Answer:
a) z (score) 1,53
b) z ( score) - 1,96
c) 200 students
Step-by-step explanation:
Normal Distribution N ( 74;10)
a) From z-table, and for 6,3 % ( 0,063 ) we find the z (score) 1,53
Note : 6,3 % or 0,063 is the area under the curve, the minimum score neded to get A
b) To fail 2,5 % ( 0,025 ) from z-table get - 1,96
c) If the group of student who did not pass the course (5) correspond to 2,5 % then by simple rule of three
5 2,5
x ? 100
x = 500/2,5
x = 200
Question 2: Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
Answer:
?
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
Let "x" be the number of nickels, of dimes, and of quarters.
The value of the nickels is 5x cents.
The value of the dimes is 10x cents
The value of the quarters is 25x cents.
Equation:
Value of nickels + Value of dimes + Value of quarters =1320 cents
5x + 10x + 25x = 1320
Sove for "x". Then you will know the number of each coin.
HCF of x minus 2 and X square + X - 6
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{x - 2}}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]
To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F
Let's solve
First expression = x - 2
Second expression = x + x - 6
Here, we have to find the two numbers which subtracts to 1 and multiplies to 6
= x + ( 3 - 2 ) x + 6
Distribute x through the parentheses
= x + 3x - 2x + 6
Factor out x from the expression
= x ( x + 3 ) - 2x + 6
Factor out -2 from the expression
= x ( x + 3 ) - 2 ( x + 3 )
Factor out x+3 from the expression
= ( x + 3 ) ( x - 2 )
Here, x - 2 is common in both expression.
Thus, H.C.F = x - 2
Hope I helped!
Best regards!!!
Answer:
x - 2
Step-by-step explanation:
by factorization method
1) x - 2
2) x^2 + x - 6
by splitting method
x^2 + 3x - 2x - 6
taking separate common from the first two terms and last two terms
x(x + 3) - 2(x + 3)
now writing x+3 once and the other term to get the right answer
(x + 3)(x - 2)
in both parts just see the similar term and write it as HCF
HCF= x - 2
and the second method by which you can get this answer is division method
how can i solve this factorial? A 6,2- P6- A 5,3 + P5
isted below are amounts (in millions of dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service company's employees? Security Service Company: 1.5 1.7 1.6 1.4 1.7 1.5 1.8 1.4 1.4 1.5 Other Companies: 1.8 1.9 1.6 1.7 1.8 1.9 1.6 1.5 1.7 1.8 Find the coefficient of variation for each of the two samples, then compare the variation. The coefficient of variation for the amount collected by the security service company is nothing%. (Round to one decimal place as needed.)
Answer:
Means:
1.55
1.73
Standard Deviation:
0.1434
0.1338
Coefficient of variation:
9.2
7.7
the limited data listed here shows evidence of stealing by the security service company's employees.
Step-by-step explanation:
Given data:
security Service Company Other Companies
x₁ x₂
1.5 1.8
1.7 1.9
1.6 1.6
1.4 1.7
1.7 1.8
1.5 1.9
1.8 1.6
1.4 1.5
1.4 1.7
1.5 1.8
n₁ = 10 n₂ = 10
To find:
coefficient of variation for each of the two samples
Solution:
The formula for calculating coefficient of variation of sample is:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%
Calculate Mean for Security Service Company data:
Mean = (Σ x₁) / n₁
= (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10
= 15.5 / 10
Mean = 1.55
Calculate Standard Deviation for Security Service Company data:
Standard Deviation = √∑(x₁ - Mean)²/n₁-1
= √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1
=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² + (−0.15)² + (−0.15)² + (−0.05)² / 10 - 1
= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 + 0.0225 + 0.0225 + 0.0025 / 9
= √0.185 / 9
= √0.020555555555556
= 0.14337208778404
= 0.143374
Standard Deviation = 0.143374
Coefficient of Variation for Security Service Company:
CV = (Standard Deviation / Mean) * 100%
= (0.143374 / 1.55) * 100
= 0.09249935 * 100
= 9.249935
CV = 9.2
CV = 9.2%
Calculate Mean for Other Companies data:
Mean = (Σ x₂) / n₂
= (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10
= 17.3 / 10
Mean = 1.73
Calculate Standard Deviation for Other Companies data:
Standard Deviation = √∑(x₂-Mean)²/n₂-1
= √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1
= √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9
= √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9
= √(0.161 / 9)
= √0.017888888888889
= 0.13374935098493
= 0.13375
Standard Deviation = 0.13375
Coefficient of Variation for Other Companies:
CV = (Standard Deviation / Mean) * 100%
= (0.13375 / 1.73) * 100
= 0.077312 * 100
= 7.7312
CV = 7.7
CV = 7.7%
Yes, the limited data listed here shows evidence of stealing by the security service company's employees because there is a significant difference in the variation.
A passenger train traveled 180 miles in the same amount of time it took a freight train to travel 120 miles. The rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
Answer:
The passenger train is moving at 45 miles per hour
Step-by-step explanation:
Let the amount of time it took the two trains to travel the distance = t.
