URGENT!!!
Which is equal to sin of angle e?
a) cos of angle D
b) cos of angle F
c) sin of angle D
d) sin of angle F

URGENT!!! Which Is Equal To Sin Of Angle E?a) Cos Of Angle Db) Cos Of Angle Fc) Sin Of Angle Dd) Sin

Answers

Answer 1

Answer:

B) cos f

Step-by-step explanation:

sin e = DF/EF

cos d = (which side is adjacent i don't even know)/EF

cos f = DF/EF

sin d = opposite (hypotenuse)/hypotenuse, doesn't make sense

sin f = DE/EF

life lesson in trig: don't try to do right triangle trig using the right angle, it won't work out


Related Questions

Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (Use 3.14 for π)
A) 15.7 cm
B) 31.4 cm
C) 62.8 cm
D) 78.5 cm

Answers

Answer:

Step-by-step explanation:

The formula for the circumference of a circle of radius r is C = 2πr.  That for a circle of diameter d is C = πd.  

If we assume that the measurements below are of radius, not diameter, then in A, 15.7 cm = 2(3.14)(r), so that r must be 2.5 cm.

Please be sure to share ALL of the instructions for each problem.

Circumference of the circle is 31.4 cm

Given that;

Value of π = 3.14

Assume;

Radius of circle = 5 cm (Approx.)

Computation:

Circumference of the circle = 2πr

Circumference of the circle = 2(3.14)(5)

Circumference of the circle = (10)(3.14)

Circumference of the circle = 31.4 cm

So, option "B" is the correct answer to the following question.

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Justin is skeet shooting. The height of the skeet is modeled by the equation h= -5t^2 +32t + 2, where h represents the height in meters and t seconds after the skeet is released. The path of Justin's bullet is modeled by the equation h= 31.5t + 1, with the same units. How long will it take for the bullet to hit the skeet? How high off the ground will the skeet be?

Answers

Final answer:

By solving the system of equations representing the paths of the bullet and the skeet, we find that the bullet will reach the skeet 3.79 seconds after the skeet's release, at a height of approximately 120 meters.

Explanation:

This problem involves solving systems of equations to determine the interaction between a projectile and target, something commonly addressed in physics as well as in mathematics. The solution involves equalizing the equations[tex](h = -5t^2 +32t + 2)[/tex] modeling the height of the skeet and (h = 31.5t + 1) the path of Justin's bullet. By solving this system of equations we find two potential times, t = 3.79 s and t = 0.54 s.

Since we can reason the skeet won't get hit before it is released, disregard t = 0.54 s. Therefore, the bullet will hit the skeet 3.79 seconds after the skeet is released. This is the time it takes for the bullet to reach the skeet. To find the height at which the bullet hits the skeet, substitute t = 3.79 into either of the two original equations (both should work). Using h = 31.5t + 1, for instance, yields approximately h = 120 meters.

So, the bullet hits the skeet 3.79 seconds after the skeet is released, at a height of about 120 meters from the ground.

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10. A circle has an arc with measure 80° and length 887. What is the
diameter of the circle?

Answers

The diameter of the whole circle is 2*pi*radius . The arc length is then 80/360*pi*radius*=88*pi
radius=88*180/80
=44*180/40
=22*180/20
=11*180/10
=11*18
=(10+1)*18
=198
The diameter is 2*198=(200-2)=400-4=396

SO BASICALLY THE ANSWER IS 396

Consider the right triangle. A right triangles with side lengths 28 meters and 45 meters. The hypotenuse is unknown. What is the length of the hypotenuse StartRoot 53 EndRoot StartRoot 1,241 EndRoot 53 m 2809 m

Answers

Answer:

The answer is 53 or Square Root (sqrt) of 2809

Step-by-step explanation:

a^2+b^2=c^2

28^2+45^2=c^2

784+2025=c^2

c^2=sqrt 2809

c = 53

The hypotenuse of the right triangle is h = 53 m

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of base of triangle BC = 45 m

The height of the triangle AB = 28 m

And , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

On simplifying , we get

AC² = AB² + BC²

AC² = 28² + 45²

AC² = 784 + 2025

AC² = 2809

Taking square roots on both sides , we get

The measure of hypotenuse AC = √2809 = 53 m

Hence , the measure of hypotenuse is 53 m

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Jason got 16 hits in his baseball tournament. Two of his hits were home runs, ten were ground balls and the rest were line drives. If Jason's mom only got to see one game during the tournament, what was the probability that she saw Jason hit a line drive?

Answers

Answer:

1/16

Step-by-step explanation:

10. Charlie biked 15 minutes home from school and then walked 12 minutes to the pizza place near his house. This trip was 3.6 miles in total. His rate on his bike is 3 miles per hour less than 5 times his walking rate. In miles per hour, what is Charlie’s speed as he walks and what is his speed as he bikes?

Answers

Answer:

3mph and 12mph

Step-by-step explanation:

GIVEN: Charlie biked [tex]15[/tex] minutes home from school and then walked [tex]12[/tex] minutes to the pizza place near his house. This trip was [tex]3.6[/tex] miles in total. His rate on his bike is [tex]3[/tex] miles per hour less than [tex]5[/tex] times his walking rate. In miles per hour.

TO FIND: Charlie’s speed as he walks and his speed as he bikes.

SOLUTION:

Let speed of charlie when he walks be [tex]x\text{ mph}[/tex]

Then speed of charlie as he biked [tex]=5x-3\text{ mph}[/tex]

Total length of trip [tex]=3.6\text{ miles}[/tex]

Total time taken[tex]=27\text{ minutes}=\frac{27}{60}\text{ hour}=\frac{9}{20}\text{hour}[/tex]

Now,

[tex]\text{Distance}=\text{speed}\times\text{time}[/tex]

distance traveled on bike [tex]=(5x-3)\times\frac{15}{60}=\frac{(5x-3)}{4}[/tex]

distance traveled by walking [tex]=x\times\frac{12}{60}=\frac{x}{5}[/tex]

As, [tex]\frac{(5x-3)}{4}+\frac{x}{5}=3.6[/tex]

     [tex]\frac{29x-15}{20}=3.6\implies 29x=87[/tex]

  [tex]\implies x=3\text{ mph}[/tex]

Speed of Charlie on bike [tex]=5x-3=12\text{ mph}[/tex]

Hence speed of charlie on bike and by walking is 12mph and 3mph respectively

If f(x)=3x-9, what is the value of f(-8)

Answers

1/3x Put the -8 in the place of the f(x) the subtract 9 you´re left with 1 then divde by 3x  and you're left with 1/3x

Carl’s square swimming pool has a volume of 1000 cubed feet. What are dimensions of his pool?

Answers

Answer: the answer is down bellow

Step-by-step explanation:

x3-10oo Dimensions ft each S.

Final answer:

The dimensions of Carl's square swimming pool, given that its volume is 1000 cubic feet, are approximately 10 feet by 10 feet by 10 feet.

Explanation:

Carl's swimming pool is a cube since all sides are equal. The volume of a cube is calculated by cubing one side (s^3). In this case, knowing that the volume is 1000 cubed feet, we can find the side length by taking the cube root of the volume. The cube root of 1000 is approximately 10 feet. Hence, the dimensions of Carl's swimming pool are 10 feet by 10 feet by 10 feet.

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What is the following quotient? StartFraction StartRoot 120 EndRoot Over StartRoot 30 EndRoot EndFraction 2 4 2 StartRoot 10 EndRoot 3 StartRoot 10 EndRoot

Answers

√120 / √30 = √(120/30) = √4 = 2

Answer:

A

Step-by-step explanation:

It's A I got it right on Edge

Find the mode for the image below

Answers

Answer:

7

Step-by-step explanation:

Mode is the number that repeats the most

7 is repeating the most

The mode for the given bar image shown is: 7

How to find the mode of the dataset?

In statistics, the mode is a measure of central tendency that refers to the value that appears most frequently in a dataset. It can be used to summarize categorical variables, while the mean and median can only be calculated for numeric variables. The mode is calculated by putting the numbers in order from least to greatest and counting how many times each number occurs.

From the given bar graph, we see that the number that occurs the highest number of times is 7 as it is the tallest bar.

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Britney can buy daffodil bulbs in packages of 3 for $3.33 or in packages of 2 for $2.68. How much money does she save by buying 12 bulbs at the better price?

