Q16. Find the value of sin 75º.​

Answer:

11 cans of cat food...........

Step-by-step explanation:

£0.79 x 11 = £8.69

£8.69 - £2 = 6.69

Answer:

Eleven (11) cans of cat food!

Answer:

x^3 + 4x^2 - 7x - 10

Step-by-step explanation:

To solve this we're going to use Polynomial multiplication, starting by multiplying (x-2)(x+1) = x^2 - 2x + x - 2 = x^2 - x - 2. Next, we will multiply (x^2 - x - 2)(x+ 5) = x^3 + 5x^2 -x^2 - 5x -2x -10 = x^3 + 4x^2 - 7x - 10.

Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

The statistical method that utilizes many separate correlations to determine which variables change in concert and can be considered functionally related is called 'principal component analysis' (PCA).

PCA is a technique used to identify patterns and relationships in multivariate data.

PCA aims to transform a set of possibly correlated variables into a smaller set of uncorrelated variables called principal components.

These components are linear combinations of the original variables and are ordered in such a way,

That the first component captures the maximum variance in the data,

The second component captures the maximum remaining variance orthogonal to the first component and so on.

By analyzing the correlations among the original variables,

PCA identifies the variables that change in concert and can be considered functionally related.

The variables that contribute most to each principal component are the ones that exhibit high correlations with each other.

And low correlations with variables in other components.

PCA helps to reveal underlying structure or dimensions in data, making it easier to interpret and understand relationships between variables.

Therefore, principal component analysis (PCA) is a statistical method that utilizes correlations among variables to identify which variables change in concert .

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Answer:

a) (tri)ABC ~ (tri)CDE

b) AA

Step-by-step explanation:

a) Given in the question (the triangles are similar)

b) AA similarity is found by the vertical angle at <ACB and <DCE and the marked angles at <D and <A.

Answer:

in simplest form=81/64

decimal=1.265625

a) The Odds of  pulling a red ball from the first bag is; 12.2%

b) The Odds of  pulling a red ball from the second bag = 10/85 = 0.1176 = 11.76%

We are given;

Number of white balls in first bag = 52

Number of green balls in first bag = 27

Number of red balls in first bag = 11

Total number of balls in first bag = 52 + 27 + 11 = 90 balls

Number of white balls in second bag = 25

Number of green balls in second bag = 25

Number of red balls in second bag = 10

Number of yellow balls in second bag = 25

Total number of balls in second bag = 25 + 25 + 10 + 25 = 85 balls

a) Odds(probability) of  pulling a red ball from the first bag = 11/90 = 0.122 = 12.2%

b) Odds(probability) of  pulling a red ball from the second bag = 10/85 = 0.1176 = 11.76%

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In ANOVA with 4 groups and a total sample size of 44, the computed F statistic is 2.33 and the p-value is d. cannot tell - it depends on what the SSE is. Therefore, the correct option is option d.

In an ANOVA with 4 groups and a total sample size of 44, with a computed F statistic of 2.33, to determine the p-value, we need to consider the degrees of freedom for both the numerator (between groups) and the denominator (within groups).

Step 1: Calculate the degrees of freedom.
Degrees of freedom between groups (DFb) = Number of groups - 1 = 4 - 1 = 3
Degrees of freedom within groups (DFw) = Total sample size - Number of groups = 44 - 4 = 40

Step 2: Use an F-distribution table or an F-distribution calculator to determine the p-value.
With DFb = 3 and DFw = 40, you can look up the critical F value in an F-distribution table or use an online F-distribution calculator.

Based on the provided information, we cannot directly tell the p-value without consulting an F-distribution table or calculator. However, you can follow these steps to determine the p-value for the given F statistic of 2.33.

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A rectangular piece of cardbord has 3D dimensions.

Rectangles are enclosed 2-D shapes with four sides, four corners, and four right angles.Equal and parallel opposite sides make up a rectangle.

The rectangle's properties are listed below:

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Answer:

10p +7t

Step-by-step explanation:

Hope this helps.

Answer:

glizzy

Step-by-step explanation:

volume of sphere is increasing at a rate of  62,832 mm3/s.

 The volume of a three-dimensional space can be determined. It is frequently numerically expressed in terms of several imperial units or SI-derived units. Volume and length are dependent on one another.

Step 1: Define an equation that relates the volume of a sphere to its radius.

V = 4/3*π*r3

Step 2: Take the derivative of each side with respect to time (we will define time as "t").

(d/dt)V = (d/dt)(4/3*π*r3)

dV/dt = 4πr2*dr/dt

Step 3: We are told in the problem statement that diameter is 100m, so therefore r = 50mm. We are also told the radius of the sphere is increasing at a rate of 2mm/s, so therefore dr/dt = 2mm/s. We are looking for how fast the volume of the sphere is increasing, or dV/dt.

dV/dt = 4π(50mm)2*(2mm/s)

dV/dt = 62,832 mm3/s

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Answer:

Equation of a straight line is given as y = mx+c

m = slope or gradient or dy/dx or y2 - y1/ x2 - x1

c = intercept

y = 2x - 7

y = -x + 1

y = 2x - 10

Step-by-step explanation:

Using y = mx+c

A. m=2 y=-7 x=0

-7= 2*0 + c

-7=c

y = 2*x - 7

y = 2x - 7

B. x1=3 x2=-2 y1=-4 y2=1

m = y2 - y1/ x2 - x1

m = 1+4 / -2-3

m = 5/-5 which is equal to -1

using any value for y and x, let's use x1 and y1

-2 = -1*3 + c

-2 = -3 + c

1 = c

y = -1*x + 1

y = -x + 1

C. x1=6 x2= 5 y1= 2 y2=0

m = y2 - y1/ x2 - x1

m = 0-2 / 5-6

m = -2/-1 which is equal to 2

using any value for y and x, let's use x1and y1

2 = 2*6 + c

2 = 12 + c

-10 = c

y = 2*x -10

y = 2x - 10

The perimeter of the Christian's sandbox is 24 feet.

The given two quadrialterals are similar

Let us find the remaining lengths of Christian's sandbox

By proportional equation

36/8=18/x=27/y=18/z

4.5=18/x=27/y=18/z

x=18/4.5 = 4

y=27/4.5 = 6

z=4

The perimeter is sum of all the sides

So perimeter of Christian's sandbox is 8+6+4+4

24 feet

Hence, the perimeter of the Christian's sandbox is 24 feet.

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The quotient of 4 and \(\frac{1}{3}\) is equal to 12.

In Mathematics, quotient is a mathematical expression that is simply used to represent division i.e the division of a number by another number.

Translating the word problem into an equation, we have:

The quotient of 4 and \(\frac{1}{3}\) ;

\(\frac{4}{\frac{1}{3} }\)

Simplifying further, we have:

\(4 \times \frac{3}{1} = 12\)

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Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.

The profit is the difference between the total revenue and the total cost.

The total cost is the cost per scone multiplied by the number of scones baked:

total cost = r0,53/scone × 204 scones = r108,12

The total revenue is the selling price per scone multiplied by the number of scones sold:

total revenue = r2,00/scone × 171 scones = r342,00

Therefore, the profit is:

profit = total revenue - total cost

profit = r342,00 - r108,12

profit = r233,88

Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.

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Answer:

-17.7

Step-by-step explanation:

-9.1-14.6-(-6)

-9.1-14.6+6

-23.7+6

-17.7

The length of HG after the dilation by the factor of 2 is 6.6.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

\(D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\)

We are given that;

The points H(-3,-5) & G(2, 2)

Dilation = 2

Now

D^2= (2+3)^2 + (2+5)^2

D^2= 25+49

D^2= 74

D=8.6

After dilation =8.6-2

=6.6

Therefore, the distance by the given dilation will be 6.6

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(a) The given partial differential equation (PDE) 2uxx + 5uxy - 12uyy = 0 can be solved using the method of characteristics.

(b) The given PDE 9uxx - 12uxy + 4uyy = 0 can be solved using the method of characteristics.

(c) The given PDE uxx - uxy - 6uyy = xsiny can be solved using the method of variation of parameters.

(d) The given PDE uxx + uxy - 6uyy = xy can be solved using the method of separation of variables.

(e) The given PDE uxx - 2uxy = cos(2x)sin(3y) can be solved using the method of separation of variables.

(f) The given PDE uxx - uxy + uy = x^2 + y^2 can be solved using the method of Green's functions.

(g) The given PDE uxxxx - 2uxxyy + uyyyy = ex - 2y can be solved using the method of separation of variables.

Partial differential equations (PDEs) are equations that involve partial derivatives of an unknown function with respect to multiple variables. Solving PDEs involves finding a function that satisfies the given equation. Each of the given PDEs can be solved using different methods based on the nature of the equation.

In PDE (a), the method of characteristics can be used to solve it. This method involves finding characteristic curves along which the PDE can be reduced to a system of ordinary differential equations. By solving this system, we can obtain the solution to the PDE.

PDE (b) can also be solved using the method of characteristics, similar to PDE (a). The characteristic curves will provide the necessary information to solve the equation.

PDE (c) requires the method of variation of parameters. This method involves assuming a particular solution and then finding a complementary solution using a trial function. By combining these solutions, we can obtain the complete solution to the PDE.

PDE (d) can be solved using the method of separation of variables. This method involves assuming a solution of the form u(x, y) = X(x)Y(y) and then substituting it into the PDE. By separating the variables and solving the resulting ordinary differential equations, we can find the complete solution.

PDE (e) can also be solved using the method of separation of variables. By assuming a solution of the form u(x, y) = X(x)Y(y) and substituting it into the PDE, we can separate the variables and solve the resulting ordinary differential equations to obtain the solution.

PDE (f) requires the method of Green's functions. This method involves finding a Green's function for the given PDE and then using it to represent the solution as an integral involving the Green's function and the given source term.

PDE (g) can be solved using the method of separation of variables. By assuming a solution of the form u(x, y) = X(x)Y(y) and substituting it into the PDE, we can separate the variables and solve the resulting ordinary differential equations to obtain the complete solution.

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Answer:

896 meters sq

Step-by-step explanation:

Step 1. Find the area of each square

Big square: 36 x 36 = 1296

Small square: 20 x 20 = 400

Step 2. Find the area of the shaded region only

big square A - small square A = ONLY shaded region area

1296 - 400 = A

896 \(m^{2}\) = A

I hope this helps!

To calculate the axis of symmetry, you must first identify the shape of the figure in question. The calculation for finding the axis of symmetry is different for each shape.

Rectangle: In a rectangle, the axis of symmetry is the midline, which runs vertically through the center of the figure. To calculate the axis of symmetry, divide the width of the rectangle in half and draw a line from the midpoint of the top side to the midpoint of the bottom side.

Parallelogram: In a parallelogram, the axis of symmetry is also the midline, which runs vertically through the center of the figure. To calculate the axis of symmetry, divide the width of the parallelogram in half and draw a line from the midpoint of the top side to the midpoint of the bottom side.

Axis of symmetry is a straight line that separates a two-dimensional figure into two mirror-image halves. The line runs vertically through the center of the figure and can be found in a variety of shapes, including rectangles, parallelograms, and parabolas.

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Answer:

D

Step-by-step explanation:

Answer:

I don't have Idea

The credit to interest revenue on the loan when the note becomes due will be $412.5

Interest revenue is the amount of money earned when money is learnt to others at an interest rate.

The amount Mike Co loaned the employee for 9 months = $11,000

The annual interest rate of the loan = 5%

The amount the employee will pay when the loan comes due in 2018 = The interest and the amount loaned

The interest on the loan can be calculated using the simple interest formula, which is;

Interest, I = Principal × Rate × Time

The principal on the loan = $11,000

The interest rate on the loan per annum = 5% = 0.05

The duration of the loan = 9 months = (9/12) = 3/4 of a year

Therefore; I = 11,000 × 0.05 × (3/4) = 412.5

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The scenario that is an example of simple random sampling is option C: "A supermarket wants to study the buying habits of its customers. They choose every 20th customer entering the supermarket to fill out the survey."

Simple random sampling is a method of selecting a sample from a population in which every member of the population has an equal chance of being chosen.

In option C, the supermarket chooses every 20th customer entering the store, which ensures that each customer has an equal chance of being selected. Therefore, this is an example of simple random sampling.

Options A, B, and D do not meet the criteria for simple random sampling, as they involve selecting specific regions, asking for opinions from readers, or mailing questionnaires to students, which does not ensure that every member of the population has an equal chance of being selected.

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The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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The population was 6.98 million in 1900. The population of New York decreased with respect to time.

What is an exponential function?

An exponential function is a mathematical function with the formula f (x) = axe, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.

The population of New York state can be modeled by

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513t}}\)

P is the population and t is the number of years since 1800.

The difference between the year 1900 to 1800 is 100.

Putting t = 100 in the given model:

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513\times 100}}\)

\(P(t)=\frac{19.71}{1+61.22e^{-3.513}}\)

P(t) = 19.71/2.8248

P(t) = 6.9774

P(t) = 6.977 (rounded to the nearest thousands)

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The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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