Answer:
The scale factor is 60
Step-by-step explanation:
The drawing is measured in inches and the billboard is measured in feet. First, convert 15 feet to 180 inches. Then use the ratio \(\frac{180}{3}\) to find that the scale factor is 60. This means the length of the billboard will be 600 inches or 50 feet.
Which graph models a function showing a piece of equipment that has an original value of $5,000 and whose value decreases by 15% each year?
Answer:
Step-by-step explanation:
its the 3rd option
Answer:
c
Step-by-step explanation:
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
S:{10}
S:{3}
S:{2}
S:{0}
Hence, when \(n=10\) the given inequality is true.
What is the inequality?
An inequality is said to be sharp if it cannot be relaxed and still be valid in general.
Here given that,
Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.
So,
\(2(n + 2) < 5(n-1)\)
When
\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)
Hence, when \(n=10\) the given inequality is true.
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please help meeee!!!
Answer:
195 feet? (I know the answer but I'll leave the rest to you about typing it either cm2 or those stuff.
Step-by-step explanation:
To work this out so, congruent means identical. We already have the answer to EF so 13 x ? But BC = 15 feet. And BC = FG So,
13 x 15 = 195.
Hope this helps
Plz help me if you can asap topic is measurements
Answer:
I'm unsure
Step-by-step explanation:
Answer my question
im being timed
Answer:
the third one
Step-by-step explanation:
(c) how large a sample size is necessary if the width of the 95% interval is to be 0.45? (round your answer up to the nearest whole number.)
Answer:
171/400 or 0.4275
Step-by-step explanation:
multiply the expressions and simplify
derive the decision boundaries in the above case. • derive the conditional mle estimator of θ.
The form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.
what is decision boundaries.?
Decision boundaries refer to the dividing lines or regions that separate different classes or categories in a classification problem. They are determined based on the features or attributes of the data and the classification algorithm being used. The decision boundary serves as a threshold or criterion for assigning new or unseen data points to specific classes based on their feature values.
To derive the decision boundaries in the given case, more specific information or context is needed. Decision boundaries are determined based on the specific classification or grouping criteria and the underlying data distribution. Please provide additional details or specifications regarding the problem or classification task.
Regarding the conditional maximum likelihood estimator (MLE) of θ, more information is required to proceed with the derivation. The MLE involves finding the parameter value that maximizes the likelihood function based on the observed data and any relevant assumptions or models. Please provide the specific context, assumptions, and the form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.
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A circle has an area of 254.469. What is the radius? (round to the nearest whole number)
Answer:
c = 2 r π = 2 * 9.0048 * 3.14159 = 56.55 units
find the area and the circumference of the circle round your answers to the nearest hundredth
Answer:
Circumference= 50.27
Area= 201.06
on a bicycle, courtney rides for 2 hours and is 24 miles from her house. after riding for 9 hours, she is 101 miles away.what is courtney's rate
Courtney rides for two hours on a bicycle, traveling 24 miles from her home. She has ridden for nine hours and is now 101 miles away. Courtney travels at a speed of 6 mph.
Let x represent the duration in hours and y the distance in miles.
Courtney travels 24 miles from her home after a two-hour ride.
She has traveled 101 miles after riding for nine hours.
rate is the slope
We divide the change in hours by the change in miles to find the rate.
\(Slope=\frac{y_{2} - y_{1} }{x_{2}-x_{1} } \\Slope=\frac{101-24}{9-2} \\Slope= \frac{77}{7} \\Slope=11\)
Therefore, Courtney's speed is 11 mph.
The speed of something or someone is shown to us. If you know how far and how long it took, you can find the average speed of an object.
The distance covered in a given amount of time would also double if one were to speed up. We need to know how far an object has traveled in order to determine its speed, and the slowest speeds are measured over the longest time periods.
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(430-24)What size feeder conductor (in ampere) is required for two motors. Motor 1) 7 ½ horsepower single phase, 230 volts (40 ampere) ; Motor 2) 5 horsepower single phase 230 volts (28 ampere) Terminals rated for 75 C.
To determine the size of the feeder conductor required for two motors, we must add the full-load current of each motor together. This will be our total amperage load. We will be using the ampere ratings of Motor 1 and Motor 2 provided in the question.
