find a · b. |a| = 2, |b| = 7, the angle between a and b is 2/3

the question is that the zeros of the polynomial f(x)=(x−5)5(x+1)7 are x=5 and x=-1, and their multiplicities are 5 and 7, respectively.

the zeros and their multiplicities is as follows:

To find the zeros of the polynomial, we set each factor equal to zero and solve for x.

For the factor (x−5)5, we get x=5 as the only zero.

For the factor (x+1)7, we get x=-1 as the only zero.

To determine the multiplicities of the zeros, we count the number of times each zero appears as a factor.

Since (x−5)5 is a factor of the polynomial, the zero x=5 has a multiplicity of 5.

Similarly, since (x+1)7 is a factor of the polynomial, the zero x=-1 has a multiplicity of 7.

the zeros of the polynomial f(x)=(x−5)5(x+1)7 are x=5 and x=-1, and their multiplicities are 5 and 7, respectively.

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Answer:

Step-by-step explanation:To solve the quadratic equation x² - 3x - 10 = 0 using the quadratic formula, we first identify the values of a, b, and c:

a = 1

b = -3

c = -10

Now, we can apply the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we have:

x = (-(-3) ± √((-3)² - 4(1)(-10))) / (2(1))

Simplifying further:

x = (3 ± √(9 + 40)) / 2

x = (3 ± √49) / 2

x = (3 ± 7) / 2

This gives us two possible solutions:

x₁ = (3 + 7) / 2 = 10 / 2 = 5

x₂ = (3 - 7) / 2 = -4 / 2 = -2

Therefore, the solutions to the equation x² - 3x - 10 = 0 are x = 5 and x = -2.

To convert the polar equation r = 4sin(θ) + 4cos(θ) into a Cartesian equation, we can use the identities:

x = r cos(θ)

y = r sin(θ)

Substituting r = 4sin(θ) + 4cos(θ) into these identities, we get:

x = (4sin(θ) + 4cos(θ))cos(θ) = 4sin(θ)cos(θ) + 4cos²(θ)

y = (4sin(θ) + 4cos(θ))sin(θ) = 4sin²(θ) + 4sin(θ)cos(θ)

Simplifying these expressions using the trigonometric identity sin²(θ) + cos²(θ) = 1, we obtain:

x = 4cos(θ) + 4cos²(θ)

y = 4sin(θ) + 4sin(θ)cos(θ) = 4sin(θ) + 4cos(θ)sin(θ)

Therefore, the Cartesian equation for the curve is:

(x - 4)² + y² = 16

This equation represents a circle with center (4, 0) and radius 4. The original polar equation r = 4sin(θ) + 4cos(θ) can be interpreted as the distance from the origin to a point on the circle, measured along a line that makes an angle of θ with the positive x-axis.

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Answer:

2sqrt(26)

Step-by-step explanation:

sqrt(2^2+ 8^2+ 6^2)

=2×sqrt(26)

Answer:

1.440kg

Step-by-step explanation:

12 × 120=1440g

converting g to kg, divide by 1000 as 1000g = 1kg

Answer is therefore given as 1.440kg

If nominal wages and prices are not flexible, then the short-run aggregate supply curve is vertical.

This means that the economy is operating at full employment, and any increase in aggregate demand will not result in an increase in output but rather lead to higher prices.

In other words, the economy is supply-constrained, and there is no excess capacity to produce more output in response to an increase in demand.

In a severe recessionary gap, the economy is operating below its potential output, and there is excess capacity in the economy. However, if nominal wages and prices are not flexible, firms cannot adjust their prices downwards,

and wages cannot be reduced, leading to a situation where the short-run aggregate supply curve is vertical.

This results in a situation where any increase in aggregate demand will not lead to an increase in output, and the economy remains stuck in a recessionary gap with high unemployment and low output.

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Thomas considers cohesion to be the presence of strong positive bonds between members of a group. In his perspective, cohesion represents a sense of unity, attachment, and solidarity among individuals within the group.

Cohesion, according to Thomas, goes beyond mere cooperation or coordination of activities. It encompasses the emotional and social aspects of group dynamics, emphasizing the quality and strength of the relationships between members. The existence of strong positive bonds implies that individuals feel connected, trust each other, and have a shared sense of identity and purpose.

Thomas likely believes that cohesive groups are characterized by mutual support, collaboration, and a sense of belonging. Members are more likely to work together effectively, communicate openly, and have a higher level of commitment to group goals. Cohesion may also contribute to increased satisfaction, motivation, and overall well-being within the group.

Thomas's perspective aligns with the socio-emotional aspect of group cohesion, emphasizing the interpersonal connections and social dynamics that contribute to the cohesiveness of a group.

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To solve the given problem, let's break it down into two parts:

(a) At what time did the man arrive back in Ibadan?

We can calculate the time taken for the initial journey from Ibadan to Lagos using the formula:

Time = Distance / Speed

Time = 142 km / 60 km/h

Time = 2.37 hours

The motorist then spent an additional 5/2 hours in Lagos.

