Answers
The angles in triangle LJK from smallest to largest are K (38.7°) < L (58.7°) < J (73.6°).
Describe Triangles?In geometry, a triangle is a three-sided polygon with three angles and three sides. Triangles are one of the fundamental shapes in geometry, and they play an essential role in many areas of mathematics and science.
The sides of a triangle are the line segments that connect its vertices, and the angles of a triangle are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
Triangles can be classified based on the size of their sides and angles. A scalene triangle has no sides or angles that are equal, while an isosceles triangle has two sides that are equal and two angles that are equal. An equilateral triangle has three sides that are equal, and all three angles are equal.
To determine the order of the angles in triangle LJK from smallest to largest, we can use the Law of Cosines to calculate the measures of the angles opposite each side:
cos(L) = (J² + K² - L²) / 2JK
cos(K) = (J² + L² - K²) / 2JL
cos(J) = (K² + L² - J²) / 2KL
where L, J, and K are the measures of angles opposite sides of lengths KL, LJ, and JK, respectively.
Using the given side lengths, we can calculate the cosines of each angle as follows:
cos(L) = (18² + 14² - 16²) / (2 * 18 * 14) = 0.5207
cos(K) = (18² + 16² - 14²) / (2 * 18 * 16) = 0.7738
cos(J) = (14² + 16² - 18²) / (2 * 14 * 16) = 0.1154
To find the measures of the angles, we can take the inverse cosine (cos⁻¹) of each value:
L = cos⁻¹(0.5207) = 58.7°
K = cos⁻¹(0.7738) = 38.7°
J = cos⁻¹(0.1154) = 73.6°
Therefore, the angles in triangle LJK from smallest to largest are:
K (38.7°) < L (58.7°) < J (73.6°)
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The angles in the triangle from smallest to largest are J, K, L. the sides in the triangle from shortest to longest as follows LN, MN, LM.
Describe Triangles?In geometry, a triangle is a three-sided polygon with three angles and three sides. Triangles are one of the fundamental shapes in geometry, and they play an essential role in many areas of mathematics and science.
The sides of a triangle are the line segments that connect its vertices, and the angles of a triangle are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
Triangles can be classified based on the size of their sides and angles. A scalene triangle has no sides or angles that are equal, while an isosceles triangle has two sides that are equal and two angles that are equal. An equilateral triangle has three sides that are equal, and all three angles are equal.
For Triangle LJK:
We can use the Law of Cosines to find the angles in the triangle:
cos(L) = (J² + K² - L²) / (2JK)
cos(K) = (J² + L² - K²) / (2JL)
cos(J) = (K² + L² - J²) / (2KL)
Plugging in the given values, we get:
cos(L) = (18² + 14² - 16²) / (21814) = 0.156
cos(K) = (16² + 14² - 18²) / (21614) = 0.429
cos(J) = (18² + 16² - 14²) / (21816) = 0.783
Using the inverse cosine function, we can find the angles:
L = acos(0.156) = 80.7 degrees
K = acos(0.429) = 65.9 degrees
J = acos(0.783) = 33.4 degrees
Therefore, the angles in the triangle from smallest to largest are: J, K, L.
For Triangle LMN:
We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the third angle:
angle LNM = 180 - 46 - 98 = 36 degrees
Since angle LMN is the smallest angle, we can order the sides in the triangle from shortest to longest as follows:
LN, MN, LM
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The complete question is:
1) Order the angles in the triangle from smallest to largest.
In Δ LJK, LJ= 16 Yd, JK= 18 yd, KL= 14 yd
2) Order the sides in the triangle from shortest to longest.
In ΔLMN, ∠ LMN= 46°, ∠ NLM= 98°, ∠ MNL= 36°
Related Questions
Please look at picture, I need it done by tomorrow
Answers
The shortest route when it crawls sideways is; 4 + 6/π
How to solve Pythagoras theorem?
We are given that;
Diameter of base of cylinder = 6/π m
Height of cylinder = 4 m
Now, we want to find the shortest route from C to point A of the image. The shortest route would be the hypotenuse AC formed by the right angle triangle ABC.
