What value of k makes the equation true? (5a^2b^3)(6a^kb)=30a^6b^4

Answers

Answer 1

The value of K will be equal to 4 for an expression (5a²b³)(6a[tex].^k[/tex]b)=30a⁶b⁴.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

We have an expression given as:-

(5a²b³)(6a[tex].^k[/tex]b)=30a⁶b⁴.

The mathematical properties we knew

[tex]x^mx^n = x^{m+n}[/tex]

[tex]x^m[/tex]÷[tex]x^n=x^{m-n}[/tex]

So the expressions will be written as:-

(5. 6 . a². a[tex].^k[/tex] .b³ .b =  30a⁶b⁴.

30 ( [tex]a^{2+k}[/tex])([tex]b^{3+1}[/tex]) =  30a⁶b⁴.

Comparing the terms we will get:-

[tex]a^{2+k}[/tex] = a⁶

2 + k = 6

k = 6 - 4

k = 4

Therefore the value of K will be equal to 4 for an expression (5a²b³)(6a[tex].^k[/tex]b)=30a⁶b⁴.

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Related Questions


Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?

Answers

Step-by-step explanation:

hope it helps you understand

The table shows the results of a survey of 200 randomly selected people on whether they like watermelon, cantaloupe, or both.

A 4-column table with 3 rows. The first column has no label with entries cantaloupe, not cantaloupe, total. The second column is labeled watermelon with entries 93, 66, 159. The third column is labeled not watermelon with entries 16, 25, 41. The fourth column is labeled total with entries 109, 91, 200.

Which is the marginal relative frequency for the people who do not like cantaloupe?

StartFraction 25 Over 91 EndFraction
StartFraction 66 Over 200 EndFraction
StartFraction 91 Over 200 EndFraction
StartFraction 66 Over 91 EndFraction

Answers

The marginal frequency for the people who do not like cantaloupe is StartFraction 91 Over 200 EndFraction/

The correct option is (C),

What is Marginal Relative frequency?

Marginal Relative Frequency is the ratio between the frequency of a row total or column total to the total frequency of the data.

Given:

                               Watermelon      Not watermelon     Total

Cantaloupe                  93                       16                         109

Not cantaloupe           66                       25                         91

Total                             159                       41                          200

Hence, the Marginal Relative frequency is = 91/200 = 0.455

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HELP ME PLEASEEE

Beatrice writes down every expression that appears in this problem set, one after the other, linking them with
+ signs between them. She is left with one very large expression on her page. Is that expression a polynomial expression? That is, is it algebraically equivalent to a polynomial?
What if she wrote - signs between the expressions instead?
What if she wrote × signs between the expressions instead?

Answers

Is that expression a polynomial expression?

yes because they are terms linked into one expression.

What if she wrote - signs between the expressions instead?

it would still be considered a polynomial.

What if she wrote × signs between the expressions instead?

no because it would be one huge term

can someone please do this for me ​

Answers

The range is from the maximum point into infinity that is [4, infty) and the vertex is at (0, 4)

Vertex, domain and range of a function

The given graph is a parabola. It represents the graph of a quadratic equation.

From the shown graph, the parabola has a maximum point at (0, 4). This is also the vertex of the graph

The domain area values along the x-axis while the range lies on the y-axis. From the graph shown, the domain is [-2, 2] (x lies between -2 and 2)

The range is from the maximum point into infinity that is [4, infty)

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please help!!! picture has the question and answer choices in it

Answers

Answer:

5x-y≥ 1  

Step-by-step explanation:

Find the slope of the line to be :

y = 5x -1     <=====  the shaded area is less than or equal (because it is a SOLID line...not dashed)  to this :

y ≤ 5x-1      re-arrange to

5x-y ≥ 1

Please answer this thanks

Answers

Answer: down below

Step-by-step explanation:

1. How many hay bales did the farmer sell?

To do that, you need to divide the weight of a hay bale by the total weight of the hay bales that the farmer sold.

