Answer:
d) 360
Step-by-step explanation:
To solve this problem, we can use a Venn diagram. Let R, C, and J represent the sets of students who like rock, country, and jazz, respectively. We can fill in the diagram with the given information:
J
/ \
/ \
/ \
RC-----C
\ /
\ /
\ /
R
We know that:
The total number of students surveyed is 500.
9 students like all three types of music, so we can put 9 in the intersection of all three sets (RCJ).
24 like rock and country, so we can put 24 in the intersection of R and C (RC).
29 like rock and jazz, so we can put 29 in the intersection of R and J (RJ).
29 like country and jazz, so we can put 29 in the intersection of C and J (CJ).
We can calculate the number of students who like only one type of music by subtracting the number of students who like two or three types of music from the total number of students surveyed:
Total = R + C + J - RCJ
500 = 204 + 164 + 129 - 9
We can use this equation to solve for R, C, and J:
R = 204 - 24 - 29 - 9 = 142
C = 164 - 24 - 29 - 9 = 102
J = 129 - 29 - 29 - 9 = 62
So there are 142 students who like rock only, 102 students who like country only, and 62 students who like jazz only. Therefore, the total number of students who like exactly one type of music is:
142 + 102 + 62 = 306
Therefore, the answer is (d) 360.
General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot?General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot?
We may calculate the distance from Carlos and the tree as [tex]D = 781.23[/tex] ft using trigonometric relationships.
Is calculus more difficult than trigonometry?Many functions in trigonometry offer excellent illustrations of how calculus may be used in practical situations. By the way, basic trigonometry primarily deals with the algebraic features of circular functions, therefore basic calculus is not always simpler than basic trigonometry. On the other hand, calculus is fundamentally non-algebraic in nature.
Trigonometry: SOH CAH TOA or not?The mnemonic SOHCAHTOA makes it simple for us to recall the three primary trigonometric ratios.
Then one of the cathetus of the triangle is equal to:
[tex]275ft - 6ft = 269ft[/tex]
That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.
Then we can use the relation:
Where:
[tex]a=19^{0}[/tex]
opposite cathetus [tex]=269ft[/tex]
adjacent cathetus [tex]=D[/tex]
Replacing that, we get
[tex]tan(19^{0} ) = 269ft/D[/tex]
Solving for D, we get:
[tex]D = 269ft/tan(19^{0} ) = 781.2ft[/tex]
So we conclude that Carlos is at [tex]781.23[/tex] ft of the tree.
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4 sec x csc x = 8 csc x
Find all solutions in the interval of [0,2pi)
Enter results in radians.
As a result, x = pi/6 is the only answer in the range [0,2pi).
What is the radian of a pi?When quantifying the angles of trigonometry or periodic functions, radians are frequently taken into account. Radians are always expressed in units of pi, with pi equivalent to either 3.14 or 22/7.
We can start by simplifying the left-hand side of the equation using the identity:
csc x = 1/sin x
4 sec x csc x = 4(1/cos x)(1/sin x) = 4/(cos x sin x)
Substituting this back into the original equation, we get:
4/(cos x sin x) = 8 csc x
Multiplying both sides by cos x sin x, we get:
4 = 8 sin x
Dividing both sides by 8, we get:
sin x = 1/2
This means that x is either pi/6 or 5pi/6, since these are the two angles in the interval [0,2pi) where sin x = 1/2.
However, we need to check if these solutions satisfy the original equation.
For x = pi/6:
4 sec x csc x = 4 sec(pi/6) csc(pi/6) = 4(2) (2/√3) = 16/√3
8 csc x = 8 csc(pi/6) = 8(2/√3) = 16/√3
So, x = pi/6 is a solution.
For x = 5pi/6:
4 sec x csc x = 4 sec(5pi/6) csc(5pi/6) = 4(-2) (-2/√3) = 16/√3
8 csc x = 8 csc(5pi/6) = 8(-2/√3) = -16/√3
So, x = 5pi/6 is not a solution.
Therefore, the only solution in the interval [0,2pi) is x = pi/6.
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Explain why y−7x−5=2/6.
Answer:
the expression
y -7/x-5 = 1/3 or 2/6
Step-by-step explanation:
Cross multiplying both sides:
3(y-7) = x - 5
3y - 21 = x - 5
3y - x = 21 - 5
3y - x = 16
The simplified equation is 3y-x=16.
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= -4.9t^2+29.4t +1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?
In response to the given question, we have that The baseball takes 3 function seconds to reach its highest point as a result.
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The formula for the height of the baseball is [tex]h(t) = -4.9t2 + 29.4t + 1.[/tex]
A = -4.9 and B = 29.4 in this instance. The vertex's x-coordinate is as follows:
[tex]x = -b/2a = -29.4/(2*(-4.9)) = 3[/tex]
We need to assess h(3) in order to determine the maximum height:
[tex]h(3) = -4.9(3)^2 + 29.4(3) + 1 = 44.1[/tex]
Hence, the baseball may reach a height of up to 44.1 metres.
The x-coordinate of the vertex, which we discovered to be 3, may be used to determine how long it takes the baseball to reach its maximum height. The baseball takes 3 seconds to reach its highest point as a result.
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Express the following expression as a function of an acute angle less than 45°:
cot (-859°)
cot (-859°) can be expressed as cot 41° an acute angle which is less than 45°
What is trigonometry?Trigonometry is used in navigation directions. Estimate the direction you need to place your compass to get a straight line. With the help of a compass and navigation trigonometric functions, it's easy to find a place or find the distance to see the horizon.
What is mathematical expression?A Mathematical Statement which contains numbers and variables.
Angle: The two straight lines meeting at the vertex(a common point)
According to the question:
cot (-859) can be expressed as:
cot (-859 + 360x2)= cot (-859 +720)= cot (139)= cot (180 -139)= cot 41°(or)cot(-859) = cot(-859 + 180°x5)= cot (859 +900)= cot (41)°
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Using a protractor and a ruler draw a triangle with a side length of 4 inches that is between angles of 50 and 65
Using a protractor and a ruler we drew a triangle with a side length of 4 inches that is between angles of 50 and 65 as shown in the figure.
What are triangles?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. The total of a triangle's three sides is the perimeter of the triangle. The space a triangle occupies is known as its area. The area is obtained by taking half of the product of base and altitude.
Now we are asked to draw a triangle with a side length of 4 inches that is between angles of 50° and 65°.
First, let us mark the 50° angle.
Draw a straight line of 4 inches using the ruler as the base.
Keep the protractor on top at one of the ends of the line.
Mark the 50° angle.
Draw a straight line passing through the marked point using the ruler.
Now move the protractor to the other end of the line.
Mark the angle 65°.
Draw a straight line passing through the marked point using the ruler until it meets the 50° angle line.
This is a triangle with angles of 50 and 65 degrees.
Therefore, using a protractor and a ruler we drew a triangle with a side length of 4 inches that is between angles of 50 and 65 as shown in the figure.
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The nth term of a sequence is 3n + 1.
Work out the 5th term of this sequence.
Answer:
[tex]3[/tex]×[tex]5[/tex][tex]=15[/tex]
[tex]15+1=16[/tex]
A company that uses job order costing reports the following information. Overhead is applied at the rate of 60% of direct materials. The company has no beginning Work in Process or Finished Goods inventories. Jobs 1 and 3 are not finished by the end of March, and Job 2 is finished but not sold by the end of March. Determine the total dollar amount of Finished Goods Inventory at the end of March.
Answer: To determine the total dollar amount of Finished Goods Inventory at the end of March, we need to calculate the total cost of the jobs that have been completed during March and have been transferred to the Finished Goods Inventory.
From the information given, we know that the company has no beginning Work in Process or Finished Goods inventories, so all the costs incurred during March are related to the jobs started during the month.
Let's start by calculating the total cost of Job 2, which is finished but not sold by the end of March. We will then use this cost to calculate the total cost of the jobs that have been completed during March and transferred to the Finished Goods Inventory.
Job 2:
Direct materials: Rs. 10,000
Direct labor: Rs. 8,000
Overhead applied: 60% x Rs. 10,000 = Rs. 6,000
Total cost of Job 2: Rs. 24,000
Now, let's calculate the total cost of the jobs that have been completed during March:
Job 1:
Direct materials: Rs. 6,000
Direct labor: Rs. 4,000
Overhead applied: 60% x Rs. 6,000 = Rs. 3,600
Total cost of Job 1: Rs. 13,600
Job 3:
Direct materials: Rs. 8,000
Direct labor: Rs. 5,000
Overhead applied: 60% x Rs. 8,000 = Rs. 4,800
Total cost of Job 3: Rs. 17,800
Total cost of jobs completed during March: Rs. 13,600 + Rs. 17,800 = Rs. 31,400
Since the company has no beginning Finished Goods Inventory, the total cost of the jobs completed during March and transferred to the Finished Goods Inventory is equal to the total cost of the Finished Goods Inventory at the end of March.
Therefore, the total dollar amount of Finished Goods Inventory at the end of March is Rs. 31,400.
Step-by-step explanation:
Everything step by step
The number of touchdowns scored by the defense of the professional football team in the season was C. 10 touchdowns.
How to find the number of touchdowns ?The team scored a total of 242 points, and the defense scored about 24% of those points, which is:
0.24 x 242 = 58.08
This means that the defense scored approximately 58 points during the season. If a touchdown is worth 6 points, we can find the number of touchdowns scored by the defense by dividing the total number of points scored by 6:
58 / 6 = 9.67
So the defense scored approximately 9.67 touchdowns during the season. Since we can't have a fraction of a touchdown, the closest whole number answer would be 10 touchdowns.
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In a certain weather forecast, the chances of a thunderstorm are stated as "5 in 23." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Therefore, the likelihood of a thunderstorm is roughly 0.2174, or a 21.74% chance that one will occur.
What is probability?The study of random events or phenomena falls under the category of probability, which is a branch of mathematics. It is a way to quantify the possibility or likelihood of an event happening. A number between 0 and 1, where 0 denotes an improbable occurrence and 1 denotes a certain event, is used to express probability. By dividing the number of favorable outcomes by the total number of possible outcomes, one can determine the probability of an occurrence. In many disciplines, including statistics, economics, engineering, and science, probability is used to make predictions and well-informed choices in uncertain situations.
given
We must divide the amount of beneficial outcomes (chances of a thunderstorm) by the total number of possible outcomes in order to express the suggested degree of likelihood as a probability value between 0 and 1 inclusive.
When the likelihood of a thunderstorm is stated as "5 in 23," it indicates that out of a possible 23, 5 outcomes are likely to be favorable.
Therefore, the likelihood of a rainstorm is:
P (thunderstorm) is the ratio of the number of successful outcomes to all other possible outcomes.
Thunderstorm P(thunder) = 5 / 23
As a result, the probability value for the indicated degree of likelihood can be expressed as:
P(thunderstorm)= 5/230.2174
Therefore, the likelihood of a thunderstorm is roughly 0.2174, or a 21.74% chance that one will occur.
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scatter plot, label each axis, and choose a
Over the last 8 snowstorms, Julian recorded the amount of
snowfall to the nearest inch and the amount of time it took him
to shovel his driveway. He recorded the data in the table.
Snowfall (in.)
2
5
8
18
10
6
12
14
Time Shoveling
1
2
2
5
3
2
4
4
Answer:
Have a good day and time and I6ykjjuu7ttggfszd to the 5tjyyv
first increase and then rework each by decreasing
a. 400 by 20%
b. 650 by 30%
c.820 by 45%
d. 150 by 2,5%
e. 300 by 5%
f. 420 by 2,5%
Answer:
a. 480 Then 384
b. 845 Then 591.5
c. 1,189 Then 653.95
d. 153.75 Then 149.90625
e. 315 Then 299.25
f. 430.5 Then 419.7375
K
A golf ball is hit with an initial velocity of 140 feet per second at an inclination of 45° to the horizontal In physics, it is established that the height h of the golf ball is given by the function
- 32x²
h(x)=-
140²
where x is the horizontal distance that the golf ball has traveled Complete parts (a) through (g)
(a) Determine the height of the golf ball after it has traveled 100 feet
h= feet (Round to two decimal places as needed)
Answer:
6.25 seconds
Step-by-step explanation:
Using the the equation
h = 100t − 16t^2
The ball hits the ground, when h = 0, solving below equation:
100t − 16t^2 = 0
4t(25 - 4t) = 0
t = 0 seconds, this is the starting point when ball was hit
25 - 4t = 0 ⇒ 4t = 25 ⇒ t= 25/4 = 6.25 seconds later the ball hits the ground
i need help with this ecuation
Answer: y = 4/3x+1
Step-by-step explanation:
Answer:
y=4/3 + 1
Step-by-step explanation:
There are different ways to do this for finding slope, you can use the formula or you can do rise over run. How to find rise over run you count how many places up so our current place is (-3,-3) and we are trying to find (3,5) so if you were to start with rise, you rise 8 places then run you go either left or right in our case right, you move 6 places. So our fraction would be 8/6 or simplified 4/3. But using the formula to make sure we got the right answer, our formula is y2-y1/x2-x1 so that would look like 5- -3/3- -3. To solve on our top side two negatives give us a positive so the top is 8 and then bottom is 6 so we get 8/6 or 4/3. But our slope intercept would be y= 4/3x +1.
8. Kelli runs 2 1/4miles on Monday.
Each day after she runs the same 1 1/3 mile route every morning. Her goal is to run at least 4 miles by the
end of the week.
Part A: Which inequality represents the
least number of days that Kelli
needs to run to reach her goal?
Part B: What is the least number of
days after Monday that Kelli needs
to run to reach her goal?
The inequality which represents the least number of days that Kelli needs to run to reach her goal is
2 1/4 + 1/3d ≥ 4.
The least number of days after Monday that Kelli needs to run to reach her goal is 5.25 days
Which inequality represents the least number of days that Kelli needs to run to reach her goal?Monday= 2 1/4 miles
Other days of the week = 1/3 miles
Her goal =™4 miles
Number of days = d
2 1/4 + 1/3d ≥ 4
subtract 2 1/4 from both sides
1/3d = 4 - 2 1/4
1/3d = 4 - 9/4
1/3d = 16-9 /4
1/3d = 7/4
divide both sides by 1/3
d = 7/4 ÷ 1/3
d = 7/4 × 3/1
= 21/4
d = 5.25 days
Hence, Kelli will reach her goal in at least 5.25 days.
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Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Two times a number increased by 5 is 15. a. 2n(5) = 15 n = 1.5 c. 2n + 5 = 15 n = 20 b. 2n + 5=15 n = 5 d. n + 5 = 15 n = 10 Please select the best answer from the choices provided
Please help on this fast
Answer:
21 miles per gallon
Step-by-step explanation:
find the gradient of the line:
change in y = 105 - 21 = 84
change in x = 5 - 1 = 4
gradient is change in y/ change in x
= 84/4 = 21
Select ALL the true equations.
(a) 5 + 0 = 0
(b) 15 ⋅ 0 = 0
(c) 1.4 + 2.7 = 4.1
(d) 2/3 ⋅ 5/9 = 7/12
(e) 4 & 2/3 = 5 − 1/3
Answer:
b,c,e
Step-by-step explanation: a: 5+0=5
b:15x0 =0
c: 1.4+2.7=4.1
d:2/3 x 5/9
e:4& 2/3 =5-1/3
Write an expression for the shaded region.
The expression for the given Venn Diagrams are:
(AпB) U (BпC)(AUC) - (AnB) +(AnBnC)(AUC) - [(AnC) + (BnC)] + (AnBnC)What is a Venn Diagram?A Venn diagram employs circles or other shapes that overlap to show the logical connections between two or more groups of objects.
They frequently serve to visually group objects while highlighting how they differ and how they are similar.
The union of two sets A and B is a new set that contains all the elements that are in A or in B or in both. It is denoted by A ∪ B.
Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.
The intersection of two sets A and B is a new set that contains all the elements that are in both A and B. It is denoted by A ∩ B.
Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.
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Given the following table with selected values of f (x) and g(x), evaluate f (g(2)).
x –5 –4 –1 2 4 7
f (x) 0 2 7 –1 –6 –4
g(x) –8 –1 2 4 7 1
–4
2
4
–6
Looking at the table again, we can see that f(4) is -6. Thus, f (g(2)) is -6.
What is value?Value is the worth of something, based on its importance, usefulness, or desirability. It is something that has a desired quality, such as excellence, utility, or desirability. Value can be physical, such as a commodity, or intangible, such as respect, loyalty, or knowledge. Value is determined by both the individual and the society in which they live. Value can be assigned to both tangible and intangible things, such as a house, an education, or a friendship. Value is a subjective measure and can vary greatly from person to person.
The answer is -6. To evaluate f (g(2)), we need to determine what g(2) is first. Looking at the table, we can see that g(2) is 4. Therefore, we need to find the value of f(4). Looking at the table again, we can see that f(4) is -6. Thus, f (g(2)) is -6.
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How do you solve problems with integers?
first, you must identify which operation you need to fo first.
then, you need to think about which ______ _____ you need to use.
To solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
What is integers ?
Integers are a set of whole numbers that include both positive and negative numbers, as well as zero. Integers can be represented on a number line that extends infinitely in both directions.
To solve problems with integers, you need to understand the basic operations such as addition, subtraction, multiplication, and division. You also need to know the rules and properties of integers, such as the commutative, associative, and distributive properties, as well as the rules for adding, subtracting, multiplying, and dividing positive and negative integers.
When solving a problem with integers, you should first identify which operation you need to perform first based on the order of operations. This order is typically remembered with the acronym PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). Once you have identified the operation, you can use the appropriate mathematical technique to solve the problem.
Therefore, to solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
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Divide Katrina's number line into
eighths. Divide Eric's number line into
fourths. Show a point on Katrina's
number line that is less than 1. Show
a point on Eric's number line that is
greater than 1. Write fractions to label
the points you picked.
1. A point less than 1 in Katrina's number line is [tex]\frac{3}{8}[/tex]
2. A point greater than 1 in Eric's number line is 1[tex]\frac{1}{4}[/tex]
What is a number line and how do you identify point less or greater than 1?A number line is a straight line with numbers placed at equal distances from each other.
To identify a line less than 1 in a number line divided into 8, we need to know the value of what each point would be
Each values in Katrina's number line should be 0, [tex]\frac{1}{8}[/tex], [tex]\frac{2}{8}[/tex] , [tex]\frac{3}{8}[/tex], [tex]\frac{4}{8}[/tex], [tex]\frac{5}{8}[/tex], [tex]\frac{6}{8}[/tex], [tex]\frac{7}{8}[/tex] 1
To identify the line greater than 1 in a number line divided into 4, we need to know the values of what each points would be
Each values in Eric's number line should be 1, 1[tex]\frac{1}{4}[/tex], 1[tex]\frac{2}{4}[/tex], 1[tex]\frac{3}{4}[/tex], 2
Check the images below to get a proper view of how your number line should look like.
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f(x)=−5x3−4x2+8x and g(x)=−4x2+8, find (f−g)(x) and (f−g)(−2).
Answer:
(f-g)(x) = -5x^3 + 8x - 8.
(f-g)(-2) = 16.
Step-by-step explanation:
To find (f-g)(x), we need to subtract g(x) from f(x) and simplify:
(f-g)(x) = f(x) - g(x)
= (-5x^3 - 4x^2 + 8x) - (-4x^2 + 8)
= -5x^3 - 4x^2 + 8x + 4x^2 - 8
= -5x^3 + 8x - 8
Therefore, (f-g)(x) = -5x^3 + 8x - 8.
To find (f-g)(-2), we substitute x = -2 into the expression we just found:
(f-g)(-2) = -5(-2)^3 + 8(-2) - 8
= -5(-8) - 16 - 8
= 40 - 24
= 16
Therefore, (f-g)(-2) = 16.
How much would 17 computers, 18printers, 5DVDs, and 30 cd’s cost ?
The cost for 17 computers, 18 printers, 5 DVDs, and 30 CDs would be around $12,125.
What is cost?Cost is the amount of money or resources that must be exchanged for goods, services, or activities. It is typically associated with the purchase of goods and services and related to production, labor, and other expenses. Cost is a crucial factor in business operations, as it affects both the budget and the profitability of any venture. In addition to monetary costs, businesses may also incur opportunity costs, which are the costs associated with foregoing alternative investments or activities.
The cost of 17 computers, 18 printers, 5 DVDs, and 30 CDs would depend heavily on the type, brand, and quality of the items being purchased. However, an estimate of the cost of these items can be made.
Computers can range from $200 to $2,000, depending on the type and specs. An average cost for 17 computers would be around $10,000. Printers can range from $50 to $500, depending on the type and specs. An average cost for 18 printers would be around $2,000. DVDs can range from $2 to $25, depending on the type and specs. An average cost for 5 DVDs would be around $50. CDs can range from $1 to $10, depending on the type and specs. An average cost for 30 CDs would be around $75.
In total, the cost for 17 computers, 18 printers, 5 DVDs, and 30 CDs would be around $12,125.
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Use the same values for t and q and your inspection from part b to determine the number of sides that should be contained in your envelope and your partner's envelope combined
Answer: From part b, we know that the number of sides in my envelope is t + q = 10 + 6 = 16, and the number of sides in my partner's envelope is 2t - q = 20 - 6 = 14.
To determine the number of sides in both envelopes combined, we add these values: 16 + 14 = 30.
Therefore, the combined number of sides in both envelopes is 30.
Step-by-step explanation:
A register has 5376 business cards to give out the register gives out an equal number of business cards in 48 days until there are no more business cards live how many business cards does the register give out each day a 111 business cards be 112 business cards C1 130 business cards D1 114 business cards you have to divide 48÷5376
Answer: 112 business cards
Step-by-step explanation:
We will divide the number of business cards by the number of days cards were handed out to see how many cards were handed out per day.
5,376 cards / 48 days = 112 business cards
QUESTION 18
Consider the following argument: If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's
nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it
isn't the case that Shaun eats popping candy while drinking a can of soda. What is the logical form of this argument?
O a. Affirming a disjunct
b. Denying the antecedent
O c. Affirming the consequent
d. Modus Tollens
Oe. Modus Ponens
If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it isn't the case that Shaun eats popping candy while drinking a can of soda. The logical form of this argument is denying the antecedent. The Option B is correct.
How is "denying the antecedent" a logical form in the statement?If we represent the argument in logical symbols, it would look like this:
P: Soda streams out of Shaun's nose when he eat candy Q: Soda does not streams out of Shaun's nose when he doesnt eat candyThe argument can be summarized as follows:
If P, then Q.
Not P.
Therefore, not Q.
This is the form of denying the antecedent, where the argument asserts that if P is true, then Q must also be true. However, the argument then proceeds to deny the antecedent by claiming that P is not true, and therefore, Q must not be true either.
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1) Write an algebraic expression, The quotient of g and 4 added to 15
2) Write an algebraic expression, 6 minus the difference of y and 3
3) Write an algebraic expression, the product of a number d and 8
The algebraic expressions for the given questions are found as:
1) g/4 + 15.
2) 6 - y + 3
3) d * 8
What are algebraic expressions?
A mathematical expression made up of variables, constant algebraic numbers, and algebraic operations are known as an algebraic expression. Everything with a variable value is anything whose value changes over time. Variables in expressions are often represented by letters of the alphabet. Finding the simplified term of the given expression is the goal of simplifying the algebraic expression. We must first understand how to join like terms, factor a number, and the order of operations before we can factorise or simplify the expression. When like terms are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.
1) The quotient of g and 4 is given by g/4.
Now, this is added to 15.
So the algebraic expression is g/4 + 15.
2) The difference between y and 3 is y - 3.
Now from 6, this difference is subtracted.
So the expression becomes,
6 - (y-3) = 6 - y + 3
3) The product of two numbers is found by multiplying the numbers.
So the expression is :
d * 8
Therefore the algebraic expressions for the given questions are found according to the given statements.
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Solve : select all answer that apply
|-4+5x|=16
x= -11
x = -12/5
x= 4/5
x= 4
x = 3/4
By solving the equation we know that the correct value of (D) x is 4.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The four mathematical operations of addition, subtraction, multiplication, and division are also used in simple equations, either singly or in combination.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the value of the variable x is 7.
So, solve for the given equation:
|-4+5x|=16
5x - 4 = 16
Now, by looking at the equation we can tell that the value of x needs to be 4 as follows:
5x - 4 = 16
5(4) - 4 = 16
20 - 4 = 16
16 = 16
Therefore, by solving the equation we know that the correct value of (D) x is 4.
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Complete question:
Solve : select all answers that applies
|-4+5x|=16
A. x= -11
B. x = -12/5
C. x= 4/5
D. x= 4
E. x = 3/4
For part b, both answers I got come up as incorrect so I need help figuring out what the correct answers are. Im not sure why they’re wrong, this is a Elementary Statistics homework problem
For the new height requirements, this branch of the military requires women's heights to be at least 2.52 in and at most 6.96in.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
We are given that;
Mean= 63.8 in
Standard deviation= 2.3 in
Requirement of women height= 58in - 80in.
Now,
To find the minimum and maximum height requirements for this branch of the military, we need to use the standard normal distribution formula, which converts any normal distribution to a standard normal distribution with a mean of 0 and a standard deviation of 1.
We can find the z-scores for the minimum and maximum heights as follows:
For the minimum height requirement:
z = (58 - 63.8) / 2.3 = -2.52
For the maximum height requirement:
z = (80 - 63.8) / 2.3 = 6.96
Using a standard normal distribution table or calculator, we can find the corresponding probabilities for these z-scores:
For a z-score of -2.52, the probability is 0.0059 or 0.59%
For a z-score of 6.96, the probability is very close to 1, or 100%
Therefore, the new height requirements for this branch of the military are:
At least 58 inches, which corresponds to a z-score of -2.52
At most 80 inches, which corresponds to a z-score of 6.96
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