convert to slope-intercept form:
2x+5y=0

The density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]

The density function of [tex]U = Y1^2 +Y2^2[/tex]  is given by the formula [tex]f_U(u) = (1/2π)∫_0^∞ f_Y1(y_1)f_Y2(√(u-y_1^2)) dy_1[/tex]. This can be calculated as follows:

Let u ≥ 0, then

[tex]f_U(u) = (1/2π)∫_0^∞ (1/√(2π))e^(-(y_1^2/2))(1/√(2π))e^(-(√(u-y_1^2)^2/2)) dy_1[/tex]

[tex]= (1/2π)∫_0^∞ (1/2π)e^(-u/2) dy_1= (1/2π)e^(-u/2) ∫_0^∞ (1/2π) dy_1= (1/2π)e^(-u/2)[/tex]

Therefore, the density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]

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Answer:

initial speed (u)= 0m/s (at rest)

final speed (v)= 20m/s

time taken (t)= 2seconds

we have,

acceleration;a= (v-u)/t

=(20-0)/2

=10m/s²

Answer:

[tex]10\frac{m}{s^{2}}[/tex]

Step-by-step explanation:

Let u = Initial speed [tex](\frac{m}{s})[/tex]

     v = Final speed [tex](\frac{m}{s})[/tex]

     t = time (seconds)

     a = Acceleration

According to this question:

[tex]u= 0 \frac{m}{s}[/tex] (i.e starts at rest)

[tex]v = 20 \frac{m}{s}[/tex]

[tex]t = 20s[/tex]  

a = ?

[tex]a = \frac{v - u}{t}[/tex]

  = [tex]\frac{20 \frac{m}{s} - 0\frac{m}{s}}{2s}[/tex]

  = [tex]\frac{20\frac{m}{s}}{2s}[/tex]

Acceleration= [tex]10\frac{m}{s^{2} }[/tex]

By multiplication, we know that the product of the numbers 6 and 4 1/12 comes between the whole numbers 24 and 25 respectively.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication.

Multiply in mathematics refers to the continual addition of sets of identical sizes.

One of the fundamental mathematical processes is multiplication.

The result of multiplying two or more numbers together is known as the product.

So, we have:
6 * 4 1/12

6 * 48+1/12

6 * 49/12

49/2

24.5

Which is: 24 < 24.5 < 25

Therefore, by multiplication, we know that the product of the numbers 6 and 4 1/12 comes between the whole numbers 124 and 25 respectively.

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Answer:

18 Square inches

Step-by-step explanation:

Surface Area of original prism: 54 square inches

Surface Area of similar prism:

1/3 x 54

=18 square inches

Answer:

There are several factors that can cause ordinary least square (OLS) estimates of a simple regression model, y = β0 + β1x + u, to be biased:

1. Non-random sampling: If the sample used in the regression analysis is not random, then the OLS estimates may be biased. For example, if the sample only includes people who live in a specific area or only those who are a certain age, then the estimates will not be representative of the population as a whole.

2. Endogeneity: If one of the independent variables in the model is correlated with the error term, then the OLS estimates will be biased. This occurs when there is a omitted variable that is related to both the dependent variable and one of the independent variables.

3. Multicollinearity: When two or more independent variables in the model are highly correlated with each other, it can cause the OLS estimates to be biased. This occurs because the estimates become unstable when the variables are highly correlated.

4. Non-constant variance: If the variance of the errors in the model is not constant, then the OLS estimates will be biased. This occurs when the errors are not homoscedastic.

5. Specification error: If the wrong variables are included or excluded from the model, then the OLS estimates will be biased. This occurs when the model is misspecified.

The value of p is 15

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Davey reads 58 pages on Saturday and on rest of the days p pages per day

Therefore everyday he reads 58+p pages per day

If he reads for 10 days and he reads a total 1408 pages then we have

In a week there is one Saturday

thus

9p+58=1408

9p=1350

p=15

Thus on the other days p is equal to 15 pages per day.

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The complete question is Davey reads 58 pages on Saturday and p pages on other days and on a span of 10 days he reads 1408 pages. Find the value of p.

Step-by-step explanation:

what is the total number of students in the class?

a)The probability that daily production is less than 27.6 liters is given by the equation P ( x < 27.6 ) = 0.014179

b) The probability that daily production is more than 49.4 liters is given by the equation P ( x > 49.4 ) = 0.02275

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the probability that daily production is less than 27.6 liters be represented as P

Now , the equation will be

a)

The observed value of x = 27.6 L

The mean of the sample μ = 39 L

The standard deviation of the sample σ = 5.2 L

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 27.6 - 39 ) / 5.2

z = -2.19231

Now ,the p value from the z table is

P ( x < 27.6 ) = 0.014179

And , the probability is P ( x < 27.6 ) = 0.014179 = 1.418 %

Therefore , the probability that daily production is less than 27.6 liters is given by P = 1.418 %

b)

The observed value of x = 49.4 L

The mean of the sample μ = 39 L

The standard deviation of the sample σ = 5.2 L

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 49.4 - 39 ) / 5.2

z = 2

Now ,the p value from the z table is

P ( x < 49.4 ) = 0.97725

P ( x > 49.4 ) = 1 - P( x < 49.4 ) = 0.02275

And , the probability is P ( x > 49.4 ) = 0.02275 = 2.275 %

Therefore , the probability that daily production is more than 49.4 liters is given by P₁ = 2.275 %

Hence , the probabilities are solved

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Answer:

The probability of selecting a peach is 8/14, or approximately 0.57.

The probability of not selecting a peach is 6/14, or approximately 0.43.

The total of these two probabilities is 1, because any given selection must either be a peach or not a peach.

The probability of selecting a plum cannot be determined because the number of plums in the bowl is not specified.

The sum of the probabilities of selecting a peach and a plum cannot be determined for the same reason as in 4.

Step-by-step explanation:

The probability that a randomly selected student is male, given that the student speaks french is 0.3636.

Total number of student in a maths class is 25.

Out of those 25 students 14 are females.

And the remaining student 11 are male

The number of students who can speak French are from female side 7 and from male side is 4

So total number of students who can speak french is 11

Using the probability formula,

P = favorable outcome/Total

Probability that a randomly selected student is male, given that the student speaks french is,

P = 4 / 11

P = 0.3636

Therefore, The probability that a randomly selected student is male, given that the student speaks french is 0.3636.

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Answer:

Part A: The Interquartile Range for the males' data is estimated to be around 24-28.

Part B: The difference between the median values of the two data sets is estimated to be around 16.

Part C: Both the male and female data sets appear to follow a normal distribution. Due to the outlier present in the male data set, the mean would not be the best measure of center for this data set. Instead, the median would be a more appropriate measure of center for both data sets.

Part D: The possible reason for the outlier in the data set could be that the movie was more popular among male viewers on the day they chose to attend than it was among female viewers.

Answer:

b = -10

Step-by-step explanation:

Two vectors are orthogonal if and only if their dot product is zero. The dot product of v and w is given by:

(v · w) = (5i + 2j) · (4i + bj) = 5 * 4 + 2 * b = 20 + 2b.

For v and w to be orthogonal, we need the dot product to be zero, which means 20 + 2b = 0, so:

2b = -20

b = -10

Therefore, b = -10 makes the vectors v and w orthogonal.

If  a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting

a) 0 defective resistors: 0.3164

b) 1 defective resistor: 0.4219

c) 3 defective resistor: 0.0469

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Probability

First step is to calculate the probability for a defective resistor and non-defective resistor:

Probability=3/12

Probability =0.25

Non-defective resistor:

Probability=(1-0.25)

Probability=0.75

Now  let find the probabilities for defective resistors from 0 to 3

P(0)=1(0.75)^4 ×(0.25)^0

P(0)=0.3164

P(1)=4(0.75)^3× (0.25)^1

P(1)=0.4219

P(2)=6(0.75)^2× (0.25)^2

P(2)=0.2109

P(3)=4(0.75)^0×(0.25)^3

P(3)=0.0469

P(4)=1(0.75)^0 × (0.25)^4

P(4)=0.0039

Hence,

a. P(0)=0.3164

b. P(1)=0.4219

c. P(3)=0.0469

Therefore If  a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting 0 defective resistors: 0.3164, 1 defective resistor: 0.4219, 3 defective resistor: 0.0469.

