The mean time that a certain model of light bulb will last is hours is 900 hours and the required percentage of bulbs is 2.5%
Here,
x is the time that a certain bulb will last.
(in houses.
μ=900 hours;
σ=1200 hours.
The standardized value for a light bulbs lasts 1100 hours, is,
z=x-μ/σ
z=1100-900/100=2
We know, for a bell-shaped distance, Approximately,
68% of the data falls within M-uσ;
By rule (ii), here,
95% of the data falls within (μ-2σ,u+2σ)
(900-2x100,900+2x100)
(700,1100)
So (100-95=5%) falls outside of (700,1100)
Since, the distance is symmetric (i.e. bell-shaped); we find the percentage of bulbs that is expected lo lase longer than 1100 hours, is
5/2% =2.5%
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.What does the standard deviation means?Image result for standard deviationA standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.To learn more about standard deviation visit:
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What kind of transformation converts the graph of f(x)=
–
9(x+6)2–3 into the graph of g(x)=
–
9(x–4)2–3?
The kind of transformation which converts the graph of f(x) into the graph of g(x) is vertical shrink .
What is transformation in graph?
A graph transformation is a procedure that modifies an existing graph or graphed equation to create different version of the following graph.
It is given that the functions are :
f(x) = -9(x+6)2 - 3
g(x) = -9(x-4)2 - 3
We know that if we perform transformation that meant the graph of f(x) is transformed into the graph of g(x).
i.e.,
f(x) = -9(x+6)2 - 3
f(x) = -18(x+6) - 3
f(x) = -18x - 128 - 3
f(x) = -18x - 72 - 56 - 3
f(x) = -9(x-4)2 - 3 - 56
f(x) = g(x) - 56
or g(x) = f(x) + (-56)
So , as we are adding f(x), this suggests that the transformation is one of the vertical shrink type.
Therefore, the kind of transformation which converts the graph of f(x) into the graph of g(x) is vertical shrink .
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Could someone help explain this asap
x-7/8=-3/4
Answer: x=1/8
Step-by-step explanation:
[tex]\displaystyle\\x-\frac{7}{8}=-\frac{3}{4} \\\\ x-\frac{7}{8}+\frac{7}{8}=-\frac{3}{4}+\frac{7}{8}\\\\x=-\frac{3}{4} +\frac{7}{8} \\\\ x=\frac{7}{8}-\frac{3*2}{4*2}\\\\ x=\frac{7}{8} -\frac{6}{8} \\\\x=\frac{7-6}{8} \\\\x=\frac{1}{8}[/tex]
59265 divided by the 8th power x 596 x 427
59265 divided by a number raised to the 8th power × 596 × 427 is presented as follows;
[tex]15082468380 \times {x}^{ - 8} [/tex]
How can the given expression be simplified?The given number to be divided is 59265
Let x represent the number that is raised to the 8th power, we have;
The number by which 59265 is divided = x⁸
The number by which the result is multiplied = 596 × 427
Therefore, we have;
[tex] \frac{59265}{x^8} \times 596 \times 427 = \frac{59265}{ {x}^{8} } \times 254492 [/tex]
The above expression can be expressed using the rules of indices as follows;
[tex]\frac{59265 \times 254492}{ {x}^{8} } =15082468380 \times {x}^{ - 8} [/tex]
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Use the provided ruler to measure the length of the segment. What is the length of the segment to the nearest tenth of a centimeter?
The length of the segment is {Blank} centimeters.
The length of the segment to the nearest tenth of a centimeter is 105.0 cm
What is the length of the segment to the nearest tenth of a centimeter?The given parameter is the line segment
When the line segment is measured by a meter rule, we have the length to be
Length = 105 cm
When approximated to the nearest tenth, we have:
Length = 105.0 cm
Hence, the length of the segment to the nearest tenth of a centimeter is 105.0 cm
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What percent of 61 is 70?
Answer:
42.7
Step-by-step explanation:
What percent of 61 is 70?
61 --> Base number
0.7 --> Percent
61 x 0.7 = 42.7
Answer:
61/70 as a percentage is 87.1429%
Step-by-step explanation:
kayke mixes 1/6 pound of salt with 1/8 bucket of water to make a saline solution. how much salt does she need for a full bucket of water?
She will need 1.34 pounds of salt for a full of bucket of water.
It is given that, Kayke mixes 1/6 pound of salt with 1/8 bucket of water to make a saline solution.
With 1/8 bucket of water she mixes 1/6 pound of salt.
1/8 bucket of water = 1/6 pounds of salt
Now, using unitary method to find salt needed to use for a full bucket of water.
So,
1 bucket of water = 8/6 pounds of salt
= 1.34 pounds of salt.
She will need 1.34 pounds of salt for a full of bucket of water.
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Which of the following sentences is true?
O 29.6> 29.65
O 7.602> 7.612
O 17.25 17.252
O21.51 < 21.49
Please help leve 8th grade math!
The required solutions are,
1) point A on the triangle is the center of dilation.
2) Triangle ABC is the original triangle.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
1) As shown in the figure, after dilation the only initial point that does not change points A. So it could be concluded that point A is the center of dilation.
2) since the scale factor is of 1/2 implies that the dilated figure is lower than the size of the original figure hence, triangle ABC is the original triangle.
Thus, the required solutions are,
1) point A on the triangle is the center of dilation.
2) Triangle ABC is the original triangle.
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f the recommended adult dosage for a drug is d (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417d(a + 1). suppose the dosage for an adult is 100 mg. (a)
The slope of graph is 4.17 (a+1). It represents the annual rise in dose a.
Who are pharmacists ?Excellent understanding of medications, their mechanisms of action, side effects, interactions, mobility, and toxicity are prerequisites for practicing pharmacy. Thus, pharmacists are the key healthcare professionals who maximize the use of medicine for the benefit of patients. They are also the world's foremost authorities on drug therapy.
The pharmacist use equation C= 0.0417 d (a+1)
Applying in (mg)
So d = 100 mg
Therefore c = 0.0417×100 (a+1)
C= 4.17 (a+1)
4.17 (a+1) is the slope for the graph of c, which reflects the annual rise in dose a.
kid requires. Given that a newborn is age 0, the appropriate dosage is
c(0) = 4.17 (a+1)
Complete question is -If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417D(a + 1). Suppose the dosage for an adult is 200 mg.
(a) Find the slope of the graph of c. What does it represent?
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10. ratios that express the same relationship between two quantities
Answer:
In fact, they're called equivalent ratios, which are ratios that express the same relationship between two numbers. The ratios 60/1 and 120/2 are equivalent because the relationship between the two parts of the ratios didn't change. According to the ratio 60/1, you travel 60 miles for every hour you drive.14 Oct 2021
if a number is divisible by two co-prime numbers then it is also divisibe by their product true or false
Answer:
Hello,
Answer TRUE.
Step-by-step explanation:
a | n is read, a divide n.
if a | n => n=a*q
if b | n => b | a*q , since gcd(a,b)=1, b | q ==> b=q*k
n=a*q=a*b*k=(a*b)*k so a*b | n
Draw an area model that demonstrates that the quotient of 2080 and 40 is 52 explain how the model relates to the calculation
We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.
Given that,
52 is the quotient of 2080 and 40.
The expression can be represented by
2080/40=52
We divide 2080 as 1200+800+80
(1200+800+80)/40=1200/40+800/40+80/40
(1200+800+80)/40=30+20+2
(1200+800+80)/40=52
An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor. Using number bonds, we may divide the rectangle's enormous area into a number of smaller boxes to simplify the calculation. The product or quotient is then obtained by adding to obtain the area of the entire.
We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.
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write an equation to answer the question below.
Lela purchased 3 mechanical pencils and a notebook that cost $5. Her purchase totaled $11. How much was each pencil? Use p to represent the cost of each pencil.
The cost of each pencil is $2
What are algebraic expressions?Algebraic expressions are expressions comprised of variables, terms, factors, coefficients, and constants.
They are also made up of arithmetic operations such as addition, subtraction, multiplication division, etc
From the information given, we have that 'p' represents the cost of each pencil
The equation is represented as;
3p + $5 = $11
collect like terms
3p = $11 - $5
subtract like terms
3p = $6
Make 'p' the subject of formula
p = $6/3
p = $2
Thus, the cost of each pencil is $2
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the distance between given points. (-4,1) and (0, 4)
7 gallons = how many pints
Answer:
56 pints hope this helps Brainliest please
Step-by-step explanation:
Answer:
7 gallons = 56 liquid pints!
Explanation= 1 gallon = 8 pints
1/100,1/4,0.2 least to greatest
1/100 < 0.2 < 1/4 is the correct order of the given numbers arranged from least to greatest.
