Solve the initial value problem yy' + x = x2 + y2 with y(3) = -V40. a. To solve this, we should use the substitution help (formulas) U = u' = help (formulas) Enter derivatives using prime notation (e.g., you would enter y' for dy dx b. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. help (equations) c. The solution to the original initial value problem is described by the following equation in x, y. help (equations)

The probability that the number of these selected teens that have heard of a fax machine is exactly six is 0.225 and the probability that the number is more than 8  is 0.064.

The first probability can be calculated using binomial distribution formula, where the number of success (teens who have heard of a fax machine) is 6 and the number of trials is 12. The probability of success is 0.49. The calculation is:

[tex](12 choose 6) * (0.49)^6 * (0.51)^(12-6) = 0.225[/tex]

The second probability can be found by summing the probabilities of having more than 8 teens out of 12 who have heard of a fax machine. This can be calculated using binomial distribution formula for 9, 10, 11, and 12 success. The calculation is:

[tex](12 choose 9) * (0.49)^9 * (0.51)^(12-9) + (12 choose 10) * (0.49)^10 * (0.51)^(12-10) + (12 choose 11) * (0.49)^11 * (0.51)^(12-11) + (12 choose 12) * (0.49)^12 * (0.51)^(12-12)\\ = 0.064[/tex]

So the answer is (0.225, 0.064).

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Water output rate of Chang family was 30 L per hour and the water output rate of Robinson family was 35 L per hour.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the water output rate of Chang family and y be the water output rate of Robinson family.

x + y = 65

25x + 15y = 1275

Multiplying the first equation throughout with 15,

15x + 15y = 975

Subtracting 15x + 15y = 975 from 25x + 15y = 1275,

10x = 300

x = 30

y = 65 - 30 = 35

Hence the water output rate of Chang family and the Robinson family is 30 L per hour and 35 L per hour respectively.

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The polynomial in this problem is factored as follows:

x² - 12x + 27 = (x + 9)(x + 3).

The polynomial for this problem is defined as follows:

x² - 12x + 27.

The format to factor the polynomial is given as follows:

x^2+(a+b)x+ab=(x+a)(x+b)

Which means that:

The two numbers that satisfy this are:

-9 and -3.

As a product of it's linear factors, the polynomial is factored as follows:

(x + 9)(x + 3).

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Answer:

SAS

Step-by-step explanation:

2 sides if 20in. , the middle one is the same for both, and both have 22° angles

14. A. The total area to be painted is 144 ft²

B. Total cost to paint wall is 12.8$

The shape of the wall to be painted is rectangular and to find out the area to be painted by subtracting the total area of the wall from the area of the door and the area of the window.

The total area of the walls painted is equal to X

Total wall area = T

door area is equal to D

The window area is equal to W

X= T - ( D+W)

X= (12*15) -((8*3) +(4*3))

X= 180-(24+12)

X=180-36

X= 144 ft²

Per 90ft² needs $8, so if you want to paint all 144ft² it will be

144 :90= 1.6

this 1.6 multiply with $8 =12.8$

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From the figure if PQRST~DEFGH then ∠P is 109 degrees and ∠F is 99 degrees.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given that PQRST is a polygon which is similar to the DEFGH

Similar polygons are two polygons with the same shape, but not the same size.

Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.

∠C≅∠T

∠P≅∠D

So ∠P is 109 degrees.

∠F is 99 degrees.

Hence, from the figure if PQRST~DEFGH then ∠P is 109 degrees and ∠F is 99 degrees.

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Answer:

[tex]-\frac{28}{3}[/tex]

Step-by-step explanation:

[tex]\frac{-3-(-1/5)}{(1/10)-(-1/5)}=-\frac{28}{3}[/tex]

a) The equation with infinite number of solutions is 3x + 9 = 3x + 9

b) The equation with no solution is 3x + 9 = 3x

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

3x + 9 = 0   be equation (1)

Now , when the value of an equation is 0 , we can solve for x

Subtracting 9 on both sides of the equation , we get

3x = -9

Divide by 3 on both sides , we get

x = -3

So , the value of x = -3 and has only one solution

Now , when the coefficients and the variables of the equation are same on both sides , we get

3x + 9 = 3x + 9

So , 3x = 3x

x = x

And , the equation have infinite number of solutions

Now , when the value of the equation is not defined or does not equates , we get

3x + 9 = 3x

Subtracting 3x on both sides of the equation , we get

9 = 0

So , the equation is false and has no solutions

Hence , the equations are solved

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The amount of money that is due after 4.5 years is equal to $7,754.4.