Thus, using Pythagoras theorem, the length AC is;
AC = √((6/π)² + 4²)
AC = √(36/π² + 16)
AC = (1/π)√(36 + 16π² )
AC = 2/π)√(9 + 4π²)
However, we are told it can't take that route but crawl sideways and so it takes the distance CD + DA = 4 + 6/π
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Find the slope and y-intercept for the given linear inequalities;then graphs the given linear inequalities. 1. 6>2x+y m=? b=? 2. x<3y-6 m=? b=?
Answers
Answer:
6 > 2x + y
To find the slope and y-intercept for this linear inequality, we need to write it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Rearranging the given inequality, we get:
y > -2x + 6
Comparing this with y = mx + b, we can see that the slope is -2 and the y-intercept is 6.
So, the slope is m = -2 and the y-intercept is b = 6.
To graph this linear inequality, we can draw the line y = -2x + 6 (which has a slope of -2 and y-intercept of 6) as a dashed line (since y > -2x + 6, not y = -2x + 6). Then we shade the region above the line, since all the points in that region satisfy the inequality y > -2x + 6.
x < 3y - 6
Again, we need to write this inequality in slope-intercept form to find the slope and y-intercept. Rearranging, we get:
3y > x + 6
Dividing both sides by 3, we get:
y > (1/3)x + 2
So, the slope is m = 1/3 and the y-intercept is b = 2.
To graph this linear inequality, we draw the line y = (1/3)x + 2 (which has a slope of 1/3 and y-intercept of 2) as a dashed line (since x < 3y - 6, not x = 3y - 6). Then we shade the region below the line, since all the points in that region satisfy the inequality x < 3y - 6.
Joey’s family wants to save $5000 to finance a vacation trip to a popular amusement park. If they save $240 at the beginning of each month and the fund is invested to earn 5% compounded monthly, how long will it take them to save enough money to take the trip?
Answers
It will take Joey's family approximately 21 months to save enough money, compounded monthly at a 5% interest rate, to finance their vacation trip to the amusement park.
To determine the time it will take to save enough money, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r,
where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of periods.
Given:
Desired future value (FV) = $5000,
Monthly payment (P) = $240,
Monthly interest rate (r) = 5% / 12 = 0.05 / 12 = 0.004167.
We need to solve for the number of periods (n) in the formula. Rearranging the formula, we have:
n = log(1 + (FV * r) / P) / log(1 + r),
where log denotes the logarithm with base 10.
Plugging in the given values, we get:
n = log(1 + ($5000 * 0.004167) / $240) / log(1 + 0.004167).
Using a calculator, we find that n is approximately 20.998, which rounds up to 21.
Therefore, it will take Joey's family approximately 21 months to save enough money, compounded monthly at a 5% interest rate, to finance their vacation trip to the amusement park.
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You are studying the lengths of time people spend reading books
each day. You randomly select 50 people and observe that, in average, they spend 25 minutes
reading books each day. Find the probability that the mean time they spend reading each day is
between 24.7 and 25.5 minutes? Assume that o=1.5 minutes and also you can use the Central
Limit Theorem.
Answers
The probability that the mean time people spend reading books each day is between 24.7 and 25.5 minutes, assuming a population standard deviation of 1.5 minutes and using the Central Limit Theorem, is approximately 0.881 or 88.1%.
How to find the probability?Since we have a sample size of 50, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean. We know that the population standard deviation is 1.5 minutes. Therefore, the standard error of the mean is:
SE = σ/sqrt(n) = 1.5/sqrt(50) ≈ 0.212
To find the probability that the mean time spent reading is between 24.7 and 25.5 minutes, we need to standardize the sample mean using the formula:
z = (x - μ) / SE
where x is the sample mean, μ is the population mean (which is not given, but we can assume is equal to the sample mean of 25), and SE is the standard error of the mean calculated above.
