Answer:
4 middle carriages have 162 passengers
Step-by-step explanation:
Since every 10 consecutive carriages have 398 passengers, then each carriage has 398/10 = 39.8 passengers.
Since there are 36 carriages in the train, then there are 36 * 39.8 = 1428 passengers in the train.
Therefore, there are 1400 - 1428 = -28 passengers missing.
This means that each carriage has 39.8 - (-28/36) = 39.8 + 0.78 = 40.58 passengers.
So, the 4 middle carriages have 4 * 40.58 = 162.32 passengers.
Rounding to the nearest whole number, we can say that 4 middle carriages have 162 passengers.
Answer:
192
Step-by-step explanation:
If a train with 36 carriages holds 1400 passengers, 398 in any 10 consecutive carriages, you want to know the number in the 4 middle carriages.
ModelThe first 30 carriages will hold 3·398 = 1194 passengers, so there must be 1400 -1194 = 206 in the remaining 6 carriages. The same would be true counting carriages from the other end.
Then the 10 +6 carriages at either end of the train must hold 398 +206 = 604 passengers. That leaves 1400 -2·604 = 192 passengers in the middle 4 carriages.
What is the answer to this problem solving for X? (12x-8=10x+6)
What is the sum of the measures of the interior angles of a 20-sided figure?
Responses
3,240°
360°
3,600°
180°
Answer:
3,240°
Step-by-step explanation:
The sum of the measures of the interior angles of a polygon with n sides can be found using the formula:
(n-2) * 180°
So, for a 20-sided figure, the sum of the interior angles would be:
(20-2) * 180° = 18 * 180° = 3,240°
help on both problems
Answer:
the shape is different
Step-by-step explanation:
you draw the shapes
a store sells cereal for $2.99 and milk for $4.99. a shopper wants to spend at least $12 but no more than $25 on groceries. what is one possible combination of cereal and milk the shopper can buy and still stay in their budget?
The possible combination of cereal and milk the shopper can buy and still stay in their budget is:
12 ≤ 2.99x + 4.99y ≤ 25 (x , y ∈ N)
Inequality:The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
"Information available from the question"
A store sells cereal for $2.99 and milk for $4.99.
A shopper wants to spend at least $12 but no more than $25 on groceries.
To find the possible combination of cereal and milk the shopper can buy and still stay in their budget.
Now, According to the question:
Let x represents the shopper buy and y represent the milk.
Then represents the inequality according to the information.
A store sells cereal for $2.99
It write 2.99x
And for the milk is 4.99y
So,
12 ≤ 2.99x + 4.99y ≤ 25 (x , y ∈ N)
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Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn.
The experimental probability of not selecting a heart is (D)P(not heart) = 77.5%
How to find the experimental probability ?The experimental probability that a heart is selected is:
= Number of times hearts was selected / Number of times Lisa drew a card
= 9 / 40
This then means that the experimental probability of not selecting a heart is:
= 1 - experimental probability of selecting a heart
= 1 - 9 / 40
= 31 / 40
= 0. 775
= 77. 5 %
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The question is:
Determine the experimental probability of not selecting a heart.
(A) P(not heart) = 9%
(B) P(not heart) = 10%
(C) P(not heart) = 67.5%
(D)P(not heart) = 77.5%
Camden just accepted a job at a new company where he will make an annual salary of $43000. Camden was told that for each year he stays with the company, he will be given a salary raise of $2000. How much would Camden make as a salary after 7 years working for the company? What would be his salary after tt years?
The solution is, the salary of the Luke after 10 years is 98000 dollars & the salary of the Luke after t years is 53000+4500t .
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
Given data:
* The starting salary of the Luke in the new company was,
S1 = 53000
* The salary raise given to Luke each year is,
R = 4500
(a). The salary of the Luke after 10 years is,
S = S1 +R*10
S = 53000 + ( 4500* 10)
S = 98000
Thus, the salary of the Luke after 10 years is 98000 dollars.
(b). After the t years,
S = S1 +R*t
S = 53000 + ( 4500* t)
S = 53000+4500t
Thus, the salary of the Luke after t years is 53000+4500t .
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6 Find the area of the figure. 5. 3 in. 10 in. 4 in. 7 in. A 101. 8 square inches B 43. 9 square inches C 64. 9 square inches D 78. 6 square inches
The area of the rectangle would be equal to the sum of the areas of these 12 squares.
