Answer:
2.09 seconds.
Step-by-step explanation:
We are given...
y = 70 feet
v0 = 0 feet/second
a = 32 feet/second^2
We need to find t using the following equation...
y = v0 * t + (1/2) * a * t^2
70 = 0 * t + (1/2) * 32 * t^2
70 = (1/2) * 32 * t^2
70 = 16t^2
16t^2 = 70
t^2 = 4.375
t = sqrt(4.375)
t = 2.091650066
So, it will take the toy about 2.09 seconds to hit the ground.
Hope this helps!
The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7. The manufacturer wants to be certain that the mean battery life exceeds 25 hours in accelerated lifetime testing.
Construct a 90%, two sided confidence interval on mean life in the accelerated test.
Answer:
The confidence interval is [tex]25.16 < \mu < 26.85[/tex]
Step-by-step explanation:
From the question we are given a data set
25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.
The mean of the this sample data is
[tex]\= x = \frac{\sum x_i}{n}[/tex]
where is the sample size with values n = 10
[tex]\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}[/tex]
[tex]\= x = 26[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }[/tex]
substituting values
[tex]= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }[/tex]
[tex]\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }[/tex]
[tex]\sigma = 1.625[/tex]
The confidence level is given as 90% hence the level of significance is calculated as
[tex]\alpha = 100 -90[/tex]
[tex]\alpha =10[/tex]%
[tex]\alpha = 0.10[/tex]
Now the critical values of [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table as
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining the critical values of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because we are considering two tails of the area under the normal curve
The margin of error is evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645 * \frac{1.625 }{\sqrt{10} }[/tex]
[tex]MOE = 0.845[/tex]
The 90%, two sided confidence interval is mathematically evaluated as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
[tex]26 - 0.845 < \mu < 26 + 0.845[/tex]
[tex]25.16 < \mu < 26.85[/tex]
Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours
What are the solutions of the quadratic equation (x – 8)2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
Ox=-11 and x = -18
x= -2 and x = 5
x= 2 and x = -5
x= 11 and x = 18
Answer:
Its D
Step-by-step explanation:
x=11 and x=18
a cylinder has a diameter 14cm and height of 11cm calculate the curved surface area of the cylinder (take pi=22/7 up
Answer:
484 cm^2.
Step-by-step explanation:
The length of the circumference = diameter * pi
= 14 * 22/7
The area of the curved surface = circumference * height
= 14 * 22/7 * 11
= 484.
Could someone answer the question with the photo linked below? Then explain how to solve it?
Answer:
b = sqrt(57)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
8^2 + b^2 = 11^2
64+ b^2 = 121
Subtract 64
b^2 = 121-64
b^2 =57
Take the square root of each side
b = sqrt(57)
A train covers certain distance in two parts. Distance covered in first part is 200% more than the distance covered in second part while speed of train is in the ratio 2 : 1 in first and second part respectively. If average speed of train is 64 km/hr, then find the speed of train in first part? (in kmph)
Answer:
Part A speed=96*2=192km/h
Step-by-step explanation:
Two parts, parts A and part B
Part A=200% more than B
Let part B=x
Part A=200 more than B
=2x
Speed ratio=2:1
Average speed of train=64km/h
Let Part A speed=2x
Part B speed=x
A:B=2:1
Total ratio =3
Speed in the part A can be calculated thus:
Totatl speed= ratio of speed in part A / total ratio
64=2x/3
192=2x
x=96km/h
Part A speed=96*2=192km/h
Which of the following pairs consists of equivalent fractions? 12/18 and 10/15 12/20 and 10/25 8/16 and 3/4 5/3 and 3/5
Answer:
12/18 and 10/15
Step-by-step explanation:
12/18 simplifies into 2/3
10/15 simplifies into 2/3
12/20 simplifies into 3/5
10/25 simplifies into 2/5
8/16 simplifies into 1/2
3/4 simplifies into 3/4
5/3 simplifies into 5/3
3/5 simplifies into 3/5
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
What is a fraction number?
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
Let's check all the options, then we have
A) 12/18 and 10/15
12/18 and 10/15
2/3 and 2/3
Yes, they are equivalent fraction numbers.
