A) The area of the walls is 700 ft²
B) The area of the doors, windows, and rectangular opening is 226ft²
C) The area that Kamrie will paint is 474 ft², and she will need to purchase 2 cans of paint.
How did we arrive at the above?Part A:
The area of each of the short walls is
10 ft x 15 ft
= 150 sq ft.
So, the total area of the four walls is:
2(200 sq ft) + 2(150 sq ft)
= 700 sq ft
Part B:
The area of the three windows along the long wall is
3 ft x 8 ft
= 24 sq ft each, so their total area is
3(24 sq ft)
= 72 sq ft
The area of the two windows along the short wall is also
3 ft x 8 ft = 24 sq ft each,
so their total area is
2(24 sq ft)
= 48 sq ft
The area of the rectangular opening along the other long wall =
7 ft x 8 ft = 56 sq ft.
So, the total area of the doors, windows, and rectangular opening is
72 sq ft + 48 sq ft + 56 sq ft
= 176 sq ft
Part C:
To determine the area that Kamrie will paint, we need to subtract the area of the doors, windows, and rectangular opening from the total area of the walls
700 sq ft - 176 sq ft
= 524 sq ft
To determine how many cans of paint Kamrie needs to buy, we divide the area to be painted by the coverage per can
524 sq ft ÷ 415 sq ft/can
≈ 1.26 cans
So Kamrie needs to buy at least 2 cans of paint to cover the entire living room.
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A bike shop has 11 red bikes, 3 blue bikes, 4 orange bikes, and 12 sliver bikes
Answer:
It Does. Cool
Answer:
c.) silver bikes
Step-by-step explanation:
Given the bike shop has 11 red bikes, 3 blue bikes, 12 silver bikes
here, the number orange bikes = 4
Given for every 1 orange bike there 3 __ bikes
Divide each number of bikes by the number of orange bikes
For 11 red bikes
= 11/4 = 2.75 [which means for 1 orange bike 2.75 red bikes ]
For 3 blue bikes
= 3/4 = 0.75 [ which means for 1 orange bike 0.75 blue bikes ]
For 12 silver bikes
= 12/4 = 3 [ which means for 1 orange bike 3 silver bikes ]
For every 1 orange bike, there are 3 silver bikes.
Solve for x
X
18
24
16
Answer: should be 24?
Step-by-step explanation:
im not sure
Match the orange graph above to the corresponding equation.
The equation for the orange graph is the one in the last option:
f(x) = -3x³
Which is the equation for the orange graph?We can see that the orange graph seems to be:
A cubic function.It has a negative leading coefficient, because when x > 0 the graph goes downwards.The graph is narrower than the parent cubic function, then the leading coefficient is larger than 1.From the given options, the only one that matches all these options is the last one:
f(x) = -3x³
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Find the area
Round to nearest tenth
Forty-two divided by seven plus the quantity three divided by six
Therefore , the solution of the given problem of expression comes out to be 6.5 is the abbreviated numerical expression.
What is an expression?Shifting numbers, which can be expanding, variable diminishing, or blocking, should be used instead of random estimations. Only through exchanging goods like tools, expertise, or answers to problems could they assist one another. The explanation on the reality equation may include the justifications, elements, or mathematical claims for tactics like increased argumentation, falsification, and blending.
Here,
The mathematical expression is expressed as follows:
=> 42 / 7 + (3 / 6)
We can use the division operations to make the expression simpler:
=> 7 /42 = 6
=> 6 / 3 = 0.5.
The statement is thus more easily expressed as follows:
=> 6 + 0.5
When we add the two numbers, we get:
=> 6.5
Therefore, 6.5 is the abbreviated numerical expression.
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The complete question is " Write and simplify this numerical expression. Forty-two divided by seven plus the quantity three divided by six"
Course Activity: Pythagorean Triples
Question
Determine if each set of numbers can be the lengths of the sides of a right triangle.
Select the correct text in the table.
(
52
b
12 13
12 35
5
10
8
12
20
99
Pythagorean triple?
Yes No
2013 Yes No
5√5 Yes No
15 Yes No
101 Yes No
the correct response to the question is: Yes, No, Yes, No and Yes.
How to determine if set of numbers can be the lengths of the sides of a right triangle?We can determine if each set of numbers can be the lengths of the sides of a right triangle by evaluating each set.
Evaluating each set :
#1 :
5, 12, 13
5² + 12² = 13²
25 + 144 = 169
169 = 169
It is a Yes
#2 :
12, 35, 20
12² + 35² = (20√3)²
144 + 1225 = 400*3
1369 ≠ 1200
It is a No
#3 :
5, 10, 5√5
5² + 10² = (5√5)²
25 + 100 = 25(5)
125 = 125
It is a Yes
#4 :
8, 12, 15
8² + 12² = 15²
64 + 144 = 225
208 ≠ 225
It is a No
#5 :
20, 99, 101
20² + 99² = 101²
400 + 9801 = 10201
10201 = 10201
It is a Yes
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The question lacks some details, see complete question in the attached image.
Jim recorded the points a group of students scored during a gaming session in the dot plot below. Which measure of center would be best to use for this distribution? A. interquartile range B. mean C. mode D. median
Answer: median
Step-by-step explanation:
A is not a center of measure and nethier ia mode and since the data is skewd it is the median and if it is not skewd it is the mean
100 points! Algebra question, photo attached. Please show as much work as possible. Thank you!
Given:
[tex]\sqrt{z+5}+4\leq 13[/tex]
Move 4 to the right side:
[tex]\sqrt{z+5}\leq 9[/tex]
Simplify
[tex]z+5 \leq 81[/tex]
Move 5 to the right side:
[tex]z\leq 76[/tex]
Find singularity points
Find non-negative values for radicals: [tex]z\geq -5[/tex]
Combine the intervals
[tex]z\leq 76 \ \text{and} \ z\geq -5[/tex]
Merge overlapping intervals
[tex]-5\leq z\leq 76[/tex]
Answer:
[tex]\longrightarrow \boxed{\bold{-5\leq z\leq 76}}[/tex]Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
The method you would use to prove the two triangles are congruent include the following: B. ASA.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
you did not provide enough information to answer the question
if necessary.
21. A company makes specialized fish tanks, like the one shown below. If 1 gallon = 0.134 ft³, how many
gallons of water will it take to fill the fish tank completely?
9 ft
2 ft
3 ft
V = 6
It would take about 402.985 gallons of water to fill the fish tank completely.
What is the amount of water?To calculate the number of gallons of water it would take to fill the fish tank completely, we need to multiply the dimensions of the fish tank in cubic feet by the conversion factor to convert cubic feet to gallons.
Given:
Length = 9 ft
Width = 2 ft
Height = 3 ft
Conversion factor: 1 gallon = 0.134 ft³
Step 1: Calculate the volume of the fish tank in cubic feet
Volume = Length × Width × Height = 9 ft × 2 ft × 3 ft = 54 ft³
Step 2: Convert cubic feet to gallons
54 ft³ × (1 gallon / 0.134 ft³) ≈ 402.985 gallons
So, it would take approximately 402.985 gallons of water to fill the fish tank completely.
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To purchase $14,500 worth of restaurant equipment for her business, Debra made a down payment of $1300 and took out a business loan for the rest. After 2 years of paying monthly payments of $585.04, she finally paid off the loan.
(a) What was the total amount Debra ended up paying for the equipment (including the down payment and monthly payments)?
(b) How much interest did Debra pay on the loan?
The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60
(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.
Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200
Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments
Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]
Total amount paid = $1,300 + $13,200 + $14,041.60
Total amount paid = $28,541.60
Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.
(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.
Total interest paid = Total amount paid - Total amount borrowed - Down payment
Total interest paid = $28,541.60 - $13,200 - $1,300
Total interest paid = $14,041.60
Therefore, the amount of interest Debra paid on the loan was $14,041.60.
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Is (3, 5) a solution to this system of equations?
y = 5
Y= -5/3x+10
yes
E
Answer:
no
Step-by-step explanation:
-5/3x+10=5
-5/3x=5-10=-5
3x=-5/-5=1
=>x=1/3
Really need on 1 through 10
The locations of the angles in the right triangle, and the number pairs indicates that we get;
ΔMKJ ~ ΔMLK, ΔMKJ ~ ΔKLJ, ΔMLK ~ ΔKLJΔXZW ~ ΔXYZ, ΔXZW ~ ΔZYW, ΔXYZ ~ ΔZYWx = 4.8x = 14 14/29x = 18 6/13x = 11 121/32512·√36·√516·√38·√6What is a right triangle?A right triangle is a triangle that has one 90° interior angle.
1. The three similar triangles are; ΔMKJ, ΔMLK, and ΔKLJ
2. The three similar triangles are; ΔXZW, ΔXYZ, ΔZYW
3. The area of the triangle is; (1/2) × 8 × 6 = 24, which indicates;
(1/2) × 10 × x = 24
x = 24/((1/2) × 10) = 4.8
x = 4.8
4. The area of the triangle is; (1/2) × 21 × 20 = 210, which indicates;
(1/2) × 29 × x = 210
x = 210/((1/2) × 29) = 420/29 = 14 14/29
x = 14 14/29
5. The area of the triangle is; (1/2) × 20 × 48 = 480, which indicates;
(1/2) × 52 × x = 480
x = 480/((1/2) × 52) = 240/13 = 18 6/13
x = 18 6/13
6. The area of the triangle is; (1/2) × 13.2 × 22.4 = 147.84, which indicates;
(1/2) × 26 × x = 147.84
x = 147.84/((1/2) × 26) = 3696/325 = 11 121/325
x = 11 121/325
The geometric mean of a pair of numbers can be obtained as follows;
7. The geometric mean is; √(16 × 27) = √(432)
√(432) = 12·√3
8. The geometric mean is; √(5 × 36) = √(180)
√(180) = 6·√5
9. The geometric mean of the number is; √(24 × 32) = √(768)
√(768) = 16·√3
10. The geometric mean of the numbers is; √(8 × 48) = √(384)
√(384) = 8·√6
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There are spiders and dogs in Veronica's backyard. Veronica sees 240 legs in total. The total number of animals (spiders and dogs) is 3 times the amount of spiders. How many spiders are in the backyard?
There are 15 spiders in the backyard. The correct option is D
To solve this problemLet's begin by resolving the issue using algebra. Let's use "s" for the quantity of spiders and "d" for the quantity of dogs in the backyard.
As a result of the difficulty, we know that there are 3 times as many animals as there are spiders.
s + d = 3s
Simplifying this equation, we get:
d = 2s
We also know that there are 240 legs in the backyard, with each dog having 4 legs and each spider having 8. Thus, we can create the following equation:
8s + 4d = 240
Substituting d = 2s, we get:
8s + 4(2s) = 240
Simplifying and solving for s, we get:
16s = 240
s = 15
Therefore, there are 15 spiders in the backyard.
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Find the volume of a tissue box that has the following dimensions:
Length=20 cm
Width= 5 cm
Height= 12 cm
Volume=______
Answer:
1,200
Step-by-step explanation:
The formula is Length x Width x Height so it will be 20 x 5 x 12 and you get 1,200.
Hope this helps!
Find the 61st term.
O, 6, 12, 18, 24, ...
61st term = [?
Answer: i think its 366
Step-by-step explanation:
i just did 61X6
The committee members will spend money to rent the following equipment:
• 2 fog machines
• 1 sound equipment set-up
• 1 disco ball
They already spent $855 on lighting and $462 on costumes.
Each audience member will receive a gift that costs $1.15 each.
What is the total amount of money, in dollars, the committee will spend on the talent show?
Item
Spotlight
Fog machine
Sound equipment set-up
Disco ball
Cost Per Item
$ 45 each
$ 40 each
$165 each
$ 45 each
Answer:
1,607 plus the amount of people multipled by 1.15
Step-by-step explanation:
2 fog machines = $80
1 sound equipment = $165
1 disco ball = $45
80+165+45+855+462= $1,607
Please help me I don’t understand this
Answer:
the required answer are -8,0,4
A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 70 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Therefore , the solution of the given problem of percentage comes out to be 14 gallons of the first brand and 56 gallons of the second brand must be utilised.
What is percentages?In statistics, a figure or metric than may be presented as a percentage or 100 is denoted by the abbreviation "a%". Another unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this. Additionally, there are no indications or predetermined ratios of any component to the whole. Numbers are effectively integers since they frequently add up to 100.
Here,
Let's write "x" for the first brand's (35% pure antifreeze) number of gallons and "y" for the second brand's (60% pure antifreeze) number of gallons.
Given:
70 gallons of mixture are required in total.
Desired antifreeze content in the combination is 55%
Based on the information provided, we can construct the following system of equations:
=> Equation 1: x + y = 70
=> Equation 2: 0.5*70 = 0.55x + 0.60y
=> x = 70 - y
=> 0.35(70 - y) + 0.60y = 0.55 * 70
=> 24.5 - 0.35y + 0.60y = 38.5
=> 0.25y = 14
=> y = 56
=> x = 70 - 56
=> x = 14
In order to get 70 gallons of a mixture that contains 55% pure antifreeze, 14 gallons of the first brand and 56 gallons of the second brand must be utilised.
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Convert the rectangular coordinates (-√√2, -√2) into polar form.
Express the angle using radians in terms of 7 over the interval
0 ≤0 < 27, with a positive value of r.
The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)
Converting into polar formTo convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).
r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)
To find the value of θ, we can use the following formula:
θ = atan(y/x)
where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.
θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians
However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.
To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.
θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians
So the polar form of the rectangular coordinates (-√√2, -√2) is:
(2√(1 + √2), 15π/28)
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Find the angles of △ABC given that a=11, b=20, and c=18.
Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.
The angles of △ABC are approximately:
A ≈ 36.1 degrees
B ≈ 55.9 degrees
C ≈ 101.3 degrees
Angles of triangle calculation.
To find the angles of △ABC, we can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where C is the angle opposite the side c.
Using the given values, we can substitute and solve for cos(C):
18^2 = 11^2 + 20^2 - 2(11)(20)cos(C)
324 = 441 + 400 - 440cos(C)
cos(C) = -17/440
C ≈ 101.3 degrees
We can now use the Law of Sines to find the other angles:
sin(A)/a = sin(C)/c
sin(A)/11 = sin(101.3)/18
sin(A) ≈ 0.593
A ≈ 36.1 degrees
sin(B)/b = sin(C)/c
sin(B)/20 = sin(101.3)/18
sin(B) ≈ 0.820
B ≈ 55.9 degrees
Therefore, the angles of △ABC are approximately:
A ≈ 36.1 degrees
B ≈ 55.9 degrees
C ≈ 101.3 degrees
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Explain your plan for improving your math skills.
Answer:
To improve my math skills, I plan on doing the following:
1. Practice, practice, practice: I will practice math problems regularly, starting with simple problems and gradually increasing the difficulty level.
2. Use online resources: There are many online resources available that provide tutorials, practice problems, and videos to help with math skills. I will utilize these resources to supplement my learning.
3. Work with a tutor: I will consider working with a tutor if I need additional help with math concepts or if I'm struggling with specific problems.
4. Study regularly: I will set aside time each day to study math, even if it's just for a few minutes.
5. Ask questions: I will ask my teacher or tutor for help if I don't understand a concept or if I'm struggling with a problem.
6. Stay positive: I will maintain a positive attitude towards math and believe in my ability to improve my skills.
By following these steps, I'm confident that I can improve my math skills and become more confident in my abilities.
Answer:
"My plan for improving my math skills is to focus more on understanding and going over new concepts and practice problems. I also will try studying math concepts online and using a method of solving extra problems and applying math in the real world to better understand."
Step-by-step explanation:
Solve the following triangles:
A = 60 degree, a = 4, b = 5
The solution of missing sides and angle is: A = 60°, B = 34.8°, C = 85.2° a = 4, b = 5, c = √21
What is the main purpose of trigonometry and how many kinds of trigonometry are there?Trigonometric functions are used to obtain unknown angles and distances from known or measured angles in geometric drawings.
Basics of Trigonometry deals with measuring angles and problems related to angles. There are six basic trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent. All important trigonometric concepts are based on these trigonometric relationships or functions.
Solving a triangle means determining all its angles and sides. In this case, we are given angle A and sides a and b, and we want to find the remaining angles and sides.
First, we can use the law of cosines c to find the third side:
c² = a²+ b² - 2ab cos(A)
c² = 4² + 5² – 2(4)(5) cos(60)
c² = 16 + 25 - 40 cos (60)
c² = 41-20
c² = 21
c = √21
Now that we have all three sides, we can use the law of cosines to find the remaining angles:
cos(B) = (a²+ c² – b²) / (2ac)
cos(B) = (4² +(√21)² – 5²) / (2(4) (√21))
cos(B) = (16 + 21 - 25) / (8√21)
cos(B) = 12 / (8√21)
B = cos⁻¹ (12 / (8√21))
cos(C) = (a²+ b² – c²) / (2ab)
cos(C) = (4² + 5² – (√21)²) / (2(4)(5))
cos(C) = (16 + 25 - 21) / 40
cos(C) = 20/40
C = cos⁻¹ (20/40)
Simplifying trigonometric functions:
B ≈ 34.8°
C = 85.2°
Therefore, the solution is:
A = 60°, B = 34.8°, C = 85.2°
a = 4, b = 5, c = √21
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3. Gabe has $100. He plans to buy a jersey for $55. He will spend the rest of his money on T-shirts, which cost $15 each. Which inequality could Gabe use to find s, the number of T-shirts he can buy?
