The inequality for the given sentence would be:
4x ≥ 18. This means that the product of x and 4 is greater than or equal to 18.
The inequality "4x ≥ 18" is read as "four times x is greater than or equal to 18". This means that the value of x must be equal to or greater than 4.5 for the inequality to hold true.
To solve the inequality, we can divide both sides by 4, which gives us:
x ≥ 4.5
This means that any value of x that is equal to or greater than 4.5 will satisfy the original inequality.
For example, x = 5 would satisfy the inequality because: 4(5) = 20, which is greater than or equal to 18.p
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I am so confused someone please help me
Answer:
C
Step-by-step explanation:
Answer:
D. 192
Step-by-step explanation:
192 possible combinations.
[tex]12 * 8 = 192[/tex]
Think of it this way. If you can choose a shirt and pants with colors blue and green for each, You combinations would be blue blue, green green, blue green, and green blue. 2 options and 2 options.
[tex]2 * 2 = 4[/tex]
Another example with ice cream, flavor and topping.
Choose 1 option from each category.
Flavors: Vanilla, Chocolate, Strawberry
Toppings: Caramel, Sprinkles, M&Ms
All Combinations:
Vanilla, Caramel
Vanilla, Sprinkles
Vanilla, M&Ms
Chocolate (with the three toppings)
Strawberry (with the three toppings)
9 total combinations, [tex]3 * 3 = 9.[/tex]
Multiply the number of options for each category.
Simplify the expression. Negative 19 plus the quantity negative 4 and five tenths plus 6 and 87 hundredths end quantity divided by 3 all times 5 squared minus 7 and 3 tenths 19. 6 −18. 4 31. 45 −6. 55
The expression can be simplified by breaking it down into its individual components. we multiply this by 5 squared, which simplifies to 25 x 5 = 125. Lastly, we subtract 7.3 from 125 to get 117.7, which is the final answer.
First, we can evaluate the expression inside the parentheses, which is -4.5 + 6.87. This evaluates to 2.37. We then divide this by 3 to get 0.79. Next, we multiply this by 5 squared, which gives us 79. Lastly, we subtract 7.3 from 79 to get 71.7, which is the final answer.
The expression can be expanded by breaking it down into its individual parts. First, we have -19, which is already in its expanded form. Next, we can expand the expression inside the parentheses, which is -4.5 + 6.87. This can be expanded to -4 + 0.5 + 6 + 0.87, which simplifies to -4 + 6 + 0.87 = 2.87. We then divide this by 3 to get 0.79. Next, we multiply this by 5 squared, which simplifies to 25 x 5 = 125. Lastly, we subtract 7.3 from 125 to get 117.7, which is the final answer.
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The number of views of Video A was 250 on the day it was posted. The number of views increased by 30% each day….
Need this by Monday, please help.
50 pts. !!
Answer:
I gotta get you to do a little bit so I can't give you the direct answer -_-
Step-by-step explanation:
Lets start with this question, what is 30% of 250?
We multiply 250*0.3, which gives us an increase of 75 the first day
__________________________________
Second day: 250+75=325 views
325*0.3=97.5
__________________________________
Third day: 422.5
422.5*0.3=126.75
__________________________________
We add the increases, which is 75+97.5+126.75
This gives us 299.25
Now we just have to find the fourth day and average it! (which I trust you know how to do, just helping you get the jist of it)
Hope I helped!
Name the angle in the drawing
I am almost 99% sure it would be (A). < TRS
Given that W is directly proportional to the square of V, and W=50 when V=5 , find W when V=9 .