The area of a rectangle is a measure of the amount of space it covers. It is calculated by multiplying the length and the width of the rectangle.
For a rectangle with sides of 3 cm and 4 cm, the area can be found by multiplying 3 by 4. The formula for finding the area of a rectangle is
=> A = l * w,
where l is the length and w is the width.
So, for the rectangle with sides 3 cm and 4 cm, the area would be
=> A = 3 * 4 = 12 square centimeters.
To visualize this, imagine a rectangle with sides of 3 cm and 4 cm. If you placed 12 squares of 1 cm each inside this rectangle, it would fill up the entire rectangle without any space left.
Complete Question:
Find the areas of the rectangles whose sides are:
(a) 3 cm and 4 cm
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point p partitions directed segment AB in the part to part ratio of 4:4. If A(5,-7) and B(1,-1), find the y-coordinate of P. Round your answer to 2 decimals
Using the fact that P is the midpoint of the segment AB, we will see that its y-value is -4.
How to find the y-coordinate of P?We know that point P partitions directed segment AB in the part to part ratio of 4:4.
Notice that the ratio is equivalent to 1:1
So point P is just the midpoint of the segment, remember that for a segment whose endpoints are (a, b) and (c, d), the midpoint is:
M= ( [a+ c]/2, [b + d]/2)
P is the midpoint of (5,-7) and (1,-1), then the value of the y-coordinate of P is:
y = (-7 + (-1))/2
y = (-7 - 1)/2
y = -4
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The temperature in Duluth, Minnesota was -23F at sunrise. By noon, the temperature had risen 19 degrees. What was the temperature (in degrees Fahrenheit) at noon?
Answer:
Step-by-step explanation:
-23 + 19 = -4
At noon the temperature was -4 degrees F.
7)
3)
5)
Determine if the two triangles are congruent. If they are, state how you know.
2)
1)
A
6)
SSS?
SAS?
Some triangle pairs are congruent triangles but some others are not, because:
Congruent; 2 pairs of corresponding angles and 1 corresponding side Congruent; 2 pairs of corresponding sides and 1 corresponding angleCongruent; 2 pairs of corresponding angles and 1 corresponding sideCongruent; 3 pairs of corresponding sidesNot congruent; only 2 pairs of corresponding sidesCongruent; 1 pair of corresponding side and 2 corresponding anglesNot congruent; only 3 pairs of corresponding anglesNot congruent; only 3 pairs of corresponding anglesA pair of triangles is congruent if they have one of these criterias:
SSS (three corresponding sides)SAS (2 pairs of corresponding sides and 1 pair of corresponding angle between those side pairs)ASA (2 pairs of corresponding angles and 1 pair of corresponding side between those angle pairs)AAS (2 pairs of corresponding angles and 1 pair of corresponding side not between the angles)HL (Congruent hypotenuse and 1 pair of corresponding side)Let's explore each triangle pairs we have:
Pair 1
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles .
Pair 1 meet ASA rules --> Congruent triangles
Pair 2
Pair 2 has 1 corresponding angle and 2 pairs of corresponding sides
Pair 2 meets SAS rules --> congruent triangles
Pair 3
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles.
Pair 3 meet ASA rules --> Congruent triangles
Pair 4
Pair 4 has 3 corresponding sides and meets SSS rules --> congruent triangles
Pair 5
Pair 5 only has 2 corresponding sides --> not congruent triangles
Pair 6
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides not between the angles.
Pair 6 meet AAS rules --> Congruent triangles
Pair 7
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 7 also has another 2 corresponding angles. In total, pair 7 has 3 corresponding angles.
Pair 7 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.
Pair 8
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 8 also has another 2 corresponding angles. In total, pair 8 has 3 corresponding angles.
Pair 8 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.
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please can you solve the question
`
Answer:
x = 115°
y = 50°
Step-by-step explanation:
it is an isosceles triangle, the angles at the base are congruent, x is the opposite angle of 115°, therefore the same value, to find y we subtract the two 65° angles from the sum of the internal angles of the triangle (180°) and we have 50 ° which is the value of Y, look at the figure to understand better
Help please (will mark as brainlest)
[tex] - a {x}^{2} + 2x + a - 5[/tex]
The value:[tex] - 183[/tex]
the length of a rectangle is 6 more than twice the width. the perimeter is 150 meters. find the length and width.
Answer:
The length is 52 meters and the width is 23 meters.
Step-by-step explanation:
Let l stand for length, and w stand for width.
l = 2w + 6
The length is 6 more than twice the width.
2l + 2w = 150
Twice the length plus twice the width is the perimeter of a rectangle.
2(2w + 6) + 2w = 150
4w + 12 + 2w = 150
6w + 12 = 150
6w = 138
w = 23
l = 2(23) + 6
l = 46 + 6
l = 52
thomas buys a case of bottled water. the case contains 36 bottles of water and costs $4.69. thomas will sell each bottle of water for $0.75 at a school event. how much profit will thomas earn if he sells all the bottles of water
Answer: $ 0.62
Step-by-step explanation:
First, find out the cost of each bottle:
$4.69/ 36 bottles = $0.1297
= $0.13
Therefore, the profit is:
$0.75 - $0.13 = $ 0.62
8. Given that cos 68° 0.743, what is the sine of the
complementary angle?
The sine of the complementary angle of 68° is 0.375.
What is a complementary angle?
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
The complementary angle of 68° is calculated as;
θ = 90 - 68°
θ = 22°
sin (22° ) = 0.375
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How many subsets are there of the set N = {1}?
Answer:
A Set With One Element
So any set with one element will have 2 subsets.
Step-by-step explanation:
complaints about an internet brokerage firm occur at a rate of 5 per day. the number of complaints appears to be poisson distributed. a. find the probability that the firm receives 6 or more complaints in a day. probability
The probability of a day in which the company receives 6 or more complaints is 0.3721 likely, or about 37.21%.
What is probability ?A subfield of mathematics called probability is concerned with the investigation of uncertain events. It is the measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. The higher the probability, the more likely it is that the event will occur.
Given that the number of complaints per day follows a Poisson distribution with a rate parameter λ = 5.
Assume X is a random variable that represents the daily complaint rate.
The probability of receiving 6 or more complaints can be calculated as follows:
we can calculate the probability of X being less than 6 complaints per day as follows:
P(X < 6) = F(5) = e^(-λ) * Σ(λ^k / k!, k=0 to 5)
where e is the base of the natural logarithm, Σ denotes the sum from k=0 to 5, and k! denotes the factorial of k.
Substituting the value of λ = 5, we get:
P(X < 6) = e^(-5) * Σ(5^k / k!, k=0 to 5)
= 0.0337 + 0.1404 + 0.1755 + 0.1463 + 0.0916 + 0.0404
= 0.6279
Therefore, the probability of receiving 6 or more complaints in a day is:
= 1 - 0.6279
= 0.3721
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Travis decided to make a frame for his birthday. The frame will be cut out of a piece of steel, and the final area of the frame should be 30in². The inside of the frame has to be 11in by 6 in The area of the piece of steel before cutting out the frame is A = (11+2x)(6+2x)in²
the width of the frame is 0.806 inches.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given this, Travis decided to make a frame for his birthday. The frame will be cut out of a piece of steel, and the final area of the frame should be 30in².
Since,
Area of frame = total area - cut out area
In our case, it is given that,
Total area = (11+2x)(6+2x)in²
cut out area = 11*6 = 66
So,
30 = (11+2x)(6+2x) - 66
(11+2x)(6+2x) = 96
66 + 12x +22x +4x² = 96
4x² + 34x -30 = 0
x = 0.806 in
therefore. the width of the frame is 0.806 inches.
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Complete question:
The double number line shows that Henrik has a mass of 60\,\text{kg}60kg60, start text, k, g, end text. A double number line with 2 tick marks. The line labeled Mass, kilograms, reads from left to right: 0, 60. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. A double number line with 2 tick marks. The line labeled Mass, kilograms, reads from left to right: 0, 60. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. Complete the table to show different percentages of Henrik's mass. Mass (\text{kg}kgstart text, k, g, end text) Percentage 100\%100%100, percent of 60\,\text{kg}60kg60, start text, k, g, end text 20\%20%20, percent of 60\,\text{kg}60kg60, start text, k, g, end text 40\%40%40, percent of 60\,\text{kg}60kg60, start text, k, g, end text
The double number line is discussed below.
What is number line?In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
Given is a double number line.
A double number line diagram uses a pair of parallel number lines to represent equivalent ratios.
The locations of the tick marks match on both number lines.
The tick marks labeled 0 line up, but the other numbers are usually different.
The lines in a double number line diagram are similar to the number lines students have seen in earlier grades in that -
Numbers correspond to distances on the line (so that the distance between, say, 0 and 12 is three times the distance between 0 and 4).We can choose what scale to use (i.e., whether each interval represents 1 unit, 2 units, 5 units, etc.).The lines can be extended as needed.Therefore, the double number line is discussed above.
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What type of proof is used extensively in Geometry?
one-column proof
two-column proof
three-column proof
inductive proof
none of the above
The only sort of proof among the following options in the question that is frequently employed in geometry is the 'two-column' proof.
What is geometry?Geometry is the area of mathematics that deals with the characteristics of space and the shapes of particular things as well as the interactions between them in space.
A two-column geometric proof consists of a list of assertions and the justifications for each one's truth.
The statements are listed in a left-hand column, while the justifications for the statements are listed in a right-hand column.
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(Projectile Motion) Mary is outside her apartment building. She needs to pass her key to John, who is 6 m above the ground floor of the building. Mary has no time to run upstairs, so she throws the key towards John. Suppose the height, h m, of the key above the ground floor at time t seconds is given by h = -11t² + 20t + 1. Is it possible for John to catch the key? Justify your answer.
Match the exponent expression to it's correct solution.
The matching is as follow:
x²³ / x³ --> [tex]x^{20[/tex]
[tex]x^{14}/ x^{17}[/tex] --> 1/x³
[tex]x^{19}/ x^{33}[/tex] --> 1/[tex]x^{14[/tex]
[tex]x^{16}/ x^7[/tex] --> [tex]x^9[/tex]
What are exponent and Power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
Given:
We will use the Property of exponent and power
[tex]x^m/ x^n[/tex] = [tex]x^{m-n[/tex]
1. x²³ / x³
Using the property
x²³ - ³ = [tex]x^{20[/tex]
2. [tex]x^{14}/ x^{17}[/tex]
Using the property
= [tex]x^{14- 17}[/tex]
= [tex]x^{-3[/tex]
= 1/x³
3. [tex]x^{19}/ x^{33}[/tex]
Using the property
= [tex]x^{19-33}[/tex]
= [tex]x^{-14}[/tex]
= 1/[tex]x^{14[/tex]
4. [tex]x^{16}/ x^7[/tex]
Using the property
= [tex]x^{16-7}[/tex]
= [tex]x^9[/tex]
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If the first 4 questions are True/False and the last 4 questions are Multiple Choice (a, b, c, or d). What is the probability that they will get them all correct?
The probability of getting all 8 questions correct is 1/4096 or approximately 0.024%.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The probability of getting a True/False question correct is 1/2, since there are only two possible answers. The probability of getting a multiple-choice question correct is 1/4 since there are four possible answers.
So, for the first 4 True/False questions, the probability of getting them all correct is (1/2)⁴ = 1/16.
For the last 4 multiple-choice questions, the probability of getting them all correct is (1/4)⁴ = 1/256.
The total probability of getting all 8 questions correct is the product of the probabilities of getting each set of questions correct:
(1/16) x (1/256) = 1/4096
So, the probability of getting all questions correct is 1/4096 or about 0.024%.
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A new refrigerator has a price of $480.00. The store will discount the price by 15% if the purchaser pays in cash. What is the cash price of the refrigerator?
The cash price of the refrigerator is $408.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, a new refrigerator has a price of $480.00.
The store will discount the price by 15% if the purchaser pays in cash.
Now, the discount is
15% of 480
= 15/100 ×480
= 0.15×480
= 72
Now, 480-72
= $408
Therefore, the cash price of the refrigerator is $408.
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Draw a rectangle on graph paper with vertices whose coordinates are (-1, 2), (-1, -4), (3, -
4), and (3, 2).
(Graph paper provided in the jamboard in Q1).
Part A: Find the perimeter and area of the rectangle. Show your work.
Part B: Multiply the coordinates of the vertices of the rectangle by 3. State the new vertices.
Part C: Draw the rectangle whose vertices are those you found in Part B. Find the perimeter and area of this new rectangle.
Show your work.
Part D: Compare the perimeter of the rectangle in Part C to the perimeter of the original rectangle. (list each and then compare).
Part E: Compare the area of the rectangle in Part C to the area of the original rectangle. (list each and then compare).
The area of the new rectangle is 9 times the previous area and the perimeter of the new rectangle is 3 times the previous area
Part A: Find the perimeter and area of the rectangle.From the question, we have the following parameters that can be used in our computation:
(-1, 2), (-1, -4), (3, -4), and (3, 2).
See attachment for the points, where we have
Length = 4 and width = 6
Using area and perimeter formulas, we have
Area = 4 * 6 = 24
Perimeter = 2 * (4 + 6) = 20
Part B: Multiply the coordinates by 3Here, we have
New = (-3, 6), (-3, -12), (9, -12), and (9, 6).
Part C: Find the new perimeter and area of the rectangle.See attachment for the points, where we have
Length = 12 and width = 18
Using area and perimeter formulas, we have
Area = 12 * 18 = 216
Perimeter = 2 * (12 + 18) = 60
Part D: Comparison of the areasThe area of the new rectangle is 9 times the previous area
i.e. 216/24 = 9
Part E: Comparison of the perimetersThe perimeter of the new rectangle is 3 times the previous area
i.e. 60/20 = 3
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something2730 (question 7 only)
Answer:2737
Step-by-step explanation:
B and D meet at a 75º, as does A and C
9=p-12;29,30,31 with one is the answer I said 29 and was wrong help me !!!
Answer: The equation 9 = p - 12 can be solved for p by adding 12 to both sides:
p = 9 + 12 = 21.
So the correct answer to the question "29, 30, 31 with one is the answer" would be 30, as it is the only one that equals 21.
Step-by-step explanation:
5 subtracted from 1/3 of 20
IN FRACTIONS
The least common multiple of 3 and 5 is 15, so we convert 5 to 15/3.So the answer is 5/3.
The calculation in fractions:
1/3 of 20 = (1/3) * 20 = 20/3
5 subtracted from 1/3 of 20 = 20/3 - 5
To simplify the expression 20/3 - 5, we need to subtract 5 from 20/3 by finding a common denominator between 5 and 20/3. The least common multiple of 3 and 5 is 15, so we convert 5 to 15/3:
20/3 - 5 = 20/3 - 15/3 = (20 - 15)/3 = 5/3
So the answer is 5/3.
Fractions are a way of representing numbers as ratios of two integers. The top number of a fraction is called the numerator, and the bottom number is called the denominator. The numerator represents the number of parts of the whole that are being considered, and the denominator represents the number of equal parts that make up the whole.
For example, the fraction 1/2 represents 1 part out of 2 equal parts that make up the whole.
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which rule uses actual probability distributions to determine if hiring decisions have had adverse impact on minority groups? multiple choice question. the prima facie rule the standard deviation rule the four-fifths rule the bona fide occupational qualification rule
The prima facie rule uses actual probability distributions to determine if hiring decisions have had adverse impact on minority groups.
What do you mean by prima facie rule?The "prima facie" rule refers to a legal standard or a evidentiary standard used in the field of employment discrimination law. In the context of employment discrimination, a prima facie case refers to the minimum evidence required to establish a presumption of discrimination.
The term "prima facie" comes from Latin and means "at first sight" or "on its face." In other words, a prima facie case of discrimination is established if, at first sight, the evidence suggests that discrimination has taken place. Once a prima facie case has been established, the burden of proof shifts to the employer to provide a non-discriminatory explanation for the actions in question.
It is more commonly used in legal and ethical contexts to refer to a case or argument that is initially strong enough to establish a point, but may be challenged or overcome by further evidence or argument.
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convert 4582 base 10 to base 2
Answer:
458210 in binary
10001111001102
To convert decimal number 4582 to binary, follow these steps:
Divide 4582 by 2 keeping notice of the quotient and the remainder.
Continue dividing the quotient by 2 until you get a quotient of zero.
Then just write out the remainders in the reverse order to get binary equivalent of decimal number 4582.
Using the above steps, here is the work involved in the solution for converting 4582 to binary number:
4582 / 2 = 2291 with remainder 0
2291 / 2 = 1145 with remainder 1
1145 / 2 = 572 with remainder 1
572 / 2 = 286 with remainder 0
286 / 2 = 143 with remainder 0
143 / 2 = 71 with remainder 1
71 / 2 = 35 with remainder 1
35 / 2 = 17 with remainder 1
17 / 2 = 8 with remainder 1
8 / 2 = 4 with remainder 0
4 / 2 = 2 with remainder 0
2 / 2 = 1 with remainder 0
1 / 2 = 0 with remainder 1
Then just write down the remainders in the reverse order to get the answer, The decimal number 4582 converted to binary is therefore equal to :
1000111100110