So, for the lower bound of 24.7 minutes:
z = (24.7 - 25) / 0.212 ≈ -1.42
And for the upper bound of 25.5 minutes:
z = (25.5 - 25) / 0.212 ≈ 2.36
We can then use a standard normal distribution table or calculator to find the probability that z is between -1.42 and 2.36, which represents the probability that the sample mean is between 24.7 and 25.5 minutes:
P(-1.42 < z < 2.36) ≈ 0.881
Therefore, the probability is 0.881 or 88.1%.
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Consider the following statement. For all positive real numbers r and s, vr + Str + VS. Some of the sentences in the following scrambled list can be used in a proof by contradiction for the statement. But this is a contradiction because r and s are positive. Simplifying the equation gives 0 = 2V75 | But this is a contradiction because r and s are negative. Squaring both sides of the equation gives r + s = r + 2yrs + s. Squaring both sides of the equation gives r + s = r + 2rs + s. By the zero product property, at least one of vror vs equals 0, which implies r or s equals 0. Construct a proof by contradiction of the statement by using the appropriate sentences from the list and putting them in the correct order. 1. Suppose not. That is, suppose there exists positive real numbers r and s such that r + s = ✓r + VS. 2. But this is a contradiction because r and s are positive. 3. ---Select--- 4. ---Select--- 5. --Select--- 6. Thus we have reached a contradiction and have proved the statement.
Answers
The proof by contradicting of the statement by using appropriate sentences from the list are:
1. Suppose not. That is, suppose there exists positive real numbers r and s such that r + s ≠ √r + √s.
2. Squaring both sides of the equation gives r + s = r + 2√rs + s.
3. Simplifying the equation gives 0 = 2√rs.
4. By the zero product property, at least one of √r or √s equals 0, which implies r or s equals 0.
5. But this is a contradiction because r and s are positive.
6. Thus, we have reached a contradiction and have proved the statement.
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The proof by contradicting of the statement by using appropriate sentences from the list are:
1. Suppose not. That is, suppose there exists positive real numbers r and s such that r + s ≠ √r + √s.
2. Squaring both sides of the equation gives r + s = r + 2√rs + s.
3. Simplifying the equation gives 0 = 2√rs.
4. By the zero product property, at least one of √r or √s equals 0, which implies r or s equals 0.
5. But this is a contradiction because r and s are positive.
6. Thus, we have reached a contradiction and have proved the statement.
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Help is very much appreciated
Answers
Check the picture below.
a. Find the value of that maximizes the area of the figure.
(12-4x) ft
12 ft
b. Find the maximum area.
The maximum area is
(x + 2) ft
square feet.
Answers
Step-by-step explanation:
Area of trapezoid height x average of bases
area = (x+2) * ( 12-4x + 12)/2
= (x+2) (12-2x) = 12x -2x^2 +24 -4x
area = -2x^2 +8x+24 will be a maximum at x = - b/2a = -8/(2*-2) = 2
x=2
Max area = 32 ft^2
Find the volume of a sphere with a surface
area of 16 square feet. Round your answer
to the nearest hundredth.
The volume is about
cubic feet.
Answers
The approximate volume of the sphere is 6.01 ft³.
What is the volume of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).
Given that the surface area of the sphere is 16 square feet.
First, we determine the radius r:
Surface area = 4πr²
Hence
16 = 4πr²
Dividing both sides by 4π, we get:
r² = 16/4πr
r = √( 16/4πr )
r = 1.128 ft
Plugging in the value of r that we just found, we get:
Volume = (4/3)πr³
Volume = (4/3) × 3.14 × (1.128 ft)³
Volume = 6.01 ft³
Therefore, teh volume is 6.01 ft³.
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What is the angle measure of x? (numbers only)
Answers
Answer:30 degrees
Step-by-step explanation:
S = O/H
sin-1(6/12) = 30
how to properly measure the volume of water in a calibrated glass device, such as a graduated cylinder ?