Answer:
k=2 when W=50,V=5
W=162 when V=9,k=remains constant
Step-by-step explanation:
W=V²
W=kV²
50=k×5²
50=k×25
50=25k
divide both sides by 25
k=2
k remains constant
W=KV²
W=2×9²
W=2×81
W=162
Après avoir factorisé le nombre de gauche,résoudre l'équation ci-dessous
x²+(5+4x)x=0
ce site est anglais frère
Answer:
5
Step-by-step explanation:
0+(5+4*0) (* signifie multiplier)
0+5
5
Find the coordinate of A if the midpoint of bar (AB) is at (-2,3) and B is at (1,1). A is at:
Answer:
Point A = (-5,5)
Step-by-step explanation:
Explanation is given in the picture...
A company orders 27 boxed lunches from a deli for $245. 70. If each boxed lunch costs the same amount, what is the unit cost of each boxed lunch?
A company pays $245.70 for 27 boxed lunches from a deli. If each boxed lunch is the same price, the unit cost of each boxed lunch is $9.10.
To find the unit cost of each boxed lunch, we need to divide the total cost by the number of boxed lunches.
Total cost of 27 boxed lunches = $245.70
Unit cost of each boxed lunch = Total cost / Number of boxed lunches
Unit cost of each boxed lunch = $245.70 / 27
Unit cost of each boxed lunch = $9.10 (rounded to two decimal places)
Therefore, the unit cost of each boxed lunch is $9.10.
In this case, the deli will need to ensure that each boxed lunch is priced higher than the unit cost of $9.10 to make a profit. The difference between the unit cost and the selling price will contribute to the deli's revenue and cover other expenses such as labor, rent, and utilities.
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Allen is buying a video game that originally costs $49. He has a 10% off coupon and will have to pay a 6% sales tax. Which expression will calculate the total amount allen will pay for the video
The expression that will calculate the total amount allen will pay for the video is 0.9p(1.06)
In this case, let's use the variable "p" to represent the original price of the video game. The expression for the discounted price would then be:
0.9p
This is because Allen will pay 90% of the original price, which is the same as multiplying the original price by 0.9.
Next, we need to calculate the sales tax on the discounted price. To do this, we can use another expression:
0.06(0.9p)
This expression represents the amount of sales tax that Allen will have to pay on the discounted price. We multiply 0.06 (or 6%) by 0.9p (the discounted price) to get the tax amount.
Finally, we can calculate the total amount Allen will pay by adding the discounted price and the sales tax:
0.9p + 0.06(0.9p)
Simplifying this expression, we can factor out 0.9p:
0.9p(1 + 0.06)
And then simplify the sum in the parentheses:
0.9p(1.06)
This is our final expression for the total amount Allen will pay for the video game.
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If you are standing on Earths surface , what is the distance from your eye to the horizon ? If the earths radius is 6,371,000
The distance from your eyes to the horizon is approximately 4.7 kilometers (2.92 miles).
What is surface?The surface refers to the two-dimensional, flat, or curved boundary of a three-dimensional object. For example, the surface of a sphere is a curved two-dimensional boundary that encloses the three-dimensional space inside the sphere.
According to question:The distance from your eye to the horizon on the Earth's surface depends on your height above the surface. Assuming that you are standing on a flat surface and your eyes are at an average height of about 1.7 meters (5.6 feet) above the ground, the distance to the horizon.
distance to horizon = √(2Rh + h²)
where R is the radius of the Earth (6,371,000 meters) and h is the height of your eyes above the ground (1.7 meters).
Plugging in the values, we get:
distance to horizon = √(2 x 6,371,000 x 1.7 + 1.7²) = 4,690 meters (approximately 15,387 feet or 2.92 miles)
Therefore, if you are standing on the Earth's surface with your eyes at an average height of 1.7 meters, the distance from your eyes to the horizon is approximately 4.7 kilometers (2.92 miles).
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a student takes an exam containing 16 true or false questions. if a student randomly guesses on the entire exam, what is the expected value of the number of incorrect answers? do not round your answer.
In this case, the probability of getting a question wrong is 0.5, and there are 16 questions, so the expected value of incorrect answers is 0.5 x 16 = 8.
The expected value of the number of incorrect answers on a 16-question true or false exam with random guessing is 8. This is because there are an equal number of true and false answers, and the chance of getting each one correct is 50%. Therefore, the expected value of incorrect answers is 8.
To calculate the expected value, you need to multiply the probability of getting a question wrong by the number of questions.
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= 13 680,00(0,551368)
Answer:
=7542,71
Step-by-step explanation:
13 680.00 x 0.551368
=7542,71424
round off to the second decimal place
=7542,71
A retailer buys a coat bulk at a uint price of $45 the coat is marked up 80% to sell in the store. What is the price of the coat in the store
The price of the coat in the store is $81 after a retailer buys a coat bulk at a unit price of $45 the coat is marked up 80% to sell in the store.
The retailer buys the coat at a unit price of $45 and marks it up by 80%. To calculate the markup, we need to first find 80% of $45, which is
0.8 x $45 = $36.
We can then add the markup to the cost price to get the selling price:
$45 + $36 = $81.
Therefore, the price of the coat in the store is $81.
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1. Alexandra earns $59, 904.00 in gross pay each year. If she must pay $998.40 in taxes and $345.00 each month for medical, dental, and vision insurance, what is Alexandra's net pay each month? Show work.
-$3,780.40
-$3,824.20
-$3,648.60
-$3,546.70
Alexandra's net pay each month, using mathematical operations, is C. $3,648.60.
What is the net pay?The net pay is the difference between the gross pay or earning and the total deductions.
The net pay per month can be computed following these steps:
Gross earnings per year = $59,904.00
Monthly taxes = $998.40
Annual taxes = $11,980.80 ($998.40 x 12)
Monthly medical, dental, and vision insurance = $345.00
Annual medical, dental, and vision insurance = $4,140 ($345 x 12)
Total deductions and taxes = $16,120.80 ($11,980.80 + $4,140)
Annual net pay = $43,783.20 ($59,904.00 - $16,120.80)
Monthly net pay = $3,648.60 ($43,783.20/12)
Thus, monthly, Alexandra will earn a net pay of Option C.
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Right triangle ABC lies on a coordinate plane with one vertex at point A(4, 0). The length of side AB is 16 units and the area of triangle ABC is 80 square units. 20 Type the correct answer in each box. Use numerals instead of words. Find the coordinates of point B and point C. The coordinates of point B are (4, ), and the coordinates of point C are ( ,-16).
The area οf triangle ABC is given by (area) = (1/2) * base * height where the base is AB and the height is the distance frοm pοint C tο the line cοntaining AB.
Since AB has a length οf 16, the height must be 10 (since 1/2 * 16 * 10 = 80).
Let's call the cοοrdinates οf pοint C (x, y). Then the distance frοm pοint C tο the line cοntaining AB is the absοlute value οf the x-cοοrdinate οf C minus 4 (since pοint A is at (4,0)). We can use this tο set up an equatiοn:
(1/2) * 16 * 10 = (1/2) * 12 * |x - 4|
Simplifying, we get:
80 = 6 * |x - 4|
Dividing bοth sides by 6, we get:
|x - 4| = 40/6 = 20/3
Since the distance must be pοsitive, we can drοp the absοlute value and sοlve fοr x:
x - 4 = 20/3 οr x - 4 = -20/3
Sοlving fοr x in each case, we get:
x = 4 + 20/3 = 32/3 οr x = 4 - 20/3 = 4/3
Since pοint C must have a y-cοοrdinate οf -16, the cοοrdinates οf pοint C are (32/3, -16) οr (4/3, -16).
Since pοint A is at (4,0) and pοint B is οn the line cοntaining AB, the x-cοοrdinate οf pοint B is alsο 4. The y-cοοrdinate οf pοint B can be fοund using the Pythagοrean theοrem:
[tex]AC^2 + BC^2 = AB^2[/tex]
Substituting in the cοοrdinates οf A, B, and C, we get:
[tex](4 - 4/3)^2 + (-16 - 0)^2 = 16^2[/tex]
Simplifying, we get:
256/9 + 256 = 256
Multiplying bοth sides by 9, we get:
256 + 2304 = 2304
Sο the calculatiοn is incοnsistent, which means that nο pοint C satisfies the given cοnditiοns. This is likely due tο a mistake in the οriginal prοblem statement.
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Shroff ate pizza at a party and told his friends that he ate 52/78 of a pizza. Can you help his friends understand what fraction of a pizza he really ate?
The fraction of pizza that Shroff ate is 2/3 of a pizza.
The Greatest Common Factor (GCF) is the largest number that divides evenly into two or more integers. It is also known as the Greatest Common Divisor (GCD).
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by that number.
The GCD of 52 and 78 is 26 (because 26 is the largest number that divides evenly into both 52 and 78).
So, to simplify the fraction, we divide both the numerator and denominator by 26:
52/78 = (52 ÷ 26) / (78 ÷ 26) = 2/3
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emma covered a gift box in the shape of a rectangular prisim. It was 8 inches long, 4 inches wide, and 7 inches high. What is the total surface area of the gift box?
The tοtal surface area οf the gift bοx is 232 square inches.
What is rectangle?A rectangle is a 2D shape that has fοur sides and fοur right angles. Oppοsite sides are parallel and οf equal length. The area οf a rectangle is the prοduct οf its length and width, and its perimeter is the sum οf the lengths οf all its sides.
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height οf the rectangular prism, respectively.
Substituting the given values, we get:
SA = 2(8x4) + 2(8x7) + 2(4x7)
SA = 64 + 112 + 56
SA = 232
Therefοre, the tοtal surface area οf the gift bοx is 232 square inches.
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Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation 1 = 707.6t + 39,090 where t is the number of years after 2015. (a) What t-value corresponds to 2025? t10 (b) Find the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 46,166 (c) In what year is the U.S. per capita real disposable income expected to exceed $50,000?
The t-value for the year 2025 is t = 10, the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 is $46,166 and the U.S. per capita real disposable income expected to exceed $50,000 is 2030.
Given equation is 1 = 707.6t + 39,090
(a) To find what t-value corresponds to 2025.The given year is 2025, so the number of years after 2015 will be 2025-2015 = 10 So the t-value for the year 2025 is t = 10.
(b) To find the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 Substitute t = 10 in the given equation1 = 707.6t + 39,0901 = 707.6(10) + 39,0901 = 7,076 + 39,0901 = 46,166So, the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 is $46,166.
(c) To find in what year is the U.S. per capita real disposable income expected to exceed $50,000.Substitute 50,000 for 1 in the equation, we get50,000 = 707.6t + 39,09050,000 - 39,090 = 707.6t10,910 = 707.6t10,910/707.6 = t15.41 ≈ 15 years. So, the U.S. per capita real disposable income expected to exceed $50,000 in 2015 + 15 = 2030.
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I NEED HELP ON THIS ASAP!
A graph of each inequality is shown in the grid below.
A shape which the solution region represent is a rectangle.
How to determine and graph the solution for this system of inequalities?In order to graph the solution for the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;
0.4r ≤ 120 .....equation 1.
r ≥ 4(360/5) .....equation 2.
By evaluating the given system of inequalities, we have;
r ≤ 120/0.4
r ≤ 300
r ≥ 4(360/5)
r ≥ 4(72)
r ≥ 288
By combining the system of inequalities, we have:
288 ≤ r ≤ 300
Based on the graph (see attachment), we know that the solution to the given system of inequalities is the shaded region between the solid line, as well as the point of intersection of the lines representing each inequality.
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where would (-8,-6) be located of a coordinate plane
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Answer:
If Sharon has 300 channels with her cable service, then her monthly cost is calculated as follows:
300 channels × $0.20 per channel = $60
This means that Sharon's current cable bill is $60 per month. If she switches to Great Vista Satellite, her monthly cost will be $180, which is $120 more than her current bill. This increase in cost can be represented by the equation:
$120 = 300 channels × $0.20 per channel × m
where "m" is the number of months Sharon has to subscribe to the satellite service to break even.
Simplifying the equation, we get:
m = $120 ÷ ($0.20 × 300 channels) = 2
Therefore, Sharon will have to subscribe to the satellite service for 2 months to break even. After that, she will start saving $0.20 per channel per month compared to her cable service.
the function operation and then find the domain.
The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).
The Domain of function:The domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined.
In other words, it is the set of values of x for which the function has a corresponding output value (also known as the dependent variable).
Here we have
f(x) = 4x + 3
g(x) = x² - 5x + 6
Then f(x) · g(x) can be calculated as follows
=> (4x + 3) [ x² - 5x + 6 ]
Using distributive property, we get:
=> 4x (x² - 5x + 6) + 3(x² - 5x + 6)
=> 4x³ - 20x² + 30x + 3x² - 15x + 18
=> 4x³ - 17x² + 15x + 18
Hence, f(x).g(x) = 4x³ - 17x² + 15x + 18
The domain of the function f(x) = 4x³ - 17x² + 15x + 18 is all real numbers since there are no restrictions or conditions that would make the function undefined for any value of x.
Therefore,
The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).
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The price of petrol is increased from R12,58 per litre to R13,28 per litre. Determine the percentage increase in the price.
Answer: 5.56%
Step-by-step explanation:
Deduct the original price from the price that reflects the increase to get the increment.
R13 28-R 12,58 = R, 70
Place the increase on the original price and multiply by 100%
R, 70/R 12,58 x 100/1
Percentage increase = 5.56%
To check, calculate 5.56%o of 12,58 and add to 12,58, you will get R13,28
Percy took a total of 12 quizzes over the course of 4 weeks. How many weeks of school will Percy have to attend this quarter before he will have taken a total of 15 quizzes? Assume the relationship is directly
Answer:
5 weeks
Step-by-step explanation:
To solve this problem, we can use the idea of proportionality. We know that the number of quizzes Percy takes is directly proportional to the number of weeks he attends school. This means that we can set up a proportion:
12 quizzes / 4 weeks = 15 quizzes / x weeks
We can cross-multiply to get the following:
12x = 60
Then we can solve for x:
x = 60/12 = 5
Therefore, Percy will have to attend 5 weeks of school to take a total of 15 quizzes.
PLEASE HELP IM STUCK
A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 40% discount. Otherwise, you get a 25% discount. The table shows the results of 500 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25% discount, does this seem like an appropriate method? Explain.
Discounts
1 2 3 4 5 6 7 8 9
Card number 10 47 52 47 59 66 54 51 47 45 32
The relative frequency for a 10% discount is []
The total number of customers is 500. We need to find the number of customers who received each discount.
For a 10% discount, customers received cards labeled 2, 4, 8, or 10. The total number of customers who received one of these cards is:
47 + 47 + 51 + 45 = 190
Therefore, the relative frequency for a 10% discount is:
190 / 500 = 0.38 or 38%
For a 40% discount, customers received cards labeled 7 or 9. The total number of customers who received one of these cards is:
54 + 47 = 101
Therefore, the relative frequency for a 40% discount is:
101 / 500 = 0.202 or 20.2%
For a 25% discount, customers received cards labeled 1, 3, 5, or 6. The total number of customers who received one of these cards is:
52 + 59 + 66 + 32 = 209
Therefore, the relative frequency for a 25% discount is:
209 / 500 = 0.418 or 41.8%
Based on the table, it seems that a large percentage of customers are receiving the 25% discount (41.8%). If the manager of the store wants approximately half of the customers to receive this discount, it may not be appropriate to use this method. However, it is also important to consider other factors, such as the store's profit margins and overall sales volume, when determining the best discount strategy.
Identify the total number of customers, which is given as 500 in the table.
For the 10% discount, add up the number of customers who received cards labeled 2, 4, 8, or 10. In the table, the corresponding counts are given as 47, 47, 51, and 45, respectively. Add these numbers together to get the total number of customers who received a 10% discount:
47 + 47 + 51 + 45 = 190
To find the relative frequency for a 10% discount, divide the number of customers who received a 10% discount (190) by the total number of customers (500):
190 / 500 = 0.38 or 38%
Therefore, the relative frequency for a 10% discount is 38%.
Repeat steps 2 and 3 for the other two discounts. For the 40% discount, add up the number of customers who received cards labeled 7 or 9, which are given as 54 and 47 in the table, respectively:
54 + 47 = 101
Then, find the relative frequency for a 40% discount by dividing the number of customers who received a 40% discount (101) by the total number of customers (500):
101 / 500 = 0.202 or 20.2%
Therefore, the relative frequency for a 40% discount is 20.2%.
Finally, for the 25% discount, add up the number of customers who received cards labeled 1, 3, 5, or 6, which are given as 52, 59, 66, and 32 in the table, respectively:
52 + 59 + 66 + 32 = 209
Then, find the relative frequency for a 25% discount by dividing the number of customers who received a 25% discount (209) by the total number of customers (500):
209 / 500 = 0.418 or 41.8%
Therefore, the relative frequency for a 25% discount is 41.8%.
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x-3/3 - x-2/3 = 1/9 (find the value of x)
Hence, in answering the stated question, we may say that equation (3x - 9 - 3x + 6)/9 = 1/9 => -3/9 = 1/9
What is equation?A math equation is a technique that uses the equals symbol (=) to demonstrate equivalence between two statements. An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. The equal sign separates the integers 3x + 5 and 14 in the equation 3x + 5 = 14. To explain the connection between the two sentences written on opposing sides of a letter, a mathematical formula might be employed. The logo and the software are frequently the same. For instance, 2x - 4 = 2.
To solve this equation, we can start by simplifying the left-hand side using a common denominator:
[tex](x - 3)/3 - (x - 2)/3 = 1/9\\(3(x - 3) - 3(x - 2))/9 = 1/9\\[/tex]
[tex](3x - 9 - 3x + 6)/9 = 1/9\\-3/9 = 1/9[/tex]
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The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a
mean diameter of 22 mm and a standard deviation of 2.5 mm. After they are picked and washed, tomatoes with
diameter of at most 15 mm or at least 30 mm are rejected and not sold. What proportion of such tomatoes are
rejected?
Find the z-table here.
0.0033
0.0201
0.9799
0.9967
The proportion of cherry tomatoes that are rejected due to being at most 15 mm or at least 30 mm in diameter is approximately 0.0040, or 0.4%.
We need to first determine the z-scores corresponding to these values in order to determine the percentage of cherry tomatoes that are rejected because they are either at most 15 mm or at least 30 mm in diameter. Where x is the diameter, is the mean diameter, and is the standard deviation, we can apply the formula.
The z-score for a 15 mm diameter is z = (15 - 22) / 2.5 = -2.8. The z-score for a 30 mm diameter is z = (30 - 22) / 2.5 = 3.2.
As the tomatoes that go outside the range between these two z-scores are the ones that are rejected, we are interested in learning what percentage of tomatoes do so. The area under the normal curve outside of this range can be calculated using a calculator or a conventional normal distribution table.
Left of z = -2.8 is the area of 0.0033, while right of z = 3.2 is the area of 0.0007. We multiply these two probabilities together to get the total area outside of this range: 0.0033 + 0.0007 = 0.0040.
As a result, 0.4%, or around 0.0040, of cherry tomatoes are rejected because they have a diameter of at least 30 mm and no more than 15 mm.
The option that comes the closest to the correct response is 0.0033. That is not the appropriate answer since it only considers the region to the left of z = -2.8 and excludes the region to the right of z = 3.2.
