Answer:
Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.
Step-by-step explanation:
In statistics, the 68–95–99.7 rule, also recognized as the Empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean, respectively.
Then,
P (µ - σ < X < µ + σ) = 0.68
P (µ - 2σ < X < µ + 2σ) = 0.95
P (µ - 3σ < X < µ + 3σ) = 0.997
he random variable X can be defined as the amount of time a certain brand of light bulb lasts.
The random variable X is normally distributed with parameters µ = 1300 hours and σ = 90 hours.
Compute the interval of hours that represents the lifespan of the middle 68% of light bulbs as follows:
Thus, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.
What is the slope of the line that passes through the points (-6, 1) and (-6,-4)?
Write your answer in simplest form.
Answer:
horizontal line
Step-by-step explanation:
The slope formula is m=(y2-y1)/(x2-x1)
-6+6/-4-1
y2-y1 = 0
Construct an isosceles triangle ABC in which AB=AC = 9 cm and BÂC = 45°. Measure ABC and BC
Answer:
m∠ABC = 67.5°BC = =6.888301782572 cmStep-by-step explanation:
ABC is an isosceles triangle
Then
m∠ABC = m∠ACB
The sum of the interior angles of a triangle is equal to 180°
Then
m∠ABC + m∠ACB + m∠BAC = 180°
Then
m∠ABC + m∠ACB + 45 = 180°
Then
2 × m∠ABC = 180°
Then
m∠ABC = (180−45)÷ 2 = 67.5°
Law of SIN :
[tex]\frac{9}{\sin \left( 67.5\right) } =\frac{BC}{\sin \left( 45\right) }[/tex]
[tex]BC=\frac{9}{\sin \left( 67.5\right) } \times \sin \left( 45\right) ==6.888301782572[/tex]
f(x) = xWhat is g(x)?
11(x) = x²
g(x)
O A. g(x) = -3x2
B. g(x) = x2 - 3
Oc. g(x) = -x²
O D. g(x) = -x2 - 3
what is 3 1/2 - 2 7/8=
Step-by-step explanation:
[tex] = 3 \frac{1}{2} - 2 \frac{7}{8} \\ [/tex][tex] = \frac{3 \times 2 + 1}{2} - \frac{2 \times 8 + 7}{8} \\ [/tex][tex] = \frac{7}{2} - \frac{23}{8} \\ [/tex]Now...find the lcm...[tex] = \frac{7}{2} \times \frac{4}{4} - \frac{23}{8} \times \frac{1}{1} \\ [/tex][tex] = \frac{28}{8} - \frac{23}{8} \\ [/tex][tex] = \frac{28 - 23}{8} \\ [/tex][tex] = \frac{5}{8} \\ [/tex]Answer:
5/8
Step-by-step explanation:
3 + 1/2 - 2 - 7/8
⇒ 3 - 2 = 1
1/2 - 7/8 = ?
⇒ 4/8 - 7/8 = -3/8
1 - 3/8 = 5/8
Alternative approach:
7/2 - 23/8(converted mixed numbers to fractions)
(7 × 8) - (23 × 2) ÷ 2 × 8
= 56 - 46 ÷ 16
= 10/16
= 5/8
Solve the equation.
4x – 2 = -3x2 + 3x
x = [ ? ],
Answer:
[tex]x = - 4[/tex]
Step-by-step explanation:
[tex]4x - 2 = - 3 \times 2 + 3x[/tex]
Calculate the product:
[tex]4x - 2 = - 6 + 3x[/tex]
Rearrange the terms:
[tex]4x - 3x = - 6 + 2[/tex]
Combine like terms:
[tex]x = - 6 + 2[/tex]
Calculate:
[tex]x = - 4[/tex]
Answer:
x = 1/2
Step-by-step explanation:
Combine exponents
4x-x-2=-3^2+3xx
4x-x-2=-3x^2+3x^2
Combine like terms
4x-2=-3x^2+3x^2
4x-2=0
Add 2 to both sides
4x-2=0
4x-2+2=0+2
Simplify:
Add the numbers
4x-2+2=0+2
4x=0+2
Add the numbers again
4x=0+2
4x=2
Divide both sides by the same factor
4x=2
4x/4 = 2/4
Simplify:
Cancel terms that are in both the numerator and denominator
4x/4 = 2/4
X= 2/4
Divid the numbers
X= 2/4
X= 1/2
Solution/ Answer
x= 1/2
Hope this helps
There are two boys and 23 girls, what’s the ratio of girls to all children?
