The standard deviation of the data will be;
⇒ 4.13
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The data set is,
⇒ 23, 19, 28, 30, 22
Now,
Since, The data set is,
⇒ 23, 19, 28, 30, 22
Hence, The mean = 23 + 19 + 28 + 30 + 22 / 5
= 122/5
= 24.4
So, The standard deviation is;
√ (23 - 24.4)² + (19 - 24.4)²+(28 - 24.4)² + (30 - 24.4)² + (22 - 24.4)²/ (5-1)
⇒ √ 1.96 + 29.16 + 12.96 + 31.36 + 5.76 / 4
⇒ √ 81.2/4
⇒ √20.3
⇒ 4.13
Thus, The standard deviation of the data will be;
⇒ 4.13
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To calculate the standard deviation of the data set, we can use the formula:
$$ \sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n} (x_i - \mu)^2} $$
Where:
$x_i$ is each data point
$\mu$ is the mean of the data set
$n$ is the number of data points
For the data set given, the mean is $\mu = 24.4$
Plugging in the values into the formula, we get:
$$ \sigma = \sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i - 24.4)^2} = \sqrt{\frac{1}{5}( (23-24.4)^2 + (19-24.4)^2 + (28-24.4)^2 + (30-24.4)^2 + (22-24.4)^2 )} $$
After evaluating the expression, we get:
$$ \sigma = \sqrt{\frac{1}{5}(1.96 + 5.76 + 3.36 + 5.76 + 0.36)} = \sqrt{\frac{1}{5}(18.2)} = \sqrt{3.64} = 1.91 $$
So the standard deviation of the data set is 1.91.
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Pamela's age is three times Jiri's age. The sum of their ages is 28 . What is Jiri's age?
Answer:
So, if we say Jiri's age is j (we can pick any letter), then Pamela's age is 2j, right?
j + 2j = 72
j is the same as 1j, but we wouldn't call you 1James, just James.
3j = 72
To isolate j, we do the opposite operation to both sides.
3j/3 = 72/3
j/j = 1, so that cancels out. 72/3 = 24.
j = 24
Jiri is 24 years old.
Answer:
Jiri is 7 years old.
explanation:
3j + j = 28
4j = 28
4j/4 = 28/4
j = 7
this can be proven:
Pamela's age: 3×7 = 21
the sum of their ages = 28
7 + 21 = 28
please help Me ASAPPPP!
Answer:
AOB = 65°
DOE = 35°
AOC = 90°
EOB = 115°
DOB = 85°
Hope this helps!
How fast was a driver going if it left skid marks that were 63 feet long on wet concrete? (The
coefficient of friction is 0.97)?
O 61 mph
31 mph
O 334 mph
43 mph
The required speed of the driver is 33.4 mph.
To determine how fast was a driver going and if it left skid marks that were 63 feet long on wet concrete. (The coefficient of friction is 0.97)?
What is speed?Speed is the ratio of distance traveled to time taken to travel that distance.
What is friction?Friction is defined as resistance force from one surface to the other between two solid materials caused by reciprocal movement is called friction. And the force applied is called friction force.
Since from given
f = 0.97
left skid marks that were 63 feet long on wet concrete.
d = 63 feets
g = 9.8
V = √( 2g * F * D )
V = √(2 * 9.8 * 0.97 * 63 )
V = 33.4mph
Thus, The required speed of the driver is 33.4 mph.
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3)
6 cm
5 cm
I
7 cm
5 cm
6 cm
Answer:
29
Step-by-step explanation:
Answer each question about the following arithmetic series:
12 + 18 + 24 + 30 + . . . + 198
What is the value of the arithmetic series?
