Help me please, an explanation would be nice as well

Help Me Please, An Explanation Would Be Nice As Well

Answers

Answer 1

Answer:

Option (A). 44.1

Step-by-step explanation:

In the figure attached,

Triangle XYZ is am obtuse triangle having,

m∠XZY = 133°

m(YZ) = 21 units

m(XZ) = 27 units

By Cosine rule,

(XY)² = (XZ)² + (YZ)² - 2(XZ)(YZ)cosθ

Where θ is the angle opposite to side XY.

(XY)² = (27)² + (21)² - 2(27)(21)cos(133)°

        = 1943.38614

XY = √1943.38614

XY = 44.084

     ≈ 44.1 units

Therefore, length of side XY = 44.1 units

Option (A) will be the answer.


Related Questions

Which linear equation shows a proportional relationship? y equals one fourth times x minus 5 y equals negative one fourth times x y = −4x+ 1 y = 4

Answers

Answer: -1

Step-by-step explanation: I did this on khan

Toasty Hands is a manufacturer of battery-powered heated gloves. Its top of the line model currently sells for $279, and it expects sales of 440,000 pairs in the next year. Its estimate of the demand for gloves suggests that if it cuts the price to $239 it could sell 540,000 pairs. What is the absolute value of the elasticity coefficient for Toasty Hands' gloves? Round your answer to two decimals. 1st attempt

Answers

The absolute value of the elasticity coefficient for Toasty Hands' gloves is 394,265.23.

The elasticity coefficient is calculated as follows:

Elasticity coefficient = (Change in demand)/(Change in price) * (Original price)/(Original demand)

In this case, the change in demand is 540,000 - 440,000 = 100,000 pairs. The change in price is 239 - 279 = -40. The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get:

Elasticity coefficient = (100,000)/(-40) * (279)/(440,000) = -394,265.23

The absolute value of the elasticity coefficient is 394,265.23. This means that the demand for Toasty Hands' gloves is elastic, meaning that a small change in price will lead to a large change in demand.

Here is a more detailed explanation of the calculation:

The change in demand is calculated by subtracting the original demand from the new demand. In this case, the new demand is 540,000 pairs, and the original demand is 440,000 pairs. So the change in demand is 540,000 - 440,000 = 100,000 pairs.

The change in price is calculated by subtracting the original price from the new price. In this case, the new price is $239, and the original price is $279. So the change in price is 239 - 279 = -40.

The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get the elasticity coefficient of -394,265.23.

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Please help me with these problems!

Please help me with these problems!

Answers

Answer:

143880000 people have dogs and b.

Step-by-step explanation:

327,000,000 * .44(44 percent) = 143880000

the sample of 437 is much smaller than the entire state of texas, so it is incorrect to assume that the small amount of people is representative of the entire state.

Answer:

Step-by-step explanation:

3)

327 Million → 100%

x → 44%

100x = 44×327

100x = 14388

x = 14388/100

x = 143.88 Million people

4) D

I hope I've helped you.

classify each structure according to its functional class. compound a contains a carbonyl bonded to two alkyl groups. compound b contains an oxygen bonded to two alkyl groups. compound c contains a carbonyl bonded to propyl and n h c h 3. compound d is a nitrogen bonded to three alkyl groups.

Answers

The classification of the compounds according to their functional class: A | Aldehyde

B | Alcohol

C | Ketone

D | Amine

Compound A contains a carbonyl group (C=O) bonded to two alkyl groups (R-). This is the general structure of an aldehyde. Aldehydes are characterized by their strong, sweet odor.

They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound B contains an oxygen atom (O) bonded to two alkyl groups (R-). This is the general structure of an alcohol. Alcohols are characterized by their ability to dissolve other polar compounds, such as water. They are also used in a variety of products, such as solvents, cleaners, and fuels.

Compound C contains a carbonyl group (C=O) bonded to a propyl group (CH3CH2CH2-) and an amino group (NH2). This is the general structure of a ketone.

Ketones are characterized by their strong, sweet odor. They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound D contains a nitrogen atom (N) bonded to three alkyl groups (R-). This is the general structure of an amine. Amines are characterized by their basic properties. They are also used in a variety of products, such as pharmaceuticals, plastics, and fertilizers.

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Combine like terms to create an equivalent expression.

Combine like terms to create an equivalent expression.