Answer:
23:25
Step-by-step explanation:
Answer:
23/25 23 to 25 23:25
Step-by-step explanation:
Two boys 23 girls=25 children
girls=23
23/25
tan A = 2.053 what is the measure of angle A
Answer:
A =64.03
Step-by-step explanation:
tan A = 2.053
A = Arctan( 2.053)
A =64.03
When looking for interesting facts, avoid using
A. Lists of statistics
B. Quotes from famous people
C. Reliable sources
D. Humor
Answer:
D: humor.
Step-by-step explanation:
it's just common sense. I am not a gen z so I should know.
Find the roots of the quadratic equation x^2 + 7x + 10 = 0 by using the quadratic formula
Answer:
x = -2, -5
Step-by-step explanation:
x^2 + 7x + 10 = 0
The factors of 10 are as follows:
1, 10
2, 5
We can combine 2 and 5 to make 7
(x +2) (x + 5) = 0
One of these brackets must equal 0 to make the answer 0, as you are multiplying them together
If x + 2 = 0, x = -2
If x + 5 = 0, x = -5
Therefore, x = -2, -5
Hey there!
Answer :x = -5 or x = -2 ✅Explanation :QUADRATIC EQUATION:
ax² + bx + c = 0 where a ≠ 0
The sign of the discrimant (b² - 4ac) determines the number of real-number solutions :
If the discrimant is positive, the equation has two real-number solutions.If the discrimant is equal to zero, the equation has one real-number solution.If the discriminant is negative, the equation has no real-number solution.The solutions of the equation, also called roots, can be obtained with the QUADRATIC FORMULA :
[tex]x = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
---------------------------------------------------------------
▪️ x² + 7x + 10 = 0
(1) Substitute the letters in the general quadratic equation with their values in the given expression:
a = 1b = 7 c = 10(2) Determine the sign of the discriminant:
[tex]{b}^{2} - 4ac \\ \\ \Longrightarrow {7}^{2} - 4(1)(10) \\ \\ \Longrightarrow 49 - 40 \: \: \: \: \: \: \: \: \: \\ \\ \Longrightarrow \red{9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
The discrimant is positive ; the equation has two real-number solutions.
(3) Determine the roots of the equation :
a)[tex]x_1 = \frac{ - b \: - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_1 = \frac{ - 7 - \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = \frac{ - 7 - 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{10}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \green{ \boxed{ \red{x_1 = - 5}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
(b)[tex]x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 7 + \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2 = \frac{ - 7 + 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{4}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \red{ \boxed{ \green{x_2 = - 2}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Therefore, x = -5 or x = -2
▪️ Learn more about quadratic equations :
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A manufacturer inspects 1000 cars and finds that 988 cars have no defects. What is the experimental probability that a car chosen at random will have no defects? If there are 2500 cars in a company, predict the number of cars that are likely to have no defects.
The experimental probability is the number of cars with no defect/ total cars inspected: 988/100 = 0.988
multiply total cars by experimental probability
2500 x 0.988 = 2470
Answer:
98.8%; 2470 cars
Step-by-step explanation:
Marci needs to rent a storage. She needs to determine the volume of the storage unit. If the storage unit is 8 feet high, what is the volume of the storage unit
Wendy’s Big Bacon Classic contains how many calories after calculating the
nutrients below?
44 grams Carbohydrate= _____ Calories
36 Grams of Fat= ______ Calories
37 Grams of Protein= _____Calories
explain please thanks
Answer:
44 grams carbohydrates = 176 calories
36 gram of fat = 324 calories
37 gram of protien = 148 calories
44 grams of Carbohydrates = 176 calories
36 grams of Fat = 324 calories
37 grams of Protein = 148 calories
To calculate the number of calories from each macronutrient (carbohydrates, fat, and protein), you need to know the caloric content per gram for each nutrient.
The caloric content per gram is as follows:
- Carbohydrates: 1 gram = 4 calories
- Fat: 1 gram = 9 calories
- Protein: 1 gram = 4 calories
Now, let's calculate the number of calories for each macronutrient in the Wendy's Big Bacon Classic:
1. Carbohydrates:
Calories from Carbohydrates = 44 grams × 4 calories/gram
Calories from Carbohydrates = 176 calories
2. Fat:
Calories from Fat = 36 grams × 9 calories/gram
Calories from Fat = 324 calories
3. Protein:
Calories from Protein = 37 grams × 4 calories/gram
Calories from Protein = 148 calories
In total, the burger would have 176 + 324 + 148 = 648 calories.
To know more about Carbohydrates:
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Which type of question is most useful in a group discussion?
A. Closed questions
B. Open questions
C. Multiple choice questions
D. Written responses
Answer:
B
Step-by-step explanation:
it is B I am so sorry if it is wrong
x^2+4x-4=0
Solve by factoring.
Answer:
1) As it is the coeficient of x² is 1, we need to find two numbers whose Sum S(x)=3 and the same numbers whose product is 2, P(x)= 2
S(x) = ( ) + ( ) =3
P(x) = ( ) * ( ) =2
S(x) = ( 2 ) + ( 1 ) =3
P(x) = ( 2 ) * ( 1 ) =2
These numbers in bold will be coeficients of x.
Rewrite the Trinomial x²+ 3x +2 as x² +2x+1x+2
So x²+3x+2 =x²+2x+1x+2
x² +2x+x+2 Put the x in evidence
x(x+2)+1(x+2) Find the Maximum Common Divider
(x+1)(x+2)
2) x²+x-6=0
Applying the same procedure. Which two integer number whose sum is 1 and whose Product is -6?
S(x) = ( 3 ) + ( -2 ) =1
P(x) = ( 3 ) * ( -2 ) =-6
Rewrite
x²+x-6
x²+3x-2x-6 Group them
x(x+3)-2(x+3) Common Term
(x+3)(x-2)
3) Since the a coeficient is ≠ 1, a little adjustment must be made on our algorithm for -2x²+4x+30=0
Firstly multiply a*c, in this case -2 * 30 = -60
Which two numbers multiplied by themselves will turn out to be -60 and whose sum is -60? Since we're working with integers factoring out may be very helpful.
P(x)= ( 10 ) * ( - 6 ) = -60
S(x) = ( 10 ) + ( -6 ) = 4
Rewriting
-2x²+10x-6x+30 Group them
2x(x+5) -6(x+5)
(2x-6)(x+5) Inserting the -1 to finally adjust
-1(2x-6)(x+5)
4) Explanation is the same principle as a≠1
3x²+4x-4=0
P(x) = ( 6 ) * (-2 ) = -12
S(x) = ( 6 ) + ( -2 ) = 4
3x²+4x-4 = 3x²+6x-2x-4
3x²+6x -2x+4
3x(x+2)-2(x-2)
(3x-2)(x+2)
The other ones are just applications of these, above.
Step-by-step explanation:
PLS URGENT! WILL GIVE BRAINLIEST!!!!
A certain company's main source of income is a mobile app. The function h models the company's annual profit (in millions of dollars) as a function of the price they charge for the app (in dollars).
Which of these statements are true?
(A) Greater app price always relates to greater profit.
(B) Greater app price relates to greater profit as long as the app's price is more than about 7 dollars.
(C) The largest possible profit the company can make is 7 million dollars.
(D) The largest possible profit the company can make is about 40 million dollars.
Thank you! God Bless!
Answer:
(C) The largest possible profit the company can make is 7 million dollars
Step-by-step explanation:
Proverbs 3:5-6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Trust in the Lord with all your heart
and lean not on your own understanding;
in all your ways submit to him,
and he will make your paths straight.
_________________________________________________________
Have a blessed day!!
:)
A coordinate grid with a line labeled y equals negative 2 x plus StartFraction 3 over 2 EndFraction and passes through the points (9, 1.5) and (1, 0.5). m = –3 and b = negative StartFraction 2 over 3 EndFraction. m = –2 and b = m equals negative 3 and b equals negative StartFraction 1 over 3 EndFraction. m = 2 and b = negative StartFraction 2 over 3 EndFraction. m = m equals StartFraction 3 over 2 EndFraction and b equals negative StartFraction 2 over 3 EndFraction and b = m equals negative StartFraction 3 over 2 EndFraction and b equals negative StartFraction 2 over 3 EndFraction m = -2 and b = m equals negative 2 and b equals negative StartFraction 2 over 3 EndFraction
The line given by the equation y = 2x + 3/2 have a slope (m) of 2 and y-intercept (b) of 3/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation of a line is:
y = mx + b; where m is the slope and b is the y-intercept
The line given by the equation y = 2x + 3/2 have a slope (m) of 2 and y-intercept (b) of 3/2
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A shop has 31 plant pots.
