The length AC of the missing sides of the given triangle above would be;
AC= 15.6cm
AB = 9cm
How to calculate the length of the missing sides of the triangle?To calculate the length of the missing sides of the triangle, the sin rule of used such as;
a/sinA = b/sinB
a = 18
A = 90°
b =AB= ?
B = 30°
That is:
18/sin90 = b/sin 30°
b = 18×0.5/1
= 9
Using Pythagorean formula;
c² = a² +b²
18² = 9²+b²
b² = 324-81
b² = 243
b = √243
= 15.6cm
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Samir has a collection of coins. He wants to find out how many dimes he has without having to count them. According to the U.S. Mint report, a dime has a mass of approximately 2.27 grams. If the total weight of Samir's dime collection is 47.67 grams, about how many dimes are in Samir's coin collection?
Answer:
21
Step-by-step explanation:
47.67 divided by 2.27 = 21
Which statement below best describes whether or not the triangles are similar and
why?
A. ∆XXXXXX ~ ∆TTTTTT by AA similarity.
B. ∆XXXXXX ~ ∆TTTTTT by ASA similarity.
C. ∆XXXXXX ~ ∆TTTTTT by SSS similarity.
D. There is not enough information to determine similarity.
Find f'(x). f(x) = 4 In (8 + 9x) f'(x)=0
The derivative of f(x) = 4 ln(8 + 9x) is f'(x) = 36/(8 + 9x).
To find the derivative of f(x), we use the chain rule and the derivative of ln(u) = 1/u. Let u = 8 + 9x, then f(x) = 4 ln(u). Using the chain rule, we have:
f'(x) = (d/dx)(4 ln(u)) = 4 (d/dx)ln(u) = 4(1/u) (du/dx)
To find du/dx, we take the derivative of u with respect to x, which is simply 9. Therefore:
f'(x) = 4(1/u) (du/dx) = 4(1/(8 + 9x)) (9) = 36/(8 + 9x)
Therefore, the derivative of f(x) is f'(x) = 36/(8 + 9x).
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willow brook national bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. on weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. assume the poisson probability distribution can be used to describe the arrival process. determine the following operating characteristics for the system, assuming poisson arrivals and exponential service times. (round your answers to four decimal places where necessary. report time in minutes.)
The expected number of customers in the system is 0.96.
Given that the arrivals to the drive-up teller window occur at a rate of 0.4 customers per minute, and the service times are exponentially distributed, we can use queuing theory to determine the operating characteristics of the system.
What is the expected number of customers waiting in line?
We can use the queuing formula Lq = (λ^2) / (μ(μ-λ)), where λ is the arrival rate and μ is the service rate. Here, λ = 0.4 and μ is the reciprocal of the average service time, which we need to calculate.
Assuming the bank tellers can serve customers in an average of 2 minutes, then μ = 1/2 = 0.5.
Plugging these values into the formula, we get:
Lq = (0.4^2) / (0.5(0.5-0.4)) = 0.16 customers
Therefore, the expected number of customers waiting in line is 0.16.
What is the expected time a customer spends in the system?
We can use the queuing formula W = (1/μ) + (Lq/λ), where μ is the service rate and λ is the arrival rate, and Lq is the expected number of customers waiting in line.
Using the same values of λ and μ as before, we can calculate Lq as 0.16 customers. Plugging these values into the formula, we get:
W = (1/0.5) + (0.16/0.4) = 2.4 minutes
Therefore, the expected time a customer spends in the system is 2.4 minutes.
What is the expected number of customers in the system (i.e., both waiting and being served)?
We can use the queuing formula L = λW, where λ is the arrival rate and W is the expected time a customer spends in the system.
Plugging in the values of λ and W that we calculated earlier, we get:
L = 0.4 x 2.4 = 0.96 customers
Therefore, the expected number of customers in the system is 0.96.
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a car is traveling at a steady speed. it travels 2 1/2 miles in 3 1/3 minutes. how far will it travel in 25 minutes. in 1 hour?
Answer:
Step-by-step explanation:
The car will travel 30 2/3 miles in 45 minutes.Oct
A hot air balloon starts at an elevation of 300 feet. Then, it ascends at a rate of 600 feet per minute. what is the slope of the line?
Answer:
m = 600 feet/minute
Step-by-step explanation:
In this scenario, the elevation of the hot air balloon can be represented as a linear function of time. Let's use t to denote time in minutes and h(t) to denote the elevation of the balloon in feet at time t.
We know that the balloon starts at an elevation of 300 feet, so we can write the equation of the line as:
h(t) = 600t + 300
The slope of the line represents the rate of change of the elevation with respect to time, which is the same as the rate at which the balloon is ascending. Therefore, the slope of the line is equal to the ascent rate of the balloon, which is 600 feet per minute.
So the slope of the line is:
m = 600 feet/minute
Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.
To completely stain the bottom rectangular prism, Seth had to cover
624
square inches of wood. For one of the cubes to be completely stained, he had to cover
square inches of wood. To completely stain the top rectangular prism, he had to cover
square inches of wood.
Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of
square inches.
The missing options from the surface area problem are;
1. 680in²
2. 128in²
3. 240in²
4. 1048.in²
How is this so?1) To completely stain the bottom of the rectangular prism,
We must remove the area base of the cubes from the surface area of the base (cuboid)
(6 x 8 x 2) + (22 x 8 x 2) + (22 x 6 x 2) - (4 x 4 x2)
= 48 x 2 + 22 x 10 + 22 x 12 - 32
= 680in²
2) For one of the cubes to be stained, he had to cover
4 x 4 x 8
= 128in²
3) To completely stain the top rectangular prism, he had to cover
(18 x 5 x 2) + (2 x 5 x 2) + (18 x 2 x 2) - (4 x 4 x 2)
= 18 x 10 + 2 x 10 + 18 x 4 - 32
= 240in²
4) Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of
= 680 + 128 + 240
= 1,048in²
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Which angles are adjacent angels?
Answer:
KJL and IJL
Step-by-step explanation:
(picture)
complete it
Answer:
749, 715, 710
Step-by-step explaination:
What is the bohr diagram for Titanium +4charge ions.
Answer:
Step-by-step explanation:
thats the link for the diagram
Answer:
The nucleus of a titanium atom has 22 protons and 26 neutrons
If you search online for 'Bohr's diagram for titanium' it might help.
__
It will become Ti ^4+
Bohr diagrams indicate how many electrons fill each principal shell. This means that they can achieve a stable configuration and a filled outer shell by donating or losing an electron. As a result of losing a negatively-charged electron, they become positively-charged ions.
Using the 100/50/20 Rule for daily fluid requirements (DFR). Calculate the following questions, do not round the patient's weight but round all final answers to a whole number. 1-10 kg = 100ml/kg/day 11-20 kg = 50ml/kg/day (+ 1000 mL/day for 1* 10kg) Over 20kg = 20mL/kg/day (1500 mL/day for 1s 20kg) 18. An infant weighs 11 pounds. What is the required amount of fluid per day in ml? I 19. A child weighs 31 lbs and 8 ozs. What is the required amount of fluid per day in ml? If no oral fluids are consumed, what is the hourly IV flow rate to maintain proper hydration?
18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.
19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.
If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.
Daily Fluid Requirements (DFR)The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.
The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.
This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.
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Can you help me solve this question
Select ALL the sequences of transformations that could take Figure P to Figure Q
Answer:
a reflection then a reflection
Parent volunteers at Centerville High School are processing yearbook order forms. Students have an option to get the basic yearbook or a deluxe option, which includes engraving and a protective cover. In Mrs. Lane's class, 27 basic yearbooks and 28 deluxe yearbooks were ordered, for a total of $4,135. The students in Mr. Burton's class ordered 16 basic yearbooks and 8 deluxe yearbooks, for a total of $1,720. How much does each option cost?
The basic yearbook option costs $80, and the deluxe yearbook option costs $120.
To find the cost of each yearbook option, we can set up a system of equations based on the given information. Let's denote the cost of a basic yearbook as 'B' and the cost of a deluxe yearbook as 'D'.
From Mrs. Lane's class:
27B + 28D = 4135 (equation 1)
From Mr. Burton's class:
16B + 8D = 1720 (equation 2)
To solve this system of equations, we can use either substitution or elimination. Let's use the elimination method:
Multiplying equation 2 by 2, we have:
32B + 16D = 3440 (equation 3)
Now, subtract equation 3 from equation 1 to eliminate 'D':
(27B + 28D) - (32B + 16D) = 4135 - 3440
Simplifying, we get:
-5B + 12D = 695 (equation 4)
Now we have a new equation relating only 'B' and 'D'. We can solve this equation together with equation 2 to find the values of 'B' and 'D'.
Multiplying equation 4 by 8, we have:
-40B + 96D = 5560 (equation 5)
Adding equation 2 and equation 5:
16B + 8D + (-40B + 96D) = 1720 + 5560
Simplifying, we get:
-24B + 104D = 7280
Dividing the equation by 8, we have:
-3B + 13D = 910 (equation 6)
Now we have a new equation relating only 'B' and 'D'. We can solve this equation together with equation 2 to find the values of 'B' and 'D'.
Now, we have the following system of equations:
-3B + 13D = 910 (equation 6)
16B + 8D = 1720 (equation 2)
Solving this system of equations will give us the values of 'B' and 'D', which represent the cost of each yearbook option.
Solving the system of equations, we find:
B = $80 (cost of a basic yearbook)
D = $120 (cost of a deluxe yearbook)
Therefore, the basic yearbook option costs $80, and the deluxe yearbook option costs $120.
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On a coordinate plane, an exponential function approaches y = 0 in quadrant 2. It increases into quadrant 1 and goes through (1, 2) and (2, 8). Which functions could represent a reflection over the y-axis of the given function? Check all that apply. g(x) = –One-half(4)x g(x) = 0.5(4)–x g(x) = 2(4)x g(x) = One-half (one-fourth)x g(x) = One-half (one-fourth)–x
Answer:
B.) D.) ^above
Step-by-step explanation:
Just a trust lol
Answer:
B and D
Step-by-step explanation:
Edge 2022
someone plzz help me i don't know if its right I'm lost out of time
Answer:
12. 30
13. 3
Step-by-step explanation:
Help please!! I am freaking out!!
The yellow portion of this pie chart represents 35%
How many degrees are in the angle formed by the edges of the yellow region?
Answer:
100.8
Step-by-step explanation:
100%=360
35%=?
35/100*360=100.8
Answer:
The correct answer is 126
Find the value of x in the isosceles triangle shown below.
52
V52
2
Answer:
the answer is x = 6
Step-by-step explanation:
Buy-Rite Pharmacy has purchased a small auto for delivering prescriptions. The auto was purchased for $26,000 and will have a 6-year useful life and a $5,500 salvage value. Delivering prescriptions (which the pharmacy has never done before) should increase gross revenues by at least $33,500 per year. The cost of these prescriptions to the pharmacy will be about $28,000 per year. The pharmacy depreciates all assets using the straight-line method. The payback period for the auto is closest to (Ignore income taxes. ): (Round your answer to 1 decimal place. )
The payback period for the auto is approximately 8 years.
Buy-Rite Pharmacy has purchased an auto for delivering prescriptions. The auto was purchased for $26,000, and it has a useful life of 6 years with a $5,500 salvage value. By delivering prescriptions, the pharmacy aims to increase gross revenues by at least $33,500 per year. The pharmacy will incur a cost of $28,000 per year for these prescriptions.
Using the straight-line method, the annual depreciation of the auto is ($26,000 - $5,500) / 6 = $3,917. This means that the total cost of the auto over 6 years will be $26,000 - $5,500 + ($3,917 x 6) = $43,502.
To calculate the payback period, we need to determine how long it will take for the increased gross revenues to cover the cost of the auto.
The net increase in revenues will be $33,500 - $28,000 = $5,500 per year. Therefore, the payback period is $43,502 / $5,500 = 7.9 years, which is rounded to 8 years.
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A dressmaker sells a shirt for $75. If she makes a 25% profit, how much did it cost her to make the shirt?
Answer: $56.25
Step-by-step explanation:
x = cost to make the shirt
x + 75(0.25) = 75
x = 75 - 18.25 = 56.25
6. The discount price of a hat is $18. What is the regular price?
The store offers a 20% discount btw .
Answer:$22.50 regular price
Step-by-step explanation: RP=Regular Price
RP-20%of RP=18
RP-0.20RP=18........RP =1RP
1RP-0.20RP=18
0.80RP=18
RP=18/0.80
RP=$22.50
Answer:
22.50
Step-by-step explanation:
other answer is cryptic so here is a full explaination
To find the regular price of the hat, we need to determine the amount of the discount and then add that amount to the discount price.
The discount on the hat is 20% of the regular price, or 20/100 * regular price. The discount price is $18, so we can set up the equation:
discount price = regular price - (20/100 * regular price)
Substituting the known values into the equation, we get:
$18 = regular price - (20/100 * regular price)
Solving for the regular price, we find that the regular price is $22.50. This is the price of the hat before the discount.
A person earns $32,600 one year and receives a 5% raise in salary. What is the new salary?
Jim takes great pride in decorating his float for the homecoming parade for his high school. With the $5,000 he has to spend, Jim buys 5,000 carnations at $0.30 each, 4,000 tulips at $0.60 each, and 300 irises at $0.25 each. Write an inequality which describes how many roses, r, Jim can buy if roses cost $0.80 each.
Jimmy may purchase \(820\) roses for $\(0.80\) each, which is an inequality.
What is a good illustration of inequality?The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in lieu of the equals sign. That is an illustration of inequality. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
Is India a country with inequality?Throughout the recent past, wealth disparity in India has grown, with the wealthy gap ranking among the widest among various comparable nations. According to household polls, inequality may have decreased slightly along with the recent slowdown in growth.
\(r = (5000 - [(5000 * 0.3) + (4000 * 0.6) + (300 * 0.25)])0.8\)
\(r = (5000 - [1500 + 2400 + 75])0.8\)
\(r = (5000 - 3975)0.8\)
\(r = 1025(0.8)\)
\(r = 820\)
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The demand function Q and cost function C(Q) of a commodity are given by the equations Q=20−0,01P C(Q)=60+6Q where P and Q are the price and quantity, respectively. The total revenue function (TR) in terms of P is a. TR=20−0,01P. b. TR=P(120−0,01P2) c. TR=20P−0,01P2. d. TR=P2(20−0,01P2) If the production function is given by Q=300L−4L where Q denotes output and L denotes the size of workforce, calculate the value of marginal product of labour if L=9. a. 11 b. 16 c. 46 d. 146 A firm has the following total and cost functions: TR=20Q−4Q2TC=16−Q2 where Q is the number of unites produced and sold (in thousands). How many units should be produced to maximise the profit? a. 3,333 units. b. 1,714 units. c. 1,333 units. d. 3333 units.
We can conclude that there is no profit-maximizing level of production, and the correct option is e.
None of the above.
Part A The given demand function of a commodity is Q = 20 - 0.01P, and the given cost function is C(Q) = 60 + 6Q.
We need to find out the total revenue function TR in terms of P.
Now, the total revenue is calculated by the multiplication of price and quantity.
Therefore, we can write that TR = P × QSubstituting the value of Q from the demand function, we get;TR = P (20 - 0.01P)TR = 20P - 0.01P²
Therefore, the correct option is c. TR = 20P - 0.01P².
Part BWe are given a production function that is Q = 300L - 4L, where L denotes the size of workforce.
We need to find out the value of the marginal product of labor when L = 9.
Marginal product of labor (MPL) can be calculated as the derivative of the production function with respect to L.
Therefore, we get;MPL = dQ/dL= 300 - 8LNow, substituting the value of L = 9, we get;MPL = 300 - 8(9)MPL = 300 - 72MPL = 228Therefore, the correct option is d. 228Part C
The given total revenue function is TR = 20Q - 4Q², and the given total cost function is TC = 16 - Q²/3.
We know that profit (π) can be calculated as π = TR - TC
Substituting the given values, we get;π = 20Q - 4Q² - (16 - Q²/3)π = -4Q² + (20 - Q²/3)π = -4Q² + 60/3 - Q²/3π = -13Q²/3 + 20Now, we can find the optimal value of Q by differentiating the profit function with respect to Q and equating it to zero.
Therefore, we get;dπ/dQ = -26Q/3 = 0Q = 0
Therefore, we can conclude that there is no profit-maximizing level of production, and the correct option is e.
None of the above.
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which of the following assumptions for a two-way anova is false? the samples must be dependent. the groups must have the same sample size. the sample populations must be normally or approximately normally distributed. the variances of the populations must be equal.
The samples must be dependent is the false assumptions all other assumptions about the two-way ANOVA is correct. Option A is the correct answer.
According to the levels of two categorical variables how the mean of quantitative variables changes is estimated by A two-way ANOVA. When you want to know how two independent variables, in combination, affect a dependent variable we can use a two-way ANOVA.
The samples must be dependent is the false assumption because samples are supposed to be independent, not dependent multicollinearity is minimized. the assumption of the two-way ANOVA is the Independence of variables, Homoscedasticity, and Normal distribution of variables.
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Jerry is saving his money. He started with $15.00. If he adds $10.00 to his savings
each month, how much will he have saved after 2.5 months?
Answer:
$40
Step-by-step explanation:
use y = mx + b
y = amount saved = ?
m = amount saved per week = $10
x = time (in months) saving = 2.5
b = money jerry started with = $15
plug in:
y = (10)(2.5)+15
y = $40
Goode Manufacturing pays Betty Robert's a $1770 monthly salary plus a 14% commission on merchandise she sells each month. assume Betty's sales were $99,200 for last month. calculate the following amounts: 1.amount of commission? gross pay?
Given:
Betty's monthly salary = $1770
Commision on sales = 14%
Betty sales for last month = $99,200
1. The amount of commission is 14% of $99,200.
Therefore, we have:
\(\frac{14}{100}\times99200=0.14\times99200=\text{ \$13888}\)The amount of commission is $13,888
2. The gross pay.
Gross pay is the amount Betty receives before taxes and deductions.
Gross pay = Salary + Commission
Thus, the gross pay is:
$13888 + $1770 = $15,658
ANSWER:
1. Commission = $13,888
2. Gross pay = $15,658
help!!!!!! what is 3/4 + 1/12?
Answer:
37/56
Step-by-step explanation:
Anyone please solve and explain part b
Answer:
f(2) = -6
f inverse of 1/2 is 17/2
Step-by-step explanation:
We are given a function \(\displaystyle \large{f(x) = \frac{6}{2x-5}}\)
To solve for part (a), we have to substitute x = 2 in f(x).
\(\displaystyle \large{f(2)=\frac{6}{2(2)-5} \\\displaystyle \large{f(2)=\frac{6}{4-5}=\frac{6}{-1}=-6\)
Therefore, f(2) is -6.
Now we solve for part (b), we see the notation which is a minor different similar to f(x). We see that there is exponent of -1 between f and 1/2. The part (b) indicates that the function is an inverse of f(x).
\(\displaystyle \large{y=f^{-1}(x) \longrightarrow x=f(y)}\)
To solve for part (b), first we solve for x in the function. Let f(x) = y.
\(\displaystyle \large{y=\frac{6}{2x-5}}\)
Multiply both sides by 2x-5.
\(\displaystyle \large{y(2x-5)=\frac{6}{2x-5}(2x-5)}\\\displaystyle \large{y(2x-5)=6}\)
Divide both sides by y-term.
\(\displaystyle \large{\frac{y(2x-5)}{y}=\frac{6}{y}}\\\displaystyle \large{2x-5=\frac{6}{y}}\\\displaystyle \large{2x=\frac{6}{y}+5}\\\displaystyle \large{x=\frac{6}{2y}+\frac{5}{2}}\\\displaystyle \large{x=\frac{3}{y}+\frac{5}{2}}\)
Then swap x and y which we receive \(\displaystyle \large{y=\frac{3}{x}+\frac{5}{2}}\)
Therefore, \(\displaystyle \large{f(x)=\frac{6}{2x-5} \longrightarrow f^{-1}(x)=\frac{3}{x}+\frac{5}{2}}\)
Thus, \(\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{3}{\frac{1}{2}}+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=6+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{17}{2}}\)
____________________
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I can find the perimeter and area of the rectangle
Answer:
A = 72, P = 38
Step-by-step explanation:
Area can be found by getting the area of the overall figure, and then subtracting the blank space in the corner
12 * 7 = 84
3 * 4 = 12(invisible rectangle in top right)
84 - 12 = 72
Perimeter can be found by adding all of the sides
12 + 7 + (12-4) + 3 + 4 + (7-4)
The numbers in brackets are the unlabeled sides on the top and left.
Answer:
\(P=38\\ A=72\)
Step-by-step explanation:
To find the perimeter (P), add up all of the side lengths of the figure:
(numbers in parenthesis are the unlabeled values in the figure).
\(12+7+(8)+3+4+(4)=38\)
To find the area of the figure (A), multiply the length and width of the original rectangle \((12*7=84)\). Then, subtract this amount (84) minus the area of the missing rectangle in the top left corner \((4*3=12)\).
Subtract the required values: \(84-12=72\).
Therefore, the perimeter of the figure is 38 units, and the area of the figure is 72 units.