A 55 + 15s ≤ 100
B 15 + 55s ≤ 100
C 55 + 15s ≤ 100
D 15 + 55s ≤ 100
can someone please help me ASAP
please show your work on paper
Wrong Answers Will Be Reported !
The expressions are solved to give;
1.n = 1
2. h = 1
3. x = -5
4. n = 1/4
5. x = 7/2
6. p = 2/3
7. x = -12
8. n = 3
9. c = -1
10. x = 6
What are algebraic expressions?These are expressions that are made up of term, variables, constants, factors and coefficients.
They are also made up of mathematical operations.
From the information given, we have;
1. 5n + n = 2n + 4
collect and add the like terms
4n = 4
Make n subject
n = 1
2. 5h + 2 = h - 2
collect and add the like terms
4h = 4
h = 1
3. 2x - 1 = 3x + 4
collect and add or subtract the like terms
-x = 5
x = -5
4. n = n + 1/5
cross multiply
4n = 1, n = 1/4
5. x + 5 = 3x - 2
collect like terms
-2x = -7
x = 7/2
6. p = p + 2/4
cross multiply
3p = 2
p = 2/3
7. 4(2 + x) = 3x - 4
expand the bracket
8 + 4x = 3x - 4
collect like term
x = -12
8. 5n + 2 = 3n + 4
collect like terms
n = 3
9. 3c - 2 = -3c - 8
collect like terms
6c = - 6
c = -1
10. 3x + 1 = 2x - 5
collect the like terms
x = 6
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in a survey, 1500 adults in a country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean is lower: 38.4 hours and upper 43.5. Which of the following represents a reasonable interpretation of the results
The average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.
Based on the survey results of 1500 adults, we can be 95% confident that the true mean number of hours worked in the previous week for the entire population of the country lies between 38.4 hours and 43.5 hours.
This means that if we were to repeat this survey multiple times, 95% of the time the sample mean would fall within this range. Therefore, we can conclude that the average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.
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The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $75,000 10-year term policy for a 25-year-old male. Round your answer to the nearest cent. A 5-column table with 6 rows titled Term Insurance. Column 1 is labeled Age with entries 20, 21, 22, 23, 24, 25. Column 2 is labeled 5-year term male with entries 2 dollars and 43 cents, 2.49, 2.55, 2.62, 2.69, 2.77. Column 3 is labeled 5-year term female with entries 2.07, 2.15, 2.22, 2.30, 2.37, 2.45. Column 4 is labeled 10-year term male with entries 4.49, 4.57, 4.64, 4.70, 4.79, 4.85. Column 5 is labeled 10-year term female with entries 4.20, 4.36, 4.42, 4.47, 4.51. a. $363.75 c. $183.75 b. $207.75 d. $338.25
None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.
what is rounding ?
Rounding is a mathematical process of approximating a number to a specified degree of accuracy. It involves replacing a number with a simpler, but close value that is easier to work with or understand.
In the given question,
The question asks us to find the annual premium for a $75,000 10-year term policy for a 25-year-old male, using the table of annual life insurance premiums per $1,000 of face value.
First, we need to find the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. Looking at the table, we can see that the premium for a 10-year term policy for a 25-year-old male is $4.79 per $1,000 face value.
To find the annual premium for a $75,000 policy, we need to multiply the premium per $1,000 face value by 75. So:
Annual premium = $4.79 per $1,000 x 75 = $359.25
Rounding this answer to the nearest cent gives us:
$359.25 ≈ $359.26
Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male is $359.26.
None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.
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Find cos (A) I need help with this question
Answer:
[tex]\frac{8}{10}[/tex]
Step-by-step explanation:
[tex]cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}[/tex]
Answer:
Answer:
\frac{8}{10}
10
8
Step-by-step explanation:
\begin{gathered}cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}\end{gathered}
cos(A)=
hypotenuse
adjacent
=
AC
AB
=
10
8
Kendra invests $5800 in an account that earns 5.2% annual interest compounded quarterlyHow much will be in the account after 5 years? Round to the nearest cent.
Answer:
30508
Step-by-step explanation:
5800(1+0.052)^5
Find the indicated functional value for the ceiling function: f(−0.75)?
A. -1
B. 1
C. 2
D. 0
The ceiling function, denoted by ⌈x⌉, gives the smallest integer that is greater than or equal to x. Therefore, ⌈-0.75⌉ is the smallest integer that is greater than or equal to -0.75.
Since -1 is the smallest integer that is greater than or equal to -0.75, we have:
⌈-0.75⌉ = -1
Therefore, the functional value for the ceiling function at -0.75 is -1.
The answer is option A.