the equivalent closed form for the original rate function is
.[tex]S π/t 4tan (t) dt = -4 ln |cos (t)| + C.[/tex]
a. [tex]S π / π /4 5t+4 / t² + 1 dt[/tex]We can write this rate function as a sum of two functions by expanding the denominator:
[tex]S π / π /4 5t+4 / (t² + 1) dt = S π / π /4 5t+4 / (t² + 1) (t+1/t - 1/t) dt = S π / π /4 5t+4 (t+1 - 1/t²) dt = S π / π /4 5t+4 (t+1) dt - S π / π /4 5t+4 (1/t²) dt[/tex]
Now, integrating the two functions gives us the closed form:
[tex]S π / π /4 5t+4 (t+1) dt = 5/2 (t² + 2t + 2) + CS π / π /4 5t+4 (1/t²) dt = -5/2 (t + 1/t) + C[/tex]
Therefore, the equivalent closed form for the original rate function isS π / π /4 5t+4 / t² + 1 dt = 5/2 (t² + 2t + 2) - 5/2 (t + 1/t) + C.
b. S π/t 4tan (t) dt
We can use a trig identity to change the form of this rate function:
S π/t 4tan (t) dt = S π/t 4 (sin (t) / cos (t)) dt = 4/cos (t) S π/t sin (t) dt
Integrating the rate function gives us the closed form:
S π/t 4tan (t) dt = 4/cos (t) S π/t sin (t) dt = -4 ln |cos (t)| + C.
Therefore, the equivalent closed form for the original rate function is:
S π/t 4tan (t) dt = -4 ln |cos (t)| + C.
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Samantha and Christian own competing taxicab companies. Both cab companies charge a one-time pickup fee for every ride, as well as a charge for each mile traveled. Samantha charges a $3.50 pickup fee and $1.30 per mile. The table below represents what Christian's company charges.
Christian's company charges $0.8 per mile than Samantha's.
What is the rate of change?In Mathematics and Geometry, the rate of change can be calculated by using the following mathematical equation (formula);
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x for Christian's company;
Rate of change, m = (43.50 - 22.50)/(20 - 10)
Rate of change, m = 21/10
Rate of change, m = 2.1
Therefore, the difference between the charges by Christian's company and Samantha's company can be calculated as follows;
Difference in charges = 2.1 - 1.30
Difference in charges = $0.8.
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Write 735 as the product of its prime factor.
Answer:
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Step-by-step explanation:
[tex]735 = 7 \times 105[/tex]
[tex]735 = 7 \times 3 \times 35[/tex]
[tex]735 = 7 \times 3 \times 5 \times 7[/tex]
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
The zero product property, says that if a product of two real numbers is 0, then one of the numbers must be 0.
a. Write this property formally using quantifiers and variables.
b. Write the contrapositive of your answer to part (a).
c. Write an informal version (without quantifier symbols or variables) for your answer to part (b).
The zero product property states that if the product of two real numbers is 0, then one of the numbers must be 0.
The contrapositive of the above answer is "If neither of the numbers is 0, then the product is not 0."
In other words, if two non-zero numbers are multiplied, then the result is non-zero.
a) We can use the zero-product property to factorize the expression as an example of[tex](x - 2) (x - 3) = 0[/tex], and obtain the two roots of the equation, [tex]x = 2[/tex]and [tex]x = 3[/tex]. Therefore, the zero-product property is a powerful tool that allows us to solve complex problems and equations involving algebraic expressions and real numbers.
b) A non-zero product can only be obtained by multiplying two non-zero numbers. So, if the product is zero, then at least one of the factors must be zero as well. This is the informal version of the contrapositive of the zero product property.
c)The zero product property is an essential concept in algebra that involves the understanding of real numbers and their product. It is widely used in algebra and calculus to solve equations and expressions that involve polynomial functions, quadratic equations, and exponential functions.
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Answer to where the lines Intersect PLEASE Y=3x-6, Y=2x
Answer:
(6,12)
Step-by-step explanation:
3x - 6 = 2x
x - 6 = 0
x=6
y=2*6
y=12
Solve for x and y 100 points
The solution to the system of equations is x = 16/5 and y = 11/5.
What are the four equation systems?Graphing, substitution, elimination, and matrices are the four methods for solving systems of equations.
Using the substitution method, we can find x and y.
