The average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.
What is Standard deviation?
Standard deviation is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
To determine whether there is evidence to support the claim that the average age of lifeguards in Ocean City is greater than 24 years at a 5% level of significance, we need to perform a one-tailed t-test. A one-tailed t-test is used to test whether the mean of a sample is significantly greater than (or less than) a certain value.
To perform the t-test, we first need to calculate the t-statistic, which is defined as:
[tex]t = (mean - null value) / (standard error / \sqrt{n} )[/tex]
where mean is the mean age of the sample of lifeguards, null value is the value that the null hypothesis is testing against (in this case, 24 years), standard error is the standard error of the mean age, and n is the number of lifeguards in the sample.
Plugging in the values from the problem, we get:
[tex]t = (24.7 - 24) / (standard \ error / \sqrt{36} )\\\\= 0.7 / (standard\ error / 6)[/tex]
The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:
[tex]standard \ error = population \ standard\ deviation / \sqrt{(n)}[/tex]
Plugging in the values from the problem, we get:
standard error = / sqrt(36) = / 6 =
Substituting this value back into our expression for t, we get:
t = 0.7 / ( 6)
= 1.8
For a one-tailed t-test at a 5% level of significance, the critical value is 1.645. This means that if the t-statistic is greater than 1.645, we can reject the null hypothesis and conclude that there is evidence to support the claim.
So we can reject the null hypothesis and conclude that there is evidence to support the claim that the average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.
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What is the probability that the spinner will not land on a 5 or 8? 5 points
Answer:
3/4
Step-by-step explanation:
Based on the spinner attached :
Faces are in equal divisions ; number of faces = 8
Probability the spinner will not land on a certain number = 1 - P(spinner lands on that number)
P(spinner lands on 5) = 1 /8
P(spinner will not land on 5) = 1 - 1/8 = 7/8
P(spinner lands on 8) = 1/8
P(spinner will not land on 8) = 1 - 1/8 = 7/8
Hence,
P(spinner will not land on 5 or 8)
Required outcome = (1, 2, 3, 4, 6, 7) = 6
Total possible outcomes = (1.2, 3, 4, 5, 6, 7, 8) = 8
P(spinner will not land on 5 or 8). = 6/8 = 3/4
Which of the following points are located 3 units from (-4,-2) ?
Spider Rock is located in Canyon de Chelly National Park in Arizona. A surveyor stands 370 feet from the base of Spider Rock. From a point 5.5 feet above the ground, he measures the angle of elevation to the top of Spider Rock to be 65°. According to the surveyor's measurements, what is the height of Spider Rock? Round your answer to the nearest tenth. A. 178.0 ft. B. 340.8 ft. C. 413.7 ft. D. 799.0 ft.
Answer:
799 feet
Step-by-step explanation:
We solve using the Trigonometric function of Tangent.
tan theta = Opposite /Adjacent
From the above question, we have the height of the surveyor = 5.5 feet
theta = Angle of elevation = 65°
Adjacent = 370 feet
Let Opposite = height + height of spider rock
tan 65° = h - 5.5 /370 feet
Cross Multiply
tan 65° × 370 feet = h - 5.5
793.46756059 feet = h - 5.5
h = 793.46756059 feet + 5.5
h = 798.96756059 feet
Approximately = 799 feet
The height of the Spider rock = 799 feet
PLEASE HELP ME!! I WILL GIVE BRAINLIEST. ITS DUE IN AN HOUR
Answer:
p-3=8.25
p=11.25
Answer:
p - 3 = 8.25 and 11.25
Step-by-step explanation:
hi there!
the question is asking us to first find out which equation we can use to solve this wordy problem.
its not going to be answers 1 or 3 since they are adding/ multiplying more on to our wooden plank, when the question is stating that we are subtracting 3 inches off.
knowing that now, our answer is p - 3 = 8.25 or 4 !
now all we have to do is add 3 to 8.25 to get our answer of how long the plank was before we cut it
3 + 8.25
= 11.25
p = 11.25 <---------------- our final answer!
i hope this helped you! i hope you have a good rest of your day :)
( im sorry if this this late!! )
What is the slope of the line?
2
-2
1/2
1
Answer:
the answer to the question is 1
mo played 30 games of chess he won 18 of these games what fraction of the games did he win give your answer in its simplest form
Answer:
18/30
Step-by-step explanation:
The lines graphed below are perpendicular. The slope of the red line is 4.
What is the slope of the green line?
Answer: -1/4
Step-by-step explanation:
so lets just eliminate some of the choices here.
4 and -4 are 4/1 or -4/-1 and it doesnt go up or down 4 here so those can be ruled out. If we look at which way the green line is facing, positive goes up on the graph, but green line is going down so we can rule out 1/4. So all that is left is -1/4, so there's your slope.
Sin(x)=sqrt3/2 solutions of
Answer:
pi/3+2pin, 2pi/3+2pi(n)
Answer:
the next one is c - pi/2
Step-by-step explanation:
A street light is 21 feet high and casts a 40-foot shadow. At the same time, a cell-phone
tower next to the street light casts a 57-foot shadow. Which proportion can be used to find
the height, H, of the cell-phone tower?
Answer:
21/H = 40/57
Step-by-step explanation:
Melissa works at Best Buy and gets paid $250 a week plus
commission. She earns $15 for every cell phone she sales.
Which function can be used to find t, the amount of money
Melissa will receive on her weekly paycheck for selling n
number of cell phones?
A.
t=250x + 15
C. t = 15x
B.
t = 15x + 250
D. Not Here
Answer:
option b is correct
I hope it helps
HELP! I'LL MARK YOU BRAINLIST
Step-by-step explanation:
are in the solution:
(3,1)
(-1,2)
(6,0)
(0,0)
are not
(-2,-1)
(0,-4)
Need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
write the expression in standard form
2x-(5+4x)
Answer:
- 2x - 5
Step-by-step explanation:
2x - (5 + 4x)
2x - 5 - 4x
- 2x - 5
Answer: The answer is -2x - 5
Step-by-step explanation:
» What is the area of this trapezoid?
Remember to include in. Or in^2
Answer:
20 Inches
Step-by-step explanation:
Ok here is how you do it so the formula for a trapezoid is base 1 plus base 2 divided by 2 times the height. so, in this case the two bases are 2 in and 6 in so we add those together and get 8 then, we divided 8 by 2 and we get 4.
Then now, we multiply 4 and 5 for our height and get 20 inches.
A man wants to build around water fountain with diameter, d = 11.28 feet. The man is trying to put up a fence around the build with some wire. What is the length of the wire that the man needs to complete the task?
Answer:
35.44
Step-by-step explanation:
2 times pi times radius.
Carson can choose one vehicle (car or truck), one color (blue, red, or silver), and one type of transmission (standard or automatic). How many possible outcomes are there?
Answer:
12 possible outcomes
Step-by-step explanation:
Choosing 1 vehicle from 2 = 2C1 = 2
Choosing 1 color from 3 = 3C1 = 3
Choosing 1 type from 2 = 2C1 = 2
Number of possible outcomes :
2C1 * 3C1 * 2C1
2 * 3 * 2
= 12 different possible outcomes
Solve the right triangle shown in the figure, given the following measures. Remember, exact lengths can be approximated on a calculator. For example, StartRoot 2 EndRoot almost-equals 1.414. Angle A = 45 degrees, side A B = 12 StartRoot 2 EndRoot centimeters, Angle C = 90 degrees a. Side B C = 6 StartRoot 3 EndRoot centimeters, angle B = 45 degrees, Side A C = 6 StartRoot 3 EndRoot centimeters b. Side B C = 6 StartRoot 2 EndRoot centimeters, angle B = 45 degrees, Side A C = 6 StartRoot 2 EndRoot centimeters c. Side B C = 24 centimeters, angle B = 45 degrees, Side A C = 24 centimeters
Answer:
D. BC = 12cm, <B = 45, AC = 12cm
Step-by-step explanation:
Edge 2021
The measures of the lengths and angles are: BC = 12cm, <B = 45, AC = 12cm
What are right triangles?A right triangle is a triangle that has one of its angle measure to be 90 degrees.
From the question, we have:
Angle B = 45 degrees
Since angle B is 45 degrees, then the legs of the triangle are equal (i.e. 12 cm)
Hence, the measures of the lengths and angles are: BC = 12cm, <B = 45, AC = 12cm
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3x+4y=25 x+5y=23
What does the variable of x and y represent in the system of equations
x= 1/27
Heart if it helps!
Easy questions just a bit of help no rush 100 points to do this
Is this a test or do you need help
State if the three numbers can be the measures of the sides of a triangle.
5, 12, 10
Yes or No
Answer:
yes
Step-by-step explanation:
One pair of parallel sides proves a quadrilateral to be a parallelogram
True
False
The measures of three of the interior angles of a quadrilateral are 60o, 110o, and 90o What is the measure of the fourth angle of this quadrilateral?
Answer:
100 degrees
Step-by-step explanation:
sum of angles in a quadrilateral = 360
missing angle = 360 - (60 + 110 + 90) = 100
How to find surface area of rectangular prism?
Answer:
.
Step-by-step explanation:
........
In ΔQRS, the measure of ∠S=90°, QR = 7.7 feet, and SQ = 6.5 feet. Find the measure of ∠R to the nearest tenth of a degree.
Answer:
57.6°
Step-by-step explanation:
It is always helpful to draw a picture. Also, you need to memorize all the definitions of the trig functions. For example,
sine of an angle = opposite side/hypotenuse
In your case, SQ is opposite side to angle R and QR is the hypotenuse
Therefore, sin R = 6.5/7.7
m∠R = arcsin (6.5/7.7) = 57.6°
-5x - 5 > 15 solve this inequality
Answer:
-5×-5>15
+5 +5
-5×>20
÷-5 ÷-5
x<-4
whe you divide by a negativr you flip the sign
Which rule defines S, for an = 3(0.7)n?
Sn=7(0.7n)
Sn = 2.1(0.7n)
Sn= 7(1-0.7n)
Sn= 2.1(1-0.7n)
Answer: C
Sn= 7(1-0.7n)
Step-by-step explanation:
The rule that defines S for [tex]a_n = 3(0.7)^n[/tex] is:
[tex]S_n = 7(1 - 0.7^n)[/tex]
The rule of S means that we calculate the rule that defines the sum of n terms of the geometric progression.
Given that:
[tex]a_n = 3(0.7)^n[/tex]
Rewrite as:
[tex]a_n = 3 (0.7)^n \times 1[/tex]
Replace 1 with 0.7/0.7
[tex]a_n = 3 (0.7)^n \times \frac{0.7}{0.7}[/tex]
Rewrite as:
[tex]a_n = 3 *0.7 \times \frac{(0.7)^n}{0.7}[/tex]
Apply law of indices
[tex]a_n = 3 \times 0.7 \times (0.7)^{n-1}[/tex]
[tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]
The n term of a geometric progression is:
[tex]a_n = ar^{n-1}[/tex]
Compare [tex]a_n = ar^{n-1}[/tex] to [tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]
[tex]a = 2.1[/tex] --- the first term
[tex]r = 0.7[/tex]
The sum of n terms of a geometric progression is:
[tex]S_n = \frac{a(1 - r^n)}{1 -r}[/tex]
This gives:
[tex]S_n = \frac{2.1(1 - 0.7^n)}{1 -0.7}[/tex]
[tex]S_n = \frac{2.1(1 - 0.7^n)}{0.3}[/tex]
[tex]S_n = 7(1 - 0.7^n)[/tex]
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find the missing side. round to the nearest tenth.
Answer:
A. 5.2
Step-by-step explanation:
I was taught how to do this using the SOH CAH TOA method.
Step 1: Circle your given angle.
Step 2: Label O, H, and A. The line across from your circled angle will be labeled O. The side across from the right angle is H. The last unmarked side is A.
Step 3: Cross off the useless side, in this case, that would be A because there is no corresponding information.
Step 4: Identify if it is sine, cosine, or tangent using SOH CAH TOA. In this case, you only have an O and H so we will use SOH.
Step 5: Set up the equation. The equation is [tex]\frac{sine(31)}{1} =\frac{x}{10}[/tex]. We will use sine of the given angle is equal to the side marked O over the side marked H.
Step 6: Solve for x until x is by itself, then enter into your calculator.
You will enter [tex]sine(31) * 10[/tex] into your calculator and round if necessary.
if f (x) = 8 (5x - 2) find f (x)
Answer:
f-1(x) = (x - 16)/40
B
Step-by-step explanation:
Call f(x) = y
Interchange x and y
x = (5y + 2)*8 Remove the brackets
x = 40y + 16 Subtract 16 from both sides
x - 16 = 40y Interchange the left and right sides
40y = x - 16 Divide by 40
y = (x - 16)/40
f-1(x) = (x - 16)/40
Calculate the product below and give your answer in scientific notation.
(1.3 x 10-^2) (0.05) = ?
Answer:
1 Simplify 1.3\times 101.3×10 to 1313.
(13-2)\times 0.05
(13−2)×0.05
2 Simplify 13-213−2 to 1111.
11\times 0.05
11×0.05
3 Simplify.
0.55
0.55
The product of (1.3 x 10⁻²) and (0.05) is 0.065x 10⁻²
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find the product of (1.3 x 10⁻²) and (0.05)
Multiplication is a method of finding the product of two or more numbers
First multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.
1.3×0.05=0.065
So 0.065x 10⁻² is the value of product (1.3 x 10⁻²) and (0.05)
Hence, the product of (1.3 x 10⁻²) and (0.05) is 0.065x 10⁻²
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can someone help me with my perfect square homework? thank you.
Answer:
Any better explanation
Answer:
49
Step-by-step explanation:
Given
v² - 14v
To complete the square
add ( half the coefficient of the v- term )² to v² - 14v
v² - 14v + (- 7)²
= v² - 14v + 49
= (v - 7)² ← a perfect square