Δ ABC and ΔDEF are similar triangles. If m∠A =104∘and m∠E = 36∘, what is ∠C?
1. 36
2. 40
3. 76
4. 104

We can sum up the results of all three cases to get the total number of strings with exactly 4 occurrences of a or 4 occurrences of b or 4 occurrences of c. Total number of strings = C(12, 4) * 2^8 + C(12, 4) * 2^8 + C(12, 4) * 2^8.

To find the number of strings of length 12 over the alphabet {a, b, c} that have exactly 4 occurrences of a, 4 occurrences of b, or 4 occurrences of c, we can use combinatorics.

First, let's consider the case of a string length of 12.

We have three possibilities: exactly 4 occurrences of a, exactly 4 occurrences of b, or exactly 4 occurrences of c. We will calculate each case separately and then sum up the results.

Case 1: Exactly 4 occurrences of a.

We have 12 positions in the string and we need to choose 4 of them to place the a's. The remaining 8 positions can be filled with b's or c's, giving us 2 options for each position. Therefore, the number of strings with exactly 4 occurrences of a is C(12, 4) * 2^8.

Case 2: Exactly 4 occurrences of b.

Similar to Case 1, we have 12 positions and we need to choose 4 of them to place the b's. The remaining 8 positions can be filled with a's or c's, giving us 2 options for each position. So, the number of strings with exactly 4 occurrences of b is C(12, 4) * 2^8.

Case 3: Exactly 4 occurrences of c.

Again, we have 12 positions and we need to choose 4 of them to place the c's. The remaining 8 positions can be filled with a's or b's, giving us 2 options for each position. Hence, the number of strings with exactly 4 occurrences of c is C(12, 4) * 2^8.

If the length of the string is 17, the approach will remain the same. We will calculate the number of strings with exactly 4 occurrences of a, 4 occurrences of b, or 4 occurrences of c using the formula mentioned above. The only difference will be in the length of the string and the number of positions to be chosen for each case. We will have C(17, 4) instead of C(12, 4), and the remaining positions will be filled with the remaining characters from the alphabet.

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Answer:

10.42

Step-by-step explanation:

Brainliest plz

answer : 960

Step-by-step explanation:

624÷65/100

960

The trigonometric integral ∫tan(x)sec(x) dx can be solved by applying a substitution. By letting u = sec(x), the integral simplifies to ∫(u^2 - 1) du. After integrating and substituting back in the original variable, the final answer is given by 1/3(sec^3(x) - sec(x)) + C, where C is the constant of integration.

To solve the integral ∫tan(x)sec(x) dx, we can use the substitution method. Let u = sec(x), which implies du = sec(x)tan(x) dx. Rearranging this equation, we have dx = du/(sec(x)tan(x)) = du/u.

Now, substitute u = sec(x) and dx = du/u into the original integral. This transforms the integral to ∫(tan(x)sec(x)) dx = ∫(tan(x)sec(x))(du/u). Simplifying further, we get ∫(u^2 - 1) du.

Integrating ∫(u^2 - 1) du, we obtain (u^3/3 - u) + C, where C is the constant of integration. Substituting back u = sec(x), we arrive at the final answer: 1/3(sec^3(x) - sec(x)) + C.

In conclusion, the trigonometric integral ∫tan(x)sec(x) dx can be evaluated as 1/3(sec^3(x) - sec(x)) + C, where C represents the constant of integration.

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Type I error refers to rejecting a true null hypothesis, while Type II error refers to failing to reject a false null hypothesis. Types of statistical analyses include descriptive statistics, inferential statistics, correlation analysis, regression analysis, etc.

Type I error is a false positive, and Type II error is a false negative. Examples of Type I errors include convicting an innocent person in a criminal trial and rejecting a new drug that is actually effective. Examples of Type II errors include failing to convict a guilty person in a criminal trial and accepting a new drug that is actually ineffective.

Various statistical analyses can be applied to the data collected in research studies, depending on the research question and the type of data. Some common types of statistical analyses include descriptive statistics, inferential statistics, correlation analysis, regression analysis, t-tests, analysis of variance (ANOVA), and chi-square tests. Descriptive statistics are used to summarize and describe the characteristics of the data, while inferential statistics are used to draw conclusions and make inferences about the population based on sample data. Correlation analysis examines the relationship between two or more variables, regression analysis explores the relationship between a dependent variable and one or more independent variables, t-tests compare means between two groups, ANOVA analyzes differences among three or more groups, and chi-square tests examine the association between categorical variables.

Type I error, also known as a false positive, occurs when we reject a null hypothesis that is actually true. This means we conclude that there is a significant effect or relationship when there is none in reality. For example, in a criminal trial, a Type I error would be convicting an innocent person. Another example is rejecting a new drug that is actually effective, leading to the rejection of a potentially beneficial treatment.