WILL GIVE BRAINLIST!!!!! :))

Answers

Answer:

The better but is 3 for $3.33

12 for $13.32

Step-by-step explanation:

3.33/3 = 1.11

2.68/2 = 1.34

The better buy is 3 for $3.33

1.11 x 12 = 13.32

1.34 x 12 = 16.08

A gardener is planting two types of trees:
Type A is 10 feet tall and grows at a rate of 21 inches per year.
Type B is 7 feet tall and grows at a rate of 25 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the
same height.​

Answers

9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.

Step-by-step explanation:

The given is,

                Type A is 10 feet tall and grows at a rate of 21 inches per year

                Type B is 7 feet tall and grows at a rate of 25 inches per year

Step:1

             Convert the rate of grows of tree inch to feet,

             For Tree A,

                   Rate of grow, A = 21 inches per year

                                              = 21 × 0.0833333      ( 1 inch = 0.0833333 feet)

                                             = 1.75 feet per year

              For Tree B,

                   Rate of grow, B = 25 inches per year

                                              = 25 × 0.0833333     ( 1 inch = 0.0833333 feet)

                                             = 2.08333 feet per year

Step:2

           Difference in the tall of  Tree A & B,

                                               = 10 - 7

                                              = 3 feet

           Difference in the rate of grow of tree A & B,

                                                = 2.08333 - 1.75

                                               = 0.3333325 feet per year

Step:3

           Year take to both trees are same height,

                                               [tex]= \frac{Difference in the height of tree A & B}{Difference in the rate of grows of A & B}[/tex]

                                               [tex]= \frac{3}{0.3333325}[/tex]

                                               [tex]= 9.00[/tex]

                                               = 9 years

Step:4

            Check for solution,

            Height of tree = Height of Tree + (Rate of grow × Years)

            For A,

                                    = 10 + ( 1.75 × 9 )

                                   = 25.75 feet.........................................(1)

            For B,

                                   = 7 + ( 2.08333 × 9 )

                                    = 25.74999

                                   ≅ 25.75 feet.....................................(2)

          From Equation (1) and (2),

                  25.75 feet = 25.75 feet

Result:

          9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.

One of the parks mounds is 63 feet in height. If the top of the mound is rectangular in shape with a perimeter of 322 yards, what could be the side lengths of the rectangle?

Answers

Answer:

see the explanation

Step-by-step explanation:

we know that

The perimeter of rectangle is given by the formula

[tex]P=2(L+W)[/tex]

where

L is the length

W is the width

In this problem we have

[tex]P=322\ yd[/tex]

substitute

[tex]322=2(L+W)[/tex]

simplify

[tex]L+W=161\ yd[/tex]

so

The side lengths of the rectangle could be any pair of values whose sum must equal 161 yards

see the attached figure to better understand the problem

With the given height approximate the length of the rectangle

[tex]L=144\ ft[/tex]

Convert to yards

[tex]1\ yd=3\ ft[/tex]

so

[tex]144\ ft=144/3=48\ yd[/tex]

Find the width

[tex]48+W=161\\W=161-48\\W=113\ yd[/tex]

therefore

The side lengths of the rectangle could be 48 yd by 113 yd

What is the y-intercept of y = 50 - 1?

Answers

Answer:

49 or -1

Step-by-step explanation:

(im going to assume you meant y=50-1 and not y=50x-1)

The intercept would literally be 49 since 50-1=49

y=50x-1 would mean the y intercept is -1

Answer:

the y intercept is (0,49) Plz give branliest i need to level up

Step-by-step explanation:

50 - 1 = 49

y always equals 49

so the y axis is at x coordinate 0 and y intercept is at the y axis

so the point is (0,49)

PLEASE HELP TUME LIMIT IS 10 MINUTES

Answers

Answer:

similar and congruent

Step-by-step explanation:

those are the only words i know

Answer:

congruent and similar

Step-by-step explanation:

this is 23 points please help me or i’m gonna fail

Answers

Answer:

A

Step-by-step explanation:

Can someone plz help me with this hint it’s not D plz someone help me I’m not sure I understand this

Answers

Answer:

The answer is C, or 3/5.

A middle school has 6th, 7th, and 8th-grade students. Which of the following would be a random sample of the students
A.) Surveying all of the teachers
B.) Surveying the students who buy their lunch in the cafeteria
C.) Surveying everyone whose last name begins with a G
D.) Surveying every 10th student who is on the class rosters

Answers

the answer would probably be d.

Answer:

c

Step-by-step explanation:

because you wount have a good esstimite you would only have the kids that start with G please mark as brainliest

15. A scale drawing of a rectangular field has a length of 4.5 inches and a width of
3 inches. If the scale is 0.5 inch : 10 feet, what is the actual width of the field?
A. 6 feet
B. 15 feet
C. 30 feet
D. 60 feet​

Answers

3/0.5 = 6
6 x 10 = 60
D


JK Fitness Center offers two membership plans. The tables represent the monthly cost, in dollars, of each membership plan based on the
number of visits to the fitness center.
PART A: At a certain number of visits, both plans will cost the same. At that number, how much will both plans cost, in dollars?

PART B: Which plan is more expensive at the 10th visit?
Write the number of the plan in the box.

Answers

Step-by-step explanation:

From the looks of it, Plan A is 25 + 2x and plan B is 40 + x.

Part A:

25 + 2x = 40 + x

x  = 15

plug in any: 40 + 15 = $55

Part B:

Plan A = $45

Plan B = $50

Plan B is $5 more expensive.

After 15 number of visits, both plans cost $55 and at the 10th visit, plan 2 is more expensive than plan 1.

What is Arithmetic Sequence?

Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Part A :

From the table, we can clearly express both plans as Arithmetic sequence.

Plan 1 : First term, a = 27 and common difference, d = 2

Plan 2 : First term, a = 41 and common difference, d = 1

Let n be the number of visits that both plans costs the same.

27 + 2(n - 1) = 41 + (n - 1)

27 + 2n - 2 = 41 + n - 1

2n + 25 = n + 40

n =  15

Cost = 41 + (15 - 1) = $55

Part B :

We have to find the 10th term.

For plan 1 :

Cost at 10th visit = 27 + 2(10 - 1) = $45

For plan 2 :

Cost at 10th visit = 41 + (10 - 1) = $50

The plan 2 is more expensive at the 10th visit.

Hence at the 10th visit, plan 2 is more expensive.

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Given: f(x) = 3 - X; g(x) = -2x
Find g[f(x)]

Answers

Answer:

g[f(x)] = -2(3 - x) = -6 + 2x

Step-by-step explanation:

When we substitute the function f(x) for x in g(x) = -2x, we get the composition g[f(x)]:

g[f(x)] = -2(3 - x) = -6 + 2x

Final answer:

To find g[f(x)], we substitute (3 - x) from f(x) into g(x). The solution to g[f(x)] is -6 + 2x.

Explanation:

The question asks us to find the composition of the functions f(x) and g(x), specifically g[f(x)]. To do this, we first evaluate f(x) and then use that result as the input for g(x).

Given that f(x) = 3 - x, we substitute x in g(x) for the entire function f(x).

g(f(x)) = g(3 - x) since g(x) = -2x.

Now we replace the x in g(x) with (3 - x): g(3 - x) = -2(3 - x).

This simplifies to g(f(x)) = -6 + 2x.

The composition g[f(x)] is therefore -6 + 2x.




If each cube has edges 1.5 centimeters long, what is the volume of the prism outlined in blue?

A) 9 cm3

B) 15.5 cm3

C) 81 cm3

D) 91.125 cm3

Answers

Answer:

The answer is D) 91.125 cm3

Step-by-step explanation:

Consider the possible solution to each inequality. Choose Yes or No for
each question
a. Is 8.3 a solution of 73.8 S 9x?
Yes No
b. Is 6.5 a solution of 12x < 78?
Yes No
c. Is -7 a solution of 9x > 45?
Yes No
d. Is 17 a solution of 15 - X2-2? o Yes No
e. Is 6 a solution of x + 12 > 18?
Yes No

Answers

The answer is below!

Q: Consider the possible solution to each inequality. Choose Yes or No for

each question

a. Is 8.3 a solution of 73.8 S 9x?

b. Is 6.5 a solution of 12x < 78?

c. Is -7 a solution of 9x > 45?

d. Is 17 a solution of 15 - X2-2?

e. Is 6 a solution of x + 12 > 18

Answer :

No

No

Yes

No

No

Two similar triangles are shown on the coordinate grid: A coordinate plane is shown. Triangle ABC has vertices A at negative 3 comma 2, B at negative 1 comma 0, and C at negative 2 comma negative 1. Triangle A prime B prime C prime has vertices A prime at 6 comma 4, B prime at 2 comma 0, and C prime at 4 comma negative 2. Which set of transformations has been performed on triangle ABC to form triangle A’B’C’?

Answers

Answer:

i will go with c

Step-by-step explanation:

Find the range of each data set.

Answers

Answer:

set one 11

set two 208

set to has a wider spread of data

Step-by-step explanation:

Answer:

11 for question number 1.

208 for question number 2.

Step-by-step explanation:

1. Range: 12 - 1 = 11

2. Range: 230 - 22 = 208

is 0.3π rational or irrational

Answers

Answer:

irrational

Step-by-step explanation:

Answer:

0.3π is a irrational number.

Step-by-step explanation:

Hope this helps! :)

Ten students on student council are running for president, vice president, and
secretary. How many different permutations are there for the 3 positions?

Answers

Answer:

Step-by-step explanation:Using the word "HAPPY" (let's distinguish the P's as P1 and P2). ... The first person is the president , the 2nd is the Vice President and the 3rd is the Secretary so it ... Q-Four different items have to be placed in three different boxes.

Final answer:

There are 720 different permutations for filling the three positions (president, vice president, and secretary) among ten students on the student council.

Explanation:

The question asks for the number of different permutations there are for three positions (president, vice president, and secretary) among ten students on the student council.

This is a classic permutation problem in which order matters.

To calculate this, we can use the formula for permutations of 'n' items taken 'r' at a time, which is denoted as nPr and calculated as

n! / (n-r)!

where

'!' denotes factorial.

For this case, with ten students (n=10), and selecting three positions (r=3), the calculation would be:

10! / (10-3)! = 10! / 7! = 10 x 9 x 8 = 720.

Therefore, there are 720 different permutations available for the three positions on the student council.

What is 7 divided by 588

Answers

Answer:

84

Step-by-step explanation:

7 go's in to 58 8 time's bring the 8 down

you get 28 4 x 7 is 28 so it is 84

Help me! Write an equation to describe the relationship in each table. Check out the attachment to see the tables!

Answers

Let’s look at the first table. Set up the rule: y=kx You want to replace the variables with the numbers in the chart. Let’s do 11=k21. Since y is smaller than x we would most likely use a fraction or decimal. Now what we want to do is divide 11 by 21. This should give you the result of 0.5238095238 or ≈0.52 so the rule is y=0.52x.

Now let’s look at the second chart. Let’s do 1=k4. Same thing, divide 1 by 4 which will give you the result of 0.25. The rule of this table is y=0.25x.

These equations capture the linear relationships observed in the tables, allowing you to predict the value of y for any given value of x within these patterns.

In Table 1, you can observe that as the value of x decreases by 1, the value of y also decreases by 1. This suggests a linear relationship between x and y, where y is a function of x. The equation that describes this relationship is:

[tex]\[ y = x - 10 \][/tex]

In Table 2, there is a similar linear relationship between x and y. As x decreases, y also decreases, and the change in y is consistent. The equation for this relationship is:

[tex]\[ y = \frac{x}{4} + 5 \][/tex]

In both equations, the slope is -1 in the first table and 1/4 in the second table, indicating that for each unit change in x, there is a corresponding change in y. The y-intercepts in these equations are -10 and 5, respectively, representing the values of y when x is 0.

These equations capture the linear relationships observed in the tables, allowing you to predict the value of y for any given value of x within these patterns.

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The probable question may be:

Write an equation to describe the relationship in each table. Table 1: x= 25, 24, 23, 22, 21. y= 15, 14, 13, 12, 11. Table 2: x= 36, 28, 16, 12, 4. y= 9, 7, 4, 3, 1.

What is the surface area of the triangular prism shown below
???

Answers

Given:

Given that the base of the triangle is 4 cm.

The height of the triangle is 3 cm.

The height of the prism is 8 cm.

The other side of the triangle is 5 cm.

We need to determine the surface area of the triangular prism.