Answers

Answer:

\(\frac{3}{2}\) y - 5

Step-by-step explanation:

Given

- \(\frac{1}{2}\) (- 3y + 10) ← multiply each term in the parenthesis by - \(\frac{1}{2}\)

= \(\frac{3}{2}\) y - 5

3y-10
———. or 3/2y - 5
2

simplify 2/3(6x−1/6)+3x

Answers

Answer:

7x - 1/9

Step-by-step explanation:

2/3 (6x - 1/6) + 3x

12x/3 - 2/18 + 3x

4x - 1/9 + 3x

7x - 1/9

After simplifying, the value of expression is,

⇒ 7x - 1/9

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 2/3 (6x - 1/6) + 3x

Now, We can solve the expression as;

⇒ 2/3 (6x - 1/6) + 3x

⇒ 2/3 × 6x - 2/3 × 1/6 + 3x

⇒ 4x - 1/9 + 3x

⇒ 7x - 1/9

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A paper cup, which is in the shape of a right circular cone is 16 cm deep and has a radius of 4 cm. Water is poured into the cup at a constant rate of 2cm3/sec. At the instant the radius is 3cm, what is the rate of change of the radius

Answers

When the radius of the cup is 3 cm, the rate of change of the radius is approximately -0.214 cm/sec. This means that the radius is decreasing at a rate of about 0.214 cm/sec.

We can use related rates to find the rate of change of the radius of the cup when the radius is 3cm. Let's begin by finding an equation that relates the height and the radius of the cone.

We know that the cup is a right circular cone, so the formula for the volume of a cone is:

V = (1/3)π\(r^2\)h

where V is the volume, r is the radius, and h is the height.

We are given that the cup is 16 cm deep and has a radius of 4 cm, so we can use these values to find the constant of proportionality in our equation. Plugging these values in, we get:

V = (1/3)π(\(4^2\))(16)

V = 64π

Now we can take the derivative of both sides of the equation with respect to time:

dV/dt = (1/3)π(2r)(dr/dt)h + (1/3)π\(r^2\)(dh/dt)

We are given that water is poured into the cup at a constant rate of 2 cm^3/sec. This means that dV/dt = 2. We are also given that the radius is changing at a certain rate when it is 3 cm, so dr/dt = ? and r = 3. We need to find dh/dt, the rate of change of the height.

We can plug in the values we know and solve for dh/dt:

2 = (1/3)π(2(3))(dr/dt)h + (1/3)π(\(3^2\))(dh/dt)

2 = 2π(3)(dr/dt)h + 3π(dh/dt)

2 = 6π(dr/dt)h + 3π(dh/dt)

2 = 2π(3)(dr/dt)(16/r) + 3π(dh/dt) (substituting h in terms of r using the similar triangles)

2 = 32π(dr/dt)/r + 3π(dh/dt)

2 = 32π(dr/dt)/3 + 3π(dh/dt) (substituting r=3)

Now we can solve for dh/dt:

2 = 32π(dr/dt)/3 + 3π(dh/dt)

2 - 32π(dr/dt)/3 = 3π(dh/dt)

dh/dt = (2 - 32π(dr/dt)/3) / (3π)

Substituting the given values, we get:

dh/dt = (2 - 32π(dr/dt)/3) / (3π)

dh/dt = (2 - 32π(0.2)/3) / (3π) (since the volume of a cone is (1/3)π\(r^2\)h, taking the derivative of this equation gives dh/dt = 0.2(dr/dt))

dh/dt ≈ -0.214 cm/sec

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PLZ HELP GIVING ALL MY POINTS VERY URGENT

PLZ HELP GIVING ALL MY POINTS VERY URGENT

Answers

Answer:

88ft²

Step-by-step explanation:

Hey There

So first we want to find the area of the square

to do that we do 8x8 which equals 64

then we want to find the area of the triangle

to do so we multiply the base (8) and the height and divide that by 2

8x6=48

48/2=24

then we add the two together

24+64=88

88ft² is your answer :)

Answer:

hi I know that the other person already answered so I'm answering so u can give them brainliest

c::

The surface area of the Pacific Ocean is approximately 62,460,000 million square miles. What is this number
written in scientific notation?

Answers

The surface area of the Pacific Ocean is approximately 62,460,000 million square miles which is 6.246 * 10¹³ miles² in scientific notation.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The surface area of the Pacific Ocean is approximately 62,460,000 million square miles which is 6.246 * 10¹³ miles² in scientific notation.

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Help... it’s multiple choice math

Help... its multiple choice math

Answers

Answer:

D

Step-by-step explanation:

This is equivalent to t < 4.

clearly this is not part of the set.

In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent О А categorical dataO B quantitative data O C e ither categorical or quantitative data. O D since the numbers are sequential, the data is quantitative.

Answers

The numbers on the mailboxes could be considered either categorical or quantitative data. The correct Option is C: Either categorical or quantitative data.

The numbers on the mailboxes can be considered either categorical or quantitative data, depending on the context in which they are being used.

If the numbers are simply labels for the mailboxes, with no inherent numerical value or order, then they can be considered categorical data. In this case, the numbers would be treated as labels for the different categories or groups, rather than as measurements with numerical significance.

On the other hand, if the numbers are being used to represent a quantity or a position in a sequence, then they can be considered quantitative data. For example, if the numbers represent the physical location of the mailbox within a building, or the order in which mail is sorted and delivered, then they can be treated as numerical measurements.

Therefore, without further context, the numbers on the mailboxes could be considered either categorical or quantitative data.

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The population of a city is P(t)=9e "
P(t)=9 e^{0.05 t} (in millions), where t is measured in years. (a) Calculate the doubling time of the population. (b) How long does it take for the population to triple in size? (c) How long does it take for the population to quadruple in size? (a) (b) (c)

Answers

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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The volume, in cubic feet, of a right cylindrical silo of height h and radius r is V = πr2h. The height of the silo is h(r) = 3.5r. Which statements are true regarding the functions described? Check all that apply. To get a volume of 100 cubic feet, the radius must be 2 feet. The domain of V(h(r)) is restricted to values of r greater than 0. The output of V is the input of h. V(h(r)) = 3.5πr3 The volume depends on the radius of the cylinder.

Answers

Volume of a cylindrical silo is given by,

\(V=\pi r^{2}h\)

Here, \(V=\) Volume of the silo

\(r=\) Radius of the cylindrical silo

\(h=\) Hight of the silo

And height of the silo is defined by the function,

\(h(r)=3.5r\)

Option (1)

To get the volume of \(100\) cubic feet, radius must be \(2\) feet.

Height of the silo can be derived from the function,

\(h(2)=3.5(2)\)

      \(=7\) feet

Therefore, volume of the silo = \(\pi r^{2} h\)

                                                 = \(\pi (2)^2(7)\)

                                                 = \(28\pi\)

                                                 = \(87.96\) feet³

Since, \(87.96<100\) cubic feet

Statement is false.

Option (2)

Since, \(V=\pi r^{2} h\)

And \(h(r)=3.5r\)

Therefore, \(V[h(r)]=\pi r^{2}(3.5r)\)

\(V[h(r)]=3.5\pi r^{3}\)

Domain of the function 'V' will be \(r>0\).

Statement is true.

Option (3)

Output of V is the input of h.

From the function,

\(V[h(r)]=3.5\pi r^{3}\)

Volume (output value) of the silo depends on the output value of \(h(r)\).

Therefore, statement is false.

Option (4)

\(V[h(r)]=3.5\pi r^{3}\)

Volume depends on the radius of the cylinder.

Since, output value of the volume depends on the radius.

Statement is true.

Options (2) and (4) are true.

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Answer:

bde

Step-by-step explanation:

Alicia had 4 1/8 tons of fertilizer spread evenly across 2 1/6 acres of land. How many tons of fertilizer are on each acre?

1 23/24
1 47/52
6 7/24
8 15/16

Answers

We are required to find the number of tons of fertilizer are on each acre

The tons of fertilizer are on each acre of land is 1 47/52 tons

Given:

Total tons of fertilizer Alicia has = 4⅛ tons

Total acres of land = 2¹/6 acres

Tons of fertilizer on each acre of land = Total tons of fertilizer Alicia has ÷ Total acres of land

= 4 1/8 ÷ 2 1/6

= 33/8 ÷ 13/6

= 33/8 × 6/13

= (33 × 6) / (8 × 13)

= 198 / 104

= 1 94/104

= 1 47/52

Therefore, the tons of fertilizer are on each acre of land is 1 47/52 tons

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mia rides her bike 32 miles in 8 hours. At this rate, how far will she ride in 3 hours?​

Answers

Answer: 12

Step-by-step explanation:

32/8= 4. She rides 4 miles an hour. So 4 x 3= 12

Answer: 12miles

Step-by-step explanation:In 1 mile she will ride 32/8 =4miles per hour

In 3hours She will ride 4×3miles

A directed segment ST¯¯¯¯¯ is partitioned from S (−5,0) to T in a 32 ratio at point M (10, 15). What are the coordinates of point T?

Answers

Answer:

Point T = (4,9)

Step-by-step explanation:

Given:

S (−5,0)

M (10, 15)

m1:m2 = 3:2

Find:

Point T

Computation:

X = [m1x2 + m2x1] / [m1+m2]

Y = [m1y2 + m2y1] / [m1+m2]

X = [(3)(10) + (2)(-5)] / [3+2]

Y = [(3)(15) + (2)(0)] / [3+2]

X = 20 / 5 = 4

Y = 45 / 5 = 9

Point T = (4,9)

Natalie i working two ummer job, making $11 per hour babyitting and $10 per hour landcaping. Lat week Natalie earned a total of $86 and worked 3 time a many hour babyitting a he worked hour landcaping. Determine the number of hour Natalie worked babyitting lat week and the number of hour he worked landcaping lat week

Answers

The number of hours Natalie worked babysitting last week is 6hrs and the number of hours she worked landscaping last week is 2 hrs.

Let x be the number of hours Natalie worked babysitting and y be the number of hours she worked landscaping. Then, the total earnings were 11x + 10y = $86.

Also, x = 3y, because she worked 3 times as many hours babysitting as she did landscaping.

Substitute x = 3y into the first equation:

11(3y) + 10y = $86

Expanding the first term we get,

33y + 10y = $86

Combining terms,

43y = $86

Dividing both sides by 43 we get,

y = $2

So, Natalie worked y = 2 hours of landscaping.

To find the number of hours she worked babysitting, substitute y = 2 into x = 3y as follows -

x = 3(2) = 6

So Natalie worked x = 6 hours babysitting.

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Help Please. Need answer immediately

Help Please. Need answer immediately

Answers

Answer:

7.5 feet per second

Step-by-step explanation:

Answer:

I believe it is 7.5 feet per second

Step-by-step explanation:

Do 225 divided by 30

GIVEN THAT AD = 5 and BC = 24, what is the radius of circle A?

GIVEN THAT AD = 5 and BC = 24, what is the radius of circle A?

Answers

Answer:

12

Step-by-step explanation:

B to C looks like your diameter so half of 24 is 12.

I don't understand by when it's saying the cost of the amount of lemonade cups and advertising

Answers

Think of It AS TeaSpoons Like Adding Sugar To Something But Instead it’s The Size Of A Cup So They Are Pouring The Amount Of Cups of lemonade or whatever and creating that cost

The 7th term of the geometric sequence 13, 26, 52, 104, ... is

The 7th term of the geometric sequence 13, 26, 52, 104, ... is

Answers

832

let first term = n

second term = 2 x n

third term = 4 x n

forth term = 8 x n

therefore we can concluded that the multiple are the sum of itself ( 2+2= 4, 4+4=8, 8+8=16, 16+ 16=32,) some the seventh term will be 32 + 32 which is 64 .

therefore

seventh term = 64 x n

= 64 x 13 = 832

In which quadrant(s) do the graphs of y = x^2 and y = 3x +10 intersect?

Answers

Answer:

Step-by-step explanation:

y=3x+10

y=x²

x²-3x-10=0

x²-5x+2x-10=0

x(x-5)+2(x-5)=0

(x-5)(x-2)=0

x=5,2

when x=5,y=5²=25

point of intersection is (5,25)

when x=2

y=2²=4

so point of intersection is (2,4)

which shows that they intersect in first quadrant.

2/3x-5=x-8 please show your work.

Answers

Given the expression 2/3x-5=x-8

we need to find the value of x from the expression as shown;

collect the like terms:

2/3x-5=x-8

2/3 x - x = -8+5

Find the LCM

(2x-3x)/3 = -3

-x/3 = -3

Cross multiply

-x = -3(3)

-x = -9

Multiply both sides by -1

-1(-x) = -1(-9)

x = 9

Hence the correct value of x is 9

Find the 2 numbers whose product is -78 and sum is -7.​

Answers

Answer:

The two numbers are -18 and 11 or 7 and -14, since the order of the numbers does not matter in finding their product and sum.