On the other hand, a Type II error, also known as a false negative, occurs when we fail to reject a null hypothesis that is actually false. In this case, we fail to detect a significant effect or relationship when one exists. For instance, in a criminal trial, a Type II error would be failing to convict a guilty person. In the context of medical testing, a Type II error would occur if we accept a new drug as ineffective when it is actually effective, resulting in the approval of an ineffective treatment.

Various statistical analyses can be applied to research study data depending on the research question and the type of data collected. Descriptive statistics are used to summarize and describe the characteristics of the data, such as measures of central tendency (e.g., mean, median) and variability (e.g., standard deviation, range). Inferential statistics are used to make inferences and draw conclusions about the population based on sample data, such as hypothesis testing and confidence interval estimation.

Correlation analysis examines the relationship between two or more variables and determines the strength and direction of their association. Regression analysis explores the relationship between a dependent variable and one or more independent variables, allowing us to predict the value of the dependent variable based on the independent variables.

T-tests are used to compare means between two groups, such as comparing the average test scores of students who received a specific intervention versus those who did not. Analysis of variance (ANOVA) analyzes differences among three or more groups, such as comparing the performance of students across different grade levels.

Chi-square tests examine the association between categorical variables, such as analyzing whether there is a relationship between gender and voting preference. These are just a few examples of the statistical analyses commonly applied to research study data, and the specific choice of analysis depends on the research question and the nature of the data.

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The point-slope form of the line is y -3 = 5(x + 1).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The slope of the line shown in the graph is 5.

And line passes through point (-1, 3).

So,

If a line passes through a point (x₁ ,y₁) and have a slope m,

then the equation of line is,

y - y₁ = m(x - x₁)

So,

y -3 = 5(x + 1)

Therefore, the equation of the line is y -3 = 5(x + 1).

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The theoretical and experimental probabilities are equal.

Probability determines the likelihood of a random event occurring. The ratio of the number of favorable outcomes to the total number of possible outcomes is known as theoretical probability.

Theoretical probability = number of odd sides/ die sides

Here given that the numbers that are odd comes 6

So,

6/20 = 3/10 theoretical probability

The outcome of an experiment that has been repeated multiple times is used to calculate experimental probability.

Experimental probability = number of times Tani landed on a odd number  divided by the number of times the experiment was performed

6/ 20= 3/10.

Therefore here , both experimental and theoretical probabilities are equal.

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Complete question :

In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728? 137,982 142,398 292,389 392,097

Answer:

137,982

Step-by-step explanation:

The value of digit 3 in 143, 728

3 in 143,728 is in the 1000 thousand place, hence, digit 3 has a value of :

3 * 1000 = 3000

Therefore, 10 times the value of digit 3 will be :

3000 * 10 = 30000

Feom the options given, we obtain the option where 3 has a value of 30000 if the number is expressed in expanded form:

The answer is 137,982

3 here is in the 10 thousand place = 3 * 10,000 =. 30,000

Here's an example of a triple integral that is difficult to integrate with respect to z first, but easy if we integrate with respect to x first: ∫_0^π/2 ∫_0^cos(x) ∫_0^(x sin(y)) e^z dz dy dx

If we try to integrate this triple integral with respect to z first, the integrand becomes a function of z that depends on both x and y, which makes the integration difficult. Specifically, we would have to integrate e^z with respect to z, while x and y are treated as constants. This would result in an expression that is a function of x and y, which we would then have to integrate with respect to y and x, respectively.

On the other hand, if we integrate with respect to x first, we can factor out the e^z term and integrate it with respect to x. This leaves us with an integral that is easy to integrate with respect to y and z. Therefore, we can write: ∫_0^π/2 ∫_0^cos(x) ∫_0^(x sin(y)) e^z dz dy dx

= ∫_0^π/2 ∫_0^1 ∫_0^y e^z dx dz dy.

Integrating with respect to x, we get: ∫_0^π/2 ∫_0^1 ∫_0^y e^z dx dz dy = ∫_0^π/2 ∫_0^1 ye^z dz dy

= ∫_0^π/2 (1 - e^y) dy

= π/2 - 1.

Therefore, the value of the triple integral ∫_0^π/2 ∫_0^cos(x) ∫_0^(x sin(y)) e^z dz dy dx is π/2 - 1.

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The probability that both Event A (the first die is 4 or less) and Event B (the second die is even) will occur is 1/3.

To find the probability that both Event A and Event B will occur, we need to calculate the individual probabilities of each event and then multiply them together.

Event A: The first die is 4 or less.

