The train travels an average 12 miles/hr
We always need to be working in the same units, so lets convert the trains speed to minutes since the time traveled is in minutes.
12 miles / 60 min = 0.2 miles/min
students who score within 22 points of the number 78 will pass a particular test. write this statement using absolute value notation and use the variable x for the score.
The statement using absolute value notation will be x - 78 ≤ 22.
The student will pass the test which scores 22 points for the number 78
Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.
In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.
Le the score of student be = x
Forming the absolute value notation -
This can be expressed as,
x - 78 ≤ 22.
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Brick San Antonio playing a game of counter Rick ha ome counter Selma ha twice a many counter a Rick Tony ha ix counter Leton Selma in total they have 54 counter the number of count a Rick ha: the number of count a Tony ha = 1: P work out the value of paid
The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let R represent the number of counters Rick has.
Let S represent the number of counters Selma has.
Let O represent the number of counters Tony has.
Let T represent total number of counters.
Translating the word problem into an algebraic equation, we have;
S = 2R .....equation 1.
O = 2R - 6 ......equation 2.
T = R + S + O ......equation 3.
Substituting equation 1 and equation 2 into equation 3, we have:
T = R + S + O
54 = R + 2R + 2R - 6
54 = 5R - 6
5R = 54 + 6
5R = 60
R = 60/5
R = 12 counters.
For Tony, the number of counters is given by:
O = 2R - 6
O = 2(12) - 6
O = 24 - 6
O = 18 counters.
In ratio form, we have:
O = 1:P
O = 1:(18/12)
O = 1:1.5
The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
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simplify the algebraic expressions completely.
7. (4-4). K
and
simplify the algebraic expression completely.
d+12-8/4+5
Answer:
see below
Step-by-step explanation:
7. (4-4). K =0
d+12-8/4+5 = d+12-2+5 =d+15
A line has a slope of –1/3 and a y-intercept of 5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
The answer in intercept form will be
[tex] - 1 \div 3 = 5 \div 3x + c \\ [/tex]
13. FURNITURE Sai is rearranging his furniture. He wants his couch to sit along the 20-foot wall,
labeled AC on the diagram. He wants the left side of his couch to sit at a point B so that the
ratio of AB to BC is 1:2. What distance from the left side of the wall should Randall place the left side of his couch?
The value of distance after calculating are AB = 4 ft and BC = 16 ft.
What is ratio?
A ratio is a comparison between two numbers or quantities. It is typically expressed as a fraction, with the first number being divided by the second number. Ratios are often used to compare values or to express a portion of a whole.
It is given in the question, that Ladd is rearranging his living room furniture. He wants his couch to sit along the 20-ft wall.
To find the length of AB and BC we need to relate them using the equations.
AB + BC = 20 ft (from the diagram) ----------- (Equation 1)
∵ AB : BC = 1 : 4
⇒ 4AB = BC
Substituting, BC = 4AB into equation 1.
AB + 4AB = 20 ft
5AB = 20 ft
AB = 4 ft
Plugging AB = 4 ft into equation 1.
4 + BC = 20
BC = 20 ft - 4 ft
BC = 16 ft
Thus, the value of sides AB = 4 ft and BC = 16 ft , and here AB and BC are in ratio 1:4.
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Multi step trig problem
The value of x is 14.28 units, this is determined using the trigonometric functions.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the sides and angles of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Consider the smaller triangle:
Sin (30) = Opposite side ÷ Hypotenuse
0.5 = Opposite side ÷ 10
Opposite side = 5
Consider the bigger triangle:
Sin (22) = Opposite side ÷ Hypotenuse
0.37 = 5 ÷ x
x = 5 / 0.35
x = 14.28
Hence, the value of x is 14.28 units, this is determined using the trigonometric identities.
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An angle of 2. 5 radians is subtended by an arc of a circle with a radius of 10cm. What is the length, in cm, of the arc?
