Answers
The surface areas of the prisms are listed below:
Case 1: 94 in²
Case 2: 72 cm²
Case 3: 40.5 m²
Case 4: 39.1 mm²
Case 5: 130 ft²
Case 6: 136 m²
How to find the surface area of a prism
In this problem we find six cases of prisms, whose surface areas have to be found. Surface area is the sum of the areas of all faces in the prism. Face have either a rectangular or a triangular form, whose area formulas are:
Rectangle
A = b · h
Triangle
A = 0.5 · b ·h
Where:
A - Areab - Widthh - HeightNow we proceed to determine the surface areas:
Case 1
A = 2 · (4 in) · (5 in) + 2 · (3 in) · (4 in) + 2 · (5 in) · (3 in)
A = 40 in² + 24 in² + 30 in²
A = 94 in²
Case 2
A = 2 · 0.5 · (3 cm) · (4 cm) + (5 cm) · (4 cm) + (5 cm) · (3 cm) + (5 cm)²
A = 12 cm² + 20 cm² + 15 cm² + 25 cm²
A = 72 cm²
Case 3
A = 2 · (3 m) · (7 m) + 2 · (6 m) · (7 m) + 2 · (6 m) · (3 m)
A = 10.5 m² + 21 m² + 9 m²
A = 40.5 m²
Case 4
A = 2 · 0.5 · (4 mm)² + 2 · (4 mm) · (3 mm) + (5.7 mm) · (3 mm)
A = 16 mm² + 6 mm² + 17.1 mm²
A = 39.1 mm²
Case 5
A = 2 · (10 ft) · (5 ft) + 2 · (5 ft) · (1 ft) + 2 · (10 ft) · (1 ft)
A = 100 ft² + 10 ft² + 20 ft²
A = 130 ft²
Case 6
A = 2 · 0.5 · (6 m) · (4 m) + 2 · (7 m) · (5 m) + (7 m) · (6 m)
A = 24 m² + 70 m² + 42 m²
A = 136 m²
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Related Questions
Divide. Give the Quotient and Remainder. 520 / 22
Answers
Answer:
Quotient=23 and remainder=14
Altogether the Green Team jumped 10264 times. The Yellow Team did 759 fewer jumps than the Green Team. How many jumps did the Yellow Team do?
Answers
true or false The area of an object's net is the same as the surface area of the object.
Answers
Answer:
True
hope it helps :) !!!
Answer:
the answer is true, it's the objects net is the same as the surface area.
the given curve is rotated about the y-axis. find the area of the resulting surface. y = 1/4 x^2 − 1/2 ln(x), 3 ≤ x ≤ 5
Answers
To find the area of the resulting surface when the given curve y = 1/4x^2 - 1/2 ln(x) is rotated about the y-axis, we can use the Surface of Revolution formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from a to b
Here, a = 3 and b = 5.
First, we need to find the derivative of y with respect to x (dy/dx):
y = 1/4x^2 - 1/2 ln(x)
dy/dx = (1/4 * 2x) - (1/2 * 1/x) = x/2 - 1/(2x)
Now, let's plug this into the Surface of Revolution formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + (x/2 - 1/(2x))^2)] dx from 3 to 5
We will now integrate the expression within the brackets with respect to x from 3 to 5. This might be challenging to solve analytically, so we may need to use a numerical integration method or a calculator to find the exact value.
Once the integration is completed, you will obtain the surface area of the curve when rotated about the y-axis.
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A rectangular hotel room is 3 meters by 8 meters. The owner of the hotel wants to recarpet the room with carpet that costs $33.38 per square meter. How much will it cost to recarpet the room?
Answers
The amount it will cost to recarpet the the whole room is $891.12
What is area ?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
For example, the area of a circle is given as: A = πr², where r is the radius and π is constant.
The room takes the shape of a rectangle, therefore,
Area of the room = l× w, where l is the length and w is the width.
