Write as a product
2xy^2-y-2x+y^3

The p-value of the test statistic is given as follows:

0.0606.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

We have a right-tailed test, as we are testing if the proportion is greater than a value.

As we have a right-tailed test, the p-value is one subtracted by the p-value of z = 1.55, hence:

1 - 0.9394 = 0.0606

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Answer:

[tex]A = 3.18259788 cm^2[/tex]

Step-by-step explanation:

[tex]A = nr^2 tan(\pi /n)A = 16tan(\pi/16)[/tex]

Answer:

G. t = 10.50h

Step-by-step explanation:

10.50/per hour and h is per hour so 10.50*h

Answer:

10.50h

Step-by-step explanation:

the number of cars that entered at IN is [tex]12[/tex].

Based on these observations, we can set up an equation to solve for the number of cars entering at IN:

Let's assume the number of cars entering at IN is "x".

Number of cars exiting at C [tex]= 12[/tex] (given)

Number of cars exiting at  [tex]A = 0[/tex] (since cars exiting at A do not return)

Number of cars exiting at   [tex]B = 0[/tex] (since cars exiting at B do not return)

Number of cars exiting at C = Number of cars entering at C + Number of cars exiting at A + Number of cars exiting at B

[tex]12 = x + 0 + 0[/tex]

Simplifying the equation, we get:

[tex]12 = x[/tex]

Therefore, the number of cars that entered at IN is 12.

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The minimum numbers of pots of each size which Andrea has to sell in a month so that she can pay the monthly rent is 150 small, 100 medium and 50 large.

The price of a small flower pot = RM10

The price of a medium flower pot = RM15

The price of a Large flower pot = RM40

Let

small flower pot = s

Medium flower pot = m

Large flower pot = l

s = m + l

m = 2l

Amount of Andrea's rent = RM300 per month

300 = s + m + l

substitute s and m into the equation

300 = (m + l) + 2l + l

300 = (2l + l) + 2l + l

300 = 2l + l + 2l + l

300 = 6l

divide both sides by 6

l = 300/6

l = 50

Recall,

m = 2l

m = 2(50)

m = 100

Therefore,

s = m + l

s = 100 + 50

s = 150

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Answer:

The tan(a) is the degree value of the angle shown. In this case, the unknown degree is A, and it wants you to use the Tangent method. Using the formula to get 27°

Step-by-step explanation:

Tangent (A) = opposite (√17)  over adjacent (8)

So it would be Tan(A)= √17/8

To easily solve this use a calculator

Find the tan button, (use the inverse tangent or tan-1)

then sub values

tan-1(√17/8)

27.26 or 27°

For future questions here's a helpful chart:

Answer:

Step-by-step explanation:

True.

To calculate Jane's debt-to-income ratio, we need to divide her total liabilities by her total income. However, the prompt only gives us the sum of Jane's assets and liabilities, not her income.

Assuming that Jane's assets are not considered as part of her income, we can conclude that she falls within the recommended amount, since her total liabilities ($2,300) divided by her total income (which we don't know but is presumably greater than her liabilities) would be less than 15%.

The value of f'(0) in given equation is -1/3.

This is the case because quadratum is the Latin word for square, and since the area of a square of side length x is given by x², a polynomial equation having exponent two is known as a quadratic ("square-like") equation.

Since the integral of f(x) is a rational function, we can use the reverse power rule to find the derivative of f(x). According to the reverse power rule, if

[tex]∫f(x)x^n dx[/tex] = F(x) + C

where F(x) is a rational function, then

f(x) = d/dx (F(x) + C) = F'(x)

Now, let's evaluate the given integral:

∫[tex]f(x)x^2(x-7)^7[/tex]dx

Using integration by substitution with u = x-7 and du = dx, we can rewrite the integral as:

[tex]∫f(u+7)(u+7)^2 u^7[/tex]du

Expanding (u+7)², we get:

∫[tex]f(u+7)(u^2+14u+49) u^7[/tex]du

Expanding further and distributing f(u+7), we get:

∫[tex](f(u)u^9 + 14f(u)u^8 + 49f(u)u^7 + ... + f(u)7^9 + 14f(u)7^8 + 49f(u)7^7)[/tex]du

Since the integral is a rational function, the only non-zero term in the expansion must be a constant multiple of u². Therefore, we have:

∫[tex]f(x)x^2(x-7)^7[/tex] dx = k ∫u^2 du = (1/3)ku³ + C

where k is some constant.

Now, we know that f(0) = -2, so we can find k as follows:

∫[tex]f(x)x^2(x-7)^7[/tex] dx = (1/3)k(0-7)³ + C = -343k/3 + C

But we also know that the integral is a rational function, so it must be equal to (ax² + bx + c)/d for some constants a, b, c, and d. Therefore,

(1/3)k(0-7)³ + C = (ax² + bx + c)/d

Substituting x = 0 and using f(0) = -2, we get:

(1/3)k(-7)³ + C = c/d = -2

Solving for k, we have:

(1/3)k(-7)³+ C = -2

k = -18/(343C)

Substituting this expression for k into the integral, we have:

∫[tex]f(x)x^2(x-7)^7[/tex]dx = (-6/(49C))u³+ C'

where C' is some constant. Finally, using the reverse power rule, we have:

f(x) = d/dx (-6/(49C))(x-7)³ + C''

f(0) = -2 implies C'' = -2

So, at x = 0, we have:

f'(0) = (-6/(49C)) * 3(-7)² = 18/(49C)

Substituting the expression we derived for k, we get:

f'(0) = 18/(49(-18/(343C))) = -1/3

Therefore, the value of f'(0) is -1/3.

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Let's assign the variable "x" to the height of the smaller plant. Since we know that the larger plant grows twice as fast, its height would be "2x". Let's say the total height of the plants together is 90 cm, so we can write the equation: x + 2x = 90

Let's assign the variable "x" to the height of the smaller plant. Since we know that the larger plant grows twice as fast, its height would be "2x". Let's say the total height of the plants together is 90 cm, so we can write the equation:

x + 2x = 90

Simplifying the equation, we get:

3x = 90

x = 30

Therefore, the height of the smaller plant is 30 cm and the height of the larger plant is 2x = 60 cm.

To sketch a graph of the equation, we can plot the values of x (height of smaller plant) on the x-axis and the values of 3x (total height of the two plants) on the y-axis. The graph would be a straight line with a slope of 3 and intersecting the y-axis at 90 (the total height of the plants).

For the second equation, let's say we want to model the growth of the smaller plant over time. We can use the equation:

y = 0.5x + 10

where "y" is the height of the smaller plant (in cm) and "x" is the number of weeks since planting. The equation assumes that the plant starts at a height of 10 cm and grows at a rate of 0.5 cm per week. To sketch the graph, we can plot the values of x on the x-axis and the values of y on the y-axis. The graph would be a straight line with a slope of 0.5 and intersecting the y-axis at 10.

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Approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

A woman or girl who identifies as Hispanic or Latino, which usually refers to persons of Spanish-speaking origin or lineage from Latin America or Spain, is referred to as a "Hispanic female."

The proportion of Hispanic females with the disease is 1 in 750, which can be expressed as:

1 / 750 = 0.001333

This means that for every 750 Hispanic females, one is expected to have the disease.

To calculate the expected number of Hispanic females with the disease in a group of 26,000, we can multiply the proportion by the total number of Hispanic females:

0.001333 * 26,000 = 34.658

So we would expect approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

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A graph of the lattice points of the inverse are shown below.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this scenario and exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = log₂(-x + 3) - 4

x = log₂(-y + 3) - 4

log₂(-y + 3) = x + 4

[tex]2^{x + 4} = -y + 3\\\\y = -2^{x + 4} + 3[/tex]

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Complete Question:

The function f(x) = log₂(-x + 3) - 4 is graphed below. Plot all lattice points of the inverse. Use the labeled points as your guide.

5.

y = -x + 5

6.  the point of contact is (-1, 6).

7.  the radius is √26

8. The standard form equation of a circle with center (h, k) and radius r is: (x - 2)^2 + (y - 3)^2 = 26

9. Line AB = AB

Line BC = BC

Line AC = AC

10. The equation of a circle with center (h, k) and radius r is:

(x - 4)^2 + (y + 3)^2 = 16^2

the equation of the line passing through (2, 3) with slope -1:

y - 3 = (-1)(x - 2)

y - 3 = -x + 2

y = -x + 5

We can find the intersection point of this line and the given tangent line by solving the system of equations:

y = x + 7

y = -x + 5

When we add these equations, we have:

2y = 12

y = 6

We can then substitute into either equation gives x = -1.

Hence, the point of contact is (-1, 6).

We  find the radius, Using the distance formula, :

r = √[(2 - (-1))^2 + (3 - 6)^2] = √26

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The area should be 47.5 CM.

Answer:

Step-by-step explanation:

The figure you see here is a trapezoid.

Area = [tex]\frac{(a + b)h}{2}[/tex] = [tex]\frac{(6 + 13)(5)}{2}[/tex] = [tex]\frac{(19)(5)}{2}[/tex] = [tex]\frac{95}{2}[/tex] = 47.5 cm

By algebra properties, the product of the two binomials (4 · x + 1) · (2 · x² - 2) is equal to (4 · x) · (2 · x²) + (- 2) · (4 · x) + 1 · (2 · x²) + 1 · (- 2). (Correct choice: B)

In this question we find the product of two binomials, the former is a linear binomial and the latter is a quadratic binomial. This can be done by algebra properties. First, write the entire expression:

(4 · x + 1) · (2 · x² - 2)

Second, use distributive property twice:

(4 · x + 1) · (2 · x²) + (4 · x + 1) · (- 2)

(4 · x) · (2 · x²) + 1 · (2 · x²) + (- 2) · (4 · x) + (- 2) · 1

8 · x³ + 2 · x² - 8 · x - 2

Third, use commutative property:

(4 · x) · (2 · x²) + (- 2) · (4 · x) + 1 · (2 · x²) + 1 · (- 2)

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The value of x in the triangle is 80°.

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Let the third angle in triangle be y. Thus:

y = 180 - 115  (angle on a straight line)

y = 65°

Also:

35 + x + y = 180 (angle in a triangle)

35 + x + 65 = 180

x = 180 - 65 - 35

x = 80°

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Answer:

19.6 in²

Step-by-step explanation:

area of circle = π r²

= π (3 1/2)²

= π (5/2)²

= π 25/4

= 22/7 x 25/4

= 275/14

=19.6 in²

The  net income that would have been if the allowance method had been used is:$696,200.

Net income

Using this formula

Net income=Net income+ Accounts uncollectible-( Sales ×Estimated sales rate)

Let plug in the formula

Net income=$715,000+$48,600-($6,740,000×1%)

Net income=$715,000+$48,600-$67,400

Net income=$696,200

Therefore The  net income that would have been if the allowance method had been used is:$696,200.

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To compare % and ¾, we can convert them both to decimals or both to fractions.

Method 1: Converting to decimals

% = 0.01 x % value

So, % = 0.01 x 100 = 1

¾ = 0.75

Now, we can compare the decimals: 1 > 0.75

Therefore, % is greater than ¾.

Method 2: Converting to fractions

% = 100%

So, % = 100/100 = 1

¾ = 6/8 (we can simplify by dividing both numerator and denominator by 2)

Now we can compare the fractions:

100/100 > 6/8

By cross multiplying, we get:

100 x 8 > 6 x 100

800 > 600

Therefore, % is greater than ¾.

Answer: Using both methods, we have shown that % is greater than ¾.

A system of equations that can be used to determine the dollar amount of phone sales is:

P = 2C

0.07P + 0.03C = 85

Let's define the variables:

Let P represent the total dollar amount of phone sales Colton made.

Let C represent the total dollar amount of computer sales Colton made.

We are given that Colton earns a 7% commission on phone sales and a 3% commission on computer sales. We are also given that Colton had twice as much in phone sales as he had in computer sales and earned a total of $85 in commission.

We can write the following system of equations:

P = 2C (Colton had twice as much in phone sales as he had in computer sales)

0.07P + 0.03C = 85 (Colton earned a total of $85 in commission)

Now we have a system of equations:

P = 2C

0.07P + 0.03C = 85

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The area of sector and perimeter of the sector are 29.04 cm² and 21.12 cm respectively.

The area of the shaded region is 53.81π cm².

The exact area of the shaded region is 3π - 4 - 2√2 cm².

To find the area and perimeter of a sector, we use the formulas:

Area of sector = (θ/2) * r²

Perimeter of sector = r + r + θ * r

Using these formulas, we can find the area and perimeter of the sector with r=4cm and θ=4.53 radians:

Area of sector = (4.53/2) * 4²

Area of sector  = 29.04 cm²

Perimeter of sector = 4 + 4 + 4.53 * 4

Perimeter of sector = 21.12 cm

To find the area of the shaded region in the sector with r = 12 cm and θ = 1.5 radians, we need to subtract the area of the triangle from the area of the sector.

The angle of the triangle is:

180° - (θ * 180°/π) = 180° - (1.5 * 180°/π)

The angle of the triangle = 68.66°

The radius of the sector is r=12cm, and the central angle is θ=1.5 radians. The area of the sector = (θ/2) * r^2 = (1.5/2) * 12^2 * π

The area of the sector = 81π cm^2

To find the height of the triangle, we can use the sine function:

sin(68.66°) = h / 12

h = 12 * sin(68.66°) = 11.03 cm (rounded to two decimal places)

The base of the triangle is the chord of the sector, which has length:

2 * r * sin(θ/2) = 2 * 12 * sin(1.5/2)

length = 10.28 cm (rounded to two decimal places)

The area of the triangle = (1/2) * base * height = (1/2) * 10.28 * 11.03

The area of the triangle = 56.66 cm²

The area of the shaded region is:

Area of sector - Area of triangle = 81π - 56.66

The area of the shaded region = 53.81π cm²

To find the exact area of the shaded region in the circle with centre O and radius OA=2√2, we first need to find the radius OB. We can use the cosine rule to find the length of OB:

OB^2 = OA^2 + AB^2 - 2 * OA * AB * cos(BOA)

OB^2 = (2√2)^2 + 2^2 - 2 * 2√2 * 2 * cos(135°)

OB^2 = 8 + 4√2

So the radius OB is √(8 + 4√2).

The angle of the sector OAB is:

135° * π/180° = 3π/4 radians

The area of the sector OAB is:

(3π/4) * (2√2)^2 / 2 = 3π cm^2

The area of triangle OAB = (1/2) * OA * OB * sin(OAB) = (1/2) * 2√2 * √(8 + 4√2) * sin(135°)

The area of triangle OAB = (4 + 2√2) cm²

The area of the shaded region = Area of sector OAB - Area of triangle OAB

The area of the shaded region = 3π - (4 + 2√2)

Area of the shaded region = 3π - 4 - 2√2 cm^2

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Answer:

The customer has 3 choices for dessert: brownie, cookie, or cake.

For bread, the customer can choose from 3 options: wheat, rye, or white.

Therefore, the customer has 3 choices for dessert and 3 choices for bread, making a total of 3 x 3 = 9 different meal choices.

The large count condition is met because all expected counts are greater than 5.

Now to determine if the data provides convincing evidence that the two population proportions differ, we can conduct a hypothesis test.

Let p1 be the proportion of adults who exercise regularly and got sick in the past year, and p2 be the proportion of adults who do not exercise regularly and got sick in the past year.

The null hypothesis is that the two population proportions are equal: H0: p1 = p2

The alternative hypothesis is that the proportion of those who exercise regularly who got sick in the past year is smaller than the proportion of those who do not exercise regularly: Ha: p1 < p2

We can use a two-sample z-test for proportions to test this hypothesis. The test statistic is given by:

where p_hat is the pooled sample proportion:

p_hat = (x1 + x2) / (n1 + n2)

In this case, we have:

n1 = 50, x1 = 18, n2 = 75, x2 = 56

p_hat = (18 + 56) / (50 + 75) = 0.455

We can also calculate the expected counts using the formula provided:

n1p_hat = 500.455 = 22.75

n1*(1-p_hat) = 500.545 = 27.25

n2p_hat = 750.455 = 34.13

n2(1-p_hat) = 75*0.545 = 40.88

The large counts condition is met because all expected counts are greater than 5.

To calculate the test statistic, we have:

z = (0.18 - 0.747) / sqrt(0.592 * (1 - 0.592) * (1/50 + 1/75)) = -2.36

Using a standard normal table, we find the p-value to be 0.0091 for a one-tailed test. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is convincing evidence that the proportion of those who exercise regularly who got sick in the past year is smaller than the proportion of those who do not exercise regularly.

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After mapping Circle D to Circle B using translation and dilation, we may say that Circle B and Circle D are similar.

A circle is a spherical shape without boundaries or edges.

A circle is a closed shape, a two-dimensional shape, and a curved shape in geometry.

A circle is made up of a collection of points that are all evenly spaced apart from the circle's center and lay on a plane.

So, circles B and D should be translated so that their centers are the same.

Circle B would be translated into 8 units to the left and 1 unit up.

Circle D would be enlarged until it was the same size as circle B.

The scaling factor would be discovered.

Comparison of their radii

Scale factor = 4/2 = 2 where radius of B/radius of D

ThereforeHencesame radius and center.

Therefore, after mapping Circle D to Circle B using translation and dilation, we may say that Circle B and Circle D are similar.

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Complete question:

Prove that the two circles shown below are similar. Circle B is shown with a center at negative 1, 5, and a radius of 4. Circle D is shown with a center of 7, 4, and a radius of 2.

Answer:

2.5 years. Since the interest compounded is quarterly and an annual interest rate of 10% (That's $100 dollars per interest compounded), this means that after a year you will have gained $400 dollars in interest. Thus in order to double you money ($2,000) it will take 2 and a half years.

Step-by-step explanation:

Double your money:  2 x $1,000 = $2,000 (This will be the final total)

10% of 1000 is 100.

Quarterly = 4

4 x $100 = $400 back in interest per year.

2.5 x $400 = $1,000

or

$1,000/$400 = 2.5 (years)

$1,000 (from the initial deposit) + $1,000 (from interest) = $2,000

Based on the question on rational functions;

1. The domain in interval notation is: (-∞, -7) ∪ (-7, 1) ∪ (1, 8) ∪ (8, ∞)

2. The discontinuities are:

x = 1: Hole (since (x-1) was canceled out)

x = -7: Vertical asymptote (since it's still in the denominator)

x = 8: Vertical asymptote (since it's still in the denominator)

3. If a factor in the denominator can be canceled out with a factor in the numerator, then the discontinuity at that value of x is a hole. If a factor in the denominator cannot be canceled out, then the discontinuity at that value of x is a vertical asymptote.

4.  The end-behavior of r(x) is determined by the ratio of the highest-degree terms, which is x/x² = 1/x. Using limit notation, we have:

lim (x → ∞) r(x) = 0

lim (x → -∞) r(x) = 0

5.  Since the degree of the numerator (1) is less than the degree of the denominator (2), the horizontal asymptote is y = 0.

6. The x-intercept is (-6, 0). The y-intercept is (0, - 0.12)

For the rational function, to determine whether each discontinuity is a hole or a vertical asymptote, we factor the numerator and denominator to see if there is any common factor that can be canceled out.

(x) = [(x-1)(x+6)] / [(x-1)(x+7)(x-8)]

We can see that (x-1) is a common factor and can be canceled out. So, the simplified function is:

r(x) = (x+6) / [(x+7)(x-8)]

To find the x-intercepts, set r(x) equal to 0 and solve for x:

0 = (x+6) / [(x+7)(x-8)]

This means x + 6 = 0, so x = -6. The x-intercept is (-6, 0).

To find the y-intercept, set x = 0:

r(0) = (0+6) / [(0+7)(0-8)] = 6 / (-56) = -3 / 28

So, the y-intercept is (0, -3/28).

The above answers is based on the following questions as seen in the picture;

Rational Functions

1. Consider the following rational function

r(x) = (x2-x)(x+6)

        (x-1)(x+7)(x-8)

a. Write the domain of r(x)in interval notation

b. Find the discontinuities of r(x) and label each as a hole or a vertical asymptote.

c. Explain how you decide if there is a hole or a vertical asymptote. d. What terms in r(x)determine the end-behavior? Describe the end-behavior of r(x), using limit notation.

e. If there is a horizontal asymptote, write the equation of the

horizontal asymptote

f. Find the x- and y-intercepts of r(x)

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Answer:

C. 1,620 m³

Step-by-step explanation:

always remember, for a volume we need to (one way or another) multiply measurements of 3 dimensions with each other.

so, if each of the 3 dimension measurements triples, then that factor 3 is used in the multiplication 3 times.

and the volume is multiplied by 3×3×3 = 27.

and 60 m³ × 27 = 1,620 m³

Answer:

Hello, The answer to your question is,

[tex]x=[/tex] −[tex]\frac{2}{t^3}[/tex]

hope this help :)
(correct me if i am wrong and im sorry)

Step-by-step explanation:

Answer:   $2,800

Step-by-step explanation:

Since each computer is worth $400, we know that for 3 computers, the price would be $1,200 (400 x 3 = 1,200). We know that the fourth computer would have a discount of 50% off.  50% is equal to 1/2, so 400 x 1/2 is equal to $200. For four computers, the price would be $1,400. If we want to find the amount for 8 computers, we have to do 1,400 x 8. The answer to this is 2,800.

The expected value of a prize is $245.00.

In probability theory, a probability distribution is a function that describes the likelihood of obtaining the different possible outcomes of a random variable. The function assigns a probability to each possible outcome, such that the probabilities add up to 1.

There are two types of probability distributions: discrete and continuous. A discrete probability distribution is used when the random variable takes on a finite or countable number of values, such as the outcome of rolling a dice or the number of students in a class. A continuous probability distribution is used when the random variable can take on any value within a certain range, such as the height or weight of a person.

Now the expected value of a prize is the sum of each possible prize value multiplied by its corresponding probability.

Using the table provided, we can calculate the expected value as:

Expected value = $0.00(0.81) + $100.00(0.1) + $500.00(0.07) + $10,000.00(0.02)

Expected value = $0.00 + $10.00 + $35.00 + $200.00

Expected value = $245.00

Therefore, the expected value of a prize is $245.00.

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