Since the two trains traveled the distance at the same time,
Rate of the passenger train =[tex]\frac{180}{t}[/tex]
Rate of the freight train = [tex]\frac{120}{t}[/tex]
Where t is in hours.
From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as
[tex]\frac{120}{t}= \frac{180}{t}-15[/tex]
from the above equation, we can now get our value for t as
[tex]\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours[/tex]
We have our time of travel for the two trains as 4 hours.
The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour
Carla drove her truck 414 miles on 18 gallons of gasoline. How many miles did she drive per gallon?
Answer:
23 miles per gallon
Step-by-step explanation:
414 miles = 18 gallons
=> 18/18 gallons = 414/18 miles
=> 1 gallon = 23 miles
So, she drove 23 miles per gallon.
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top
Weight of man and paint = 160 + 5 = 165 total pounds.
Gravitational force is independent of the path taken so we can ignore the radius of the silo.
Work done = total weight x height
The problem says he climbs to the top so overall height is 90 feet
Work = 165 lbs x 90 ft = 14,850 ft-lbs
g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06
Answer: A) 0
P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.
We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.
The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.
Answer:
7/11 = 0.6363...
Step-by-step explanation:
7 + 4 = 11
probability of winning: 7/11 = 0.6363...
The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]
Given that the odds of the horse winning the race is 7:4
Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:
[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]
From the given question;
The probability of the horse winning the race is:
[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]
[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]
Learn more about probability here:
https://brainly.com/question/11234923?referrer=searchResults
The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in
Answer:
396 in^2
Step-by-step explanation:
The perimeter of a triangle is given by the formula:
● P = 2w+2L
L is the length and w is the width
■■■■■■■■■■■■■■■■■■■■■■■■■■
The width hereis 18 inches and the perimeter is 80 inches.
Replace w by 18 and P by 80 to find L.
● P= 2L+2w
● 80 = 2L + 2×18
● 80 = 2L + 36
Substrat 36 from both sides
● 80-36 = 2L+36-36
●44 = 2L
Divide both sides by 2
● 44/2 = 2L/2
● 22 = L
So the length is 22 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area of a rectangle is given by the formula:
● A= L×w
● A = 22×18
● A = 396 in^2
Solve for x: x/25 > 5
Answer:
x>125
Step-by-step explanation:
Answer:
x > 125
Step-by-step explanation:
Multiply each side by 25, so it now looks like this: x > 125I hope this helps!
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?
Answer:
8.8 pounds
Step-by-step explanation:
Given the following :
Combined weight loss which occurred within a week = 28 kg
Number of days in a week = 7 days
1 kilogram (kg) = 2.2 pounds
Combined weight loss in pounds that occurs within a week:
Weight loss in kg × 2.2
28kg * 2.2 = 61.6 pounds
Assume weight loss occurred at a constant rate :
Weight lost by the group per day :
(Total weight loss / number of days in a week)
(61.6 pounds / 7)
= 8.8 pounds daily
Answer:
88
Step-by-step explanation:
Found the answer and I am doing the quiz rn lel
find m<SPT in degrees
Answer: 60°
Step-by-step explanation:
∠UQR = 180°
∠UQR = ∠UQ + ∠QR
180° = 115° + ∠QR
65° = ∠QR
∠QRT = 180°
∠QRT = ∠QR + ∠RS + ∠ST
180° = 65° + ∠RS + 55°
180° = 120° + ∠RS
60° = ∠RS
Given the two functions, which statement is true?
fx = 3^4, g(x) = 3^x + 5
Answer:
third option
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Given
g(x) = [tex]3^{x}[/tex] + 5 ← this represents a shift up of 5 units
Thus g(x) is the graph of f(x) translated up by 5 units
Answer:
[tex]\boxed{\sf{Option \: 3}}[/tex]
Step-by-step explanation:
g(x) is translated up 5 units compared to f(x). In a vertical translation, when the graph is moved 5 units up, 5 is added to the function. When the graph is moved 5 units down, 5 is subtracted from the function. The graphs are shifted in the direction of the y-axis.
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 80 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 20°. How far away from the building is the sculpture? Round your answer to the nearest hundredth.
Answer:
219.80 feet
Step-by-step explanation:
Tan 20= 80/b
Tan 20= 0.363970234266
(0.363970234266)b=80
b= 219.80 feet
The distance between the sculpture and the bottom of the building is required.
The distance between the building and sculpture is 219.80 feet.
Trigonometry[tex]\theta[/tex] = Angle of depression = Angle of elevation = [tex]20^{\circ}[/tex]
p = Height of building = 80 feet
b = Required length
From the trigonometric ratios we have
[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow b=\dfrac{p}{\tan\theta}\\\Rightarrow b=\dfrac{80}{\tan 20}\\\Rightarrow b=219.80\ \text{feet}[/tex]
Learn more about trigonometry:
https://brainly.com/question/23899312
What is 2 cm converted to feet?
Answer:
0.065617 ft
Step-by-step explanation:
Answer:
0.0656168 feet.
Step-by-step explanation:
“Type ‘equal, supplementary, complementary, or vertical in the space provided’”
Answer:
Supplementary
Step-by-step explanation:
When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.
