Answer:
Median: 88, First Quartile: 84, Third Quartile: 92, IQR (interquartile range): 8
Step-by-step explanation:
1. Sort the numbers in numerical order (like 1, 2, 3, etc.)2. Find the number that is in the middle3. Find all the quartiles by finding the median of the lower and upper halves of the list4. Subtract Q1 (quartile 1) and Q3 (quartile 3) like this: Q3 - Q1 to get IQR
Gerda discovers that the lifetime of light bulbs is normally distributed with mean 1000 hours and standard deviation 100 hours. if gerda buys 50 bulbs, how many of them are expected to last less than 800 hours? give your answer correct to the nearest integer.
Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 5. If the volume of rectangular prism B is 5125 km°, find the volume of rectangular prism A, the preimage
The volume of the rectangular prism A, the preimage is 41km^3
How to determine the volume?The given parameters are:
Volume B = 5125km^3
Scale factor, k = 5
The volume of B is calculated using:
B = A * k^3
So, we have:
5125 = A * 5^3
Divide both sides by 5^3
A = 41
Hence, the volume of rectangular prism A, the preimage is 41km^3
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If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)? startfraction (5 x) over x endfraction startfraction 1 over (5 x) endfraction 5 (startfraction 1 over x endfraction) 5 (5 x)
The composition of the two given functions is:
(k°h)(x) = 1/5x
How to get the composition of the functions?
Here we have the functions h(x) = 5x and k(x) = 1/x.
We want to get (k°h)(x), which is equal to:
k(h(x))
Then we have:
k(h(x)) = 1/h(x)
Replacing h(x) we get:
k(h(x)) = 1/h(x) = 1/(5x)
So the composition is just one over 5x.
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Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x i)(x – 2) f(x) = 3(x 4)(x – i)(x i)(x – 2)
The polynomial function with leading coefficient of 3 and root -4, i, and 2 all with multiplicity of 1 is f(x) = 3(x+4)(x-i)(x+2)
Polynomial function
The Leading coefficients are the numbers written in front of the variable with the largest exponent.
Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.
The multiplicity is the number of times a given factor appears in the factored form of the equation of a polynomial.
Therefore, the polynomial f(x) = 3(x+4)(x-i)(x+2) has a root -4 , 1 and -2.
The leading coefficient is 3. The multiplicity is all one.
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Answer:
d
Step-by-step explanation:
The half-life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.
Answer:
442.302 kg
Step-by-step explanation:
amount = 487 (1/2)^(t/36) where t is the number of days.
if t = 5
amount = 487(.5)^(5/36)
= 442.302 kg
8 3/4 - 5 2/3 what is the answer
Answer:
3 1/12
Step-by-step explanation:
In a right-angled triangle, the sum of the squares of the three sides is 72. What is the length of the hypotenuse?
Answer:
The hypotenuse has a length of 6
Step-by-step explanation:
Remark
The first step is to create the 2 equations needed to solve this problem.
Then substitute one into the other.
Equations
c^2 + a^2 + b^2 = 72
c^2 = a^2 + b^2
Solution
c^2 + a^2 + b^2 = 72 The sum of the sides each squared of a right triangle = 72
c^2 = a^2 + b^2 The pythagorean theorem says the hypotenuse of the right triangle = the sum of the squares of two smaller sides. You can substitute the hypotenuse squared into the top equation for a^2 + b^2
c^2 + c^2 = 72
2c^2 = 72
c^2 = 36
c = 6. minus 6 is meaningless
Will mark branlyest (Polynomial Functions)
1. Find the zeros: 2x^2 + 12x + 18 = 0
A . {-3}
B .{3}
C .{-9}
D.{-3,3}
2. Find the x-intercepts: 2r^2 = 5r + 3
A. {-1/2,3}
B.{-1/2,-3
C.{1/2,3}
D.{1/2,-3}
Answer:
1. A
2. A
Step-by-step explanation:
Question 1
1 Factor out the common term 2.
2(x^2+6x+9)=0
2 Rewrite x^2+6x+9 in the form a^2+2ab+b^2a, where a=x and b=3.
2(x^2+2(x)(3)+3^2)=0
3 Use Square of Sum: (a+b)^2=a^2+2ab+b^2(a+b).
2(x+3)^2=0
4 Divide both sides by 2.
(x+3)^2=0
5 Take the square root of both sides.
x+3=0
6 Subtract 3 from both sides.
x=-3
Question 2
1 Move all terms to one side.
2r^2-5r-3=0
2 Split the second term in 2r^2-5r-3 into two terms.
2r^2+r-6r-3=0
3 Factor out common terms in the first two terms, then in the last two terms.
r(2r+1)-3(2r+1)=0
4 Factor out the common term 2r+1.
(2r+1)(r-3)=0
5 Solve for r.
r=-1/2,3
what is the initial value of the linear relationship of -2, 3
What is the value of x innthe equation 1.5(x+4)-3=4.5(x-2)
[tex]~~~~~~1.5(x+4)-3 = 4.5(x-2)\\\\\implies 15(x+4) -30 =45(x-2)~~~~~~~~;[\text{Multiply both sides by 10]}\\\\\implies 3(x+4)-6=9(x-2)~~~~~~~~~~;[\text{Divide both sides by 5]}\\\\\implies 3x+12-6=9x-18\\\\\implies 3x+6=9x-18\\\\\implies 9x-3x = 18+6\\\\\implies 6x = 24\\\\\implies x = \dfrac{24}6\\\\\implies x =4[/tex]
If point a is at (-1,2) and point b is at (11,-7), what is length of line ab?
Answer:
15
Step-by-step explanation:
Distance formula: [tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
Plug in (-1,2) and (11, -7):
[tex]d=\sqrt{(11-(-1)^{2}+(-7-2)^{2} } = d=\sqrt{(12)^{2}+(-9)^{2} }=\sqrt{144+81} = \sqrt{225} = 15[/tex]
What’s the area formula, of 48m
Answer:
The area formula of a circle is [tex]A=\pi* r^2[/tex] where r is the radius and in this case our r is 48 m. So we would just plug in 48 m into r which would get squared and then multiplied by pi to give us [tex]7,238.23\ m[/tex].
Hope this helps! Let me know if you have any questions
Answer:
[tex]\pi[/tex]r²
Step-by-step explanation: Youre welcome :)Evaluate for f(-2)
f(x) = 3/2x - 4
Answer:
f(-2) = -7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify given function.
[tex]\displaystyle f(x) = \frac{3}{2}x - 4[/tex]
Step 2: Find f(-2)
[Function] Substitute in x:∴ the function when x = -2 is equal to -7.
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---
Topic: Algebra I
Write the product using exponents.
Answer:
3^4
Step-by-step explanation:
because I took the test
PLEASE HELP ME I NEED ANSWERS
help will give brainliest
Answer:
0.7°
Step-by-step explanation:
From the figure:
CF = 4000.2 miles, CE = 4000.01 miles
so FT = √CF² - CT², TE = √CE² - CT²
so FT = 40 miles, TE = 8.94 miles
so ½ × 4000.2 × 4000.01
xsin angle FCE = ½ × 4000 × 140 + 8.94
so sin angle FCE = 0.0122
so angle FCE = 0.7°
so m SB = 0.7°
HOPE THIS HELPS AND HAVE A NICE DAY <3
3Your new mobile phone costs £360.
The probability you leave it on the bus is 0.1.
The probability someone will hand it in to lost property and you will recover it
is 0.4.
The cost of insurance to cover the loss of the phone is £30.
Should you pay for this control measure?
List any assumptions that you make
Assuming you have to pay 30 pounds for somebody handing it in to lost property, you'll have a 0.5 probability that you'll have to pay the 30 pounds if you lose the phone.
Also assuming there are no other ways to lose your phone, you have a 0.5 probability (50% chance?) to lose your phone.
Also assuming the "control measure" is the insurance and you won't have to pay a larger amount, you'll probably be better off paying the 30 pounds instead of the larger amount because you have such a high chance of losing your phone.
I apologize if I misunderstood the question.
The spinner is divided into 8 equal-sized sections. enter the probability of the arrow landing on a section labeled 4 on the first spin
Answer: 1/8
Step-by-step explanation:
in order to make a specific shade of green paint a panter mixes 1 1/2 quarts of blue paint 2 cups of green paint and 1/2 gallion of white paint how much of each collor is needed to make 100 cups of this shade of green paint
Answer:
37.5 cups of blue
12.5 cups of green
50 cups of white
Of the last 15 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize?
Answer:
40% or 2/5
Step-by-step explanation:
won = 6
total no. of people = 15
probability of winning = 6/15 = 2/5
2/5*100
=40%
• A bag contains 5 orange, 3 yellow, and 5 black marbles. What are the odds of picking an orange marble?
Answer:
The odds will be 5/13.
Step-by-step explanation:
There are 13 marbles total in this situation. 5 orange, 3 yellow and 5 black (5+3+5) will give us 13 as our overall total. Now, because we have 5 orange marbles available, we'll write this as a 5/13 odds/ chance of picking an orange marbles because it is how many orange marbles are present over how many marbles there are total.
Also! You can't simplify this any further, thus you'd have 5/13 odds.
Carl makes $10.25 per hour, h, plus a daily bonus of $25. Which equation represents his total earnings, t, each day?
Answer:
10.25 × h + 25= t
Step-by-step explanation:
he gets 10.25 for every hour, so you do 10.25 × h, than for his extra bonus of 25 dollars a day, you add 25. than t shows the final earnings
Roberta grows pea plants, some in shade and some in sun. she picks 8 plants of each type at random and
records the heights.
shade plant heights (in.) 7 12 7 10 8 12 8 8
sun plant heights (in.) 19 24 21 22 23 19 20 20
express the difference in the means as a multiple of their ranges.
the difference in the means is times the ranges.
The image is the question
Answer:
6h^2 - 19h + 15
Find two numbers that their sum is -19 and their product is 90.
Hence, the numbers will be -9 and -10
6h^2 - 9h - 10h + 15
3h(2h - 3) -5(2h - 3)
(2h - 3)(3h - 5)
please help! this is due soon and im a bit confused
Evaluate each expression.
6! =
3! - 2!=
61/
3!
=
Answer:
6! = 720
3! - 2! = 4
6! ÷ 3! = 120
Step-by-step explanation:
I used a calculator. ^v^
math help questions
After 1 year, the initial investment increases by 7%, i.e. multiplied by 1.07. So after 1 year the investment has a value of $800 × 1.07 = $856.
After another year, that amount increases again by 7% to $856 × 1.07 = $915.92.
And so on. After t years, the investment would have a value of [tex]\$800 \times 1.07^t[/tex].
We want the find the number of years n such that
[tex]\$856 \times 1.07^n = \$1400[/tex]
Solve for n :
[tex]856 \times 1.07 ^n = 1400[/tex]
[tex]1.07^n = \dfrac74[/tex]
[tex]\log_{1.07}\left(1.07^n\right) = \log_{1.07}\left(\dfrac74\right)[/tex]
[tex]n \log_{1.07}(1.07) = \log_{1.07} \left(\dfrac74\right)[/tex]
[tex]n = \log_{1.07} \left(\dfrac74\right) = \dfrac{\ln\left(\frac74\right)}{\ln(1.04)} \approx \boxed{8.3}[/tex]
Answer:
25 years
Step-by-step explanation:
total = before × percent ( in decimal ) × time
1400 = 800 × 0.07 × t
1400 = 56 × t
1400 ÷ 56 = 25
t = 25
Hope this was helpful!
Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a decimal to the nearest hundredth.
Answer:
The probability as a decimal to the nearest hundredth is 0.550.55.
Step-by-step explanation:
61 cash, 5 debit card, and 45 credit card.
\color{steelblue}{61}+5+45=
61+5+45=
\,\,\color{indianred}{111}
111
There were a toal of 111 customers. 61 paid with cash.
Probability the next customer will pay with cash:
\frac{\color{steelblue}{61}}{\color{indianred}{111}}=
111
61
=
\,\,0.549549...
0.549549...
\approx
≈
\,\,0.55
0.55
Round to the nearest hundreth
The probability that the next customer will pay with cash is 0.55.
What is the formula for probability?Probability is the ratio of the number of favorable events divided by the total outcome.
We have, given that, Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.
The total number of payments is,
61+45+5=111.
We have to find the probability that the next customer will pay with cash as a decimal to the nearest hundredth.
The number of the favorable outcome for the customer will pay with cash is 61, and the total number of outcomes is 111.
Therefore, the probability is,
P(A)=61/111
P(A)=0.5495.
Therefore, the probability of the nearest hundredth is 0.55.
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Billy has 10 bouncy balls. His brother has 30 bouncy balls. He washed 10 of his and 10 of his brother. How many bouncy balls do they have left?
Answer:
20
Step-by-step explanation:
10 + 30 = 40
40 - 10 = 30
30 - 10 = 20
answer is 20
Answer:
20 bouncy Balls!
Step-by-step explanation:
10+30 - 20 = 20
The product of two consecutive integers is 72. the equation x(x 1) = 72 represents the situation, where x represents the smaller integer. which equation can be factored and solved for the smaller integer? x2 x – 72 = 0 x2 x 72 = 0 x2 2x – 72 = 0 x2 2x 72 = 0
The equation that can be factored and solved for the samller integer is x² + x - 72 = 0
How to form an equation?The product of two consecutive integers is 72. The equation that represents the situation is as follows:
x(x + 1) = 72
where
x = smaller numberTherefore,
x(x + 1) = 72
x² + x = 72
x² + x - 72 = 0
Therefore, the equation that can be factored and solved for the samller integer is x² + x - 72 = 0
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