Answer:
0.99 probability that at least one trip will last less than an hour
Step-by-step explanation:
For each time that the machine is used, there are only two possible outcomes. Either it lasts more than an hour, or it does not. The probability of a trip lasting more than an hour is independent of other trips. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
0.8 probability of lasting more than one hour.
So [tex]p = 0.8[/tex]
20 trips
So [tex]n = 20[/tex]
Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour?
Either all the trips last for more than an hour, or at least one does not. The sum of the probabilities of these outcomes is decimal 1. So
[tex]P(X = 20) + P(X < 20) = 1[/tex]
We want P(X < 20). So
[tex]P(X < 20) = 1 - P(X = 20)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 20) = C_{20,20}.(0.8)^{20}.(0.2)^{0} = 0.0115[/tex]
[tex]P(X < 20) = 1 - P(X = 20) = 1 - 0.0115 = 0.9885[/tex]
0.9885 probability that at least one trip will last less than an hour
Rouding to the nearest hundreth.
0.99 probability that at least one trip will last less than an hour
A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is 950 ft2. If the length of the pool is 8 feet longer than the width, find the dimensions of the pool.
Answer:
[tex]x \approx 21.080\,ft[/tex], [tex]y = 29.080\,ft[/tex]
Step-by-step explanation:
The total area of the pool and the walkway is:
[tex](x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^{2}[/tex]
[tex](x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^{2}[/tex]
[tex]x^{2} + 20\cdot x + 84\,ft^{2} = 950\,ft^{2}[/tex]
[tex]x^{2} + 20\cdot x - 866\,ft^{2} = 0[/tex]
The roots of the second-order polynomial is:
[tex]x_{1} \approx 21.080\,ft[/tex] and [tex]x_{2} \approx -41.081\,ft[/tex]
The only possible root is:
[tex]x \approx 21.080\,ft[/tex]
The other dimension of the pool is:
[tex]y = x + 8\,ft[/tex]
[tex]y = 21.080\,ft + 8\,ft[/tex]
[tex]y = 29.080\,ft[/tex]
This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 163 people in the first group and this group will be administered the new drug. There are 160 people in the second group and this group wil be administered a placebo. After one year, 13% of the first group has a second episode and 14% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups.
Answer:
Δπ Min = -0.0709
Δπ Max = -0.0535
Step-by-step explanation:
Here we have
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})-(\mu_{1}-\mu _{2} )}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Where:
[tex]{\hat{p_{1}}[/tex] = 13% = 0.13
[tex]\hat p_{2}[/tex] = 14% = 0.14
n₁ = 163
n₂ = 160
Therefore, we have;
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Plugging the values gives
z = -0.263
CI 90% = critical z = [tex]\pm[/tex]1.644
The minimum difference in true proportion = -0.0709
The maximum difference in true proportion = 0.0535.
Evaluate 4 - 2f when f = 1.
Answer:
2
Step-by-step explanation:
4 -2f
Let f =1
4 - 2(1)
Multiply and divide first
4 -2
2
Complete the division. The remainder is 0. The quotient is
X^2 - X - 12
-X^2 + x + 12
12x^2 - X-1
12x^2 + x + 1
Answer:
The first option....x^2-x-12
Step-by-step explanation:
Answer: x^2-x-12
Step-by-step explanation: correct answer
Amy deposited $460 into a savings account that pays 3.2% annual interest. In 5 years, how much interest will she have earned?
Answer:
$73.60
Step-by-step explanation:
take 460 times .032 witch is 14.72 then times that by 5
In a test of the effectiveness of garlic for lowering cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.9 and a standard deviation of 15.8. Use a 0.01 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Answer: We do not sufficient evidence that mean is greater than 0.
Step-by-step explanation:
Since we have given that
n = 36
mean = 0.9
Standard deviation = 15.8
at 0.01 level of significance,
Hypothesis would be:
[tex]H_0:\mu =0\\\\H_1=\mu\neq 0[/tex]
Standard error of mean would be :
[tex]\dfrac{\sigma}{\sqrt{n}}=\dfrac{15.8}{\sqrt{36}}=\dfrac{15.8}{6}=2.63[/tex]
statistic value would be :
[tex]t=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{0.9-0}{2.63}\\\\t=\dfrac{0.9}{2.63}\\\\t=0.342[/tex]
Degree of freedom = df = 36-1=35
So, p value = 2.4377
Since 2.4377 > 0.342, we will not reject null hypothesis.
Hence, We do not sufficient evidence that mean is greater than 0.
Find the volume of this prism
Answer:
840cm cubed
Step-by-step explanation:
720+120
A square pizza box has a width of 24”. What it the area of the largest circular pizza that could fit in the box?
Answer:
452.16 inches squared
Step-by-step explanation:
Answer:
452.39 in.^2
Step-by-step explanation:
since the width of the box is 24, the diameter of the circles is also 24.
using 12 as the radius, we plug it into the equation pi(12)^2 and we get 452.39 in^2
what is 5x-(x-2)>2x-4(x-8)
Answer:
x > 5
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(4x + 2) - (2x - 4 • (x - 8)) > 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
6x - 30 = 6 • (x - 5)
Equation at the end of step 3 :
6 • (x - 5) > 0
Step 4 :
4.1 Divide both sides by 6
Solve Basic Inequality :
4.2 Add 5 to both sides
x > 5
(X+1)(x+8) in standard form
x²+9x+8
Step-by-step explanation:Rewrite
(x+1)(x+8)
Distribute
x²+8x+1x+8
Simplify
x²+9x+8
Answer:
[tex]x^{2}[/tex] + 9x + 8 i hope this helps! :)
Step-by-step explanation:
distribute the x to the x and 8 [tex]x^{2}[/tex] + 8x
distribute the 1 to the x and 8 x + 8
put the two together [tex]x^{2}[/tex] + x + 8x + 8
combine like terms [tex]x^{2}[/tex] + 9x + 8
I dont know how to do this, i mean i do but its hard
Answer:
Step-by-step explanation:
opposite= 8 : the length opposite angle c
adjacent=15 : the length next to angle c, not the hypotenuse
hypotenuse= 17 : the hypotenuse will always be opposite the right angle
[tex]sinC=\frac{opposite}{hypotenuse}\\ \\sinC=\frac{8}{17}[/tex]
[tex]cosC=\frac{adjacent}{hypotenuse}\\\\cosC=\frac{15}{17}[/tex]
[tex]tanC=\frac{opposite}{adjacent} \\\\tanC=\frac{8}{15}[/tex]
A tree grows 6 feet per year. Which rates are equivalent to 6 feet per year? Select all that apply. A. 2 inches per year B. 18 inches per year C. 12 feet in 4 years D. 72 inches per year E. 2 yards per year F.18 feet in 3 years
Answer:
D is correct E is correct F is correct
Step-by-step explanation:
72/12=6 ft per year
2 yards= 6 ft per year
18/3=6 ft per year
The equivalent rates to 6 feet per year are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.
Explanation:The student is asking about equivalent rates. To determine which rates are equivalent to 6 feet per year, we need to compare each option against the given rate. The conversion factors needed for this problem are:
1 foot = 12 inches1 yard = 3 feetOption A: 2 inches per year is not equivalent to 6 feet per year.
Option B: 18 inches per year is equivalent to 6 feet per year because 18 inches is 1.5 feet, and thus, 1.5 feet multiplied by 4 would give us 6 feet in 4 years.
Option C: 12 feet in 4 years is equivalent to 6 feet per year because dividing 12 feet by 4 years gives us 3 feet per year, which is half of the given rate.
Option D: 72 inches per year is equivalent to 6 feet per year because 72 divided by 12 is 6.
Option E: 2 yards per year is equivalent to 6 feet per year because 2 multiplied by 3 is 6.
Option F: 18 feet in 3 years is equivalent to 6 feet per year because dividing 18 feet by 3 years gives us 6 feet per year.
Thus, the equivalent rates to 6 feet per year from the options given are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.
Learn more about Equivalent Rates here:
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Find the value of the unknown
Answer:
a= 35°
b=70
c=70
Step-by-step explanation:
if u need explanation comment and I'll explain
Richard and Linda enjoy visiting Hilton Head Island, South Carolina. The distance from their home to Hilton Head is 813 mi, so the drive takes them days. Richard and Linda travel twice as far the first day as they do the second day. How many miles do they travel each day?
Answer:
distance travelled first day is 542 miles while that travelled on second day = 271 miles.
Step-by-step explanation:
please kindly see the attached files for details
Richard and Linda travel 542 miles on the first day and 271 miles on the second day to reach Hilton Head Island, with the total distance being 813 miles.