630
1,260
3,360
6,336
Answer:
(c) 3360
Step-by-step explanation:
Given
The above arithmetic series where:
[tex]T_1 = 12[/tex] --- first term
[tex]d = 6[/tex] --- the common difference (18 - 12 = 6)
[tex]T_n = 198[/tex] --- The last term
Required
The value of the series
First, we calculate n using:
[tex]T_n = T_1 + (n - 1)d[/tex]
This gives:
[tex]198 = 12 + (n - 1)*6[/tex]
Collect like terms
[tex]198 - 12 = (n - 1)*6[/tex]
[tex]186 = (n - 1)*6[/tex]
Divide both sides by 6
[tex]31 = (n - 1)[/tex]
Make n the subject
[tex]n = 31 + 1[/tex]
[tex]n=32[/tex]
The sum of the series is:
[tex]S_n= \frac{n}{2}(T_1 + T_n)[/tex]
So, we have:
[tex]S_n= \frac{32}{2}(12 + 198)[/tex]
[tex]S_n= \frac{32}{2}*210[/tex]
[tex]S_n= 16*210[/tex]
[tex]S_n= 3360[/tex]
5. Today, everything at a store is on sale. The store offers a 20% discount.
a. The regular price of a T-shirt is $18. What is the discount price?
b. If the regular price of an item is x dollars, what is the discount price in dollars?
C. The discount price of a hat is $18. What is the regular price?
Answer:
Step-by-step explanation:
20% = 20/100 = 0.2
The amount you need to pay for a T shirt is
Cost = original amount(100% - 20%)
Original amount = 18
100% - 20% = 80%
80% = 80 / 100 = 0.8
What this means is that you will pay 80% of the original cost.
Cost = 18*0.8
Cost = $14.40
Part B
Cost = 0.8 * x
Part C
Selling price = 0.8*Original Cost
Selling price = 18
18 = 0.8 * x
18/0.8 = x
x = 22.5
The original price was $22.50
What is 3 1/8 times 4
12.5
You can search for any mathematical expression, using functions such as: sin, cos, sqrt, etc. You can find a complete list of functions here.
(
)
%
AC
7
8
9
÷
4
5
6
×
1
2
3
−
0
.
=
+
Rad
Deg
x!
Inv
sin
ln
π
cos
log
e
tan
√
Ans
EXP
xy
=
123
Fx
Answer:
12 1/2
would be the answer
Điều kiện nf>=5;n(1-f)>=5 trong loại kiểm định giả thuyết " so sánh tỉ lệ tổng thể với số cho trước ", (với n là cỡ mẫu, f là tỉ lệ mẫu) có nghĩa là gì ?
Answer:
Step-by-step explanation:
(-0.3)2 ÷ (-0.2)+(-2.56)
Answer:
−0.2542372881
in this sum, each letter stands for one of the digits 0 to 9
F O U R
+ O N E
= F I V E
can you replace the letters by digits to get s correct sum.( the first digit of a number cannot be zero so neither F nor O is zero)
Answer:
7 4 5 0
F O U R
+
4 8 1
O N E
=7 9 3 1
F I V E
Hope this is correct:)
PLEASE HELP ASAP !!!!!!!
Answer:
143º
Step-by-step explanation:
You want to find m<HBD
which is m<HBA minus m<BAD
180º minus 37º equals 143º
m<HBD is equal to 143º
Please give me brainliest
Can anyone who sees this answer my latest question?
I need help with it very soon.
Answer:
143 !
Step-by-step explanation:
DUE IN 5 MINUTES PLEASE HELP ASAP
Step-by-step explanation:
jannsonparker is correct and should be marked brainliest.
this is just an illustration for you
Yesterday, Marissa walked 1 1/2 miles from school to the ice
cream shop and 2/3 of a mile from
the ice cream shop to her house. How many miles did Marissa walk in all?
Ill give brainliest
Answer:
2 1/6 miles
Step-by-step explanation:
1 1/2 miles + 2/3 miles = 2 1/6 miles
Helpp!!
I need to pass
Answer:
the answer is 32%
Step-by-step explanation:
NEED Explain! for Branliest
Answer:
1) True for inequality B.
2) True for inequality A.
3) True for inequality B.
4) True for both inequality A and inequality B.
Step-by-step explanation:
Solve each inequality.
Inequality A:
[tex] -5y + 2 \le 14 [/tex]
Subtract 2 from both sides.
[tex] -5y \le 12 [/tex]
Divide both sides by -5. Remember that the inequality sign changes direction.
[tex] y \ge -\dfrac{12}{5} [/tex]
[tex] y \ge -2.4 [/tex]
Inequality B:
[tex] \frac{1}{4}(3y - 6) \le 5 [/tex]
Multiply both sides by 4.
[tex] 3y - 6 \le 20 [/tex]
Add 6 to both sides.
[tex] 3y \le 26 [/tex]
Divide both sides by 6.
[tex] y \le \dfrac{26}{3} [/tex]
[tex] y \le 8 \dfrac{2}{3} [/tex]
The four answers on the right side are:
1) True for inequality B.
2) True for inequality A.
3) True for inequality B.
4) True for both inequality A and inequality B.
If F is the function defined by F(x)=3x−1 find the solution set for F(x)=−7.
Answer:
C is your answer.
Step-by-step explanation:
Hope is right, you're welcome, and good luck on your work.
please don't forget to click in the ❤, and on the ⭐.
The required solution for F(x) = -7 is x = -2.
F is the function defined by F(x)=3x−1
What are functions?
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
F(x) = 3x-1
Now F(x) = -7
⇒-7 = 3x-1
x = -2
Thus, the required solution for F(x) = -7 is x = -2.
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What are the values of x and y?
Answer:
Solution given;
we have
Cos 30=adjacent/hypotenuse
Cos 30=12/x
x=12/cos30
x=8√3
and
Sin 30=opposite/hypotenuse
Sin30=y/x
y=sin30*x
y=sin30*8√3
y=4√3
Option D.
x=8√3 and y=4√3 is a required answer.
find the value of 4th terms by using 3n-2
Answer:
Step-by-step explanation:
[tex]4^{th} term \ means \ n = 4\\\\3n - 2 = 3 \times 4 - 2 = 12 -2 = 10[/tex]
Which is a correct first step for solving this equation?
- 32 + 2 - 52 - 7 = 4x + 2
Answer:
-8x - 5 = 4x + 2
If 21% of males and 15% of females in a given state play the guitar what is the probability that a randomly selected subject in the state plays the guitar given that the subject is male
Answer: if we were to say that the population was 50% male and 50% female, than 21% of the males would play the guitar and 15% of the females would also play the guitar, if it is talking about the population in geteral, than 21% of men and 15% of female play the guitar, but the remaining 64% of people don't play the guitar.... i don't think this is the answer, so if you chose my first case, the answer would be 0.105 for males or 10.5 % or percent of males play guitar in the state
Step-by-step explanation: chose one of my cases
Answer:0.21
Step-by-step explanation:
PLATO
Please can you help with no 5
Answer:
0.0046
Step-by-step explanation:
1/6 *1/6 *1/6 = 0.00462963
mrs smith had 27 students in her class last year and this year she had 30 students in her math class. what is the percentage change
Answer:
the answer is 24%
Step-by-step explanation:
quizzes.com
Which equations represent two vertical asymptotes of the function y = 3 cot(4∕3x)?
A) x = 0 and x = 3π∕4
B) x = 0 and x = 3π∕8
C) x = –3π∕8 and x = 3π∕8
D) x = – 3π∕4 and x = 3π∕4
Answer:
A) x = 0 and x = 3π∕4
Step-by-step explanation:
cot 0° = oo (infinite)
4/3 x = 0
=> x = 0
cot 180° = oo (infinite)
4/3 x= 180
x = 3/4 × 180
= 135°
= ¾π
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 15% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of eight adult friends, what is the probability of the following?