There are 6 possible outcomes for the first die (numbers 1 to 6), and out of those, 4 outcomes (numbers 1, 2, 3, and 4) satisfy the condition. Therefore, the probability of Event A is 4/6, which simplifies to 2/3.

Event B: The second die is even.

For a fair six-sided die, there are 3 even numbers (2, 4, and 6) out of a total of 6 possible outcomes. Therefore, the probability of Event B is 3/6, which simplifies to 1/2.

To find the probability that both events will occur, we multiply the probabilities of Event A and Event B:

Probability of both events occurring = Probability of Event A * Probability of Event B

P = (2/3) * (1/2)

P = 2/6

P = 1/3

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Answer:u wrong it’s 12)63)?62?)/?

Step-by-step explanation:

a) The amount Rihanna will borrow in an auto loan is R14,800.

b) The monthly auto payment will be R326.28.

c) The total amount of interest that Rihanna will pay is R861.44

d) The total payment for the car, including the down payment is R17,661.44

e) The total annual premium is R1,850.

The cost of the car Rihanna is buying = R18,300

Trade in allowance = R1,500

Down payment = R2,000

Number of months for the mortgage = 48 months (4 years x 12)

a) Car loan = R14,800 (R18,300 - R1,500 - R2,000)

b) Monthly payment at 2.8% APR = R326.28 ($22.046 x R14,800/$1,000)

d) The total payment for the car = R17,661.44 [(R326.28 x 48) + R2,000]

c) The total amount of interest = R861.44 (R17,661.44 - R2,000 - R14,800)

e) Liability insurance = 100/300/50

Liability insurance coverage for a 19-year-old driver = R54 (R450 x 12) x 1.0%

Collision insurance: R1,776 (R148 x 12)

Comprehensive insurance: R1,020  (R85 x 12)

Deductible for each insurance type = R500

Total annual premium with deductible = R1,850 (R54 + R1,776 - R500 + R1,020 - R500)

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The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

A) 3:2

Step-by-step explanation:

45:30

divide by 5

9:6

divide by 3

3:2

There are 600 students including the seventh and eighth graders at the party.

This problem uses the concept of percentages to define the conditions that are laid in front of us.

Let the original  number of students be S , and the number of seventh graders be   = 0.60S

We know that percent is used to convey the mathematical term of a fraction multiplied by 100.

Total students  after 20 eighth graders arrive = S + 20

And we have that

Number of seventh graders / total number of students  =  58%

.60S  / [ S + 20 ]  =   .58    we multiply both sides by  S +  20

0.60S  =0 .58 [ S + 20]

.60S  = .58S + 11.6   we subtract  0.58S from  both the sides

0.02S = 11.6  we divide both the sides  by .02

S  = 11/6 / 0.02 =    580

So the total number of students = 580 + 20  = 600 .

Hence there are 600 students at the party at that time.

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Answer:

w=42m

Step-by-step explanation:

Length × Width = Area

80 × w = 3360

divide both sides by 80

w=42 m

please give brainliest

The area of circle is with radius 3xy³ is 9πx²y⁶.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2.

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius. Circumference of circle = 2π (Radius)

area of circle=πr²

=π×(3xy³)²

=9πx²y⁶

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Step-by-step explanation:

The scientific notation of any number is given by :

\(N=a\times 10^b\)

a is any real no and b is any integer

The scientific notation of 345,000,000 should be \(3.45\times 10^8\) but Jorden wrote 34.5×10⁷. He is incorrect. He should have shifted decimal before 4 such that power of 10 becomes 8.

The top of the ladder is moving down at a rate of 0.6 feet/second or approximately 16.8 feet/second when the foot of the ladder is 5 feet from the wall.

The crime rate at the end of May is rising by approximately 1080 crimes per month. The top of the ladder is moving down at a rate of 16.8 feet/second when the foot of the ladder is 5 feet from the wall.

To find how fast the crime rate is rising at the end of May, we need to calculate the derivative of the crime rate function with respect to time. The derivative of C(T) = T - 652 + 120 is dC/dT = 1. This means that the crime rate is rising at a constant rate of 1 crime per degree Fahrenheit.

At the end of May, the temperature is 72°F, and the rate at which the temperature is rising is 9°F per month. Therefore, the crime rate is rising at a rate of 9 crimes per month.

For the ladder problem, we can use similar triangles to set up a proportion. Let h be the height of the ladder on the building, and x be the distance from the foot of the ladder to the wall.

We have the equation x/h = 5/h.

Differentiating both sides with respect to time gives (dx/dt)/h = (-5/h²) dh/dt.

Given that dx/dt = 3 feet/second and x = 5 feet, we can substitute these values into the equation to find dh/dt.

