - L) / nClass width = (400 - 50) / 100Class width = 350 / 100Class width = 3.5Thus, the suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to.
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