(Please help) Solve.

-4+4(-8+2n) = -37+8n

Answer:

72

Step-by-step explanation:

because 60 * 0.05 is 3

3*4=12

60+12=72

y = (At + B) e^(rt)

where A = -r/2 and B = 3r/2, as expected.

When the two roots of the characteristic equation are both equal to r, we say that the roots are equal or repeated. In this case, the general solution to the corresponding second order linear homogeneous ODE with constant coefficients is of the form:

y = (At + B) e^(rt)

where A and B are constants to be determined by the initial or boundary conditions.

However, the form given in the question, (at+b)âe^rt, is not correct. The â symbol is not standard notation for mathematical expressions and its meaning is unclear. It is possible that it was intended to represent a coefficient or parameter, but without more information, we cannot determine its value or significance.

To see why the correct form of the solution is y = (At + B) e^(rt), we can use the method of undetermined coefficients. Suppose that y = e^(rt) is a solution to the homogeneous ODE with repeated roots. Then, we can try the solution y = (At + B) e^(rt) and see if it satisfies the ODE.

Taking the first and second derivatives of y, we get:

y' = A e^(rt) + r(At + B) e^(rt) = (Ar + r(At + B)) e^(rt)

y'' = A r e^(rt) + r^2(At + B) e^(rt) = (Ar^2 + 2rAt + r^2B) e^(rt)

Substituting y, y', and y'' into the homogeneous ODE with repeated roots, we get:

(Ar^2 + 2rAt + r^2B) e^(rt) = 0

Since e^(rt) is never zero, we can divide both sides by e^(rt) to get:

Ar^2 + 2rAt + r^2B = 0

This is a linear equation in A and B, and we can solve for them by using the initial or boundary conditions. For example, if we are given that y(0) = 1 and y'(0) = 0, we have:

y(0) = A e^(0) + B e^(0) = A + B = 1

y'(0) = (Ar + rB) e^(0) + A e^(0) = Ar + A = 0

Solving this system of equations, we get:

A = -r/2, B = 3r/2

Therefore, the general solution to the homogeneous ODE with repeated roots is:

y = (-rt/2 + 3r/2) e^(rt)

which can be rewritten as:

y = (At + B) e^(rt)

where A = -r/2 and B = 3r/2, as expected.

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Answer:

Her mother

Step-by-step explanation:

1.8 KM is less then 2.1 KM

Answer: 300

Step-by-step explanation:

From the question, we are informed that Mr Gaines is catering his company picnic and that he will pay $18.45 for 3 people to eat the barbecue lunch. This means each person spends:

= $18.45/3

= $6.15

With a budget of $1850.00, the number of people that he'll be able to feed will be:

= $1850/$6.15

= $300 people

Answer:

49/30

Or

1 19/30

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

6 times 8 =48

   4            4

4/48=12

Answer:

63

Step-by-step explanation:

Answer:

B,C, and E

Step-by-step explanation:

Got it right on the assignment

If the yearly cost for the dental claims are normally distributed , then the yearly cost at which 35% of the employee fall at or below is $91.35  .

In the question ,

it is given that ,

the yearly cost for the dental claims are normally distributed ;

and the mean (μ) is 105 , standard deviation(σ) is 35 .

we know that the z value that corresponds to 35th percentile from standard normal table is : z = -0.385  ;

let the yearly cost be "x" ;

the yearly cost can be calculated using the formula ;

x = z×(σ) + μ

x = (-0.385)×35 + 105

Simplifying further ,

we get ;

x = 91.525

x ≈ 91.53

Therefore , the correct option is (d) 91.53  .

The given question is incomplete , the complete question is

The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of $105 and a standard deviation of $35. what is the yearly cost at which 35% of the employees fall at or below is ?

(a) $118.48

(b) $127.29

(c) $82.71

(d) $91.53

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The correct pointers are as follows:

17: The student performed better on the new GRE because their percentile rank is higher than the old GRE. (The statement in the question is incorrect.)

18: Yes, z-scores can be used to compare scores that were scored on different scales or different units of measurement. (The first statement is the correct answer.)

Based on the provided information, the student performed better on the new GRE compared to the old GRE. This conclusion is drawn from the percentile ranks of the two scores.

The old GRE score has a percentile rank of 70.88%, while the new GRE score has a percentile rank of 97.72%. A higher percentile rank indicates a better performance relative to other test takers. Therefore, the student performed better on the new GRE because their percentile rank is higher.