Mathematically, compound interest can be calculated by using this mathematical expression:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the compound interest formula, we have;

Future value, A(t) = 6,500(1 + 0.0396/2)^{2 × 4.5}

Future value, A(t) = 6,500(1 + 0.0198)^{9}

Future value, A(t) = 6,500(1.0198)^{9}

Future value, A(t) = 6,500(1.19298523508730964)

Future value, A(t) = $7,754.4.

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The percentage of data under the shaded region is 68%.

The 68 95 99 rule, commonly referred to as the empirical rule in statistics, asserts that given normal distributions, 68% of observed data points will fall within one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

From the given table the shaded region is one standard deviation away.

Therefore, By the empirical rule, the percentage of data underneath this normal curve is 68%.

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The graphed piecewise function is the one in option C.

y = x² + 2    if x < 1

y = -x + 2  if x ≥ 1

Here we can see the graph of a piecewise function.

The first part seems to be a quadratic function, with an y-intercept of 2, and ends with an open circle at x = 1, then we have something of the form:

quadratic equation for x < 1

And then we have a linear equation that has a closed circle at x = 1, so we have:

linear equation for x ≥ 1

Then the correct option is C.

y = x² + 2    if x < 1

y = -x + 2  if x ≥ 1

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[tex] \frac{1}{4} \sqrt{3} \: a {}^{2} [/tex]

Step-by-step explanation:

for equilateral triangle

Based on the survey results, the statement that is the most accurate is B. Students who play a sport do not tend to play a musical instrument.

A table where each cell shows the frequency (or proportion) obtained for that row and column combination for the two variables.

The rows represent the categories for one category variable, the columns represent the categories of a second category variable.

Hence, from the given two-way table, it is seen that the response of the students are recorded and the statement that is the most accurate is B. Students who play a sport do not tend to play a musical instrument.

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The table below shows the survey results of 100 students who were asked 2 questions: “Do you play a sport?” and “Do you play a musical instrument?” Based on the survey results, which statement is the most accurate?

Students who play a sport also tend to play a musical instrument.

Students who play a sport do not tend to play a musical instrument.

Students who do not play a sport tend to play a musical instrument.

Students who do not play a sport also tend not to play a musical instrument.

The line that goes between the coordinates (-6, 5) & (-3, -3) has the equation y = -8/3 x + 13, as stated in the question.

A line is an infinitely long, completely straight, one-dimensional form that has no thickness and may be drawn in both directions. In order to stress that a line has no "flutters" anywhere along its length, it is occasionally referred to as a straight line or, more formally, a straight line (Casey 1893).

y - y1 = m (x - x1)

By using formula :

m = (y2 – y1) / (x2 - x1)

In other (x1, Y1)& are the two pairs on the line (x2, y2).

m = ( -3 - 5) / (-3 - (-6)) = (-8) / (-3 + 6) = -8 / 3

Due to this reason, the line has a slope of -8/3.

Afterwards when, we may input either points (-6, 5) and slope (8/3), respectively, into the generate the result of both the line to obtain:

y - 5 = -8/3 (x - (-6))

Expanding the right-hand side, we get:

y - 5 = -8/3 x + 8

Finally, rearranging the terms, we get:

y = -8/3 x + 8 + 5

y = -8/3 x + 13

Consequently, the line's equation becomes y = -8/3 x + 13 and it passes through to the coordinates (-6, 5) & (-3, -3).

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The complete question is: Complete the equation of the line through (-6,5)(−6,5)left parenthesis, minus, 6, comma, 5, right parenthesis and (-3,-3)(−3,−3)left parenthesis, minus, 3, comma, minus, 3, right parenthesis.

The relative extrema for the following function. f (x )equals 3 x minus x cubed is (1, 2)

Using the first derivative test, you may check for any sign changes of f′ around the critical points of a given function and discover relative extrema, or local maxima and minima.

A critical point must transition from rising, or positive f′, to decreasing, or vice versa, at that point for the function to be said to have local extrema.