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L line

-2

-1

-15.5

-3.5

grph

Answer:

Below

Step-by-step explanation:

x = price last year

x * .096 = price increase   (.096   is 9.6% in decimal form)

price THIS year  is    x     +    x * .096  

                                = 1.096 x

so:

86.80 = 1.096 x     divide both sides of the equation by 1.096

  79.20 = x = original price

The answer choice which is equivalent to sec (x) among the given answer choices is; 1 / cos(x).

It follows from the task content that the answer choice which is equivalent to sec (x) is to be determined among the given answer choices.

From trigonometric ratios concept, it follows that the inverses of the 3 basic trigonometric ratios are as follows;

1 / sin x = csc (x)

1 / cos x = sec (x)

1 / tan x = cot (x)

On this note, it follows that the answer choice which is equivalent to sec (x) is; 1 / cos x.

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Complete the table representing a linear function with y = 10 and x = 9

The general form of a linear function is:

y = mx + c,

where m is the slope and c is the y-intercept

slope(m) = (y2-y1)/(x2-x1)

From the table:

point 1: x1 = 1, y1 = 0

point 2: x2 = 5, y2 = 40

slope(m) = (40-0)/(5-1) = 40/4 = 10

For the missing points:

x1 = 1, y1 = 0 and x2 = 2, y2 = y (unknown)

m = (y2-y1)/(x2-x1)

10 = (y-0)/(2-1)

10 = y/1

y = 10

x1 = 1, y1 = 0 and x2 =  x (unknown), y2 =90

m = (y2-y1)/(x2-x1)

10 = (90-0)/(x-0)

10 = 90/x

10x = 90

x = 90/10

x = 9

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Using the arithmetic operation of division, the value for expression 43.94 ÷ 5.2 is 8.45 where decimal point is before 4 and after 8.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The expression is given as - 43.94 ÷ 5.2

Use the arithmetic operation of division -

43.94 / 5.2

Remove the decimal point by multiplying the numerator and denominator by 100.

(43.94 × 100) / (5.2 × 100)

4394 / 520

Now perform the operation of division -

4394 / 520 = 8.45

June says the decimal point should be after 4.

She is incorrect as the result shows that the decimal point is before 4.

Therefore, June is incorrect in her statement.

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When a distribution is tilted to the left, the correct response is "mean median".

The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey. The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean.

Here,

For a distribution that is skewed left, it means that the values tend to be clustered towards the lower end of the scale and there is a long tail towards the higher end. In such a distribution, the mean is usually lower than the median.

So, the correct answer is "mean < median" when a distribution that is skewed left.

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Check the picture below.

now, we're assuming the street is a straight line and the line above the 100° is also another straight line, so hmmm the shaded polygon is really a 6-sided polygon, a hexagon.

[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 \\\\\\ 142+72+148+130+80+\measuredangle 1=720\implies 572+\measuredangle 1=720\implies \boxed{\measuredangle 1=148}[/tex]

The domain of the graphed function is interpret as follows:

The domain represents a 10-month period of flower production.

The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.

The input variable, represented by the x-axis, is defined as follows:

Number of Months.

Hence the correct option is given by the fourth option, as x ranges from 0 to 10.

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the value of x is  16.97

Given that:

The right angled triangle has hypotenuse of 18 units

Its one other side measures 6 units.

The length of unknown side is denoted by length x units.

To find:

Value of x

The Pythagoras theorem states that:

"In a right angled triangle, the square of length of its hypotenuse is equal to sum of square of other two sides' lengths"

Using Pythagoras theorem for given right triangle we have:

Thus, for given right triangle, the value of x is given as:

18²=[tex]x^{2} +[/tex]6²

324=[tex]x^{2}[/tex]+36

[tex]x^{2}[/tex]=324-36

[tex]x^{2}[/tex]=288

[tex]x[/tex]=√288

[tex]x[/tex]=16.97

the value of x is  16.97

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Each population must be at least 10 times as large as its corresponding sample of the following checks must be made .

What does confidence interval mean?

When you conduct your experiment again or resample the population in the same way, you may anticipate your estimate to fall inside a specific range of values a certain proportion of the time. This is known as the confidence interval.

What does the term "confidence interval" mean?

A 95% confidence level in statistics simply means that the researcher has seen one conceivable interval from a vast number of possible ones, from which 19 out of 20 intervals contain the true value of the parameter.      

                              Confidence intervals are used by statisticians to assess a sample variable's level of uncertainty.

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Answer:

Step-by-step explanation:

4(x+11)

The number of vendors selling maize or gari Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. 16 sell wheat and maize, 10 sale gari and rice, 42 sell maize, and 6 sell gari.

To assess the trading strategies used by traders to complete a trade transaction, mathematical analysis is employed. Moreover, probability theory is used to evaluate the usefulness of money management strategies.

Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. Ten sell rice and gari, sixteen sell rice and maize, and forty-two sell maize.

Determine the quantity of dealers selling gari of corn using the formula below:

P(G ∪ R ∪ M) = P(G) + P(R) + P(M) - P(G ∩ R) - P(R ∩ M) - P(G ∩ M) + P(G ∩ R ∩ M)

59 = 26 + 8 + 15 - 10 - 16 - P(G ∩ M) + 42

59 - 42 = 49 - 26 - P(G ∩ M)

P(G ∩ M) =  - 17 + 23

P(G ∩ M) = 6

Hence, there are 6 dealers selling gari or corn.

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The factorization of the given quadratic equation by grouping is (2y + 1) (4y + 1)

Factorization is a method of finding factors for any quadratic expression, polynomial, or algebraic expression.

For a polynomial of the form ax^2 + bx + c, rewrite the middle term as a sum of two terms whose product is a×c = 8 × 1 = 8 and whose sum is b = 6.

Given that:

8y² + 6y + 1

8y² + 2y + 4y + 1

Factor out the greatest common factor from each group.

2y(4y + 1) + 1(4y + 1)

(2y + 1) (4y + 1)

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Answer:

Below

Step-by-step explanation:

For compounding annually , the formula would be

4x  =  x  ( 1+ .1)^n      x = deposit amount    4x = quadrupled

                    i = decimal interest (.10)      and n = years

  you can divide 'x' out of the equation to get :

4 = (1.1)^n     solve for 'n'  by taking LOG of both sides

log 4 = n log 1.1

log 4/log 1.1 = n = 14.54 years  - ~~ 15 years

The sum of two consecutive integers 157 can be found by using the formula: x + (x + 1) = 157, where x represents the first integer.

Solving for x:

x + (x + 1) = 157

2x + 1 = 157

2x = 156

x = 78

So, the two consecutive integers are 78 and 79. The product of these integers is 78 * 79 = 6162.

Answer:

6162.

Step-by-step explanation:

Let's call the two consecutive integers x and x + 1. We know that their sum is 157, so we can write an equation:

x + (x + 1) = 157

Expanding and solving for x:

2x + 1 = 157

2x = 156

x = 78

So, the two consecutive integers are 78 and 79. The product of these integers is 78 * 79 = 6162.

The equation of line is y = -4x + 100 and the temperature of the coffee after 10 minutes is given by A = 60°C

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the temperature be represented as y

Let the number of minutes be represented as x

Now , the initial temperature is 100°C

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 100 )

Let the second point be Q ( 5 , 80 )

Now , the slope of the line between the points is ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 100 - 80 ) / ( 0 - 5 )

Slope m = 20 / -5

Slope m = -4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 100 = -4 ( x - 0 )

y - 100 = -4x

Adding 100 on both sides of the equation , we get

y = -4x + 100

Now , when x = 10 minutes ,

y = -4 ( 10 ) + 100

y = -40 + 100

y = 60°C

Hence , the equation is solved and temperature after 10 minutes is 60°C

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