Solving for dh/dt, we get dh/dt = (-5/h²)(dx/dt) = (-5/25)(3) = -3/5 = -0.6 feet/second.

Therefore, the top of the ladder is moving down at a rate of 0.6 feet/second or approximately 16.8 feet/second when the foot of the ladder is 5 feet from the wall.

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The sum of the angle measures of a polygon with s sides can be calculated using the formula:

(s - 2) * 180 degrees

We can use this formula to solve for s:

2 = (s - 2) * 180

Dividing both sides by 180:

2 / 180 = (s - 2)

Solving for s:

s = 2 + 2 / 180 = 2 + 1 / 90 = 2 + 1 / 90 * 180 / 180 = 2 + 2 / 3

So the number of sides of the polygon is s = 2 + 2 / 3 = 4 2/3.

Since a polygon must have a whole number of sides, s cannot be a fraction, which means this answer is not a valid solution for the number of sides of a polygon. I don't think the problem as stated does not have a valid solution.

Answer:

69 i think

Step-by-step explanation:

it is either 69 or 83

The probability that none are mechanical engineering majors is 0.51.

The number of students who are not mechanical engineering majors is 100 - 49 = 51. The probability of choosing a student who is not a mechanical engineering major in one draw is 51/100. The probability of choosing five students in a row who are not mechanical engineering majors is (51/100)^5. Thus, the answer is (51/100)^5 = 0.1517816.

Probability refers to potential. From 0 to 1 is used to express the value. To determine how likely an event is to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment. The complete number of possibilities that can occur should be known before calculating the likelihood that a certain event will occur.

The complete question is:-

In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?My info I know: The mechanical engineers account for 49% of the students, making 51% not mechanical engineers? Do I take five out of the 51, so 0.05 X 0.51?

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Answer:6. 7 8.22 10.24 7.12 9.22 11.9

Step-by-step explanation:

Answer:

6y=7

7x=12

8m= 22

9 n= 22

10 x= 24

11 y=9

Answer:

y=7x−5

Explanation:

We have; y=x4+2x2−x

First we differentiate wrt x;y=x4+2x2−x

∴dydx=4x3+4x-1

We now find the vale of the derivative at (1,2) (and it always worth a quick check to see that y=2 when x=1) we have dydx=4+4−1=7

So at the tangent passes through the coordinate (1,2) and has gradient m=7

We now use y−y1=m(x−x1) to get the equation of the tangent:

∴y−2=7(x−1)

∴y−2=7x−7

∴y=7x−5

The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is  (9.7, 14.7).

1. Identify the given information:
  - Confidence level (c) = 0.95
  - Sample mean (x) = 12.2
  - Sample standard deviation (s) = 3.0
  - Sample size (n) = 8

2. Determine the degrees of freedom (df) for the t-distribution:
  - df = n - 1 = 8 - 1 = 7

3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:
  - You can use a t-table or an online calculator for this.
  - The t-value for a 0.95 confidence level and 7 df is approximately 2.365.

4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):
  - ME = t-value * (s / sqrt(n))
  - ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5

5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):
  - Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7
  - Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7

So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).

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The sum of the 1st and three-term of the GP is 87.75.

What is geometric progression?

A geometric progression often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.

Here, we have

Given:  3rd term is 27 and whose 6th term is 8​

Let the GP terms are a, ar, ar², ar³, ar⁴ and ar⁵,

Given ar² = 27 and ar⁵ = 8

Take the ratio of the sixth term to the third term:

ar⁵ / ar² = 8/27 => r³ = (2/3)³

r = 2/3

We know that

ar² = a(2/3)² = 27

=> a(4/9) = 27

=> a = 27*9/4 = 243/4

So, the terms are 243/4, 243/4*(2/3), 243/4*(4/9), 243/4*(8/27), 243/4*(16/81), 243/4*(32/243)

= 243/4 + 27

= 60.75 + 27

= 87.75

Hence, the sum of the 1st and three-term of the GP is 87.75.

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Answer: \(x=\Large\boxed{\frac{2}{5} }\)

Step-by-step explanation:

Given equation

\(-5x-(-6-4x)=-2(3x-4)\)

Expand the parenthesis

\(-5x+6+4x=-2\times3x-2\times(-4)\)

\(-5x+6+4x=-6x+8\)

Combine like terms

\(-x+6=-6x+8\)

Add 6x on both sides

\(-x+6+6x=-6x+8+6x\)

\(5x+6=8\)

Subtract 6 on both sides

\(5x+6-6=8-6\)

\(5x=2\)

Divide 5 on both sides

\(5x/5=2/5\)

\(x=\Large\boxed{\frac{2}{5} }\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

28 cents roughly

Step-by-step explanation: