what is the equivalent property of 8(4x - 3)
Answer:
=32x−24
Step-by-step explanation:
What is the factors for x squared plus 5x - 6
Answer:
=[tex](x-1)(x+6)[/tex]
Step-by-step explanation:
Answer:
[tex]x^{2} +5x-6=(x-1)(x+6)[/tex]
Step-by-step explanation:
Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?
ANSWER: A
After plotting the above equation on the coordinate plane, we can see the graph of the function.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
We have two parametric equations:
x = 1 – t² and
y = 2t
t = y/2 and
0 ≤ t² ≤ 5
1 ≤ 1 - t²≤ 4
1 ≤ x≤ 4
Plug the above value in x = 1 – t²
x = 1- (y/2)²
x = 1 - y²/4
4x = 4 - y²
y² = 4(1 - x)
Thus, after plotting the above equation on the coordinate plane, we can see the graph of the function.
Learn more about the parametric function here:
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Suppose X has an exponential distribution with mean equal to 11. Determine the following: (a) (Round your answer to 3 decimal places.) (b) (Round your answer to 3 decimal places.) (c) (Round your answer to 3 decimal places.) (d) Find the value of x such that . (Round your answer to 2 decimal places.)
Answer:
[tex]P(X > 11) = 0.368[/tex]
[tex]P(X > 22) = 0.135[/tex]
[tex]P(X > 33) = 0.050[/tex]
[tex]x = 33[/tex]
Step-by-step explanation:
Given
[tex]E(x) = 11[/tex] --- Mean
Required (Missing from the question)
[tex](a)\ P(X>11)[/tex]
[tex](b)\ P(X>22)[/tex]
[tex](c)\ P(X>33)[/tex]
(d) x such that [tex]P(X <x)=0.95[/tex]
In an exponential distribution:
[tex]f(x) = \lambda e^{-\lambda x}, x \ge 0[/tex] --- the pdf
[tex]F(x) = 1 - e^{-\lambda x}, x \ge 0[/tex] --- the cdf
[tex]P(X > x) = 1 - F(x)[/tex]
In the above equations:
[tex]\lambda = \frac{1}{E(x)}[/tex]
Substitute 11 for E(x)
[tex]\lambda = \frac{1}{11}[/tex]
Now, we solve (a) to (d) as follows:
Solving (a): P(X>11)
[tex]P(X > 11) = 1 - F(11)[/tex]
Substitute 11 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{1}{11}* 11})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{11}{11}})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-1})[/tex]
Remove bracket
[tex]P(X > 11) = 1 - 1 + e^{-1}[/tex]
[tex]P(X > 11) = e^{-1}[/tex]
[tex]P(X > 11) = 0.368[/tex]
Solving (b): P(X>22)
[tex]P(X > 22) = 1 - F(22)[/tex]
Substitute 22 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{1}{11}* 22})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{22}{11}})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-2})[/tex]
Remove bracket
[tex]P(X > 22) = 1 - 1 + e^{-2}[/tex]
[tex]P(X > 22) = e^{-2}[/tex]
[tex]P(X > 22) = 0.135[/tex]
Solving (c): P(X>33)
[tex]P(X > 33) = 1 - F(33)[/tex]
Substitute 33 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{1}{11}* 33})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{33}{11}})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-3})[/tex]
Remove bracket
[tex]P(X > 33) = 1 - 1 + e^{-3}[/tex]
[tex]P(X > 33) = e^{-3}[/tex]
[tex]P(X > 33) = 0.050[/tex]
Solving (d): x when [tex]P(X <x)=0.95[/tex]
Here, we make use of:
[tex]P(X<x) = F(x)[/tex]
Substitute [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X<x) = 1 - e^{-\lambda x}[/tex]
So, we have:
[tex]0.95 = 1 - e^{-\lambda x}[/tex]
Subtract 1 from both sides
[tex]0.95 -1= 1-1 - e^{-\lambda x}[/tex]
[tex]-0.05=- e^{-\lambda x}[/tex]
Reorder the equation
[tex]e^{-\lambda x} = 0.05[/tex]
Substitute 1/11 for [tex]\lambda[/tex]
[tex]e^{-\frac{1}{11} x} = 0.05[/tex]
Solve for x:
[tex]x = -\frac{1}{1/11}\ ln(0.05)[/tex]
[tex]x = -11\ ln(0.05)[/tex]
[tex]x = 32.9530550091[/tex]
[tex]x = 33[/tex] --- approximated
3/4 x 25 please bro and i need to make this longerrrr
Answer:
18.75
Step-by-step explanation:
18.75
ILL GIVE BRAINLEST !!!!
Enter an equation for the function that includes the points. Give your answer in the form a(b*). In the
event that a = 1, give your answer in the form b*.
(1, 12) and (2, 144)
The equation is f(x)=
Find the radius of the circle. The center of the circle is (2, -3) and a point that lies on the circle is (-1, -2).
Answer:
[tex]\displaystyle r = \sqrt{10}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Geometry
Definition of a radius - the center of a circle to any point to the circumferenceAlgebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Center (2, -3) → x₁ = 2, y₁ = -3
Circumference point (-1, -2) → x₂ = -1, y₂ = -2
In this case, the distance d from the center to the circumference point would be the radius r of the circle.
Step 2: Find Radius r
[Distance Formula] Define equation [Radius]: [tex]\displaystyle r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute in points [Radius]: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2--3)^2}[/tex][Radius] [√Radical] (Parenthesis) Simplify: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2+3)^2}[/tex][Radius] [√Radical] (Parenthesis) Subtract/Add: [tex]\displaystyle r = \sqrt{(-3)^2+(1)^2}[/tex][Radius] [√Radical] Evaluate exponents: [tex]\displaystyle r = \sqrt{9+1}[/tex][Radius] [√Radical] Add: [tex]\displaystyle r = \sqrt{10}[/tex]Reflect a figure with vertices A(1,2) B (3,6), C(-1,2), and D(-2,-2)
across the x-axis. Find the coordinates of the new image.
A) C(-1,2) --> C' (-1,-2)
B) B(3,6) --> B' (3,-6)
C) A(1,2) --> A' (1,-2)
D) D(-2,-2)--> D' (-2,2)
Answer:
1,2 = 1,negative2
3,6 = 3,negative 6
-1,2 = negative 1, negative 2
-2,-2 = negative2, 2
Step-by-step explanation:
Sorry all i could do was reflect the coordinates across the x-axis.
The figure reflected along x-axis will have vertices A(1, -2), B (3, -6), C(-1, -2), and D(-2, 2).
What is reflection along the x-axis?When we reflect a figure along the x-axis the coordinate point of y changes its sign, (x, y) becomes (x, - y).
Think of holding the x-axis with two fingers and rotating it.
Given, we reflect a figure with vertices A(1,2) B (3,6), C(-1,2), and D(-2,-2)
across the x-axis.
∴ The rotated coordinate will be A(1, -2), B (3, -6), C(-1, -2), and D(-2, 2).
learn more about translation here :
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what unfortunate mistake did the champion ice skater make with his gold medal
Answer:
He Had It Bronzed
Step-by-step explanation:
Hope this help pls mark as brainlest!!
The lifetimes of a certain brand of light bulbs are known to be normally dsitributed with a mean of 1700 hours and standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.20 that the sample mean lifetime is more than how many hours?
A. 1652.
B. 1725.
C. 1752.
D. 1670.
Answer:
1742 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Single light:
Mean of 1700 hours and standard deviation of 400 hours, which means that [tex]\mu = 1700, \sigma = 400[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{400}{\sqrt{64}} = 50[/tex]
The probability is 0.20 that the sample mean lifetime is more than how many hours?
This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.84 = \frac{X - 1700}{50}[/tex]
[tex]X - 1700 = 50*0.84[/tex]
[tex]X = 1700 + 50*0.84[/tex]
[tex]X = 1742[/tex]
SOMEONE PLZZ HELP, I HAVE A TEST AND DONT KNOW HOW TO DO THIS!!
The medical practice you are working at has seen an average of 22.4 patients a day for the past 3 months. 3/4ths of those patients have insurance in one form or another.
What is the discriminate of y=x^2-8x+2
Answer:
56
Step-by-step explanation: Use the values of a, b, and c to find the discriminant.
Answer:
[tex]\Delta =56[/tex]
Step-by-step explanation:
We are given:
[tex]y = x^2 - 8x + 2[/tex][tex]y=x^2-8x+2[/tex]
So, a = 1, b = -8, and c = 2.
The discriminant (symbolized by Δ) is given by:
[tex]\Delta =b^2-4ac[/tex]
So, our discriminant in this case will be:
[tex]\Delta=(-8)^2-4(1)(2)=64-8=56[/tex]
Since our discriminant is a positive value, our equation has two real roots.
What is the fraction shown above?
12+22+32+...+102 =?
Answer:
750 is the answer. Hope it helps!
An Airbus A320 jet flies 5 hours west with a 40-mph tailwind. Returning against the wind takes 7 hours. Find the speed of the jet with no wind.
Answer:
The speed of the jet with no wind is 240 miles per hour.
Step-by-step explanation:
The speed of the jet with no wind is equivalent to the speed of the jet relative to wind. Physically speaking, we have the following system of linear equations under the assumption that both speeds of wind and jet are constant:
In favor of wind
[tex]\frac{s}{t_{F}} = v_{W}+v_{J/W}[/tex] (1)
Against wind
[tex]-\frac{s}{t_{A}} = v_{W} -v_{J/W}[/tex] (2)
Where:
[tex]s[/tex] - Travelled distance, measured in miles.
[tex]t_{F}[/tex], [tex]t_{A}[/tex] - Time, measured in hours.
[tex]v_{W}[/tex] - Wind speed, measured in miles per hour.
[tex]v_{J/W}[/tex] - Jet speed relative to wind, measured in miles per hour.
If we know that [tex]t_{F} = 5\,h[/tex], [tex]t_{A} = 7\,h[/tex], [tex]v_{W} = 40\,\frac{mi}{h}[/tex], then the speed of the jet with no wind is:
[tex]\frac{s}{5} = 40 + v_{J/W}[/tex] (3)
[tex]-\frac{s}{7} = 40-v_{J/W}[/tex] (4)
[tex]\frac{s}{5}-40 = 40 +\frac{s}{7}[/tex]
[tex]\frac{s}{5}-\frac{s}{7} = 80[/tex]
[tex]\frac{7\cdot s - 5\cdot s}{35} = 80[/tex]
[tex]2\cdot s = 2800[/tex]
[tex]s = 1400\,mi[/tex]
From (3), we find that speed of the jet with no wind is:
[tex]v_{J/W} = \frac{s}{5}-40[/tex]
[tex]v_{J/W} = \frac{1400}{5}-40[/tex]
[tex]v_{J/W} = 240\,\frac{mi}{h}[/tex]
The speed of the jet with no wind is 240 miles per hour.
At a deli, Joe bought 2.2 pounds of coleslaw for $7.15. What was the unit price?
Answer:
$3.25 for 1 pound of coleslaw
Step-by-step explanation:
i think,.
What is the difference between the greatest and the smallest rational numbers
given below?
7/15,11/20,2/5,12/25
Answer:
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
Step-by-step explanation:
Step(i):-
Given that the rational numbers
[tex]\frac{7}{15} , \frac{11}{20} ,\frac{2}{5} ,\frac{12}{25}[/tex]
we have to find that the difference between the greatest and the smallest rational numbers
solution:-
The greatest rational number = [tex]\frac{11}{20}[/tex]
Convert into decimal = 0.55
The smallest rational number = [tex]\frac{2}{5}[/tex]
Convert into decimal = 0.4
The difference between the greatest and smallest rational number
[tex]= \frac{11}{20} - \frac{2}{5}[/tex]
= [tex]\frac{11-8}{20}[/tex]
[tex]=\frac{3}{20}[/tex]
Final answer:-
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
I need the answers ASAP
Answer:
Image attached
Step-by-step explanation:
Just wandering, no hate, you can post answers on brainly but can't read an analog clock.
BTW I've got one in my house
2. Two boxes are being shipped at a facility. One
box weighs 25.09 pounds, and the other box
weighs 25.018. Which box weighs more? Explain
and prove your answer.
Answer:
i think 25.09 weighs more
Step-by-step explanation: well simply 25.018 has more decimal places down therefore making it a smaller number
sorry if you get it wrong :c
solve and recieve brain list I took a better picture
Please help me!!!!!!!!!!
Help quick plzzzzz Plzzzzzzzzzzzzz
12873t456473892220-209873
I’ll give you 15 points if you know the answers to this question
It would be B)no.
Hope This Helps!
3/4 divided by 1/5 PLEASE ANSWER
Answer:
3.75
Step-by-step explanation:
To make it a fraction form answer, you multiply the dividend numerator by the divisor denominator to make a new numerator.
Furthermore, you multiply the dividend denominator by the divisor numerator to make a new denominator:
To make the answer to 3/4 divided by 1/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
15/4 = 3.75
The answer is rounded to the nearest four decimal points if necessary.
15/4 is an improper fraction and should be written as 3 3/4.
Answer:
3.75
Step-by-step explanation:
Please help me!!!!
Ernest bought some cans of paint and 4/5 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 2/5 of a liter of additive in each can. How many cans of paint did Ernest buy?
Answer:
He bought 2 cans of paint
Step-by-step explanation:
If he put ⅖ in each, and ⅘ total, he would have had 2 cans
Quantity of special paint additive Ernest bought = [tex] \tt \frac{4}{5} \: of \: a \: litre [/tex]
Quantity of additive he put in each can = [tex] \tt \frac{2}{5} \: of \: a \: litre [/tex]
Number of cans of paint he bought :
[tex] =\tt \frac{4}{5} \div \frac{2}{5} [/tex]
[tex] = \tt\frac{4}{5} \times \frac{5}{2} [/tex]
[tex] = \tt\frac{4 \times 5}{5 \times 2} [/tex]
[tex] =\tt \frac{20}{10} [/tex]
[tex]\color{plum} = \tt2 \: paint \: cans[/tex]
▪︎Therefore, Ernest bought 2 paint cans.
7. Which of the following expressions contains like terms?
5xy - 13y
5x - 13xy
5xy - 13x
5xy - 13xy
Answer:
The last one
Step-by-step explanation:
Due to there being xy's in both terms
Let f(x) = 4x - 1, h(x) = - X-3.
Find (f o h)(-5).
Answer:
(f o h)(-5)=-33
Step-by-step explanation:
Let f(x) = 4x - 1, h(x) = - X-3.
(f o h)=4(-x-3)-1
(f o h)=-4x-12-1
(f o h)=-4x-13
(f o h)(-5)=-4(-(-5))-13
(f o h)(-5)=-20-13
(f o h)(-5)=-33
Which statement is true if a is the fourth root of 16, Show your work
a x a x a x a = 16
a = 164
4a = 16
a = 16/4
Given:
The statement is " a is the fourth root of 16".
To find:
The true statement for the given statement.
Solution:
The given statement is
a is the fourth root of 16.
Mathematically, it can be written as
[tex]a=\sqrt[4]{16}[/tex]
Taking power 4 on both sides.
[tex]a^4=(\sqrt[4]{16})^4[/tex]
[tex]a\times a\times a\times a=16[/tex]
Therefore, the correct option is A.
A true statement , if a is the fourth root of 16 is
a x a x a x a = 16
Important Information :
'a' is the fourth root of 16'a' is the fourth root of 16 can be written as
[tex]a=\sqrt[4]{16}[/tex]
To remove fourth root, we take exponent 4 on both sides
[tex]a=\sqrt[4]{16}\\(a)^4=(\sqrt[4]{16})^4[/tex]
Exponent 4 and fourth root will get cancelled
[tex]a^4=16\\a \cdot a\cdot a \cdot a=16[/tex]
a x a x a x a = 16
A true statement , if a is the fourth root of 16 is
a x a x a x a = 16
learn more about the radicals here:
brainly.com/question/1799883
Find the difference.
4-(-8)=
Answer:
4
Step-by-step explanation:
subtract negative 4 by negative 8