To begin, let us solve the first equation for x:
2x + 3y = 13
2x = 13 - 3y
x = (13 - 3y)/2
This expression for x can now be substituted into the second equation:
x - y = 1
[(13 - 3y)/2] - y = 1
To remove the denominator, multiply both sides by 2:
13 - 3y - 2y = 2
Simplifying:
13 - 5y = 2
Taking 13 off both sides:
-5y = -11
-5 divided by both sides:
y = 11/5
Now that we've discovered y, we can plug it back into either of the original equations to find x. Let's look at the first equation:
2x + 3y = 13
2x + 3(11/5) = 13
To eliminate the fraction, multiply both sides by five:
10x + 33 = 65
Taking 33 away from both sides:
10x = 32
Divide both sides by ten:
x = 16/5
As a result, the system of equations solution is x = 16/5 and y = 11/5.
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any statistical test that is used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools would be inappropriate. explain why in a few sentences.
It is not appropriate to use a statistical test to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools because this would only compare the mean ratios of the two groups.
There are several statistical tests that can be used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools.
However, some statistical tests may not be appropriate for this scenario.
The main reason for this is that the normal distribution of data may not be assumed in this situation. This is because student-to-teacher ratios may not be normally distributed, with some schools having much higher ratios than others, resulting in skewed data.
In this scenario, a nonparametric statistical test may be more appropriate because it makes fewer assumptions about the distribution of data. The Wilcoxon rank-sum test, for example, may be used to compare the student-to-teacher ratios of the top 10 and bottom 10 schools because it does not assume normality. The Mann-Whitney U test is another nonparametric test that can be used to compare the two groups' ratios.
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The ordering and transportation cost €C for components used in manufacturing process is approximated by the function below, where C is measured in thousands of dollars and is the order size in hundreds_ C(x) = s(x x+3 (a) Verify that C(3) C(6) _ c(3) (b) According to Rolle's Theorem, the rate of change of the cost must be for some order size in the interval (3 answer to the nearest whole number:) components Find that order size (Round vour Need Help? Ialkto Tutor
The value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
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A line has a slope of – 9 and passes through the point (1, – 3). Write its equation in slope-intercept form.
Answer:
yytyyyyy
Step-by-step explanation:
Work out the angle x. Give your answers to the nearest whole number. ABCD is a rectangle. ABC is an isosceles triangle, with AB = AC. A B X X = 11 cm O 13 cm [2] C B A X C 15 cm X = O 19 cm [3] D ABC is a right-angled triangle. D lies on BC, and DC = DB. BC = 16 cm. A X = t 23 cm O [4] C B
WILL GIVE AS BRANLIEST ANSWER IF THE ANSWER IS GIVEN IN UNDER 7 MINS
The value of the missing sides of the triangle given above include the following;
2.)X = 65°
3.) X = 60°
4.) X = 20°
How to calculate the value of the missing side of the triangles?For question 2.)ABC = isosceles triangle
AB = AC = 13 cm
BC = 11cm
There is an angle bisector at <A which divides lime BC into two equal parts at D.
BD = 11/2 = 5.5 cm
Cos∅ = adjacent/hypothenuse
Cos X = 5.5/13
cos X = 0.423076923
X = Cos -1(0.423076923)
X = 65°
For question 3.)The two diagonals divides the given rectangle into two opposite equilateral triangles which has each of its sides equal to 60°.
For question 4.)ABC = right angle triangle
Line D divides BC into two equal parts = DC and DB
BC = 16cm (opposite)
DC = 16/2 = 8cm
AB = 23 cm( adjacent)
AC = hypothenuse = BC²+ AB²
AC² = 16²+23²
= 256 + 529
= 785
AC = √785
= 28
<CAB = sin ∅ = opposite/hypothenuse
sin∅ = 18/28
= 0.642857142
∅= sin -1 (0.642857142)
∅ = 40°
Therefore X = 40/2 = 20°
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Please help!
The object above is symmetrical through Z. If Y = 11 inches, Z = 13 inches, and H = 6 inches, what is the area of the object?
A. 6.5 square inches
B. 78 square inches
C. 31 square inches
D. 156 square inches
the correct area of the symmetrical object is option (B). 78 square inches.
Definition of SymmetryIf two more identical parts can be separated from a form and arranged in an orderly fashion, the shape is said to be symmetrical. For instance, when you are instructed to cut out a "heart" from a sheet of paper, all you need to do is fold the paper, draw one-half of the heart at the fold, and then cut it out. After you do this, you will discover that the second half precisely matches the first half.
In the first part of the object
Area of the object=½×H×Z
=½×13×6
=39 square inches
Given that object above is symmetrical through Z.
So, the area of 2nd part of object will also be 39 square inches
Hence total area is 78 square inches.
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In Bitcoin, the standard practice for a merchant is to wait for n confirmations of the paying transaction before providing the product. While the network is finding these confirming blocks, the attacker is building his own branch which contradicts it. When attempting a double-spend, the attacker finds himself in the following situation. The network currently knows a branch crediting the merchant, which has n blocks on top of the one in which the fork started. The attacker has a branch with only m additional blocks, and both are trying to extend their respective branches. Assume the honest network and the attacker has a proportion of p and q of tire total network hash power, respectively. 1. [10 pts] Let az denote the probability that the attacker will be able to catch up when he is currently z blocks behind. Find out the closed form for az with respect to p,q and z. Detailed analysis is needed. (Hint: az satisfies the recurrence relation az=paz+1+qaz−1) 2. [10 pts] Compared with the Bitcoin white paper, we model m more accurately as a negative binomial variable. m is the number of successes (blocks found by the attacker) before n failures (blocks found by the honest network), with a probability q of success. Show that the probability for a given value m is P(m)=(m+n−1m)pnqm.
In Bitcoin, when a merchant waits for n confirmation of a payment transaction before providing the product, there is a risk of a double-spend attack. In this situation, the network is aware of a branch crediting the merchant, which has n blocks on top of the one in which the fork started.
By simulating m as a negative binomial variable, P(m) = (m + n - 1m)pnqm can be used to more precisely compute this probability for a given value of m.
The attacker, on the other hand, has a branch with only m additional blocks. If we assume the honest network and the attacker have a proportion of p and q of the total network hash power, respectively, the probability of the attacker catching up when he is currently z blocks behind is given by az = paz+1 + qaz−1, where a is a constant.
To calculate the probability more accurately, we can model m as a negative binomial variable.
This is the number of successes (blocks found by the attacker) before n failures (blocks found by the honest network), with a probability q of success.
The probability for a given value m is then given by P(m) = (m + n - 1m)pnqm.
Thus, when dealing with a double-spend attack in Bitcoin, the probability that the attacker will be able to catch up is given by az = paz+1 + qaz−1, where a is a constant.
This probability can be more accurately calculated by modeling m as a negative binomial variable, with the probability for a given value m given by P(m) = (m + n - 1m)pnqm.
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the probability that deshawn palys basketball after school is 20% the probability that he talks to friends after school is 45% he says the p b or t is 65% explain dans error
Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
How do we find the error?Given:
Probability of Deshawn playing basketball after school = 20%Probability of Deshawn talking to friends after school = 45%Probability of Deshawn doing either basketball or talking to friends after school = 65%Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%
Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%
The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
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1,500 decagrams = 150 kilograms.
True?
False?
Answer: FALSE
Step-by-step explanation:
1500 decagram = 15 kg
1 decagram = 0.01 kg
1500 decagram = 1500/0.01 kg
= 1500/100 kg
1500 decagram = 15kg
Thomas bought 120 whistles, 168 yo-yos and 192 tops. He packed an equal amount of items in each bag. A) What is the maximum number of bag that he can get?
Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.
To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.
To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:
168 = 1 * 120 + 48
120 = 2 * 48 + 24
48 = 2 * 24 + 0
Therefore, the GCD of 120 and 168 is 24.
Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0
Therefore, the GCD of 120, 168, and 192 is 24.
So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:
Total number of items = 120 + 168 + 192 = 480
Number of bags = 480 / 24 = 20
Therefore, Thomas can get a maximum of 20 bags.
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Kelly took three days to travel from City A to City B by automobile. On the first day, Kelly traveled 2/5 of the distance from City A to City B and on the second day, she traveled 2/3 of the remaining distance. Which of the following is equivalent to the fraction of the distance from City A to City B that Kelly traveled on the third day.A) 1−2/5−2/3B) 1−2/5−2/3(2/5)C) 1−2/5−2/5(1−2/3)D) 1−2/5−2/3(1−2/5)E) 1−2/5−2/3(1−2/5−2/3)
The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).
What is the fraction?The fraction represents a portion or part of a whole.
There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.
The fractional distance traveled on day one = ²/₅
The remaining fractional distance = ³/₅ (1 - ²/₅)
The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)
The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)
Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.
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A soccer team won 11 games last year. This year they won 13 games. What was the percent increase in the number of games won?
A) 84.6%
B) 2%
C)15.4%
D)18.2%
The required percent increase in the number of games won is approximately 18.2%.So, Option D) is correct.
What is percentage?In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).
According to question:The percent increase in the number of games won can be calculated as follows:
[tex]$\text{Percent increase} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100%$$[/tex]
In this case, the old value is the number of games won last year, which is 11, and the new value is the number of games won this year, which is 13. Substituting these values into the formula, we get:
[tex]$\text{Percent increase} = \frac{13 - 11}{11} \times 100% = \frac{2}{11} \times 100% \approx 18.18%$$[/tex]
Therefore, the percent increase in the number of games won is approximately 18.18%.
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What is the circumference of the circle? Use 3.14 for π. circle with a segment drawn from the center of the circle to a point on the circle labeled 5 inches 31.40 inches 78.50 inches 15.70 inches 246.49 inches
[tex] \Large{\boxed{\sf C = 31.40 \: inches}} [/tex]
[tex] \\ [/tex]
Explanation:The circumference of a circle can be calculated using the following formula:
[tex] \Large{\sf C = 2 \pi r } [/tex]
Where:
C is the circumference of the circle.r is its radius.[tex] \\ [/tex]
Since "a segment drawn from the center of a circle to a point on the circle" is actually the definition of the radius of said circle, we can take r = 5 inches.
[tex] \\ [/tex]
Applying our formula and using 3.14 for π, we get:
[tex] \sf C = 2 \times 3.14 \times 5in \\ \\ \implies \boxed{\boxed{\sf C = 31.4 \: inches = 31.40 \: inches}} [/tex]
Answer:
31.40 inches
Step-by-step explanation:
The circumference of a circle can be calculated using the formula:
[tex]\large\rm{Circumference = 2 \cdot \pi \cdot Radius}[/tex]Given:
Radius = 5 inchesSubstitute the given value into the formula:
[tex]\large\rm{Circumference = 2 \cdot 3.14 \cdot 5\: inches}[/tex]Simplifying the expression:
[tex]\large\rm{Circumference = \boxed{\rm{31.40\: inches}}}[/tex][tex]\therefore[/tex] The circumference of the circle is 31.40 inches.
If a can of paint can cover 600 square inches, how many cans of paint are needed to cover 1,880 square inches
Answer:
1,880 sq in ÷ 600 sq in/can ≈ 3.13 cans
If you want you can round that to 4 cans.
In 915. 23, the digit 3 is in the
place.
Answer:
hundreth
Step-by-step explanation:
the 2 is in the tenth and the 3 is in the hundreth
The manager of a computer network has collected data on the number of times that service has been interrupted on each day over the past 500 days. The results are as follows:INTERRUPTIONS PER DAY (x)1) Does the distribution of service interruptions follow a Poisson distribution? (Use the 0.01 level of significance.) 8Q2) Referring to the data in problem, at the 0.01 level of significance, does the distribution of service interruptions follow a Poisson distribution with a population mean of 1.5 interruptions per day?
In the following question, among the conditions given, Yes, the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day at the 0.01 level of significance.
This can be determined using a hypothesis test. The null hypothesis is that the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day, and the alternative hypothesis is that it does not.
A chi-square test for goodness of fit is conducted using the given data to test the null hypothesis. The results of this test show that the chi-square statistic is less than the critical value, indicating that the null hypothesis should be accepted and the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day.
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which of the following was traditionally an assumption underlying the independent samples t-test question 10 options: a) scores must be drawn from a normally distributed population b) variances should be unequal in both groups c) data should be at the nominal level d)all of the above
The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.
What is a t-test?A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.
The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.
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Segment addition and midpoints.
EH=EF+FH, we can replace the found values with EF and FH to get EH=12+7=19.
How to solve the problem?A line segment is a path between two measurable points. Line segments have a defined length so they can form the sides of any polygon.
To solve this problem, we can write EH in terms of EG and FH, taking advantage of the fact that F is between E and G, and G is between F and H. First, notice that EG+GF=EF. Substituting the given values, we get EF=9+3=12.
Then GF+FH=GH, so FH=GH-GF. Substituting in the given values, GH=10 and GF=3, so FH=10-3=7.
Finally, since EH=EF+FH, we can substitute the found values into EF and FH to get EH=12+7=19. Therefore EH = 19
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Nonresponse bias occurs when ________.
A) the population has been divided into strata
B) portions of the population are excluded from the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents
Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.
Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.
Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.
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the graph represents the number of different tacos ordered for an office lunch. in total, how many tacos were ordered?
Answer:
do you have the graph to solve it?
we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?
Probability of D2 being sunny = 0.78.
On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.
Therefore, we need to find the chances that D2 is sunny.
There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.
Now, Let us find the probability of D2 being sunny.
We have the following possible cases for D2.
D1 = Sunny; D2 = Sunny
D1 = Sunny; D2 = Rainy
D1 = Rainy; D2 = Sunny
D1 = Rainy; D2 = Rainy
The probability of D1 being sunny is 0.9.
When a sunny day follows a sunny day, the probability is 0.8.
When a sunny day follows a rainy day, the probability is 0.6.
Therefore, the probability of D2 being sunny is given by the formula:
Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.
Therefore, the probability that D2 is sunny are 0.78 or 78%.
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9. Seven more than the quotient of a number b
and 45 is greater than 5.
Any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as: b ∈ (-90, ∞)
What is inequality?An inequality is a mathematical statement that compares two values or expressions using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
According to question:Starting from the given inequality:
7 + (b/45) > 5
We can solve for b by first subtracting 7 from both sides:
b/45 > 5 - 7
Simplifying the right-hand side:
b/45 > -2
Multiplying both sides by 45 to isolate b:
b > -2 * 45
b > -90
Therefore, any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as:
b ∈ (-90, ∞)
For example, x > 5 is an inequality that states that x is greater than 5, while y ≤ 10 is an inequality that states that y is less than or equal to 10.
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Please look at the photo and let me know the three answers ASAP!! Thank you!!
a) Increase in the amount spent on entertainment is $1.82
b) Money spent who doesn't work any hours is $11.36
c) Money spent who works 8 hours is $25.92
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
Given line equation is; y = 1.82x + 11.36 Compare with y = mx + c
(a) The slope (m) of the line is 1.82, which means that for every increase of one hour worked, the predicted increase in the amount of money spent on entertainment is $1.82.
(b) For a student who doesn't work any hours, we can substitute x = 0 into the equation of the line of best fit:
y = 1.82x + 11.36
y = 1.82(0) + 11.36
y = 11.36
Therefore, the predicted amount of money spent on entertainment for a student who doesn't work any hours is $11.36.
(c) For a student who works 8 hours, we can substitute x = 8 into the equation of the line of best fit:
y = 1.82x + 11.36
y = 1.82(8) + 11.36
y = 25.92
Therefore, the predicted amount of money spent on entertainment for a student who works 8 hours is $25.92
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A study suggests that the 25% of 25 year olds have gotten married. You believe that this is incorrect and decide to collect your own sample for a hypothesis test. From a random sample of 25 year olds in census data with size 776, you find that 24% of them are married. A friend of yours offers to help you with setting up the hypothesis test and comes up with the following hypotheses. Indicate any errors you see.H0p^=0.24Hap^≠0.24
The null hypothesis (H0) proposed by the friend is H0: p^ = 0.24, where p^ represents the sample proportion of 25 year olds who are married. The alternative hypothesis (Ha) is Hα: p^ ≠ 0.24.
The error in the hypotheses is that the alternative hypothesis is not in line with the problem statement, which suggests that the 25% figure is incorrect.
The appropriate alternative hypothesis would be that the true proportion of 25-year-olds who are married is not equal to 0.25. Therefore, the correct alternative hypothesis would be Ha: p^ ≠ 0.25.
In summary, the correct set of hypotheses for this problem would be:
H0: p^ = 0.25 (Null hypothesis)
Ha: p^ ≠ 0.25 (Alternative hypothesis)
We would use a significance level and statistical test to determine whether we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
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(4) 2. Determine the exact answer for each of the calculations in question 2.1 above, by working out the errors caused by rounding, and compensating for them. 2.2.1. 723 + 586 2.2.2. 2850-1155
What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.
According to the question:
To find the zeros of the function
f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.
So we start with the equation:
x² + 7x - 60 = 0
Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:
x² + 7x - 60 = (x + 12)(x - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 12 = 0 or x - 5 = 0
Solving for x, we get:
x = -12 or x = 5
The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.
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