<AOB (40°) and <BOC (140°) are not equal angles.
<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.
<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.
<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.
What is the measure of FEG?
A. 30 degrees
B. 40 degrees
C. 50 degrees
D. 70 degrees
Please include ALL work!! <3
Answer:
C. 50 degrees
Step-by-step explanation:
Because 6x + 5x = 110° and x = 10
5×10 = FEG 50°
What is 28% of 58?
Hhhhhhh
Answer:
16.24
Step-by-step explanation:
of means multiply
28% * 58
Change to decimal form
.28 * 58
16.24
Answer:
[tex]\Large \boxed{\mathrm{16.24}}[/tex]
Step-by-step explanation:
[tex]28\% \times 58[/tex]
[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]
[tex]\displaystyle \frac{28}{100} \times 58[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{1624}{100} =16.24[/tex]
algebra pyramid please answer !! be the first to be marked as a brainliest .
Answer:
The first pyramid:
63x
39x 24x
23x 16x 8x
The second pyramid:
162x
82x 80x
4x 78x 2x
The third pyramid:
12a+2b
9a+b 3a+b
9a b 3a
The fourth pyramid:
-19a
-5a -14a
3a -8a -6a
Step-by-step explanation:
All that an alegbra pyramid is is adding the two terms below it.
So you can see how I added the terms that lied below each number, such as in number 1: I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.
Hope this helped!
Theresa bought 2 pineapples for $6. She be wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part A
Using the diagram, find the constant of proportionality in terms of dollars per pineapple.
Answer:
$3 per pineapple
Step-by-step explanation:
Hey there!
If 2 pineapples are $6,
6 / 2 = 3
So 1 pineapple is $3.
Hope this helps :)
Answer:
3 dollars for 1 pineapple
Step-by-step explanation:
well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.
A car enters a turnpike 22 miles north of a town. The car teavels north at an average speed of 64 miles per hour. How far is the car from the town after 4 hours? Explain how you can use linear function to solve this problem. Then, solve the problem.
Answer:
distance traveled can be modeled by a linear functionthe car is 260 miles north of townStep-by-step explanation:
a) When the speed is constant, the distance traveled is proportional to the travel time, a linear relationship. The distance traveled can be added to the initial distance to obtain the total distance (from town). This relation is a linear function. It can be modeled by the equation ...
d(t) = 4 + 64t . . . where t is travel time in hours, d(t) is the distance in miles
b) After 4 hours, the distance north of town is ...
d(4) = 4 +64(4) = 260
The car is 260 miles from the town after 4 hours.
Answer: Distance is a function of time. The constant rate of change is 64. Write the equation y = 64x + 22. Substitute 4 in for x to get 278 miles.
Step-by-step explanation:
What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)
Answer:
hello attached is the missing part of your question and the answer of the question asked
answer : 0.2951
Step-by-step explanation:
Given data:
number of persons allowed in the elevator = 15
weight limit of elevator = 2500 pounds
average weight of individuals = 152 pounds
standard deviation = 26 pounds
probability that an individual selected weighs more than 166 pounds
std = 26 , number of persons(x) = 15, average weight of individuals(u) = 152 pounds
p( x > 166 ) = p( x-u / std, 166 - u/ std )
= p ( z > [tex]\frac{166-152}{26}[/tex] )
= 1 - p( z < 0.5385 )
p( x > 166 ) = 1 - 0.70488 = 0.2951
Need Assitance
*Show Work*
Answer:
66 2/3 %
Step-by-step explanation:
First find the students not in the 8th grade
24 - 8 = 16
16 students are not in the 8th grade
Take the fraction of the students not in the 8th grade over the total
16/24 = 2/3
Change to a decimal
.66666666666
Multiply by 100 to change to a percent
66.666666%
66 2/3 %
Answer:
66.67% of students are not in eighth grade
Step-by-step explanation:
8/24=1/3
1/3=0.33333333333
1-0.33333333333=0.66666666667
0.66666666667=66.67%
What is the missing statement in step 10 of the proof?
Answer:
c/sin C = b/sin C
Step-by-step explanation:
Look at the statement in the previous step and the reason in this step.
c sin B = b sin C
Divide both sides by sin B sin C:
(c sin B)/(sin B sin C) = (b sin C)/(sin B sin C)
c/sin C = b/sin B
Can somebody please solve this problem for me!
Answer:
x = 200.674
Step-by-step explanation:
tan∅ = opposite/adjacent
Step 1: Find length of z
tan70° = 119/z
ztan70° = 119
z = 119/tan70°
z = 43.3125
Step 2: Find length z + x (denoted as y)
tan26° = 119/y
ytan26° = 119
y = 119/tan26°
y = 243.986
Step 3: Find x
y - z = x
243.986 - 43.3125 = x
x = 200.674
Mark each of the following as true or false and explain how you know.
true false false true...is the quick answer
Remember that negatives are always less than positive numbers.
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width of board is 10 cm. If he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
Answer:
The answer is 216
Step-by-step explanation:
if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.