Area = 3×8 = 24 m²
The cost of 1m² = $33.38
therefore the cost for 24m²
= 24× 33.8
= $801.12
therefore the cost to recarpet the room is $801.12
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From the list of numbers, write down
a. a square number
b. a multiple of 13
c. a factor 186
d. the prime number
Answers
a. 64
b. 65
c. 62
d. 61
Answer:
a) a square number:64
b) a multiple of 13:65
c) a factor of 186:62
d)the prime number:61,67
Depreciation by Three Methods; Partial Years Perdue Company purchased equipment on April 1 for $41,550. The equipment was expected to have a useful life of three years, or 5,700 operating hours, and a residual value of $1,650. The equipment was used for 1,000 hours during Year 1, 2,000 hours in Year 2, 1,700 hours in Year 3, and 1,000 hours in Year 4. Required: Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by (a) the straight-line method, (b) the units-of-activity method, and (c) the double-declining-balance method. Note: Round all final values for each depreciation method and each year to the nearest whole dollar
Answers
a) The depreciation expenses for Year 1 to Year 4 using the straight-line method are $2,632, $5,263, $4,211, and $2,632, respectively.
b) Using the units-of-activity method, the depreciation expenses are $7,000, $14,000, $11,900, and $7,000, respectively.
c) Using the double-declining-balance method, the depreciation expenses are $4,658, $11,172, $7,302, and $2,640, respectively.
a) To calculate the depreciation expense for each year using the straight-line method, the company needs to first determine the depreciable cost of the equipment. This is the cost of the equipment minus its estimated residual value.
The depreciable cost is $41,550 - $1,650 = $39,900.
To calculate the annual depreciation expense using the straight-line method, divide the depreciable cost by the useful life of the equipment, which is three years.
Year 1: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632
Year 2: ($39,900 ÷ 3) × (2,000 ÷ 5,700) = $5,263
Year 3: ($39,900 ÷ 3) × (1,700 ÷ 5,700) = $4,211
Year 4: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632
b) To calculate the depreciation expense using the units-of-activity method, the company needs to first determine the depreciation rate per unit of activity. This is the depreciable cost of the equipment divided by its total estimated hours of use.
The depreciation rate per unit of activity is $39,900 ÷ 5,700 hours = $7 per hour.
Year 1: $7 × 1,000 hours = $7,000
Year 2: $7 × 2,000 hours = $14,000
Year 3: $7 × 1,700 hours = $11,900
Year 4: $7 × 1,000 hours = $7,000
c) To calculate the depreciation expense using the double-declining-balance method, the company needs to first determine the straight-line depreciation rate. This is the depreciable cost of the equipment divided by its useful life.
The straight-line depreciation rate is $39,900 ÷ 3 years = $13,300 per year.
The double-declining-balance depreciation rate is twice the straight-line rate, or $13,300 × 2 = $26,600.
Year 1: $26,600 × (1,000 ÷ 5,700) = $4,658
Year 2: ($39,900 - $4,658) × (2,000 ÷ 5,700) = $11,172
Year 3: ($39,900 - $4,658 - $11,172) × (1,700 ÷ 5,700) = $7,302
Year 4: ($39,900 - $4,658 - $11,172 - $7,302) × (1,000 ÷ 5,700) = $2,640
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the graph below displays the amount of time to the nearest hour spent on homework per week for a sample of students. which measures of center and variability would be most appropriate to describe the given distribution? group of answer choices mean and standard deviation mean and iqr median and standard deviation median and iqr median and range
Answers
The Median and IQR are most appropriate to describe the measures of center and variability of distribution. The histogram depicts the distribution of time is positively skewed. So, option(b) is right one.
We have a graph present in above figure, which showes the amount of time in hours spent on homework per week for a sample of students. We have to select correct measures of center and variability. The graph is a histogram. From the graph we can see that the data is positively skewed. Now for skewed distribution we prefer median over mean as mean is more sensitive to the outliers. As the data(time) is in ratio scale we can use any of the measures of dispersion; but for skewed distribution IQR is preferred because of its robustness. In a word both median and IQR can handle outliers. Thus the appropriate answer is Median and IQR, option (c).
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Complete question :
The above figure complete the question
the graph below displays the amount of time to the nearest hour spent on homework per week for a sample of students. which measures of center and variability would be most appropriate to describe the given distribution? group of answer choices
a) mean and standard deviation
b) mean and iqr
c) median and standard deviation
d) median and iqr
e) median and range
What if the dimension of the original rectangle in Exercise 1 had been multipled by 1/2? How would the area have been affected
Answers
If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.
What is the area of the rectangle?To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
According to the given information:The area of a rectangle is calculated by multiplying its length and width. If the dimensions of a rectangle are multiplied by a factor of k, then the new area of the rectangle is equal to k times the original area.
In this case, the dimensions of the original rectangle are multiplied by 1/2, which means that the new length and width of the rectangle are 1/2 times the original length and width. Therefore, the new area of the rectangle is equal to (1/2) times the original length multiplied by (1/2) times the original width. This can be simplified to 1/4 times the original area. Therefore, the area of the new rectangle is one-fourth of the area of the original rectangle.
Therefore, If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.
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Graph a line with a slope of 3/4 that contains the point (2,-3)
Answers
Step-by-step explanation:
[tex] - 3 = \frac{3}{4} (2) + b[/tex]
[tex] - \frac{6}{2} = \frac{3}{2} + b[/tex]
[tex]b = - \frac{9}{2} [/tex]
[tex]y = \frac{3}{4} x - \frac{9}{2} [/tex]
Alternately, starting at (2, -3), go up 3 units, then right 4 units, to (6, 0). Draw a line that goes through these points.
Find the unknown measures. Round lengths
to the nearest hundredth and angle
measures to the nearest degree.
D
2.1
E
5.3
angle D-
Answers
Answer:
A correct option is option (b).
Given,
Trigonometric ratios:
The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
The given triangle is right angle triangle then
Now, calculate the angles.
Again,
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Step-by-step explanation:
Question 8(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Answers
The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.
Explain about the box plot:The distribution of data is shown using a boxplot, which is a standardised method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum").
It can reveal information about your outliers' values. Boxplots can also show you how tightly that data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.The lower and upper quartiles are shown on the left and right sides of a box and whisker plot, respectively. The interquartile range, which contains 50% of the data, is covered by the box. The median is the vertical line which it divided the box in half.For the case of -
A total of 100 distinct gummy vitamins that are offered worldwide were counted for their milligrammes of vitamin C content.
The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.
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To landscape his 70 ft by 60 ft backyard, Austin is planning first to put down a 4 inch layer of topsoil. He can buy bags of topsoil at $2.50 per 3-ft3 bag, with free delivery. Or he
can buy bulk topsoil for $22.00/yd, plus a $20 delivery fee. Which option is less expensive?
I need volume of soil, cost of bags and cost of bulk
Answers
Answer:
To calculate the volume of soil needed, we first convert the dimensions of the backyard to feet:
Length = 70 ft
Width = 60 ft
Depth = 4 in = 4/12 ft = 1/3 ft
Volume = Length x Width x Depth
Volume = 70 ft x 60 ft x (1/3) ft
Volume = 1400 ft³
Option 1: Bags of topsoil
Each bag of topsoil contains 3 ft³ of soil, so the number of bags needed is:
Number of bags = Volume / Bag size
Number of bags = 1400 ft³ / 3 ft³ per bag
Number of bags = 467 bags
The total cost of bags of topsoil is:
Cost = Number of bags x Cost per bag
Cost = 467 bags x $2.50 per bag
Cost = $1167.50
Option 2: Bulk topsoil
The volume of topsoil needed is 1400 ft³, which is equivalent to:
Volume = 1400 ft³ / 27 ft³ per yd³
Volume = 51.85 yd³ (rounded to two decimal places)
The cost of bulk topsoil is:
Cost = Volume x Cost per yd³ + Delivery fee
Cost = 51.85 yd³ x $22.00 per yd³ + $20.00 delivery fee
Cost = $1153.70
Therefore, buying bulk topsoil is less expensive than buying bags of topsoil. The cost of bulk topsoil is $1153.70, while the cost of bags of topsoil is $1167.50
Answer:
Bulk is less expensive
Step-by-step explanation:
First convert inches to feet: 4 in x 1 ft/12 in =0.333 ft
Volume of topsoil needed = 70 x 60 x 0.333 = 1400 ft³
Bagged topsoil: 1400 ft³ x $2.50/3 ft³ = $1166.67
Bulk: 1400 ft³ x 1 yd³/27 ft³ x $22.00/yd³ + $20 = $1160.74
Bulk is just a little cheaper
wo random samples of earnings of professional golfers were selected. one sample was taken from the professional golfers association, and the other was taken from the ladies professional golfers association. at , is there a difference in the means? the data are in thousands of dollars. use the critical value method with tables. pga lpga
Answers
in general, to perform a hypothesis test comparing the means of two independent samples using the critical value method, you would follow these steps:
State the null and alternative hypotheses. For example, the null hypothesis could be that there is no difference in means between the two populations (i.e., H0: µ1 - µ2 = 0), and the alternative hypothesis could be that there is a significant difference in means (i.e., Ha: µ1 - µ2 ≠ 0).
Determine the level of significance, α, which represents the probability of rejecting the null hypothesis when it is actually true. For example, if α = 0.05, then there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).
Calculate the test statistic. The most common test statistic for comparing the means of two independent samples is the t-test. The formula for the t-test is:
t = (x1 - x2) / [s^2pooled/n1 + s^2pooled/n2]^0.5
where x1 and x2 are the sample means, s^2pooled is the pooled variance (calculated using the two sample variances and sample sizes), and n1 and n2 are the sample sizes.
Determine the critical value(s) from the t-distribution table based on the degrees of freedom (df) and level of significance (α). The degrees of freedom for a two-sample t-test is calculated as:
df = n1 + n2 - 2
Compare the test statistic to the critical value(s). If the absolute value of the test statistic is greater than the critical value(s), then reject the null hypothesis; otherwise, fail to reject the null hypothesis.
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Ok so I cant figure out how to find the angle of measure "C" I got measure "A" and "B" but don't understand "C"
Answers
Answer: The answer is 84
The total of the angels of the triangle always equals 180. So 62+34=96 therefor 96-180=84.
Blocks of cheese are cut at the deli and weights are shown in the table below:
Cheddar
Colby Jack
Havarti
Feta
0.753 lb
0.634 lb
0.749 lb
0.696 lb
Part A
Round each block of cheese to the nearest hundredth of a pound.
Explain how you rounded.
Part B
Order the blocks of cheese from least to greatest based on their weights before
rounding and after rounding. Will both lists be in the same order? Explain.
Answers
This prompt is about rounding figures up. We can conclud t that where the above are given, both lists are not in the same order.
Why is this so?To round up the first order to the second decimal place we have:
Cheddar 0.75 lbColby Jack: 0.63 lb Havarti: 0.75 lbFeta: 0.70 lbRounding the second batch of cheese and ordering them from the least to greatst, we have:
Colby Jack - 0.63 lbFeta = 0.70 lbCheddar 0.75 lbHavarti: 0.75 lbHence, we can submit that they are both not in the same eorder.
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what is the value of x, in units?
Answers
Answer: 12 units
Step-by-step explanation: see both shapes are the same just one is flipped and its small meaning the first shape without numbers is only double of the shape with numbers so you answer would be 12 units
small shape x 2 gives all your answers to the big shape
TOO
EASY
BYE
Solve for x. Round your answer to the nearest tenth and type it in the blank without units.
Answers
The opposite side of the right triangle (x) is approximately 6.888 inches long.
Right angle triangleTo solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:
sin(35) = opposite/12
To solve for the opposite, we can multiply both sides by 12:
opposite = 12 * sin(35)
sin(35) as approximately 0.574:
opposite = 12 * 0.574
opposite ≈ 6.888
Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.
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An athlete is in a boat at point AA, 1/2 mi from the nearest point on a straight shoreline. She can row at a speed of 2mph run at a speed of 4mph. Her planned workout is to row to point D and then run to point C further down the shoreline. However, the current pushes her at an angle of 28from her original path so that she comes ashore at point B 3mi from her destination at point CHow many minutes will her trip take? Round to the nearest minute.
Answers
Rounding to the nearest minute, the athlete's trip will take approximately 96 minutes.
Let's start by drawing a diagram to better visualize the situation:
A x D C
o-----x------------x
| |
| |
| |
| |
| |
| |
B |
o------------o
Here, point A is where the athlete starts, point B is where she comes ashore due to the current, point C is her intended destination on the shoreline, and point D is the point where she switches from rowing to running.
From the diagram, we can see that the distance AB is 3 miles, and the distance AC is 3 + 1/2 = 3.5 miles.
We can use the Pythagorean theorem to find the distance BC:
[tex]BC^2 = AB^2 + AC^2[/tex]
[tex]BC^2 = 3^2 + 3.5^2[/tex]
[tex]BC^2 = 12.25[/tex]
BC = sqrt(12.25)
BC = 3.5
So the distance the athlete needs to travel on foot is 3.5 miles.
Let's first calculate the time it takes for her to row to point D:
Time to row to D = Distance / Speed
Time to row to D = 1/2 / 2
Time to row to D = 1/4 hours
Next, let's calculate the time it takes for her to run from D to C:
Time to run to C = Distance / Speed
Time to run to C = 3.5 / 4
Time to run to C = 7/8 hours
Now, we need to find the time it takes her to travel from B to C.
We can use the law of sines to find the angle between AB and BC:
sin(28) / 3 = sin([tex]\theta[/tex]) / 3.5
sin(theta) = 3.5 * sin(28) / 3
sin(theta) = 0.5407
theta = arc sin(0.5407)
theta = 33.15 degrees
Therefore, the angle between AB and BC is approximately 33.15 degrees.
We can use this angle and the distance BC to find the distance the athlete actually traveled from B to C:
Distance traveled from B to C = BC * sin([tex]\theta[/tex])
Distance traveled from B to C = 3.5 * sin(33.15)
Distance traveled from B to C = 1.925 miles
Finally, we can calculate the total time of the trip:
Total time = Time to row to D + Time to run to C + Time to travel from B to C
Total time = 1/4 + 7/8 + (1.925 / 4)
Total time = 0.25 + 0.875 + 0.48125
Total time = 1.60625 hours
To convert this to minutes, we can multiply by 60:
Total time = 1.60625 * 60
Total time = 96.375 minutes.
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the probability a visitor to the home page of a website views another page on the site is 0.2. assume that 200
Answers
The probability that at least one visitor views another page on the site is very high, close to 1. This suggests that the website is engaging and visitors are likely to navigate beyond the home page.
Assuming that 200 visitors come to the home page of the website, we can use the binomial distribution to calculate the probability that at least one visitor views another page on the site.
Let X be the number of visitors who view another page. Then X follows a binomial distribution with n = 200 and p = 0.2.
P(X ≥ 1) = 1 - P(X = 0)
[tex]= 1 - (0.2)^0 * (0.8)^200= 1 - 0.8^200[/tex]
≈ 1
Therefore, the probability that at least one visitor views another page on the site is very high, close to 1. This suggests that the website is engaging and visitors are likely to navigate beyond the home page.
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40 out of 200 visitors to the homepage are expected to view another page on the site.
The probability that a visitor to a website's homepage views another page on the site and how it relates to 200
visitors.
The probability is 0.2.
To find out how many visitors out of 200 are likely to view another page on the site, you can follow these steps:
Identify the given probability, which is 0.2 in this case.
Multiply the probability by the total number of visitors (200).
So, the calculation would be:
0.2 × 200 = 40
Based on the given probability, approximately 40 out of 200 visitors to the homepage are expected to view another
page on the site.
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I need help solving this equation. I keep getting the +/- mixed up.
12-tx2-pn=12-t(2-x)2-pm
12-tx2-pn=12-4t+4tx-tx2-pm
Eliminate the 12 and tx2
-pn=-4t+4tx-pm
-4tx=-4t + pn-pm
divide both sides by -4t
x=1 - (pm-pn)/4t
I am not sure if this is right, but I have x= 1-(pm-pn)/4t
Answers
It looks like you did a great job solving the equation, and your final answer is correct. Here is a brief summary of the steps you took:
your final answer is correct[tex]: x = 1 - (pm - pn) / 4t[/tex]
Mathematics has been classified into many branches. Arithmetic is the branch that handles numbers and their operations. Arithmetic taught us addition, subtraction, multiplication and divisions of two or more numbers. Geometry is all about shapes and their construction using different tools like a compass, ruler and pencil. Algebra is another interesting branch where we express our daily life situations in numbers and letters (variables).
1. Expanded the equation: [tex]12 - tx^2 - pn = 12 - t(2 - x)^2 - pm[/tex]
2. Simplified: [tex]12 - tx^2 - pn = 12 - 4t + 4tx - tx^2 - pm[/tex]
3. Eliminated the 12 and tx^2 terms: -pn = -4t + 4tx - pm
4. Rearranged the equation:[tex]-4tx = -4t + pn - pm[/tex]
5. Divided both sides by [tex]-4t: x = 1 - (pm - pn) / 4t[/tex]
So, your final answer is correct[tex]: x = 1 - (pm - pn) / 4t[/tex]
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As a daffodil grows, it increases in height by 3 inches every 2 days. If the daffodil plant starts at 1 inch on day one, what will the height be on day 2?
Answers
Answer: If the daffodil start at 1 inch on day one, and only 1 day has passed, it will grow half of what it would in 2 days because half of 2 is 1. So the current height 1 inch + how much it will grow in one day (1.5 inches) = the final height (2.5 inches) Hope this helps :D
Step-by-step explanation:
Select THREE expressions that are equivalent
to 15x + 9y.
A. 15(x + 9y)
B. 3(5x + 3y)
C. 5(3x + 3y)
D. 9(15x + y)
E. 5x + 5x + 5x + 5y + 4y
F. x + 3x + 6x + 5x + y + 6y + y + y
Answers
ADF
Thats not the answer those are just my favorite letters
Suppose that Leni and Thom are lawyers and each has a taxable income of $230,000. They can't decide if they should be married in December or in January. If they marry in December, then they are considered married for the entire tax year and could file a joint return. If they get married in January of the next year, they would file a separate return each as a single taxpayer. Examine Schedules X and Y-1. Which filing status would yield the lower tax? If so, by how much? is there really a marriage penalty?
Answers
Answer:
1. Neither would yield the lower tax.
2. (not sure yet about how much)
3. and there is not really a marriage penalty.
help simplify 53b−7b−6b+1 if b=25 plsssssssssssssss
Answers
Answer:
53b - 7b - 6b + 1 with b = 25 simplifies to 1001.
Step-by-step explanation:
To simplify 53b - 7b - 6b + 1 with b = 25, we substitute 25 for b and simplify the expression as follows:
53b - 7b - 6b + 1 = 53(25) - 7(25) - 6(25) + 1
= 1325 - 175 - 150 + 1
= 1001
Therefore, 53b - 7b - 6b + 1 with b = 25 simplifies to 1001.
$480, 15% interest, 1.5 years. Find the interest to the nearest cent for each principal, interest rate, and time.
Answers
The simple interest earned after 3 years on $500 at an interest rate of 6% is $90.
Simple interest is a type of interest that is calculated based only on the initial amount borrowed or invested, called the principal amount, and does not take into account any additional interest earned on the interest over time.