Answers
To properly measure the volume of water in a calibrated glass device such as a graduated cylinder, follow these steps:
Place the graduated cylinder on a flat, level surface.Record the volume to the nearest graduation mark, taking care to estimate any volume that falls between two graduation marks.Repeat the measurement several times to ensure accuracy and consistency.If the water is not clear, you may need to compensate for the effects of the air bubbles that are trapped in the water by gently tapping the cylinder. This will release the bubbles and help to give a more accurate reading.Read the scale of the cylinder from the bottom of the meniscus, which is the curved surface of the liquid. The meniscus should be read at eye level to eliminate parallax error.If necessary, adjust the cylinder so that the scale is straight and the meniscus is centred over the scale.Always rinse the graduated cylinder with distilled water before and after each use to prevent contamination and ensure accuracy.To know more about graduated cylinder:
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The world's largest pizza, upon its completion, "measured 122 feet, 8 inches in diameter, weighed 26,883 pounds, and contained 9,920 pounds of flour, 3,960 pounds of cheese, 1 763 pounds of mushrooms, 1,984 pounds of tomato puree, and 1,984 pounds of chopped tomatoes." Clearly, this was a massive undertaking. A few questions:
-Identify which type of manufacturing process this was. What considerations, from a planning standpoint, do you think were made? How might the process change if you were planning the manufacturing process for a pizza available at pie craft? What about a pizza that you can buy in the frozen section of the supermarket? What are the elements [of the manufacturing process] that change as we transition from the world's largest pizza, to a completely standardized frozen one?
Answers
The type of manufacturing process used to create the world's largest pizza can be classified as batch processing. Considerations such as ingredient sourcing, logistics, equipment capacity, and coordination among multiple teams were likely made during the planning stage. The process would change when planning the manufacturing process for a pizza available at Pie Craft or a pizza in the frozen section of a supermarket, with a shift towards more standardized and automated production methods.
World's Largest Pizza:
The manufacturing process for the world's largest pizza was a massive undertaking due to its size and quantity of ingredients. It involved batch processing, where a specific quantity of the product was produced at one time. During the planning stage, considerations were made regarding ingredient sourcing, logistics, equipment capacity, and coordination among multiple teams.
Pizza at Pie Craft:
If planning the manufacturing process for a pizza available at Pie Craft, a more standardized and streamlined approach would be adopted. The emphasis would be on consistency and quality. This would involve creating standardized recipes, portion control, and training staff to follow specific procedures. Some manual steps might still be involved, but automation could be introduced to streamline processes such as dough mixing and ingredient assembly.
Frozen Supermarket Pizza:
For a pizza in the frozen section of a supermarket, the manufacturing process would undergo significant changes. It would be highly automated and designed for mass production. The emphasis would be on consistency, convenience, and shelf life. The dough would be mechanically mixed, shaped, and portioned, while ingredients would be applied using automated systems. Packaging and freezing processes would also be optimized to maintain product quality.
In summary, the manufacturing process for the world's largest pizza was a massive undertaking, involving batch processing and careful planning regarding ingredient sourcing, logistics, and equipment capacity. For a pizza at Pie Craft, a more standardized approach would be adopted with a balance of manual and automated processes. In contrast, a frozen supermarket pizza would undergo a highly automated process to achieve consistency, convenience, and extended shelf life.
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joan took out a loan of $600. when she paid it back 2 years later, she paid $684. assuming her interest was calculated using simple interest, what was her interest rate?
Answers
Answer:
14% interest
Step-by-step explanation:
all you have to do is divide the $684 by the $600
Answer:
you just have to 600-684 and 600 minus 600 is zero so it's 84
There is no strong evidence that the temporal (time) pattern of \( M>8 \) eruptions (super-eruptions) is anything other than random. True False
Answers
False. There is no strong evidence to support the claim that the temporal pattern of super-eruptions (M>8 eruptions) is random.
The statement claims that the temporal pattern of super-eruptions is random, implying that there is no specific pattern or correlation between the occurrences of these large volcanic eruptions. However, scientific studies and research suggest otherwise. While it is challenging to study and predict rare events like super-eruptions, researchers have analyzed geological records and evidence to understand the temporal patterns associated with these events.
Studies have shown that super-eruptions do not occur randomly but tend to follow certain patterns and cycles. For example, researchers have identified clusters of super-eruptions that occurred in specific geological time periods, such as the Yellowstone hotspot eruptions in the United States. These eruptions are believed to have occurred in cycles with intervals of several hundred thousand years.