To calculate the total time taken for the return journey from Lagos to Ibadan, we use the formula:

Time = Distance / Speed

Time = 142 km / 80 km/h

Time = 1.775 hours

Adding the time spent in Lagos to the return journey time:

Total time = 2.37 hours + 5/2 hours + 1.775 hours

Total time = 6.145 hours

Therefore, the man arrived back in Ibadan approximately 6.145 hours after he left.

(b) To find the average speed for the total journey, we use the formula:

Average Speed = Total Distance / Total Time

The total distance covered in the round trip is 2 times the distance between Ibadan and Lagos, which is:

Total Distance = 2 x 142 km

Total Distance = 284 km

Average Speed = 284 km / 6.145 hours

Average Speed = 46.22 km/h

Therefore, the average speed for the total journey is approximately 46.22 km/h.

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The requried equation of the graph shown is y = sin (x - π/2).

The curve shown in the graph is of the sine function with some trasformation given as,
The graph of sinx is shifted π/2 units left, so the equation of the graph is given as,
y = sin (x - π/2)

Thus, the requried equation of the graph shown is y = sin (x - π/2).

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Answer:

Bottom left

Step-by-step explanation:

It covers the most points

Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).

Explanation:
To determine the depth at a particular node in a tree, we count the number of edges from the root to that node.
Without more information about the tree, it is impossible to determine the depths of nodes 23 and 70. However, if we assume that the root of the tree is at depth 0, and that the tree is binary (each node has at most two children), then we can make an educated guess.
Based on the given options, we can eliminate choices B and C, as they contradict each other.
Option A suggests that node 23 is two levels below the root, while node 70 is at the root level. This is possible if node 70 is the root of the tree, and node 23 is its child.
Option D suggests that node 23 is two levels below the root, while node 70 is three levels below the root. This is possible if node 70 is a grandchild of node 23.

Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).

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There were 16 ounces of oil in the lantern at noon.

Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.

We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:

x - rt = y

where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:

x - 2r = 12

And at 4 pm:

x - 4r = 8

Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:

2r = 4

r = 2

Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:

x - 2(2) = 12

x - 4 = 12

x = 16

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Wage differential is due to discrimination = 700 - 700 = 0 .The Oaxaca decomposition is a method used to estimate the portion of the wage differential between two groups (in this case, male and female workers) that can be attributed to discrimination.

The decomposition breaks down the wage differential into two components: the explained component and the unexplained component.The explained component represents the portion of the wage differential that can be attributed to differences in observable characteristics between the two groups, such as years of schooling.

The unexplained component represents the portion of the wage differential that cannot be explained by observable characteristics and is often interpreted as the component related to discrimination or unobserved factors.

To calculate the Oaxaca decomposition, we need to follow these steps:

Step 1: Calculate the average wage of male workers (wm) and female workers (wf) using the given equations:

wm = 500 + 100s, where s = 14 years (average years of schooling for men)

wm = 500 + 100(14) = 1900

wf = 300 + 75s, where s = 12 years (average years of schooling for women)

wf = 300 + 75(12) = 1200

Step 2: Calculate the explained component of the wage differential by estimating the wage differential that can be explained by the differences in observable characteristics (years of schooling) between the two groups.

Explained wage differential = [500 + 100(14)] - [300 + 75(12)] = 700

Step 3: Calculate the unexplained component of the wage differential, which is the portion that cannot be explained by observable characteristics and may be attributed to discrimination or unobserved factors.

Unexplained wage differential = Actual wage differential - Explained wage differential

Unexplained wage differential = 700 - 700 = 0

In this case, the unexplained component of the wage differential is zero, indicating that none of the wage differential can be attributed to discrimination. All of the wage differential can be explained by the differences in observable characteristics (years of schooling) between male and female workers.

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Answer:

D. Yes

Step-by-step explanation:

The measurement units for each is described below.

The metric system is a measurement system. It is utilized in calculations and research all over the world. Here are some instances of how we use the metric system to measure things:

a. distance from Florida to Texas is:  Kilometers (km)

b. length of a car is :  Meters (m)

c. thickness of a cell phone is:  Millimeters (mm)

d. height of a coffee mug is: Centimeters (cm)

e. mass of a cookie is: Grams (g)

f. mass of a large watermelon is:  Kilograms (kg)

g. mass of small feather is:  Milligrams (mg)

h. capacity of a large bottle of lemonade is : Liters (L)

i. capacity of a small food coloring bottle is : i. Milliliters (mL)

j. capacity of a swimming pool is:  Cubic meters (m³)

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To calculate the probability that at least 30 of the women in the sample will not meet the age requirement, we need to use the binomial distribution formula:

P(X >= 30) = 1 - P(X < 30)

where X is the number of women who do not meet the age requirement, and P(X < 30) is the cumulative probability of X being less than 30.

The probability of a woman not meeting the age requirement is given as 0.2, so the probability of a woman meeting the age requirement is 0.8. We are sampling 200 women, so the number of women who do not meet the age requirement follows a binomial distribution with n = 200 and p = 0.2.

