Mathematics College

PLEASE HELP ASAP PLEASE PLEASE

Answers

Answer 1

Answer:

transitive property

Step-by-step explanation:

This is the answer by definition.

Answer 2

The substitution property is demonstrated in the case of m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so, m∠AZF=m∠SZW+m∠LZF.

In order to find the value of the unknown, the substitution property is a concept in algebra that is used to substitute the value of a given variable or quantity into an expression.

According to the substitution property of equality, "If two variables x and y are equal, then x can be substituted for y in any equation or expression, and y can be substituted for x in any equation or expression."

According to the question, m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so by the substitution property, on substituting the value of m∠AZL+m∠LZF in the first expression, we get, m∠AZF=m∠SZW+m∠LZF.

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Related Questions

The graph shows a system of inequalities.

Graph of two inequalities. One is a solid line increasing from left to right passing through negative 3 comma 0 and 0 comma 3, and it has shading below the line. The second is a solid upward opening parabola with a vertex at 1 comma negative 4 and x-intercepts at negative 1 comma 0 and 3 comma 0. This parabola is shaded inside the curve.

Which system is represented in the graph?

A. y > x2 –2x – 3
y > x + 3
B. y < x2 – 2x – 3
y < x + 3
C. y ≥ x2 – 2x – 3
y ≤ x + 3
D. y > x2 – 2x – 3
y < x + 3

Answers

The graphed system of inequalities is:

y ≥ x^2 - 2x - 3y ≤ x + 3

So the correct option is the third one.

Which system is represented by the graph?

On the graph we can see that the two lines are solid, so we need to use the symbols ≤ and ≥. (If instead, we had dashed lines, then we would need to use the symbols > and <).

We also can see that the region above the parabola is shaded (the shaded region represents the region of solutions for each inequality), and the region below the line is shaded, then the system of inequalities is of the form:

y ≥ parabola.y ≤ line.

Only with that, we conclude that the correct option is the third option:

y ≥ x^2 - 2x - 3y ≤ x + 3

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The length of a rectangle is 3 m longer than its width.
If the perimeter of the rectangle is 34 m, find its area.

Answers

Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

There were 48 peaches in a carton. The average mass of all the peaches was 0.17 kg. What was their total mass?

Answers

Answer:

8.16 Kg

Step-by-step explanation:

average is calculated as

average = [tex]\frac{sum}{count}[/tex]

here average = 0.17 and count = 48 , then

0.17 = [tex]\frac{sum}{48}[/tex] ( multiply both sides by 48 )

8.16 = sum

that is total mass = 8.16 Kg

I need help with this question

Answers

The cost of goods sold using LIFO is $99.

Cost of goods sold using LIFO

Using this formula

Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]

Let plug in the formula

Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]

Cost of goods sold=$58.5+(7 units×$5.80)

Cost of goods sold=$58.5+$40.6

Cost of goods sold=$99.1

Cost of goods sold=$99 (Approximately)

Therefore the cost of goods sold using LIFO is $99.

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Suppose you are in charge of setting up tables and ordering
appetizers and cookies for an awards dinner. The principal
expects 168 seventh-graders and 112 eighth-graders to attend
the dinner. Each grade will have dinner in a separate room.
1. Decide how many tables and how many chairs per table you will need, based on
the following criteria:
• No more than 15 tables in each room, and no more than 15
chairs per table.
• All tables in both rooms must have the same number of chairs.
Only 280 chairs can be ordered.
●

Answers

Answer: 10 tables in each room 14 kids at each table

QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP

WILL GIVE BRAINLIEST FOR ACCURATE ANWSER

Answers

The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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The volume of this regular pentagonal pyramid is 82.5 cubic meters. What is the height of the pyramid?

Answers

the height of the pentagonal pyramid is 5. 70 meters

Volume of a regular pentagonal pyramid

The formula for determining the volume of a regular pentagonal pyramid is given as;

V=5/12tan(54°)ha^2

Where

a is the base edgeh is the height

We have the volume to be;

volume = 82. 5 cubic centers

height = h

a = 5m

Substitute the values

[tex]82. 5 = \frac{5}{12}[/tex] × [tex]tan 54[/tex] × [tex]h[/tex] ×[tex]5^2[/tex]

[tex]82. 5 = 0. 42[/tex] × [tex]1. 3764[/tex] × [tex]25[/tex] × [tex]h[/tex]

Make 'h' subject of formula

[tex]h = \frac{82. 5}{14. 45}[/tex]

h = 5. 70 meters

The height of the pentagonal pyramid is 5. 70 meters

Thus, the height of the pentagonal pyramid is 5. 70 meters

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A bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km away. Write a formula expressing the dependence of the variable s on t, where s is the distance between the bicyclist and the station in km, t - the duration (time) of his travel in hours. Using the formula, find: d for t=3.5

Answers

1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t

2. the distance travelled at time t = 3.5 h is 18 Km

What is speed?

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

1. How to determine the formula expressing the dependence of the variable s on t

From the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.

Thus, we shall determine the distance travel in time t as follow

Speed = 12 Km/hTime = tDistance in time t = ?

Speed = distance / time

12 = distance / t

Cross multiply

Distance = 12 × t

Distance in time t = 12t

But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:

s = 60 - 12t

Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t

2. How to determine the distance at t = 3.5 hours

The distance at t = 3.5 hours can be obtained as illustrated below:

Time (t) = 3.5 hoursDistance (s) = ?

s = 60 - 12t

s = 60 - (12 × 3.5)

s = 60 - 42

s = 18 Km

Thus, the distance travelled at t = 3.5 hours is 18 km

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Target Costing

Instant Image Inc. manufactures color laser printers. Model J20 presently sells for $460 and has a product cost of $230, as follows:

Direct materials $175
Direct labor 40
Factory overhead 15
Total $230
It is estimated that the competitive selling price for color laser printers of this type will drop to $400 next year. Instant Image has established a target cost to maintain its historical markup percentage on product cost. Engineers have provided the following cost-reduction ideas:

Purchase a plastic printer cover with snap-on assembly, rather than with screws. This will reduce the amount of direct labor by 15 minutes per unit.
Add an inspection step that will add six minutes per unit of direct labor but reduce the materials cost by $20 per unit.
Decrease the cycle time of the injection molding machine from four minutes to three minutes per part. Forty percent of the direct labor and 48% of the factory overhead are related to running injection molding machines.
The direct labor rate is $30 per hour.

a. Determine the target cost for Model J20, assuming that the historical markup on product cost and selling price are maintained.
$fill in the blank 1
per unit

b. Determine the required cost reduction.
$fill in the blank 2
per unit

c. Evaluate the three engineering improvements together to determine if the required cost reduction (drift) can be achieved. Do not round interim calculations but round your final answers to two decimal places.

1. Direct labor reduction $fill in the blank 3
per unit
2. Additional inspection $fill in the blank 4
per unit
3. Injection molding productivity improvement $fill in the blank 5
per unit
Total savings $fill in the blank 6
per unit

Answers

The target cost for Model J20 is $2000.

The required cost reduction is $30.

The total saving will be $30.3.

How to compute the cost?

The target cost will be:

= Sales price - (100% × Target cost)

= 400 - (100% × Y)

Y + Y = 400

2Y = 400

Y = 400/2 = 200

Target cost = $200

Therefore, the target cost is $200.

The required cost reduction will be:

= $230 - $200

= $30

The required cost reduction is $30.

The three engineering improvements together will be:

Direct labor reduction = 7.5

Additional inspection = 17

Injection molding = 5.8

Total savings = 30.3

The total savings is $30.3.

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An agricultural company called Phatsima Pty. Ltd. owns an rectangular fuel tank that measures 75 cm by 65 cm by 30 cm.