Given that, 1/100, 1/4 and 0.2 and we have to arrange them from least to greatest. So, basically we have to arrange them in ascending order.
1/100 can be written in decimal form as 0.01
1/4 can be written in the decimal form as 0.25
and 0.2 is already in the decimal form.
Now, we have 0.01, 0.25 and 0.2 and we have to arrange them from least to greatest.
Out of 0.01, 0.25 and 0.2, 0.01 is the smallest and 0.25 is the greatest.
0.01 < 0.2 < 0.25
This is the arrangement of the given number in decimal form.
1/100 < 0.2 < 1/4
This is the correct order of 1/100, 1/4 and 0.2 arranged in ascending order.
Therefore, 1/100 < 0.2 < 1/4 is the required answer.
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What is the mean of numbers 3,6,9,12,15,18
Answer: 10.5
Step-by-step explanation:
The mean is all of the numbers in a system added together then divided by the amount of numbers in a system.
3 + 6 + 9 + 12 + 15 + 18 = 63
63 / 6 = 10.5
please answer and thanks
Answer:
c=(d-4a)/3
Step-by-step explanation:
d=4a+3c, solve for c
d-4a=4a-4a+3c ==> isolate the 3c by subtracting 4a from both sides
d-4a=3c
(d-4a)/3=3c/3 ==> isolate c by dividing 3 on both sides of the equation
c=(d-4a)/3
if the federal debt is $24 trillion, and if this debt were divided equally among 300 million people, then how much would each person owe? describe how to estimate mentally the answer to the federal debt problem, and explain briefly why your strategy makes sense.
Using the concept of division we can find the amount of money each person owes.
Why should we use Division?Division is one of the fundamental operations used in mathematics which involves breaking a bigger value into smaller groups with the same number of components.
The federal debt =$24 trillion=$24000000
(one trillion=1000000 million)
The value in trillion is converted to million by multiplying by 1000000.
The number of people the amount to be equally distributed= 300 million
Amount of money equally distributed among each person
=[tex]\frac{Total debt amount}{number of people}[/tex]
=[tex]\frac{24000000}{300}[/tex]
=80000
The amount each person owes is $80000
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6 x (8.7 1.05) =
2 decimales
Answer:
0.522
0.063
Step-by-step explanation:
6 x 8.7 = 52.2
6 x 1.05 = 6.3
If we move them both two decimal places then...
0.522
0.063
Square root of 81/9 - 7 Times Square root of 4
Answer: -125
Step-by-step explanation:
√81/9 = 9/3 =3
√4 = 2∧7 = 128
3-128 = -125
Suppose xy > 0. Describe the points whose coordinates are solutions to the inequality.
The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.
x ≠ 0y ≠ 0Sign(x) =sign(y)Which points are solutions of the inequality?
We want to find points of the form (x, y) that are solutions of the inequality:
x*y > 0
Clearly x and y must be different than zero.
So, for example if x = -1, y can be any negative number, for example y= -3
x*y > 0
(-1)*(-3) > 0
3 > 0
This is true.
Now if x = 1, y must be positive. LEt's take y = 103, then:
x*y > 0
1*103 > 0
103 > 0
Then we have 3 conditions:
x ≠ 0y ≠ 0Sign(x) =sign(y)The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.
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I need help with these!
The results of the three cases are listed below:
g ° f (x) = 8 · x + 5 h ° g (- 3 · x) = - 36 · x - 9 f ° g (- 3) = - 14How to evaluate the composition between two functionsIn this problem we find three cases of composition between two functions, each of which has to be evaluated. The definition of the composition between the two functions f and g is presented below:
f ° g (x) = f( g(x) ) (1)
Where x is the input variable of the composite function.
In other words, the input of the function f is the output of the function g.
Now we proceed to find the expressions of the each of the two cases:
Case 1
g ° f (x) = g( f(x) )
g ° f (x) = 4 · (2 · x + 2) - 3
g ° f (x) = 8 · x + 8 - 3
g ° f (x) = 8 · x + 5
Case 2
h ° g (- 3 · x) = h [g (- 3 · x)]
h ° g (- 3 · x) = 3 · [4 · (- 3 · x) - 3]
h ° g (- 3 · x) = 3 · (- 12 · x - 3)
h ° g (- 3 · x) = - 36 · x - 9
Case 3
f ° g (- 3) = f( g(- 3) )
f ° g (- 3) = 3 · [2 · (- 3) + 1] + 1
f ° g (- 3) = 3 · (- 5) + 1
f ° g (- 3) = - 15 + 1
f ° g (- 3) = - 14
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The graph of a quadratic function touches, but does not cross, the x-axis at x = 4. Which function represents this
situation?
Oy=x²-16
Oy=x²-4x
Oy=x²-8x+16
O y=x² + 8x + 16
Correct answer is C. y = x2 - 8x + 16 is the quadratic equation.
How do you figure out the equation?The answer to the question is:
x = 4
The graph has a multiplicity of 2 at x = 4 since it only touches this value and does not cross it.
The equation is then shown as follows:
y = (x - 4)^2
Expand
y = x^2 - 8x + 16
The quadratic equation is y = x2 - 8x + 16 as a result.
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The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Select two options. = –1 = 4 –15 + y1 =16 = y1
The equations which can be solved to determine the coordinates of the other endpoints are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.
What equations can be solved to determine the other endpoint K of the line JK?It follows from the task content that the equation which can be solved to obtain the coordinates of the other endpoint, K be identified.
Since the coordinates of the midpoint can be determined as follows;
x-coordinate of the midpoint;
x = (x1 + x2)/2; where x1 = 4 and x = -1.
Therefore, -1 = (4 + x2)/2 is the first required equation.
y-coordinate of the midpoint;
y = (y1 + y2)/2; where y1 = -15 and y = 8.
Therefore, 8 = (-15 + y2)/2 is the other required equation.
Ultimately, the required equations are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.
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pls tell me answer Im in advanced class having a hard time with this ?
Answer: last one
Step-by-step explanation:
a car valued at $28,000 depreciates at a rate of 20% per year. what will the car be worth after 6 years?
The value of the car after 6 years will be $7340 .
The Depreciation can be calculated using the formula
A = P( 1 - r/100)ⁿ
where , A = amount , P = principal , r = rate of deprecation , n = time period
In the question ,
it is given that
the value of the car (P) = $28000
rate of deprecation (r) = 20% per year
time period (t) = 6 years
Substituting the values in the Depreciation formula we get ,
Amount = 28000*( 1 - 20/100 )⁶
= 28000*(80/100)⁶
= 28000*(0.80)⁶
= 28000*0.26214
= 7339.92
≅ 7340
Therefore , the value of the car after 6 years will be $7340 .
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A bathtub has 8 gallons of water in it. it is draining at a constant rate of 6 gallons every 5 minutes. write an equation that for the amount of water in the tub. when will it be empty?
If a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub
Given,
The total quantity of water in the tub = 8 gallons
The quantity of water draining for every 5 minutes = 6 gallons
The quantity of water draining for every 1 minutes = [tex]\frac{6}{5} =1.2[/tex] gallons
Consider the number of minutes as x
Then the equation for the amount of water in the tub
f(x)= 8 - 1.2x
The number off minutes take to empty the tub = Total quantity of water / Quantity of water draining per minute
=[tex]\frac{8}{1.2}=6.67[/tex] minutes
Hence, if a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub.
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Which is larger?
3/5 or 4/7
Answer:
3/5 is bigger
Step-by-step explanation:
if the numerator is the same then the one with the smaller denominator is bigger
how many different 7-plate license plates are possible if the first 2 places are for letters and the other 5 are for numbers?
If the first two spaces are for letters and the remaining five are for numbers, then 67,600,000 distinct seven-plate license plates are possible.
What is permutation and combination?Putting things or numbers in order is known as a permutation. Combinations are a way to choose items or numbers from a collection of items or groups of items without regard to their order.
What function do combination and permutation learning serve?We can count the number of ways an item set can be rearranged using permutations. When counting combinations, we look at how many options we have from a larger pool of available items. Important statistical concepts include combinations and permutations.
According to the given information:We know that :
It consists of 10 digits and 26 letters.
Due to the repetition of letters and numbers. Since the first two positions are letters, first can be filled in.
26 * 26 = 676 ways.
Five more spots may then be filled.
10 * 10 * 10 * 10 * 10 = 100000ways
If the first two spaces are really for letters and the remaining five spaces are for numbers, then there are a variety of 7-place license plates that can be made.
26 * 26 * 10 * 10 * 10 * 10 * 10 = 67,600,000ways.
If the first two spaces are for letters and the remaining five are for numbers, then 67,600,000 distinct seven-plate license plates are possible.
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