Step-by-step explanation:

Given the product of two numbers is -78 and their sum is -7, we can use algebra to find these two numbers. Let's call these numbers x and y. Then, we have:

x * y = -78
x + y = -7

We can use the second equation to solve for one of the variables and then substitute it into the first equation to find the other variable. For example, solving for x:

x = -7 - y
x * y = -78
(-7 - y) * y = -78
-7y - y^2 = -78
y^2 + 7y + 78 = 0

This is a quadratic equation which can be solved using the quadratic formula or factoring. The two solutions for y are -14 and 11. Then, we can use the second equation to find x:

x = -7 - y
x = -7 - (-14) = 7
x = -7 - 11 = -18

So, the two numbers are -18 and 11 or 7 and -14, since the order of the numbers does not matter in finding their product and sum.

2. The following set of count readings was made in a gradient-free γ-ray field, using a suitable detector for repetitive time periods of one minute: 18,500;18,410; 18,250;18,760;18,600;18,220;18,540;18,270;18,670;18,540. (a) What is the mean value of the number of counts? (b) What is its standard deviation (S.D.)? (c) What is the theoretical minimum S.D. of the mean? (d) What is the actual S.D. of a single reading? (e) What is the theoretical minimum S.D. of a single reading?

Answers

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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What is the volume of the Cylinder ? Use 3 14 round the answer to the nearest hundredth . h = 7in r = 7in

What is the volume of the Cylinder ? Use 3 14 round the answer to the nearest hundredth . h = 7in r =

Answers

Answer:

V = 1077.02 in³

Step-by-step explanation:

To find the volume of a cylinder, we use this formula:

V = πr²h

Let's plug in what we know.

V = (3.14)(7)²(7)

Evaluate the exponent first.

V = (3.14)(49)(7)

Multiply.

V = 1077.02 in³

Hope this helps!

Help please help please

Help please help please

Answers

Answer:

 \(option \ C\)  \(3\frac{1}{3}\)

Step-by-step explanation:

\(\frac{|2a| - b}{3} \ , \ given \ a = \ 7 \ , \ b \ =\ 4\\\\\frac{|2 \times 7| - 4}{3} = \frac{14 - 4}{3} = \frac{10}{3} = 3\frac{1}{3}\)

The answer is c my guy

How many faces, vertices, and edges does a right rectangular pyramid have? 4 faces, 5 vertices, and 7 edges 5 faces, 5 vertices, and 8 edges 5 faces, 8 vertices, and 11 edges 6 faces, 8 vertices, and 12 edges

Answers

Answer:

Rectangular pyramid : Faces, Vertices, Edges = 5 , 5 , 8 respectively

Step-by-step explanation:

Rectangular pyramid is a 3D shape, with base as rectangle & triangle face corresponding to each side of base (on the top)

Faces = 5 { 1 rectangular base face , 4 triangular faces above}

Vertices = 5 { 4 vertices of rectangle, 1 vertice on top - where triangles' tips intersect}

Edges = 8 {4 edges of rectangle at base , 4 edges of triangles above}

Answer:

b. 5, 5, 8

Step-by-step explanation:

i did the assignment and this was the correct answer <3

what is 5x98 (x343)=

Answers

Answer:

168,070

Step-by-step explanation:

Multiplication, 5 x 98 = 490. 490 x 343 = 168,070

what is the t* associated with 98% confidence and df = 37?

Answers

When constructing a 98% confidence interval with a sample size of 37, the t* value to use for determining the margin of error or the width of the confidence interval is approximately 2.693.

To find the t* value associated with a 98% confidence level and degrees of freedom (df) equal to 37, we can refer to a t-distribution table or use statistical software. The t* value represents the critical value that separates the central portion of the t-distribution, which contains the confidence interval.

In this case, with a 98% confidence level, we need to find the t* value that leaves 1% of the distribution in the tails (2% divided by 2 for a two-tailed test). With df = 37, we can locate the corresponding value in a t-distribution table or use software to obtain the value.

Using a t-distribution table or software, the t* value associated with a 98% confidence level and df = 37 is approximately 2.693. This means that for a sample size of 37 and a confidence level of 98%, the critical value falls at approximately 2.693 standard deviations away from the mean.

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