Z-scores can be used to compare scores that were measured on different scales or different instruments of measurement. Z-scores standardize the data by converting it into a common scale, allowing for meaningful comparisons.

By using z-scores, we can analyze the raw data without the need for standardization. Therefore, the statement "Yes, because z-scores show us the raw data without needing to standardize it" is incorrect. Z-scores enable us to compare measurements across different scales or instruments by placing them on the same standardized scale.

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The two numbers that satisfy the given conditions are -12 and -2.

Let's represent the first number by "x" and the second number by "y". Based on the problem statement, we can set up two equations:

x = 2y - 8 (Equation 1) x² + y² = 52 (Equation 2)

Equation 1 represents the relationship between the two numbers as given in the problem statement. The first number is 8 less than twice the second number. Equation 2 represents the sum of squares of the two numbers, which is given as 52.

We can solve Equation 1 for x in terms of y:

x = 2y - 8 x + 8 = 2y y = (x + 8)/2

Now we can substitute this expression for y into Equation 2 and simplify:

x² + y² = 52 x² + [(x + 8)/2]² = 52 x² + (x² + 16x + 64)/4 = 52 4x² + x² + 16x + 64 = 208 5x² + 16x - 144 = 0

We now have a quadratic equation in terms of x. We can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 5, b = 16, and c = -144. Plugging these values into the formula gives us:

x = (-16 ± √(16² - 4(5)(-144))) / 2(5) x = (-16 ± √(16² + 2880)) / 10 x = (-16 ± √(2916)) / 10 x = (-16 ± 54) / 10

We get two possible values for x: x = 2.8 or x = -12. We can check these values by substituting them back into Equation 1 and seeing if they satisfy Equation 2. However, we notice that the first value is not a whole number, which suggests that it may not be a valid solution. Therefore, we will discard x = 2.8 and use x = -12.

Using x = -12 in Equation 1, we can solve for y:

x = 2y - 8 -12 = 2y - 8 -4 = 2y y = -2

So the two numbers are x = -12 and y = -2. We can check that these values satisfy Equation 2:

x² + y² = 52 (-12)² + (-2)² = 52

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Complete Question:

The sum of the squares of two numbers is 52. If the first number is 8 less than twice the second number, what are the numbers?

Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.

To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.

To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.

Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.

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The slope of the line passing through the points (0, 30) and (8, 18) is -1.5.

Given is a graph of a line passing through the points (0, 30) and (8, 18).

To find the slope of the line passing through two points, you can use the formula:

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

Let's use the points (0, 30) and (8, 18) to calculate the slope:

x1 = 0

y1 = 30

x2 = 8

y2 = 18

slope = (18 - 30) / (8 - 0)

= -12 / 8

= -1.5

Therefore, the slope of the line passing through the points (0, 30) and (8, 18) is -1.5.

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The average family size in Neighborhood Q is 2.7 while in Neighborhood S it is 3.7. Additionally, the maximum family size in Neighborhood Q is 6 while in Neighborhood S it is 5.

These facts suggest that Neighborhood Q has smaller families on average, but also has at least one significantly larger family compared to Neighborhood S.

The neighborhood that appears to have a bigger family size is Neighborhood S. To determine this, calculate the average family size for each neighborhood: Neighborhood Q has an average of (6+3+1+2+3+2+5+1+2)/9 = 25/9 ≈ 2.78 people per family, and Neighborhood S has an average of (5+2+4+3+5+3+2+4+5)/9 = 33/9 ≈ 3.67 people per family. Since 3.67 is greater than 2.78, Neighborhood S has a larger average family size.

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Answer:

2x - y = -8

Step-by-step explanation:

The magnitude and the direction angle of the vector are given as follows:

The points that define the vector are given as follows:

m(-15, 16) and n(2,-6).

Considering m as the starting point and n as the endpoint, the vector is defined by the subtraction of the coordinates of n by the coordinates of m, hence:

v = (2 - (-15), -6 - 16) = (17, -22).

The magnitude of the vector is given by square root of the sum of the squares of the components, hence:

|v| = sqrt(17² + (-22)²) = 27.80.

The direction angle is the arc tangent of the division of the vertical component of the vector by the horizontal component of the vector, hence:

θ = arctan(-22/17)

θ = -52.3.

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Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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Answer:

3.75

Step-by-step explanation:

just add 5 cent for each extra pop

The effects of the reduction in each statistical measure of the data-set is given as follows:

a. The shape of the data-set remains constant.

b. Both the mean and the median will be subtracted by 500.

c. The standard deviation and the IQR remain constant.