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Write an equation of the graph shown in terms of cosine:
Answers
Answer:
Step-by-step explanation:
A squiggly line can refer to a variety of different shapes or patterns. To create an equation using cosine that resembles a squiggly line, you can use a combination of sine and cosine functions with different frequencies and amplitudes. Here's an example equation that produces a squiggly pattern:
y = A * cos(B * x) + C * sin(D * x)
In this equation, A, B, C, and D are constants that you can adjust to modify the shape and characteristics of the squiggly line. By experimenting with different values for these constants, you can create various squiggly patterns. Keep in mind that the specific equation may vary depending on the exact shape and features you have in mind for the squiggly line.
Can somebody help with this?
Answers
Answer:
The height of the pyramid is 11.8 cm to the nearest tenth of a cm
Step-by-step explanation:
The formula of the volume of a pyramid is V = \(\frac{1}{3}\) × A × h, where
A is the area of its baseh is its height∵ A right rectangular pyramid has base dimensions of 23.2 cm, 17.0 cm
∵ The area of the rectangle = Length × width
→ Assume that the length is 23.2 and the width is 17.0
∴ A = 23.2 × 17.0
∴ A = 394.4 cm²
∵ Its volume is 1552.4 cm³
∴ V = 1552.4 cm³
→ Substitute A and V in the rule above
∵ 1552.4 = \(\frac{1}{3}\) × 394.4 × h
∴ 1552.4 = \(\frac{1972}{15}\) h
→ Divide both sides by \(\frac{1972}{15}\)
∴ 11.80831643 = h
→ Round it to the nearest tenth of a cm
∴ h = 11.8 cm
∴ The height of the pyramid is 11.8 cm to the nearest tenth of a cm
Any help is appreciated!!
Answers
Answer:
rip
Step-by-step explanation:
What is the slope of the line through ( 3.3) and ( 1.1)?
Answers
Answer:
slope = -2
Step-by-step explanation:
slope = m = y2-y1/x2-x1
given points (-3,3) and (-1,-1)
plug in to slope formula
m = -1 - 3 / -1 - (-3)
m = -4 / 2
m = - 2
On September 1, 2024, Bahamas Airlines borrows $39.1 million, of which $6.2 million is due next year. Show how Bahamas Airlines would report the $39.1 million debt on its December 31, 2024, balance sheet. (Enter your answers in dollars, not millions. For example, $5.5 million should be entered as 5,500,000.)
Answers
To report the $39.1 million debt on its December 31, 2024, balance sheet, Bahamas Airlines would classify the debt into two categories: current liabilities = $6,200,000 and long-term liabilities = $32,900,000.
To report the $39.1 million debt on its December 31, 2024, balance sheet, Bahamas Airlines would classify the debt into two categories: current liabilities and long-term liabilities.
Current Liabilities: The portion of the debt that is due within the next year, which is $6.2 million, would be reported as a current liability. This amount represents the short-term portion of the debt that needs to be repaid within the next year.
Long-Term Liabilities: The remaining portion of the debt, which is the difference between the total debt and the current liability, would be reported as a long-term liability. In this case, it would be $39.1 million - $6.2 million = $32.9 million.
Therefore, Bahamas Airlines would report the $39.1 million debt on its December 31, 2024, balance sheet as follows:
Current Liabilities:
Debt due within the next year: $6,200,000
Long-Term Liabilities:
Debt due after one year: $32,900,000
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If a function is y = x - 8 , then what is the value of the function when x is 10
Answers
Answer:
2
Step-by-step explanation:
Simplify
y = x - 8
Substitute
y = 10 - 8
10 - 8 = 2, so y = 2
after subsituting what is the first step when evaluatingb 4y+9 over 7 when y=8
Answers
4(8)+9/7
Then solve it
32+9/7
(224+9)7
233/7
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answers
Answer: C. \(f(n) = -4(-3)^{n-1}\)
Step-by-step explanation: The formula for a geometric sequence is \(ar^{n-1}\), where a = first term in the sequence
r = common ratio
n = position of term
Here they already told us a = -4, so we have to figure out r. We can see that in the sequence -4, 12, -36, 108... the terms are being multiplied by -3, which is why the negative and positive terms alternate.
