Answer:
The probability is [tex]P(X > 25 ) = 1.667[/tex]
Step-by-step explanation:
From the question we are told that
The maximum wait is [tex]b = 30 \ minutes[/tex]
The minimum wait would be [tex]a = 0\ minutes[/tex]
Generally the probability that you will wait more than 25 minutes for a bus is mathematically represented as
[tex]P(X > 25 )[/tex]
Now given that the time a person waits is uniformly distributed and that the maximum is 30 then we can evaluate the above probability as
[tex]P(X > 25 ) = P(25 < X < 30 ) = \frac{30 - 25}{30 - 0}[/tex]
[tex]P(X > 25 ) = 1.667[/tex]
Two integers are relatively _________ if and only if their only common positive integer factor is 1.
Answer:
Two integers are relatively primes if and only if their only common positive integer factor is 1.
Step-by-step explanation:
The prime number is one whose only divisor is 1 and itself.
The prime factors of a whole number are the exact prime divisors of that whole number. In other words, every composite number can be written as a multiplication of two or more prime factors.
So, two integers are relative primes if they have no prime factor in common, or, put another way, if they have no common divisor other than 1.
So, two integers are relatively primes if and only if their only common positive integer factor is 1.
A fisherman leaves his home port and heads in the direction N 70 ° W. He travels d1 = 40 mi and reaches Egg Island. The next day he sails N 10 ° E for d2 = 65 mi, reaching Forrest Island.
(a) Find the distance between the fisherman's home port and Forrest Island. (Round your answer to two decimal places.)
(b) Find the bearing from Forrest Island back to his home port. (Round your answer to one decimal place.)
S ° E
Answer:
A)82.02 mi
B) 18.7° SE
Step-by-step explanation:
From the image attached, we can see the angles and distance depicted as given in the question. Using parallel angles, we have been able to establish that the internal angle at egg island is 100°.
A) Thus, we can find the distance between the home port and forrest island using law of cosines which is that;
a² = b² + c² - 2bc Cos A
Thus, let the distance between the home port and forrest island be x.
So,
x² = 40² + 65² - 2(40 × 65)cos 100
x² = 1600 + 4225 - (2 × 2600 × -0.1736)
x² = 6727.72
x = √6727.72
x = 82.02 mi
B) To find the bearing from Forrest Island back to his home port, we will make use of law of sines which is that;
A/sinA = b/sinB = c/sinC
82.02/sin 100 = 40/sinθ
Cross multiply to get;
sinθ = (40 × sin 100)/82.02
sin θ = 0.4803
θ = sin^(-1) 0.4803
θ = 28.7°
From the diagram we can see that from parallel angles, 10° is part of the total angle θ.
Thus, the bearing from Forrest Island back to his home port is;
28.7 - 10 = 18.7° SE
given log6=0.778,find log36.
Answer:
We know that
1 ) log a^n = n log a
Now ,
log 6 = 0.7782 ----( 1 )
log 36 = log 6²
= 2 log 6
= 2 × 0.7782
= 1.5564
-3|2•8-4•5|+(16-7)/3
Answer:
-9
Step-by-step explanation:
-3|16-20|+9/3
-3|-4|+3
-3*4+3
-12+3
-9
Which symbol is needed between -2? |-3| to make a true statement? PLS HELP
60 points!!!!!!!!!!!!!!!
A. <
B. >
C. =
Answer:
[tex]\Huge \boxed{<}[/tex]
Step-by-step explanation:
-2 ? |-3|
Solve for absolute value.
Apply rule : |-a| = a
|-3| = 3
-2 ? 3
-2 is less than 3.
The less than symbol is “<”.
-2 < 3
Please help Simplify (3^6)^18
Answer:
when we put an exponent on a number which already has an exponent, the exponents are multiplied
we have: [tex]3^{6^{18} }[/tex]
= [tex]3^{108}[/tex]
(3)^6×18
(3)^108
now if you want to further simplify it then just simply calculate 3^108 on the calculator
to make it clear (3^6)^18 and 3^6^8 are two different situations
in the first one the power will be multiplied by the second power
and in the second one 6 will be multiplied by itself 8 times
15 points?
Solve for A
5/A = P
A = ????
That’s all it says
Please state what A is.
Answer:
A = 5 / P
Step-by-step explanation:
5 / A = P
A = 5 / P
Someone, please help me with this.
Answer:
x = 14
Step-by-step explanation:
To solve this problem, we must remember that the addition of two angles that create a straight line should have a sum of 180 degrees.
From this information, we can create the following equation.
(7x - 1) + (6x - 1) = 180
Eliminating the parentheses and grouping like terms gives us:
(7x + 6x) + (-1 + -1) = 180
Simplifying inside the parentheses on the left side produces:
13x - 2 = 180
Next, we should add 2 to both sides to isolate the variable term:
13x = 182
Finally, we should divide by 13 to get the x by itself on the left side of the equation:
13x/13 = 182/13
x = 14
Therefore, the answer to your question is x = 14.
Hope this helps!
Answer:
x = 14
Hope it helps u
plz mark it as brainlist
If g(x)=a x f(x+b) how is f(x) transformed to get g(x)
Answer:
a: -2f(x+4)
Step-by-step explanation:
Took the quiz, got 100%.
The function f(x) = ∛x is transformed to obtain g(x) = -2f(x + 4). Option A is correct.
The function f(x) = ∛x is shifted horizontally to the left by 4 units.
This means that every point on the graph of f(x) is moved 4 units to the left.
After the horizontal shift, the function is reflected vertically and stretched vertically by a factor of 2.
The reflection indicates that the graph is flipped upside down, and the stretching means that the graph is elongated vertically by a factor of 2.
By applying these transformations to the function f(x) = ∛x, we obtain the function g(x) = -2f(x + 4).
The negative sign indicates the vertical reflection, and the factor of 2 represents the vertical stretching.
The horizontal shift of 4 units is applied to the argument of the function, which is (x + 4)
To learn more on Graph transformations click:
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which statement is true about the value of |-5|
WILL GIVE BRAINLIEIST!!
The efficiency of a motor can be measured by the percent of input power that the motor uses. E(c) models the efficiency (in percentage points) of a certain motor as a function of the power inputs current c (in amperes). Match each statement with the feature of the graph that most closely corresponds to it.
Answer:
The matches are:
Feature: Increasing or decreasing interval (specifically, a decreasing interval)
Statement: As the input power's current grows beyond 1 ampere...
Feature: Relative minimum or maximum (specifically, relative maximum)
Statement: At its most efficient, the motor uses...
Feature: x-intercept
Statement: The motor loses all efficiency when the current...
Step-by-step explanation:
The first statement describes a decreasing interval, specifically the decreasing efficiency beyond 1 ampere of input current
The second statement describes a relative maximum, specifically the maximum efficiency at an input current of 1 ampere
The third statement describes an x-intercept, specifically the efficiency hitting 0% when the input current is ≥ 3 amperes
Answer:
(a) x -intercept with the last statement (the one at the bottom)
(b) Relative maximum with the second (middle) statement.
(c) Increasing or decreasing with the first (top) statement.
See details below:
Step-by-step explanation:
(a) The x-intercept goes with the info on what happens when the graph crosses the horizontal axis, so it goes with the third statement given:
The motor loses all efficiency when the current hits 3 amps.
(b) Relative max: agrees with what happens at the maximum the curve shows reaching approximately 50% value in the vertical scale:
At its most efficiency the motor uses about 50% of the input power
(c) Increasing or decreasing interval: The function clearly increases from values of the horizontal variable starting at around 0.4, up to a value of 1, and from then onwards it decreases. So it agrees with:
As the input grows more than 1 ampere, the motor becomes less efficient.
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios.
Answer:
6:8 and 9:12
Step-by-step explanation:
The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.
What are Equivalent Ratios?When compared to one another, equivalent ratios are defined as having the same values.
For example, 8/16, 4/8 and 1/2 re equivalent ratios because:
Given:
The table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, then
ratio = 3:4.
This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.
so,
6/8 = 3/4
9/12 = 3/4
Thus, 6/8 = 9/12 = 3/4, which is equivalent.
Hence, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
Learn more about equivalent ratios here:
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A linear trend equation is used to represent time series values when the data are changing by equal what? a. proportions b. amounts c. percentsd. percents and proportions
Answer: Amounts
Step-by-step explanation:
Time series analysis are the method which are used by researchers to analyze the time series data so as to get the features of the data and to also derive meaningful statistics.
A linear trend equation is used to represent time series values when the data are changing by equal amounts.
A........ divides a two - dimensional shape into two congruent shapes
Answer:
A diagonal. (A rectangle is divided into two triangles by a diagonal, for example.)
The diagonal of a triangle divides a two dimentional shape into two congruent shapes.
The congruent shapes are equally the same
Evaluate
Algebraic
Expressions
A large waffle cone costs $2.06 dollars more than a
sugar cone. The sugar cone is 1.56.
What is the cost of the waffle cone?
Answer:
The waffle cone is $3.62.
First, say what your variables are.
w = large waffle cone
s = sugar cone
Next, create two equations given the data in the word problem.
[tex]2.06 + s = w[/tex]
[tex]s = 1.56[/tex]
Because you have what the sugar cone is valued at, replace the s in the first equation with 1.56 and solve.
[tex]2.06 + (1.56) = w[/tex]
[tex]w = 3.62[/tex]
A standard number cube is rolled. Calculate: P(rolling a 5)
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Total no. of outcomes = 1,2,3,4,5,6
No. of times 5 is on the cube =1
Therefore, probability of getting a 5 = [tex]\frac{1}{6}[/tex]
Starbucks repurchased over $7,208.7 million of its common stock in 2018. Did this repurchase increase or decrease Starbucks’ ROE?
Can someone help me QUICK lol sorry!! B is the midpoint of AC. If AB=8x+2, and BC = 4x+18. Find AC
Answer:
AC = 12x + 20
Step-by-step explanation:
Combine the terms:
AB + BC = AC
AB = 8x + 2
BC = 4x + 18
Plug in the corresponding terms to the corresponding variables:
(8x + 2) + (4x + 18) = AC
AC = 8x + 4x + 18 + 2
AC = 12x + 20
12x + 20 is your answer for AC.
~
Answer:
68
Step-by-step explanation:
8x+2=4x+18
8x-4x=18-2
4x=16
x=4
Now we substitute it back in:
8(4)+2+4(4)+18-
32+2+16+18=
68
Choose the best definition for the following term: variable
Step-by-step explanation:
a variable is a quantity that may change within the context of a mathematical problem or experiment
I hope this was helpful
What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement
Answer:
Parametric tests are used for interval and ratio data and Non parametric tests are used for ordinal and nominal data.
Step-by-step explanation:
Parametric tests are used for interval and ratio data and Non parametric tests are used for ordinal and nominal data.
The interval data shows data with differences or intervals.
The ratio data is the one in which statistical inferences is used and can be added ,subtracted , multiplied, or divided.
Ordinal data is one in which we measure quantitative data such as height , weight but is in order.
Nominal data is one in which we measure quantitative data such as hair color eye color without order or which does not require order or sequence.
Write the set of all real numbers greater than 19 and less than 32 in set-builder notation.
The set-builder notation is {x|
Answer: {xI x ∈ R, 19 < x < 32}
Step-by-step explanation:
This notation is:
{xI condition1, condition2, ...}
The first condition is:
From what set we take the values of x?
From the set of real numbers.
x ∈ R
The other conditions are the limitations that we have for x, in this case:
19 < x < 32
Then we can write this as:
{xI x ∈ R, 19 < x < 32}
Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 32. Is Theodore correct? A Yes, the triangles are similar with a scale factor of 32. B No, the triangles are similar with a scale factor of 21. C No, the triangles are similar with a scale factor of 23. D No, the triangles are similar with a scale factor of 43.
*Correct Question:
Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 3/2. Is Theodore correct?
A. Yes, the triangles are similar with a scale factor of 3/2.
B. No, the triangles are similar with a scale factor of 2/1.
C. No, the triangles are similar with a scale factor of 2/3.
D. No, the triangles are similar with a scale factor of 4/3.
Answer:
C. No, the triangles are similar with a scale factor of 2/3.
Step-by-step explanation:
∆TUV is the original triangle. After transformation, the size reduced to give us ∆WXY. This means ∆TUV was reduced by a scale factor to give ∆WXY. The scale factor should be a fraction, suggesting, the original size of the ∆ was reduced upon transformation.
Thus, the ratio of their corresponding sides = the scale factor.
This is: [tex] \frac{8}{12} = \frac{16}{24} = \frac{12}{18} = \frac{2}{3} [/tex]
If you multiply the side length of ∆TUV by ⅔, you'd get side length of ∆WXY.
So, Theodore is wrong.
Round 3.802 to the nearest tenth.
Answer:
3.8
Step-by-step explanation:
.8 is in the tenths
Suppose "35" cars start at a car race. In how many ways can the top 3 cars finish the race?
The number of different top three finishes possible for this race of 35 cars is 39,270. (Use integers for any number in the expression.)
Answer:
The value is [tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]
Step-by-step explanation:
From the question we are told that
The total number of cars is [tex]n = 35[/tex]
The number cars considered is [tex]r = 3[/tex]
Generally the number of different top three finishes possible for this race of 35 cars is mathematically represented as
[tex]\left n } \atop }} \right. P_r = \frac{n!}{(n - r) !}[/tex]
[tex]\left 35 } \atop }} \right. P_3 = \frac{35! }{(35 - 3) !}[/tex]
[tex]\left 35 } \atop }} \right. P_3 = \frac{35 * 34 * 33 * 32! }{32 !}[/tex]
[tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]
Which of the following relations represent a function? A. {(-1,-1),(0,0),(2,2),(5,5)}. B. None of these. C. {(0,3),(0,-3),(-3,0),(3,0). D. {(-2,4),(-1,0),(-2,0),(2,6)
Answer:
A
Step-by-step explanation:
In a list of ordered pairs, a relation that is a function will not have any repeated x-values.
A -- a function (x-values are {-1, 0, 2, 5} with no repeats)
B -- irrelevant
C -- not a function (x-values are {0, 0, -3, 3} with 0 being repeated)
D -- not a function (x-values are {-2, -1, -2, 2} with -2 being repeated)
Evaluate R C F · dr, where F(x, y, z) = 5xi − 5yj − 3zk and C is given by the vector function r(t) = hsin t, cost, ti, where 0 ≤ t ≤ π.
Answer:
[tex]\mathbf{ - \dfrac{3 \pi^2}{2}}[/tex]
Step-by-step explanation:
Given that:
F(x, y, z) = 5xi - 5yj - 3zk
The objective is to evaluate the [tex]\int _c F \ dr .C[/tex]
and C is given by the vector function r(t) = (sin t, cost, t) where 0 ≤ t ≤ π
[tex]F(r(t)) = 5 \ sint \ i - 5 \ cost \ j - 3t \ k[/tex]
∴
[tex]\int_c F . \ dr = \int ^{\pi}_{0} ( 5 \ sint \ i - 5 cos t \ j - 3 t \ k ) ( cos \ t , - sin \ t , 1 ) \ dt[/tex]
[tex]=\int ^{\pi}_{0} ( 5 \ sint \ cost+ 5 cos t \ sin t - 3 t) dt[/tex]
[tex]=\int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt -3 \int ^{\pi}_{0} \ dt[/tex]
[tex]= \int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt - 3 [\dfrac {t^2}{2}]^{\pi}_{0} \ \ dt[/tex]
[tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0} - \dfrac{3}{2}(\pi)^2[/tex]
By dividing 2 with 10 and integrating [tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0}[/tex]; we have:
[tex]=5(sin^2t -sin^2 0) -\dfrac{3 \pi^2}{2}[/tex]
[tex]=5(0) -\dfrac{3 \pi^2}{2}[/tex]
[tex]= 0 - \dfrac{3 \pi^2}{2}[/tex]
[tex]\mathbf{= - \dfrac{3 \pi^2}{2}}[/tex]
What is an equation of the line that passes through the points (5,-2) and (2, -5)?
Put your answer in fully reduced form.
Answer:
it would be -4
Step-by-step explanation:
because a positive and negative 5 cancel each other out.
and a negative 2 plus a positive 2 is a negative 4.
4) A bay contains 18 balls out of which ac balls
are white :
one ball is drawn at random
what is the probability that it is white
ii) at two more white balls are put in the
bag
the probability of craving a white ball
& times than that it was before. Find a
Answer:
find a what?because it dont tell us what to find
What value(s) of x will make each equation below true?
2x – 6 = 3x +1-x-7
The answer is any value that you put in for x would make the equation true. When you simplify the whole equation it looks like this: 2x - 6 = 2x - 6, therefor you could replace x with any value.
is 289 a prime number
Answer:
No
Step-by-step explanation:
Factors of 289 are = 1, 7, 289
answer
no
explanation
the factor of 289= 1 , 17