Using a binomial calculator or software, we can find that P(X < 30) = 0.1656. Therefore, the probability of at least 30 women not meeting the age requirement is:

P(X >= 30) = 1 - P(X < 30) = 1 - 0.1656 = 0.8344

Therefore, the probability that at least 30 of the women in the sample will not meet the age requirement is 0.8344, or approximately 83.44%.

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In this problem, we are asked to find two numbers whose difference is 48 and whose product is a minimum.

To approach this problem, we can use the fact that the product of two numbers is minimized when the numbers are closest to each other. Therefore, we can let x be the smaller of the two numbers, and then the larger number is x + 48.

The product of these two numbers is:

P = x(x + 48) = x^2 + 48x

To find the minimum value of P, we can take the derivative of P with respect to x and set it equal to zero:

dP/dx = 2x + 48 = 0

Solving for x, we get:

x = -24

Substituting this value of x into the expression for P, we get:

P = (-24)^2 + 48(-24) = 576 - 1152 = -576

Therefore, the two numbers whose difference is 48 and whose product is minimized are -24 and 24. Note that the smaller number, -24, is negative, but this makes sense since the problem did not specify that the numbers had to be positive.

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Answer:

6000

Step-by-step explanation:

solved

The area of the garden is 272 ft².

We have,

The garden has two shapes:

Rectangle and a triangle.

Now,

Length = 12 ft

Width = 20 ft

Area of the rectangle.

= Length x Width

= 12 x 20

= 240 ft²

And,

Base = 8 ft

Height = (20 - 12) = 8 ft

Area of the triangle.

= 1/2 x base x height

= 1/2 x 8 x 8

= 32 ft²

Now,

Area of the garden.

= 240 + 32

= 272 ft²

Thus,

The area of the garden is 272 ft².

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Answer:

x = 46

Step-by-step explanation:

These 2 angles would add up to 180 degrees.

So 41 + (3x+1) = 180

Let's solve for x.

41 + 3x + 1 = 180

Combine like terms.

42 + 3x = 180

subtract 42 from both sides

3x = 180-42

3x = 138

divide both sides by 3

x = 46

To answer the question most efficiently , the standard form of the quadratic equation is the most suitable.

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero.

The highest power of a quadratic function is 2.

To solve a quadratic function efficiently, we need to put the function in standard form. i.e We arrange the power in descending order.

For example, a quadratic functionf(x)= 5x-2 +x² is not in standard form. To solve this we need to put it in a form of f(x) = x²+5x -2.

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The correct option is B, the displacement is 1.5 meters.

Displacement is defined as the difference between the final position and the initial position.

Here we can see a graph that gives the velocity as a function of time.

The velocity at t = 7s is 0m/s

The velocity at t = 8s is  3m/s

Then the acceleration in that interval is:

A = (3m/s - 0m/s)/(8s - 7s) = 3m/s²

And the position will be:

P = (1/2)*3m/s²*(t - 7s)²

Now take the differenve between the positions at t = 8s and t = 7s, we will get:

displacement =  (1/2)*3m/s²*(8s - 7s)² -  (1/2)*3m/s²*(7s - 7s)² = 1.5m

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The value of the investment after 4 years is equal to $9844.40.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]A(t) = P_{0}e^{rt}[/tex]

Where:

When time, t = 4 years, the future value can be calculated as follows:

[tex]A(t) = 7500e^{0.068 \times 4}\\\\A(t) = 7500e^{0.272}[/tex]

A(t) = 7500(1.31258700131)

A(t) = 9844.4025 ≈ $9844.40.

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Answer:

b

Step-by-step explanation:

The correct expression which is equivalent to 12.8 - 3s + 15.5 + 8s is,

⇒ 5s + 28.3

We have to given that;

Expression to solve is,

⇒ 12.8 - 3s + 15.5 + 8s

Now, WE can simplify as;

⇒ 12.8 - 3s + 15.5 + 8s

Combine like terms,

⇒ 12.8 + 15.5 - 3s + 8s

⇒ 28.3 + 5s

⇒ 5s + 28.3

Thus, The correct expression is,

⇒ 5s + 28.3

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The balance of the savings account 9 years from now will be $1,980.58.

To find the balance of the savings account 9 years from now, we can use the formula for compound interest:

[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]

where A is the ending balance, P is the principal (starting balance), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Substituting the given values, we get:

A = 1530(1 + 0.03/1)⁹

A = 1530(1.03)⁹

A = 1530(1.295376)

A = 1980.58

Therefore, the balance of the savings account 9 years from now, rounded to the nearest cent, will be $1,980.58.

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Answer:

m = -1/4

Step-by-step explanation:

Slope = rise/run (y2 - y1) / (x2 - x1)

Points (−7, 5) (−3, 4)

We see the y decrease by 1, and the x increase 4, so the slope is

m = -1/4

Answer:

The answer is 121/16 or 7.5625

Step-by-step explanation:

(-2¾)²

(-11/4)²

=121/16 or 7.5625