The formula to get the full-load current (FLC) is :Full-Load Current (FLC) = Horsepower x 746 / Voltage x Efficiency x Power FactorMotor
1- Full-Load Current (FLC) = 7.5 x 746 / 230 x 0.86 x 0.8 = 40 amps Motor
2:Full-Load Current (FLC) = 5 x 746 / 230 x 0.86 x 0.8 = 28 amps
Total Amperage Load = FLC of Motor 1 + FLC of Motor 2Total Amperage Load = 40 + 28 = 68 amps
Since, we have the amperage load, we can now refer to the NEC Table 310.16 to get the correct size of the feeder conductor.
We will assume that the conductors are copper, the terminals are rated for 75 degrees Celsius, and that the feeder is in free air. According to the NEC Table 310.16, a 4 AWG (American Wire Gauge) copper conductor is required for a 75-degree Celsius temperature rating and a 68-amp load.
Therefore, a 4 AWG copper conductor is required for this setup.
What size feeder conductor (in ampere) is required for two motors?The size of the feeder conductor required for two motors is 4 AWG copper wire with a total amperage load of 68 amps.
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Playtime Toy Shop is having its annual holiday sale, when every toy in the store gets marked down. During the sale, Max purchases 6 Wild Wheels diecast cars to add to his collection, each at $2 less than its full price. Max pays a total of $57. How much does each Wild Wheels diecast car cost at full price?
Answer:
$11.50
Step-by-step explanation:
Let x be the full price of the Wild Wheels diecast car.
Given that Max purchases 6 wild wheels diecast cars at $2 less than its full price, and paid a total of $57.
The equation that represents this is,
6x - 12 = 576x−12=57
6x = 696x=69
x = 11.50x=11.50
The cost of each Wild Wheels diecast car at full price is $11.50.
Answer: $11.50
Step-by-step explanation:
Playtime Toy Shop is having a sale on Wild Wheels. They are now being sold for $2 less than the original price. Max buys 6 Wild Wheels for $57.
SO the equation would be...
6(w-2)=57
Now you just solve the equation
6(w-2)=57
Distribute 6.
6w-12=57
Add 12 to both sides.
6w=69
Divide by 6 on both sides.
w=11.5
Therefore each hat would be $11.50.
help please!! ill mark you as brainliest if it’s correct
Answer:
\( {6}^{2} \times \pi \times 15 + \frac{1}{2} \times \frac{4}{3} \times \pi \times {6}^{3} = 19 \times {6}^{2} \times 3.14 = 2147.76\)
Answer:
Step-by-step explanation:
Hemisphere Formula: ( 2 / 3 ) πR = V
Substitution: ( 2 / 3 ) 3.14 * 6 = 12.56
Cylinder Formula: πR^2 * H = V
Substitution: 3.14 * 6^2 * 15 = 1695.6
1695.6 + 12.56 = 1708.16
Please give me Brainliest if I'm correct ! :)
Express the relationship between x + 2 and -2x + 8 as a single equation
Answer:
\(= -2x^2 +4x+ 16\)
Step-by-step explanation:
From the given equation:
\((x+ 2 ) \ and \ (-2x +8)\)
As a single equation, we have:
\(= (x + 2) \ \times \ ( -2x + 8) \ = 0\)
open brackets
\(\implies -2x^2 +8x +(-4x) + 16\)
\(= -2x^2 +4x+ 16\)
I=$180
P=___
r=4.5%
t=3 years
what’s p?
Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
The value for Simple Interest is given as = $180
The value for rate is given as = 4.5%
The value for time is given as = 3 years
To find the value for Principal amount, follow the formula for Simple Interest -
SI = P R T/100
Where P is the principal amount, R is the rate and T is the time.
Substitute the values in the equation -
180 = (P × 4.5 × 3)/100
180 = 13.5P / 100
P = (180 × 100) / 13.5
P = 18000 / 13.5
P = 1333.33
Therefore, the value for principal amount is $1333.33.
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In the diagram at right, ABC ~ADE . Homework Help ✎ Draw each triangle separately on your paper. Be sure to include all measurements in your diagrams. Calculate the length of DE.
The length of DE is 4.9 cm.
