factorise 3(x-y)^2 - 2(x-y)

The Z-test statistic is 2.61 and the P-value is 0.0046. Based on the results, it can be inferred that older students exhibit more positive attitudes towards school compared to the average U.S. college student. To conduct the test, certain assumptions are necessary in addition to assuming the known value of σ: the sample is randomly selected from the population, and the population follows a normal distribution.

(a) The null hypothesis is H0: µ = 117 and the alternative hypothesis is Ha: µ > 117, and we will test the null hypothesis using the Z test statistic.

The test statistic Z is calculated as:

Z = (x¯ - µ) / (σ / sqrt(n))

where x¯ is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values we get, Z = (133.8 - 117) / (23 / sqrt(40))Z = 2.61The P-value corresponding to Z = 2.61 is 0.0046 using a Z table.

(b) The P-value of the test is 0.0046, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that older students have better attitudes toward school than the average U.S. college student.

(c) The assumptions required for the test in addition to the assumption that the value of σ is known are:

The sample is a random sample from the population.

The population is normally distributed, or the sample size is large enough (n > 30) for the Central Limit Theorem to apply.

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After dilating Triangle ABC with a scale factor of 1/4, the new coordinates of A', B', and C' are A'(2,1), B'(3,1), and C'(4,3), respectively.

To dilate Triangle ABC with a scale factor of 1/4, we need to multiply the coordinates of each vertex by the scale factor.

Let's apply the scale factor to each coordinate:

A' = (8 * 1/4, 4 * 1/4)

  = (2, 1)

B' = (12 * 1/4, 4 * 1/4)

  = (3, 1)

C' = (16 * 1/4, 12 * 1/4)

  = (4, 3)

Therefore, after dilating Triangle ABC with a scale factor of 1/4, the new coordinates of A', B', and C' are (2,1), (3,1), and (4,3) respectively. The scale factor of 1/4 shrinks the original triangle by a factor of 1/4 in both the x and y directions, resulting in a smaller triangle with the new coordinates.

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In this equation x=18

Work Shown:

5x-12=3x+24

Add 12 to both sides

5x-12+12=3x+24+12

Simplify

5x=3x+36

Subtract 3x from both sides

5x-3x=3x+36-3x

Simplify

2x=36

Divide both sides by two

2x/2 = 36/2

Simplify

x=18

Answer:

x=18

Step-by-step explanation:

1. Add 12 to both sides

5x-12 +12 = 3x+24 +12

2. Simplify

5x=3x+36

3. Subtract -3x from both sides

5x-3x=3x+36-3x

4. Simplify

2x=36

5. Divide both sides by same factor (2)

2x/2=36/2

6. Simplify

ANSWER: x=18

The area of the square is 144 \(cm^{2}\).

Let x be the side of the square. Then the length of the triangle is (x+4). Perimeter is the length of all sides of a geometric figure combined. For an equilateral triangle, it's equal to thrice the length of one side. For a square, it's four times the length of one side. The Perimeter of the Triangle is 3(x+4) & the Perimeter of the square is 4x.

We know, both these perimeters are equal. Hence,

4x = 3(x+4)

To further simplify the above equation.

4x = 3x + 12

x = 12

Hence, the length of one side of the square is 12 cm. The area of the square can be calculated as follows:

Area = \((side)^{2}\)

Area = 12 * 12

Area = 144 \(cm^{2}\)

Hence, the Area of the Square is 144 \(cm^{2}\)

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Answer:True

Step-by-step explanation:The y-axis is vertical and the x is horizontal

Answer:

$4

Step-by-step explanation:

Step one:

given data

Each bagel cost $2.00

Also, the cost function is given as

\(F(x)=2x\)

Step two:

Required

The total cost of bagels purchased

From the cost function, we can see already that Ayden Bought 2 Bagel, hence if one bagel cost $2 then

\(F(x)=2(2)\\\\F(x)=4\)

The two bagels will cost $4

the equation of the tangent line at the point (1, 0) is x = 1

Given function is  sin(xy) + cell = 1We are to find the equation of the tangent line at the point (1, 0). We are going to use the following formula for finding the equation of tangent line:y - y1 = m(x - x1)We have to first find the derivative of the function. Hence, by differentiating sin(xy) + cell = 1 w.r.t x, we get the following:$$y\cos(xy)\frac{dy}{dx} + ce^{ll} = 0 \\\frac{dy}{dx} = \frac{-ce^{ll}}{y\cos(xy)}$$Therefore, the slope of the tangent at (1, 0) is given by:$$m = \frac{-ce^{ll}}{0\cos(1 \times 0)} \\= -\infty$$.

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The equation of the tangent line to the curve sin(xy) + x cos(y) = 1 at the point (1,0) is y = -x + 1.

The equation of the tangent line to the curve sin xy + cell = 1 at the point (1,0) is y = -x + 1:

To find the equation of the tangent line to the curve sin(xy) + x cos(y) = 1 at the point (1,0), we can use the following steps:

Step 1: Find the partial derivative with respect to x

To find the partial derivative of the function sin(xy) + x cos(y) = 1 with respect to x, we treat y as a constant and differentiate with respect to x.

