Answers
Answer:
? = 35°Step-by-step explanation:
Let the angle be x
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
7 is the hypotenuse
4 is the opposite
sin x = 4/7
x = sin-¹ 4/7
x = 34.85
x = 35° to the nearest degree
Hope this helps you
Related Questions
A local animal rescue organization receives an average of 0.55 rescue calls per hour. Use the Poisson distribution to find the probability that during a randomly selected hour, the organization will receive fewer than two calls.A) 0.087
B) 0.894
C) 0.317
D) 0.106
Answers
Answer:
B) 0.894
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
A local animal rescue organization receives an average of 0.55 rescue calls per hour.
This means that [tex]\mu = 0.55[/tex]
Probability that during a randomly selected hour, the organization will receive fewer than two calls.
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.55}*(0.55)^{0}}{(0)!} = 0.577[/tex]
[tex]P(X = 1) = \frac{e^{-0.55}*(0.55)^{1}}{(1)!} = 0.317[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.577 + 0.317 = 0.894[/tex]
Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.
Answers
Answer:
m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)
Step-by-step explanation:
Use sin to solve m∠A
sin x = 12/42 Simplify
sin x = 0.2857 Use the negative sin to solve for x
sin^-1 x = 17 degrees
Add together all of the angle measures to solve for m∠B
17 + 90 + x = 180 Add
107 + x = 180
-107 -107
x = 73 degrees
Use Pythagorean Theorem to solve for b
12^2 + x^2 = 42^2 Simplify
144 + x^2 = 1764
-144 -144
x^2 = 1620 Take the square root of both sides
x = 40
A penny, a nickel, a dime, and a quarter are tossed. What is the probability of obtaining exactly two tails on the tosses?
Answers
p
=
0.5
of heads or tails, we can model the probability of X out of N coins landing head side up with the binomial distribution:
(=∣)=()(1−)−
P
(
x
=
X
∣
p
)
=
(
N
X
)
p
X
(
1
−
p
)
N
−
X
Substituting the probability =0.5
p
=
0.5
and =4
N
=
4
into this pdf, we get:
(=)=(4)0.50.54−
P
(
x
=
X
)
=
(
4
X
)
0.5
X
0.5
4
−
X
To get the probability that three or more heads are obtained, we sum all the probabilities for ≥3
x
≥
3
, i.e.
(≥3)=∑=34(4)0.50.54−
P
(
x
≥
3
)
=
∑
x
=
3
4
(
4
X
)
0.5
X
0.5
4
−
X
(≥3)=(43)0.54+(44)0.54
P
(
x
≥
3
)
=
(
4
3
)
0.5
4
+
(
4
4
)
0.5
4
(≥3)=4(0.54)+0.54
P
(
x
≥
3
)
=
4
(
0.5
4
)
+
0.5
4
(≥3)=5(0.54)
P
(
x
≥
3
)
=
5
(
0.5
4
)
(≥3)=5(116)
P
(
x
≥
3
)
=
5
(
1
16
)
(≥3)=516=0.3125
P
(
x
≥
3
)
=
5
16
=
0.3125
Note: This particular question is simple enough to do without the above equation. One must recognize that there are 24
2
4
possible outcomes in the sample space of this four coin flip. Four of these outcomes have one coin which landed tails (one outcome for each different value of coin) i.e. three heads, and only one outcome exists where all coins are heads. These make up 5 of the 16 possible outcomes. Each are equally likely due to the equal probability of heads or tails for each coin, so we get the same answer as above.
there are 11 people in an office with 6 different phone lines. if all the lines begin to ring at once, how many groups of 6 people can answer these lines?
Answers
T_11
Expect_6 phones
This is a permutation problem
Therefore 11p6= 11!/(11-6)! = (5!*6*7*8*9*10*11)/5! = 6*7*8*9*10*11 (ANSWER)
Answer:
one group
Step-by-step explanation:
there is only one group of six people in the office since the office only has 11 people.
Please answer this correctly
Answers
Answer:
0
Step-by-step explanation:
3 cards
P( odd) = 1 odd/ 3 cards = 1/3
No replacement
2 cards 6,8
No odds
P( odd) = 0/2
P( odd, no replacement, odd) = 1/2 * 0 = 0
A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?
Answers
Answer:
50 miles
Step-by-step explanation:
hello,
let's note x the number of miles travelled heading west,
it takes 1 hour to travel 25 miles
so it takes x/25 hours to travel x miles
we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles
so in 7-x/25 hours it travels 19(7-x/25) miles
we can write, as the total distance is 145 miles
[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]
we can verify
50 miles heading West takes 2 hours
in 5 hours it travels 19*5 = 95 miles
the total is 145 miles
so this is correct
hope this helps
Help me plzzzzz!!!!
Answers
Answer:124
Step-by-step explanation:
2x + 8 + x - 2 = 180
Add like terms
3x + 6 = 180
Subtract the 6 from both sides
3x + 6 - 6 = 180 - 6
3x = 174
Divide by 3
x = 58
Now we have to find the measure of angle ACD
2(58) + 8 = 124
A farmer divided his land into 2 groups of sections randomly. There is no difference in the quality of the soil between the 2 groups of land. He used Type A seeds in the first group and Type B seeds in the second group. After 3 months, the heights of the crops are measured across the two groups of land sections. Is the study observational or experimental? If it is an experiment, what is the controlled factor?
Answers
Answer:
Experiment
Time..
Step-by-step explanation:
It is an experimental study. An experimental study is a type of study in which all conditions are under the control of the researcher.
The control factor in this case may includes the time...before measurements.
Here we must answer different things about the experiment that the farmer performed. We will see that this is an experiment and the controlled factors are:
Quality of the soil.Wheater.Hours of daylight.What he did is divide his land in two equal parts, and then use different types of seeds in each one of the two parts.
After 3 months, he measures the height of the crops.
The questions are:
Is the study observational or experimental?
It is experimental, because the farmer assigned two areas and he decided what type of seed went into each area.
If it is an experiment, what are the controlled factor?
The controlled factors are the things that are the same for both of the groups of sections and that are relevant for the growth of the seeds. These things are:
Quality of the soil.Wheater.Hours of daylight.If you want to learn more about experiments, you can read:
https://brainly.com/question/11256472
A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?
Answers
Answer:
41°, 56°, 83°
Step-by-step explanation:
We can find the largest angle from the law of cosines:
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab))
C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°
Then the second-largest angle can be found the same way:
B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°
Of course the third angle is the difference between the sum of these and 180°:
A = 180° -82.8192° -55.7711° = 41.4096°
Rounded to the nearest degree, ...
the angles of the triangle are 41°, 56°, 83°.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.
Answers
Answer:
to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]
The resulting function can be written as
[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]
Step-by-step explanation:
Hello,
f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0
and [tex]f(x)\geq 0[/tex]
so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]
and then we can write
[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]
hope this helps
What tool is used to draw circles
Answers
Answer:
Pair of compasses.
Step-by-step explanation:
These are used to inscribe circles/arcs.
Compasses are used in maths, navigation,e.t.c.
Hope it helps.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 130
x = 69; 90% confidence
a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603
Answers
Answer:
d. 0.459 < p < 0.603
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.531.
[tex]p=X/n=69/130=0.531[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]
The 90% confidence interval for the population proportion is (0.459, 0.603).
What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answers
Answer:
[tex]y = 4x-3[/tex]
Step-by-step explanation:
The coordinates are (-0.5,-5) and (2,5)
Finding the slope, m:
=> Slope = [tex]\frac{rise}{run}[/tex]
=> Slope = [tex]\frac{5+5}{2+0.5}[/tex]
=> Slope = [tex]\frac{10}{2.5}[/tex]
=> Slope = 4
Now, y-intercept, b:
Taking any of the two coordinate and putting it in the slope intercept equation:
=> Point = (x,y) = (2,5)
So, x = 2, y = 5
=> [tex]y = mx+b[/tex]
=> 5 = (4)(2) + b
=> 5 = 8 + b
=> b = 5-8
=> b = -3
Now, Putting in slope intercept equation:
=> [tex]y = mx+b[/tex]
=> [tex]y = 4x-3[/tex]
Gradient (m) = x2-x1
y2-y1
considering
y1 = -5 y2 = 5
x1 = -0.5. x2 = 2
m = 2-(-0.5)
5-(-5)
m = 5.5
10
m = 11. = 0.55
20
equation of a line is given by
y-y1 = m+(x-x1)
y-(-5) =0.55 + {x-(-0.5)}
y+5 = 0.55 + x+0.5
making y the subject
y = 0.55 +0.5 -5 + x
y = -3.95 + x
A surveyor is trying to find the height of a hill. He/she takes a ‘sight’ on the top of the hill and find that the angle of elevation is 40°. He/she move a distance of 150 metres on level ground directly away from the hill and takes a second ‘sight’. From this point, the angle of elevation is 22°. Find the height of the hill, correct to 1 d.p.
Answers
Answer:
The height of the hill is 116.9 meters.
Step-by-step explanation:
The diagram depicting this problem is drawn and attached below.
From Triangle ABC
[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]
From Triangle XBC
[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]
Therefore:
[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]
Therefore, the height of the hill
[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]
The height of the hill is 116.9 meters.
What is the solution to the equation below? Round your answer to two decimal places. 4+4•log2 x=4
Answers
Answer:
Option (C)
Step-by-step explanation:
Given expression is,
[tex]4+4\times \text{log}_2(x)=14[/tex]
By subtracting 4 from both the sides of the equation.
[tex]4\times \text{log}_2(x)=14-4[/tex]
Now divide the equation by 4
[tex]\text{log}_2(x)=\frac{10}{4}[/tex]
[tex]\text{log}_2(x)=2.5[/tex]
[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]
[tex]x=(2)^{2.5}[/tex]
[tex]x = 5.657[/tex]
x ≈ 5.66
Therefore, Option C will be the correct option.
4+4•log2 x=14
x= 5.66
what is 18576939*47 Thanks!!!!!
Answers
Answer:
873116133
Step-by-step explanation:
18576939 × 47
Multiply the numbers.
= 873116133
Answer: 873116133
Step-by-step explanation:
‘Hope this helps:)
Suppose that early in an election campaign, a telephone poll of 800 registered voters shows that 460 favor a particular candidate. Just before Election Day, a second poll shows that 520 of 1,000 registered voters now favor that candidate. At the 0.05 significance level, is there sufficient evidence that the candidate's popularity has changed?
Answers
Answer:
Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion that support the candidate has significantly changed.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=800 has a proportion of p1=0.58.
[tex]p_1=X_1/n_1=460/800=0.58[/tex]
The sample 2, of size n2=1000 has a proportion of p2=0.52.
[tex]p_2=X_2/n_2=520/1000=0.52[/tex]
The difference between proportions is (p1-p2)=0.05.
[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]
As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
How would I Evaluate 8×5÷10?
Answers
Answer:
4
Step-by-step explanation:
8×5÷10
PEMDAS says multiply and divide from left to right
40÷10
4
Answer:
4
Step-by-step explanation:
Follow the PEMDAS order of operations
8*5=40
40÷10=4
=4
OR
8x5÷10
8x0.5=4
=4
Have a good day and stay safe!
Please answer this correctly
Answers
Answer:
100%
Step-by-step explanation:
First, let's determine the probability for each of the conditions.
For P(greater than 2), we will have the cards 3, 4, 5, 6, 7, and 8.
For P(less than 3), we will have the cars 2.
In other words, every single card fits the conditions.
Thus, P(greater than 2 or less than 3)=7/7=100%
100%
Answer:
100%
Step-by-step explanation:
Greater than 2 is 3, 4, 5, 6, 7, 8
And less than 3 is 2 so that’s all the numbers which is 100%
a bag contains only red and blue counters the probability that a counter is blue is 0.58 A counter is picked at random What is the probability that it is red
Answers
Answer:
0.42
Process:
1 - 0.58
0.42
Prime factorization of 45
A. 2³×5
B. 3²×5
C. 5²×3
D. 5²×9
Answers
Answer:
Hello, your answer is:
B. 3²×5
Step-by-step explanation:
Prime factorization of 45 is:
45 = 9 x 5
= 3²×5
Hope this helps you.. Good Luck
Answer:
B. 3² × 5
Step-by-step explanation:
45 can be written as a product of its prime factors.
45 = 3 × 3 × 5
45 = 3² × 5
A tabletop has an area of 12 square feet and a perimeter of 16 ft. What are the dimensions of the table? 2 ft by 6 ft 2 ft by 8 ft 4 ft by 3 ft 4 ft by 4 ft
Answers
Answer:
2 ft by 6
Step-by-step explanation:
The dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Since, the area of a rectangle is:
Area = length x width
We know that the area of the table is 12 square feet,
So, we can write:
12 = length x width
And, use the formula for the perimeter of a rectangle:
Perimeter = 2 x length + 2 x width
We know that the perimeter of the table is 16 feet, so we can write:
16 = 2 x length + 2 x width
Now we have two equations with two variables (length and width), which we can solve simultaneously as.
Let's rearrange the second equation to solve for length:
16 = 2 x length + 2 x width
16 - 2 x width = 2 x length
8 - width = length
Now we can substitute this expression for length into the first equation:
12 = length x width
12 = (8 - width) x width
12 = 8w - w²
We can rearrange this equation into standard quadratic form:
w² - 8w + 12 = 0
Now we can use the quadratic formula:
where a = 1, b = -8, and c = 12
w = (-(-8) ± √((-8)² - 4(1)(12))) / 2(1)
w = (8 ± √(16)) / 2
w = 4 ± 2
Hence, w = 2
w = 6
So the possible values for the width are 2 and 6.
If the width is 2 feet, then the length is:
length = 8 - width = 6 feet
If the width is 6 feet, then the length is:
length = 8 - width = 2 feet
Therefore, the dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ3
A survey of enrollment at 35 community colleges across the United States yielded the following figures:
6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622
a. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."
b. Construct a histogram of the data.
c. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
d. Calculate the sample mean.
e. Calculate the sample standard deviation.
f. A school with an enrollment of 8000 would be how many standard deviations away from the mean?
Answers
Answer: (a) The chart is in the first attachment named table frequency.
(b) The histogram is in the second attachment named frequency vs. enrollment
(c) Mode
(d) x = 9071.4
(e) s = 6677.64
(f) It is -0.16 standard deviation away
Step-by-step explanation:
(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.
(d) To calculate sample mean of a frequency data:
1) Find the midpoint for each interval;
2) Multiply each midpoint for its correspondent frequency;
3) Sum up each multiplication obtained in the previous step;
4) Sum up all the frequencies;
5) Divide the sum in step 3 by the sum in step 4;
For this chart:
x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]
x = 9071.4
(e) To find the standard deviation:
1) With each midpoint, calculate its square;
2) Multiply the midppoint square by its correspondent frequency;
3) Use the following formula to determine the sample standard:
s = √∑f.M² - n(μ)² / n-1
For this chart:
s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]
s = 6677.64
(f) To find how many standard deviations away is the enrollment:
z = [tex]\frac{8000-9071.4}{6677.64}[/tex]
z = - 0.16
8000 enrollments are -0.16 standard deviations away from the mean.
Sandy can fold 6 towels in 3 minutes. If she continues at this rate, how many minutes will it take her to fold 36 towels?
Answers
Hey there! :)
Answer:
x = 18 minutes.
Step-by-step explanation:
To solve this equation, set up a ratio.
# of towels over time taken:
[tex]\frac{6}{3} = \frac{36}{x}[/tex]
Cross multiply:
6x = 108
Divide both sides by 6:
6x/6 = 108/6
x = 18 minutes.
Answer:
In eighteen minutes she will have folded all 36
Find the value of x that makes A||B
Answers
Answer:
For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15°
The mean of 100 numerical observations is 51.82 what is the value of all 100 numbers
Answers
Answer: 5182
To get the value of all 100 numbers you would need to multiply.
Step-by-step explanation:
51.82x100= 5182
[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!
Answers
Answer:
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
Step-by-step explanation:
[tex]\frac{5x-11}{2x^2+x-6}[/tex]
Factor the denominator.
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
The fraction cannot be simplified further.
Answer:
[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]solution,
[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]
Hope this helps..
Jimmie invested $13,000 at 5.23% compounded monthly.
What will Jimmie's account balance be in 42 years?
Answers
Answer:
116370.197$
Step-by-step explanation:
Jimmie invested $13,000 at 5.23% compounded monthly.
Jimmie's account balance (B) after 42 years:
B = principal x (1 + rate)^time
= 13000 x (1 + (5.23/100)/12)^(42 x 12)
= 116370.197$
Please answer this correctly without making mistakes
Answers
Answer:
<
Step-by-step explanation:
750,000,000 times 10^5 can be expressed as 7.5 times [tex]10^{11}[/tex]
7.55 times 10^13 is greater than 7.5 times 10^11.
Answer:
The appropriate sign that makes the statement true is <
Hope this helps you
Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?
Answers
Answer:
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
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 \leq x) = \frac{x - a}{b-a}[/tex]
Uniform distribution from 0 to 4.8 seconds.
This means that [tex]a = 0, b = 4.8[/tex]
61% of the time a person will wait at least how long before the wave crashes in?
This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]
[tex]x = 4.8*0.39[/tex]
[tex]x = 1.872[/tex]
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.