Some are blue, some are yellow and the rest are red.
There are five more blue pots than yellow pots.
There are four times as many blue pots as there are red pots..
Calculate how many pots there are of each colour.
Answer:
16 blue, 11 yellow, and 4 red
Step-by-step explanation:
Give the degree of the polynomial. 10yx^5w^4-w^3v^5-5x^11-6
10yx⁵w⁴ - w³v⁵ - 5x¹¹ - 6
Degree = biggest exponent = 11
[tex] \sqrt[3]{800} [/tex]
between 2 and 3
between 4 and 5
between 9 and 10
Calculate the following 87124 + 14997=
Answer:
87124 + 14997 = 102121
Hope it helpz~ uh..
Carry on learning :)
Answer:
102121
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
X =
Answer:
26°
Step-by-step explanation:
x + 64° = 90° ( being complementary angles)
x = (90 - 64)°
x = 26°
Answer:
x = 26°
Step-by-step explanation:
x + 64° = 90° [right angle]
x = 90° - 64°
x = 26°
Yesterday the price of a can beans at five supermarkets was $2.02, $2.11, $1.99,$2.32, and $2.26, respectively but today each supermarket raised it's price by $0.10. what today's mean price of a can of beans at five supermarkets?
a.2.14
b.2.34
c. 2.24
d.2.04
Answer:
the answer is C
Step-by-step explanation:
add them all together with the 0.10C increase which gives you 11.2 then divide by the number of different beans which is 5 and it gives you 2.24
Find the surface area
Answer:
A≈9248.85
Step-by-step explanation:
A=2πrh+2πr2=2·π·32·14+2·π·322≈9248.84877
find the volume of a right prism with base area 32 cm² and height 1.5 cm
Answer:
1536
Step-by-step explanation:
volume=baseareaxheight
. =32cmsquarex1.5cm
. =1536cm
If the answer is correct please vote
A machine produces 225 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?
Answer: 375 bolts
Step-by-step explanation:
Just do 225*(40/24)
sin(x)
1 – cos(x) – cot(x) = csc(x)
Pls help..
Answer:
pls find given attachment
rewrite! Write an new and equivalent equation that is easier to solve
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given - an equation in a standard formTo do - simplify the equation so as to obtain an easier oneSince the equation provided isn't in it's general form , let's first convert it ~
General form of a Linear equation -
[tex]\bold{ax + b = 0}[/tex]
The equation after getting converted will be as follows ~
[tex] - 7 + ( \frac{4x + 2}{2} ) = 8 \\ \\ \implies \: \frac{ - 14 + 4x + 2}{2} = 8 \\ \\ \implies \: - 14 + 4x + 2 = 16 \\ \\ \implies \: 4x = 16 + 14 - 2 \\ \\ \implies \: 4x = 28 \\ \\\bold{ General \: form \: \dashrightarrow \: 4x - 28 = 0}[/tex]
hope helpful ~
WILL GIVE BRAINLIEST 50 POINTS
∆ABC is mapped to ∆A'B'C' using each of the given rules in the table below. Place a checkmark in the correct column for each mapping to state if the resulting mapping would make ∆ABC congruent or not congruent to ∆A'B'C'.
∆ABC is congruent to ∆A^' B^' C'
∆ABC is NOT congruent to ∆A^' B^' C'
(x,y) → (x+5,y)
(x,y) → (5x,5y)
(x,y) → (.5x,.5y)
(x,y) → (x,-y)
(x,y) → (-x,-y)
Answer:
(x+5,y) = Yes
(5x,5y) = No
(.5x,.5y) = No
(x,-y) Yes
(-x,-y) Yes
Step-by-step explanation:
V
Write 8.4% as a fraction in simplest form.
Answer:
21/250
Step-by-step explanation:
Converting percentage to fraction :
Divide by 100%8.4%/100%8.4/100Multiply both sides by 10 to remove the decimal8.4 x 10 / 100 x 1084/1000Divide both sides by 4(84/4)/(1000/4)21/250help me pleaseeeeeeeeeeeeeeeeeeeeeeee
