Using the formula of speed, the speed of first trains is 45 mph and the speed of second train is 60 mph.
In the given question, we have to find the speed of each.
Two trains going in opposite directions leave at the same time.
One train tavels 15 mph faster than the other.
In 6 hours the trains are 630 miles apart.
Let the speed of the first vehicle be s mph, then according to the question, the speed of the second vehicle would be (s+15) mph.
Let the first vehicle covers the distance D(1) and the second one D(2) in the prescribed time.
So, find the distance covered by the first vehicle in 6 hours by using the formula
Distance = Speed × Time
So the distance D(1) is;
D(1) = s*6
D(1) = 6s
So the distance D(2) is;
D(2) = (s+15)*6
D(2) = 6s+90
Since, after 6 hours both the vehicles are at the distance 630 miles. So, the sum of the two distances D(1) and D(2) will be equal to 630.
D(1)+D(2) = 630
Puttimg the value of D(1) and D(2)
6s+6s+90=630
Simplifying
12s+90=630
Subtract 90 on both side we get
12s=540
Divide by 12 on both side we get
s=45 mph
So the value of speed of the faster vehicle
s+15 = 45+15
s+15 = 60 mph
Hence, the speed of first train is 45 mph and the speed of second train is 60 mph.
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If there are 20 boxes of bicycles/tricycles total and 48 wheels total how many tricycles were ordered?
write and graph a system of linear equations to model the situation
The system of equations is:
x + y = 20
2x + 3y = 48
And its graph can be seen in the image at the end.
How to write and solve the system of equations?Let's define the variables:
x = number of boxes with a bicycley = number of boxes with a tricycle.Each bicycle has 2 wheels, each tricycle has 3 weels, and we know that there are 20 boxes and 48 wheels, then the system of equations is:
x + y = 20
2x + 3y = 48
To solve the system graphically we just need to graph both lines on the same coordinate axis and see at which point do the lines intersect, the graph is below.
The solution is x = 12, y = 8.
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Sparx homework
I really need help on how to solve this!
Answer:
a] 5 dogs
b] 16 dogs
Step-by-step explanation:
The minimum number of dogs that could have a mass of more than 26 kg is 5. This is because dogs with a mass of 30 ≤ x ≤ 40 have a frequency of 5. The dogs in the 20 ≤ x ≤ 30 range could be more than 26 kg, but they could also be less than 26 kg, so these are not included in the minimum.
The maximum number of dogs that could have a mass of 26 kg is 16 because both dogs in the 30 ≤ x ≤ 40 range (5) and 20 ≤ x ≤ 30 range (11) could weigh more than 26 kg. 11 + 5 = 16, giving us our answer for the maximum.
the dimensions of col a and nul a add up to the number of columns in a.
a. true
b. false
Using Rank theorem , the dimensions of col A and Null A add up to the number of colmns in A. It is true statement.
The rank of matrix A denoted as rank(A) is the dimension of the column space Col(A).
The nullity of matrix A written as nullity(A) is the dimension of the null space Nul(A)
Rank Theorem:
If A is a matrix with n columns, then
Rank (A) + nullity (A) = n
In other words we can say that
dim (Col(A) ) in column space + dim (Nul(A)) in empty space = total number of columns in A
The rank theorem is really important theorem.
It is gives a strong relationship between the Null space ( all possible vector x such that Ax = 0) and the column space (the set of vectors b matching Ax=b) explain the two main objectives. The more freedom we have for choosing x, the less freedom we have for choosing b, and vice versa.
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what is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time?
Using the concepts of probability, we got that 0.063 is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time
We know very well that probability is defined as the fraction of number of favorable outcomes to the total number of outcomes.
Here, we are rolling a 6-faced dice.
Getting 3 on the top face of dice is same as the any number getting from 1 to 6 on the top face of the dice.
So, every number has equal probability to come on the top face, therefore the probability of getting 3 on the top face of dice is (1/6)
Now, similarly total number of marbles in the bag=6 blue +3 black+8 orange marble=17 marbles.
Now, picking one marble from 17 marble is can be done in [tex]^1^7C_1[/tex] ways, similarly choosing 1 blue marble from 6 marble can be done in [tex]^6C_1[/tex] ways.
So, probability of picking 1 blue marble randomly=6/17
Now, the probability of picking 1 blue marble from 17 marbles along with rolling dice probability is given by =(6/17)×(1/6)=(1/17)=0.063
Hence, the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time is 0.063
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What is the value of x? Show your work. 20x⁰ 8x° 17x
PLEASE I NEED HELP
Answer:
x = 8
Step-by-step explanation:
the exterior angles of a triangle sum to 360° , that is
20x + 8x + 17x = 360
45x = 360 ( divide both sides by 45 )
x = 8
A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
The 95% confidence interval for the average apple weight is (119.14, 125.86).
An apple typically weighs 120 grams with a 12-gram standard deviation, according to one manufacturer. The average weight of an apple was 122. 5 grams, according to statistics created from a sample of 49 apples that were randomly chosen from a shipment.
Let, n = 49
x = 122.5
σ = 12
To calculate and interpret a 95% confidence interval for the average apple weight, use the formula;
⇒ (x ± 1.96*σ/√n)
⇒ (122.5 ± 1.96*12/√49)
⇒ (119.14, 125.86)
Consequently, the average apple weight has a 95% confidence interval of (119.14, 125.86).
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Which of the following is the solution of
the system of equations shown?
A. (2, 2)
B. (-2, 2)
C. (2,-2)
D. (-2,-2)
(The answer isn’t B. I already tried that)
PLEASE HELP ASAP!! PLEAZE 20 PIINTS
Factor -1/2 out of 1/2x+6
Answer:
-x-12
Step-by-step explanation:
1/2x+6
first divide by -1/2 or multiply by -2(its the reciprocal)
-2(1/2x+6)
-2*1/2x+6*-2
-x-12
Question 10(Multiple Choice Worth 2 points)
(Adding and Subtracting with Scientific Notation MC)
Simplify (3.7 x 10-9) - (8.2 x 10-8). Write the final answer in scientific notation.
O-7.83 x 10-8
-7.83 x 10-9
O-4.5 x 10¹
O-4.5 x 10-¹
The simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.
We will solve the given expression using laws of exponents.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
(3.7 x 10^-9) - (8.2 x 10^-8)
= (3.7 x 10^(-1 -9)) - (8.2 x 10^-8)
= (3.7 x 10^-1 x 10^-8) - (8.2 x 10^-8)
= (0.37 x 10^-8) - (8.2 x 10^-8)
= (0.37 - 8.2) x 10^-8
= - 7.83 x 10^-8
So, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) is - 7.83 x 10^-8.
Thus, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.
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Evaluate the expression when a = -6 and y=4. y-9a
(can someone help? I'm not used to how this is formatted.)
Answer: 58
Step-by-step explanation:
First you substitute the values, so
4-9*-6
Then you solve using order of operations
Answer:
58
Step-by-step explanation:
y-9a
Let a = -6 and y=4
Substitute the values in
4 -9(-6)
Multiply first
4 + 54
Add
58
(-8,-4), (-1, -3), and (0, -2).
How do I graph this ?
Answer:
Refer to photo for drawing
Step-by-step explanation:
1. Draw the x y plane
2. Identify -8, -1, 0 on x plane
3. Identify -4, -3, -2 on y plane
4. Mark the intersection point (-8,-4) with x
5. Mark the intersection point (-1,-3) with x
6. Mark the intersection point (0,-2) with x
7. Draw a straight line through the x mark
Given the equation y=2-(x-3)^2
Find the cordinates of the vertex of the curve it describes
Find the x intercept
Find the y intercept
Answer:
Y= -7
X= 4.4
Step-by-step explanation:
Y= 2 - ( x-3)^2
When x= 0
Y= 2- ( 0-3)^2
Y will equals -7
When y = 0
(x-3)= √2
X = 4.4
how many thousandths are in one hundredth
Answer:
ten thousands
Step-by-step explanation:
Ten thousandths are in one hundredth.
What is fraction?
Fractions represent parts of a whole. In mathematics, fractions are represented as numbers that define part of a whole. A fraction can be a part or subset of any quantity of a whole, and a whole can be any number, value, or thing.
All fractions consist of a numerator and a denominator, separated by horizontal bars called fraction bars.
The denominator indicates the number of parts into which the whole is divided. Placed at the bottom of the break below the break bar. The
counter indicates how many sections of the fraction are displayed or selected. Placed at the top of the break above the break bar.
As we know ,
one hundredth is 1/100
one thosandth is 1/1000
But now , 10 × 1/1000 = 1/100
This means that there are 10 thousandths in one hundredth.
Hence, ten thousandths are in one hundredth.
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Fatima paid for 5 pallets of grass to be delivered. Each pallet of grass cost $129. 95. Fatima paid $76. 20 for delivery. What is the total amount fatima paid?.
Fatima paid $129.95 for pallet of grass cost and $ 76.20 for delivery. The total amount Fatima paid is $725.95.
Pallet Grass Cost: The quality and type of grass you want will impact the overall cost of sod. Most homeowners pay between $150 and $450 per pallet of sod for their yards or an average of $300. When it comes to square footage, sod costs between $0.35 and $0.85, or an average of $0.60 per square foot.
Given in the question:
Number of Pallets = 5
Cost of each pallet = $129.95
Total amount spend on Pallets
= Number of Pallets × Cost of each pallet
= 5 × $129.95 = $ 649.75
Also given;
Amount spend on Delivery = $76.20
Total Amount Paid by Fatima
= Total amount spend on Pallets + Amount spend on Delivery
= $649.75 + $76.20
= $ 725.95
Hence Fatima paid a total amount of $725.95.
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What is a confidence interval? Choose the best description.
A range of probabilities, constructed with a sample, that describes where a population parameter will occur.
A range of values, created using a sample, within a population parameter that has a certain probability of occurring.
A range of values used to estimate where the sample statistic is likely to occur
Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.
Reason: E.g. P(a<x>b) = 0.95
confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.
A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.
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PLEASE HELP WILL GIVE 100 POINTS AND BRAINLEST ANSWER BOTH QUESTIONS TWO ANSWERS FOR EACH!!
Circumcenter is equidistant from the vertices, perpendicular bisectors will cross. Incentre is equidistant from the sides. Where the angle bisector cross incenter
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
We have to choose the properties of circumcenter.
Circumcenter is equidistant from the vertices.
It is equidistant from the three vertices of the triangle, and thus you can construct a circle centered at the circumcenter and circumscribing the triangle.
and perpendicular bisectors will cross.
We have to choose the properties of incenter.
Incentre is equidistant from the sides.
Where the angle bisector cross incenter
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Can someone please help
Answer:
The measure of angle 1=52
The measure of angle 2=58
The measure of angle 3=31
Step-by-step explanation:
The measure of angle 1 is 52 because the angle out of the triangle is 128. The measure of angle 1 plus 128 equals 180. Using this info you could do 180-128, which equals 52. The measure of angle 1 equals 52.
The measure of angle 2 is 58 because I already know 2 of the values of the triangle, in which Angle 2 is also in. One triangle adds up to 180. The values of the other 2 angles are 52 and 70. Using this information I can use the equation 52+70+x=180, which you then simplify to 122+x=180. X equals 58. The measure of angle 2 equals 58
The measure of angle 3 is 31 because the angle out of the triangle is 70. The missing angle plus 70 equals 180. Using this info I could do 180-70. The missing angle is 110. There is already one given angle, and I have figured out the other, using this info I can now finally find the measure of angle 3. I can find this out by using the equation 110+39+x=180. You would then simplify the equation to 149+x=180. X equals 31. The measure of angle 3 equals 31.
527.8317 Find the digits in the tens place, in the hundredths place, and in the thousandths place for the following number.
Adding two negatives makes a bigger number? Is this true or false? Explain.
Answer: False, adding two negatives does not make a bigger number. I know this because when adding the two negatives, the absolute value will get bigger. However, the value of the number gets smaller.
y=-.06(5.5-1)(5.5-10)
Answer:
I don't know if its right.
Ans:1.215
Of the 250 sheep in a flock, 34% are white. What is the total number of white sheep in the flock?
10 A factory produces lemon-scented widgets. Each widget is cheaper, the more that are produced, but costs will go up if too many widgets are produced, due to storage requirements. The accountant for the factory says that the costs for producing x thousands of units a day can be approximated by the formula C = 0.04x2 - 8.504x + 25302. Find the daily production level that will minimize the costs. Be sure to show your work and include units of measurement.
The daily production level that will minimize the costs is 106300 units.
How to calculate the production level?From the information, the function is given as C = 0.04x² - 8.504x + 25302.
c = cost
From the function, the following can be deduced:
a = 0.04
b = 8.504
c = 25302
Then, -b/(2a) will be:
= -8.504 / (2 × 0.04)
= 106.300
Note that production level will minimize the cost in thousands.
The production level will now be:
= 106.300 × 1000
= 106300 units
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the points (7, 18) and (3, 14) fall on a particular line. What is its equation in slope-intercept form?
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{7}}} \implies \cfrac{ -4 }{ -4 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{ 1}(x-\stackrel{x_1}{7}) \\\\\\ y-18=x-7\implies {\Large \begin{array}{llll} y=x+11 \end{array}}[/tex]
If you buy an AED 50 meal with a 5% tax.
The tax amount to be paid is AED
Answer:
2.5 dhs
Step-by-step explanation:
5% of AED50
50x5/100=250/100
=AED2.5
Determine if they given ordered pair is a solution to the given system
Answer:
Step-by-step explanation:To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.
A farmer estimates that he will harvest 7250 bushels of wheat. The weather is perfect during the growing season, so he harvests 1 more bushels of wheat than expected. How many bushels of wheat does the farmer harvest?
The number of bushels of wheat does the farmer harvest is 7251 bushels of wheat
The farmer's estimated number of bushels of wheat in the harvest = 7250 bushels
The weather is perfect during the growing season
The number of additional bushels of wheats harvested = 1 bushels
The number of bushels of wheat does the farmer harvest = The farmer's estimated number of bushels of wheat in the harvest + The number of additional bushels of wheats harvested
Substitute the values in the equation
The number of bushels of wheat does the farmer harvest = 7250 + 1
Here we haver to use the addition
Add the terms
= 7251 bushels of wheat
Hence, the number of bushels of wheat does the farmer harvest is 7251 bushels of wheat
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During a race, all members of a rowing team should keep the oars parallel to produce maximum speed. Let m∠1 = 6x + 18 and m∠2 = 9x +12, and x = 10.
What type of angle pair are angles 1 and 2? (3 points)
Find the measure of angles 1 and 2. Show your steps. (4 points)
Are the oars parallel? Which theorem would be used to prove that the oars are parallel? (3 points)
∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.
What are consecutive angles?A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.
Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and
m∠2 = 9x+12, and x = 10.
Putting the value of x, we get,
m∠1 = 6x + 18 = 6*10 + 18 = 78°
m∠2 = 9x+12 = 9*10 + 12 = 102°
m∠1 + m∠2 = 180°
Therefore, ∠1 and ∠2 are consecutive angles pairs.
We can prove that oars are parallel by converse of consecutive angles theorem.
Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel
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find the exact values of sin 2u, cos 2u, and tan 2u using double-angle formulas.
13.) sin u=3/5, 0 < u < pi/2
15.) tan u= 1/2, pi < u < 3pi/2
The exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
sin u=3/5, 0 < u < pi/2
tan u= 1/2, pi < u < 3pi/2
We need to find sin 2u, cos 2u, and tan 2u
sin2u=2sinucosu
tanu=sinu/cosu
1/2=3/5/cosu
cosu=3/5×2
cosu=6/5
So sin2u=2(3/5)(6/5)
sin2u=36/25
cos2u=1-2sin²u
=1-2(36/25)²
=1-2(1296/625)
=1-4.14
=-3.142
cos2u=-3.142
tan2u=sin2u/cos2u
Substitute the values of sin2u and cos2u
sin2u=36/25/(-3.142)
=1.44/-3.142
=-0.458
Hence, the exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u
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(2,-2) and (0,-1)
what is the linear equation
The linear equation of the given points (2, -2) and (0, -1) is y = (-1/2)x - 1
The first point = (2, -2)
The second point = (0, -1)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (-1 - -2) / (0 - 2)
= -1+2 / -2
= 1 / -2
= - 1/2
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values in the equation
y - -2 = (-1/2) (x-2)
y + 2 = -1/2 x + 1
y = (-1/2)x + 1 -2
y = (-1/2)x - 1
Hence, the linear equation of the given points (2, -2) and (0, -1) is y = (-1/2)x - 1
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