So, start by determining the first derivative of f,

f(x) = 3x-x³

f'(x) = 3 - 3x²

To determine the function's critical points,

f' = 0

3 - 3x² = 0

3x² = 3

x = 1

Putting value of 1 in f(x) = 3x-x³ = 3-1 = 2

So the local maxima is (1,2)

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a-1. The null hypothesis for the treatments is: μDay = μAfternoon = μNight

a-2. The alternate hypothesis for the treatments is: Not all means equal.

b. The decision rule for treatments is to use an analysis of variance (ANOVA) with a significance level of 0.05. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a difference in the mean production rate by shift.

c-1. The null hypothesis for the blocks is: μS = μL = μC = μT = μM

c-2. The alternate hypothesis for the blocks is: Not all means are equal. The decision rule for blocks is the same as for treatments, use an ANOVA with a significance level of 0.05. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a difference in the mean production rate by employee.

d & e. The ANOVA table is shown below:

Source SS df MS F p-value

Treatments 144.0 2 72.0 13.09 0.0047

Blocks 48.0 4 12.0 2.18 0.18

Error 60.0 8 7.5

Total 252.0 14

f-1. Based on the ANOVA results, we can reject the null hypothesis for the treatments (p-value = 0.0047 < 0.05) but not for the blocks (p-value = 0.18 > 0.05).

f-2. The results indicate that there is a difference in the mean production rate by shift, but there is not enough evidence to conclude that there is a difference in the mean production rate by employee. This suggests that the difference in production rate is due to the shift worked, rather than the specific employee.

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Total weight of the science project is, 158.3 pounds

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Aimee weighed the four parts of her science project at 42.6 pounds, 37.25 pounds, 29.45 pounds, and 49 pounds.

Hence, Total weight of the science project is,

⇒ 42.6 + 37.25 + 29.45 + 49 pounds

⇒ 158.3 pounds

Thus, Total weight of the science project = 158.3 pounds.

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Answer: [tex]\sqrt{2} *3i[/tex]

Step-by-step explanation:

1. separate using the radical rule

sqrt{-a}=sqrt{-1}\sqrt{a}

[tex]\sqrt{-18} = \sqrt{-1} *\sqrt{18}[/tex]

2. imaginary numbers

[tex]\sqrt{-1} = i[/tex]

3. solve the rest regularly

[tex]\sqrt{18} = \sqrt{2} *3[/tex]

4. combine

[tex]\sqrt{2} *3*i =\sqrt{2}*3i[/tex]

Mathematical induction is a method used to prove statements for all positive integers.

To prove the formula 1 + 2 + 3 + ... + (n-1) + n = n(n+1)/2 using induction,

we first show it holds for the base case n = 1.

When n = 1, the formula becomes 1 = 1(1+1)/2, which is true.

Then, we assume the formula holds for some integer k, and prove it holds for k+1.

Inductive step: Assume that the formula holds for some integer k, i.e., 1 + 2 + ... + (k-1) + k = k(k+1)/2. We need to prove that the formula also holds for k+1.

So, 1 + 2 + ... + (k-1) + k + (k+1) = k(k+1)/2 + (k+1) = (k+1)(k+2)/2, which shows that the formula holds for k+1 as well.

By repeating this process, we conclude the formula holds for all positive integers.

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The system of linear inequality to model the situation is as follows:

A system of linear inequality is two or more inequalities that can be solved simultaneously to make the inequalities valid.

Inequalities must have the inequality symbols, including:

The cost of soil per bag = $4.00

The cost of plants each = $10.00

The total number of plants ≥ 4

The total budget ≤ $80

Let the number of plants = p

Let the number of soil bags = b

p ≥ 4... Inequality 1

10p + 4b ≤ 80... Inequality 2

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Write the system of linear inequality to model the situation.

The mathematical expression, for the given mathematical phrase, 8 less than y times 28, is 8-28y

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, a mathematical phrase, 8 less than y times 28,

Converting it into a mathematical expression,

8-28y

Hence, the mathematical expression, for the given mathematical phrase, 8 less than y times 28, is 8-28y

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The limits lim csc(x) cot(x) and lim x→6 (x - 6) cos(x-6) can be solved using direct substitution.

The Squeeze Theorem is a way to solve limits without using direct substitution or other methods from the notes. This theorem states that given three functions f(x) ≤ g(x) ≤ h(x) and lim x→c f(x)=lim x→c h(x)=L, then it follows that lim x→c g(x)=L. This theorem is useful for situations where direct substitution is difficult or impossible to do. For example, the limit x→0 lim x cos(x) cannot be solved using direct substitution because the function cos(x) is undefined at x = 0. In this case, the Squeeze Theorem can be used to solve the limit. By defining a lower bound and an upper bound, we can use the Squeeze Theorem to conclude that lim x→0 lim x cos(x) = 1. The same is true for the limit x→0 lim x’ sin(1/x). By defining a lower bound and an upper bound, we can use the Squeeze Theorem to conclude that lim x→0 lim x’ sin(1/x) = 0.

