If f(7) = 9 and f’(7) = 3, estimate f(7.3).

If F(7) = 9 And F(7) = 3, Estimate F(7.3).

Answers

Answer 1

Answer:

[tex]f(7.3)\approx9.9[/tex]

Step-by-step explanation:

Use point-slope form

[tex]y-y_1=m(x-x_1)\\y-9=3(x-7)\\y-9=3x-21\\y=3x-12[/tex]

[tex]f(7.3)=3(7.3)-12=21.9-12=9.9[/tex]


Related Questions

Vince is saving for a new mobile phone. The least expensive model Vince likes costs $225.90. Vince has saved $122.35. He used this solution to determine how much more he needs to save.

225.90 less-than-or-equal-to 122.35 + a. 225.90 minus 122.35 less-than-or-equal-to 122.35 minus 122.35 + a. 103.55 less-than-or-equal-to a.

Vince says that based on the solution, he should save a maximum of $103.55.

Is Vince correct?
Vince is correct because he found the correct solution to the inequality.
Vince is correct because he should save at least $103.55.
Vince is not correct because he wrote the wrong inequality to represent the situation.
Vince is not correct because he should have interpreted the solution as having to save a minimum of $103.55.

Answers

In light of the solution, Vince is correct in believing that he should only save up to $103.55.

How to determine with an example?

1. a: to formally decide (something), particularly because of facts or evidence: to establish (something) precisely or with authority. Title of the land has now been determined by the town. The land's legal owner has been established by the town. A particular committee will choose the new policy.

Vince is accurate because he perceived the solution correctly.

The inequality 225.90 ≤ 122.35 + a show that the cost of a phone ($225.90) is lower than or equal to the sum of Vince's saved money ($122.35) plus the remaining amount he needs to save (a).

The inequity can be made simpler by taking 122.35 off of both sides to get 103.55 ≤ a. Hence, Vince now needs to put aside at least $103.55 in order to buy the cheapest phone he loves.

In light of the solution, Vince is correct in believing that he should only save up to $103.55.

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Solve the triangle PQR(find m < P, m < Q, and the length of side r. See Attached.

Answers

The following are the values for the angles and side of the right triangle using the trigonometric ratio: P = 28.6137, Q = 61.3863, and r = 14.0112

What is trigonometric ratios?

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan P= 6.71/12.3 {opposite/adjacent}

P = tan⁻¹(6.71/12.3)

P = 28.6137

Q = 180 - (90 + 28.6137) {sum of interior angles of a triangle}

Q = 61.3863

sin P = 6.71/r {opposite/hypotenuse}

sin 28.6137 = 6.71/r

r = 6.71/sin 28.6137 {cross multiplication}

r = 14.0112

Therefore, the values for the angles and side of the right triangle using the trigonometric ratio are: P = 28.6137, Q = 61.3863, and r = 14.0112

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given: circle a externally tangent to circle b. a common internal tangent is segment ab line s line r

Answers

Circle A externally tangent to circle B, a common internal tangent is line r. so, the correct answer is A).

In a configuration where Circle A is externally tangent to Circle B, a common internal tangent is a line that is tangent to both circles and lies between them. This line is commonly referred to as the "direct common tangent" or "line of centers" and is denoted by letter r.

Line r is the direct common tangent because it passes through the centers of both circles and is perpendicular to the line segment that connects their centers. It also separates the two circles into distinct regions. Therefore, line r is the correct answer.

Line s is a common external tangent because it is tangent to both circles but lies outside of them, while segment AB is not a tangent but rather a chord of Circle A. So, the correct option is A).

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___The given question is incomplete, the complete question is given below:

Given: Circle A externally tangent to Circle B.

A common internal tangent is

A. line r

B. Line s

C. Segment AB

Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.

Answers

Important points to conduct a survey are; to gather information, make informed decisions, evaluate programs or services, identify trends, assess needs.

What is the need to conduct a survey?

Surveys are conducted for a variety of reasons, including gathering information, making informed decisions, evaluating programs or services, identifying trends, and assessing needs. By using surveys, organizations can collect valuable data that can be used to inform decisions, improve programs or services, and better understand their target audience.

Surveys, also known as questionnaires, are used to gather information from a targeted group of individuals or a population. Surveys are an important tool for collecting data in a structured manner and can be used for a variety of reasons. Here are some of the reasons why surveys are conducted:

To gather informationTo make informed decisionsTo evaluate programs or servicesTo identify trendsTo assess needs

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Mr. Roy captures 15 snapping turtles near some wetland by his house. He marks them with a “math is cool” label and releases them back into the wild. 6 months later, he captures another 15 snapping turtles – 4 of which were marked. Estimate the population of snapping turtles in the area to the nearest whole number. Show your work.

Answers

Answer: 56

Step-by-step explanation:

One possible method to estimate the population of snapping turtles in the area is by using the mark and recapture method, also known as the Lincoln-Petersen index.

According to this method, the population size can be estimated by dividing the number of marked individuals in the second sample by the proportion of marked individuals in the combined sample. In other words:

Estimated population size = (Number of individuals in sample 1 × Number of individuals in sample 2) / Number of marked individuals in sample 2

Using the information provided in the problem, we can fill in the formula as follows:

Estimated population size = (15 × 15) / 4

Estimated population size = 56.25

Rounding to the nearest whole number, we get an estimated population size of 56 snapping turtles in the area.

Let G
be a group. Say what it means for a map φ:G→G
to be an automorphism. Show that the set-theoretic composition φψ=φ∘ψ
of any two automorphisms φ,ψ
is an automorphism. Prove that the set Aut(G)
of all automorphisms of the group G
with the operation of taking the composition is a group.

Answers

a) An automorphism of a group G is a bijective map φ:G→G that preserves the group structure. That is, φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹ for all a, b ∈ G.

b) The set-theoretic composition φψ of any two automorphisms φ, ψ is an automorphism, as it preserves the group structure and is bijective.

c) The set Aut(G) of all automorphisms of G, with the operation of composition of maps, is a group. This is because it satisfies the four group axioms: closure, associativity, identity, and inverses. Therefore, Aut(G) is a group under composition of maps.

An automorphism of a group G is a bijective map φ:G→G that preserves the group structure, meaning that for any elements a,b∈G, we have φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹. In other words, an automorphism is an isomorphism from G to itself.

To show that the set-theoretic composition φψ is an automorphism, we need to show that it satisfies the two conditions for being an automorphism. First, we have

(φψ)(ab) = φ(ψ(ab)) = φ(ψ(a)ψ(b)) = φ(ψ(a))φ(ψ(b)) = (φψ)(a)(φψ)(b)

using the fact that ψ and φ are automorphisms. Similarly,

(φψ)(a⁻¹) = φ(ψ(a⁻¹)) = φ(ψ(a))⁻¹ = (φψ)(a)⁻¹

using the fact that ψ and φ are automorphisms. Therefore, φψ is an automorphism.

To show that Aut(G) is a group, we need to show that it satisfies the four group axioms

Closure: If φ,ψ∈Aut(G), then φψ is also in Aut(G), as shown above.

Associativity: Composition of maps is associative, so (φψ)χ = φ(ψχ) for any automorphisms φ,ψ,χ of G.

Identity: The identity map id:G→G is an automorphism, since it clearly preserves the group structure and is bijective. It serves as the identity element in Aut(G), since φid = idφ = φ for any φ∈Aut(G).

Inverses: For any automorphism φ∈Aut(G), its inverse φ⁻¹ is also an automorphism, since it is bijective and preserves the group structure. Therefore, Aut(G) is closed under inverses.

Since Aut(G) satisfies all four group axioms, it is a group under composition of maps.