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Suppose q=ce kt satisfies the differential equation dq dt=−0. 03q. What (if anything) does this tell you about the values of c and k
This tells us that c and k must be related such that ck = -0.03.This differential equation tells us that the rate of change of q with time (dq/dt) is equal to a negative constant, -0.03.
This differential equation tells us that the rate of change of q with time (dq/dt) is equal to a negative constant, -0.03. This means that q is decreasing over time. Therefore, c and k must be related such that ck = -0.03, since this constant is the product of c and k. This tells us that c and k must be related, but does not tell us the exact value of either c or k.
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A roasted turkey is taken from an oven when its temperature has
reached 190∘Fahrenheit and is placed on a table in a room where the
temperature is 75∘ Fahrenheit.
Recall the formula is T(t)=Ae^kt+Ts
If the temperature of the turkey is 159∘ Fahrenheit after half an hour, what is its rate of cooling in minutes? Give answers accurate to at least 5 decimal places.
rate of cooling of the turkey in minutes is 41.13545
The formula for finding the rate of cooling of a roasted turkey is provided in the question. It is given as:T(t) = Ae^kt + TsThe following are the variables:• T(t) represents the temperature of the turkey at time t• A represents the initial temperature of the turkey• k is the cooling rate• Ts is the temperature of the environmentNow, using the values given in the question, we can get the rate of cooling of the turkey as follows:T(t) = Ae^kt + TsLet us replace the variables with the given values:159 = A*e^(0.5k) + 75 => A*e^(0.5k) = 84 => A = 84/e^(0.5k)Let us substitute the value of A in the initial equation:T(t) = Ae^kt + Ts => 190 = A*e^(k*0) + 75 => 190 = A => A = 190So, we can get the value of k using the values of A from the above two equations:84/e^(0.5k) = 190 => e^(0.5k) = 84/190 => e^(0.5k) = 0.4421052631578947 => k = (ln0.4421052631578947) / 0.5 = -0.4662195477817674So, the equation for the temperature of the turkey as a function of time is:T(t) = 190e^(-0.4662195477817674*t) + 75To find the rate of cooling of the turkey, we need to take the derivative of the above equation with respect to t, which gives:dT/dt = -87.75877428502014*e^(-0.4662195477817674*t)This is the rate of cooling of the turkey. To find the rate of cooling in minutes, we substitute t = 0.5 in the above equation and simplify to get:dT/dt = -41.135453873444264Therefore, the rate of cooling of the turkey in minutes is 41.13545 (accurate to at least 5 decimal places).
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Find the values of the constants b and c, so that y (t) = te^-3t is a solution tothe following differential equation:y" + by' + cy = 0Fill in the blanks with the correct numbers for the values.of the constants b and c:
The value of the constants b and c, so make y(t) = te^-3t is a solution to the differential equation y" + by' + cy = 0 are b = 3 + 2√(c-3) and c = 3 + (b-3)^2.
The differential equation given is: y'' + by' + cy = 0. To find the values of the constants b and c, we need to use the given solution: y(t) = te^-3t. To begin, we can use the product rule for derivatives to write the second derivative of y(t) as follows:
y''(t) = e^-3t(t^2 - 3t + 3)
Now, we can substitute this expression into the original differential equation:
e^-3t(t^2 - 3t + 3) + bte^-3t + ce^-3t = 0
Next, we can rearrange and factor this equation as follows:
e^-3t(t^2 + (b-3)t + (c-3)) = 0
This equation can be satisfied if and only if the polynomial in parentheses has a root at t = 0, which implies that the discriminant of the polynomial must be equal to zero:
(b-3)^2 - 4(c-3) = 0
Finally, we can solve this equation for b and c, giving us:
b = 3 + 2√(c-3)
c = 3 + (b-3)^2
Therefore, the constants b and c that make y(t) = te^-3t a solution to the differential equation are b = 3 + 2√(c-3) and c = 3 + (b-3)^2.
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