The length of the arc of the given circle with radius 10 cm and an angle of 2.5 radians subtended by an arc of a circle is equal to 25 cm.
Let 'y' represents the length of the arc of the given circle.
Radius 'r' of the given circle is equal to 10 cm
Angle 'α' subtended by an arc of a circle is equal to 2.5 radians.
length of the arc = Angle subtended by an arc × Radius of the circle
⇒ y = rα
⇒ y = 10 × 2.5
⇒ y = 25 cm
Therefore, the length of the arc of a circle for the given radius 10cm and subtended angle 2.5 radians is equal to 25 cm.
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are the following statements true or false? false 1. if two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix. false 2. if is zero, then two rows or two columns are the same, or a row or a column is zero. false 3. the determinant of is the product of the diagonal entries in . false 4. .
Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.
What is matrix ?
A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,
1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.
2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.
3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.
4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.
Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.
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why does the man with the tattooing pen urge hannah not to forget the number on her arm in devil's arithmetic
The character Hannah is sent back in time to the Holocaust in Jane Yolen's book "The Devil's Arithmetic," where the Nazis tattoo a number on her arm.
The guy who tattooed Hannah's arm begs her not to forget the number because it serves as a powerful reminder of the significance of remembering and never forgetting the past and acts as a permanent reminder of the crimes done during the Holocaust. Hannah must remember the number since it is also a way of tracking and identifying people within the concentration camp.
Hannah is questioned about her name by the prisoner who is in charge of tattooing the ladies. That person is Chaya Abramowicz, she responds. She is wearing his daughter's outfit, he informs her. She had the same name, Chaya. He advises her to live for all the Chayas in the world and to never forget her prisoner number.
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Buddy walks 5000 feet due North, then turns and walks 4000 feet due East. If he walked in a straight line from his starting position to his final position, how many miles would he walk?
Answer: 1.2 miles
You can find the answer by using the pythagorean theorem.
a^2 + b^2 = c^2.
(5000)^2 + (4000)^2 = c^2
25 million +16 million = c^2
41 million = c^2
Take the square root of both sides in order to get the value of C.
C = about 6,403 feet.
1 mile = 5280 feet
6403/5280 = 1.2
Buddy would walk about 1.2 miles
5x+y=9
10x−7y=−18
in substitution
Substitution is a method for solving systems of equations that involves solving for one variable in one equation and then substituting that value into the other equation.
Here's how we can use substitution to solve the system of equations:
5x+y=9
10x−7y=−18
Solve one equation for one variable, for example:
y = 9 - 5x
Substitute this expression of y into the other equation:
10x - 7(9 - 5x) = -18
Solve the equation resulting from the substitution
10x - 63 + 35x = -18
45x = 45
x = 1
Substitute this value of x back into one of the original equations to find the value of y.
5(1) + y = 9
y = 4
So the solution is (x,y) = (1,4)
You can check this solution by substituting it back into both original equations.
A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9. 5° (see figure). Find the change in elevation for a car descending the 4-mile stretch. (Round your answer to two decimal places. )
The change in elevation of the car is 0.66mile.
Now, According to the question:
Trigonometric functions are immensely useful when real-life examples form a right triangle. In such cases, sine, cosine, or tangent functions are used based on the given information to determine the unknown value. For example, suppose we are looking at the top of a building and we know the height of the building and our distance from the base of the building, using the tangent function, we can easily calculate the angle made by the line of sight above the ground.
d = 4 miles is the distance covered by the car on the inclined road.
θ = 9.5° is the angle made by the road above the horizontal.
Let:
h be the change in elevation of the car.
Using the sine function, we write:
[tex]sin\theta= \frac{opposite side}{hypontenuse}[/tex]
[tex]sin\theta =\frac{h}{d}[/tex]
h = dsinθ
h = (4 mile)(Sin(9.5°))
h ≈ 0.66 mile
Therefore, the change in elevation of the car is 0.66mile.
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Select the correct answer from the drop-down menu.
This scatter plot was created using daily stock market returns. Which type of function fits the data of the graph best?
Percent Daily Return
6.00%
4.00%
2.00%
0.00%
-2.00%
-4.00%
A
-6.00%
-8.00%
-10.00%
1-Mar-18
●
6-Mar-18 11-Mar-18 16-Mar-18 21-Mar-18 26-Mar-18 31-Mar-18 5-Apr-18
A best explains the relationship between the stock's return and time.
A Linear Function best explains the relationship between the return and time.
What is the scatter plot?
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.
It is given that this scatter plot was created using daily stock market returns.
To determine which type of function fits the data of the graph best see the points of the graphs.
The scatter plot is not forming a parabola or curved graph so it can be a quadratic function.
The scattered in such a form that only a straight line can be the best fit for the scatter plot.
Therefore, a linear function is the best representation.
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find the distance from the given point to each of the following. (3, 9, -7) (a) the xy-plane 7 correct: your answer is correct. (b) the yz-plane 3 correct: your answer is correct. (c) the xz-plane 9 correct: your answer is correct. (d) the x-axis correct: your answer is correct. (e) the y-axis correct: your answer is correct. (f) the z-axis correct: your answer is correct.
Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.
What is axis ?
An axis is a line about which a body rotates or a system oscillates. In mathematics and physics, an axis is often represented as a straight line that serves as a reference point for the measurement of coordinates.
The correct answers are :
(a) The distance from the point (3, 9, -7) to the xy-plane is the distance from the point to the z-axis, which is 7, since the xy-plane is at z = 0
(b) The distance from the point (3, 9, -7) to the yz-plane is the distance from the point to the x-axis, which is 3, since the yz-plane is at x = 0
(c) The distance from the point (3, 9, -7) to the xz-plane is the distance from the point to the y-axis, which is 9, since the xz-plane is at y = 0
(d) The distance from the point (3, 9, -7) to the x-axis is the distance from the point to the x-axis, which is 0, since the point is already on the x-axis
(e) The distance from the point (3, 9, -7) to the y-axis is the distance from the point to the y-axis, which is 0, since the point is already on the y-axis
(f) The distance from the point (3, 9, -7) to the z-axis is the distance from the point to the z-axis, which is 0, since the point is already on the z-axis
Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.
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Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
The surface area of the rectangular prism is 182m²
How to determine the surface areaIt is important to note that the surface area of a rectangular prism is expressed as;
Surface area = 2(wl + hw + hl)
Where;
w is the width of the rectangular prismh is the height of the rectangular prisml is the length of the rectangular prismNow, from the diagram show, we have the values as;
Length = 3
Height = 7
Width = 7
Substitute the values into the formula
Surface area = 2(7×3 + 7×3 + 7 ×7)
multiply the values
Surface area = 2(21 + 21 + 49)
expand the bracket
Surface = 182m²
Thus, the value is 182m²
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you were taking a multiple-choice test that has six questions. Each of the questions has five answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, and how many ways can you answer the questions?
The number of ways to answer the questions is given as follows:
15,625.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, there are six questions, each with five possible options, hence the number of ways to answer the questions is calculated as follows:
5^6 = 15,625 ways.
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What is the slope of the line through the points (4,10) and (2, 20)
A fresh fish retailer receives a shipment of sardines in sealed packs. Together, there were 3 pounds in 12 packs. If the retailer received 48 packs of sardines, how many pounds were in the shipment?
Answer:
So, the question is asking how many pounds are there in 48 shipments if ever 12 shipments are 3 pounds, so what you want to do is so how many times 12 will go into 48 and then multiply that by 3!
48/12 = 4
4 * 3 = 12
The total 48 shipments weigh 12 pounds!
Step-by-step explanation:
Hope it helps! =D
Answer:
The weight of one pack of sardines is 3 pounds / 12 packs = 0.25 pounds/pack
So the weight of 48 packs of sardines is 0.25 pounds/pack * 48 packs = 12 pounds.
Determine the value of x in the figure.
The value of x in the figure shown above is equal to 4.
What are parallel lines?In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
By critically observing the image of this geometric figure, we can reasonably infer and logically deduce that it is a type of quadrilateral with both pairs of opposite sides being parallel to each other and the opposite angles (vertical angles) are equal and congruent:
Side length A = Side length B
4 + 6 = 6 + x
10 = 6 + x
By collecting like terms, we have the following:
x = 10 - 6
x = 4 units.
In conclusion, the value of x is equal to 4 units.
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At the third step, Han subtracts 39 from 39. How do you know that these numbers represent hundredths?
Answer: Because 2 places to the right of the the decimal.
Step-by-step explanation:
5/10 the students in Sam's class are girls. Of the girls, of them wear glasses. What
fraction of the student's wear glasses?
As 5/10 are Girls in Class And 1/5 of the girls wear glasses So on overall girls wear glasses is 1/10 in the whole class.
The fraction 5/10 is equal to 1/2 of the total and 1/5 of the girls wear glasses so if you multiply 1/2 and 1/5 you get 1/10, To get a total fraction of girls who wear glasses overall will be by multiplying both the fraction. So,
1/5*1/2 = 1/10
Here the answer is produced by multiplying the numerator with the numerator and similarly denominator with the denominator to get the answer of total friction of girls wearing glasses in the whole class.
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It costs $5 per hour to rent a snowboard from a certain ski rental company, plus a $50 deposit. Another ski rental company charges $10 per hour to rent a snowboard, plus a $25 deposit. For what number of hours is the cost to rent a snowboard the same at each company? What is the cost of renting a snowboard for this number of hours?
The number of hours for which the cost is the same would be 5 hours.
The cost of renting a snowboard for 5 number of hours would be same as that point i.e. $5
By costs, what do you mean?
Costs are really the monetary value of purchases made for use by a company or other accounting entity of supplies, service, labor, products, equipment, and other items.
The cost of renting a snowboard from the first company is $5 per hour + $50 deposit = $5x + $50.
The cost of renting a snowboard from the second company is $10 per hour + $25 deposit = $10x + $25. To find the number of hours for which the cost is the same, we set the two costs equal to each other and solve for x:
$5x + $50 = $10x + $25
$5x - $10x = $25 - $50
$5x = $25 - $50
$5x = -$25
x = -5
As we will not take cost in negative so it would be 5
So, we can say that the cost is same at any point of time.
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Multiselect Allce takes an art class after school once a week. At each class,
she buys a bottle of juice for $1.25 and a bag of pretzels for $0.85. Select all
expressions that represent the amount of money, in dollars, Alice spends after
attending 8 art classes.
Answer:
$16.8
Step-by-step explanation:
u got to trust me
Answer: $16.8
im sure its this it has to be
y-0.8x=0.5
5y-2.5-4x
Answer:
x = -1
Step-by-step explanation:
y-0.8x=0.5
5y-2.5-4x
Get y by itself.
y = 1.3
Put 1.3 into the second equation
5(1.3) - 2.5 - 4x
6.5-2.5 - 4x
4 - 4x = 0
Get x by itself
-4x = 4
x = -1
I hope this was able to help you :D
You spin a ball of mass 0.18 kg that is attached to a string of length 0.98 m at ω = 5.2 rad/s in a circle. What is the ball’s angular momentum?
The angular momentum of the the ball is 4.16kgrad/sec
What is angular momentum?Angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity. This means that the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. It is measure d in kgrad/sec
angular momentum = mass × angular velocity
mass = 0.18kg
angular velocity = 5.2 rad/s
therefore angular momentum = 0.18× 5.2
= 4.16 kg rad/s
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The prism below is made of cubes which measure 1/4 of a foot on one side. What is the volume? A. 13/4 cubic feet B. 80 cubic feet C. 20 cubic feet D.5/4 cubic feet
The volume of the prism in this problem is given as follows:
C. 9/16 cubic feet.
How to obtain the volume of the rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:
Volume = length x width x height.
For this problem, two of the dimensions are formed by three cubes, hence their measures are:
3 x 1/4 = 3/4 foot.
The remaining dimensions is composed by four cubes, hence the measures are:
4 x 1/4 = 1 foot.
Hence the volume is given as follows:
V = 1 x 3/4 x 3/4
V = 9/16 cubic feet.
Missing InformationThe problem is given by the image presented at the end of the answer.
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An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2184 feet and Plane B is just taking off. Plane A is gaining altitude at 30.25 feet per second and Plane B is gaining altitude at 75.75 feet per second.
They will be equal at the same altitude at x= 48 seconds
How to determine when they will be equal?Assume the question is when the planes will be at the same altitude.
A is 2184+30.25x, where x is the number of seconds.
The aircraft B is 75.75x
They will be equal at the same altitude if
75.75x=2184+30.25x
Collecting like terms and making x the subject of the relation
75.75x -30.25x = 2184
45.5x = 2184
Making x the subject
x = 2184/45.5
x=48 seconds
The two airplanes will be at the same altitude at 48 seconds
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note: enter your answer and show all the steps that you use to solve this problem in the space provided. use the circle graph shown below to answer the question. the image is a color pie chart divided into 5 portions, and is titled pets owned by sixth graders.
starting from the 12 o'clock position at the top and going clockwise toward the right is dark blue portion labeled dogs, 45 percent. next portion if 30 sixth graders own birds, how many sixth graders were surveyed?
Total number sixth graders were surveyed is 600.
"percent" is Latin for "out of 100," so 5 % is literally 5 out of 100
Now--if it were 5 kids with birds, you would know that there were 100 total kids. But it's 30 kids, which is way more than 5; so your total number of kids is going to be way more than 100.
So what you need to do here is figure that "30 sixth graders own birds
i.e. 30 is 5% of some number."
How many times bigger than 5 is 30? (6 times, because 5 x 6 = 30, or you can think of it as 30 divided by 6 = 5)
So if you had to do 5 TIMES 6 to get to 30, you have to do 100 TIMES 6 to get the total number sixth graders were surveyed.
What's 100 x 6?
= 600.
So your total number sixth graders were surveyed is 600.
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A newspaper charges a flat
fee plus a charge per day to
place a classified ad.
Number
of Days
2
4
6
Total
Charges
($)
8
13
18
Answer: This problem can be represented by the equation y = mx + b, where y is the total charges, x is the number of days, m is the charge per day, and b is the flat fee.
To find the values of m and b, we can use the given data points to solve for the equation.
For x = 2, y = 8, so 8 = m * 2 + b
For x = 4, y = 13, so 13 = m * 4 + b
For x = 6, y = 18, so 18 = m * 6 + b
We can then use a system of equations to solve for m and b:
m * 2 + b = 8
m * 4 + b = 13
m * 6 + b = 18
Using substitution or elimination methods:
m = 2
b = 2
Therefore, the equation is: y = 2x + 2
This means that the flat fee is $2 and the charge per day is $2.
Step-by-step explanation:
what is the probability that two randomly generated strings of length 9 in the dna alphabet ({a, c, g, t}) are identical?
The probability that two randomly generated strings of length 9 in the DNA alphabet is 729.
We have to find the probability that two randomly generated strings of length 9 in the DNA alphabet (a, c, g, t) are identical.
Probabilities are based on occurrences, and events can result from one or more observations or experiment results.
The total number of alphabet in word DNA is 3.
So, the probability that two randomly generated strings of length 9 in the DNA alphabet = 9 × 9 × 9
The probability that two randomly generated strings of length 9 in the DNA alphabet = 729
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