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Solve the following equations graphically (a) .12x - 4y = 12​

Answers

Answer:

12x-4y=12

-4y= -12x+12
___________ [divide everything by -4]

-4

Y=3x+3

Step-by-step explanation:


on the y axis is 3 and the slope is 3

Using the data table, what is the probability that Baxter’s Shelties will NOT have a Tri-Color puppy this year? Justify your decision.

Answers

This is right because I’m right and I’m always right sk yes

PLEASE ANSWER THIS QUESTION, 20 POINTS!!

Answers

Answer:

∠1 = 50

∠2 = 50

∠3 = 80

∠4 = 130

∠5 = 130

Step-by-step explanation:

∠1 = 180 - 130 = 50

∠2 = ∠1 = 50

∠3 = 180 - ∠1 - ∠2 = 180 - 50 - 50 = 80

∠4 = 180 - ∠2 = 180 - 50 = 130

∠5 = ∠4 = 130

PLEASEE HELP ITS DUE TONIGHT!!!
Find the area of the shaded region

Answers

Answer: 84

Step-by-step explanation:

Area of whole rectangle = lb = 11x9 = 99

Area of Inner rectangle = lb = 5x3 = 15

Area of Shaded region = Area of whole rectangle - Area of Inner rectangle
                                      = 99 - 15

                                      = 84

Answer:

Area of shaded region = 84 units²

Step-by-step explanation:

Area = Area of bigger - Area of smaller

[tex] { \tt{area = (11 \times 9) - (5 \times 3)}} \\ \\ { \tt{area = 99 - 15}} \\ \\ { \tt{area = 84 \: units {}^{2} }}[/tex]

Find the slope of the following graph and enter your result in the empty box.

Answers

Answer:

1

Step-by-step explanation:

slope = rise/run = 1/1 = 1

John plans to practice piano at least 2 hours this weekend.
If he practices 1 hours on Saturday and 14 hours on Sunday, will he meet his goal?

Answers

Answer:

Yes

Step-by-step explanation:

Yes because 1+14=15 hours and that is more than two

9. find the second decile of the following data set 24, 64, 25, 40, 45, 34, 14, 26, 28, 24, 58, 51 d2

Answers

The second decile of the given data set, "24, 64, 25, 40, 45, 34, 14, 26, 28, 24, 58, 51"  is 24.

To find the second decile of a data set, we first need to arrange the data in order from lowest to highest, that is :

⇒ 14, 24, 24, 25, 26, 28, 34, 40, 45, 51, 58, 64

The second decile represents the value that divides the data into two parts, where 20% of the data is below the value and 80% of the data is above the value.

Since there are 12 data points in this set,

So, 20% of the data is equal to 0.2 × 12 = 2.4.

Since we cannot have a fractional data point, we round up to 3.

So, the second decile is the third value in the ordered data set.

which is 24.

Therefore, The second decile is 24.

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10 POINTS!! ASAP please help me find the area and also the outer perimeter!!!

Answers

Answer:

area of semi circle =pi r^2/2

3.14*6*6/2=56.2

area of rectangle=lb

=20*12=240

240+56.2=296.2

rounding it it will become 300 ft sqr

perimeter of rectangle without including 4th side=20+12+20=52

perimeter of semicircle=pi r+d (d is not needed here)

3.14*6=18.84

so total perimeter=52+18.84=70.84ft

Step-by-step explanation:

Given that x + 1/2 = 5, what is 2*x^2 - 3x + 6 - 3/x +2/x^2

pls help me soon

Answers

Sure, let's solve this step-by-step:

First, we need to solve for x in the equation x + 1/2 = 5.

We can do this by subtracting 1/2 from both sides, giving us x = 4 1/2.

Now, we can substitute x = 4 1/2 into the equation 2*x^2 - 3x + 6 - 3/x +2/x^2.

We can simplify the equation by multiplying both sides by x^2, giving us:

2*x^2 - 3x + 6 - 3/x +2 = 10*x^2 - 3x + 6.

Now, we can combine all of the terms with x:

10*x^2 - 6x + 6 = 0.

Finally, we can solve the equation using the quadratic formula:

x = 3/5 or x = 2.

Therefore, the answer to the equation is 10*(3/5)^2 - 6(3/5) + 6 = 4.8, or 10*2^2 - 6(2) + 6 = 16.

Find the circumference of the circle. Use 3.14 for the value of π, Round your answer to the nearest tenth.

Enter your answer and also show your work to demonstrate how you determined your answer.

Answers

The circumference of the circle is 18.22




C= 2•3.14•r
C= 2• 3.14• 2.9
C= 5.8

what is the square root of 36 divided by 5 times 12 divided by the cube root of 343 rounded to the nearest 2 decimal point

Answers

Answer:

  2.06

Step-by-step explanation:

You want the value of the numerical expression √36÷5×12÷∛343.

Calculator

This is a straightforward calculator problem. Your pocket calculator, or any of numerous calculator apps, online calculators, or spreadsheets can evaluate this expression for you.

The attachment shows the result is 2.06.

__

Additional comment

As expressed in this problem statement, the expression is ...

  [tex]\dfrac{\sqrt{36}\times12}{5\times\sqrt[3]{343}}=\dfrac{6\cdot12}{5\cdot7}=\dfrac{72}{35}[/tex]

If you mean something else, you need to identify the quantities that need to be considered as a unit.

can you help me to solve this question?

Answers

The asymptotes of the function f(x) = (2x² - 5x + 3)/(x - 2) are given as follows:

Vertical asymptote at x = 2.Oblique asymptote at: y = 2x - 3/2.

How to obtain the asymptotes of the function?

The function for this problem is defined as follows:

f(x) = (2x² - 5x + 3)/(x - 2)

The vertical asymptote is the value of x for which the function is not defined, hence it is at the zero of the denominator, and thus it is given as follows:

x - 2 = 0

x = 2.

The oblique asymptote is at the quotient of the two functions, hence:

(mx + b)(x - 2) = 2x² - 5x + 3

mx² + (b - 2m) - 2b = 2x² - 5x + 3.

Hence the values of m and b are given as follows:

m = 2.-2b = 3 -> b = -3/2.

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A binomial probability experiment is conducted with the given parameters compute the probability of X successes in the N independent trials of the experiment an equals 10P equals 0.35 and X equals 3​

Answers

Therefore, the probability of getting exactly 3 successes in 10 independent trials of a binomial probability experiment with probability of success 0.35 is approximately 0.213.

What is Probability?

Probability is a branch of mathematics that deals with the measurement and analysis of random events. It is a way of quantifying the likelihood of an event occurring. Probability can be expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.

The concept of probability is used in a wide range of fields, including statistics, physics, engineering, economics, and finance. It helps us make predictions about the likelihood of future events and make informed decisions based on those predictions.

by the question.

To compute the probability of X successes in N independent trials of a binomial experiment, we use the following formula:

[tex]P(X = x) = (N choose x) * p^x * (1-p)^(N-x)[/tex]

where "N choose x" is the binomial coefficient, given by:

[tex](N choose x) = N! / (x!(N-x)!)[/tex]

In this case, we are given that:

N = 10 (number of independent trials)

p = 0.35 (probability of success in each trial)

X = 3 (number of successes)

Therefore, we can compute the probability of X successes as:

[tex]P(X = 3) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3)[/tex]

Using a calculator, we can calculate:

[tex](10 choose 3) = 120 / (3! * 7!) = 120 / (6 * 5040) = 0.1666666670.35^3 = 0.042875(1-0.35)^(10-3) = 0.338915[/tex]

Putting it all together:

[tex]P(X = 3) = 0.166666667 * 0.042875 * 0.338915 = 0.00240157[/tex]

Substituting these values into the formula, we get:

[tex]P(X = 3) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3)[/tex]

[tex]= (10! / (3! * 7!)) * 0.35^3 *0.65^7[/tex]

≈ 0.213

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What type of exercise is ideal for a client who is new to strength training and learning new movement patterns

Answers

Answer:

For a client who is new to strength training and learning new movement patterns, it is ideal to start with bodyweight exercises and light resistance training. This will help them focus on proper form and technique without risking injury. Additionally, exercises that engage multiple muscle groups and involve functional movements, such as squats, lunges, and push-ups, are recommended as they provide a good foundation for overall strength and fitness. It is important to progress slowly and gradually increase resistance over time as the client becomes more comfortable with the movements and their strength improves. A certified personal trainer or strength coach can provide guidance and create a tailored program to meet the individual needs and goals of the client.

assuming w1, w2, and w3 are 0-1 integer variables, the constraint w1 w2 w3 < 1 is often called a

Answers

The constraint w1 w2 w3 < 1, where w1, w2, and w3 are 0-1 integer variables, is often called a packing constraint. The packing constraint w1 w2 w3 < 1 limits the number of variables that can be set to 1 and is used to control the number of items that can be selected in integer programming problems.

A packing constraint is a type of constraint used in integer programming that limits the number of items that can be selected from a set of items. In this case, the constraint limits the number of variables that can take the value 1 to be less than 1.

The term "packing" comes from the idea of packing items into a container. In the context of integer programming, packing constraints are used to limit the number of items that can be "packed" into a container (i.e., set to 1), while ensuring that the total value of the packed items meets certain requirements or constraints.

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Write the sentence as an equation. j plus 309 equals 313

Answers

Answer:j+309=313

Step-by-step explanation:

313-309=4

J=4

the larger leg of a right triangle is 7cm more than the smaller leg the hypotenuse is 17cm find each leg

Answers

Answer:

So the lengths of the legs are approximately 8.6 cm and 15.6 cm.

Step-by-step explanation:

Let's call the smaller leg "x" and the larger leg "x + 7". According to the Pythagorean theorem, we know that:

x^2 + (x + 7)^2 = 17^2

Expanding the square on the left side and simplifying, we get:

2x^2 + 14x - 210 = 0

Dividing both sides by 2, we get:

x^2 + 7x - 105 = 0

Now we can solve for x using the quadratic formula:

x = (-7 ± sqrt(7^2 - 4(1)(-105))) / 2(1)

x = (-7 ± sqrt(649)) / 2

x ≈ -15.6 or x ≈ 8.6

Since we're dealing with lengths of sides in a triangle, we can't have a negative value for x. So we discard the negative solution and conclude that the smaller leg is approximately 8.6 cm.

To find the larger leg, we add 7 to x:

x + 7 ≈ 15.6 cm

8. A rectangle is inch longer
than it is wide.
Let w=width.
Let = length.
Graph=w+
l=w

Answers

By the values of w and l we can plot the graph as shown in figure.

Define the term graph?

A graph in x-y axis plot is a visual representation of mathematical functions or data points on a Cartesian coordinate system. The x-axis represents the horizontal or independent variable, while the y-axis represents the vertical or dependent variable. A line or curve is drawn connecting the plotted points to show the relationship between the two variables.

Our equation is;

[tex]l = w +\frac{1}{2}[/tex]

Table between w and l can be draw as;

w            l

1         [tex]1+\frac{1}{2}[/tex] = 1.5

2        [tex]2+\frac{1}{2}[/tex] = 2.5

3        [tex]3+\frac{1}{2}[/tex] = 3.5

4        [tex]4+\frac{1}{2}[/tex] = 4.5

By these values we can plot the graph as shown in figure.

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how many positive integers are less than or equal to 200 are relatively prime to either 15 or 24 but not both

Answers

The number of positive integers less than or equal to 200 that are relatively prime to either 15 or 24 but not both is 48 + 64 - 4 = 108.

To solve this problem, we need to count the number of positive integers less than or equal to 200 that are relatively prime to either 15 or 24 but not both.

