Answer:
720 ways
The number of ways in which the promotion can be made is 720 ways
Step-by-step explanation:
Given that;
The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president.
This is a permutation problem because the order of selection is relevant. They will be promoted to various positions.
N = nPr = n!/(n-r)!
n = 10, r = 3
Substituting the values;
N = 10P3
N = 10!/(10-3)! = 10!/7!
N = 720 ways
The number of ways in which the promotion can be made is 720 ways
Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square increasing when the area of the square is 49 cm2
Answer:
70cm/sStep-by-step explanation:
Area of a square with side of length L is expressed as A = L². The rate at which the area is increasing will be expressed as dA/dt.
dA/dt = dA/dL * dL/dt where
dL/dt is the rate at which each side of the square is increasing.
Since dA/dL = 2L, dA/dt = 2L dL/dt
Given dL/dt = 5cm/s and the Area of the square = 49 cm²
49 = L²
L = √49
L = 7cm
dA/dt = 2(7) * 5
dA/dt = 14*5
dA/dt = 70cm/s
The rate at which the area of the square is increasing is 70cm/s
Use PQR below to answer the question that follows:
Answer:
Angle P is congruent to itself due to the reflexive property.
Explanation:
Angle P must be congruent to angle S through corresponding angle theory.
Otherwise, it wouldn't prove ΔPQR is similar to ΔSTR.
Answer:
Angle P is congruent to itself due to the reflexive property.
Step-by-step explanation:
The straight line L has equation y = 1/2x+7 The straight line M is parallel to L and passes through the point (0, 3). Write down an equation for the line M.
Answer:
y = [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Parallel lines have equal slopes
line M crosses the y- axis at (0, 3) ⇒ c = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line M
A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed. The sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using the rejection region method at a significance level of 0.05.
Answer:
Yes, it contradict this prior belief as there is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes.
Test statistic t=2.238>tc=1.708.
The null hypothesis is rejected.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the true average escape time is significantly higher than 6 minutes (360 seconds).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=360\\\\H_a:\mu> 360[/tex]
The significance level is 0.05.
The sample has a size n=26.
The sample mean is M=370.69.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=24.36.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{24.36}{\sqrt{26}}=4.777[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{370.69-360}{4.777}=\dfrac{10.69}{4.777}=2.238[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=26-1=25[/tex]
The critical value for a right-tailed test with a significance level of 0.05 and 25 degrees of freedom is tc=1.708. If the test statistic is bigger than 1.708, it falls in the rejection region and the null hypothesis is rejected.
As the test statistic t=2.238 is bigger than the critical value t=1.708, the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes (360 seconds).
You have a choice of receiving a wage of $39,000 per year,$2630 per month,$665 per week and 52 weeks of work per year
Answer:
$39,000
Step-by-step explanation:
This is the best answer because you recieve the most money. 2630*12 is 31560 dollars, and 665*52= $34580.
The perimeter of a rectangular city park is 1,428 feet. The length is 78 feet more than twice the width. Find the length and width of the park.
Answer:
Length = 502 ft
Width = 212 ft
Step-by-step explanation:
Recall the formula for the perimeter of a rectangle of length "L" and width "W":
Perimeter = 2 L + 2 W = 1428 ft
Now, since the length is 78 ft more than twice the width, then we can write this in mathematical form as:
L = 2 W +78
so, 2 W = L -7 8
and now replace "2 W" with it equivalent "L - 78" in the first perimeter equation and solve for "L":
2 L + L - 78 = 1428
3 L = 1428 + 78
3 L = 1506
L = 1506/3
L = 502 ft
Then the width W can be obtained via:
2 W = L - 78
2 w = 502 -78
2 W = 424
w = 212 ft
Which of the following is the graph of f(x)= |x| reflected on the x-axis, translated 3units left, 4 units up, and dilated by a factor of 4?
Answer:
Step-by-step explanation:
Reflecting on the x-axis is multiplying the formula by a -1. That is, the resulting form is pointing up. When translated to the left 3 units, the tip of the graph is at the point (-3,0). Then when shifted 4 units up the tip is at (-3,4). Dilated by a factor of 4 will affect the values in x, but not the values in y. So the tip remains at the point (-3,4) which corresponds to the second graph
The second graph is the right one.
The weight of people in a small town in Missouri is known to be normally distributed with a mean of 186 pounds and a standard deviation of 29 pounds. On a raft that takes people across the river, a sign states, "Maximum capacity 3,417 pounds or 17 persons." What is the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds?
Answer:
the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166
Step-by-step explanation:
The summary of the given statistical data set are:
Sample Mean = 186
Standard deviation = 29
Maximum capacity 3,417 pounds or 17 persons.
sample size = 17
population mean =3417
The objective is to determine the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds
In order to do that;
Let assume X to be the random variable that follows the normal distribution;
where;
Mean [tex]\mu[/tex] = 186 × 17 = 3162
Standard deviation = [tex]29* \sqrt{17}[/tex]
Standard deviation = 119.57
[tex]P(X>3417) = P(\dfrac{X - \mu}{\sigma}>\dfrac{X - \mu}{\sigma})[/tex]
[tex]P(X>3417) = P(\dfrac{3417 - \mu}{\sigma}>\dfrac{3417 - 3162}{119.57})[/tex]
[tex]P(X>3417) = P(Z>\dfrac{255}{119.57})[/tex]
[tex]P(X>3417) = P(Z>2.133)[/tex]
[tex]P(X>3417) =1- 0.9834[/tex]
[tex]P(X>3417) =0.0166[/tex]
Therefore; the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166
Write the equation of each line in slope-intercept form.
(If possible please show work)
Answer:
y= 3x+2
Step-by-step explanation:
i think im sorry if its wrong
I need help on question 8.
Answer:
50.18°
Step-by-step explanation:
∠BAD = ∠BAC +∠CAD
102° = (8x+17)° +(9x+11)° . . . . . substitute given values
102 = 17x +28 . . . . . . . . . . simplify, divide by degrees
x = (102 -28)/17 = 74/17 . . . . . solve for x
Then the angle of interest is ...
∠CAD = (9x +11)° = (9(74/17) +11)° = 50 3/17°
∠CAD ≈ 50.18°
The scheduled commuting time on the MTA Marc train from BWI to DC is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be less than 70 minutes
Answer:
60% probability that the commuting time will be less than 70 minutes
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X < x) = \frac{x - a}{b-a}[/tex]
Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes.
This means that [tex]a = 64, b = 74[/tex]
What is the probability that the commuting time will be less than 70 minutes
[tex]P(X < 70) = \frac{70 - 64}{74 - 64} = 0.6[/tex]
60% probability that the commuting time will be less than 70 minutes
Solve the system of equations. {y=30x+20 y=10x2−80
Answer:
(x, y) = (-8/3, -60)
Step-by-step explanation:
y = 30x + 20
y = 10 * 2 - 80 → y = 20 - 80
y = 30x + 20
y = -60
30x + 20 = -60
x = -8/3
(x, y) = (-8/3, -60)
Hope this helps! :)
Actividad 1.1
Investigue sobre el tema de diferenciabilidad en un punto para encontrar los valores de "a" y "b" tales que
la función
definida a continuación sea diferenciable en t = 2, luego construya su gráfica.
at +b, sit < 2
f(t) = {2t2 – 1, si 2 st
1
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उपरोक्त लिंक पर क्लिक करें, निम्नलिखित प्रश्न का उत्तर दें, फिर, मैं आपके प्रश्न का उत्तर दूंगा। (यदि आप मदद की जरूरत है, यह टिप्पणी करने के लिए उत्तर दें।)
uparokt link par klik karen, nimnalikhit prashn ka uttar den, phir, main aapake prashn ka uttar doonga. (yadi aap madad kee jaroorat hai, yah tippanee karane ke lie uttar den.)
Please answer this correctly
Answer:
7/8 chance
Step-by-step explanation:
There are 7 numbers that are either even or greater than 2: 2, 3, 4, 5, 6, 7, and 8. There is a 7/8 chance choosing either of those.
Answer:
7/8
Step-by-step explanation:
there are 6 numbers that are greater than 2: 3,4,5,6,7,8
there are 4 even numbers: 2,4,6,8
If A and Bare dependent events, which of these conditions must be true?
Answer:
Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.
Also, Two events are said to be independent if the outcome or occurrence of the first does not affects the outcome or occurrence of the second so that the probability is not changed.
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Answer:E. P(B\A)≠P(B)
Step-by-step explanation:
What is the most accurate statement about correlations? a. Apparent correlations between two or more variables can stimulate investigation and present possible solutions to be explored. b. Correlations prove cause-and-effect relationships. c. Correlations are not useful as statistical analysis tools. d. All of these choices
Answer:
a. Apparent correlations between two or more variables can stimulate investigation and present possible solutions to be explored.
Step-by-step explanation:
Correlation is a scenario, where an action X causes another action Y to occur, but one of the actions does not really need to affect the other's occurrence. Correlation occurs because of the tendency of people to seek the relationship between events. The fact that two events are happening at the same time does not necessarily imply a cause and effect relationship, although there might be a possibility of such.
Correlation is used in scientific studies to draw the relationship between two events, but it does not stop at that. Through investigation has to be made to confirm that there is indeed a correlation.
What are the intercepts?
Answer:
A, C, E, and F.
Step-by-step explanation:
To find the y-intercept, simply plug in 0 for x since y-intercepts are (0,y):
[tex]f(0)=\frac{(0-3)(0+4)(0-1)}{(0+2)(0-12)} =\frac{(-3)(4)(-1)}{(2)(-12)} =\frac{12}{2(-12)}=-1/2[/tex]
[tex](0,-1/2)[/tex]
To find the x-intercepts, plug in 0 for y since x-intercepts have the format (x,0):
[tex]0=\frac{(x-3)(x+4)(x-1)}{(x+2)(x-12)}[/tex]
[tex]0=(x-3)(x+4)(x-1)[/tex]
[tex]x=3, -4, 1[/tex]
[tex](-4,0), (1,0), (3,0)[/tex]
The correct choices are:
A, C, E, and F.
Please help will definitely say thanks
Answer:
[tex]\mathrm{Image \: below.}[/tex]
Explanation:
Ruby talks about a 3D shape, so sphere.
Shriya talks about the points that are equal in distance from the opposite points, the diameter, she is right.
Abhishek's definition is not shown completely in the photo, so by process of elimination, he is incorrect.
Solve (x – 3)2 = 5.
O A. X = 5+ 3
O B. X = 8 and x = -2
O C. X = 3 + 5
O D. X=-3+5
Step-by-step explanation:
(x - 3)2 = 5
2x - 6 = 5
2x = 5 +6
2x = 11
x = 11/2
x = 5.5
Answer: so what was the answer
Step-by-step explanation:
The probability of rolling two dice at the same time and getting a 4 with either die or the sum of the dice is 6
Answer:
Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6. We have already found 12 potential outcomes, and have yet to exhaust all of the possibilities of the first die. But with a second dice, there will be 24 different possibilities.
Step-by-step explanation:
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Sam has stamps from Malaysia, Thailand and New Zealand. The ratio of the number of stamps from Malaysia to the number of stamps from Thailand is 3:2.The ratio of the number of stamps from New Zealand to the number of stamps from Thailand is 6:5. What fraction of Sam's stamps is from Malaysia?
Answer:
21
Step-by-step explanation:
9 plus 10= 21
The ratio shows how many times one value is contained in another value.
The ratio of stamps from Malaysia, Thailand, and New Zealand is
15M : 10T : 12N
The fraction of stamps from Malaysia is 15/37.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of the number of stamps from Malaysia to the number of stamps from Thailand is 3:2.
This can be written as,
Number of stamps from Malaysia = 3M
Number of stamps from Thailand = 2T
Multiply both by 5.
Number of stamps from Malaysia = 15M ____(1)
Number of stamps from Thailand = 10T _____(2)
The ratio of the number of stamps from New Zealand to the number of stamps from Thailand is 6:5.
Number of stamps from New Zealand = 6N
Number of stamps from Thailand = 5T
Multiply both by 2.
Number of stamps from New Zealand = 12N _____(3)
Number of stamps from Thailand = 10T _____(4)
From (1), (2), (3), (4) we get,
15M : 10T : 12N
The fraction of stamps from Malaysia.
= 15/37
Thus,
The fraction of stamps from Malaysia is 15/37.
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The life in hours of a battery is known to be normally distributed, with a standard deviation of 1.25 hours. A random sample of 10 batteries has a mean life x = 40.5 hours.
a) Is there evidence to support the claim that battery life exceeds 40 hours? Use
α = 0.05.
b) What is the P-value for this test?
Answer:
a) Test statistic
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
b)
p- value = 0.8962
Step-by-step explanation:
Step(i):-
Given sample size 'n' =10
Mean of the sample x⁻ = 40.5 hours
Mean of of the Population μ = 40 hours
Standard deviation of the Population = 1.25 hours
Step(ii):-
Null Hypothesis:H₀: μ = 40 hours
Alternative Hypothesis :H₁ : μ < 40 hours
step(ii):-
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{40.5 -40}{\frac{1.25}{\sqrt{10} } }[/tex]
Z = 1.265
Level of significance = 0.05
Z₀.₀₅ = 1.96
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
Step(iii):-
P - value
P( Z < 1.265) = 0.5 + A( 1.265)
= 0.5 + 0.3962
= 0.8962
P( Z < 1.265) = 0.8962
i ) p- value = 0.8962 > 0.05
Accept H₀
There is no significant
The battery life is not exceeds 40 hours
the figure below shows a square ABCD and an equilateral triangle DPC:
Answer: c) SAS Postulate
Step-by-step explanation:
DP = PC Sides are congruent
∠ADP ≡ ∠BCP Angles are congruent (angles are between the sides)
AD = BC Sides are congruent
To finish the proof, we can state that ΔADP ≡ ΔBCP by the Side-Angle-Side (SAS) Postulate
You have different video games. How many different ways can you arrange the games side by side on a shelf? You can arrange the different video games in nothing different ways.
Answer:
See Explanation below
Step-by-step explanation:
This question has missing details because the number of video games is not stated;
However, you'll arrive at your answer if you follow the steps I'll highlight;
The question requests for the number of arrangement; That means we're dealing with permutation
Let's assume the number of video games is n;
To arrange n games, we make use of the following permutation formula;
[tex]^nP_n = \frac{n!}{(n-n)!}[/tex]
Simplify the denominator
[tex]^nP_n = \frac{n!}{0!}[/tex]
0! = 1; So, we have
[tex]^nP_n = \frac{n!}{1}[/tex]
[tex]^nP_n = n![/tex]
Now, let's assume there are 3 video games;
This means that n = 3
[tex]^3P_3 = 3![/tex]
[tex]^3P_3 = 3 * 2 * 1[/tex]
[tex]^3P_3 = 6\ ways[/tex]
So, whatever the number of video games is; all you have to do is; substitute this value for n;
f(x) = 9 + 4x f(0) = f(-1) = Find the value of x for which f(x) =6 x=
Answer: x=-3/4
Step-by-step explanation:
Since we know f(x)=6, we can set it equal to the equation.
6=9+4x [subtract 9 on both sides]
-3=4x [divide both sides by 4]
x=-3/4
Find all the missing side lengths for the following triangles.
Answer:
Step-by-step explanation:
A) u = 4 v = 4/(sqrt)3
B) b = 5 c = 10
C) b = 2(sqrt)2 a = 4
D) m and n are both 7(sqrt)2/2
The missing side lengths for the three triangles are 10√3, 12, and 8. The first triangle is a 30-60-90 triangle, the second triangle is a 45-45-90 triangle, and the third triangle is a right triangle. The missing side lengths were found using the properties of special triangles and the Pythagorean Theorem.
Here are the missing side lengths for the following triangles:
Triangle 1:
The missing side length is 15.
The triangle is a 30-60-90 triangle, so the ratio of the side lengths is 1:√3:2. The hypotenuse of the triangle is 20, so the shorter leg is 10 and the longer leg is 10√3. The missing side length is the longer leg, so it is 10√3.
Triangle 2:
The missing side length is 12.
The triangle is a 45-45-90 triangle, so the ratio of the side lengths is 1:1:√2. The hypotenuse of the triangle is 12√2, so each of the legs is 12. The missing side length is one of the legs, so it is 12.
Triangle 3:
The missing side length is 8.
We can use the Pythagorean Theorem to find the missing side length. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 10 and one of the other sides is 6. Let x be the missing side length.
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]
100 = 36 +[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 64
x = 8
Therefore, the missing side length is 8.
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I hat is the length of leg s in the right triangle shown
Answer:
s=5
Step-by-step explanation:
This triangle is right and with two equal sides since it has two congruent angle so we will use the pythagorian theorem:
s²+s² = (5[tex]\sqrt{2}[/tex])²2s² = 25*2 divide both sides by 2s² = 25s = 5Solve the problem. The scores on a certain test are normally distributed with a mean score of 60 and a standard deviation of 5. What is the probability that a sample of 90 students will have a mean score of at least 60.527? Write your answer as a decimal rounded to 4 places.
Answer:
15.87%
Step-by-step explanation:
We have to calculate the value of z:
z = (x - m) / (sd / n ^ (1/2))
where x is the value to evaluate, m is the mean, n is the sample size and sd is the standard deviation, we replace:
p (x <60,527) = z = (x - m) / (sd / n ^ (1/2))
p (x <60,527) = z = (60,527 - 60) / (5/90 ^ (1/2))
z = 1
if we look in the attached table, for z = 1 it is 0.8413
p (x> 60,527) = 1 - 0.8413
p (x> 60,527) = 0.1587
Therefore the probability is 15.87%
A U.S. dime has a diameter of about 18 millimeters. What is the area of one side of a dime to the nearest square millimeter? Use 3.14 as an approximation for pi. The area of one side of a U.S. dime is approximately _____ square millimeters.
Area of one side of a U.S. dime is approximately 254 square millimeters.
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.
Given that U.S. dime has a diameter of about 18 millimeters.
We need to find the area of one side of a dime to the nearest square millimeter.
Diameter=18 millimeters
Diameter is two times of radius
D=2R
18=2R
Divide both sides by 2
Radius is 9 millimeters.
Area of dime=πr²
=3.14×(9)²
=3.14×81
=254 square millimeters.
Hence, area of one side of a U.S. dime is approximately 254 square millimeters.
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A boat, which moves at 13 miles per hour in water without a current, goes 80 miles upstream and 80 miles back again in 13 hours. Find the speed of the current to the nearest tenth.
Answer:
Speed of current is 3 miles per hour.
Step-by-step explanation:
Speed of boat without current, u = 13 miles/hr
Let speed of current = v miles/hr
Speed upstream = (13 - v) miles/hr
Speed downstream = (13 + v) miles/hr
Distance traveled upstream, [tex]D_1[/tex] = 80 miles
Distance traveled downstream, [tex]D_2[/tex] = 80 miles
Total time taken, T ([tex]T_1+T_2[/tex]) = 13 hours
Formula for Total Time taken:
[tex]Time= \dfrac{Distance}{Speed}[/tex]
Time taken in Upstream:
[tex]T_1 = \dfrac{80}{13-v}\ hours[/tex]
Time taken in Downstream:
[tex]T_2 = \dfrac{80}{13+v}\ hours[/tex]
[tex]T = T_1+T_2 = 13\ hours\\\Rightarrow 13 = \dfrac{80}{13-v}+\dfrac{80}{13+v}\\\Rightarrow 13 = 80(\dfrac{13+v+13-v}{13^2-v^2})\\\Rightarrow 13^2-v^2 = \dfrac{80(26)}{13}\\\Rightarrow 169-v^2 = 80\times 2\\\Rightarrow v^2 = 169-160 = 9\\\Rightarrow v = 3\ miles/hr[/tex]
So, speed of current is 3 miles/hr