Two cities are 45 miles apart train one is 70 mph train 2 is 60 mph
Answer:
Hi! I'm pretty sure the question is: Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two towns at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
I have had a similar question before, and I will answer yours. :)
Step-by-step explanation:
T1 - the time the trains are moving to each other.
For time T1, the first train will go the distance of 70*t.
The second train, for time t, will go the distance 60*t.
Both for time t1 - 70t+60(t1) = (70+60)*(t1).
45 - (70+60)*t is the distance between trains that left after t hours.
For the first time, they will be 10 miles apart when they are moving into each other
45 - (70+60)*t = 10
45-10 = (70+60)*t
35 = 130*t
t=35/130 h =7/26 h = 0.27 h
The train meets when distance = 0
45 - (70+60)*t = 0
45 = 130t
t =45/130 h = 9/26 h = 0.35 h when trains met.
Trains began to move apart from each other after 9/26 h moving,
After t2 time trains will be (70+60)*(t2) = 130*(t2) mi apart from each other.
130*(t2) = 10
t2 = 1/13h = 0.08h after they met, they are apart from each other 10 mi.
So after the beginning of the movement, it will be time when they met + time when they were moved 10 mi apart from each other
9/26 h+1/13h = 11/26 h = 0.42 h
There are 11 counters in a bag.
8 of the counters are green.
3 of the counters are blue.
Sid takes at random two counters from the bag.
Work out the probability that Sid takes one counter of each colour
(Hint: Fractions can be written in the form a/b. eg [tex]\frac{5}{28}[/tex] would be written as 5/28)
The probability of Sid takes at random counters from the bag is 24/55
The total number of counters = 11
Total number of green counters = 8
Total number of blue counters = 3
Probability = Number of favorable outcomes / Total number of outcomes
Total number of outcome = 55
Number of outcome that Sid will get both green = 28
Number of outcome that Sid will get both blue = 3
Number of favorable outcome = 55 - 28 - 3
= 24
Probability = Number of favorable outcomes / Total number of outcomes
= 24/55
Hence, the probability of Sid takes at random counters from the bag is 24/55
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a professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. the professor has informed us that 8.75 percent of her students received grades of a. what is the minimum score needed to receive a grade of a?
The minimum score needed to receive a grade of 'a' is 87.92
Given that,
At a nearby university, a professor noticed that her students' exam results were regularly distributed, with a mean of 73 and a standard deviation of 11. 8.75 percent of the professor's students achieved grades of A, she told us.
Mean = μ = 73
Standard deviation = σ = 11
Using the standard normal table,
⇒ P(Z > z) = 8.75%
⇒ 1 - P(Z < z) = 8.75%
= 1 - P(Z < z) = 0.0875
= P(Z < -1.36) =1- 0.0875
= P(Z < 1.3563) =0.9125
∴ Z = 1.3563 ( Using standard normal z-table )
Using z-score formula ;
x= z * σ + μ
x=1.3563 * 11 + 73
x=87.92
So, the minimum score needed to receive a grade of 'a' is 87.92
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Write the set A = {1, 2, 3, 4, 5, …} in set-builder form and descriptive form.
(please notice that it is an infinite set)
a. The set in set builder form A = {x : x ∈ N}
b. the set in descriptive form, A = {set of natural numbers}
What is a set?A set is a collection of well defined items.
What is set builder form?Set builder form is a way of enumerating a set by using a set of rules which define its elements.
What is descriptive form?Descriptive form is a way of enumerating the elements of a set in words.
a. How to write the elements of the set in set builder form?Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N, we identify each element of the set as x and give it a rule that x is an element of N. That is x ∈ N.
So, in set builder form A = {x : x ∈ N}
b. How to write the elements of the set in descriptive form?Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N.
In descriptive form, we write that A = {set of natural numbers}
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The map above is being reduced by a scale factor of 1/9 and printed for the subway
station. How many square inches will the new map take up?
O 315 square inches
O 72 square inches
24 square inches
O 35 square inches
Answer:
35 square inches
Step-by-step explanation:
21x15=315
315/9=35
Therefore, the answer is 35 square inches
What is the solution to this inequality? x - 1 . 5 > 2 . 5 Question 1 options: x < 4 x < 1 x > 1 x > 4
The solution to the inequality is X > 4
InequalityInequality is a set of mathematical expression which the individual side is not equal to other side
To solve for x in the inequality x - 1 . 5 > 2, we followed the step;
Step 1: Add 1.5 to both sides
x - 1.5 + 1.5 > 2 . 5 + 1.5
X > 4
Therefore, the solution to the inequality is X > 4
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can somone please help meeeeeeee
Answer:
121.5
Step-by-step explanation:
1.5 x 9 x 9 (the equation for volume (minus the 1/2 inch that Isaac's grandmother said to leave out) = 121.5
max and orlena bought 23 acres of land for $110,400. they bought some of the acres at $4000 per acre and some at $6300 per acre. how many acres did they buy at each price?
They bought 15 acres at $ 4000 per acre and 8 acres at $6300 per acre
Let,
They bought x acres at $ 4000
and ( 23-x ) acres at $ 6300
From information,
By using algebra,
4000x + 6300(23-x) = 110,400
4000x - 6300x+ 144900 = 110,400
-2300x = 110,400-144900
- 2300x = - 34500
x =34500 /2300
x = 15
x = 15
They bought 15 acres at $ 4000 per acre
(23 - 15 ) = 8 acres at $6300 per acre
Hence, they purchased 8 acres for $6300 per acre and 15 acres for $4,000 each.
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whats the answer to "The x -intercept is" and how do i find it
The x-intercept of the function represented on the graph is 3
How to complete the blank of the x-intercept?The graph represents the given parameters
To determine the x-intercept of the graph, we set y = 0
This means that the x-intercept of the graph is the point, where the line of the graph crosses the x-axis
For the graph, we have
When y = 0, the function has a value of 3
This means that
x-intercept is 3
Hence, the x-intercept of the graph is 7
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Hello, I am finding inverse functions and ran into this fraction. How would I simplify from here to find Y by itself?
The inverse function for the function f(x) = (1 -2x) / 3x is 1/3x+2.
Inverse function:
Inverse function means a function that serves to “undo” another function.
For example,
if f(x) produces y, then putting y into the inverse of f produces the output x.
Given,
Here we have the function f(x) = (1 -2x) / 3x.
Now, we need to find the inverse function f⁻¹.
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables by interchange the value of x by y and the value of y as x.
Then we get,
x = (1 - 2y)/3y
Now, solve the equation
x = (1 - 2y)/2y
for y, then we get,
y = 1/(3x + 2)
Therefore, the inverse function is 1/3x+2.
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1/2x-7=1/3(x-12) Explain or show your reasoning.
Answer: x=18
Step-by-step explanation:
It just does ok
Evaluate the expression below without using a calculator
With the help of trignometric identities we can say that the answer is = 0.672355, nearly.
What is trignometric equation?A trigonometric equation is any equation that contains a trigonometric function. Up until now we have introduced trigonometric functions, but not fully explore them. In the lessons within this SparkNote on trigonometric equations, we'll learn exactly how to solve trigonometric equations.As mentioned in Trigonometric Identities, a trigonometric equation that holds true for any angle is called a trigonometric identity. There are other equations, though, that only are true for certain angles.They are generally known as conditional equations, but in this text we'll just call them equations. We'll learn some techniques for solving general equations, as well as how to derive an infinite number of solutions to an equation based on a single solution to that equation.acc to our question-
cos(75)= 2-√3tan(22/7)= 1+√2.sin 3π/6= √2-√√2/2Learn more about trignometric equation:
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statistical output provides a means for creating a picot question. question 3 options: a) true b) false
It is true that statistical output provides a means for creating a picot question.
What is picot question?The letters PICOT stand for patient, intervention, comparison, outcome, and (occasionally) time, which are the components of a clinical research question. A case scenario is used to frame the question in the PICOT process in order to elicit an answer. A PICOT question's main objective is uncomplicated: It is a mechanism for determining the keywords to use when looking for the strongest evidence to address a pressing clinical question. In other words, the search plan is the PICOT question. The search strategy produces an objective and successful search.
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Please help!! Im so confused on this and need help badly
Answer: 11 months
Step-by-step explanation:
You do this by 73 times 11 equals 803
Then 49 times 11 equals 539 then add on the registration fee and it equals to 779 which is less than 803
the nth term of a gp 145800. if the fist term is 2 and the common ratio is 3. find the sum of the gp
The sum of the geometric progression with the features stated in the text is given as follows:
S = 2.62 x 10^(43).
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of a finite geometric sequence with n terms is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
In this problem, the first term and the common ratio are given as follows:
[tex]a_1 = 2, n = 3[/tex]
Hence the equation is:
[tex]a_n = 2(3)^{n - 1}[/tex]
The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:
[tex]a_n = 2(3)^{n - 1}[/tex]
[tex]1458000 = 2(3)^{n - 1}[/tex]
[tex]3^{n - 1} = 729000[/tex]
[tex]3^{n - 1} = 3^{90}[/tex]
Then:
n - 1 = 90
n = 91.
Thus the sum of the sequence is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]
S = 2.62 x 10^(43).
Typing mistakeThe problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.
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what is the answer what is the answer what is the step by step answer to learn to do it
Answer: 1.01% sale tax.
Step-by-step explanation:
First you must take your tax price before and the tax price after and divide them. This gets you 1.01.
To be sure this is your answer you can multiply the 1.01% by 53 and it gives you 53.53$ (If you don't understand I suggest looking at a video from khan academy they explain things much better than I do.)
Hope that helped in some way :)
9. There is so much water in the world, that we normally measure large bodies of water in cubic
miles or cubic kilometers instead of gallons. Cayuga Lake in upstate New York contains an
estimated 9.4 km³. How many cubic miles of water does Cayuga Lake contain?
Answer:
Step-by-step explanation:
12.5km
i made that up sorry
the ratio of drummers to guitar players who tried out for a band is 10:45 .
How many times the number of drummers is the number of guitar players?
Answer:
4.5
Step-by-step explanation:
45/10=4.5
carter has 24 posters in his room. if he arranges them into 6 equal rows, how many posters will be in each row?
If he arranges them into 6 equal rows, 4 posters will be in each row.
Define division.One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.
Given,
Total posters = 24
Arranging them into 6 equal rows,
Dividing:
24÷ 6
Reciprocating,
24 × 1/6
4
If he arranges them into 6 equal rows, 4 posters will be in each row.
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Is this relation a function ?
don't need explanation just the answer
The function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statementr which best describes the graph is, the graph is streched towards the x axis by a factor of 1/3
When an object is dilated the image formed is larger or smaller, but there is a difference in the size of the shape.
the rule of function change f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8
3x = 9xk
k = 1/3
Therefore, the function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statement which best describes the graph is, the graph is streched towards the x axis by a factor of 1/3
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How do I solve these?
Applying the knowledge of congruent triangles, the measures are solved as:
6. X = 14; AC = 11; T = 14; WZ = 16; WY = 60; AB = 60; m∠A = 64°; m∠Y = 64°; m∠W = 50°
7. X = 7; YZ = 28; T = 9; WZ = 10; WY = 11; AB = 28; m∠A = 31°; m∠C = m∠W = 99°
How to Solve for the Measures of Congruent Triangles?To solve for the missing measures of triangles that are congruent to each other, recall that triangles that are congruent will have corresponding sides that are equal and also corresponding angles that are equal.
6. Triangles ABC and YWZ are congruent, therefore:
m∠A = m∠Y; m∠B = m∠W; m∠C = m∠Z
AB = WY; AC = YZ; BC = WZ
Therefore:
5X - 4 = 66
Solve for X
5X = 66 + 4
5X = 70
X = 14
AC = YZ = 11
AB = WY
5T - 10 = 4T + 4
5T - 4T = 10 + 4
T = 14
BC = WZ = 16
WZ = 16
WY = 4T + 4 = 4(14) + 4
WY = 60
AB = WY = 60
AB = 60
m∠A = m∠Y
m∠A = 180 - 50 - 66
m∠A = 64°
m∠Y = 64°
m∠B = m∠W = 50°
m∠W = 50°
7. Triangles ABC and ZYW are congruent, therefore:
m∠A = m∠Z; m∠B = m∠Y; m∠C = m∠W
AB = YZ; AC = WZ; BC = WY
Therefore:
5X - 4 = 3X + 10
Solve for x
5X - 3X = 4 + 10
2X = 14
X = 7
AB = YZ
2T + 10 = 4T - 8
2T - 4T = -10 - 8
-2T = -18
T = 9
YZ = 4T - 8 = 4(9) - 8
YZ = 28
AC = WZ = 10
WZ = 10
WY = 11
AB = YZ = 28
AB = 28
m∠A = m∠Z = 3X + 10 = 3(7) + 10
m∠A = 31°
m∠C = m∠W = 180 - 31 - 50 = 99°
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I need help like asap !!!
only numbers and decimal points
Answer:
a = 4.52 km
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (7.2)² = a² + (5.6)²
→ 51.84 = a² + 31.36
→ a² = 51.84 - 31.36
→ a = √20.48
→ [ a = 4.52 km ]
Hence, value of a is 4.52 km.
Four congruent parallelograms are joined to make the shape below.
24 cm
The total shaded area is 192 cm²
Work out the value of x.
x cm
5 cm
For the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
As given in the question,
Given four congruent parallelograms
Shaded area of the parallelogram is 192cm²
As four parallelograms are congruent
Let the area of each parallelogram is A
4A = 192
⇒A = 48cm²
For two parallelogram base length = 24cm
Base length of each parallelogram = 12cm
Area of parallelogram = base × height
48 = 12 × height
⇒ height = 4cm
Value of x = 2 times of height
= 2 (4)
= 8cm
Therefore, for the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
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What is the image of the point (-7,9) after a rotation of 90 counterclockwise?
The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
Given that,
The points (-7,9).
We have to find the image of the point after a rotation of 90° counterclockwise.
Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.
Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.
(x,y)→(y,-x)
(-7,9)→(9,7)
Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
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Indicate the distance of the segment using the given
information. Round to the nearest tenth.
5. Find AX. A(-4, 5), X (1, −2)
The distance of segment AX sis found to be 8.6 units using the distance formula.
What exactly is the distance formula?[tex]\sqrt{[x_{2}-x_{1}]^{2} + [y_{2}-y_{1}]^{2} }[/tex] is the distance formula. This works for any two points in two-dimensional space with coordinates (x₁, y₁) for the first and (x₂, y₂) for the second. You may easily remember it if you remember that it is Pythagoras' theorem, that the distance is the hypothenuse, and that the coordinate lengths are the difference between the x and y components of the points.Why do we employ the distance formula?In complex numbers, the distance formula is used to express the plane and its magnitude. Furthermore, distance formulae can be used to calculate the distance between two planes in three-dimensional or n-dimensional planes. It is also used to calculate the magnitude formula.Given: A(-4, 5), X (1, −2)
We need to find the distance of the segment AX.
Distance of AX is given as :
[tex]\sqrt{[1-(-4)]^{2} + [-2-5]^{2} } \\= \sqrt{25 + 49}\\ = \sqrt{74}\\ =8.6[/tex]
Therefore, the distance of segment AX sis found to be 8.6 units using the distance formula.
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In a circle, the length of an arc intercepted by a central angle is 12 mm, and the radius of the circle
8 is 8 mm. What is the measure, in radians, of the angle?
Answer:
1.5
Step-by-step explanation:
we calculate the circumference of this circle.
circumference of a circle=2πr
data:
r=8 mm
circumference=2(8 mm)π=16π mm
2)we calculate the measure, in radians of the angle.
We know that:
circumference of a circle=2π radians
therefore:
16π mm=2π radians.
16 π mm--------------------------2π radians
12 mm----------------------------- x
x=(12 mm * 2π radians) / 16π mm=1.5 radians.
(30 x 5) + (9 x 5) =
150 + 45 = 195
Answer:
thats correct
Step-by-step explanation:
Express 35cents to $2.25 as a ratio in its lowest terms
Answer:
7 cents:$0.45
Step-by-step explanation:
(whatever you do to one side you do the same to the other)
35 divided by 5= 7
2.25 divided by 5= 0.45
the initial number of views for a reader board was 25. the number of views is growing exponentially at a rate of 18% per week. what is the number of views expected to be four weeks from now? round to the nearest whole number.
The number of views in the four weeks round to the whole number is 48.
Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.
We have to find the number of views in the fourth week.
On the first week the increase = 25 + 25× 18%
= 25 + 25 × 18/100
= 25 + 4.5
= 29.5
The second week increase = 29.5 + 29.5 × 18%
= 29.5 + 5.31
= 34.81
The third week increase = 34.81 + 34.81 × 18%
= 34.81 + 6.2658
= 41.0758
The fourth week increase = 41.0758 + 41.0758 × 18%
= 41.0758 + 7.393644
= 48.469444
Therefore the number of views in the four weeks is 48.
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