What is length?Length is a measurement of size and it can be measured in a variety of waste including inches sentiment of metres feet miles and more. Playing these an important concept in mathematics, science and engineering and many others build it to used to calculate the dimensions of this area. And more it is also used to measure the time it takes to travel.
To solve this problem, we will need to draw each triangle separately and label the sides and angles.
In the diagram, we have triangle ABC and triangle ADE.
Triangle ABC:
We can label the sides as follows:
AB = 7 cm
BC = 5 cm
AC = 6 cm
We can also label the angles as follows:
∠ABC = 90°
∠ACB = 30°
∠BAC = 60°
Triangle ADE:
We can label the sides as follows:
AD = 7 cm
DE = ?
AE = 5 cm
We can also label the angles as follows:
∠ADE = 90°
∠DAE = 30°
∠EAD = 60°
To find the length of DE, we can use the Pythagorean Theorem.
In triangle ADE, AE = 5 cm, AD = 7 cm, and DE = ?
Using the Pythagorean Theorem, we have:
\((7 cm)^2 + (DE)^2 = (5 cm)^2\)
We can solve for DE:
\((7 cm)^2 + (DE)^2 = (5 cm)^2\)
\(49 cm^2 + (DE)^2 = 25 cm^2\)
\((DE)^2 = 24 cm^2\)
DE = √24 cm
\(DE = 4.9 cm\)
Therefore, the length of DE is 4.9 cm.
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The length of DE is 4.9 cm.
What is the triangle?
A triangle is a three-sided polygon, which is one of the simplest geometric shapes in Euclidean geometry.
To solve this problem, we will need to draw each triangle separately and label the sides and angles.
In the diagram, we have triangle ABC and triangle ADE.
Triangle ABC:
We can label the sides as follows:
AB = 7 cm
BC = 5 cm
AC = 6 cm
We can also label the angles as follows:
∠ABC = 90°
∠ACB = 30°
∠BAC = 60°
Triangle ADE:
We can label the sides as follows:
AD = 7 cm
DE = ?
AE = 5 cm
We can also label the angles as follows:
∠ADE = 90°
∠DAE = 30°
∠EAD = 60°
To find the length of DE, we can use the Pythagorean Theorem.
In triangle ADE, AE = 5 cm, AD = 7 cm, and DE = ?
Using the Pythagorean Theorem, we have:
(7cm)^2+(DE)^2 = (5cm)^2
We can solve for DE:
(7cm)^2+(DE)^2 = (5cm)^2
42cm^2+(DE)^2 = 25cm^2
(DE)^2 = 24cm^2
DE = √24 cm
DE = 4.9 cm
Therefore, the length of DE is 4.9 cm.
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please help me!
NO BOTS
Answer:
16 < 24 < 25
Step-by-step explanation:
√16 = 4
√25 = 5
A taco truck is parked at a local lunch site and customers queue up to buy tacos at a rate of one every two minutes. The arrivals of customers are completely independent of one another. It takes 50 ieconds on average to serve a customer (using a single server), with a standard deviation of 20 econds. 1. What is the average time (in seconds) it takes a customer from when they arrive to the truck until they receive their taco. seconds 2. What is the average utilization of the truck? 3. How many people, on average, are waiting in line? people 4. What is the minimum number of servers they would need to get the probability of delay to under 10% ? (Assume all servers have identical service rates.) servers
1. The average time it takes a customer from when they arrive at the truck until they receive their taco is 141.67 seconds.
2. The average utilization of the truck 141.67 seconds.
3. On average, there is 1 person waiting in line.
4. In order to achieve a delay probability of under 10%, a minimum of 1 server is required.
How to calculate the value1 The arrival rate is 1 customer every 2 minutes, which is equivalent to 0.5 customers per minute. The service rate is 1 customer per 50 seconds, which is equivalent to 1.2 customers per minute (since there are 60 seconds in a minute).
2 Average Number of Customers = (0.5 / 1.2) + 1 = 1.4167.
Average Waiting Time = 1.4167 * (50 + 50)
= 141.67 seconds.
3 The average utilization of the truck is given by the formula: Utilization = Arrival Rate / Service Rate.
Utilization = 0.5 / 1.2
= 0.4167 (or 41.67%).
The average number of people waiting in line can be calculated using the formula: Average Number of Customers - Average Utilization.