Let A be the set of positive integers less than or equal to 200 that are relatively prime to 15, and let B be the set of positive integers less than or equal to 200 that are relatively prime to 24. We want to count the number of elements in A union B but not in A intersect B.

To do this, we can use the principle of inclusion-exclusion. The number of elements in A union B is the sum of the number of elements in A and the number of elements in B, minus the number of elements in A intersect B.

The number of elements in A is phi(15) times the number of multiples of 15 less than or equal to 200, which is phi(15) times floor(200/15) = 48, where phi denotes Euler's totient function. Similarly, the number of elements in B is phi(24) times floor(200/24) = 64.

To find the number of elements in A intersect B, we need to find the number of positive integers less than or equal to 200 that are relatively prime to both 15 and 24.

Note that since 15 and 24 are relatively prime, a positive integer is relatively prime to both 15 and 24 if and only if it is relatively prime to their product 15 x 24 = 360. Thus, the number of elements in A intersect B is phi(360) times floor(200/360) = 4.

Therefore, the number of positive integers less than or equal to 200 that are relatively prime to either 15 or 24 but not both is 48 + 64 - 4 = 108.

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can someone please!!! THANK YOU PLEASE!

Answers

Answer:

84 [cm³]

Step-by-step explanation:

if to imagine the given figure as parallelepiped, then the required volume can be calculated as V[1]-V[2], where V[2] is the additional part.

finally, V=10*2*7-7*2*4=84.

All the details are in the attachment.

The length of a rectangle is 3 cm longer than twice the width. The area of the
rectangle is 90 sq cm. Find the length and the width of the rectangle.

Answers

as you know the area of a rectangle is length*width.
x=width
2x+3=length
x(2x+3)=90
now we just calculate the results
2x^2+3x=90
2x^2+15x-12x-90=0
(2x+15)(x-6)=0
we have 2 possible solutions
x=-15/2
x=6
since it cant be negative, the width is 6cm and the length 6*2+3=15
brainliest would be nice:))
x

A calico cat named Lucy has a favorite place to nap. It's a soft Matt located in front of a sunny window the mat is 12 total square feet and 4 ft long what is the width of Lucy's mat

Answers

3ft

Explanation:
Total square feet is length times width
We know the length is 4
So we can divide the total by this
12/4=3 so 3 ft

A rectangular paperboard measuring 33 inches long and 24 inches wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value 3.14 , and do not round your answer. Be sure to include the correct unit in your answer.

Answers

Answer: 565.92 square inches.

Step-by-step explanation:

To find the area of the paperboard that remains, we need to subtract the area of the semicircle from the area of the rectangle.

The rectangle has a length of 33 inches and a width of 24 inches, so its area is:

A_rect = length x width

A_rect = 33 in x 24 in

A_rect = 792 sq in

To find the area of the semicircle, we need to first find its radius. The diameter of the semicircle is the same as the width of the rectangle, which is 24 inches. So, the radius is:

r = 1/2 x diameter

r = 1/2 x 24 in

r = 12 in

The area of the semicircle is:

A_semicircle = 1/2 x pi x r^2

A_semicircle = 1/2 x 3.14 x 12^2

A_semicircle = 1/2 x 3.14 x 144

A_semicircle = 226.08 sq in

To find the area of the paperboard that remains, we subtract the area of the semicircle from the area of the rectangle:

A_remaining = A_rect - A_semicircle

A_remaining = 792 sq in - 226.08 sq in

A_remaining = 565.92 sq in

Therefore, the area of the paperboard that remains is 565.92 square inches.

the math method that returns the nearest whole number that is greater than or equal to its argument is

Answers

The math method that returns the nearest whole number that is greater than or equal to its argument is the "ceiling" function, denoted by ⌈x⌉ in mathematics.

The Ceiling function is denoted by ⌈x⌉, is a mathematical function that takes a real number x as an input and returns the smallest integer that is greater than or equal to x.

The ceiling function takes a real number x as an argument and returns the smallest integer that is greater than or equal to x.

For example, if x = 3.7, then ⌈x⌉ = 4, since 4 is the smallest integer that is greater than or equal to 3.7.

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As part of the Reconstruction Acts of 1867,Congress formally accepted Johnsons plans.harsher restrictions were forced on the South.the Freedmens Bureau lost most of its power.voting rights were granted to white men only. The bottom two steps of a stairwell are shown. Explain how to use the given measures to verify that the bottom step is parallel to the floor. the technique that illustrates how management can match the external opportunities and threats with its strengths and weaknesses to yield four sets of strategic alternatives is called a (an) Choose one point on the scatterplot. What does it represent?What type of data is best for scatter plots? please don't give a short once sentence explanation Classify the items with the appropriate region of the pharynx. Nasopharynx Superiormost portion Houses auditory tube openings Inferiormost portion Location of pharyngeal tonsil Location of the lingual tonsils Lined with pseudostratified Oropharynx ciliated columnar epithelium Location of the palatine Laryngopharynx tonsils How did the Munich Pact affect Europe 6. Modigliani and Miller assumptionsIn 1958 Franco Modigliani and Merton Miller (MM) published a set of research papers that revolutionized the theory of a corporation's capital structure. In their first research paper, MM proposed a set of assumptions that, on the surface, may seem unrealistic, but these assumptions and MM's algebraic approach provided the first significant attempt to study capital structure theory in a scientific fashion. The original assumptions that were used in MM's first study were changed by MM and other researchers as the theory of capital structure evolved.Which of the following statements are assumptions that Modigliani and Miller used in their initial (MM Proposition I) model and research paper?Check all that apply.?All investors are rational, and have the same expectations of a company's earnings (as measured by its EBIT).?Complete information is readily available to all investors and is free to all market participants.?There are no costs associated with a bankruptcy.?There are no taxeseither personal or corporate.?A firm's earnings will grow at an unpredictable rate.?The cost of debt increases with the level of debt.Consider the following statement about a firm's capital structure:The value of the firm is independent of its leverage.Is the preceding statement consistent with the conclusions of Modigliani and Miller's 1958 capital structure theory (MM Proposition I)?YesNo If the reaction quotient (Q) is smaller than the equilibrium constant (K) for a reaction then which way will the reaction proceed? a. The reaction is at equilibrium and the reaction will proceed at equal rates in the reverse and forward direction. b. The reaction will proceed to the right (products side) c. The reaction equation is required to answer this question d. The reaction will proceed to the left( reactants side) find the radius of a circle whose area is 28cm For your assignment, you will write a college admissions essay or a letter to a future employer using the Sandwich Method. Select one of these three topics for your essay/letter:Recount an incident or time when you experienced failure. How did it affect you, and what lessons did you learn?Reflect on a time when you challenged a belief or idea. What prompted you to act? Would you make the same decision again?Discuss an accomplishment or event, formal or informal, that marked your transition from childhood to adulthood within your culture, community, or family.Your essay should have three paragraphs. Each paragraph should have four-six sentences. Use matrix inversion to solve the given system of linear equations. (You previously solved this system using row reduction.)4x+y=44x3y=4 describe an example of rebellion in camps and why it was important. History of HolocaustAnswer in 3-5 sentences Which adaptation would be the most beneficial to mammals of both the taiga and marine aquatic biomes pols 1301 the role of the federal government in the implementation of social policies has decreased since the dong qichang created his qingbian mountains (fig. 25-12) in what standard format of chinese painting? The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble?A) 11B) 33C) 32D) 22 During mitosis, microtubules of the spindle apparatus attach to the _____ of the chromosomes. A) tetrads B) telomeres C) centrioles D) kinetochore proteins E) asters splunk's processing language, which is all the commands and functions needed to search through data, uses the following keyword to search through data Find the value of r so the line that passes through the pair of points has the given slope. (3, 5), (-3, r), m = 3/4 put these areas in size order starting with the smallest, 5.4m, 45,000cm, 5 X 10mm