The side length of the original cube is 8.90 inches
How to find the side length of the original cube?Let x be the side length of the original cube. After cutting off the top, the remaining rectangular box has dimensions of x-5, x-5, and x.
The volume of this rectangular box is:
(x-5)(x-5)(x) = x³ - 10x² + 25x
x³ - 10x² + 25x = 135
x³ - 10x² + 25x -135 = 0
Use cubic formula.
x =8.90
Therefore, the side length of the original cube is 8.90 inches
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help what's the answer. What is the value of 12 – 4 + 2h when h = 3?
Answer:
14
Step-by-step explanation:
To find the value of 12 – 4 + 2h when h = 3, we need to substitute the value of h into the expression and simplify.
When h = 3, we can substitute this value into the expression:
12 – 4 + 2h = 12 - 4 + 2*3 = 12 - 4 + 6 = 12 - 4 + 6 = 8 + 6 = 14
So the value of 12 – 4 + 2h when h = 3 is 14.
Answer:
12 - 4 + 2h = 14
Step-by-step explanation:
Given expression,
→ 12 - 4 + 2h
Now we have to use,
→ h = 3
Let's simplify the expression,
→ 12 - 4 + 2h
→ 12 - 4 + 2(3)
→ 12 - 4 + 6
→ 8 + 6
→ 14 => {final value}
Hence, required value is 14.
Joel's town voted on a new law. 48 out of 50
votes were in favor of the law. What is the ratio of the number of votes against the law to the number of votes in favor of the law?
The total number of votes cast is 480
What is the ratio of the number of votes against the law to the number of votes in favor of the law?Ownership of more than 50% of voting shares generally gives the right of control and consolidation. In special cases, control is possible without having to own more than 50% of voting stock.
Let x represent total number of votes.
step1:
We have been given that Joel got 50% of the votes, which was 48 votes more than Sean.
50% of total votes:50/100[tex]x[/tex]=0.50[tex]x[/tex]
Since Joel got 50% of total votes, so Sean got 40% of total votes that is
40/100[tex]x[/tex]=0.40[tex]x[/tex]
Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:
0.50[tex]x[/tex]=0.40[tex]x[/tex]+48
0.50[tex]x[/tex]-0.40[tex]x[/tex]=0.40[tex]x[/tex]-0.40[tex]x[/tex]+48
0.10[tex]x[/tex]=48
step2:
0.10[tex]x[/tex]/.10=48/.10
[tex]x[/tex]=480
Therefore, the total number of votes cast is 480
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one unit of a is made of two units of b, three units of c, and two units of d. b is composed pf one unit of e and two units of f. c is made of two units of f and one unit of d. e is made of two units of d. items a, c, d, and f have one-week lead times; b and e have lead times of two weeks. lot-for-lot (l4l) lot sizing is used for items a, b, c, and d; lots of size 50 and 180 are used for items e and f, respectively. item c has on-hand (beginning) inventory of 15; d has an on-hand inventory of 50; all other items have zero beginning inventories. we are scheduled to receive 20 units of item e in week 2; there ae no other scheduled receipts. construct simple and low-level-coded bill-to-materials (product structure tree) and indented and summarized parts lists. if 20 units of a are required in week 8, use the low-level-coded bill-of-materials to find the necessary planned-order releases for all components.
Data handling is the process of ensuring that research data is stored, archived, or disposed of in a safe and secure manner during and after the conclusion of a research project.
The following are the given details:
Item Leadtime On hand Inventory Lot sizing criteria Schedulereceipts
A 2 0 L4L 10 in week 2
B 1 0 LAL 0
C 1 10 50 0
D 2 0 50 0
E 1 50 180 50 in week 1
F 1 180 L4L 50 in week 1
The Complete MRP schedule can be seen in the attached images below:
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The gross requirements for each component are as follows:
b = 2 x a = 44 units in week 7
c = 3 x a = 66 units in week 7
d = 2 x e + 1 x c + 2 x a
= 110 units in week 3, 56 units in week 6, 44 units in week 7
e = 1 x b = 44 units in week 5
f = 2 x b + 2 x c = 88 units in week 5 and 112 units in week 6
Net requirements = Gross requirements - Projected on hand
Projected on hand = Planned order receipts - net requirements
Planned order receipts = net requirements
Planned order releases = net requirements adjusted as per the lead time
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Sarah and Thomas each roll a die. Whoever rolls the higher number wins; if they both roll the same number, neither wins. a.What is the probability that Thomas wins?
b.If Sarah rolls a 3, what is the probability that she wins?
c.If Sarah rolls a 3, what is the probability that Thomas wins?
d.If Sarah wins, what is the probability that Thomas rolled a 3
e.If Sarah wins, what is the probability that Sarah rolled a 3?
Rolls the higher number wins; if they both roll the same number, neither wins.
The answer is-
a)They both start the game with an equal chance of winning, therefore 1/2
b) If she rolls a 3, Thomas must roll a 1 or 2 for her to win, making her chance of winning 1/3.
c) Thomas has a 50% chance of winning if she rolls a three because he has to roll a 4,5 or 6 to do so.
d) In order for Sarah to win, she had to roll a 2, 3, 4, or 6. If Thomas had rolled a 1, 2, 3, 4, or 5, he would have lost. Thus, there is a 1/5 chance that he will roll a 3.
e) If Sarah wins she must have rolled a 2,3,4,5 or 6. So the probability that she rolls a three is also 1/5.
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Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. Does the normal quantile plot depict sample data from a population with a normal distribution? A. Yes. The points are evenly distributed above and below the mean, O. B. Yes. The pattern of the points is reasonably close to a straight line. C. No. The points do not lie close to a straight line. D. No. The points exhibit some systematic pattern that is not a straight-line pattern.
The points are not reasonably close to a straight line, nor is the distribution normal.
Why do normal distributions exist?
In a continuous probability distribution called a "normal distribution," the majority of data points cluster in the middle of the range, while the remaining data points taper off symmetrically toward either extreme.The range's center is also referred to as the distribution's mean. The normal distribution, also known as the Gaussian distribution, is symmetrical about the mean and shows that data that are closer to the mean are more likely to occur than data that are farther from the mean.Like any probability distribution, the normal distribution depicts the distribution of values for a variable.
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The full question is given in the image-
How do I check
89,235
-66,456
______
22,779
refer to exercise 3. calculate the mean of the random variable x and interpret this result in context.
The mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.
To calculate the mean of the random variable x, we can use the formula [tex]$\mu = \frac{1}{n}\sum x_i$[/tex], where $\mu$ is the mean, $n$ is the number of values, and $x_i$ is the value of the random variable for each observation.
In this case, the mean of x is[tex]$\mu = \frac{1}{5}\sum x_i = \frac{1}{5}(2 + 6 + 4 + 5 + 7) = 4.4$.[/tex]
Interpreting this result in context, the mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.
The mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.
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A builder wants to purchase
countertops that are 15’ long and 24” deep, plus an island countertop that is
48” x 36”, how much total square
footage will be needed for this?
The builder will need a total of 372 square feet of countertop.
SolutionFirst, let's convert all dimensions to feet:
The 15' countertops are 15 * 12 = 180 inches long.
The 24" deep countertops are 24 / 12 = 2 feet deep.
The 48" x 36" island countertop is 48 / 12 = 4 feet wide and 36 / 12 = 3 feet deep.
Next, we can calculate the square footage of each countertop:
The 15' countertops are 180 inches long and 2 feet deep, so the square footage is 180 * 2 = 360 square feet.
The island countertop is 4 feet wide and 3 feet deep, so the square footage is 4 * 3 = 12 square feet.
Finally, we can add the square footage of each countertop to find the total square footage:
360 square feet + 12 square feet = 372 square feet
Therefore, The builder will need a total of 372 square feet of countertop.
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find the third degree polynomial Q such that Q(1)=1 Q'(1)=3 Q"(1)=6 and Q'''(1)=12
Answer:
A third degree polynomial, also known as a cubic polynomial, has the form of
Q(x) = ax^3 + bx^2 + cx + d
Given that Q(1)=1, Q'(1)=3, Q''(1)=6, and Q'''(1)=12, we can use these values to find the coefficients a, b, c, and d.
Q(1) = a(1)^3 + b(1)^2 + c(1) + d = 1
Q'(1) = 3a + 2b + c = 3
Q''(1) = 6a + 2b = 6
Q'''(1) = 6a = 12
Solving for a:
6a = 12
a = 2
Using the value of a, we can substitute it back into the other equations to find b, c and d.
Q''(1) = 6a + 2b = 6
6(2) + 2b = 6
12 + 2b = 6
2b = -6
b = -3
Q'(1) = 3a + 2b + c = 3
3(2) + 2(-3) + c = 3
6 - 6 + c = 3
c = 9
Q(1) = a(1)^3 + b(1)^2 + c(1) + d = 1
2(1)^3 + (-3)(1)^2 + 9(1) + d = 1
2 + (-3) + 9 + d = 1
8 + d = 1
d = -7
Therefore, the third degree polynomial Q that satisfies the given conditions is:
Q(x) = 2x^3 - 3x^2 + 9x - 7
----------------------------------------
the polynomial Q(x) is Q(x) = x^3 + 2x^2 + x + 1
This polynomial satisfies the given conditions Q(1)=1, Q'(1)=3, Q"(1)=6, and Q'''(1)=12.
To check:
Q(1) = 1 + 2(1)^2 + 1(1) + 1 = 1
Q'(1) = 3 + 4 + 1 = 8
Q"(1) = 6
Q'''(1) = 6
It's important to note that the polynomial that I have provided may not be unique, as there may be other third degree polynomials that also satisfy the given conditions.
The depth, d, of a lake is 500 m, rounded to the nearest integer.
Write the error interval for d in the form a ≤ d < b.
Answer: The depth, d, of a lake is 500 m, rounded to the nearest integer. The error interval for d is 499.5 ≤ d < 500.5
When a value is rounded to the nearest integer, the possible error is half of the smallest unit of measurement. In this case, the smallest unit of measurement is 1 meter, so the possible error is 0.5 meters. Therefore, the error interval for d is from -0.5 meters to +0.5 meters around the rounded value of 500 meters.
This can be expressed in the form a ≤ d < b as follows:
a = 500 - 0.5 = 499.5
b = 500 + 0.5 = 500.5
So, 499.5 ≤ d < 500.5
Step-by-step explanation:
An imported item costs 500$. The retailer's plans to sell with a 70% increase in import price. After selling for a while, the seller decides to discount 20% of the first sale price and continue to discount 10% of the second sale price. Find the final sale price?
Profit is determined using the equation Profit = Selling Price - Cost Price. The final price after discount is $612.
Following this, the formula for calculating profit percentage is: profit percentage = (profit/cost price) x 100.
What is the loss percent formula?
The firm is considered to be losing money if a product's cost price is higher than its selling price; conversely, if the product's cost price is lower than its selling price, a profit might be made. Loss% is equal to Loss/CP multiplied by 100.
Profit is calculated as cost less selling price. Similar to this, the cost price is higher than the targeted selling price when a loss occurs. A profit percentage is computed by dividing the cost price by 100. 100 divided by the cost price is the loss percentage.
Determine the net profit and loss from a company's operations over the course of an accounting period with the help of the profit and loss account, also referred to as the income statement. The trading account's gross profit or loss is transferred to this account.
Given,
the cost price = $500
Selling price = 70% increase in import price
70 / 100 × $500 = $ 350
Selling price = $350 + $500
Selling price = $850
Selling price after 20% discount = 20% of $850
⇒ 0.2 × 850 = 170
⇒ Selling price after 20% discount = $850 - $170 = $680
Selling price after discount 10% = 0.10 × $680 = $68
Selling price after discount 10% = $680 - $68 = $612
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What fraction of 350 gallons is 135 litres
Answer:
10.19%
Step-by-step explanation:
1 gallon = 3.785 liters
350 gallons = 350 × 3.785 liters = 1324.75 liters
percent = part/whole × 100%
percent = 135 liters / 1324.75 liters × 100%
percent = 10.19%
A string measures 30cm. About how many inches long is the string
Answer: 11.811 inches
Step-by-step explanation:
There are about 0.3937 inches in a cm, so the answer is [tex]30(0.3937)=11.811[/tex] inches.
In the figure below, m VW=69° and m XY = 49°. Find mZXZY.
W
Y
X
Check the picture below.
Toby and his little sister are saving up money to buy a joint birthday present for their mother. Toby already has $26 saved and plans to save $14 per week from his allowance. His sister has $28 saved so far and will save $12 per week from hers. The two siblings will soon have saved the same amount towards their mother's gift. How long will that take? How much will each one have saved?
In ------- weeks, Toby and his sister will each have saved $---------
In 1 week, Toby and his sister will each have saved $40.
In how many weeks would the siblings have saved the same amount?The first step is to form a linear equation that represents the equation in the question. A linear equation is an equation that has a single variable that is raised to the power of one.
The form of a linear equation that represents the amount saved by the siblings is:
Total amount saved = amount they have already saved + (number of weeks x amount saved per week)
Amount saved by Toby = $26 + ($14 x w)
$26 + $14w
Amount saved by his sister = $28 + ($12 x w)
$28 + $12w
When the siblings have saved the same amount of money, the two above linear functions would be equal:
$26 + 14w = $28 + $12w
In order to determine the value of w, take the following steps:
Combine and add similar terms:
$14w - $12w = $28 - $26
2w = 2
Divide both sides of the equation by 2
w = 2 / 2
w = 1 week
Total amount that would have been saved = $28 + $12(1)
$28 + 12 = $40.
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2. What is the third step in proving by mathematical induction that for every positive integer n, 11" - 6 is divisible by 5, is true?
O Show that 11k - 6 is divisible by 5.
O Assume that 11¹ - 6 is divisible by 5.
O Assume that 11*+1 - 6 is divisible by 5.
Show that 11*+1 - 6 is divisible by 5
To show that 11k+1 - 6 is divisible by 5 using mathematical induction, the first step is to assume that the statement is true for any given positive integer k.
What is the third step in proving by mathematical induction that for every positive integer n, 11" - 6 is divisible by 5, is true?This means that 11k - 6 is divisible by 5.Next, we need to show that this assumption implies that 11k+1 - 6 is also divisible by 5.We can do this by substituting 11k+1 - 6 for 11k + 5 - 11 + 6, which can be simplified to 11k + 5 - 11 + 6.Then, we can subtract 11k from both sides, leaving us with 5 - 11 + 6. Finally, we can add 11 to both sides, resulting in 16, which is divisible by 5.Therefore, 11k+1 - 6 is divisible by 5.To show that 11k+1 - 6 is divisible by 5, we will use mathematical induction.First, we assume that 11¹ - 6 is divisible by 5.Then, we assume that 11*+1 - 6 is divisible by 5.To prove that the statement is true, we must show that 11*+1 - 6 is divisible by 5.We can do this by multiplying both sides of the equation by 11: 11*+1 - 6 = 5(11k - 5).This equation shows that 11k+1 - 6 is equal to 5 times 11k - 5, which is divisible by 5.Therefore, 11k+1 - 6 is divisible by 5.This completes the proof by mathematical induction that for every positive integer n, 11" - 6 is divisible by 5 is true.To learn more about the mathematical induction refer to:
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Write in point slope form and slope intercept form.
When given the point-slope form of a line, we first must identify the point and the slope in order to create a graph of the line.
How do you write point-slope form with a point slope?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.
Plug the slope and the (x, y) point values into y = mx + b, then solve for b using the substitution method.Point-slope form is represented as y y 1 = m (x x 1), where (x 1, y 1) is the supplied point and m is the given slope.
Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.
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The given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y = -6x + 30.
How do you write point-slope form with a point slope?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.
Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.
Given, x intercept = 5
which means when y = 0, x = 5 i.e. (5, 0)
And given a point (4, 6)
using the two points in slope formula
[tex]$\mathrm{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
[tex]$\mathrm{m = \frac{6- 0}{4 - 5}}[/tex]
m = 6/-1
m = -6
Now, as we have slope, put the data in point-slope form
y-y₁ = m(x -x₁)
y - 6 = -6(x - 4) ⇒ point-slope form
y - 6 = -6x + 24
y = -6x + 24 + 6
y = -6x + 30 ⇒ slope intercept form
Thus, the given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y = -6x + 30.
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A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100(extremely good quality). The stem-and-leaf display of the data is shown to the right. What percentage of the respondents rated overall television quality with a rating of 50 or below? show answer please A. 56 B. 44 C. 11 D. 40
Approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40
What is the range of the data?
The range is the spread of your data from the lowest to the highest value in the distribution. It is a commonly used measure of variability. Along with measures of central tendency, measures of variability give you descriptive statistics for summarizing your data set
The stem-and-leaf display shows that the data ranges from 0 to 100.
The leaves on the stem for the number "5" are 0, 0, 1, 2, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9.
This means that 13 of the respondents rated overall television quality with a rating of 50 or below.
To find the percentage of respondents who rated television quality 50 or below, we need to divide the number of respondents who rated television quality 50 or below (13) by the total number of respondents and multiply by 100.
13/30 * 100 = 43.333...
Hence, approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40%.
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do the ordered pairs plotted in the graph below represents a function explain
Answer: it's not a function
Step-by-step explanation:
(4,3) (4,-3)
one to many
it isn't a function.
Calcular el valor numerico de la funcion polinomica.
Gracias al que respondio :)
Los valores de las expresiones polinomicas son:
10*(1/2)^2 - 4*(1/2) = 1/2
(2/3)*(-3/4) - (1/2)*(-3/4)^2 = -25/32
¿Como resolver las expresiones?En este problema queremos encontrar los valores de dos expresiones polinomicas.
La primera es:
10*(1/2)^2 - 4*(1/2)
Primero resolvemos el cuadrado del primer termino, esto da:
10*(1/4) - 4*1/2
10/4 - 4/2
Ahora queremos tener el mismo denominador en ambas fracciones, asi reescribimos la primear como:
5/2 - 4/2
1/2
Ese es el valor numerico.
La segunda expression es:
(2/3)*(-3/4) - (1/2)*(-3/4)^2
Primero resolvemos el cuadrado, recordar que esto cancela el signo negativo:
(2/3)*(-3/4) - (1/2)*(9/16)
Ahora tomamos los productos entre fracciones:
(2/3)*(-3/4) - (1/2)*(9/16)
-6/12 - 9/32
Simplificamos ambas fracciones:
-1/2 - 9/32
Escribimos ambas fracciones con el mismo denominador:
-16/32 - 9/32 = -25/32
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Ask a question about your assignment
Answer: 146
Step-by-step explanation:
HK = GK x 2 because a rectangles diagonals are equal.
73 x 2 = 146
Answer:
146 that should be right
Find the slope of the line that goes through the points (0, 9) and (-2, -4).
Write an algebraic expression as indicated.
Roberto has a total of $4000 in two savings accounts. Let x represent the amount in one account. Write an algebraic expression for the amount in the other
account.
Answer:
4000-x
Step-by-step explanation:
both accounts - account x = account y
(x+y) - x = y
A granola bite contains 27 calories. Most of the calories come from c
grams of carbohydrates. The rest come from other ingredients. One
gram of carbohydrate contains 4 calories.
The equation 4c + 5 = 27 represents the relationship between these
quantities.
Answer the following questions:
1. What could the 5 represent in this situation?
2. Priya said that neither 8 nor 3 could be the solution to the
equation. Explain why she is correct.
3. Find the solution to the equation.
A. 5 represents the number of calories that come from other ingredients.
B. Neither 8 nor 3 satisfies the given equation, so neither 8 nor 3 can be the solution to the equation.
C. The value of c is 5.5.
What are linear equations?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given
equation 4c + 5 = 27
Where c represents the grams of carbohydrates
27 is the total number of calories that are received by the granola bite.
4 is the number of calories from 1 gram of carbohydrates and
5 is the number of calories that are received from other ingredients.
B: Priya said that neither 8 nor 3 could be the solution to the
equation.
substituting 8 and 3 in the equation,
4c + 5
4*8 + 5 = 37≠ 27
4*3 + 5 = 17≠ 27
so 8 and 3 are not solutions of the equation.