The shape of the distribution is related to how the distributions are spread around the mean.

Each observation will be reduced by $500, meaning that the spreads remain constant, hence:

The shape of the data-set remains constant.

The mean is the sum of the observations divided by the number of observations.

500 will be subtracted by each observation, hence the mean will be subtracted by 500.

The median is the middle value of the data-set. Since all values will be subtracted by 500, the middle value also will, hence the median will be subtracted by 500.

Both are measures of spread, as:

Since all measures change by the same amount, the difference between the percentiles will be the same, as will the differences squared between each observation and the mean, hence:

The standard deviation and the IQR remain constant.

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The equation of a line in slope-intercept form is  \(y = \frac{1}{8} x - \frac{41}{8}\) .

The equation of the line is given below using the slope-intercept method:

y = mx + c

where,

m = the slope of the line

c = y-intercept of the line

(x, y) represent any point on the line

To find the Slope of a line that passes through the points (2, 4) and (3, -4).

m₁ = change in y/change in x

    = y₂ - y₁ / x₂ - x₁

    = Δy/Δx

   = \(\frac{-4-4}{3-2}\)

   = \(\frac{-8}{1}\)

   = -8

Now, we find the slope of the line perpendicular to the line with the slope -8.

m₂ = -1 / m₁

    = -1 / -8

    = 1/8

So, the slope of the line is 1/8.

Next, we find the equation of a line that passes through the point (1, -5) and has a slope of 1/8.

⇒ y - y₁ = m( x- x₁)

⇒ y + 5 = \(\frac{1}{8}\) (x - 1)

Multiplying by 8 on both sides of the equation we get and then solving

⇒ 8y + 40 = x - 1

⇒ 8y = x - 41

 ⇒ \(y = \frac{1}{8} x - \frac{41}{8}\)

Therefore, the equation in slope intercept form is  \(y = \frac{1}{8} x - \frac{41}{8}\) .

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Answer:

13/15

Step-by-step explanation:

First, convert 6 1/4 to a common denominator, which is 12

6 1/4 = 6 3/12

4 1/12 - 6 3/12 = -2 1/6= -13/6

4 - 6 = -2

1/12 - 3/12= -1/6

Convert -2.5= -2 1/2= -5/2

-13/6 * -2/5 = --13/15

Negative and negative is positive, so the answer is 13/15

Answer:

Check pdf

Step-by-step explanation:

Step-by-step explanation:

Let the age of son be x then

By the question

Age of father = 3x

So Now

3x + x = 48

4x = 48

x = 48/ 4

x = 14 years

The age of the son is 14 years.

Hope it will help :)❤

Answer:

The mama bear can do it in 9

seconds. The cub can do it in 18

seconds.

Step-by-step explanation:

1/x+9+1/x=1/6

Using the together rate, it is found that it would take each bear 9 hours to open the car door alone.

The together rate is the sum of each separate rate.

In this problem, the rates are as follows:

Given

A tourist ignores the warning signs and leaves food in his car while he goes for a hike.

A mama bear and her cub open the car door in six seconds.

Together with rate: 1/6.

Mama's rate: 1/x.

Cub's rate: 1/(x + 9).

Therefore,

\(\rm \dfrac{1}{x}+\dfrac{1}{x+9}=\dfrac{1}{6}\\\\\dfrac{x+9+x}{x(x+9)}=\dfrac{1}{6}\\\\\dfrac{2x+9}{x(x+9)}=\dfrac{1}{6}\\\\ 6(2x+9)=x(x+9)\\\\12x+54=x^2+9x\\\\x^2+9x-12x-54=0\\\\x^2-3x-54=0\\\\ x^2+6x-9x-54=0\\\\ x(x+6)-9(x+6)\\\\(x-9)(x+6)=0\\\\x-9=0 \ x=9\\\\x+6=0 \ x=-6\)

The value of time can not be negative.

Hence, It would take each bear 9 hours to open the car door alone.

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Answer:

200 feet not 100% percent sure though

Step-by-step explanation:

The coefficient of the quadratic term is negative (-1), so the parabola opens downward.

The vertex is located at the point (1, 5).

the x-intercepts are -4 and 2.

the y-intercept is 8.

Axis of Symmetry is : x = 1.

graph is attached.

Here, we have,

To analyze the given quadratic equation, \($y = -x^2 - 2x + 8$\), we can determine its characteristics:

Direction of Opening:

The coefficient of the quadratic term is negative (-1), so the parabola opens downward.

Vertex:

To find the vertex, we can use the formula:

\($x = -\frac{b}{2a}$\), where a is the coefficient of \($x^2$\) and b is the coefficient of x.

In this case, a = -1 and b = -2.

Plugging these values into the formula, we get:

\($x = -\frac{-2}{2(-1)} = 1$\)

To find the corresponding y-coordinate of the vertex, we substitute the value of x into the equation:

\($y = -(1)^2 - 2(1) + 8 = 5$\)

Therefore, the vertex is located at the point (1, 5).

x-intercepts:

To find the x-intercepts, we set y equal to zero and solve for x:

\($-x^2 - 2x + 8 = 0$\)

This equation does not factor easily, so we can use the quadratic formula:

\($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$\)

In this case, a = -1, b = -2, and c = 8.

Plugging these values into the formula, we get:

\($x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(-1)(8)}}{2(-1)}$\)

\($x = \frac{2 \pm \sqrt{4 + 32}}{-2}$\)

\($x = \frac{2 \pm \sqrt{36}}{-2}$\)

\($x = \frac{2 \pm 6}{-2}$\)

Simplifying further, we have two solutions:

\($x_1 = -4$\) and \($x_2 = 2$\)

Therefore, the x-intercepts are -4 and 2.

y-intercept:

To find the y-intercept, we set x equal to zero and solve for y:

\($y = -(0)^2 - 2(0) + 8 = 8$\)

Therefore, the y-intercept is 8.

Axis of Symmetry:

The axis of symmetry is a vertical line that passes through the vertex. In this case, the line is x = 1.

To graph the equation, you can plot the vertex, the x-intercepts, the y-intercept, and then sketch the downward-opening parabola passing through these points.

graph is attached.

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Answer:

x= -1.8

Step-by-step explanation:

4x-22=9x+2(1-4x)

2(1 - 4x)

so you have to distribute

new equation

4x-22=9x+2-8x

you combine like terms on the right

9x + 2 -8

+8. +8

17x+2

new equation

4x-22=17x+2

-4x. -4x

-22=13x + 2

-2. -2

-24=13x

-24÷13= - 1.8

X= -1.8

Answer:

\(4x - 22 = 9x + 2 - 4x \\ - x = 24 \\ x = - 24\)

Answer:

Step-by-step explanation:

(x+4)² + y² = 1.5²

Since the p-value (0.0179) is less than the typical significance level of 0.05, we reject the null hypothesis. We have evidence to suggest that the true proportion of uninjured occupants in head-on collisions exceeds 0.25 based on the sample data.

To test whether the true proportion of uninjured occupants in head-on collisions exceeds 0.25, we can perform a hypothesis test using the given sample data.

Let's set up the null and alternative hypotheses:

Null Hypothesis (H₀):

The true proportion of uninjured occupants in head-on collisions is 0.25 or less.

Alternative Hypothesis (H₁):

The true proportion of uninjured occupants in head-on collisions exceeds 0.25.

To test these hypotheses, we can use the proportion test, assuming the conditions for the test are met (e.g., the sample can be considered random and independent, and the sample size is sufficiently large).

Let's calculate the test statistic (z-score) and p-value based on the sample data.

Sample proportion of uninjured occupants:

p = 95/319 = 0.2978

Sample size:

n = 319

Under the null hypothesis, assuming the true proportion is 0.25 or less, the expected proportion of uninjured occupants is 0.25.

The test statistic (z-score) can be calculated as:

z = (p - p₀) / sqrt((p₀ * (1 - p₀)) / n)

where p₀ is the assumed proportion under the null hypothesis (0.25), and n is the sample size.

Substituting the values:

z = (0.2978 - 0.25) / sqrt((0.25 * (1 - 0.25)) / 319)

z = 2.1185

To determine the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator. The p-value is the probability of observing a test statistic as extreme as the calculated z-value, assuming the null hypothesis is true.

The p-value associated with a z-score of 2.1185 is approximately 0.0179.

Finally, we can compare the p-value to the significance level (α) to make a decision. If the p-value is less than α (typically 0.05), we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

In this case, since the p-value (0.0179) is less than the typical significance level of 0.05, we reject the null hypothesis. We have evidence to suggest that the true proportion of uninjured occupants in head-on collisions exceeds 0.25 based on the sample data.

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