Arrange the values in ascending order

Answer:

Since it's increasing add 3.5% to 100%

= 103.5% of £16470.45

= 103.5/100 × 16470.45

= 17046.92

= £17046.92

Hope this helps.

Answer:

The answer is option B, reflected over the y-axis and translated 2 units down.

If a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

In forensic science, the angle of impact is the angle at which a blood droplet strikes a surface. It has a range of 0 to 90 degrees and is, by definition, an acute (or right) angle.

Police can partially reconstruct a crime scene by connecting the "strings" that lead from the spatter to an origin area and knowing the angle of contact.

If a bloodstain has a tail or pattern, the angle of impact can be used to forecast how the subsequent bloodstain would look.

So, bloodstain pattern analysis examines the patterns of bloodstains found at crime scenes in an effort to piece together the sequence of events that led to the bloodshed.

Mathematically, we will have:

The angle of impact = sin⁻¹ (wide stain/length stain)

The angle of impact = sin⁻¹ (1.5/3.0)

The angle of impact = 30°

Therefore, if a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

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The differential equation y″ + y′ + 4xy = 0 can be solved using a power series centered at x = 0. It means that we can represent y as a power series of x, i.e.,y = a0 + a1 x + a2 x2 + · · · (1).

Then, taking the derivative of (1) and substituting it into the differential equation, we get, 

y″ + y′ + 4xy = 0(a1 + 2a2x + 3a3x2 + · · ·) + (a1 + 2a2x + 3a3x2 + · · ·) + 4x(a0 + a1x + a2x2 + · · ·) = 0

Grouping the terms with the same power of x,

we get 0: 2a2 + a1 + 4a0 = 0 1: 3a3 + 2a2 + a1 = 0 n: (n + 1)an + nan−1 + (4 − n2)an−2 = 0 (for n ≥ 2).

These equations are called recursive formulas. They can be used to obtain the coefficients of the power series. In this case, we know that the power series solution converges for all x. Hence, we can use any value of n to obtain the coefficients. For simplicity, we will choose n = 0. Then, from equation 0, a0 = −a1/4.

Substituting this into equation 1, we get a1 = −2a2/3. Substituting these two into the recursive formula for n = 2, we get 

4a2 = −6a0 = 3a1a2 = 3a1/2a3 = 0

Thus, the first four non-zero terms of the power series are,

y = a0 − (a1/4)x + (3a1/32)x2 + · · ·

The recursive formula for the differential equation

y″ + y′ + 4xy = 0 is, an+2 = (n2 − 4)an/(n + 1)(n + 2).

Thus, the first four non-zero terms of each independent solution are,

y1 = 1 − x2/4 + 3x4/64 − 5x6/2304 + · · ·y2 = x − x3/3 + x5/30 − x7/630 + · · ·

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Answer:

1,4,9,25,36,49,64,81,100,121,144

Question: What numbers make up the perfect squares

Answer:  

A perfect square is a number that can be expressed as the product of two equal integers.

Step-by-step explanation:

9 9 is a perfect square because it can be expressed as 3 * 3 (the product of two equal integers) 16 16 is a perfect square because it can be expressed as 4 * 4 (the product of two equal integers)

50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

Given data: The average time it takes for Susan to get to her class is 50 minutes. And the standard deviation is 5 minutes. We have to find the proportion of Susan's trips to class would take more than 50 minutes.

Solution:To find out the required proportion, we need to calculate the Z-score first.

\(Z-score = (X - μ)/σ\)

where, X = the value of the random variable (Susan's time to get to class)

μ = the population mean (average time)σ = the standard deviation

Here, X = 50 minutes

μ = 50 minutes

σ = 5 minutes

Z-score = (X - μ)/σ

= (50 - 50)/5

= 0

The Z-score table indicates that the area under the standard normal distribution curve for a Z-score of 0 is 0.5. Therefore, 50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

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Answer:

4

Step-by-step explanation:

..........................

I think its 30!

Please let me know if its right!

The value of the definite integral ∫\(x????"(x)????(x) dx\) on the interval \([1,4]\) is -5.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.

