Answer:
z(65) = (65-64.2)/[2.81/sqrt(60)] = 0.8/(0.3279)
Step-by-step explanation:
Using the normal probability distribution and the central limit theorem, it is found that there is a 0.0154 = 1.54% probability that the mean height for the sample is greater than 65 inches.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, for samples of size n, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem:
Mean of 64.3 inches, thus [tex]\mu = 64.3[/tex]Standard deviation of 2.81 inches, thus [tex]\sigma = 2.81[/tex]Sample of 75, thus [tex]n = 75[/tex].The probability that the mean height for the sample is greater than 65 inches is 1 subtracted by the p-value of Z when X = 65, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{65 - 64.3}{\frac{2.81}{\sqrt{75}}}[/tex]
[tex]Z = 2.16[/tex]
[tex]Z = 2.16[/tex] has a p-value of 0.9846.
1 - 0.9846 = 0.0154
0.0154 = 1.54% probability that the mean height for the sample is greater than 65 inches.
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An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a green on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
The complete question is;
An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a green on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
orange brown green yellow
46 23 32 19
Answer:
probability of rolling green on the next toss of the die = 4/15
Step-by-step explanation:
We are given how many times each of the colours appeared for each toss and they are;
Orange - 46
Brown - 23
Green - 32
Yellow - 19
Thus,
Total number of tosses = 46 + 23 + 32 + 19 = 120 rolls
Thus, probability of rolling green on the next toss of die will be = number of times green appeared/total number of rolls = 32/120 = 4/15
Which expression is equivalent to 2 (5) Superscript 4?
2 times 5 times 4
2 times 5 times 5 times 5 times 5
2 times 4 times 4 times 4 times 4 times 4
10 times 10 times 10 times 10
Answer:
b
Step-by-step explanation:
The given expression can be rewritten as 2 × 5 × 5 × 5 × 5 and is equal to 1250. The correct option is (B).
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given expression is 2 × 5⁴.
It can be simplified using the rule of indices as follows,
The expression 5⁴ can be written as 4 times 5 as below,
5⁴ = 5 × 5 × 5 × 5.
Then, the expression can be evaluated as
⇒ 2 × 5 × 5 × 5 × 5
⇒ 1250
Hence, the expression can be simplified to obtain 1250.
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A soccer league has 180 players. Of those players 50% are boys. How many boys are in the soccer league?
Answer:
90 boys
Step-by-step explanation:
There are 180 players
Multiply by the percent that are boys to find the number of boys
180 * 50%
180 * .50
90
Answer:
90 boys
Step-by-step explanation:
The soccer league has 180 players, and 50% or half are boys.
Multiply the total number of players in the league by the percent that are boys.
total number of players * percent of boys
180* 50%
Convert 50% to a decimal by dividing by 100, or moving the decimal place 2 spaces to the left.
50/100=0.50
50.0–>5.0–>0.50
180*0.50
Multiply
90
There are 90 boy soccer players in the league.
An item has a listed price of 90$. If the sales tax rate is 6% how much is the sales tax (in dollars)?
Answer:
five dollars and forty cents
5.40$
Step-by-step explanation:
90+6%= 95.40
In ABC, mA = 46, mB = 105, and c = 19.8. Find a to the nearest tenth.
Answer:
a = 29.3785
Step-by-step explanation:
Given ∠A = 46° and ∠B = 105°
we know that ∠A +∠B+∠C = 180°
46° + 105° +∠C = 180°
∠C = 180 - 46 -105
∠ C = 29°
By using sine rule
[tex]\frac{a}{sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
[tex]\frac{a}{sin A} = \frac{c}{Sin C}[/tex]
Given ∠A = 46° and ∠ C = 29° and c = 19.8
[tex]\frac{a}{sin 46} = \frac{19.8}{Sin 29}[/tex]
on cross multiplication , we get
[tex]a = \frac{19.8 X sin 46}{Sin 29}[/tex]
a = 29.3785
A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 63 minutes; the return trip takes 15 minutes. What is the speed of the current?
Answer:
8 mph
Step-by-step explanation:
The speed in each direction is the speed of the boat with the speed of the current appropriately added. If x is the speed of the current, the upstream speed is 13-x; the downstream speed is 13+x.
The ratio of times is inversely proportional to the ratio of speeds, so we ahve ...
15/63 = 5/21 = (13-x)/(13+x)
5(13 +x) = 21(13 -x) . . . . . . . cross multiply
26x = 13(21 -5) = 13·16
x = 13·16/26 = 16/2 = 8
The speed of the current is 8 miles per hour.
The sum of two consecutive even integers is at most 400. The pair of integers with the greatest sum is 196 and 198. True or Flase
Answer:
False
Step-by-step explanation:
The greatest sum of two consecutive even integers would be 200 + 198, or 398
Answer:
its true
Step-by-step explanation:
Which cosine function has maximum of 0.5, a minimum of -0.5, and a period of 2(pi)/3
Answer:
The answer is "[tex]\bold{y=0.5 \cos 3 \theta}[/tex]"
Step-by-step explanation:
The choices were missing the question so the answer to this question can be defined as follows:
The answer is [tex]y= 0.5 \cos 3\theta[/tex] because:
[tex]\Rightarrow -1 \leq \cos 3 \theta \leq 1\\\\\Rightarrow -0.5 \leq \cos 3 \theta \leq 0.5\\[/tex]
So, the maximum value is = 0.5 and the minimum value is = -0.5 of [tex]\frac{2\pi}{3}[/tex].
Answer:
D. y= 0.5 cos 3 theta
Step-by-step explanation:
Probability allows one to measure effectively the risks in selecting one alternative over the others.
True
False
a circle with circumference 20 has an arc at 72 central angle. what is the length of the arc
Answer:
4 units
Step-by-step explanation:
[tex] \because \: l = \frac{ \theta}{360 \degree} \times c \\ \\ \therefore \: l = \frac{72 \degree}{360 \degree} \times 20 \\ \\ \therefore \: l = \frac{72 \degree}{18\degree} \\ \\ \therefore \: l = 4 \: units[/tex]
If f(x) = (-x)^3, what is f(-2)?
-6
-8
8
6
Answer:
The answer is 8
Step-by-step explanation:
Plug -2 in for x. The double-negative inside the parenthesis makes it positive, then do the exponent.
Answer:
-(-2)^3 = 2^3 = 8
Answer is C
Step-by-step explanation:
So we plug in the numbers. We have -2 as x. (-(-2)^3 would be our thing. Thats because our x is the negative so the negative of -2 is 2.
2^3 = 8
therefore its 8
Please help! Which statement is true, about the following of the two triangles? (Refer to image)
A: ΔADC≅Δ ACB, by the SSS congruence postulate.
B: ΔADC≅ΔACB, by the SAS congruence postulate.
C: ΔADC≅ ΔCBA, by the SSS congruence postulate.
D: ΔADC≅ΔCBA, by the SAS congruence postulate.
Answer:
The answer is C because DC = BA and DA = CB (given) and AC = CA (reflexive property).
What statement best explains The relationshipBetween numbersDivisible by 5 and 10
Answer:
a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Step-by-step explanation:
Given : Statement 'The relationship between numbers divisible by 5 and 10'.
To find : What statement BEST explains the statement?
Solution :
First we study the divisibility rules,
Rule for the number divisible by 5 is that number must end in 5 or 0.
Rule for the number divisible by 10 is that number need to be even and divisible by 5, as the prime factors of 10 are 5 and 2 and the number to be divisible by 10, the last digit must be a 0.
According to the divisibility rules Option D is correct.
Therefore, The correct statement explains the relationship between numbers divisible by 5 and 10 is a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Solve the following system of equations using the elimination method. 5x – 5y = 10 6x – 4y = 4
Answer:
x=-2,y=-4
Step-by-step explanation:
By dividing to lowest terms
5x – 5y = 10= x-y=2.......(1)
6x – 4y = 4=3x-2y=2........(2)
By elimination method
Multiply equation (1) by 3 so as to correspond with equation (2)
3(x-y)=3(2)
3x-3y=6..........(3)
Multiply equation (2) by 1 so as to correspond with equation (1)
1(3x-2y)=1(2)
3x-2y=2..........(4)
Then equation (3)-equation (4)
(3x-3y=6)
-
(3x-2y=2)
__________
-y=4
y=-4
Substitute y=-4 into equation(1)
x-(-4)=2
x+4=2
x=-2
Therefore x=-2,y=-4
Write the number one and three quarter million in figures.
Answer 1750000
Step-by-step explanation:
The number "one and three-quarter million" can be written in figures as 1,750,000.
Given the number one and three quarter million.
"One" represents the digit 1.
"Three-quarter" means three-fourths or 3/4.
In decimal form, this fraction is 0.75.
"Million" signifies a value of 1,000,000.
To represent this number in figures, we combine these components:
We start with the digit 1, representing "one."
Then we append the value 750,000, which corresponds to "three-quarter million."
Combining these two parts, we have 1,750,000.
Therefore, "one and three-quarter million" can be written in figures as 1,750,000.
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Please help. I’ll mark you as brainliest if correct!
Answer:
a= -3/8
b= 1/8
Step-by-step explanation:
To remove i from the denominator, we need to multiply the numerator and denominator by -i
[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]
This simplifies to
[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]
This further simplifies to
[tex]\frac{i-3}{8}[/tex]
This can be rewritten as
[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]
a= -3/8
b= 1/8
Answer:
[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]
Step-by-step explanation:
[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.93, P(C) = 0.95, and P(D) = 0.92. Find the probability that the machine works properly.A) 0.8128B) 0.2441C) 0.8217D) 0.7559
Answer:
D) 0.7559
Step-by-step explanation:
Independent events:
If two events, A and B are independent:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question:
Four independent events, A, B, C and D.
So
[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D)[/tex]
Find the probability that the machine works properly.
This is the probability that all components work properly.
[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D) = 0.93*0.93*0.95*0.92 = 0.7559[/tex]
So the correct answer is:
D) 0.7559
123 grams is rounded to nearest whole. Write down the minimum possible mass it could have been.
Answer:
The nearest whole is 122.99 repeated
Step-by-step explanation:
Tony rode his bicycle 3 7/10 miles to school. What is this distance written as a decimal?
Answer:
the distance written as a decimal is 3.7
37/10 = 3,7
Achievements :)
Dan and Camille each have a gift card with a combined balance of $350.00. Dan spent 1/2 of his card balance while Camille spent 1/3 of her card balance. They are both left with an equal amount on their gift cards left. What are they left with.
Will give Brainliest Talia took the bus from her home to the bank and then walked back to her home along the same route. The round trip took 0.9 hours total. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. The rate of Trip 2 is blank km/h. The time of Trip 1 is blank hours.
Answer:
The rate of trip 2 is 5 km/h
The time of trip 1 is 0.9-x
Step-by-step explanation:
The rate of trip 2 is 5 km/h because it tells you she walked at an avg speed of 5 km/h.
The time of trip 1 is 0.9-x. It's because the time in trip 2 is x, and it says the total is 0.9. So just subtract 0.9-x.
Also I took the test on edge and attached a pic.
Want Brainliest? Get this Correct The x-values in the table for f(x) were multiplied by -1 to create the table for g(x) What is the relationship between the graphs of the two functions? A. They are reflections of each other across the y-axis B. They are reflections of each other across the x-axis C. The graphs are not related D. They are reflections of each other over the line x = y
Answer:
Option (A).
Step-by-step explanation:
We choose a point from table of f(x), that is (-2, -31)
1). If this point is reflected across x-axis, rule to be followed,
(x, y) → (x, -y)
That means y coordinate of the point gets changed with opposite notation.
If (-2, -31) is reflected over the x-axis,
(-2, -31) → (-2, 31) ----------(1)
2). When a point is reflected over the y-axis,
Rule to be followed,
(x, y) → (-x, y)
(-2, -31) → (2, -31) ----------(2)
3). When a point is reflected over the line y = x
Rule to be followed,
(x, y) → (y, x)
(-2, -31) → (-31, -2) -----------(3)
By comparing f(x) and g(x) we find the relation between the functions as,
f(-2, -31) → g(2, -31)
Rule between the functions f and g matches with the rule number (2).
Therefore, function 'f' has been reflected across y axis to get the function 'g'.
Option (A) will be the answer.
what is tge surface area of tge dquare pyramid GELP IM TIMED AND ABOUT TO RUN OUT OF TIME
Answer:
Step-by-step explanation:
Problem PageQuestion A Web music store offers two versions of a popular song. The size of the standard version is 2.6 megabytes (MB). The size of the high-quality version is 4.2 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 4074 MB. How many downloads of the standard version were there?
Answer:
There were 210 downloads of the standard version.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of downloads of the standard version.
y is the number of downloads of the high-quality version.
The size of the standard version is 2.6 megabytes (MB). The size of the high-quality version is 4.2 MB. The total size downloaded for the two versions was 4074 MB.
This means that:
[tex]2.6x + 4.2y = 4074[/tex]
Yesterday, the high-quality version was downloaded four times as often as the standard version.
This means that [tex]y = 4x[/tex]
How many downloads of the standard version were there?
This is x.
[tex]2.6x + 4.2y = 4074[/tex]
Since [tex]y = 4x[/tex]
[tex]2.6x + 4.2*4x = 4074[/tex]
[tex]19.4x = 4074[/tex]
[tex]x = \frac{4074}{19.4}[/tex]
[tex]x = 210[/tex]
There were 210 downloads of the standard version.
Calculate the surface area of the egg (in μm2). The formula for calculating the surface area (SA) of a sphere is given below. SA = 4Ïr2. Use 3.14 as the value for Ï.
Answer:
[tex]31400\mu m^2[/tex]
Step-by-step explanation:
We are given that
Diameter of egg,d=[tex]100\mu m[/tex]
We have to find the surface area of egg in [tex]\mu m^2[/tex].
Radius of egg,r=[tex]\frac{d}{2}=\frac{100}{2}=50\mu m[/tex]
Surface area of sphere=[tex]4\pi r^2[/tex]
Where [tex]\pi=3.14[/tex]
Using the formula
Surface area of egg=[tex]4\times 3.14(50)^2[/tex]
Surface area of egg=[tex]31400\mu m^2[/tex]
Hence, the surface area of the egg=[tex]31400\mu m^2[/tex]
Translate the phrase into a variable expression. Use the letter d to name the variable. If necessary use the asterisk for multiplication and the slash for division. the product of 40 and distance to the finish line
Answer:
40*d
Step-by-step explanation:
The word product means multiplication, and here it is multiplying 40 and the distance(d).
Answer:
40x5
Step-by-step explanation:
A laundry basket has 24 shirts in it for our Navy 12 arete and the remaining our way what is the probability of selecting a red shirt
Answer:
[tex]P(selecting a red t-shirt)=1/2[/tex]
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW;
A laundry basket has 24 t-shirts in it. Four are Navy, 12 are red, and the rest is white. What is the probability of randomly selecting a red t-shirt
EXPLANATION
Total number of the t-shirt in the laundry basket = 24
Number of Navy t-shirt = 4
Number of red t- shirt = 12
The number of white t- shirt in the laundry basket can be calculated as follow;
Total number of t- shirt - (Number of Navy t-shirt + Number of red t- shirt)
Number of white t- shirt = 24 -(4+12)
Number of white t- shirt = 8
The probability of randomly selecting a red t-shirt = [tex]Number of red t- shirt/Total number of the t-shirt[/tex]
[tex]P(selecting a red t-shirt)=12/24[/tex]
[tex]P(selecting a red t-shirt)=1/2[/tex]
A triangle with side lengths is 5,5,8 is what type of triangle
Answer:
isosceles triangle
Step-by-step explanation:
Please answer this correctly
Answer:
676
Step-by-step explanation:
lxw
14x35
4x24
6x15
676
What’s the correct answer for this?
Answer:
I think the answer is 282.6 but my answer is 297.33.
Answer:
the answer will be 282.6m^2
but that is not entirely correct
Step-by-step explanation:
