Answer:
it is unlikely that the spinner lands on pink.
Step-by-step explanation:
[tex]1- \frac{1}{8}\\ = 7/8[/tex]
There is 7/8 chance it is not going to land on pink
15 POINTS!!!! BRAINLIEST FOR THE FIRST ANSWER!!! Solve 3-x/2≤18
Answer:
[tex]x\geq -30[/tex]
Step-by-step explanation:
Work to isolate x on one side of the inequality:
[tex]3-\frac{x}{2} \leq 18\\3-18\leq \frac{x}{2} \\-15\leq \frac{x}{2}\\-30 \leq x[/tex]
Therefore the answer is all x values larger than or equal to -30
[tex]x\geq -30[/tex]
A water wheel has a radius of 4 feet and the bottom of the wheel is 1 foot from the ground. One plank is painted white and it starts at the top of the wheel. The wheel is rolled forward through an angle of pi over 3 radians. How high from the ground is the white plank after this motion?
Answer:
The height of the plank after the π/3 rotation motion is 8.464 ft
Step-by-step explanation:
The radius of the wheel = 4 ft
The elevation of the bottom of the wheel from the bottom = 1 foot
The angle to which the wheel is rolled = π/3 radians
The height of a rotating wheel is given by the following relation
f(t) = A·sin(B·t + C) + D
Where;
D = Mid line = 4 + 1 = 5 feet
B·t = π/3
C = 0
A = The amplitude = 4
Which gives;
f(t) = 4×sin(π/3) + 5 = 8.464 ft
The height of the plank after the π/3 rotation motion = 8.464 ft.
Answer:7 ft
Step-by-step explanation:
C
Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y = ln x, y = 3, y = 5. x = 0 Find the volume V of this solid. V = ____ Sketch the region, the solid, and a typical disk or washer. (Do this on paper. Your instructor may ask you to turn in this work.)
Answer:
volume = 33965.39
Step-by-step explanation:
Attached below is a detailed solution of the problem and the required sketch
volume of this solid is calculated integrating about the axis of : 5,3
Y = In x = x = e^y
the shaded region in the sketch represent the region where the rotating takes place.
Find the equation of the line with slope – 3 and that contains the point (-2,-6). Write the equation in the form y = mx +b and
identify m and b.
Answer:
m = -3
b = 0
equation of line
y = -3x
Step-by-step explanation:
in the the equation in the form y = mx +b
m is the slope
b is the y intercept.
__________________________________________________
given slope = -3
thus,
m = -3
the required equation of line is
y = mx +b
put m = -3
y = -3x + b
to find b , we put x = -2, y = -6 as this equation contains point (-2,-6).
-6 = -3*-2 + b
=> -6 = -6 + b
=> b = -6 + 6 = 0
thus. m = -3
b = 0
equation of line
y = -3x
A car used 1/64 of a gallon of gas to drive 1/4 of a mile. At this rate, how many miles can the car travel using 1 gallon of gas?
Answer:
16 mi
Step-by-step explanation:
To find how many miles you could travel with one gallon, you want to multiply both sides of the equation by 64. This will make '1/64' to 1, so the answer should be 1/4 * 64 = 16.
2/3x-2=5/6x
A: The solution set is (_) Simplified
B: There is no solution
Pick one and if A then simplify the answer
Answer:
x = - 12
Step-by-step explanation:
2 5
--- x - 2 = --- x
3 6
2x 5
--- - 2 = ------ x
3 3 * 2
(2x) - 3 * 2 5x
---------------- = --------
3 2 * 3
x = - 12
(6,-1) and y = – 1/3x+ 1
y = 3x + [?]
Answer:
- 19
Step-by-step explanation:
Let's consider the equation as ;
y = 3x + c
( 6, -1 ) satisfies the equation ;
-1 = 3( 6) + c
c = - 18 - 1
c = -19
So the slope - intercept is (- 19)
Write an integer to describe each situation: The Stock market increased by 75 points.
Answer:
The stock market increased 75 point: 75 or +75
Answer:
The stock market increased by 75 so your answer according to my understanding is +75 or 75.
Step-by-step explanation:
Hope it will help you :)
If point Q is translated 5 units to the right an 5 units down , what are the coordinates of Q?
Answer:
Q has coordinates (qx+5, qy-5)
Step-by-step explanation:
Q has coordinates (qx, qy)
we move 5 units to the right so add 5 to the value of x
Q has coordinates (qx+5, qy)
we move 5 units down so subtract 5 from the value of y
Q has coordinates (qx+5, qy-5)
If the police have 8 suspects, how many different ways can they select 5 for a lineup?
Answer:
56 different ways
Step-by-step explanation:
This is a combination question since it deals with selection. For example, if n objects is to be selected from a pool of r objects, this can be done in nCr different ways.
nCr = n!/(n-r)!r!
According to the question, If the police have 8 suspects, the different number of ways 5 can be selected for a line up is expressed as 8C5
8C5 = 8!/(8-5)!5!
8C5 = 8!/(3!)!5!
8C5 = 8*7*6*5!/3*2*5!
8C5 = 8*7*6/3*2
8C5 = 8*7
8C5 = 56 different ways
Hence, the selection of picking 5 for a line up out of 8 suspects can be done in 56 different ways.
A five-question quiz is taken in which the first and second questions have four answer choices, the third and fourth questions have three answer choices, and the last question has five answer choices. If a student randomly marks an answer for each question, what is the expected number of questions he will answer correctly?
Answer:
1.37
Step-by-step explanation:
The student can give only 0.139 % answer correctly.
The first and second questions have four answer choices,
Probability of first and second question answer correctly is,
[tex]P_{1}=\frac{1}{4}*\frac{1}{4} =\frac{1}{16}[/tex]
The third and fourth questions have three answer choices,
Probability of third and fourth question answer correctly is,
[tex]P_{2}=\frac{1}{3} *\frac{1}{3}=\frac{1}{9}[/tex]
The last question has five answer choices.
Probability of fifth question answer correctly is,
[tex]P_{3}=\frac{1}{5}[/tex]
The probability of corrected answer is,
[tex]P=P_{1}*P_{2}*P_{3}\\\\P=\frac{1}{16} *\frac{1}{9}*\frac{1}{5}=\frac{1}{720}[/tex] = 0.139 %
Hence, The student can give only 0.139 % answer correctly.
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Roger bowled 7 games last weekend. His scores are 155, 165, 138, 172, 127, 193 , 142. What is the RANGE of Roger's scores?
Answer:
66
Step-by-step explanation:
In statistics, the formula for RANGE is given as the difference between the Highest and the Lowest value.
In the above values we are given data consisting of the 7 games that Roger bowled.
155, 165, 138, 172, 127, 193 , 142.
Step 1
We arrange from the least to the highest.
127, 138, 142, 155, 165, 172, 193
Step 2
Lowest value = 127
Highest value = 193
Step 3
Range = 193 - 127
= 66
Therefore, the range of Roger's scores is 66
You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B on the shore. B is 70 meters from you down the shore. If you can swim at a speed of 5 meters per second and run at a speed of 7 meters per second, at what point along the shore, x meters from B, should you stop running and start swimming if you want to reach the buoy in the least time possible
Answer:
[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]
Step-by-step explanation:
From the given information:
The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.
Now, let V(x) be the time needed for the runner to reach the buoy;
∴ We can say that,
[tex]\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}[/tex]
In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.
i.e
The differential of V(x) = V'(x) =0
=[tex]\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0[/tex]
[tex]-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0[/tex]
[tex]\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]
[tex]\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]
[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}[/tex]
[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}[/tex]
squaring both sides; we get
[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}[/tex]
[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}[/tex]
By cross multiplying; we get
[tex]49x^2 = 25(54^2+x^2)[/tex]
[tex]49x^2 = 25 \times 54^2+ 25x^2[/tex]
[tex]49x^2-25x^2 = 25 \times 54^2[/tex]
[tex]24x^2 = 25 \times 54^2[/tex]
[tex]x^2 = \dfrac{25 \times 54^2}{24}[/tex]
[tex]x =\sqrt{ \dfrac{25 \times 54^2}{24}}[/tex]
[tex]x =\dfrac{5 \times 54}{\sqrt{24}}[/tex]
[tex]x =\dfrac{270}{\sqrt{4 \times 6}}[/tex]
[tex]x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}[/tex]
[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]
help!!! 10 points! <33
Answer:
B and C
Step-by-step explanation:
1/5 prefer apple juice
T = prefer orange juice
9/20 prefer apple or oranger juice
First, we can subtract 1/5 from 9/20 to get 1/4 (simplified)
Equation = 9/20 - 4/20 = 5/20 = 1/4
Plug it in:
A. 9/20 + 1/4 =1/5 (Incorrect)
B. 1/5 + 1/4 = 9/20 (Correct
C. 1/4 + 1/5 = 9/20 (Correct)
D. 1/4 - 1/5 = 9/20 (Incorrect)
Answer:
1/5 + t = 9/20
t + 1/5 = 9/20
Step-by-step explanation:
1/5 are apple + unknown for orange = apple + orange
1/5 + unknown = 9/20
Let t = unknown
1/5 + t = 9/20
order doesn't matter on the left side since we are adding
t+1/5 = 9/20
x^2−4x−21 I need help with this question and please right every step of it
Answer:
[tex] \boxed{ \boxed{ \sf{ \bold{( x - 7)(x + 3)}}}}[/tex]Step-by-step explanation:
[tex] \sf{ {x}^{2} - 4x - 21}[/tex]
Here, we have to find the two numbers that subtracts to 4 and multiplies to 21
⇒[tex] \sf{ {x}^{2} - (7 - 3)x - 21}[/tex]
⇒[tex] \sf{ {x}^{2} - 7x + 3x - 21}[/tex]
Factor out X from the expression
⇒[tex] \sf{ x(x - 7) + 3x - 21}[/tex]
Factor out 3 from the expression
⇒[tex] \sf{x(x - 7) + 3(x - 7)}[/tex]
Factor out x-7 from the expression
⇒[tex] \sf{(x - 7)(x + 3)}[/tex]
Hope I helped!
Best regards!!
Answer:
[tex]\boxed{\boxed{\bold{(x - 7)(x + 3)}}}[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 4x - 21 \\ {x}^{2} - 7x + 3x - 21 \\ x(x - 7) + 3(x - 7) \\ (x - 7)(x + 3)[/tex]
A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes ofremoval, the fish population increases by 10% each month. However, factoring in all causes, 80 fishare lost each month.Give a recurrence relation for the population of fish afternmonths. How many fish are there after5 months? If your fish model predicts a non-integer number of fish, round down to the next lowerinteger
Answer:
A) P_n = 1.06(P_(n-1)) - 80
B) 887 fishes
Step-by-step explanation:
A) We are told that the lake initially contains 1000 fishes.
Thus, P_o = 1000
Now, the number of fishes increases by 6% each month
Thus, after n months, we have;
P_n = P_(n-1) + 0.06P_(n-1)
P_n = 1.06P_(n-1)
Where P_(n-1) is the population of fish in the previous month.
We are told that 80 fishes are lost each month.
Thus;
P_n = 1.06(P_(n-1)) - 80
B) We want to find out how many fishes we have after 5 months.
Thus;
P_5 = 1.06(P_(5-1)) - 80
P_5 = 1.06(P_4) - 80
We don't know P_4,thus;
P_o = 1000
P_1 = 1.06(1000) - 80 = 980
P_2 = 1.06(980) - 80 = 958.8
P_3 = 1.06(958.8) - 80 = 936.328
P_4 = 1.06(936.328) - 80 = 912.50768
Thus,
P_5 = 1.06(912.50768) - 80 = 887.2581408 ≈ 887
9 - 8x - 7 - 2x equals 4 solve for x
Answer:
x = -1/2
Step-by-step explanation:
Step 1: Write out equation
9 - 8x - 8 - 2x = 4
Step 2: Combine like terms (x)
9 - 10x - 8 = 4
Step 3: Combine like terms (constants)
-10x - 1 = 4
Step 4: Add 1 to both sides
-10x = 5
Step 5: Divide both sides by -10
x = -5/10
Step 6: Simplify
x = -1/2
2. Two researchers make a test concerning the levels of marital satisfaction among military
families. Researcher A collects a sample of 22 married couples (n = 22); Researcher B
collects a sample of 40 married couples (n = 40). All other things being equal, which
researcher has more power to detect an effect? Explain.
Answer:
Researcher B
Step-by-step explanation:
Power of statistics is the probability that a test will correctly reject a false null hypothesis.
This probability is more accurate with greater sample size as it is better representation of the population.
Therefore researcher B has more power to detect an effect since he has nearly twice sample size (40 vs 22)
Simplify. Explanation if you can.
Answer:
10
Step-by-step explanation:
This expression uses the idea of exponential edition. The basis is, when you have the same base number being multiplied, you can add the exponentials.
Consider the case of 2 * 2. We know this to be 4. When writing 2 * 2, you can write this as 2^1 * 2^1 == 2^(1+1) == 2^2 == 4. See how we added the powers to get the new exponential?
We will apply this same idea here.
10^(1/2) * 10^(1/2) == 10^(1/2 + 1/2) == 10^(1) == 10.
So, the simplified expression is 10.
Cheers.
for 1-2 use the following inequality:
3x-4< 8
which of the following represents the solution set?
a. x ≥ 4
b. x > 4
c.x ≤ 4
d. x < 4
Answer:
D
Step-by-step explanation:
3x - 4 < 8
Add 4:
3x - 4 + 4 < 8 + 4
3x < 12
Divide by 3:
3x / 3 < 12 / 3
x < 4
Answer:
D. x<4
Step-by-step explanation:
3x-4<8
3x<8+4
3x<12
x<4
Hope this helps ;) ❤❤❤
If f(x) = 5x + 3x² - 7x
g(x) = 3x - 5x2 - 2
h(x) = -9x² + 8
find g(x) + h(x)
A) -6x - 5x + 6
B) 3x3 - 14x + 6
C) 3x2 - 4x + 10
D) - 11x + 10
Answer:
the answer is going to be A. -6x - 14 x+ 6
is -17 rational or irrational?
-17 is a rational number
What is a rational number?A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Rational numbers have finite or recurring decimal expansions. Irrational numbers are numbers that can not be expressed as the ratio or fraction of two integers. Irrational numbers have non-terminating and non-repeating decimal expansions.
Whereby -17 can be expressed as the value -17/1, based on the definition of a rational number, -17 is a rational number
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The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.f(x) = 3(x2 – 8x) + 10 (-8/2)^2 = 16 What is the function written in vertex form? A.f(x) = 3(x + 4)2 – 6 B.f(x) = 3(x + 4)2 – 38 C.f(x) = 3(x – 4)2 – 6 D.f(x) = 3(x – 4)2 – 38
Answer:
D
Step-by-step explanation:
Given
f(x) = 3x² - 24x + 10 ← factor out 3 from 3x² - 24x
= 3(x² - 8x) + 10
Using the method of completing the square
add/ subtract ( half the coefficient of the x- term )² to x² - 8x
f(x) = 3(x² + 2(- 4)x + 16 - 16) + 10
= 3(x - 4)² - 48 + 10
= 3(x - 4)² - 38 ← in vertex form → D
Answer:
d
Step-by-step explanation:
What is the solution to the equation StartFraction x Over 3 EndFraction + StartFraction x Over 6 EndFraction = seven-halves? x = Three-halves x = Seven-thirds x = 3 x = 7
Answer:
x=7
Step-by-step explanation:
took the test
The required solution of the equation is x = 7.
Given that,
Solution of the equation,
x / 3 + x / 6 = 7 / 2 is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the equation?
The equation is the relationship between variables and represented as y = ax + b is example of a polynomial equation.
Here,
x / 3 + x / 6 = 7 / 2
Taking LCM on the left side
[2x + x] /6 = 7 / 2
3x / 6 = 7 / 2
x / 2 = 7 / 2
x = 7
Thus, the required solution of the equation is x = 7.
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Our library has 3,489 non-fiction books, 8,617 fiction books and 1,240 reference books. If there are 564 students and each student borrows 6 books, how many books will be left in the library?
Answer:
9,962
Step-by-step explanation:
3,489+8,617+1,240=13,346
564*6=3,384
13,346-3,384=9,962
Which list shows numbers ordered from least to greatest?
A. 1.01,2119,1.01¯¯¯¯
B. 2119,1.01,1.01¯¯¯¯
C. 1.01,1.01¯¯¯¯,2119
D. 1.01¯¯¯¯,1.01,2119
Answer:
C. 1.01,1.01¯¯¯¯,2119
Step-by-step explanation:
1.01,1.01¯¯¯¯,2119
Is arranged from the least number to the greatest number.
It shows the numbers with decimals, and it showed the number with Dec again.
Then gave a space in between then the highest number in the least follows
So option c is the answer
both the Galapagos islands and the island of Nauru are on the equator, but the Galapagos islands are at 90.30degrees West whereas the island of Nauru is at 166.56degrees East. how far is it from the Galapagos islands to Nauru traveling over the Pacific ocean along the equator, correct to the nearest km? A. list and explain each step used in solving the question. B. identify the teaching materials or methods used you want to use in understanding and solving the question. C. implement the steps in (A) to solve the question.
Answer: This is what i can do . i hope it helps:)
The angle between the longitude of the Galapagos Islands and that of Nauru is 90.30°+166.56°=256.86°.
We find the sum since these places have different longitude directions, but this is the major arc, and the minor arc will be 360°−256.86°=103.14°.
Angle between Galapagos Islands and 180°E/W = 180° - 90.30° = 89.70°
Angel between Nauru island and 180°E/W = 180° - 166.56° = 13.44°
Total angle between Galapagos Islands and Nauru = 89.70 ° + 13.44° = 103.14°.
Step-by-step explanation:
[tex]let \:\alpha \:be\:our\:teetah \\l = \frac{r \pi}{180 \°} \times \alpha \\\\= \frac{6400\pi}{180 \°} \times 103.14\\\\= 11520.848\\\\= 11521 km[/tex]
Need help solving please.
Answer:
25/36
Step-by-step explanation:
Solved in steps:
- 2/9 - ( -11/12) =- 2/9 + 11/12 = - 2*4/9*4 + 11*3/12*3 =-8/36 + 33/36 = 25/36Simplest fraction is 25/36
Given the following group of numbers (8, 12, 4, 8, 6, 0, 9, 11, 3, 10) which of the following is (are) true? The mean is 7.1 The median is 1.6 The mode is 0
Answer:
The mean is 7.1
The median IS NOT 1.6 (its 8)
The mode IS NOT 0 (its 8)
Step-by-step explanation:
The true statement is , The mean is 7.1.
What is mean, median, mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
The mode is the number that occurs most often in a data set.
here, we have,
given data, group of numbers (8, 12, 4, 8, 6, 0, 9, 11, 3, 10)
now, we get,
The mean is 7.1.
The median IS NOT 1.6 (its 8)
The mode IS NOT 0 (its 8).
hence, The true statement is , The mean is 7.1.
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anyone know dis one pls
Answer:
A - the arrow on the right points to the point -2. the arrow on the left moves 7 places to the left to the point -9.
this is what the expression is stating: -2 - 7 = -9