Therefore, the formula is: \(f(n) = -4(-3)^{n-1}\)
You can try inserting n to check it.
\(f(1) = -4(-3)^{1-1} = -4\\f(2) = -4(-3)^{2-1} = 12\\f(3) = -4(-3)^{3-1} = -36\\f(4) = -4(-3)^{4-1} = 108\)
Option C
Let's verify
f(1)=-4(-3)^0=-4f(2)=-4(-3)^1=12f(3)=-4(-3)^2=-36Hence verified
Baja Industries has recently switched its method of applying manufacturing overhead from a single predetermined overhead rate based on direct labor hours to activity-based costing (ABC). Assume that the direct labor rate is $18.00 per hour and that there were no beginning inventories. The following cost drivers and rates have been developed for allocating manufacturing overhead costs:
Activity Cost Driver Rate
Material handling Number of parts used $2.00 per part
Assembly and inspection Number of direct labor hours $25.00 per DLH
Testing Number of units tested $5.00 per unit
The following production, costs, and activities occurred during the month of August:
Direct Number of
Units Produced Material Cost Parts Used Direct Labor Hours
6,400 $208,600 142,000 26,480
(a.) Calculate the total manufacturing cost and the cost per unit for the month of August.
(b.) Assume instead that Baja Industries applies manufacturing overhead on the basis of $40.00 per direct labor hours (rather than the ABC method). Calculate the total manufacturing overhead cost applied for the month of August.
(c.) Which method of applying overhead do you think provides better information for manufacturing managers?
Answers
Cost per unit = Total manufacturing cost / Number of units produced = $1,663,240 / 6,400 = $259.88 per unit
To calculate the total manufacturing cost and cost per unit for the month of August, we need to determine the overhead cost for each activity:
1. Material handling: Number of parts used x Rate = 142,000 parts x $2.00 per part = $284,000
2. Assembly and inspection: Number of direct labor hours x Rate = 26,480 DLH x $25.00 per DLH = $662,000
3. Testing: Number of units tested x Rate = 6,400 units x $5.00 per unit = $32,000
Now, add up all the overhead costs: $284,000 + $662,000 + $32,000 = $978,000
Next, add direct material and direct labor costs:
Direct material cost = $208,600
Direct labor cost = 26,480 DLH x $18.00 per hour = $476,640
Total manufacturing cost = Direct material + Direct labor + Overhead costs = $208,600 + $476,640 + $978,000 = $1,663,240
Cost per unit = Total manufacturing cost / Number of units produced = $1,663,240 / 6,400 = $259.88 per unit
Manufacturing overhead cost = Number of direct labor hours x Rate = 26,480 DLH x $40.00 per DLH = $1,059,200
To calculate the total manufacturing overhead cost applied for the month of August using the $40.00 per direct labor hour rate.
Manufacturing overhead cost = Number of direct labor hours x Rate = 26,480 DLH x $40.00 per DLH = $1,059,200
The traditional method using a single predetermined overhead rate based on direct labor hours may not accurately capture the variation in overhead costs associated with different activities or products.
How the traditional method provides better information for manufacturing managers?The activity-based costing (ABC) method is likely to provide better information for manufacturing managers because it allocates overhead costs based on specific cost drivers related to each activity. This allows for a more accurate representation of the resources consumed by each product or process. In contrast, the traditional method using a single predetermined overhead rate based on direct labor hours may not accurately capture the variation in overhead costs associated with different activities or products.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Suzanne needs material for her school project. She buys 5.50 yards of material at $3.87 a yard. What is the total cost of the material? Round to the nearest cent. You must show your work to receive all possible points.
Answers
The total cost of the material for Suzanne is $21.29
What is the total cost of the yards bought?
The total cost of the yards is a function of the cost per yard and the number of yards that Suzanne needs for the school project.