To find the simple interest earned on $500 at an interest rate of 6% after 3 years, we can use the formula:
Simple Interest = Principal x Rate x Time
Where
Principal = $500
Rate = 6% = 0.06 (in decimal form)
Time = 3 years
Plugging these values into the formula, we get
Simple Interest = $500 x 0.06 x 3
= $90
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I have solved the question in general, as the given question is incomplete.
The complete question is:
Find the simple interest earned after 3 years on $500 at an interest rate of 6%.
URGENT PLEASE ANSWER!!! I INCLUDED THE GRAPH!
Graph the line y = 4/3x + 1.
Use the line tool and select two points on the line.
Answers
We have (0, 1) and (3, 5) as two points on the line y = 4/3x + 1.
Selecting two points on the line.The equation y = 4/3x + 1 represents a line in slope-intercept form, where the coefficient of x (4/3) represents the slope of the line and the constant term (1) represents the y-intercept.
To select two points on the line, we can choose any values for x and use the equation to find the corresponding values of y.
For example, let's choose x = 0:
y = 4/3x + 1
y = 4/3(0) + 1
y = 1
So one point on the line is (0, 1).
Now let's choose x = 3:
y = 4/3x + 1
y = 4/3(3) + 1
y = 5
So another point on the line is (3, 5).
Since both equations hold true, we can conclude that (0, 1) and (3, 5) are two points on the line y = 4/3x + 1.
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Question 5
Karin has $83,555 in a retirement account right now. Suppose she deposits $3,000 this year and then increases that by 7.5% each subsequent year. The account earns 9.8%. Find her future account value after 20 years.
Answers
The solution of the given problem of percentage comes out to be Karin's future account value would therefore be about $313,425.67 after 20 years.
What are percentages?In statistics, a figure or metric that may be presented as a percentage or 100 is denoted by the abbreviation "a%". Other unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this.
Here,
Using the compound interest calculation, we can determine Karin's account worth in 20 years:
=> A = P(1 + r)ⁿ
P =$83,555 (current balance), as given.
(Annual interest rate) r = 9.8% = 0.098
20 years, n
Let's use the following formula to determine the future account worth for each year:
Year 1: P = $83,555 (balance as of now)
(Annual interest rate) r = 9.8% = 0.098
Given that this is the first year, n equals 1.
=> A = $83,555(1 + 0.098)¹
=> A = $83,555(1.098)
=>A = $91,785.09
Year 2: P = $6,225 (current balance after deposit) = $3,000 + $3,225.
(Annual interest rate) r = 9.8% = 0.098
n = 1 year
=> A = $6,225(1 + 0.098)¹
=> A = $6,225(1.098)
=> A = $6,834.44
After 20 years, the current balance is
=> P = $12,873.51 + (20 - 1)($3,000 + 7.5% of $3,000)
= $12,873.51 + $71,132.10 = $83,005.61.
The yearly interest rate is 9.8%, or 0.098.
20 years, n
=> A = $83,005.61(1 + 0.098)²⁰
=> A = $83,005.61(3.778)
=> A = $313,425.67
Karin's future account value would therefore be about $313,425.67 after 20 years.
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PROBLEM SOLVING Bicycles in the late 1800s looked very different than they do today. a. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.
Answers
An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. If we know that B occurred, what is the probability that A occurred too? In other words, what is the conditional probability of A given B -- P(A|B)?
Answers
The conditional probability of A given B (P(A|B)) is 1/6, or approximately 0.167.
Conditional probability is the probability of an event occurring given that another event has already occurred.
It is denoted by P(A|B), where A and B are events, and P(A|B) represents the probability of event A occurring given that event B has already occurred
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
To find the conditional probability of A given B (P(A|B)), we can use the formula
P(A|B) = P(A ∩ B) / P(B)
We are given:
P(A) = 0.5 (probability of event A occurring)
P(B) = 0.6 (probability of event B occurring)
P(A ∩ B) = 0.1 (probability of both A and B occurring)
Now, we can plug in the given values into the formula:
P(A|B) = 0.1 / 0.6
P(A|B) = 1/6.
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