B) 12/20 and 10/25
12/20 and 10/25
3/5 and 2/5
They are not equivalent fraction numbers.
C) 8/16 and 3/4
8/16 and 3/4
1/2 and 3/4
They are not equivalent fraction numbers.
D) 5/3 and 3/5
5/3 and 3/5
They are not equivalent fraction numbers.
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
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Which expression is equivalent to 0.83¯ ?
Answer:
Hello There!!
Step-by-step explanation:
Your answer will be 83/99. Because, We have to expressed the 0.83¯ as a fraction in simplest form. Let x = 0.83¯ = 0.8383. Then, We have to multiply by 100 to both sides we have: 100x = 83.8383. After, Subtract (One) to (Two) we will have: 99x = 83. Then, We will divide both sides by 99 we have: x = 83/99. Therefore, the 0.83¯ as a fraction in simplest form is, 83/99. Hope This Helps!!~ Sorry, If the example confusing...
Two friends are playing tic-tac-toe. If Amy wins 3/8 of the time, Lily wins 3/10 of the time, and they tie the rest of the time, then what fraction of the time do they tie?
Answer:
13/40
Step-by-step explanation:
The period they have played can be divided into 3 parts:
● The time Amy wins
● The time Lily wins
● The time they tie
So the sum of them is the total time of playing.
Let A be the time Amy wins, L the tile Lily wins and T the time they tie .
●●●●●●●●●●●●●●●●●●●●●●●
Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.
So:
A + P + T = 1
3/8 + 3/10 + T = 1
Multiply 8 by 10 and 10 by 8 so that you get a common denominator.
Cross multiply the numerators and the denominators.
(3*10+3*8)/80 + T = 1
(30 + 24)/80 + T =1
54/80 + T = 1
(27*2)/(40*2) + T = 1
Simplify by 2
27/40 + T = 1
T = 1 - 27/40
Multiply one by 40 to get a common denominator
T = (40-27)/40
T = 13/40
So they have tied 13/40 of the time
A test was marked out of 80. Aboy scored
60% of the marks on the test. How many
marks did he score?
(A)20
(B)48
(C)60
(D)75
Answer:
B
Step-by-step explanation:
To solve this you do 80/100=.8
You than do .8×60= 48
Select the correct answer from each drop-down menu. The graph represents the piecewise function.
Answer:
1). f(x) = x² if ∞ < x < 2
2). f(x) = 5 if 2 ≤ x < 4
Step-by-step explanation:
The graph attached shows the function in two pieces.
1). Parabola
2). A straight line parallel to the x-axis.
Standard equation of a parabola is,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the given parabola is (0, 0).
Equation of the parabola will be,
y = a(x - 0)² + 0
Therefore, the function will be,
f(x) = ax²
Given parabola is passing through (-1, 1) also,
1 = a(-1)²
a = 1
Therefore, parabolic function will be represented by,
f(x) = x² if ∞ < x < 2
2). Straight line parallel to the x-axis,
y = 5 if 2 ≤ x < 4
Function representing the straight line will be,
f(x) = 5 if 2 ≤ x < 4
Answer:
Please mark me as Brainliest :)
Step-by-step explanation:
What is the list price of an article that is subject to discounts of 334 %, 10%, and 2%
if the net price is $564.48?
the answer choices are
sec y= b/6
sec y=6a
sec y=6b
sec y= 6/b
Answer:
sec y=6/b yw
Step-by-step explanation:
Combine like terms: 10 + 6y + 2x - 3
Answer:
6y +2x +7
Step-by-step explanation:
10 + 6y + 2x - 3
The only like terms are the constant
6y+2x +10-3
6y +2x +7
Answer:
2x + 6y + 7.
Step-by-step explanation:
10 + 6y + 2x - 3
= 2x + 6y - 3 + 10
= 2x + 6y + 7.
Hope this helps!
An epidemiologist is observing the decay pattern of a pathogenic bacteria after applying a vaccine. He starts with 2,000 bacteria that decay at a rate of 4.5% per hour. He will check on the bacteria in 36 hours. How many bacteria will he find? Round your answer to the nearest whole number.
Answer:
396
Step-by-step explanation:
Which ordered pair is a solution of this equation 6x-y=-4 . -2,0 -1,-2 -2,-1 0, -2
Answer:
(-1,-2)
Step-by-step explanation:
[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]
so the only one is (-1,-2)
The length, width and height are consecutive whole numbers. The volume is 120 cubic inches.
Answer:
4, 5 and 6
Step-by-step explanation:
Consecutive means right next to each other.
4 x 5 x 6 = 120 cubic inches.
4 X 5 = 20
20 X 6 = 120
The values of the consecutive numbers will be 4, 5, and 6.
Let the numbers be represented by a, a+1, and a+2.
Therefore, a(a+1)(a+2) = 120
a³ + 3a² + 2a = 120
a = 4
Therefore, a + 1 = 4+1 = 5
a + 2 = 4 + 2 = 6
Therefore, the values will be 4, 5, and 6.
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2. Write as a complex number.
Answer:
Your answer is correct ✔️
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
2√3 + 3i is the answer
Step-by-step explanation:
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75
Answer:
x = $0.50
y= $0.75
Step-by-step explanation:
1. Multiply the equations to have the same coefficients
5(6x + 6y = 7.5) → 30x + 30y = 37.5
3(10x + 5y = 8.75) → 30x + 15y = 26.25
2. Subtract the equations
30x + 30y = 37.5
- 30x + 15y = 26.25
15y = 11.25
3. Solve for y by dividing both sides by 15
y = 0.75
4. Plug in 0.75 for y into one of the equations
6x + 6(0.75) = 7.5
5. Simplify
6x + 4.5 = 7.5
6. Solve for x
6x = 3
x = 0.5
Answer:
The cost of one apple is $0.5
The cost of one orange is $0.75
Step-by-step explanation:
Given information
The cost of an apple = [tex]x[/tex]
The cost of an orange = [tex]y[/tex]
Equation to find the values are:
[tex]6x=6y=7.50\\10x+5y=8.75[/tex]
Now, convert the equations to have same coefficient as:
[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]
Now, on solving the above equation by subtracting one from another.
We get,
[tex]15y=11.25\\y=0.75[/tex]
Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].
As,
[tex]6x+4.5=7.5\\x=0.5[/tex]
Hence,
The cost of one apple is $0.5
The cost of one orange is $0.75
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Need help with this math problem
Answer:
4
Step-by-step explanation:
f(x) = 4 ^ ( x-2)
Let x=3
f(3) = 4 ^ ( 3-2)
= 4 ^ 1
= 4
Answer:
4
Step-by-step explanation:
4^(x - 2)
Plug x as 3.
4^(3 - 2)
Subtract.
4^(1)
4^1 = 4
Marcus made a sail for his toy boat. If the sail is 5 inches long and the top angle of the sail is 40°, what is the width of the bottom of the sail (w) to the nearest tenths place?
Answer:
4.2 in
Step-by-step explanation:
let us first visualize the sail as a triangular shape
the angle of the triangle from top is 40°
the height of the triangle is give as 5 in
we can apply SOH CAH TOA to solve for the base of the sail
the opposite = the base of the sail
the adjacent = the height of the sail= 5 in
therefore
Tan∅= Opp/Adj
Tan(40)= Opp/5
Opp= Tan(40)*5
Opp= 0.8390*5
Opp= 4.195 in
Hence the width of the sail is 4.2 in to the nearest tenths
Answer:
4.2
Step-by-step explanation:
What is the value of the expression below?
(-8)^4/3
Answer:
16
Step-by-step explanation:
(-8)^4/3
-(8^1/3)⁴
-(∛8)⁴
-(2)⁴
-2⁴
= 16
Answer: the ^^^^ right I check it
Step-by-step explanation:
Which of the following is the graph of the function shown above? See file
Answer:
what we have to tell
Step-by-step explanation:
please send the correct information
Answer:
The answer on PLATO is Graph Z.
Step-by-step explanation:
I just had this question and got it right!!!
Hope this Helps!!!
There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. b How many ways can we choose a Senator from a chosen state? c How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?
Answer:
a) rCn = 1176
b) 2352
Step-by-step explanation:
a)Each committee should be formed with 3 members ( no two members could be of the same state) then
Let´s fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then
rCn = n! / (n - r )! *r!
rCn = 49!/ (49 - 2)!*2!
rCn = 49*48*47! / 47!*2!
rCn = 49*48 /2
rCn = 1176
So we can choose in 1176 different ways a senator for a given state
b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.
1176*2 = 2352
the numbers of students in the 10 schools in a district are given below. ( Note that these are already ordered from Least to Greatest) 198, 216, 220, 236, 246, 252, 253, 260, 290, 319. Suppose that the number 319 from this list changes to 369. Answer the following what happens to the median? what happens to the mean?
Answer:median:249
Step-by-step explanation:
median:198] 216} 220] 236] 246 252 [253[ 260 {290[ 369
246 +252=498
498/2=249
as for the mean i will give you that later
he geometric property of any polygon feature that is represented by the ratio of the perimeter of the polygon to the circle with the same perimeter is called
Answer:
"Compactness" is the right answer.
Step-by-step explanation:
In mathematical or geometry, compactness seems to be the characteristic of some mathematical morphology or spaces which have its primary use during the analysis of parameters based upon such spaces.An accessible space protect (or set) is another series of open field sets shielding another space; i.e., every space position is throughout some series member.So that the above would be the correct answer.
a food snack manufacturer samples 9 bags of pretzels off the assembly line and weights their contents. If the sample mean is 14.2 oz. and teh sample devision is 0.70 oz, find the 95% confidense interval of the true mean
Answer:
13.7≤[tex]\mu[/tex]≤14.7Step-by-step explanation:
The formula for calculating the confidence interval is expressed as shown;
CI = xbar ± Z(б/√n)
xbar is the sample mean
Z is the value at 95% confidence interval
б is the standard deviation of the sample
n is the number of samples
Given xbar = 14.2, Z at 95% CI = 1.96, б = 0.70 and n = 9
Substituting this values into the formula;
CI = 14.2 ± 1.96(0.70/√9)
CI = 14.2 ± 1.96(0.70/3)
CI = 14.2 ± 1.96(0.2333)
CI = 14.2 ± 0.4573
CI = (14.2-0.4573, 14.2+0.4573)
CI = (13.7427, 14.6537)
Hence, the 95% confidence interval of the true mean is within the range
13.7≤[tex]\mu[/tex]≤14.7 (to 1 decimal place).
this graph shows the solution to which inequality?
Answer:
B. y > 2/3x + 1
Step-by-step explanation:
To find slope we'll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
(-3,-1) (3,3)
3 - -1 = 4
3 - -3 = 6
2/3x
The y intercept is 1,
we know this because that's the point the line touches the y axis.
Thus,
the answer is B. y > 1/3x + 1.
Hope this helps :)
The graph of the solution of an inequality is given .
The graph represents the inequality is [tex]y>\frac{2}{3} x+1[/tex]
Option B
Given :
The graph of an inequality. To find the inequality for the given graph we use linear equation [tex]y=mx+b[/tex]
where m is the slope and b is the y intercept
To find out slope , pick two points from the graph
(-3,-1) and (3,3)
[tex]slope =\frac{y_2-y_2}{x_2-x_1} =\frac{3+1}{3+3} =\frac{2}{3} \\m=\frac{2}{3}[/tex]
Now we find out y intercept b
The point where the graph crosses y axis is the y intercept
The graph crosses y axis at 1
so y intercept b=1
The linear equation for the given graph is
[tex]y=\frac{2}{3} x+1[/tex]
Now we frame the inequality . we use test point that lies inside shaded region
Lets take (4,5)
[tex]y=\frac{2}{3} x+1\\5=\frac{2}{3} (4)+1\\5=3.6\\5>3.6\\y>\frac{2}{3} x+1[/tex]
The inequality for the given graph is
[tex]y>\frac{2}{3} x+1[/tex]
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Answer:
You need to add 150 mL of 65% alcohol solution.
Step-by-step explanation:
You have 300 mL of 20% solution.
300 mL of 20% alcohol solution has 20% * 300 mL of alcohol.
You have 65% solution.
Let the volume of 65% solution you add be x.
In 65% solution, 65% of the volume is alcohol, so the amount of alcohol in x amount of 65% solution is 65% * x.
You want 35% solution.
The total amount of 35% solution you will make is 300 mL + x. The amount of alcohol in that amount of solution is 35% * (x + 300).
Equation of alcohol content:
20% * 300 + 65% * x = 35% * (x + 300)
60 + 0.65x = 0.35x + 105
0.3x = 45
x = 150
Answer: You need to add 150 mL of 65% alcohol solution.
which of the following descriptions represent the transformation shown in the image? Part 1d
Answer:
(C) Translation of 2 units right, 1 up, and a reflection over the y-axis.
Step-by-step explanation:
Ideally, we are looking for a reflection of the red image over the y-axis, and to do that, we can see how we need to move the black image.
In order for points Q and Q' to be a reflection of each other, they need to have the same y value, and be the exact same distance from the y axis, so the point that Q has to be at is (-1,-3).
Q is right now at (-3,-4) so we can translate this.
To get from -3 to -1 in the x-axis, we go right by 2 units.
To get from -4 to -3 in the y-axis, we go up one unit.
Now, if we reflect it, the triangles will be the same.
Hope this helped!
Answer:
C.
Step-by-step explanation:
When you study the images, it is clear that the black triangle has to be reflected over the y-axis to face the same direction as the red triangle. So, choice A is eliminated.
Once you reflect the black triangle across the y-axis, you have points at (-1, -1), (3, -4), and (3, -2). Meanwhile, the red triangle's coordinates are at (-3, 0), (1, -3), and (1, -1). From these points, you can tell that the x-values differ by 2 units and the y-values differ by 1 unit.
All of these conditions match the ones put forth in option C, so that is your answer.
Hope this helps!
8.43 An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 45 minutes. a. What sample size is needed if the executive wants to be 90% confident of being correct to within {5 minutes
Answer:
a
The sample size is [tex]n = 219.2[/tex]
b
The sample size is [tex]n = 537.5[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 45 \minutes[/tex]
The Margin of Error is [tex]E = \pm 5 \ minutes[/tex]
Generally the margin of error is mathematically represented as
[tex]E = z * \frac{\sigma }{\sqrt{n} }[/tex]
Where n is the sample size
So
[tex]n = [\frac{z * \sigma }{E} ]^2[/tex]
Now at 90% confidence level the z value for the z-table is
z = 1.645
So
[tex]n = [\frac{1.645 * 45 }{5} ]^2[/tex]
[tex]n = 219.2[/tex]
The z-value at 99% confidence level is
[tex]z = 2.576[/tex]
This is obtained from the z-table
So the sample size is
[tex]n = [\frac{2.576 * 45 }{5} ]^2[/tex]
[tex]n = 537.5[/tex]
For the 90% confidence interval, the sample size is 219.2 and for the 99% confidence interval, the sample size is 537.5 and this can be determined by using the formula of margin of error.
Given :
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily.From past studies, the standard deviation is estimated as 45 minutes.The formula of the margin of error can be used in order to determine the sample size is needed if the executive wants to be 90% confident of being correct to within 5 minutes.
[tex]\rm ME = z\times \dfrac{\sigma}{\sqrt{n} }[/tex]
For the 90% confidence interval, the value of z is 1.645.
Now, substitute the values of all the known terms in the above formula.
[tex]\rm n=\left(\dfrac{z\times \sigma}{ME}\right)^2[/tex] --- (1)
[tex]\rm n=\left(\dfrac{1.645\times 45}{5}\right)^2[/tex]
n = 219.2
Now, for 99% confidence interval, the value of z is 2.576.
Again, substitute the values of all the known terms in the expression (1).
[tex]\rm n=\left(\dfrac{2.576\times 45}{5}\right)^2[/tex]
n = 537.5
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