How many millilitres of fuel are needed to fill their tank?
If the fuel price is R20.35 per liter. How much will it cost to fill half of their tank?
Choose an option below that has both answers correct.

a.
1. 146 250.00 ml and 2. R 1 488.10

b.
1. 150 000.00 ml and 2. R 2 976.19

c.
1. 73 125.00 ml and 2. R 1 488.10

d.
1. 146 250.00 ml and 2. R 2 000.00

Answers

I believe that A is the answer. We can solve this by multiplying 75cm, 65cm and 30cm together. This would give us 146,250.00ml. We can then divide 146,250.00 by 1000 to receive 146.25. We then divide 146.25 by 2 to calculate how many litres there are in half a tank. This would result in 73.125. After that, we multiple 73.125 by the cost of the fuel, which is R20.35. We then receive R 1,480.09375, which can be rounded to R 1,480.10

The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?

Answers

Answer: 44

Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.

If
f(x) = 2x2 − 7,
0 ≤ x ≤ 3,
evaluate the Riemann sum with
n = 6,
taking the sample points to be midpoints.
What does the Riemann sum represent? Illustrate with a diagram.

Answers

The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625

What is Riemann sum?

Formula for midpoints is given as;

M = ∑0^n-1f((xk + xk + 1)/2) × Δx;

From the information given, we have the following parameters

x0 = 0 n = 6 xn = 3

Let' s find the parameters

Δx = (3 - 0)/6 = 0.5

xk = x0 + kΔx = 0.5k

xk+1 = x0 + (k +1)Δx

Substitute the values

= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2

We then have;

= (0.5k + 0.5k + 05.)/2

= 0.5k + 0.25.

Now f(x) = 2x^2 - 7

Let's find f((xk + xk+1)/2)

Substitute the value of (xk + xk+1)/2)

= f(0.5k+ 0.25)

= 2(0.5k + 0.25)2 - 7

Put values into formula for midpoint

M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.

To evaluate this sum, use command SUM(SEQ) from List menu.

M = - 12.0625

A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.

Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625

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25(0.3x-4)-5(1.5x-6)+100·13/4

Answers

Answer:

255 (assuming x is the variable x)

340 (assuming x is the multiplication sign)

See explanation below.

Step-by-step explanation:

I assume that x is the variable x.

25(0.3x-4)-5(1.5x-6)+100·13/4 =

= 7.5x - 100 - 7.5x + 30 + 25 × 13

= -70 + 325

= 255

If my assumption above is incorrect, and x really means the multiplication sign, then we have this:

25(0.3×-4)-5(1.5×-6)+100·13/4 =

= 25(-1.2) - 5(-9) + 100(3.25)

= -30 + 45 + 325

= 340

Question 24: [1 + 1 + 1 + 1= 4 points]
Let X be a discrete random variable with the following
x 0.2 0.4 0.5 0.8 1
P(x) 0.1 0.2 0.2 0.3 0.2 (a) Find () , the range of the random variable X

Answers

Considering the given discrete probability distribution, the range of the variable X is given by:

Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.

What is the range of a random variable?

The range of a random variable is the set of all values that the variable can assume.

From the table, we have that X can assume the values of 0.2, 0.4, 0.5, 0.8 and 1, hence the range of the variable X is given by:

Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.

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help pleaseeeee
tysm

Answers

Answer: Either Rohmbus or Parallelogram...

Step-by-step explanation: Your picture is a bit small, sry

A cylinder has radius of 4 inches and height 10inches.There’s a small cylinder inside the previous cylinder of radius of 2 inches with the same height and same centre.What is total surface area?

Answers

The surface area of the cylinder is 48π inches².

How to find the Surface area of a cylinder?

Surface area of a cylinder = 2πr(r + h)

where

r = radiush = height

Therefore,

Surface area of the smaller cylinder = 2 × π × 2(2 + 10)

Surface area of the smaller cylinder = 4π(12)

Surface area of the smaller cylinder = 48π

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Circle B has a radius of 24 units, Circle E has a radius of 9 units, and segment CD = 4. Find segment A.F. Round your answer to the nearest tenth.

Answers

The length of segment A.F in the circles given is: 62 units.

What is the Radius of a Circle?

A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.

Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].

Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].

CD = 4

DE = x

CD + DE = CE

Plug in the values into the equation

4 + x = 9

x = 9 - 4

x = 5

DE = 5

The length of segment DE is 5 units

A.F = AB + BD + DE + EF

Plug in the values into the equation

A.F = 24 + 24 + 5 + 9

A.F = 62 units.

Therefore, the length of segment A.F in the given circle is determined as: 62 units.

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Donna is putting 9 books in a row on the bookshelf she will put one of the books gullivers travel in the first spot she will put in another of the bucks a tale of two cities in the last spot in how many ways can she put the books on the shelf

Answers

There are 5,040 different ways in which she can order the books.

In how many ways can she put the books on the shelf?

We know that Donna has 9 books, but 2 of these books already have fixed positions (the first one and the last one).

So we only need to order the remaining 7 books in 7 positions.

On the first position, we have 7 options (7 books to put there).On the second position, we have 6 options (because one book is already in the first position).On the third position, we have 5 options.

And so on for the remaining positions.

The total number of different combinations in which she can order the books is given by the product between the numbers of options above, so we will get:

C = 7*6*5*4*3*2*1 = 5,040

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Evaluate 3|12−x|−4 when x=15

Answers

Answer:

Step-by-step explanation:

3 x |12 - x| - 4

3 x |12 - 15| - 4

3 x 3 - 4

9 - 4

(SAT Prep) If the lengths of two sides of a triangle are 5 and 9 which would be length of the third side?

Answers

The length of third side of triangle is 4 or 14.

According to the statement

we have given that the two sides of the triangle which are 5 and 9 and we have to find the length of the third side of triangle.

So, For this purpose, we know that the

If we had a triangle with sides a, b and c, then we can say

b-a < c < b+a

where b is larger than 'a'. This is the triangle inequality theorem

In this case, a = 5 and b = 9 so,

b-a < c < b+a

9-5 < c < 9+5

4 < c < 14

Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set.

And

We see that the numbers 4 and 14 are in this set. The values 2 and 7 are not in the set.

So, The length of third side of triangle is 4 or 14.

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Find the critical value zα/2 that corresponds to the confidence level 84%.

Answers

The critical value z_α/2 that corresponds to the confidence level 84% is; 1.41

How to find the critical value?

We want to find the two tail critical values.

This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.

Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.

However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.

From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;

z = 1.41

Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84% is; 1.41

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What is the value of y?

OA. 30°
OB. 120°
OC. 60°
60

Answers

Answer:

Step-by-step explanation:

60 + y + y = 180

2y = 120

y = 60

How many workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days?

Answers

Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

Inversely proportional relationship

Two variables are related when a change in one of them causes a change in the other.

Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.

In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.

Simple inverse rule of three

The simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.

To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:

A → B

C → X

So: [tex]X=\frac{AxB}{C}[/tex]

Amount of workers needed

The number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:

9 days → 8 workers

6 days → amount of workers

So:[tex]amount of workers=\frac{9 daysx8 workers}{6 days}[/tex]

amount of workers= 12 workers

Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

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Write the following number in scientific notation.
788,000

Answers

Answer: 788 x 10^3
Because 788 x 1000 = 788000

Answer:

788,000 =

788 x 10^3

78.8 x 10^4

7.88 x 10^5

.788 x 10^6

and so on

Find the length of the arc of a circle of diameter 14 meters subtended by a central angle of π/6 radians. Round your answer to two decimal places

Answers

The length of the arc of the circle is 3.67 meters

What is an arc?

The arc of a circle is a part of the circumference that makes up the circle

How to determine the length of the arc?

From the question, we have the following parameters

Diameter, d = 14 meters

Central angle = π/6 radians

Start by calculating the radius of the circle using

Radius, r = Diameter/2

This is so because radius is half the diameter

So, we have

r = 14 meters/2

Evaluate the quotient of 14 meters and 2

r = 7 meters

The length of the arc of the circle is then calculated using

L = Radius * Central angle

Substitute known values in the above equation

L = 7 meters * π/6

Evaluate the product of 7 and π/6

L = 3.67 meters

Hence, the length of the arc of the circle is 3.67 meters

Answers

Answer: 71

Reason:

The angles x and 71 are opposite the congruent sides. We call these the base angles. The base angles are congruent for any isosceles triangle. Therefore, x = 71.

It might help to rotate the triangle so that the angles x and 71 are flat along the ground (rather than tilted).

A local anime fan club surveyed 81 of its members regarding their viewing habits last weekend, and the following information was obtained: 40 members watched an episode of Naruto, 54 watched an episode of Death Note, 40 watched an episode of Inuyasha, 32 watched both Naruto and Inuyasha, 12 watched Naruto and Inuyasha but not Death Note, 25 watched both Death Note and Inuyasha, and 23 watched only Death Note. a. How many of the club members watched exactly one of the shows? b. How many of the club members watched all three shows? c. How many of the club members watched none of the three shows?

Answers

The solutions for the Questions are

a) Given that, the minimum requirement is 58 out of 75.

a=0.7733

b) For 16 out of a total of 75

b=0.2133

c) For 11 out of a total of 75

c =0.1466

How many of the club members watched all three shows? c. How many of the club members watched none of the three shows?

Generally, we need to determine the total number of students who exhibit each behavior by seeing the habits and assets contained inside a Venn diagram.

Therefore, let's assume that:

- In Set A, I watched one of the Naruto episodes.

Set B: Observed a new segment of the anime series Death Note.

Hence, 23 of them have seen an episode of Death as well as an episode of Naruto, which means that

(A intercept B) equals 23.

In addition to this, it is a given that 42 has seen one episode of Death Note.

This indicates that B is equal to 42.

This pertains to us:

[tex]B = (B-A)+(A \cap B)[/tex]

In this case, members of B through A are individuals who have only viewed Death Note. So

42=(B−A)+23

(B-A) = 11

Finally, It is a known fact that 39 of the members have seen at least one episode of Naruto.

Therefore, the value of A is 39.

A=(A−B)+(A intercept B)

39=(A−B)+23

(A−B)= 16

(A union B)= 42+ 39- 23

(A union B)=58

In conclusion, the total number of pupils is:

58 with at least one and 17 with none, for a total of 75

a) Given that, the minimum requirement is 58 out of 75.

a=58*100/75

a=0.7733

b) For 16 out of a total of 75

b= 16/75*100

b=0.2133

c) For 11 out of a total of 75

c= 11/75*100

c =0.1466

Answers

[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]

[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]

[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787

Mitch throws a baseball straight up in the air from a cliff that is 95 ft high. The initial velocity is 95 /ftsec. The height (in feet) of the object after t sec is given by =ht+−19t2+95t95. Find the time at which the height of the object is 114 ft. Round your answers to two decimal places.

Answers

The time at which the height of the object is 114 ft rounded to two decimal places is; 5.85 seconds

How to find the height of a projectile?

We are given;

Height of cliff = 95 ft

Initial velocity of throw = 95 ft/s

The height (in feet) of the object after t sec is given by;

h(t) = −19t² + 95t + 95.

Now, we want to find the time at which the height of the object is 114 ft. Thus, we will set h(t) = 114 ft to get;

114 = −19t² + 95t + 95.

Subtract 114 from both sides to get;

−19t² + 95t + 95 = 0

Using quadratic formula, we have;

t = [-95 ± √(95² - 4(-19 * 95))]/(2 * -19)

t = [-95 ± √(16245)]/-38

t = (-95 ± 127.4559)/(-38)

t = (-95 - 127.4559)/-38 or (-95 + 127.4559)/-38

t = 5.85 s or -0.85

Time cannot be negative and so t = 5.85 seconds

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Question 25: [1 + 2 + 2 + 2 + 2 + 1= 10 points]
Given student of classified as belonging to three colleges and gender males and Females in the following table.
Eng (E) Life (L) Sci (S) sum F 60 40 30 130
M 40 20 10 70 sum 100 60 40 200
a) [1 points] Find the probabilities whole events. () , (), (), () , and ()
b) [2 points] Find the probabilities of Intersection (AND) Events:
( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ )
( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ )
c) [2 points] Find the probabilities of Union (OR) disjoint Events:
( ∪ ) = ( ∪ ) ( ∪ ) = ( ∪ )
( ∪ ∪ ) = ( ∪ ∪ ) ( ∪ ) = ( ∪ )
d) [2 points] Find the probabilities of Union (OR) joint events: ( ∪ )
( ∪ )
e) [2 points] Find the probabilities of Conditional Probabilities
(/) (/)
(/) (/)
(/) (/)
(/) (/)
f) [1 points] Use The multiplication low for dependent events to find the Conditional probability. ( ∩ ) = () (/)

Answers

See below for the values of the probabilities

How to determine the probabilities?

The probabilities of the whole events

For event A, the probability of the whole event is calculated using

P(A) = n(A)/Total

Using the table of values, we have:

P(F) = 130/200 = 0.65

P(M) = 70/200 = 0.35

P(L) = 60/200 = 0.30

P(S) = 40/200 = 0.20

The probabilities of the intersection events

For events A and B, the probability of the intersection events is calculated using

P(A n B) = n(A n B)/Total

Using the table of values, we have:

P(F n E) = P(E n F) = 60/200 = 0.30

P(F n L) = P(L n F) = 40/200 = 0.20

P(F n S) = P(S n F) = 30/200 = 0.15

P(M n E) = P(E n M) = 40/200 = 0.20

P(M n L) = P(L n M) = 20/200 = 0.10

P(M n S) = P(S n M) = 10/200 = 0.05

The probabilities of the Union (OR) disjoint events

For events A and B, the probability of the union (OR) disjoint events is calculated using

P(A u B) = P(A) + P(B)

Using the table of values, we have:

P(E u S) = P(E) + P(S) = 100/200 + 40/200 = 0.70

P(E u L) = P(E) + P(L) = 100/200 + 60/200 = 0.80

P(E u L u S) = P(E) + P(L) + P(S) = 100/200 + 60/200 + 40/100 = 1

P(F u M) = P(F) + P(M) = 130/200 + 70/200 = 1

The probabilities of the Union (OR) joint events

For events A and B, the probability of the union (OR) joint events is calculated using

P(A u B) = P(A) + P(B) - P(A n B)

Using the table of values, we have:

P(E u F) = P(E) + P(F) - P(E n F) = 100/200 + 130/200 - 60/100 = 0.85

P(L u M) = P(L) + P(M) - P(L n M) = 60/200 + 70/200 - 20/100 = 0.55

The probabilities of the conditional probabilities

For events A and B, the conditional probability is calculated using

P(A/B) = P(A n B)/P(B)

Using the table of values, we have:

P(F/S) = P(F n S)/P(S) = 0.15/0.20 = 0.75

P(F/E) = P(F n E)/P(E) = 0.30/0.50 = 0.60

P(M/S) = P(M n S)/P(S) = 0.05/0.20 = 0.25

P(M/L) = P(M n L)/P(L) = 0.10/0.30 = 0.33

P(S/F) = P(F n S)/P(F) = 0.15/0.65 = 0.23

P(E/F) = P(F n E)/P(F) = 0.30/0.65 = 0.46

P(S/M) = P(M n S)/P(M) = 0.05/0.35 = 0.14

P(L/M) = P(M n L)/P(M) = 0.10/0.35 = 0.29

The multiplication of dependent events

For events A and B, the conditional probability is calculated using

P(A n B) = P(A) * P(B/A)

Using the table of values, we have:

P(F n L) = P(F) * P(L/F)

This gives

P(F n L) = 0.65 * (0.20/0.30)

Evaluate

P(F n L) = 0.43