Explanation:The student's question pertains to splitting a total distance into two parts, with a given ratio between the two parts. Since Richard and Linda travel twice as far on the first day as the second day, we can let the distance traveled on the second day be x miles. Therefore, the distance they travel on the first day would be 2x miles.
The total distance traveled to Hilton Head is 813 miles, so we can write an equation based on the sum of the distances traveled on both days: 2x (first day) + x (second day) = 813 miles. Simplifying this equation, we have 3x = 813 miles. Dividing both sides of the equation by 3 yields x = 271 miles.
This means that Richard and Linda travel 271 miles on the second day and 2 * 271 miles, which is 542 miles, on the first day. So, the distances Richard and Linda travel to Hilton Head Island on the first and second days are 542 miles and 271 miles, respectively.
PLEASEEEEEEEEEE HELPPPPPPPPPPP
Answer:
I would just guess, but if i were to actually think about it, i would think C. I hope it helps, and blame it on me if you fail.
Step-by-step explanation:
Which represents a quadratic function
answer:
it's the second one -7^2-x+2
explanation:
in order to be a quadratic function it has to meet this criteria: ax² + bx + c
it can't be the first one because there is no bxit can't be the third one because there has to be at least an exponent of 2it can't be the last one because a CANNOT be 0, hoped this help pls lmk if i'm right lolThe quadratic function is -7x²-x+2. Therefore, option B is the correct answer.
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
Here, the quadratic function is -7x²-x+2
Therefore, option B is the correct answer.
Learn more about quadratic function here:
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A university wants to estimate the average distance that commuter students travel to get to class with an error of ±3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles, using the Empirical Rule μ ± 3σ to estimate σ.
Answer:
A university wants to estimate the average distance that commuter students travel to get to class with an error of ±3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles, using the Empirical Rule μ ± 3σ to estimate σ.
The required sample size, n=(zσ/E)² = 21.0
Step-by-step explanation:
The estimated σ here = (range)/6 = (50/6) = 8.33
In the case of 90 % , CI value of z = 1.64
standard deviation, σ= 8.33
margin of error E = 3
The required sample size, n=(zσ/E)² = 21.0
Answer:
n = 21
Step-by-step explanation:
Solution:-
- Let denote a random variable "X" : average distance that commuter students travel to get to class.
- The population is given to be normally distributed, such that:
Range X: [ 0 , 50 ] miles
- We will use the given range coupled with the empirical rule for normal distribution to determine the mean (u) and standard deviation of population (σ):
P ( μ - 3σ < X < μ + 3σ) = 0.997 ..... (Empirical Rule)
- According to the standardized results for Z-table:
P ( -3 < Z < 3 ) = 0.997
So, P ( Z ≤ 3 ) = 1 - (1 - 0.997) / 2 = 0.9985
P ( Z ≥ -3 ) = 1 - (1 - 0.997) / 2 = 0.9985
- The standardized values for the given data can now be determined:
P ( X ≥ μ - 3σ ) = P ( Z ≥ -3 ) = 0.9985
X ≥ μ - 3σ = Upper limit - 0.9985*( Range )
X ≥ μ - 3σ = 50 - 0.9985*( 50 )
μ - 3σ = 0.075 ..... Eq1
P ( X ≤ μ + 3σ ) = P ( Z ≤ 3 ) = 0.9985
X ≤ μ + 3σ = Lower limit + 0.9985*( Range )
X ≤ μ + 3σ = 0 + 0.9985*( 50 )
μ + 3σ = 49.925 ..... Eq2
- Solve the Eq1 and Eq2 simultaneously:
2μ = 50 , μ = 25 miles
3σ = 24.925
σ = 8.30833
- Hence, the normal distribution parameters are:
X ~ N ( μ , σ^2 )
X ~ N ( 25 , 8.308^2 )
- The standard error in estimation of average distance that commuter students travel to get to class is E = ±3 miles for the confidence level of 90%.
- The Z-critical value for confidence level of 90%, Z-critical = 1.645
- The standard error estimation statistics is given by the following relation with "n" sample size.
E = Z-critical*σ /√n
n = [ Z-critical*σ /E ]^2
- Plug in the values:
n = [ 1.645*8.308/3]^2
n = 20.75306 ≈ 21
Answer: The sample size needed to estimate average distance that commuter students travel to get to class with error of ±3 miles and 90 percent confidence, is n = 21.
Wayne owns a house with a value of $215,000. He has a mortgage of $175,000 on the house. He has a car worth $12,500 with a loan of $4,000 outstanding. He has $1,875 worth of electronic equipment and a saving account of $2,400. He owes $1,275 on his credit card.
What is the amount of his assets?
What is the amount of his liabilities?
What is Wayne's net worth?
Answer:
Assets: $231,775
Liabilities: $180,275
Net worth: $51,500
Step-by-step explanation:
- Assest is something of value. ex. house, barns, tractors. To find this take...
215,000+12,500+1,875+2,400=$231,775
(All these numbers are good things he has, not debt.)
- Liability is debt you will need to repay. ex. loans or accounts payable. To find this take...
175,000+4,000+1,275=$180,275
- Net worth is the difference between your total assests and total liabilities. Knowing difference is subtraction, we should subtract assests minus liablities. To find this take...
$231,775-$180,275=$51,500
- Hope this helps! If you have any further questions or other problems you need help on please let me know as I would be glad to help.
A container contains a large unspecified number of ping-pong balls. A student takes 80 balls from the container, marks them with a blue dot, returns the marked balls to the container, and thoroughly mixes the balls. She then takes 80 balls again from the container. Of these, 16 have blue dots. She now wants to use this data to estimate the total number of ping-pong balls in the container. What is an estimate for the number of ping-pong balls in the container?
Answer:
400 ping pong balls
Step-by-step explanation:
Let the total number of ping pong balls =x
Out of x ping pong balls, 80 are marked with a blue dot
Out of 80 ping pong balls, 16 are marked with a blue dot.
Expressing it as a ratio:
x:80=80:16
[tex]\frac{x}{80}=\frac{80}{16}\\ 16x=80X80\\x=6400 \div 16\\x=400[/tex]
There are an estimate of 400 ping pong balls in the container.
A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular velocity? How far will it travel in that time? Round to the nearest tenth.
180°; 4 rev/sec
Step-by-step explanation:
The coin roll revolution = 4 rev / sec
Angle = 180° which is 1/2 of a revolution(360°).
The circumference of a circle is 2πr.
Radius of the circle, r = 10 mm
The circumference of this coin = 20π mm.
Again 180° is half of a roll,
the circumference = [tex]\frac{20\pi }{2}[/tex] = 10π
The coin travels 31.42 mm.
help pls!!!!!!!!!!! i don't know how to attempt
Answer:16
Step-by-step explanation:AC is half of ED
A fountain in the park has two circular pools that are the same size. What is the total area of the pools if the radius is 3 yards? Use 3.14 for Pi and round the approximate area to the nearest tenth, if necessary. Check all that apply.
Answer:
56.6 square yards.
Step-by-step explanation:
Given:
A fountain in the park has two circular pools that are the same size.
Question asked:
What is the total area of the pools if the radius is 3 yards ?
Solution:
First of all we will calculate the area of a circular pool.
As we know:
[tex]Area\ of\ circle=\pi r^{2}[/tex]
[tex]=\frac{22}{7} \times(3)^{2} \\ \\ =\frac{22}{7}\times9\\ \\ =\frac{198}{7} \\ \\ =28.28\ square\ yards[/tex]
Area of circular pool nearest tenth = 28.3 square yards
Now, as given that both pools are of same size.
Total area of the pools = 28.3 square yards + 28.3 square yards
= 56.6 square yards.
Thus, the total area of the pools are 56.6 square yards.
Answer:
ur answer is 56.5 and 18
Step-by-step explanation:
4.
How can you use a graph of a linear relationship to predict an unknown
value of y for a given value of x within the region of the graph?
Step-by-step explanation:
Take a look at this graph (sorry, it's small). The graph shows three data points, (0, 1), (2, 6), and (4, 8). The line is called the "line of best fit" or "regression line."
The equation for the line is y = 1.75x + 1.5 .
The data did not include a point for x = 3, but it can be predicted by finding the y-coordinate on the line that corresponds to x = 3.
Substituting x = 3 into the line's equation gives
y = 1.75(3) + 1.5 = 6.75
That's the predicted value of y for x = 3 given the linear relationship shown.