∂/∂x(sin(xy) + x cos(y)) = y cos(xy) + cos(y)

Step 2: Find the partial derivative with respect to y

To find the partial derivative of the function sin(xy) + x cos(y) = 1 with respect to y, we treat x as a constant and differentiate with respect to y.

∂/∂y(sin(xy) + x cos(y)) = x cos(xy) - sin(y)

Step 3: Find the slope of the tangent line at (1,0)

Using the partial derivatives found in steps 1 and 2, we can find the slope of the tangent line at the point (1,0).

m = -(∂/∂x(sin(xy) + x cos(y))) / (∂/∂y(sin(xy) + x cos(y)))

= -(y cos(xy) + cos(y)) / (x cos(xy) - sin(y))

When x = 1 and y = 0, we get:

m = -cos(0) / (1 cos(0))

= -1

Step 4: Find the equation of the tangent line

Using the point-slope form of a linear equation, we can find the equation of the tangent line to the curve at the point (1,0).

y - y1 = m(x - x1)

y - 0 = -1(x - 1)

y = -x + 1

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Regina needs to travel an additional 5,600 meters to get home.

The total distance Regina travels from school to the grocery store and then to her house is

4.2 km + 1.4 km = 5.6 km

To find out how much farther Regina needs to get home, we need to subtract the distance from the grocery store to her house (which we don't know yet) from the total distance she travels.

Let's say the distance from the grocery store to Regina's house is x kilometers. Then we can set up an equation

5.6 km - x km = the distance Regina needs to get home

To solve for x, we can isolate it on one side of the equation by subtracting the distance Regina needs to get home from both sides

5.6 km - (the distance Regina needs to get home) = x km

We know that Regina needs to get home, so we can substitute that into the equation

5.6 km - 0 km = x km

Simplifying, we get

x = 5.6 km

Now we know that the distance from the grocery store to Regina's house is 5.6 km. We need to convert this to meters to find out how much farther Regina needs to get home

5.6 km = 5,600 meters

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:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.

During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.

According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes

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Answer:

1248

Step-by-step explanation:

We know that

P = 960

T = 3 years

R = 10%

F = 960 + 960×10/100×3

960 + 96×3

960 + 288 = 1248

Answer:

A, B, C

Step-by-step explanation:

Original Equation: 5x=45

Dividing by 5 on both sides: 5x/5 = 45/5

The result: x=9

Check: 5(9)=45, 45 = 45.

Thus, the correct order of steps should be A, B, C.

Let me know if this helps!

Answer:

The term a⁴-3a²b²+b⁴ can't be factorised

A) $15,025.8. is the correct option. Chloe loans out a sum of $1,000 every quarter to her associates at an interest rate of 4%, compounded quarterly. She stand to get $15,025.8. if er loans are repaid after three years.

Chloe loans out a sum of $1,000 every quarter to her associates at an interest rate of 4%, compounded quarterly.

We need to find how much she stands to gain if er loans are repaid after three years.

Calculation: Semi-annual compounding = Quarterly compounding * 4 Quarterly interest rate = 4% / 4 = 1%

Number of quarters in three years = 3 years × 4 quarters/year = 12 quarters

Future value of $1,000 at 1% interest compounded quarterly after 12 quarters:

FV = PV(1 + r/m)^(mt) Where PV = 1000, r = 1%, m = 4 and t = 12 quartersFV = 1000(1 + 0.01/4)^(4×12)FV = $1,153.19

Total amount loaned out in 12 quarters = 12 × $1,000 = $12,000

Total interest earned = $1,153.19 - $12,000 = $-10,846.81

Therefore, Chloe stands to lose $10,846.81 if all her loans are repaid after three years.

Hence, the correct option is A) $15,025.8.

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Answer:

12

Step-by-step explanation:

Median data dihitung sebagai

= 1/2 (n + 1) suku ke-1

Dimana n = Jumlah suku

= 10

Langkah 1

Kami mengatur ulang

8, 9, 10, 10, 12, 12, 13, 15, 15, 17

Langkah 2

Suku 1/2 (n + 1)

1/2 (10 + 1) istilah

= 11/2 istilah

= 5,5 suku

Istilah ini antara istilah ke-5 dan ke-6

Suku ke-5 = 12

Suku ke-6 = 12

= 12 + 12/2 = 24/2

= 12

Median data adalah 12

Answer:

1,398.983

Step-by-step explanation:

The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

This given test is a test for single sample proportion

The test hypothesis are:

\(H_{o} :p=0.20\), null hypothesis

\(H_{1} :p\neq 0.20\), alternative hypothesis

The test statistic fallows a standard normal distribution and is given by:

\(Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }\)

p=0.20

X=47 plants

Sample size, n=500

x, is the sample mean:

x=X/n=47/500

x=0.094

So, test statistic is calculated as:

\(Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }\)

Z=-5.93

From the z-table, the p-value associated with Z=-5.93 is approximately 0

The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level

In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim

So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

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Answer:

k = 8

Step-by-step explanation:

Given

\(\frac{k}{6}\) = \(\frac{4}{3}\) ( cross- multiply )

3k = 24 ( divide both sides by 3 )

k = 8

Answer:

6kg pure copper and 30 kg 10% copper was mixed to give 36kg of 25% alloy

Step-by-step explanation:

Here, we want to produce 36 kg of 25% alloy

Let the Pure copper be x kg while 10% alloy be y kg

Pure copper is simply 100% copper

Thus;

x + y = 36 •••••(i)

Then;

100% of x + 10% of y = 25% of 36

= x + 0.1y = 9 •••••• ii)

From i x = 36-y

from ii, x = 9-0.1y

Equate both x

36-y = 9-0.1y

36-9 = 0.1y + y

0.9y = 27

y = 27/0.9

y = 30

x = 36-y

x = 36-30

x = 6 kg

Since r = √(x² + y²) in Cartesian coordinates, we can substitute it into the equation: x + y = √(x² + y²).

To convert the polar equation rcosθ + rsinθ = 1 into a Cartesian equation, we can use the trigonometric identities cosθ = x/r and sinθ = y/r.

Substituting these identities, we get x + y = r. Since r = √(x² + y²) in Cartesian coordinates, we can substitute it into the equation: x + y = √(x² + y²).

To identify the graph, we can rearrange the equation to form x² + y² = (x + y)², which simplifies to x² + y² = x² + 2xy + y². Canceling out the x² and y² terms, we obtain 2xy = 0.

This equation represents two perpendicular lines, one along the x-axis and the other along the y-axis, intersecting at the origin.

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An inverse does not exist for a parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

An inverse does not exist for a parabola.

One definition of a parabola includes a line and a point (the focus) (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, an inverse does not exist for a parabola.

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In this movie, the ratio of children to adults suggests that there are 27 children in attendance.

We have to give that,

There are 9 children for every 4 adults.

This means that if there were 13 people, 9 of them would be children and 4 would be adults.

Children would therefore be:

= 9 / 13

If there were 39 people, the number of children would be:

= 9/13 x 39

= 27 children

In conclusion, there are 27 children.

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The complete question is,

In the newest animated movie, for every 9 children, there are 4 adults. There are a total of 39 children and adults in the movie.

How many children are in the movie?

Answer:

11/-30 Hope this helped :)

Step-by-step explanation:

15x + 4 = -1  1/2

15x = -5  1/2

x = 11/-2*1/15

x = - 11/-30

The solution of the differential equation \(y^5 x \frac{d y}{d x}=1+x\) is \(y^6=6 \log x+6 x+723\).

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

A differential equation is an equation that contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable).

To solve the differential equation \(y^5 x \frac{d y}{d x}=1+x\), firstly, separate the variables as follows:

\(\begin{aligned}& y^5 d y=\left(\frac{1+x}{x}\right) d x \\& y^5 d y=\left(\frac{1}{x}+1\right) d x\end{aligned}\)

Integrating both sides, we get the following:

\(\begin{aligned}& \int y^5 d y=\int\left(\frac{1}{x}+1\right) d x \\& \frac{y^6}{6}=\log x+x+c\end{aligned}\)

We are given the initial condition as y(1) = 3.

Substitute x=1 and y=3, we get the following:

\(\begin{aligned}\frac{3^6}{6} & =\log 1+1+c \\c & =\frac{3^5}{2}-1 \\c & =\frac{243-2}{2}=\frac{241}{2}\end{aligned}\)

Substitute c=241/2 in the equation \(\frac{y^6}{6}=\log x+x+c\), we get the following:

\(\begin{aligned}& \frac{y^6}{6}=\log (x)+x+\frac{241}{2} \\& y^6=6 \log (x)+6 x+3(241) \\& y^6=6 \log x+6 x+723\end{aligned}\)

This is the required solution of the given differential equation.

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We can arrange the 2023 squares to cover the unit square, with overlaps allowed.

We can prove that a collection of 2023 closed squares of total area 4 can be arranged to cover a unit square by using the pigeonhole principle. Since the total area of the squares is 4, the average area of each square is 4/2023. Let's take a unit square and divide it into 2023 smaller squares of area (1/2023) each. By the pigeonhole principle, we can assign one of the 2023 squares to each of the smaller squares. Since the average area of each square is 4/2023, each of the assigned squares will overlap with at most 4 other squares. Therefore, we can arrange the 2023 squares to cover the unit square, with overlaps allowed.

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Answer:

1) y=-10x+50 (it's the only negative slope / going down option and it starts at x=0 y=50)

just substitute the x with a 9

y=-10*9 +50

y= -40

2) 0.5x +5 (only positive slop and starting point at x=0 is correctly 5)

we do need to substitute y this time, with 30 obviously

30 = 0.5x +5 |-5

25 = 0.5x | *2

50 = x

3) y=-2x +50 reasoning as before

substitute x with 4

y =-2*4 +50

y = -8 +50

y = 42

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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Answer:

when they reduced 3^2-4(6)(-7) they squared the 3 wrong 3^2 does not equal 6 so they should have written 9 instead of 6