Average Number of Customers - Average Utilization = 1.4167 - 0.4167
= 1.
4 Given that the desired delay probability is 10% (or 0.1), we can rearrange the formula to solve for the utilization:
Utilization = Delay Probability / (1 + Delay Probability).
=
Utilization = 0.1 / (1 + 0.1) = 0.0909 (or 9.09%).
The utilization we calculated represents the maximum utilization to achieve a delay probability of 10%. In conclusion, to achieve a delay probability of under 10%, a minimum of 1 server is required.
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what is the square root of 3 multiplied by 1/2 in the simplest radical form?
Answer:
usbqjqnamallqnbajabqjqnqkqlqlqllqqlqoqoqnajajhchhsgavbsujwhwjwjqqbq.
hshsjwhwjwjuwubwbwwuwhquuwqjqjqkqbqv pangit mo potang ina mo bulok wlang silbe wag kana mag ajabajajajqkqjbqiqiq
What is this? Help would be highly appreciated:)
Answer:
19
Step-by-step explanation:
straight line=180°
180-123=57
57/3=19
19*3=57
The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of. In order to determine , let G1 = 2, a number whose square is close to 5. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2. 25. 5 ÷ G2 ≠(rounded to the nearest thousandth), which is not equal to G2, so further action is necessary. Average 2. 25 and G2 to find G3 = 2. 236. 5 ÷ G3 ≠(rounded to the nearest thousandth), which is equal to G3. That means is approximately 2. 236.
The steps taken to find the √5 using the ancient method is;
5/G1 = 2.5
5/G2 = 2.222
5/G3 = 2.236
We want to find √5 with the ancient Babylonian method for calculating non-perfect squares;
We are told that G1 = 2
Thus;
5/G1 = 2.5
We are told to average 2.25 and G2 to get 2.236
This means that;
(2.25 + G2)/2 = 2.236
2.25 + G2 = 2 × 2.236
G2 = 4.472 - 2.25
G2 = 2.222
Second step is;
5/G2 = 2.222
Finally;
5/G3 = 2.236
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Answer:
2.5, 2.222, 2.236
Step-by-step explanation:
These two triangles are similar. Find side lengths a and b. The two figures are not drawn to scale
The values of a=6 and b=22.5 by using property of similar triangles that ratio of similar sides is equal.
Similar triangles are triangles that have the same shape, but not necessarily the same size. This means that the corresponding angles of the two triangles are equal, and the corresponding sides are proportional to each other.
Since the triangles are similar, then the following equivalent ratios
\(\frac{4}{10}= \frac{9}{b} =\frac{a}{15}\)
\(\frac{4}{10}= \frac{9}{b}\)
\(4b =90\)
\(b= 22.5\)
Similarly, \(\frac{4}{10} = \frac{a}{15}\)
\(10a= 60\\a= 6\)
The values of a=6 and b=22.5 by using property of similar triangles that ratio of similar sides is equal.
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The complete question is :
These two triangles are similar. Find side lengths a and b. The two figures are not drawn to scale. Diagram is shown in attached image.
A statewide survey is to be made. First, the state is subdivided into counties. Seven counties are selected at random and further sampling is conventrated on these seven counties. What type of sampling is this?
a. Simple Random
b. Non-Proportional
c. Cluster
d. Stratified
The type of sampling described in the scenario is c. Cluster sampling.
Cluster sampling involves dividing the population into clusters or groups and randomly selecting some of these clusters. In this case, the state is subdivided into counties, which act as the clusters. Seven counties are selected at random, and further sampling is concentrated on these seven counties.
Cluster sampling is commonly used when it is not feasible or practical to directly sample individuals from the entire population. Instead, clusters or groups are randomly selected, and then a sample is taken from each of these clusters. This approach can be more efficient and cost-effective compared to other sampling methods, especially when the clusters are internally heterogeneous.
In this scenario, the initial random selection of the seven counties represents the cluster sampling, as subsequent sampling is focused on these specific clusters.
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One diagonal of a rhombus is 4 in shorter than the other diagonal. The area of the diagonal is 10.5 in². Find the length of the longer diagonal.
So the length of the shorter diagonal is 3 inches. The length of the longer diagonal is 7 inches.
What is the rhombus about?Let d1 and d2 be the lengths of the longer and shorter diagonals, respectively. We know that d1 = d2 + 4, and that the area of the rhombus is given by A = (d1*d2)/2 = 10.5.
Substituting d1 = d2 + 4 into the area equation, we get:
(d2+4)*d2/2 = 10.5
Multiplying both sides by 2 and simplifying, we get:
d2²+ 4d2 - 21 = 0
Using the quadratic formula, we can solve for d2:
d2 = (-4 ± \(\sqrt{4^2-4(-21)}\)/2
d2 = (-4 ± \(\sqrt{100}\) /2
d2 = (-4 ± 10)/2
d2 = -7 or 3
Since the length of a diagonal cannot be negative, we reject the negative solution and conclude that d2 = 3. Therefore, d1 = d2 + 4 = 7, and the length of the longer diagonal is 7 inches.
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slove this for me please
Answer:
-10
Step-by-step explanation:
divide both sides by -4
simplify to v+8=-2
subtract 8 from both sides
v=-10
In the year of 2021, Lawrenceville had a gopher problem. The equation that represent this problem is f (x) = 25,000(1.95)".
What does the number in this equation represent for this situation?
25,000:
1.95:
Answer:
25000 is the amount of gophers there are at the beginning
1.95 is the amount they increase each year (95 percent).
Step-by-step explanation:
don't need one
The Police station records how many cars passed through a particular intersection for 5 consecutive days decide of a stop light needed to be installed.The data will be recorded on table of cars passing each day.Is the data continuous or discrete data?
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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Find a formula for the exponential function passing through thepoints (-1, 2/5 ) and (3,250)
The exponential function between (-1, 2/5) and (3, 250) is as follows:
\(f(x) = 2 * 5^x\)
By combining the fourth roots from both sides, we arrive at:
b = 5
When we use the expression we discovered for a and this value of b, we get:
a = (2/5) * 5 = 2
As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:
\(f(x) = 2 * 5^x\)
what are functions?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
from the question:
This is the shape of the exponential function:
f(x) = a *\(b^x\)
where a represents the starting point and b represents the exponential function's base.
We must solve the system of equations to determine the values of a and b that meet the requirements:
a * \(b^(-1)\) = 2/5 (equation 1)
a *\(b^3\)= 250 (equation 2)
We can solve for an in equation 1 by multiplying both sides by b:
a = (2/5) * b
Substituting this expression into equation 2, we get:
(2/5) * b *\(b^3\) = 250
Simplifying, we get:
\(b^4 = 3125\)
By combining the fourth roots from both sides, we arrive at:
b = 5
When we use the expression we discovered for a and this value of b, we get:
a = (2/5) * 5 = 2
As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:
\(f(x) = 2 * 5^x\)
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hello guys, can you give me the answers
The differentiation of the function y = sin(2 sin⁻¹x) is; dy/dx = d√(1 - y²)]/(√1 - x²)
How to differentiate functions?
1) We want to differentiate the function;
\(\frac{\sqrt{x + 1} + \sqrt{x - 1}}{\sqrt{x + 1} - \sqrt{x - 1} }\)
Differentiating this gives;
dy/dx = \(\frac{[(\frac{1}{2\sqrt{x + 1}} - \frac{1}{2\sqrt{x - 1}}) * \sqrt{x + 1} + \sqrt{x - 1}]}{(\sqrt{x + 1} - \sqrt{x - 1})^{2} }\)
That can be simplified to get;
dy/dx = \(\frac{\sqrt{x + 1} + \sqrt{x - 1} }{(x - 1)\sqrt{x + 1} + (-x - 1) \sqrt{x - 1}}\)
2) We want to differentiate the function;
y = sin(2 sin⁻¹x)
Differentiating the function gives;
dy/dx = [2cos(2 sin⁻¹x)]/√(1 - x²)
We know from trigonometric identity that;
cos²x = 1 - sin²x
Thus;
1 - sin²(2 sin⁻¹x) = cos²(2 sin⁻¹x)
But sin²(2 sin⁻¹x) = y²cos²(2 sin⁻¹x)
Thus; √(1 - y²) = cos(2 sin⁻¹x)
dy/dx = d√(1 - y²)]/(√1 - x²)
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