Find the slope of the line through (–9, –10) and (–2, –5). A. –five-sevenths B. seven-fifths C. five-sevenths D. –negative seven-fifths (please help much aprecciated)
Answer:
C 5/7
Step-by-step explanation:
We can find the slope of a line using
m = (y2-y1)/(x2-x1)
= (-5 - -10) /(-2 - -9)
= (-5 +10)/(-2+9)
5/7
A company is designing a new cylindrical water bottle. The volume of the bottle will be 211 cm^3. The height of the water bottle is 7.9 cm. What is the radius of the water bottle? Use 3.15 for pi
Answer:
The correct answer is 2.912 cm.
Step-by-step explanation:
A company is designing a new cylindrical water bottle.
Volume of a cylinder is given by π × [tex]r^{2}[/tex] × h, where h is the height of the cylinder and r is the radius of the cylinder.
The volume of each bottle will be 211 [tex]cm^{3}[/tex].
The height (h) of the water bottle be 7.9 cm.
Let the radius of the bottle be r cm.
∴ π × [tex]r^{2}[/tex] × h = 211 ; (π = 3.15)
⇒ [tex]r^{2}[/tex] × 24.885 = 211
⇒ r = 2.912
The radius of the water bottle is 2.912 cm.
y= 0.216 x + 32.575
what is the slope
Given:
The given equation of the line is [tex]y=0.216x+32.575[/tex]
We need to determine the slope of the equation.
Slope:
Let us determine the slope of the equation.
The general form of the equation of the line is given by
[tex]y=mx+b[/tex]
where m is the slope of the equation and b is the y - intercept.
Now, we shall compare the general form of the equation of the line with the given equation, we have;
[tex]m= 0.216[/tex] and [tex]b=32.575[/tex]
Thus, the slope of the equation of the line is [tex]m= 0.216[/tex]
the slope is 0.216
And just in case you need it the y-intercept is 32.575
I hope this was helpful :)
Venus is the planet that comes nearest to Earth. It's closest position is about 38.000,000 kilometers from Earth. Write this number expressed as a product of 38 and a power of 10. I am in 5th grade and this is for math.
Answer:
The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]
Step-by-step explanation:
In math when we're dealing with big numbers like this we express them in power of 10, since it'll be easyer to read that way. We take the parts of the number to the left that are not equal to "0", in this case 38, and multiply it by a power of 10. The expoent to this power of 10 will be the number of "0" after the 38 and before the ",". In this case the closest distance from Earth to Venus is 38,000,000 (there's a typo in the question). So we take the 38 and multiply it by [tex]10^{6}[/tex], since there are 6 zeros.
The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]
Un triángulo isósceles ,la altura al lado desigual mide 1 cm mas que longitud de ese lado . Calcula el valor de dicha altura sabiendo que el area es de 6 cm²
Answer:
Hence the required dimension is 4cm.
Step-by-step explanation:
Given:
An Isosceles triangle with uneven side=l+1 cm
Area= 6 sq cm
To Find:
Height of Triangle.
Solution:
We know that area of triangle given by,
Area=1/2*base*height.
Here height =1+base
6=1/2((b+1)*b
12=(b+1)*b.
b^2+b-12=0
(b-3)(b+4)=0
b=3 or b=-4
So length never be negative
so b=3 cm
And height=b+1=3+1=4 cm.
Each vertex of the polygon shown below forms a right angle. The side measurements given are inches. What is the area of the figure?
Given:
Given that each vertex of the polygon forms a right angle.
The measurements of the sides of the polygon were given.
We need to determine the area of the polygon.
Let us divide the polygon into 3 rectangles.
Area of the rectangle can be determined using the formula, [tex]A=length \times width[/tex]
Area of rectangle 1:
The length of rectangle 1 is 17 inches.
The width of rectangle 1 is 8.5 inches.
The area of rectangle 1 is given by
[tex]17 \times 8.5 =144.5 \ in^2[/tex]
Area of rectangle 2:
The length of rectangle 2 is 16.5 inches.
The width of rectangle 2 is (17 - 9) = 8 inches.
The area of rectangle 2 is given by
[tex]16.5 \times 8 =132 \ in^2[/tex]
Area of rectangle 3:
The length of rectangle 3 is 13 inches.
The width of rectangle 3 is 11 inches.
The area of rectangle 3 is given by
[tex]13 \times 11=143 \ in^2[/tex]
Area of the polygon:
The area of the polygon can be determined by adding the areas of the three rectangles.
Thus, we have;
[tex]Area=144.5+132+143[/tex]
[tex]Area=419.5 \ in^2[/tex]
Thus, the area of the figure is 419.5 square inches.
Hence, Option B is the correct answer.
If anyone could answer these