C: solution of the equation, 4c + 5 = 27
4c = 27 - 5
4c = 22
c = 22/5
c = 5.5
Hence 5 represents calories from another ingredient,
8 and 3 are not the solution of the equation and the solution of the equation is 5.5.
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a and b are friends. a's father d is twice as old as a and b is twice as old as his sister c. the age of d and c differ by 40 years. write a linear equation representing the given situation, assuming the ages of a and b as x and y years respectively.
The A's age is 26 years and B's age is 24 years
What is meant by linear equation? A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).Let the ages of A and B be x and y years respectively. Then, [tex]$x-y=\pm 2[/tex]Given
D's age [tex]$=2 x$[/tex]years and, C's age[tex]$=\frac{y}{2}$[/tex] years.
Clearly, D is older than C
[tex]$2 \mathrm{x}-\frac{\mathrm{y}}{2}=40 \Rightarrow 4 \mathrm{x}-\mathrm{y}=80$[/tex]
Thus, we have the following two systems of linear equations[tex]$x-y=2$[/tex].(i)
and, [tex]$4 x-y=80$[/tex](ii)
or
[tex]$x-y=-2$[/tex] (iii)
and, [tex]$4 x-y=80$[/tex]..(iv)
Subtracting equation (i) from equation (ii), we get [tex]$3 \mathrm{x}=78 \Rightarrow \mathrm{x}=26$[/tex]Putting [tex]$\mathrm{x}=26$[/tex] in equation (i), we get [tex]$\mathrm{y}=24$[/tex]or
Subtracting equation (iv) from equation (iii), we get [tex]$-3 \mathrm{x}=-82 \Rightarrow \mathrm{x}=\frac{82}{3}=27 \frac{1}{3}$[/tex]
Putting [tex]$\mathrm{x}=\frac{82}{3}$[/tex]in equation (iii), we get
[tex]$\mathrm{y}=\frac{82}{3}+2=\frac{88}{3}=29 \frac{1}{3}$[/tex]
Hence, A's age =26 years and B's age =24 years or
A's age =[tex]27 \frac{1}{3}$[/tex] years and B's age[tex]$=29 \frac{1}{3}$[/tex] years.
The complete question is,
A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B.
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Directions: solve for x round to the nearest tenth
Using the trigonometric ratios for the angle A-cosθ= Base/ Hypotenuse =11.8726
What is trigonometric?
Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.
For example, the triangle contains an angle A, and the ratio of the side opposite to A and the side opposite to the right angle (the hypotenuse) is called the sine of A, or sin A; the other trigonometry functions are defined similarly. These functions are properties of the angle A independent of the size of the triangle, and calculated values were tabulated for many angles before computers made trigonometry tables obsolete. Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures.
Here, if we consider the ∠A=θ, then AB is the base, BC is the perpendicular, and AC is the hypotenuse.
And it is given that, ∠A=θ=32°,AB=x, and C=14 units.
Now, using the trigonometric ratios for the angle A-cosθ= Base/Hypotenuse
cosA=AB/AC
cos30°=x/14
x=14×cos32°
=11.8726
≈11.9units
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S is the sum of 12, 8, 6, 4 and x. What is the value of x if x = 2/5S?
(Linear equations)
Answer:
x = 20
Step-by-step explanation:
Sum of 12, 8, 6, 4 and x is:
S = 12 + 8 + 6 + 4 + x = 30 + x
[tex]\dfrac{2}{5}S = \dfrac{2}{5}\cdot 30 + \dfrac{2}{5}x\\\\=12 + \dfrac{2}{5}x\\\\\\\textrm{But left side is nothing but x}\\\\\textrm{So we get }x = 12 + \dfrac{2}{5}x\\\\\rm{Subtract $\dfrac{2}{5}x$ from both sides}\\\\x - \dfrac{2}{5}x = 12\\\\\dfrac{3}{5}x = 12\\\\x = \dfrac{12 \cdot 5}{3} \\\\x = 20\\\\[/tex]
Verify
12 + 8 + 6 + 4 + 20 = 50
(2/5) x 50 = 20
Rashaad has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $31.40? Round to the nearest cent.
Rashaad will pay $28.26 after the discount.
What is discount?The discount equals the difference between the price paid for and it’s par value. Discount is a kind of reduction or deduction in the cost price of a product.
Given that, Rashaad has a loyalty card good for a 10% discount, he bought something at $31.40, we need to find the total amount he needs to pay after the discount,
So, the amount he will pay is (100-10) = 90% of the original amount,
90% of 31.40
= 90 % × 31.40
= 90/100 × 31.40
= 2826/100
= 28.26
Hence, he will pay $28.26 after the discount.
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On January 3, 2004, after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to Earth. It landed only six miles from its target. This accuracy is comparable to shooting an arrow at a target fifty feet away and missing the exact center by what distance?
This accuracy is comparable to shooting an arrow at a target fifty feet away and missing the exact center by the distance; 0.000001 miles
How to solve proportion word problems?Proportion word problems are simply ways of expressing proportion problems in words. For example we share oranges among three people each receiving 2, 3 and 4 respectively and as such the ratio of the proportion is 2:3:4.
Now, we are told that after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to Earth. It landed only six miles from its target. This is comparable to shooting an arrow at a target fifty feet away and missing the exact center.
Thus, if the comparable distance missed is x, then we can say that;
x/50 = 6/300000000
x = (6 * 50)/300000000
x = 3/3000000
x = 0.000001
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You should have two 2-bit inputs and 4 output bits. The logic required to calculate each bit is on the website. Come and see me if you have problems. You must build your circuit out of logic gates, you cannot use the adder circuits already built. Your assignment must be turned in as a separate .circ file along with your word file or pdf for the other problems. To verify your output, your input/output table should look like this: Using Logisim, design a 2 bit multiplier.
This answer explains how to design a 2-bit multiplier using Logarithm. The circuit requires two 2-bit inputs, A and B, and four output bits, C0, C1, C2, and C3. To build the circuit, two 1-bit full adders are used for each bit of inputs A and B and the outputs are connected accordingly. Finally, the circuit is tested to verify that it is working as expected.
Input A: 0 0
Input B: 0 0
Output C: 0 0 0 0
Input A: 0 0
Input B: 0 1
Output C: 0 0 0 1
Input A: 0 0
Input B: 1 0
Output C: 0 0 1 0
Input A: 0 0
Input B: 1 1
Output C: 0 0 1 1
Input A: 0 1
Input B: 0 0
Output C: 0 0 0 1
Input A: 0 1
Input B: 0 1
Output C: 0 0 1 1
Input A: 0 1
Input B: 1 0
Output C: 0 1 0 0
Input A: 0 1
Input B: 1 1
Output C: 0 1 0 1
Input A: 1 0
Input B: 0 0
Output C: 0 0 1 0
Input A: 1 0
Input B: 0 1
Output C: 0 0 1 1
Input A: 1 0
Input B: 1 0
Output C: 0 1 1 0
Input A: 1 0
Input B: 1 1
1. Start with two 2-bit inputs A and B.
2. Create four output bits, C0, C1, C2, and C3.
3. Create two 1-bit full adders, one for each bit of inputs A and B.
4. Connect the inputs A and B to the inputs of the two respective full adders.
5. Connect the output of the first full adder to the input of the second full adder.
6. Connect the of the second full adder to the output of C0.
7. Create two more 1-bit full adders, and connect the output of the first full adder to one of the inputs of each of the two full adders.
8. Connect the other input of each of the two full adders to the corresponding bit of the inputs A and B.
9. Connect the output of the first 1-bit full adder to the output of C1.
10. Connect the output of the second 1-bit full adder to the output of C2.
11. Create one more 1-bit full adder and connect the output of the second 1-bit full adder and the corresponding bit of the inputs A and B to the two inputs of the logarithm 1-bit full adder.
12. Connect the output of the 1-bit full adder to the output of C3.
13. Test the inputs and outputs to verify that the circuit is working as expected.
This answer explains how to design a 2-bit multiplier using Logisim. The circuit requires two 2-bit inputs, A and B, and four output bits, C0, C1, C2, and C3. To build the circuit, two 1-bit full adders are used for each bit of inputs A and B and the outputs are connected accordingly. Finally, the circuit is tested to verify that it is working as expected.
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