Answer: B (3,333 yards, 1 foot)
Step-by-step explanation: 10,000 feet / 3yards= 3,333.33 yards
3 feet in every yard so divide 10,000 by 3 and get 3,333.33 yards. since there are 3 feet in every yard the .33 is 1 foot.
Total of 18 students 5 students prefer country. what is the probability?
Answer:
27.78%
Step-by-step explanation:
We know
Total of 18 students 5 students prefer country.
What is the probability?
5/18 = 27.78%
So, the answer is 27.78%
no algebra pls thanks uv
Answer: z = 210
Step-by-step explanation: Let's assume the original price of the present was x dollars.
Amanda agreed to pay 30% of the original price, so her contribution was 0.3x dollars.
The remaining amount to be paid is (1 - 0.3)x = 0.7x dollars.
Gabriel agreed to pay 2/5 of the remaining amount, so he paid (2/5)(0.7x) = 0.28x dollars.
The balance amount to be paid by Daniel is (1 - 0.3 - 2/5)(x) = 0.42x dollars.
When the price increased by 25%, the new price became 1.25x dollars.
We can set up an equation based on Amanda's contribution and solve for x:
0.3x = 63
x = 210
Therefore, the original price of the present was $210.
MOM+DAD=FAST DAD is a multiple of 83 cryptarithm
Answer:1+1=3
Step-by-step explanation: if 1 doesn't use protection the 1 and the other 1 are going to make 3
5/9=
1/14=
12/13=
2/13=
9/11=
9/17=
To round each fraction
Answer:
Step-by-step explanation:
1. Rounded to 0.56
2. Rounded
Kara invests $3,200 into an account with a 3.1% interest rate that is compounded quarterly. How much money will be in this account after 8 years?
Answer:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the amount of money in the account after t years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Plugging in the given values:
P = $3,200
r = 0.031 (3.1% as a decimal)
n = 4 (quarterly compounding)
t = 8
A = 3200(1 + 0.031/4)^(4*8)
A = $4,100.53
Therefore, after 8 years, there will be $4,100.53 in the account.
Shallow Drilling, Inc. has 76,650 shares of common stock outstanding with a beta of 1.47 and a market price of $50.00 per share. There are 14,250 shares of 6.40% preferred stock outstanding with a stated value of $100 per share and a market value of $80.00 per share. The company has 6,380 bonds outstanding that mature in 14 years. Each bond has a face value of $1,000, an 8.00% semiannual coupon rate, and is selling for 99.10% of par. The market risk premium is 9.79%, T-Bills are yielding 3.21%, and the tax rate is 26%. What discount rate should the firm apply to a new project's cash flows if the project has the same risk as the company's typical project?
Group of answer choices
The discount rate that should be applied to a new project's cash flows is the Weighted Average Cost of Capital (WACC). To calculate WACC, you need to first calculate the cost of debt. This is done by taking the face value of the bonds ($1000) multiplied by the coupon rate (8%) multiplied by (1 - the tax rate (26%)), which equals 5.92%. The cost of debt is then calculated by taking the market value of the debt (6,380 x $1,000 x 99.1%) and dividing this by the total market value of the debt plus the market value of the equity (6,380 x $1,000 x 99.1% + 76,650 x $50 + 14,250 x $80), which equals 5.22%.
Next, you need to calculate the cost of equity using the Capital Asset Pricing Model (CAPM). This is done by taking the risk-free rate (3.21%) plus the market risk premium (9.79%) multiplied by the firm's beta (1.47), which equals 17.18%.
The WACC is then calculated by taking the cost of equity multiplied by the proportion of equity (76,650 x $50 + 14,250 x $80 divided by the total market value of the debt plus the market value of the equity) plus the cost of debt multiplied by the proportion of debt (6,380 x $1,000
Question 2
State the probability that a randomly selected, normally
distributed value lies between
a) o below the mean and o above the mean (round to
the nearest hundredths)
b) 20 below the mean and 20 above the mean (round
to the nearest hundredths)
The probability of a randomly selected, normally distributed value lying between 20 below the mean and 20 above the mean is 0.9545 (rounded to the nearest hundredth).
What is the fundamental concept of probability?A number between zero and one represents the probability that an occurrence will take place. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.
We can calculate the probabilities of a randomly chosen value falling between different z-scores using the provided standard normal distribution table.
a) The probability of a value being 0 below or above the mean is the same as the probability of a value being -1 to 1 standard deviations from the mean. According to the standard normal distribution table, the probability of a z-score between -1 and 1 is 0.6827. As a result, the probability of a randomly chosen, normally distributed value falling between 0 below and 0 above the mean is 0.6827. (rounded to the nearest hundredth).
b) The probability of a value falling between 20 and 20 standard deviations from the mean is the same as the probability of a value falling between -20/10 and 20/10 standard deviations from the mean (since the standard deviation is 10). According to the standard normal distribution table, the probability of a z-score between -2 and 2 is 0.9545. As a result, the probability of a randomly chosen, normally distributed value falling between 20 below and 20 above the mean is 0.9545. (rounded to the nearest hundredth).
To know more about probability visit:
https://brainly.com/question/30719832
#SPJ1
Question 20
There were 750 shirts in a box. 20% of them were pink and 18% were green. The
remaining shirts were either yellow or black. If there were 85 more black shirts than
yellow shirts, what was the total number of black and green shirts in the box?
Answer:
410 Black and Green shirts
Step-by-step explanation:
150 shirts were pink
135 shirts were green
so knowing this we can set up the equation 2x+85=465
there were 275 black shirts in the box
and 190 yellow shirts
therefore there were 410 Black and Green shirts in the box
A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feet tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
The cost to rent one shed of the rectangular prism shaped shed is $2772.
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
What is a prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.
Volume of prism= BH
where B= area of base and H= height
B= 11*7 = 77 feet²
H= 12 feet
Volume= 77*12=924 cubic feet
Cost =$3 per cubic foot
Total cost= 3*924= $2772
To know more about area, visit
https://brainly.com/question/27683633
#SPJ1
what is the distance between-48 and -12
Answer:36
Step-by-step explanation:-48+12
Please help me solve this my head hurts
a. Nοne οf these measure οf central tendency dοn't exist fοr this data set. Optiοn d) is cοrrect
b. As the sum οf all οbservatiοns wοuld chance, the mean wοuld be affected by the change. Optiοn a) is cοrrect
What is central tendency?In statistics, the central tendency is the descriptive summary οf a data set. Thrοugh the single value frοm the dataset, it reflects the centre οf the data distributiοn. Mοreοver, it dοes nοt prοvide infοrmatiοn regarding individual data frοm the dataset, where it gives a summary οf the dataset. Generally, the central tendency οf a dataset can be defined using sοme οf the measures in statistic.
c.
Suppοse that, the largest measurement 97 is remοved.
The number οf οbservatiοns as well as the sum οf all οbservatiοns wοuld change.
Therefοre, the median and the mean wοuld be changed and οptiοn a) and b) are cοrrect.
d.
Since there are three mοdes, the mean, median and mοde must nοt be cοmpared tο each οther fοr skewness.
Instead, it is required tο grοup data in intervals and οbserve the pattern οf classes versus frequencies, as displayed in histοgram.
Therefοre, the distributiοn appears rοughly symmetric and οptiοn c) is cοrrect.
Learn more about central tendency
https://brainly.com/question/30218735
#SPJ1
10% of the cars in my neighborhood are red, and the rest of the cars in the neighborhood are silver. We'll call "seeing a red car" a success, and "seeing a silver car" a failure for the purposes of this problem.
Suppose that I watch 3 cars pass my house and that I become interested in the probability that exactly one of the three cars is red.
Apply the binomial formula to find the probability that exactly one of the three cars is red. Be sure to clearly state the values of n, x, and p in this case.
Answer:
In this scenario, we have:
n = 3 (since we are watching 3 cars)
x = 1 (since we are interested in the probability of exactly one car being red)
p = 0.1 (since the probability of a car being red is 10%, or 0.1)
The binomial formula for calculating the probability of exactly x successes in n independent trials with a probability of success p is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
where nCx is the binomial coefficient, which can be calculated as:
nCx = n! / (x! * (n-x)!)
Using these values and the binomial formula, we can calculate the probability of exactly one of the three cars being red as:
P(1) = (3C1) * 0.1^1 * (1-0.1)^(3-1)
= (3) * 0.1 * 0.81
= 0.243
Therefore, the probability of exactly one of the three cars being red is 0.243.
. If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2
By linear equality , g >1.5 is must be true.
What are equality and inequality along a line?
Equal (=) is the symbol used in linear equations. Example. Using the inequality symbols (>,, is greater than or equal to, and is less than or equal to), linear inequalities are expressed.
x - 5 > 3x - 10 is an illustration of a linear inequality. As the larger than symbol is employed in this inequality, the LHS is strictly greater than the RHS. After being solved, the inequality appears as 2x 5 x (5/2).
If h> 3 and h - 2g= 0
H=2g
2g>3
g >1.5
Learn more about linear equality
brainly.com/question/11874554
#SPJ1
- Please help me, I don't understand
What is the specific heat of an unknown substance if 100.0 g of it at 200.0 °C reaches an equilibrium temperature of 27.1 °C when it comes in contact with a calorimeter of water. The water weighs 75. g and had an initial temperature of 20.00 °C? (Specific heat of water is 4.18 J/g°C). Show your work
Answer:The specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius (or Kelvin).
To find the specific heat of the unknown substance, we can use the following equation:
Q = m x c x ΔT
where Q is the heat gained or lost, m is the mass of the substance, c is its specific heat, and ΔT is the change in temperature.
In this problem, we know the mass and initial and final temperatures of both the unknown substance and the water, as well as the specific heat of water. We can use this information to calculate the heat gained by the water, which must be equal to the heat lost by the unknown substance:
Heat gained by water = Heat lost by unknown substance
m(water) x c(water) x ΔT(water) = m(substance) x c(substance) x ΔT(substance)
We can plug in the values we know and solve for the specific heat of the unknown substance:
m(water) = 75.0 g
c(water) = 4.18 J/g°C
ΔT(water) = 27.1 °C - 20.00 °C = 7.1 °C
m(substance) = 100.0 g
ΔT(substance) = 200.0 °C - 27.1 °C = 172.9 °C
75.0 g x 4.18 J/g°C x 7.1 °C = 100.0 g x c(substance) x 172.9 °C
Simplifying this equation, we get:
c(substance) = (75.0 g x 4.18 J/g°C x 7.1 °C) / (100.0 g x 172.9 °C)
c(substance) = 0.197 J/g°C
Therefore, the specific heat of the unknown substance is 0.197 J/g°C.
Step-by-step explanation:
Answer:
The specific heat of the unknown substance is 0.39 J/g°C.
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of energy, which states that the heat lost by the unknown substance is equal to the heat gained by the water and the calorimeter. We can express this principle mathematically as:
Q_lost = Q_gained
where Q_lost is the heat lost by the unknown substance, and Q_gained is the heat gained by the water and calorimeter.
We can calculate Q_lost using the formula:
Q_lost = m × c × ΔT
where m is the mass of the unknown substance, c is its specific heat, and ΔT is the change in temperature it undergoes.
We can calculate Q_gained using the formula:
Q_gained = (m_water + m_calorimeter) × c_water × ΔT
where m_water is the mass of the water, m_calorimeter is the mass of the calorimeter, c_water is the specific heat of water, and ΔT is the change in temperature of the water and calorimeter.
Since the system reaches an equilibrium temperature, we can set Q_lost equal to Q_gained and solve for the specific heat of the unknown substance (c).
Here's the calculation:
Q_lost = Q_gained
m × c × ΔT = (m_water + m_calorimeter) × c_water × ΔT
100.0 g × c × (200.0 °C - 27.1 °C) = (75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)
Simplifying:
c = [(75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)] / (100.0 g × (200.0 °C - 27.1 °C))
c = 0.39 J/g°C
Therefore, the specific heat of the unknown substance is 0.39 J/g°C.
Individuals who identify as male and female were surveyed
regarding their diets.
Meat-
eater
Male 35
Female 37
Total 72
.
Vegetarian Pescatarian Vegan Total
12
23
35
24
14
38
18
27
45
89
101
190
What is the probability that a randomly selected
person is a pescatarian or female? Round your
answer to the hundredths place.
Answer:
If you add all the numbers together and divide the number of females by the total number of people. It is a 5% chance that out of all the people, the group of 37 females, one would be selected.
If you add up all the numbers of people and divide by the number of pescatarians, there is an 89.5% chance of a pescatarian being selected.
all numbers added together, 72 meat eaters, and 616 pescatarians = 688
females = 37
37/688 = 0.0537 = 5.37 = rounded to hundredths place = 5%
all numbers added together = 688
number of pescatarians = 616
616/688 = .0895 = 89.5%
Step-by-step explanation:
3 Tell whether each statement is True or False.
A 20° angle and a 70° angle can be
composed into a 90° angle.
b. Three 50° angles compose an angle
that measures 350⁰.
c. A 15° angle and a 60° angle compose
an angle that measures 75°.
d. Four 50° angles can be composed
into a 200° angle.
True False
True
True
True
4 Look at the drawing of a hand fan at the right. The
False
False
Fal
d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.
what is a geometric sequence?
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed constant called the common ratio. The common ratio is denoted by the letter r.
The general formula for a geometric sequence is:a₁, a₁r, a₁r², a₁r³, ...
a. False. The sum of a 20° angle and a 70° angle is 90°, so they can compose a 90° angle.
b. False. The sum of three 50° angles is 150°, so they cannot compose an angle that measures 350⁰.
c. False. The sum of a 15° angle and a 60° angle is 75°, so they can compose an angle that measures 75°.
Therefore, d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.
To learn more geometric sequence from the given link:
https://brainly.com/question/16274868
#SPJ1
Consider the system described below with input f(t) and output y(t). Determine if the system is linear or nonlinear. Show all work. dy +3 +3ty(t)=1² f(t) dt 5. By direct integration find the Laplace transform of the signal shown. f (t) 1+6) t(s)
The system described above is nonlinear because it contains a term with y(t) multiplied by t. The Laplace transform of f(t) is (6/s²)+(1/s).
If we substitute y1(t) and y2(t) into the equation and add them together, we get:
dy1/dt + 3 + 3ty1(t) = 1² f(t) dt dy2/dt + 3 + 3ty2(t) = 1² f(t) dt
Then we can add these two equations together to get:
d(y1+y2)/dt + 3 + 3t*(y1+y2)(t) = 2*1² f(t) dt
This is not equal to the original equation with y(t), which means that the system is nonlinear.
To find the Laplace transform of f(t), we can use the formula:
L{f(at+b)} = (1/a) ×F(s-b/a)
where F(s) is the Laplace transform of f(t). In this case, we have:
f(t) = (1+6t)
So we can rewrite this as:
f(t) = (6×t+1)
Now we can use the formula to find the Laplace transform:
L{(6×t+1)} = (6/s²)+(1/s)
Therefore, the Laplace transform of f(t) is (6/s²)+(1/s).
To know more about Laplace transform, refer:
https://brainly.com/question/17062586
#SPJ4
Assuming boys and girls are equally likely, find the probability of a couple's last child being a baby boy. They have a total of 3 children not including the last child in question and all were boys before the last child was born.
Express your answer as a percentage rounded to the nearest hundredth without the % sign.
Answer:
Step-by-step explanation:
The probability of a baby being a boy or a girl is 1/2 or 50% each. Since the couple has already had three boys, the probability of the fourth child being a boy or a girl is still 1/2 or 50%, as the gender of each child is independent of the others. Therefore, the probability of the couple's last child being a baby boy is 50%.
The required probability of a couple having a baby boy when their third child is born is 1/2 / 50%.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
Given:
Assuming boys and girls are equally likely.
The first two children were both boys
According to given question we have
The probability of having a baby girl is an independent probability.
The first two children were both boys
So, it is not related to the previous child.
So required probability = 1/2 / 50%
Therefore, the required probability of a couple having a baby boy when their third child is born is 1/2 / 50%.
Learn more details about probability here:
https://brainly.com/question/11234923
mr Li wishes to give each of his five relatives in China 500 renminbi (RMB) Find the amount he would need in Singapore dollars, if the exchange rate is S$100 to RMB510.20
Exchange rate calculation.
To find out the amount in Singapore dollars that Mr Li would need to give each of his five relatives 500 RMB each, we can follow these steps:
Calculate the total amount in RMB that Mr Li needs to give:
500 RMB/relative x 5 relatives = 2500 RMB
Convert the total amount in RMB to Singapore dollars using the given exchange rate:
2500 RMB x (S$100/RMB510.20) = S$490.64 (rounded to the nearest cent)
Therefore, Mr Li would need S$490.64 to give each of his five relatives 500 RMB each, given the exchange rate of S$100 to RMB510.20.
ChatGPT
The rectangle can be made to have rotation symmetry of order 2 by colouring one of the squares blue. Put a cross in the middle of the square which would have to be made blue.
you thought
i was feeling you
£4100 is deposited into a bank paying 13.55% interest per annum , how much money will be in the bank after4 years
Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the amount of money in the account after the specified time period
P = the initial principal amount (the amount deposited)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period in years
In this case:
P = £4100
r = 13.55% = 0.1355
n = 1 (interest is compounded once per year)
t = 4 years
Plugging these values into the formula, we get:
A = £4100(1 + 0.1355/1)^(1*4)
A = £4100(1.1355)^4
A = £4100(1.6398)
A = £6717.58
Therefore, the amount of money in the account after 4 years will be £6717.58.
This is for a test, teacher said we could use any source available so help is appreciated
a. P(x) = 50x - 4000.1.
b. The company must sell at least 81 units of their product to have a positive profit.
c. The company should try to sell as many units as possible within the given range to maximize their profit.
What is revenue function?A revenue function is a mathematical equation or formula that represents the amount of money a company or organization generates from the sale of its products or services. It is a function that relates the price of a product or service to the quantity sold and represents the total revenue earned by a company at a given price and level of production.
What is profit function?A profit function is a mathematical equation or formula that represents the amount of profit a company or organization generates from the sale of its products or services. It is a function that relates the price of a product or service, the cost of production, and the quantity sold and represents the total profit earned by a company at a given price and level of production.
In the given question,
(a) The profit function can be obtained by subtracting the cost function from the revenue function as follows:
R(x) = -0.1x + 150x
P(x) = R(x) - C(x)
P(x) = (-0.1x + 150x) - (100x + 4000)
P(x) = 50x - 4000.1
Therefore, the profit function is P(x) = 50x - 4000.1.
(b) To find the minimum number of units the company must sell to have a positive profit, we need to set P(x) greater than or equal to zero and solve for x:
P(x) ≥ 0
50x - 4000.1 ≥ 0
50x ≥ 4000.1
x ≥ 80.002
Therefore, the company must sell at least 81 units of their product to have a positive profit.
(c) To find the value of r that maximizes the profit, we need to find the derivative of the profit function and set it equal to zero:
P'(x) = 50
Setting P'(x) equal to zero, we get:
50 = 0
This equation has no solution, which means that the profit function has no maximum value within the given range. However, we can see that the profit function is increasing for all values of x, which means that the profit increases as the number of units sold increases. Therefore, the company should try to sell as many units as possible within the given range to maximize their profit.
To know more about revenue function, visit:
https://brainly.com/question/28545124
#SPJ1
Which answer choice contains all the factors of 10? • A. 1, 2, 5 О B. 1, 2, 5, 10 O C. 2, 5 O D. 1, 10
Answer:
The answer would be B (1,2,5, 10)
Step-by-step explanation:
Since one can already go into any number that greater than zero it would be a factor
2x5=10 as well so two and five would be a factor
you can also do 10x1
or 1x10 so both 10 and one would be factors of ten.
In a group of rectangles, the length of each rectangle is twice the width. Is this an additive or multiplicative relationship? Explain your reasoning.
Answer:
Multiplicative
Step-by-step explanation:
If the area of the first rectangle is l*w, the area of the second would be 2w*w. The area is multiplied by 2 and the relationship is therefore multiplicative.
A local hamburger shop sold a combined total of 688 hamburgers and cheeseburgers on Monday. There were 62 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Monday? I hamburgers
Answer: 375 hamburgers
Step-by-step explanation:
Let's assume that x is the number of hamburgers sold on Monday.
According to the problem, the number of cheeseburgers sold is 62 fewer than the number of hamburgers sold. So the number of cheeseburgers sold is x-62.
The total number of hamburgers and cheeseburgers sold is 688. So we can set up an equation:
x + (x-62) = 688
Simplifying this equation, we get:
2x - 62 = 688
Adding 62 to both sides, we get:
2x = 750
Dividing both sides by 2, we get:
x = 375
Therefore, 375 hamburgers were sold on Monday.
What is the absolute
value for:
| +98|
Answer:
The absolute value of +98 is simply 98. So, | +98| = 98.
Step-by-step explanation:
Answer:
98
Step-by-step explanation:
The absolute value of a number is its POSITIVE distance from 0, so as +98 is 98 away from 0, then |+98| = 98.
(4+4i)(5-i) perform the indicated operation and express the result as a simplified complex number
Answer:
24 + 16i
Step-by-step explanation:
[tex](4+4i)(5-i)\\=(4)(5)+(4)(-i)+(4i)(5)+(4i)(-i)\\=20-4i+20i-4i^2\\=20+16i-4(-1)\\=20+16i+4\\=24+16i[/tex]
consider the following scores: 13, 18, 9, 27, 15, 15, 28, 5, 16, 21, 23, 29, 15, 15 what z-score would be earned by a person who had scored 25 points?
A person who scored 25 points in this dataset would have a z-score of 0.99.
The mean can be calculated by adding up all of the scores and dividing by the number of scores:
(13 + 18 + 9 + 27 + 15 + 15 + 28 + 5 + 16 + 21 + 23 + 29 + 15 + 15) / 14 = 18
The standard deviation can be calculated using the formula:
sqrt(sum((x - mean)^2) / (n - 1))
where x is each score in the dataset, mean is the mean of the dataset, and n is the number of scores.
Using this formula, we get:
sqrt (((13-18) ^2 + (18-18) ^2 + (9-18) ^2 + (27-18) ^2 + (15-18) ^2 + (15-18) ^2 + (28-18) ^2 + (5-18) ^2 + (16-18) ^2 + (21-18) ^2 + (23-18) ^2 + (29-18) ^2 + (15-18) ^2 + (15-18) ^2) / (14 - 1))
= 7.05
Now we can calculate the z-score of a scores of 25 using the formula:
z = (x - mean) / standard deviation
where x is the score, we are interested in, mean is the mean of the dataset, and standard deviation is the standard deviation of the dataset.
Plugging in the values, we get:
z = (25 - 18) / 7.05 = 0.99 (rounded to two decimal places)
To know more about z-score:
https://brainly.com/question/15016913
#SPJ4
PLEASE HELP MEE with all four questionsss
Therefore, the distance between the 90 degree angle and the hypotenuse is approximately 0.829 units.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight line segments that connect to form three angles. It is one of the most basic shapes in geometry and has a wide range of applications in mathematics, science, engineering, and everyday life. Triangles can be classified by the length of their sides (equilateral, isosceles, or scalene) and by the size of their angles (acute, right, or obtuse). The study of triangles is an important part of geometry, and their properties and relationships are used in many areas of mathematics and science.
Here,
1. To find HF, we can use the angle bisector theorem, which states that if a line bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the adjacent sides. Let's denote the length of HF as x. Then, by the angle bisector theorem, we have:
JF/FH = JG/HG
Substituting the given values, we get:
15/x = 18/21
Simplifying and solving for x, we get:
x = 15 * 21 / 18
x = 17.5
Therefore, HF is 17.5 cm.
2. Let's denote the length of the hypotenuse as h and the length of the leg opposite the 18-unit perpendicular as a. We can then use the Pythagorean theorem to write:
h² = a² + 18²
We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:
h = x + 6
Substituting this expression into the first equation, we get:
(x + 6)² = a² + 18²
We are also told that the leg adjacent to the angle opposite the 4-unit segment is divided into segments of length 4 and (a - 4), so we can write:
a = 4 + (a - 4)
Simplifying this equation, we get:
a = a
Now we can substitute this expression for a into the previous equation and solve for x:
(x + 6)² = (4 + (a - 4))² + 18²
Expanding and simplifying, we get:
x² + 12x - 36 = 0
Using the quadratic formula, we get:
x = (-12 ± √(12² - 4(1)(-36))) / (2(1))
x = (-12 ± √(288)) / 2
x = -6 ± 6√(2)
Since the length of a segment cannot be negative, we take the positive root:
x = -6 + 6sqrt(2)
x ≈ 1.46
Therefore, the value of x is approximately 1.46 units.
3. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the 9-unit perpendicular as b. We can then use the Pythagorean theorem to write:
h² = b² + 9²
We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:
h = x + 6
Substituting this expression into the first equation, we get:
(x + 6)² = b² + 9²
Expanding and simplifying, we get:
x² + 12x - b² = 27
We also know that the length of the leg opposite the 9-unit perpendicular is:
a = √(h² - 9²)
= √((x + 6)² - 9²)
= √(x² + 12x + 27)
Now we can use the fact that the tangent of the angle opposite the 9-unit perpendicular is equal to the ratio of the lengths of the opposite and adjacent sides:
tan(θ) = a / b
Substituting the expressions for a and b, we get:
tan(θ) = √(x² + 12x + 27) / (x + 6)
We also know that the tangent of the angle theta is equal to the ratio of the length of the opposite side to the length of the adjacent side:
tan(θ) = 9 / b
Substituting the expression for b, we get:
tan(θ) = 9 / √(h² - 9²)
Substituting the expression for h, we get:
tan(θ) = 9 / √((x + 6)² - 9²)
Since the tangent function is the same for equal angles, we can set these two expressions for the tangent equal to each other:
√(x² + 12x + 27) / (x + 6) = 9 / √((x + 6)² - 9²)
Squaring both sides, we get:
(x² + 12x + 27) / (x + 6)² = 81 / ((x + 6)² - 81)
Cross-multiplying and simplifying, we get:
x⁴ + 36x³ + 297x² - 1458x - 2916 = 0
Using a numerical method such as the Newton-Raphson method or the bisection method, we can find the approximate solution to this equation:
x ≈ 9.449
Therefore, the value of x is approximately 9.449 units.
4. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the distance we want to find as b. We can use the Pythagorean theorem to write:
h² = b² + d²
We are told that the hypotenuse is divided into segments of length 9 and 4 units, so we can write:
h = 9 + 4 = 13
Substituting this expression into the first equation, we get:
13² = b² + d²
Simplifying and solving for d, we get:
d = √(13² - b²)
Now, we need to find the value of b. We know that the hypotenuse is divided into segments of length 9 and 4 units, so we can use similar triangles to write:
b / 4 = 9 / 13
Simplifying and solving for b, we get:
b = 36 / 13
Substituting this expression for b into the equation we found earlier for d, we get:
d = √(13² - (36/13)²)
Simplifying and finding a common denominator, we get:
d =√ (169*13 - 36²) / 13²
Simplifying further, we get:
d = √(169169 - 3636) / 169
Calculating this expression, we get:
d ≈ 0.829
To know more about triangle,
https://brainly.com/question/28600396
#SPJ1
Find equations of the tangent line and normal line to the curve y
=
x
4
+
2
e
x
at the point (0,2)
The equation of the tangent line is y = 2x + 2., and the equation of the normal line is y = -1/2 x + 2.
To find the equations of the tangent and normal lines to the curve y = x⁴ + [tex]2e^{X}[/tex] at the point (0,2), we will need to find the slope of the curve at that point, and then use point-slope form to write the equations of the tangent and normal lines.
First, we can find the slope of the curve at the point (0,2) by taking the derivative of the function and evaluating it at x = 0:
y = x⁴ + [tex]2e^{X}[/tex]
y' = 4x³ + [tex]2e^{X}[/tex]
y'(0) = 4(0)³ + 2e⁰ = 2
So the slope of the curve at the point (0,2) is 2.
Next, we can use point-slope form to write the equation of the tangent line. The point-slope form of a line will be given by:
y - y₁ = m(x - x₁)
where m will be the slope of the line and (x₁, y₁) is a point on the line.
For the tangent line at (0,2), we have:
y - 2 = 2(x - 0)
Simplifying, we get:
y = 2x + 2
So the equation of tangent line is y = 2x + 2.
To find the equation of the normal line, we need to find the negative reciprocal of the slope of the tangent line (since the slopes of perpendicular lines are negative reciprocals of each other). So the slope of the normal line will be:
m = -1/2
Using point-slope form again, the equation of the normal line is:
y - 2 = (-1/2)(x - 0)
Simplifying, we get:
y = -1/2 x + 2
To know more about tangent line here
https://brainly.com/question/23265136
#SPJ4