Surface area of the triangular prism:

The surface area of the triangular prism can be determined using the formula,

[tex]SA=bh+(s_1+s_2+s_3)H[/tex]

where b is the base of the triangle,

h is the height of the triangle,

s₁, s₂, s₃ are the side lengths of the triangle and

H is the height of the prism.

Substituting b = 4, h = 3, s₁ = 4, s₂ = 3, s₃ = 5 and H = 8, we get;

[tex]SA=(4)(3)+(4+3+5)(8)[/tex]

[tex]SA=12+(12)(8)[/tex]

[tex]SA=12+96[/tex]

[tex]SA=108 \ cm^2[/tex]

Thus, the surface area of the triangular prism is 108 square cm.

Answer:

Step-by-step explanation:

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Which of the following countries has created special economic zones to reduce government regulations on the economy?A.ChinaB.JapanC.North KoreaD.South Korea List 3 antonyms for the word commissary. Help ASAP!! Based on the chemical reaction shown, the reactants and products are best classified as NH3+ NaOCl NaOH + NH2ClH3+ NaOCl NaOH + NH2Cl Stephanie is a 40 percent partner in the SKY Partnership. During the current tax year, the partnership reported ordinary income of $210,000 before payment of guaranteed payments and distributions to partners. The partnership paid guaranteed payments to partners Stephanie, Kirsten, and Yule of $30,000 each ($90,000 total). How much will Stephanie's adjusted gross income increase as a result of the above items?A. $88,000B. $48,000C. $78,000D. $66,000 Here you go good luck guys! Describe how humans and dolphins are in competition with one another. Find the iqr of the data set 0, 0, 1/4, 1/2, 1/2, 5/4, 1, 1, 1, 2, 2 In what ways are the effects of the Civil War still being felt today? A teacher bought 15 boxes of markers. Each box contained 8 markers. Estimate how many markers she bought by rounding the number of markers in a box to the nearest ten. Marvin and Pamela are married, file a joint return, and have two children, ages 9 and 11. Their combined AGI is $65,000. Marvin's earned income is $40,000; Pamela's is $25,000. They incur $6,500 of child care expenses to enable them to be employed during the current year. Their child and dependent care credit is _________.A) $1,200.B) $1,300.C) $1,800.D) $6,000. Hispanics living in the United States in the period from 1960-1980 were generally unable to get jobs unless they were prepared towork where?A) in factoriesB) on railroadsC) in agriculture D) for small businesses What fraction is greater 1/4 or 3/8 1) Social media and technology have given teenagers more ways to act negatively toward each other. 2) Teens say they believe social media has a positive impact on their lives, with some reporting that it makes them feel "depressed, less popular, less confident, and worse about themselves." 3) These teens are being bullied or are judging themselves because of what they see or experience through technology. 4) Teens should be monitored when they are online to prevent them from acting negatively toward each other. Which sentence should be revised because it presents conflicting information? Which sentence should be revised because it shows bias? Write a sentence in Spanish expressing that you explain your symptoms to the doctor.Mark this andretumSave and Exit The R.C.Willey furniture store has a sale for Memorial day weekend that if you purchase products that come over $499 a 60" TV can be purchased for only $300. This sales practice is known as ________. There are twelve contestants in an obstacle course race. You and your friend are two of the contestants. Contestants run the course one at a time and the order in which the contestants run the course is chosen at random. Find the probability that you go first and your friend goes second. Write your answer as a fraction in simplest form. Lasko's has 250,000 shares of stock outstanding, $400,000 in perpetual annual earnings, and a discount rate of 16 percent. The firm is considering a new project that has initial costs of $350,000 and annual perpetual cash flows of $60,000. How many new shares must be issued to fund the new project A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 2% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 38% of the respondents said they think their president can control the price of gasoline. c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? A mutation occurs in an original DNA template that changes the DNA, changes the RNA, but does not change the protein sequence. What kind of mutation is this. and what would be the consequence of this original change? Carbon reacts with oxygen to produce carbon dioxide (CO2 (g), Delta.Hf = 393.5 kJ/mol) according to the equation below. Upper C (s) plus 2 upper O subscript 2 (g) right arrow upper C upper O subscript 2 (g). What is the enthalpy change of the reaction? Use Delta H r x n equals the sum of delta H f of all the products minus the sum of delta H f of all the reactants.. 393.5 kJ 196.8 kJ 196.8 kJ 393.5 kJ