In other words, the total cost is the cost per yard multiplied by the number of yards of the materials bought
total cost=cost per yard*number of yards bought
cost per yard=$3.87
number of yards bought=5.50 yards
total cost=$3.87*5.50
total cost=$ 21.29
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Which property was used to simplify the expression?
distributive property
commutative property
associative property
inverse property
Answers
Answer:
distributive property
Answer:
distributive prop.
Step-by-step explanation:
fine the distributive property
1. -7(5k - 4)
2. -5172-6)
3. 5(n+6)
4. 4(3r-8)
5. (1 + 9x). -10
6. 3(5 + 5x)
Answers
2. ?
3. 5n+35
4. 12r-32
5. -90x+-10
6. 15x+15
When Nellie Newton hangs at rest in the middle of a clothesline, tensions will be the same in each side of the rope when:
a. the lengths of each rope are the same
b. the angles for both sides of the rope are equal
c. she is in equilibrium
Answers
The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.
When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.
For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.
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1. Conrad spent $48 on art supplies. The canvas for each of his paintings is an additional $2. He plans to sell his paintings for $10. a. Write an equation that could be used to find the number of paintings (p) he will need to sell to break even.
Thanks
Answers
Answer: P=6
Solution: 48+ 2p=10p
Subtract 2p from both sides. It will then make the equation 48=8p.
Divide both sides by 8 to get p alone. 48/8=6
P=6
:)
The equation for break even is 8P = 48
What is an Equation ?An equation is an expression that states the equality of two things expressed in different form.
In the given question
Conard spent $48 for art supplies
Canvas costs $2
He plans to sell his painting for $10
∴ Without the canvas his paintings costs $(10 - 2)
= $8
So, no. of paintings (P) to break even he needs to sell
8P = 48
P = 6
∴ Conard needs to sell 6 paintings to break even.
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For a population with µ = 80 and σ = 10, what is the X value corresponding to z = –2.00?
Answers
The X value corresponding to z = -2.00 is 60. The X value corresponding to z = -2.00 is 60. This means that the observation with a z-score of -2.00 is 60 units below the population mean of 80.
To find the X value corresponding to z = -2.00, we can use the formula:
z = (X - µ) / σ
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60
The z-score measures the number of standard deviations an observation is from the mean. In this case, the given z-score of -2.00 indicates that the observation is 2 standard deviations below the mean.
To find the corresponding X value, we use the formula:
z = (X - µ) / σ
Where z is the standard normal distribution value, X is the corresponding raw score, µ is the mean of the population, and σ is the standard deviation of the population.
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60
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bradley consumes an energy drink that contains caffeine. after consuming the energy drink, the amount of caffeine in bradley's body decreases exponentially. the 10-hour decay factor for the number of mg of caffeine in bradley's body is 0.2722. what is the 5-hour growth/decay factor for the number of mg of caffeine in bradley's body?
Answers
The 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. Exponential decay differs from linear decay in that the decay factor depends on a percentage of the initial sum, meaning that the amount by which the original sum may be lowered will fluctuate over time as opposed to a linear function, which reduces the original sum by the same amount each time.
Given,
10 hour decay factor = 0.2722
Let us calculate the one-hour decay factor first,
One-hour decay factor = (10 hour decay factor)^1/10 = (0.2722)^1/10 = 0.8779
Now, Calculating the 5-hour decay factor,
5 hour decay factor = ( 1 hour decay factor )^5 = (0.8779)^5 = 0.521
Hence, the 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
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What If the value of
ვ5=
Answers
Answer:
\(\large \sf \longrightarrow \: {3}^{5} \)
\(\large \sf \longrightarrow \: 3 \times 3 \times 3 \times 3 \times 3\)
\( \large\sf \longrightarrow \: 9 \times 9 \times 3\)
\( \large\sf \longrightarrow \: 9 \times 27\)
\( \large\sf \longrightarrow \: 243\)
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Answer:
243Step-by-step explanation:
3⁵
Here,
3 is base5 is index\(\large\sf{3 }^{5 }\)
\(\large\sf{=3 \times 3 \times 3 \times 3 \times 3 }\)
\(\large\bf{= 243}\)
3⁵ is known as exponential form of 243 .