The limit lim csc(x) cot(x) does not require the Squeeze Theorem and can be solved using direct substitution. By substituting x = 0 into both functions, we can see that the limit is equal to 1. Finally, the limit lim x→6 (x - 6) cos(x-6) does not require the Squeeze Theorem and can be solved using direct substitution. By substituting x = 6 into the function, we can see that the limit is equal to 0.

In conclusion, the limits lim x→0 lim x cos(x) and lim x→0 lim x’ sin(1/x) require the Squeeze Theorem and cannot be solved using direct substitution. The limits lim csc(x) cot(x) and lim x→6 (x - 6) cos(x-6) can be solved using direct substitution.

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Lindsay is more likely to think she sang more poorly than Nicole. It can be inferred that Lindsay is more likely to have negative self-evaluation despite the similar scores.

People with social anxiety disorder often have negative self-evaluations and experience intense self-consciousness in social situations, even if they have performed well. This can lead to feelings of shame, embarrassment, and low self-esteem.

So, even though Lindsay and Nicole received the same score, Lindsay's social anxiety disorder may cause her to believe that she performed poorly, despite receiving a high score. On the other hand, Nicole, not having social anxiety disorder, may be more likely to have a positive self-evaluation and feel confident about her performance, despite receiving the same score.

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Complete Question:

Both Lindsay and Nicole just completed a solo in a musical competition. The judges awarded them both 9 out of 10. Lindsay has a social anxiety disorder and Nicole does not. Based on this information,

____. what can be said?  

Answer:

Step-by-step explanation:

they cause heavy rain fall no problom

Answer:

There are 97 people who ate pizza last Friday night.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

We have

184 = watched TV

183 = hung out with friends

37 = watched TV and ate pizza, but did not hang out with friends

31 = watched TV and hung out with friends, but did not eat pizza

40 = hung out with friends and ate pizza, but did not watch TV

29 = watched TV, hung out with friends, and ate pizza

74 = he did not do any of these three activities

We need to find out the number of people eating pizza by deducting the number of people not eating pizza from the total number.

So the people not eating pizza are listed as A, B, D, G

Total = 549

Those who only ate pizza= total - (A+B+D+G)

                                          = 549- (184+183+37+31)

                                          = 549- 415= 97

There are 97 people who ate pizza, last Friday night.

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Alternate interior angles are never supplementary would be two parallel lines being intersected by a transversal, such that one pair of alternate interior angles measures 180 degrees (i.e., they are supplementary). This would show that the statement is false and that alternate interior angles can indeed be supplementary.

When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines.

A transversal intersection of two parallel lines produces same-side interior angles, whose sum is 180 degrees. As the sum of the same side interior angles is 180 degrees therefore the angles are supplementary.

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99% of the time, the student council president knows the names of 598 to 1058 students at that high school. This interval is 1000. So the president's claim is correct.

The interval is the range of numbers between two given numbers of it and includes all real numbers between the two numbers.

A real number is any number you can think of, such as 7.53, 172, 5, -0.157. As an example that can explain the interval itself, if someone says they have at least 5 books but less than 10, those book counts are included in the interval.

An interval is a series of numbers that can be written using inequalities, number lines, or interval notation. However, there is a special way of indicating whether two given numbers are within an interval, called endpoints.

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Answer:

Step-by-step explanation:

d

The area of the trapezoid is 1.56 square units

The area of trapezoid is calculated using the formula

= 1/2 (sum of bases) * height

= 1/2 (a + b) * height

In the problem the dimensions made available are

height =

base (a) = 1

base (b) = 1 3/5

substituting the values into the formula

= 0.5 (1 + 1 3/5) * 1 1/5

= 0.5 * 13/5 * 1 1/5

= 1.56 square units

The area of the trapezoid is 1.56 square units

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Answer:

$0.139/oz

$2.224/lb

Step-by-step explanation:

1 lb = 16 oz

10 oz × (1 lb)/(16 oz) = 0.625 lb

$1.39 for 10 oz of ketchup =

= $1.39 / 10 oz = $0.139/oz

= $1.39 / 0.625 lb = $2.224/lb