They should quote 150 hours so that they can get 98% of the batteries to meet the guarantee.
Given mean of 140 hours and standard deviation of 4 hours with confidence level=98%.
We have to find the lifespan which they should quote to get 98% confident that their batteries meet the guarantee.
We have to use z test for this .
μ=140 hours and σ=4 hours
Z=X-μ/σ
When p value is 0.98 then from z table z value will be 2.58.
Z=X-140/4
2.58=X-140/4
2.58*4=X-140
10.32=X-140
X=150.32
after rounding off we will get 150 hours.
Hence they should quote 150 hours of lifetime on batteries.
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Answer:
132
Step-by-step explanation:
Simplify by factoring or distributing:
1.) 2(x + 3) =
2.) 2(x + 3 + y) =
3.) −5 (2x − 3) =
4.) –5(–8w + p) =
5.) 20 + 32w =
6.) 84 + 36z =
7.) (2x - 6)(5x + 7) =
8.) (y - 10)(4y + 2) =
The following equation simplified by factoring or distributing:
2x + 62x + 6 + 2y-10x + 1540w - 5p4(5 + 8w)12(7 + 3z)12(7 + 3z)4y² - 38y - 20Factorization1.) 2(x + 3)
= 2x + 6
2.) 2(x + 3 + y)
= 2x + 6 + 2y
3.) −5 (2x − 3)
= -10x + 15
4.) –5(–8w + p)
= 40w - 5p
5.) 20 + 32w
= 4(5 + 8w)
6.) 84 + 36z
= 12(7 + 3z)
7.) (2x - 6)(5x + 7)
= 10x² + 14x - 30x - 42
= 10x² - 16x - 42
8.) (y - 10)(4y + 2)
= 4y² + 2y - 40y - 20
= 4y² - 38y - 20
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Which of the following is an example of a combination?
A. Selecting the best cake and runner-up best cake from a cake
decorating competition
B. Selecting 5 CDs to take with you on a trip from a collection of 30
CDs
C. The number of orders in which 6 people can arrive at a party if no
one arrives at the same time
D. The number of orders in which triplets can be born
Explanation:
For choice A, order matters. This is because of the positions of first place and second place are different from one another. Since order matters, we have a permutation for choice A and can rule it out.
Choices C and D are ruled out for the same reason.
Choice B is a combination. It doesn't matter what the order of the CDs are. All that matters is the group overall rather than the individual CDs.
ASAP
Match the function with the graph.
y=√x+4
b, y=√z-1
Cy=√√x-1+4
d.y=√x+1
Using translation concepts, the function is given by:
C. [tex]y = \sqrt{x - 1} + 4[/tex].
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The graphed function is the square root function shifted one unit to the right(x -> x - 1), and four units up(y -> y + 4), hence the function is:
C. [tex]y = \sqrt{x - 1} + 4[/tex].
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What is the leading coefficient of the polynomial? 5x² + 8x³ +4 - 6x² – 3x5
Answer:
In polynomial function f(x) = 5x² + 2x³ + 4 the leading coefficient is 5.
The leading coefficient of a polynomial is the coefficient of the leading term 5x².
Step-by-step explanation:
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.
Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.
Write the equation that represents the volume of the storage container in terms of its width.
The equation that represents the volume of the storage container(rectangular prism) in terms of its width is 12w + 6w²
How to find the volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
h = 6 ft
l = 2 + w
Hence,
volume of the rectangular prism = (2 + w) × w × 6
volume of the rectangular prism = (2w + w²)6
volume of the rectangular prism = 12w + 6w²
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Can someone help me out if question 37. triangle is a SSS, SAS or ASA? ASAP, gotta have an answer fast pls
Answer:
ASA Postulate
Step-by-step explanation:
The two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. (Angle, Common Side, Angle)
Please Help Asap!!! I would really appreciate it
Using the given exponential function, it is found that the colony would have 852 bacteria after 10 days.
What is the exponential function?The exponential function for the colonies' size is given as follows:
[tex]F = I(1 + r)^t[/tex]
In which:
I is the initial amount.r is the growth rate.t is the number of time periods.The parameters are given as follows:
I = 55, r = 0.73, t = 5, as 10/2 = 5.
Hence the amount will be given by:
[tex]F = 55(1 + 0.73)^5 = 852[/tex]
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The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 9,
6, 18, 2, 13, 3, 5. Using the given data, find the mean, median, and mode for this sample.
OA. mean: none, median: 6, mode: 8
B. mean: 6, median: 8, mode: none
C. mean: 8, median: 6, mode: none
OD. mean: 18, median: 8, mode: 6
Reset Selection
e
Answer:
C
Step-by-step explanation:
Mean: 9+6+18+2+13+3+5= 56/7 = 8
Median: 2,3,5,6,9,13,18 the middle number is 6
mode:none
Subtract 6x^{2}-7x-2 from 6x^{2}-2x+6
Hello!
Let's subtract!
⇒ 6x² - 2x + 6 - (6x² - 7x - 2)
⇒ 6x² - 2x + 6 - 6x² + 7x + 2
⇒ 5x + 8
∴ The difference will be equal to 5x + 8.
Answer:
Your answer is 5x+8
Step-by-step explanation:
= 6x^2-2x+6 - (6x^2-7x-2)
= 6x^2-2x+6 - 6x^2+7x+2
= 6x^2- 6x^2-2x+7x+6+2
=5x+8
Hope its helpful!
A line passes through the point (8, -5) and has a slope of 5/4. Write an equation in point-slope form for this line.
ATTACHED IS THE SOLUTION!!
What is the axis of symmetry and vertex for the function f(x)=3(x-2)^2+4?
Answer:
Axis of symmetry: x = 2
Vertex: (2,4)
Step-by-step explanation:
I need help please..
someone please please help me with this !!
9) The x-intercepts are when y=0. From the factored form, we know the x-intercepts are (-1,0) and (3,0).
10) The y-intercept is when x=0. From the standard form, we know the y-intercept is (0, -3).
picture says all 20 charecters needed
Answers:
Lower bound = 41.3
Upper bound = 41.5
===========================================================
Explanation:
49.15 is the smallest f can be while 49.24 is the largest it can be. Well technically we could have something like 49.2499 or 49.24999 and so on. We slowly approach 49.25 but never actually get there
So the variable f is between 49.15 and 49.25 inclusive of the first value but excluding the second value. We can write it as [tex]49.15 \le f < 49.25[/tex]
For similar reasoning, [tex]7.75 \le g < 7.85[/tex]
-----------------
If we wanted to subtract those variables and get the smallest result possible, then we need to pick values that are closest together. It might help to set up a number line.
This means we'd go for f = 49.15 and g = 7.85
The lower bound for f-g is f-g = 49.15-7.85 = 41.3
In contrast, the upper bound is when the two variables are spaced as far apart as possible. The upper bound is f-g = 49.25 - 7.75 = 41.5
Answer:
See below
Step-by-step explanation:
49.2 could be 49.15 <= f < 49.25
7.8 could be 7.75 <= f < 7.85
Lower bound of f- g would then be 49.15 - 7.85 > 41.3
upper bound 49.25 - 7.75 < 41.5
41.3 < f-g < 41.5
helpp. The Eiffel Tower in Paris, France is 1063 feet tall. If you took an elevator 3/4 the way up the tower, how far from the ground would you be in feet?
If the Height of Eiffel Tower in Paris is 1063 feet tall and we took an elevator 3/4 up the tower then we would be 797.25 feet from the ground.
Given The height of the Eiffel Tower is 1063 feet tall. We have taken an elevator that is 3/4 up the tower.
Height is the measurement of someone from head to foot or from base to top. It is the distance upward.
Height of The Eiffel tower is 1063 feet.
We have taken 3/4 up the elevator.
Then the height from ground to us can be calculated by multiplying 1063 by 3/4 which will be as under:
=1063*3/4
=729.25 feet
Hence if the height of the Eiffel Tower is 1063 feet then we would be 729.25 up from the ground if we have taken elevator 3/4 up the tower.
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Find the measure of the exterior angle.
Answer:
The exterior angle is 77
Step-by-step explanation:
The measure of the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
2x+11 = x +44
First we need to find x
Subtract x from each side
2x+11-x = x+44
x +11 = 44
Subtract 11 from each side
x+11-11 = 44-11
x =33
Now we can find the exterior angle
2x+11 = 2(33)+11 = 66+11 = 77
The exterior angle is 77
1.
a) Carol and Conrad together have less than $50. Carol has $10 more than Conrad how much money might Conrad have.
b) How much money might Carol have
What is the recursive formula for the geometric sequence with this explicit formula?
For the given geometric sequence, we have:
[tex]a_1 = 9\\\\a_n = (-1/3)*a_{n-1}[/tex]
So the correct option is B.
Which is the recursive formula?Here we have the geometric sequence:
[tex]a_n = 9*(-\frac{1}{3} )^{(n - 1)}[/tex]
To get the initial value of the geometric sequence, we just need to replace n by 1, so we get:
[tex]a_1 = 9*(-\frac{1}{3} )*(1 - 1) = 9[/tex]
Now, notice that the common ratio is (-1/3), this means that each term of the sequence is (-1/3) times the previous term.
[tex]a_n = (-1/3)*a_{n-1}[/tex]
Then the correct option is B.
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Find the Area-Rectangle
a = x +3
b = 2x - 1
Answer:
2x^2 + 5x - 3
Step-by-step explanation:
Area = length (a) * width (b)
(x + 3) * (2x - 1)
2x^2 + 6x - x - 3 (combine like terms)
2x^2 + 5x - 3
Brainliest, please :)
Jeremy left the house in the morning and the temperature outside was 2 degrees Celcius. Once he returned at night, the temperature was -7 degrees Celcius.
How much did the temperature decrease by?
Answer:
The temperature decreased by 9 degrees.
Step-by-step explanation:
Since the temperature in the morning was 2*C & at night, the temperature was -7*C, the temperature had to decrease using this equation => ||-7 + 2|| = x, with -2 being the temperature loss added as well. All we have to do is 7+2 = x & 9 = x, with x being the temperature drop.
Answer:
9 degrees Celcius
Step-by-step explanation:
The difference between 2 and -7 is 9.
The speed of light is 186,282 miles per second write the place name and the value of each eight in this number
Place name of eights are ten thousands place & tens place & 80000, 80 are the values respectively.
The expanded form of a number is splitting of numbers based on place value. The place are ones, tens, hundreds, thousands, ten thousand etc
that is, the number represented by the sum of each digit multiplied by its place value is called the expanded form of a number.
Example : Expanded form of 4567 is 4000+500+60+7. where 4 is in thousands place, 5 is in hundreds place, 6 is in tens place and 7 is in ones place.
Given that, The speed of light is 186,282 miles per second.
The number is 186282.
Expanding the number, we get,
186282 = 100000+80000+6000+200+80+2
Here in the number 186282, eight present in the ten thousands place and in the tens place.
Since one eight is in ten thousands place, so the value is 80000
And the another eight is in the tens place, so the value is 80.
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In the following exercises, multiply the binomials. Use any method.
247. (p + 12)(p − 5)
Answer:
Hence the expression [tex]$$(p+12)(p-5)=p^2+8p-60$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (p+12)(p-5).We have to multiply the given expression.Multiply the (p+12) by -5, multiply the (p+12) by p then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & p & + & 12 \\ \times & {} & p & - & 5 \\ \end{matrix}}[/tex]
____________
[tex]{\frac{\begin{matrix}{} & - & 5p & - & 60 \\ {{p}^2} & + & 12p & {} & {} \\ \end{matrix}}{\begin{matrix}{{p}^2} & + & 8p & - & 60 \\ \end{matrix}}}$$[/tex]
One car travels 30 meters east in 5 seconds. A second car travels 42 meters west in 7 seconds. During their respective periods of travel, the cars must have had the same _______________.
The cars must have had the same Average Speed
Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time. Even with varying speed, the values of total time and the total distance covered can be used, and with the help of the formula for average speed, we can find a single value to represent the entire motion.
The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:
[tex]\frac{Total distance covered by the object}{Total time taken}[/tex]
Given :-
Distance covered by A = 30 metersTime taken by A = 5 secondsDistance covered by B = 42 metersTime taken by B = 6 secondsSubstituting the given values in the formula for A and B respectively we get
Average Speed of A = [tex]\frac{30}{5}[/tex] m/s = 6 m/s
Average Speed of B = [tex]\frac{42}{7}[/tex] m/s = 6m/s
Thus the cars must have had the same Average Speed.
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What is the scale factor from ABC to ADEF?
5
A 3 C
D
15
OA. 2
OB. 3
OC. 3
OD. 1/1/20
E
12
Answer:
OB
Step-by-step explanation:
no clear explanation for this answer. a picture to demonstrate how i archived it will be shared
The scale factor from triangle ABC to DEF would be,
⇒ 1 / 3
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
Two triangle ABC and DEF is shown in figure.
Hence, We can formulate;
The scale factor from triangle ABC to DEF would be,
⇒ AC / DF
⇒ 3 / 9
⇒ 1 / 3
Thus, The scale factor from triangle ABC to DEF would be,
⇒ 1 / 3
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There are 20 boys and 18 girls in a class.
Find the percentage of
(i) boys in the class
(ii) girls in the class
Answer:
Step-by-step explanation:
Total Students = 20 + 18 = 38 students
For boys percentage = 20/38 * 100
Boys percentage = 52.6%
For girls percentage = 18/38 * 100
Girls percentage = 47.3%
Answer:
(i) 52.631578947368 %
(ii) 47.368421052632 %
Step-by-step explanation:
there are :
20 boys
18 girls
Total number of students 38
========================
(i) the percentage of boys in the class
[tex]=\frac{20}{38} \times100 = 52.631578947368 \ \%[/tex]
(ii) the percentage of girls in the class
[tex]=\frac{18}{38} \times100 = 47.368421052632 \ \%[/tex]
NEED HELP ASAP!
Please see the attachment below.
The angle ∠14 and angle ∠16 are the supplementary angles. Then the measure of angle ∠16 will be 188° – 5x.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The line l and the line m are parallel to each other.
The angle ∠7 = 4x – 3 and angle ∠14 = 5x – 8.
Then the measure of angle ∠16 will be
The angle ∠14 and angle ∠16 are the supplementary angles. Then we have
∠14 + ∠16 = 180°
5x – 8 + ∠16 = 180°
∠16 = 180° – 5x + 8
∠16 = 188° – 5x
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The completed construction of regular hexagon is shown below explain why act is a 30-60-90 triangle
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg.
How to explain the reasonACF is a 30º-60º-90º triangle because of the following reasons;
Based on a theorem, in a 30°-60°-90° triangle, it is said that the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg,
1 → short leg = 1
2 → hypotenuse = 2
√3 → long leg = √3
Using the Pythagorean theorem., we have that
a² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
√b² = √3
b = √3
Thus, in a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg.
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Consider functions f and g
Using successive approximation, what is the approximate solution to the equation f(x)= g(x)? Use the graph as a starting point
PLEASE THIS HAS A TIME LIMIT AND GIVE PROOF BECAUSE I REALLY NEED TO GET THIS RIGHT :((
25 POINTS AND WILL MARK BRAINLIEST
Answer:
1)D 2) Can't see the function
Question 9(Multiple Choice Worth 5 points)
(05.02 LC)
Which of the following possibilities will form a triangle?
O Side 15 cm, side = 6 cm, side = 8 cm
=
O Side 15 cm, side = 6 cm, side = 9 cm
Side = 16 cm, side = 9 cm, side = 6 cm
Side = 16 cm, side = 9 cm, side = 8 cm
Answer:
D. 16, 9, 8
Step-by-step explanation:
sum of any two sides of triangles must be greater than the third side
only the fourth option follows this rule
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 21st, 26th, 65th, and 75th percentiles. If needed, round your answers to two decimal digits. Percentile Value 21% 26% 65% 75%
The the 21st, 26th, 65th, and 75th percentiles are 19.45, 21.7, 27.85, and 29.50.
How to compute the percentile?Here, n=8
P21=(21(n+1)100)th value of the observation
=(21⋅9/100)th value of the observation
=1st observation +0.89[2nd-1st]
=15+0.89[20-15
= 19.45
P26 = (26(n+1)100)th value of the observation
=(26⋅9/100)th value of the observation
=2nd observation +0.34[3rd-2nd]
=20+0.34[25-20]
=20+0.34(5)
= 21.7
P65= (65(n+1)100)th value of the observation
=(65⋅9/100)th value of the observation
=5th observation +0.85[6th-5th]
=27+0.85[28-27
= 27.85
P75 = (75(n+1)100)th value of the observation
=(75⋅9/100)th value of the observation
6th observation +0.75[7th-6th]
=28+0.75[30-28]
= 28 + 1.50
= 29.50
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