The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

Given that ????(1) = 8, ????(4) = 7, ???? '(1) = 9, and ???? '(4) = -3, we can use the method of integrating by parts to evaluate the definite integral ∫\(x????"(x)????(x) dx\) on the interval [1, 4].

Let u = ????(x) and dv = x dx. Then du = ???? '(x) dx and v = x^2/2.

Using the method of integrating by parts, we have:

∫\(x????"(x)????(x) dx= x????(x)\) ×\(\frac{x}{2} -\)∫\((\frac{x^{2} }{2} )????'(x) dx\)

We can use the same method of integrating by parts to evaluate the second integral on the right-hand side. Let \(u=\frac{x^{2} }{2}\) and \(dv=????'(x) dx\). Then \(du=x dx\) and \(v=????(x)\).

So we have:

∫\(x????"(x)????(x) dx = x????(x)\)× \(\frac{x}{2} - \frac{x}{2} ^{2}????(x) + c\)

Where C is an arbitrary constant of integration.

We can use the given values of ????(1) and ????(4) to evaluate the definite integral:

∫\(x????"(x)????(x) dx\) = 4????(4) * 4/2 - (4^2/2)????(4) + 4????(1) * 1/2 - (1^2/2)????(1)

= 28 - 14 * 7/2 + 4 * 8/2 = 28 - 49 + 16 = -5.

Therefore, the value of the definite integral ∫\(x????"(x)????(x) dx\) on the interval [1, 4] is -5.

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Domain are the x values where the line starts and stops.

A bracket is used for a solid circle and a parentheses is used for open circles

The answer would be the second choice: (1,2)

Answer:

A

Step-by-step explanation:

Answer: the two numbers are in the question

Step-by-step explanation:

i took the test

The SymPy function that is used to display a graph of a mathematical function is plot().

SymPy is a Python library for symbolic mathematics that aims to become a full-featured computer algebra system while keeping the code as easy as possible in order to be comprehensible and easily extensible.

A plot is a graphical representation of a function or data set that is drawn in a coordinate plane. It allows you to see patterns and trends in your data that may not be apparent from looking at a list of numbers. SymPy is a Python library for symbolic mathematics that includes the plot() function for generating plots of mathematical functions.

To illustrate, the following code generates a plot of the function y = x^2 over the domain [-5,5].

Code:from sympy import plot, symbols, cosx = symbols('x')plot(x**2, (x, -5, 5))

The plot() function has the following arguments:

x: The mathematical expression for the function to plot.

(x, a, b): The tuple specifying the variable x and the domain [a,b].

The plot() function also accepts a number of other optional parameters for customizing the plot, such as the title, labels, and line style.

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Answer:

D) 12 1/14

Step-by-step explanation:

6 2/7+5 11/14

1)

6+5=11

2)

2/7+11/14=

2/7 x 2/2=4/14

3)

4/14+11/14=15/14

4)

15/14= 1 1/14

5)

11+ 1 1/14= 12 1/14

Answer:

The answer to the question is D

Step-by-step explanation:

Answer:

equation 'b':  y = -3/4x + 5

equation 't':  y = 4/3x - 2

Step-by-step explanation:

parallel lines must have the same slope

the slope of perpendicular lines must be opposite and reciprocal

The two trapezoids in the figure are similar. Thus, the value of x would be equal to 33.

A trapezoid is a quadrilateral with at least one pair of sides parallel.

The two trapezoids in the figure are similar.

Since the figures are similar, the corresponding sides have the same ratio.

Here, the side must be proportional

So,

\(\sf \dfrac{40.5}{x}=\dfrac{54}{44}\)

\(\sf 1782=54x\)

Divide 54 on both sides

\(\sf x= \dfrac{1782}{54}\)

\(\sf x=33\)

Thus, the value of x is 33.

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Sanjay’s statement that if a line has a slope of zero, then it never touches the x-axis is incorrect.

The line y = 2 is a good example to prove it. It has a slope of zero and passes through the x-axis.

An equation in slope-intercept form for a line can be written as y = mx + b, where m is the slope of the line, and b is the y-intercept. Since the slope of the line is zero, this implies that the line is horizontal. This means that the line is parallel to the x-axis, and its y-coordinate doesn't change. Therefore, a horizontal line always intercepts the y-axis and x-axis.

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The probability that the first drawing gives green ball and second drawing a red ball is 2/7

Number of green balls = 4 green balls

Number of red balls = 4 red balls

Total number of balls in the bag = 4 + 4

= 8 balls

The probability = Number of favorable outcomes / Total number of outcomes

The probability of getting green balls in first draw = 4 / 8

= 1/2

First ball drawn was not replaced before drawing the second one

The probability of getting red ball in second draw = 4 / 7

The probability that the first drawing gives green ball and second drawing a red ball = (4/8) × (4/7)

= 2/7

Hence, the  probability that the first drawing gives green ball and second drawing a red ball is 2/7

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The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer:

412.3 feet

Step-by-step explanation:

A canoe rental shop is being built near a river. An equation of the line representing the river is y=1/4x+8. Each unit in the coordinate plane corresponds to 100 feet. Approximately how far is the canoe rental shop from the river? Round your answer to the nearest whole foot. The rental shop is at (-3,3).

Solution:

The distance between a point and a line is the perpendicular distance. The perpendicular distance is the shortest distance between the point and the line.

Given a point (\(x_1,y_1\)) and a line with the equation Ax + By + C = 0, the perpendicular distance (d) is given as:

\(d=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }\)

Given the equation of the line y = 1/4 x + 8

y - 1/4 x - 8 = 0

Therefore A = -1/4, B = 1 and C = -8

The point is (-3,3), therefore \(x_1=-3,y_1=3\)

\(d=\frac{|-1/4(-3)+(1*3)+(-8)|}{\sqrt{(-1/4)^2+1^2} }\\\\d=4.123\ unit\\\\but\ 1\ unit=100\ feet\\\\ d=4.123\ unit*1\ feet=412.3\ feet\)

Answer:

412.3 feet

Step-by-step explanation:

Answer:

The transformations of f(x) are 5 units to the right, and 3 units up

Step-by-step explanation:

If g(x) = x

then f(x) = (x-5) + 3

When we have (x-y) inside parentheses, the graph moves left

If it's (x + y) then the graph moves right

With (x) + y the graph moves up

And (x) - y the graph moves down

Here we have (x-5), meaning that the graph moved 5 units to the right

and we have + 3, which means that the graph moved 3 units up

So, the transformations of f(x) are 5 units to the right, and 3 units up

If the map shows that the school is 3 inches from home , that means the Harper home is 4.47 yards away from the school .

In the question,

it is given that

the 34 inches in map is equal to 50 yards in real .

So , 34 inches = 50 yards

1 inches = 50/34 yards

So, 1 inch = 1.47 yards

given that the the distance is 3 inches in map , then in real it will be

3 inch = 3*1.47 yards

= 4.47 yards

Therefore , If the map shows that the school is 3 inches from home , that means the Harper home is 4.47 yards away from the school .

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Answer:

37.20 P=0.7+2.20

Step-by-step explanation:

There is no sufficient evidence to indicate the true standard deviation is less than 4000

What is standard deviation ?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

given that n = 16

x = 60139.7

s = 3718.06

∝ = 0.05

To test the hypothesis

H0 : = 4000

H1 :  < 4000 (claim)

test statistics

x² = ((n-1)s²) / H0²

   = (15 * 13823970.16) / (16000000)

   = 12.96

P- value = P [x² < 12.96]           DF = n-1 = 15

             = 0.3946

0.1 < P-value <0.5

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Answer:

i hated doing those

Step-by-step explanation:

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To find the domain and range of functions and represent them in different formats.

To find the domain and range of a function:

The domain refers to the set of all possible input values (x-values) for the function.

The range refers to the set of all possible output values (y-values) for the function.

To represent the function as a table, you would list the input-output pairs. For example:

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

To represent the function as a mapping, you would indicate the correspondence between the input and output values.

For example:

-3     ->   -4

-1     ->     2

0     ->     0

-3    ->     5

2     ->     4

To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.

The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.

Hence, The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

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Answer:

She will have $24 remaining.

Step-by-step explanation:

5/8 of 64 is 40

Subtract 40 from the original number, 64

You get 24