That will be 24,300 / 75 = 324 bales

2. Divide the new number (26,700) by the same number 75.

26,700 / 75 = 356 hay bales

Subtract the bales from last year to the bales from this year:

356 bales - 324 bales = 32 bales

50 POINTS .....................

Answers

The option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have data shown in the picture.

Let's suppose the regression line is:

y = mx + c

Where m is the slope of the regression line and c is the y-intercept of the line.

We can calculate the value of m and c by using the formula.

After calculating, we get:

m = 0.4925

c = -22.26

Mus. Apt. = 0.49253(IQ score) - 22.26

or

Mus. Apt. = -22.26 + 0.4925(IQ score)

Thus, the option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.

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Answer:

The option (C) Mus. Apt. = -22.26 + 0.4925[the IQ score] is the correct answer. Because the value of slope is 0.4925 and the y-intercept is -22.26.

Which set of ordered pairs represents a line that is perpendicular to the given set:
(12,3) (9.4)?

Answers

Using linear function concepts, it is found that a set of ordered pairs with a slope of 3 is perpendicular to the set (12,3), (9,4).

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

If two lines are perpendicular, the multiplication of their slopes is of -1. The set (12,3), (9,4) has the slope given by:

m = (4 - 3)/(9 - 12) = -1/3.

Hence, for the perpendicular set:

[tex]-\frac{1}{3}m = -1[/tex]

m = 3.

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What is the value of x and y?

Answers

Answer:

[tex]\fbox {x = 6 and y = 12}[/tex]

Step-by-step explanation:

Taking the tan and cos values to find x and y :

tan 60° = √3 = 6√3/x⇒ x = 6cos 30° = √3/2 = 6√3/y⇒ y = 12

Answer:

x = 6 and y = 12

Step-by-step explanation:

30-60-90 Triangle Theorem

A special right-angled triangle where:

Angles are in the ratio 1 : 2 : 3Sides are in the ratio 1 : √3 : 2  

Therefore, the formula for the sides is  b : b√3 : 2b where:

b = shortest side opposite the 30° angleb√3 = side opposite the 60° angle2b = longest side (hypotenuse) is opposite the right angle

The given triangle is a 30-60-90 triangle, therefore the ratio of its sides is  b : b√3 : 2b

We have been given the measure of the side opposite the 60° angle.

⇒ b√3 = 6√3

So b = 6

Therefore, substituting the found value of b into the formula, the sides are in the ratio:  6 : 6√3 : 12

⇒ x = 6  (shortest side)

⇒ y = 12  (longest sides)

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Need help finding the one complete period of a non transformed contangent function

Answers

One complete period of a non-transformed cotangent function is π.

The period of the function is defined as the interval after which the function value repeats itself.

For example, f(T+x)=f(x)

where T is the period of the function.

Here given that there is a non-transformed function cotangent function.

We have to find the period of the function in which interval the value of the function will repeat.

So for the function y=f(x)=cot x

the period of the function is π. means after π the value of the cotangent repeats.

cot(π+x)=cot x

Then one cycle of the cotangent graph lies between 0 and π.

Therefore One complete period of a non-transformed cotangent function is π.

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Write 3x^2+12x+20 in the form a(x+b)^2+c

Answers

The equation is written as 3(x+12)²+20.The formula for ax² + bx + c is (Ax + B)² + C.

What is the equation?

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

3x^2+12x+20

The equation is compared the equation with,ax²+bx+c

After comparing the equation we get;

a=3

b=12

c=20

The equation is written in the form as;

⇒a(x+b)^2+c

⇒3(x+12)²+20

The formula for ax² + bx + c is (Ax + B)² + C.

Hence the equation is written as 3(x+12)²+20.

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what is the simlest form of the ratio 32:48

Answers

23 steps to simplifying

Answer: 2:3

Step-by-step explanation:

First list out the factors for 32 and 48

32- 1, 2, 4, 8, 16, 32

48- 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The greatest factor they have in common is 16. So, divide both numbers by 16 to get the simplest form of the ratio.

32/16=2

48/16=3

The simplest form is 2:3

The formula for the surface area of a
sphere that has a radius 7 is shown in
the box below.
SA = 4tr-2
A sphere and one of its dimensions are
shown in the diagram below.
5 in.
What is the surface area, in square
inches, of the sphere?

Answers

Step-by-step explanation:

hope you can understand

1+1= 2+1= 3+1= 4 so that is the answer to this difficult sum

Answers

Answer:

2 = 3 = 4 = 4

MATHHH. Probability section!!! HELP!
please give the right answer.

Answers

Answer:

answer = 1/4 < 7/25

Step-by-step explanation:

the theoretical probability is that because the spinner has 4 equal sized sections, it should land on each 25 times, 25/100 is 1/4  

28/100 is the experimental probability of landing on H, so that can be simplified to 7/25 as both numbers can be divisible by 4.

Hope this helps:)

The measure of an angle is 1/2 the measure of its supplement find the measure of each supplement. Help

Answers

Answer:

।बवछॅनछॅठै रटटृ रटटृरटॅलठट

the question is below

Answers

Answer:

B. $4.75

Step-by-step explanation:

3(4) + 7 = 19

19/4=4.75

Answer:

B

Step-by-step explanation:

First, 3n + 7 while n = 4 then 3*4 = 12 + 7 = 19. Next, you do 19/4 which is
            n
equal to 4.75.



I Hope This Helped :D
           

30 POINTS PLEASE HURRY
Jonathan and Kevin each rewrote and evaluated the expression (SEE PICTURE BELOW) They arrived at different answers.

Answers

Answer:

B. took test

Step-by-step explanation:

Answer:

B. Jonathan is correct. Kevin made an error at step 3.

Step-by-step explanation:

If you are driving a train and your going over 180 mph, and you pass 20 houses, 10 stores, 3 gas stations, and 1 hospital per every ten minutes, what is the eye color of the train driver??? :) lol

Answers

If I am driving the train , the colour of the eye will be my eye colour.

What are Logical Questions ?

The questions that do not need critical reasoning while only need logical thinking to find the answer.

It is given that the "If you are driving a train and your going over 180 mph, and you pass 20 houses, 10 stores, 3 gas stations, and 1 hospital per every ten minutes"

If I am driving the train , the colour of the eye will be my eye colour.

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One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0).

Which transformations could have taken place? Select two options.

Answers

As you are only given one point the choices are quite numerous:

A. Quarter turn rotation clockwise about the origin

B. Reflection in the line y = x

C. Translation using the vector (5 -5). [5 right and 5 down]

D. Half turn rotation about point (2.5, 2.5)

E. Reduction with scale factor 1/2 with centre at (10, -5)

The last two are not likely but still only require a single transformation

Answer: C & D

Step-by-step explanation: Ro 270, Ro -90

Find the tables with unit rates greater than the unit rate in the graph then arrange these tables in order from least to greatest unit rate

Answers

Table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.

What is a graph?

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

The unit rate of the graph is;

[tex]r_g = \frac{26-0}{14-0} \\\\ r_g = \frac{13}{7} \\\\ r_g = 1.857[/tex]

The unit rate for the given tables;

[tex]\rm r_1 = \frac{26-13}{14-7}\\\\ r_1 = \frac{13}{7} \\\\ r_1 = 1.857[/tex]

[tex]\rm r_2 = \frac{26-13}{14-7} \\\\ r_2 = \frac{9}{5} \\\\ r_2 = 1.8 < 1.818[/tex]

[tex]r_3 = \frac{34-17}{18-9} \\\\r_3 = \frac{17}{9} \\\\ r_3 = 1.889 > 1.818[/tex]

[tex]\rm r_4 = \frac{42-21}{22-11} \\\\ r_4 = \frac{21}{11} \\\\ r_4 = 1.909 > 1.818[/tex]

[tex]\rm r_5 = \frac{38-19}{20-10} \\\\ r_5 = \frac{19}{10}\\\\ r_ 5 = 1.9 > 1.818[/tex]

[tex]\rm r_6 = \frac{50-25}{26-13} \\\\ r_6 = \frac{25}{13} \\\\ r_6 = 1.923 > 1.818[/tex]

[tex]r_ 7 = \frac{46-23}{24-12} \\\\ r_7 = \frac{23}{12} \\\\r_7 = 1.917 > 1.818[/tex]

Hence, table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.

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A rectangular photograph measures 24 x 19 cm. It is mounted on a card of size such that there is a 2 cm border all around. For the purposes of this question take the length of the photograph to be 24 cm. If one of the borders must be 2cm in width, determine the width of a possible length and width so that the inner and outer rectangles are similar. (I NEED HELP PLEASeeeeeeeeeeeeeeeee)

Answers

The possible length is 28cm and width is 23cm.

Rectangle is a two dimension figure with length and width.

Area of the rectangle is given by length × width.

Perimeter of the rectangle is given by 2 ( length + width ).

Given that dimension of a rectangular photograph is 24 × 19 cm.

So, Length of the rectangular photograph = 24 cm

Width of the rectangular photograph = 19cm

It is given that rectangular photograph is mounted on a card which has 2cm border all around.

Therefore, Length = 24cm + 2cm + 2cm = 28cm

Width = 19cm + 2cm + 2cm = 23cm.

Hence, the possible length so that the inner and outer rectangles are similar = 28cm

The possible width so that the inner and outer rectangles are similar = 23cm

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The possible length is 28cm and width is 23cm.

Rectangle is a two dimension figure with length and width.

Area of the rectangle is given by length × width.

Perimeter of the rectangle is given by 2 ( length + width ).

Given that dimension of a rectangular photograph is 24 × 19 cm.

Therefore, Length of the rectangular photograph = 24 cm and

Width of the rectangular photograph = 19cm

It is given that rectangular photograph is mounted on a card which has 2cm border all around.

Therefore,

Length = 24cm + 2cm + 2cm = 28cm

Width = 19cm + 2cm + 2cm = 23cm.

Hence, the possible length so that the inner and outer rectangles are similar = 28cm

The possible width for the inner and outer rectangles are similar = 23cm

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Find the solution to the system
of equations.
4
y = 2x + 2
3
2
([?], [ ])
-4-3-2/1
1 2 3 4
y=-x-3
-1
-2
3
-4

Answers

Answer:

(- 2, - 2 )

Step-by-step explanation:

the solution to the system is at the point of intersection of the 2 lines.

the 2 lines intersect at (- 2, - 2) , then

solution to the system is (2, - 2 )

Which is the best estimate to the nearest one percent of startfraction 7 over 15 endfraction?

Answers

The best estimate to the nearest one percent of the fraction; 7/15 is; 47%.

What is the best estimate of the fraction to the nearest percent?

From the task content, it follows that the fraction given whose estimate is to be determined is; 7/15.

The fraction expressed as a percentage is;

(7/15) × 100 %

= 46.667%.

Hence, when rounded to the nearest one percent; = 47%.

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rectangle has a base of 10 and a height of 5. What is the perimeter of the rectangle?

Answers

Answer:

30

Step-by-step explanation:

P=2(b+h)=2·(10+5)=30

Answer: 30

Step-by-Step Solution:

We know, Base = Length and Height = Breadth of the Rectangle.

Length (l) = 10
Breadth (b) = 5

Perimeter of the Rectangle = 2(l + b)

Therefore,
= 2(l + b)
= 2(10 + 5)
= 2(15)
= 2 * 15
=> 30

Perimeter of the Rectangle = 30

Given that h={A,E,I,O,U},which is the number of possible subsets of set h

Answers

There are 32 subsets of the set h.

We have given that h={A,E,I,O,U},

We should count the elements of the set, then put that number as the exponent of 2.

What is the subset?

A set A is a subset of another set B if all elements of set A are elements of set B. In other words, set A is contained inside set B.

Remember that 2 should always be the base in finding the number of subsets: 2^5=32

Therefore there are 32 subsets of the set h.

Here set h is denoted by small h but the set is always denoted by capital letters.

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what i the solution to this equation
6 (x - 5) = 4x + 20

Answers

6 (x - 5) = 4x + 20

6x - 30 = 4x + 20

6x - 4x = 20 + 30

2x = 50

[tex]x = \frac{50}{2} [/tex]

x = 25

Answer: The value of x = 25 ✅

Step-by-step explanation:

Hii! Do you need to know the solution to the equation [tex]\boldsymbol{6(x-5)=4x+20}[/tex]? No problem! (:

Solving Equations

     In any equation, there's a variable that we need to solve for. Here the variable is "x".

So now let's solve for x...

[tex]\twoheadrightarrow\sf 6(x-5)=4x+20[/tex]

[tex]\bullet[/tex] "distribute" 6

[tex]\twoheadrightarrow\sf 6x-30=4x+20[/tex]

[tex]\bullet[/tex] subtract "4x" from both sides

[tex]\twoheadrightarrow\sf 2x-30=20[/tex]

[tex]\bullet[/tex] add "30" to both sides

[tex]\twoheadrightarrow\sf 2x=50[/tex]

[tex]\bullet[/tex] divide both sides by "2"

[tex]\twoheadrightarrow\sf x=25\;\;\;[/tex] ✅

--

Hope that this helped! Best wishes.

[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]

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--

[tex]\bigstar\underbrace[/tex]

solve for y in 1/8^2-3y=2^y-2

Answers

The value of y is 2.33924.

What is equation?

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

Given:

(1/8)²-3y = [tex]2^{y}[/tex]-2

1/64 - 3y =  [tex]2^{y}[/tex]-2

1/64+ 2 =  [tex]2^{y}[/tex]+3y

129/2 =  [tex]2^{y}[/tex]+3y

Taking log on both side

log 129 - log 2 = y log 2 + 3 log y

2.11 - 0.301 = 0.301 y + 3 log y

1.809 = 0.301 y + 3 log y

1.809/3= 0.1 y + log y

0.603 = 0.1 y + log y

y = [tex]10^{\frac{603-100y}{1000}}[/tex]

y= 2.33924

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Which integer is the smallest? A. -84 B. -4 OC. 34 OD. 24 Advanced Placement, AP AP Central", College Board", and SAT are trademarks registered by the Colleg ACT is a trademark registered by ACT, Inc., which is not affiliated with, and does not endorse, this website. Copyright 2010-2022 edtell, LLC. All rights reserved. Portions of this software are copyrighted by other partie. Which integer is the smallest ? A. -84 B. -4 OC . 34 OD . 24 Advanced Placement , AP AP Central " , College Board " , and SAT are trademarks registered by the Colleg ACT is a trademark registered by ACT , Inc. , which is not affiliated with , and does not endorse , this website . Copyright 2010-2022 edtell , LLC . All rights reserved . Portions of this software are copyrighted by other partie .​

Answers

Answer: B -4

Step-by-step explanation: I think it is B because -4 is smaller than A,C and D.

The smallest integer among the options provided is option A, which is -84.

In the context of integers, smaller values are considered to be "less" than larger values.

In this case, we can compare the given integers to determine the smallest one.

Comparing the options:

A. -84

B. -4

C. 34

D. 24

Out of these options, -84 is the smallest integer because it has the lowest numerical value.

The negative sign indicates that it is a number less than zero, and the absolute value of 84 is greater than the absolute values of -4, 34, and 24.

Therefore, based on numerical value, -84 is the smallest integer among the options given.

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) How long does he travel at 30 km/h, if he travels 1.2 h at 20 km/h?​

Answers

Step-by-step explanation:

please mark me as brainlest

Other Questions
The world record for pole vaulting is 6.15 m. If the pole vaulters gravitational potential is 4942 J, what is his mass? If you are driving a train and your going over 180 mph, and you pass 20 houses, 10 stores, 3 gas stations, and 1 hospital per every ten minutes, what is the eye color of the train driver??? :) lol Based on this excerpt, how would you describe the relationship between the United States and the Soviet Union at this time? Write your response in 5075 words. Which answer choice describes the following sentence from "Science and the Sense of Wonder"?But what I seethose quiet, twinkling points of light. Change a Relation to Make It a Function The relation R is shown below as a list of ordered pairs. R = { (1, 4), (1, 3), (-1, 3), (2, 15) } Which ordered pairs prevent this relation from being a function? (1, 4) and (1, 3), because they have the same x-value (1, 3) and (1, 3), because they have the same y-value The formula for the surface area of asphere that has a radius 7 is shown inthe box below.SA = 4tr-2A sphere and one of its dimensions areshown in the diagram below.5 in.What is the surface area, in squareinches, of the sphere? In the film, actor Cliff Curtis says, "We are still trying to colonize one another's minds. We're still trying to tell people what to think." What do you think he means by this? How is it possible to tell people what to think? You are the owner of a parasailing company that is expanding operations to a new beachfront location, and you need to prepare a 3-year analysis for the bank that may loan you the funds to purchase your boat and parasailing equipment. A lot of business is done on a referral basis, where a company pays a fee to a 3rd party to send them customers. However, because of your well-established reputation, you already have received requests for flights to be scheduled as soon as you open the new location. Therefore, you expect to break-even the first year but must calculate the number of flights needed. You also need to determine the new break-even point in Year 2 if the location allows referrals, which you believe will cost on average about 2% of the sales price overall. Finally, you need to determine the volume needed to have $10,000 in profit in Year 3. The following information is available:Sales price per flight $175Estimated loan payment per month $350Fuel costs per flight $100Full-time scheduler salary $2,500 per monthBoat crew per flight $30$500 per month dock fee and use of a small office on a pierCalculate the Year 1 break-even quantity, contribution margin, and contribution margin ratio. Explain how the values were determined.Calculate the Year 2 break-even quantity, break-even sales, and contribution margin ratio. Explain how the values were determined.Determine the number of flights (units) needed to retain a profit of $10,000 in Year 3, assuming the company does allow for referrals.Recommend if the bank should issue the loan. How is Mr. Whites reaction different than Mrs. Whites in the excerpt?He understands more quickly that Herbert is dead.He is angrier than his wife that Herbert is dead.He is sadder than his wife that Herbert is dead.He seems less surprised that Herbert is dead. solve for y in 1/8^2-3y=2^y-2 In this speech roosevelt is advising journalists to write honestly and not always muckrake. what theme does roosevelt use repeatedly to appeal to the audience's emotions? anger and disdain good versus evil investigative versus muck-raking journalism social and economic class differences Complete the coordinate proof of the theorem. PLEASEEEEEE HELPPPPPPP!!! 50 POINTSSSSSS12 = 6^2 + 7^2 - 2 (6) (7) (cosA)solve for the cosA If the Moon had twice as much mass and still orbits Earth at the same distance, ocean bulges on Earth would besmaller.larger.unequal in size.not significantly different.none of the available options please help!!! picture has the question and answer choices in it 1. What is the length of XU?XUY36 inVZW23 in if m=p/2+3r. find the value of p if r=1 and m=5 Which event is part of the rising action in "Little Snow White"? O Snow White eats the apple and falls into a deep sleep. O Snow White lives in a kingdom with an evil queen O The prince wakes Snow White from her deep sleep. O The queen learns that she is not the fairest of them all what is meant by afterglow? A company decides to offer a monetary incentive for employees who log a specified number of hours spent exercising in an attempt to improve employee health. The average health score (higher = better) of the 75 employees who logged enough hours was 87. The mean health score for all employees (population) was 85, with a population standard deviation of 6.5. Calculate the standard error of the mean