a. no one has done a one time fling
b. at least one person has done a one time fling
c. no more than two people have done a one time fling
Answer:
[tex](a)\ P(x = 0) = 0.2725[/tex]
[tex](b)\ P(x \ge 1) =0.7275[/tex]
[tex](c)\ P(x \le 2) = 0.8948[/tex]
Step-by-step explanation:
Given
[tex]n = 8[/tex] --- 8 friends
[tex]p = 15\%[/tex] --- proportion that one-time fling
This question is an illustration of binomial probability, and it is represented as:
[tex]P(X = x) = ^nC_x* p^x * (1 - p)^{n-x}[/tex]
Solving (a): P(x = 0) --- None has done one time fling
[tex]P(x = 0) = ^8C_0* (15\%)^0 * (1 - 15\%)^{8-0}[/tex]
[tex]P(x = 0) = 1* 1 * (1 - 0.15)^{8}[/tex]
[tex]P(x = 0) = 0.85^8[/tex]
[tex]P(x = 0) = 0.2725[/tex]
Solving (b): [tex]P(x \ge 1)[/tex]
To do this, we make use of compliment rule:
[tex]P(x = 0) + P(x \ge 1) =1[/tex]
Rewrite as:
[tex]P(x \ge 1) =1 - P(x = 0)[/tex]
[tex]P(x \ge 1) =1 - 0.2725[/tex]
[tex]P(x \ge 1) =0.7275[/tex]
Solving (c): [tex]P(x\le 2)[/tex]--- Not more than 2 has one time fling
This is calculated as:
[tex]P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)[/tex]
We have:
[tex]P(x = 0) = 0.2725[/tex]
[tex]P(x = 1) = ^8C_1* (15\%)^1 * (1 - 15\%)^{8-1}[/tex]
[tex]P(x = 1) = 8* (0.15) * (1 - 0.15)^7[/tex]
[tex]P(x = 1) = 0.3847[/tex]
[tex]P(x = 2) = ^8C_2* (15\%)^2 * (1 - 15\%)^{8-2}[/tex]
[tex]P(x = 2) = 28* (0.15)^2 * (1-0.15)^6[/tex]
[tex]P(x = 2) = 0.2376[/tex]
So:
[tex]P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)[/tex]
[tex]P(x \le 2) = 0.2725 + 0.3847 + 0.2376[/tex]
[tex]P(x \le 2) = 0.8948[/tex]
PLEASE HELP I WILL MARK BRAINLIEST
Answer:
8 x 13 = 104 yd^2
Step-by-step explanation:
To find the area of a rectangle we use the basic formula:
L x W
In this case 13 is your width and 8 is your length, multiply the two given lengths to get your area which is 104.
Given the set B = {x | x = 2y + 3, where y ∈ I and 0 < y < 5}, write the elements of the set using the roster method. Note: Set I represents the set of integers.
Answer:
135787-
Step-by-step explanation:
ijjkmbnjgvnnhvbyyh
URGENT.. pls help NO links
Answer:
.83
Step-by-step explanation:
we want
(sports∩Senior)/Senior
we can see that sports∩senior= 25
and senior= 25+5+5=30
25/30= .83
Look at ZV SW and ZTSW in the image below.
Which of the following is the best description for this pair of angles?
O acute
O complementary
O straight
supplementary
Answer:
Supplementary is your answer
Please help me!
A second-hand car is advertised for $15575 cash or $1600 deposit and 24 monthly payments
of $734.70.
a What is the difference between the cash price and the HP price?
b What annual rate of interest is paid on the HP plan?
Answer:
The difference between the cash price and the HP price is $3,657.8. The annual rate of interest paid on the HP plan is 11.74% per year.
Step-by-step explanation:
Given that a second-hand car is advertised for $ 15,575 cash or $ 1600 deposit and 24 monthly payments of $ 734.70, to determine what is the difference between the cash price and the HP price and what annual rate of interest is paid on the HP plan you must perform the following calculation:
(1600 + 734.70 x 24) - 15,575 = X
(1600 + 17,632.8) - 15,575 = X
19,232.8 - 15,575 = X
3,657.8 = X
Therefore, the difference between the cash price and the HP price is $ 3,657.8.
15,575 = 100
19,232.8 = X
19,232.8 x 100 / 15,575 = X
1,923,280 / 15,575 = X
123.48 = X
(123.48 - 100) / 2 = X
23.48 / 2 = X
11.74 = X
Therefore, the annual rate of interest paid on the HP plan is 11.74% per year.
Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.02 pounds and a standard deviation of 3.83 pounds. a) What is the probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds
Answer:
0.601 = 60.1% probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 49.02 pounds and a standard deviation of 3.83 pounds.
This means that [tex]\mu = 49.02, \sigma = 3.83[/tex]
What is the probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds?
This is the p-value of Z when X = 50. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 49.02}{3.83}[/tex]
[tex]Z = 0.256[/tex]
[tex]Z = 0.256[/tex] has a p-value of 0.601.
0.601 = 60.1% probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds