The probability that battery lasts more than 3 years is [tex]e^{-0.6 }[/tex].
Parameter of Exponential Distribution
It is given that the average lifespan of the car battery = 5 years
⇒ μ = 5
And, we have to find the probability that the car battery lasts more than 3 years.
Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,
1/ λ = μ
⇒ λ = 1/5
Calculating the Probability
The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.
P(N>3) = 1 - P(N≤3)
P(N>3) = 1-F(4)
Here, F is the exponential distribution for the lifespan of the car battery.
P(N>3) = 1-(1-e^(-λn))
P(N>3) = [tex]e^{-3/5}[/tex]
Thus, the required probability is,
P(N>3) = [tex]e^{-0.6 }[/tex]
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Which of the following is a perfect square trinomial?
a. x^2+10x+25
b. x^2+6x+13
c. x^2+100
d. x^2+3x+9
Answer:
a. x² + 10x + 25
Step-by-step explanation:
because
(x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25
so, it is a perfect square of (x + 5).
Please help!!! Find the equation of the line, use exact numbers:
y=__x+__
(__ means to fill in)
The equation shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. If the orbital period of planet y is twice the orbital period of planet x, by what factor is the mean distance increased?.
The mean distance is increased by a factor of [tex]2^{3/2}[/tex] if the orbital period of planet y is twice that of the planet x.
Description of the Kepler's law.
The orbital period T and the mean distance from the sun, A, expressed in astronomical units (AU), are related in accordance with Kepler's third law.
The mathematical formula is,
T² = A³
Here, T denotes the orbital period and A represents the average separation or mean distance from the sun.
Now, if T(y) = 2T(x)
⇒ A'³(y) = 2A³(x)
A'(y) = [tex]2^{3/2}[/tex]A(y)
Thus, if orbital period of planet y is twice the orbital period of planet x, the mean distance is lengthened by a factor of [tex]2^{3/2}[/tex].
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Answer:
2 Superscript three-halves
Step-by-step explanation:
Edge
Multiple choice ( easy)
What is the length of Xpy in terms of
10 m
Options
900л m
15л m
5л m
307 m
Answer:
XPY = 15π m
Step-by-step explanation:
XPY is 3/4 of the circumference of the circle. The perimeter of a circle is given by 2πr, with r = 10m.
C = 2πr
C = 2π(10)
C = 20π
3/4 of C is (3/4)(20π)
XPY = 15π m
The following statistics describe the hourly wages paid by two firms. Firm A Firm B Sample size 50 40 Sample mean $16.5 $16 Population standard deviation $0.9 $0.85 The test statistic used to evaluate whether there is any significant difference between the mean hourly wages is:
The t-test statistic is used to evaluate whether there is any significant difference between the mean hourly wages.
What is t-test?To evaluate whether there is a statistically significant difference between the means of two variables, a t-test is an inferential statistic that is utilized.
A statistical test for assessing hypotheses is the t-test.
The difference between the means from each data set, the standard deviation of each group, and the total number of data values are the three basic data values needed to do a t-test.
There are independent and dependent T-tests.
The problem statement is established mathematically by using a sample from each of the two sets in the t-test. It presupposes that the two means are equal, which is the null hypothesis.
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Last week, Layla's Ice Cream Shoppe sold 11 sundaes with nuts and 39 without. what is the ratio of the number of sundaes without nuts
The ratio of the number of sundaes with nuts to the number of sundaes without nuts is; 11:39
How to find the sharing ratio?We are given;
Number of sundaes with nuts sold = 11
Number of sundaes without nuts sold = 39
Thus, the ratio of the number of sundaes with nuts to the number of sundaes without nuts is;
11:39
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Out of a sample 650 high school students, 321 take the bus to school every day. construct a 99% confidence interval for the population mean of high school students that take the bus to school every day.
a.ci=(43.23%,51.18%)
b.ci=(44.34%, 54.43%)
c.ci=(45.54%, 53.23%)
d.ci=(46.16%,52.16%)
A 99% confidence interval for the population mean of high school students that take the bus to school every day is b) ci=(44.34%, 54.43%)
We need to find the 99% confidence interval for the population mean of high school students that take the bus to school everyday
A confidence interval is a range of estimates for an unknown parameter. The confidence interval is calculated at the specified confidence level; the most common is the 95% confidence level, but sometimes other levels are used, such as 90% or 99%.
The confidence interval of proportions is given by:
π ± z √(π (1-π) /n)
π is the sample proportion.
z is the critical value.
n is the sample size.
For 99% confidence interval the value of z is 2.58
π = 321/650
The confidence interval is given by
=321/650 ± 2.58 √( (321/650) × [ 1 - (321/650) ] ÷ 650)
= (0.493846 ± 0.050594)
=(0.4434 , 0.5443)
=(44.34 % , 54.43 %)
Hence a 99% confidence interval for the population mean of high school students that take the bus to school every day is ci=(44.34%, 54.43%)
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If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
Answer:
Step-by-step explanation:
If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
then he started to prepare the games for this 4 friends. if each game takes 5 minutes to prepare and he prepared a total of 5 games. how many minutes did it take for andrew to prepare all the games
Answer:
25 minutes
Step-by-step explanation:
If it takes 5 minutes to prepare one game we need to multiply 5 games by 5 minutes: 5*5 = 25 minutes
Which equation describes how the parent function, y = x3, is vertically stretched by a factor of 4?
Oy=x³ +4
O y=(x+4)³
O. y=4x³
O y=x4
Answer: [tex]y=4x^3[/tex]
Step-by-step explanation:
See attached image.
The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The parent function is,
⇒ y = x³
Now, After vertically stretched by a factor of 4 we get;
The value of function is,
⇒ y = 4x³
Hence, The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
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Ann invested $9000 in an account that earns 4.7% interest compounded annually . how much did ann have in the account after 5 years
The correct answer is FV = $11,323.38
What is compound interest explain?
Compound interest is when you earn interest on both the money you've saved and the interest you earn. So let's say you invest $1,000 (your principal) and it earns 5 percent (interest rate or earnings) once a year (the compounding frequency).FV = PV x [1 + R]^N, where FV=Future Value, PV=Present Value, R=Interest rate per period, N=Number of periods.
FV = 9,000 x [1 + 0.047]^5
FV = 9,000 x 1.047^5
FV = 9,000 x 1.258152857750007
FV = $11,323.38
Therefore , the answer is $11,323.38.
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MULTIPLE CHOICE
Question 13
Which best describes the range of f(x)?
Based on the function, the range of f(x) = 2(3)^x can best be described as y > 0.
What is the range of f(x) = 2(3)^x?When a number is raised to a power, the result will always be positive even if the number is raised to a negative number.
This means that 3^x will always be positive which means that 2(3)^x will also be positive. y will therefore always be greater than 0.
Full question is:
Which best describes the range of the function f(x) = 2(3)^x?
y > 0
y ≥ 0
y > 2
y ≥ 2
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Look at sample problem 23.2. How many unpaired electrons are in (enter a number such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) 1. Ag 2. Mn3 3. Cr3
To find the unpaired electrons:
Ag+ represents the d10 system. Because there are no unpaired electrons, the system is diamagnetic.Mn3+ has the electronic structure [Ar]3d44s0. In 3d, there are four unpaired electrons.Because of the loss of three electrons, the chromium ion Cr3+ has 24e3e=21e.Therefore, unpaired electrons are:
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Given the following table with selected values of f (x) and g(x), evaluate f (g(4)).
x –6 –4 1 3 4
f (x) 4 –1 –6 1 3
g(x) 1 4 3 –4 –6
–4
–1
1
4
The value of f(x) when x is -6 is 1.
Composite functionsComposite functions are also known as function of a function. In order to get a composite functions f(g(x)).
g(4) = -6 (the value of g(x) when x is equivalent to 4 is -6)
f(g(x))= f(g(4)) = f(-6)
f(-6) = 1
The value of f(x) when x is -6 is 1.
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b. Shawn has 42 points on his computer game. He loses the
next round though which takes away 50 points. How
many total points does Shawn now have?
Answer: -8 points
Step-by-step explanation: because he lost 50, and he originally had 42, a smaller number, the answer will go into the negatives.
42-50= -8, which is how you get the answer!
Answer:
-8
Step-by-step explanation:
42-50 is the same as 50-42, except the answer is negative
Does the expected value of a random variable have to equal one of the possible values of the random variable? explain
No, just like the average (mean) it is a mathematical quantity that is determined by its mathematical definition and the everyday meaning of “expected” is only a descriptive hint toward what it represents.
What does the expected value of a random variable mean?
E[X] stands for the expected value of a random variable. The expected value of a random variable is also known as its mean, in which case we use the notation X. It can be thought of as the "average" value obtained by the random variable.Is the expected value always equal to the mean?
The primary distinction between "mean" and "expected value" is that the former is typically used to describe a frequency distribution and the latter, a probability distribution. In frequency distribution, variables and their occurrence frequencies make up the sample space.Learn more about expected value of a random variable brainly.com/question/22435257
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A landscaping company is covering this trapezoid-shaped yard with grass seed. A trapezoid with base lengths of 6 meters and 7 meters, and height 4 meters. How much area will they need to cover with grass seed
Area covered with grass seed = 10.4[tex]m^{2}[/tex].
What is trapezoid geometry?
A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.
Area of the trapezoid ={ (a+b)/2} +h
where a and b is base and h is height of the trapezoid geometry.
In the question,
a=6m , b=7m and h=4m.
According to the formula { (a+b)/2} +h.
Area covered with grass seed = {(6+7)/2} + 4
= 10.4[tex]m^{2}[/tex].
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Answer:
26
Step-by-step explanation:
GOT IT RIGHT`
Total slack is calculated by ____
Total slack is calculated by the late finish minus early finish and the late start minus the early start
What is the total slack?Total slack is simply the amount of time taken for a task to be delayed before the project finish date is delayed. It can be positive or negative.
It is calculated as the calculated as the value of the Late Finish minus the Early Finish field, and the Late Start minus the Early Start field.
Total slack = Late finish - early finish + late start - early start
Thus, the total slack is calculated by the late finish minus early finish and the late start minus the early start.
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Can someone help me with these problems please
Decide if the random variable x, is discrete or continious: x represents the temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
Answer:
Continuous
Step-by-step explanation:
Degrees don't always have to be integers. It can be 32.3 degrees, 32.31 degrees, etc.
What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?
The minimum value of c = 7x + 8y is 42. The minimum value is obtained at point (6, 0).
How to calculate the minimum value?To calculate the minimum value of the given equation w.r.t the given constraints(inequalities), the steps are:
Step 1: Identify the system of inequalities in the given constraints
Step 2: Graph those inequalities
Step 3: Identify the maximum and minimum values of x and y that satisfy the given inequalities
Step 4: Then, with the obtained coordinates solve the given equation to get the minimum value.
Calculation:The given equation is C = 7x + 8y, and the constraints list is
2x + y ≥ 0
x + y ≥ 6
x ≥ 0
y ≥ 0
Graphing these inequalities and shading the region that satisfies the given inequalities.
So, from the graph,
the x-values that satisfy all the given inequalities are [6, ∞]
the y-values that satisfy all the given inequalities are [0, ∞]
So, the required coordinate is (6, 0). By this, we can calculate the minimum value of the given equation C = 7x + 8y
Then,
C = 7(6) + 8(0) = 42 + 0 = 42
Thus, the minimum value of the given equation is 42.
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Disclaimer: The given question is incomplete. Here is the complete question.
Question: What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?
2x + y ≥ 0
x + y ≥ 6
x ≥ 0
y ≥ 0
Use quadratic regression to find a function that does the following points.
(-1,-15), (1,-7), (6,-122)
Answer:
[tex]y = -x^{2} +4x-10[/tex]
Step-by-step explanation:
I used a graphing calculator to calculate the points so I'm not sure how to do it without, but I hope this helped!
Which term best describes the figure shown below?? WILL MARK BRAINLIEST!!!
Answer:
Line LM
Step-by-step explanation:
Answer:
A line is a straight path on a plane that extends forever in both directions with no endpoints.
The answer will be lineLM
The three sides of a right triangle have integral lengths which form an arithmetic sequence. How many numbers between 1 and 2020 inclusive can be the side of the hypotenuse
There are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence. This can be obtained by forming the arithmetic sequence, equating by Pythagoras theorem and finding numbers divisible by the integral.
Find the value of hypotenuse?Let the arithmetic sequence be (a - d), a, (a+d)
Using Pythagoras theorem,
(a - d)² + a² = (a+d)²
a² -2ad + d² + a² = a² + 2ad + d²
2a² - 2ad + d² = a² + 2ad + d²
2a² - a² + d² - d² = 2ad + 2ad
a² = 4ad
a = 4d
Thus hypotenuse will be (a + d) = 4d + d = 5d
How many numbers between 1 and 2020 inclusive can be the side of the hypotenuse?Since the value of hypotenuse is 5d, the total numbers divisible by 5 between 1 and 2020 will be the number of possible sides of the hypotenuse.
There are 2020 numbers between 1 and 2020 inclusive
The numbers divisible by 5 = 2020/5 = 404
Hence there are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence.
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Mary performs this calculation. (3.0) (2.0). how many significant figures should her answer have? one two four six
Answer:
2
Step-by-step explanation:
There are only 2 numbers in the final answer (6.0), so you just need 2 significant figures.
The average amount of money held by each child in a group of 5 is $0.50. If one of the children loses a quarter, what is the new average of money held by each child
Answer:
$0.45.
Step-by-step explanation:
Total amount of money held by all 5 children
= 5 * 0.50 = $2.50.
After 0.25 is lost the total = $2.25.
So the new average = 2.25 / 5
= $0.45.
Ivan began to prove the law of sines using the diagram and equations below.
Triangle A B C is shown. A perpendicular bisector is drawn from point C to point D on side B A to form a right angle. The length of the perpendicular bisector is h, the length of C B is a, the length of C A is b, and the length of B A is c.
sin(A) = h/b, so b sin(A) = h.
sin(B) = h/a, so a sin(B) = h.
Therefore, b sin(A) = a sin(B).
Which equation is equivalent to the equation
b sin(A) = a sin(B)?
StartFraction a Over sine (uppercase B) EndFraction = StartFraction b Over sine (uppercase A) EndFraction
StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction
StartFraction sine (uppercase A) Over sine (uppercase B) EndFraction = StartFraction b Over a EndFraction
StartFraction sine (uppercase B) Over a EndFraction = StartFraction sine (uppercase A) Over b EndFraction
An equation which is equivalent to the equation bsin(A) = asin(B) is: B. [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
What is the law of sines?The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
Mathematically, the law of sines is given by this equation:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
In this context, we can infer and logically deduce that an equation which is equivalent to the equation bsin(A) = asin(B) is [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex].
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Answer: B
Explanation: sin(A)/a=sin(B)/b
How many quarters are there in 7 1/2?
Answer: 30.
Step-by-step explanation:
[tex]7\frac{1}{2} =\frac{7*2+1}{2} \\\frac{14+1}{2}=\frac{15}{2}\\ \frac{15*2}{2*2}=\frac{30}{4} \\ \frac{30}{4}=30*\frac{1}{4} .[/tex]
There are total 30 quarters in [tex]7\frac{1}{2}[/tex].
What is one quarter?A quarter is one out of four equal parts. One quarter is the same as the fraction ¼.
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction.
How to convert a mixed fraction into an improper fraction?To change a mixed fraction to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.
According to the given question.
We have a mixed fraction [tex]7\frac{1}{2}[/tex].
So, the improper fraction of the given mixed fraction is given by
[tex]7 \frac{1}{2} = \frac{15}{2}[/tex]
To find the number of quarters in the given mixed fraction, we will divide [tex]7\frac{1}{2}[/tex] by [tex]\frac{1}{4}[/tex].
Therefore,
[tex]\frac{7\frac{1}{2} }{\frac{1}{4} }[/tex]
= [tex]\frac{\frac{15}{2} }{\frac{1}{4} }[/tex]
[tex]= \frac{15\times 4}{2}[/tex]
[tex]= 15\times 2[/tex]
[tex]= 30[/tex]
Hence, there are total 30 quarters in [tex]7\frac{1}{2}[/tex].
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What is the area of the trapezoid above?
A. 188 cm²
B. 196 cm²
C. 392 cm²
D. 5,236 cm²
Answer:
B. 196cm²Step-by-step explanation:
Area = h/2 (b_1+b_2)
[tex]\sf\cfrac{7}{2}\:(22+34)[/tex]
Add 22 and 34 = 56
[tex]\sf \cfrac{7}{2} \times 56[/tex]
Let's express 7/2 * 56 as a single fraction:-
[tex]\sf \cfrac{7\times 56}{2}[/tex]
Multiply 7 and 56 = 392
[tex]\sf \cfrac{392}{2}[/tex]
Divide
[tex]\sf 196[/tex]
Therefore, the area of the trapezoid is 196cm².
_______________________
The number 321.8 is 34% of x. What is the value of x rounded to the nearest whole number?
Answer:
946
Step-by-step explanation:
Let's make an equation :
34% of x = 321.8
Covert 34% into decimal by dividing by 100 :
34 ÷ 100 = 0.34
Rewrite equation with decimal form :
0.34x = 321.8
Divide both sides by x to make x the subject :
x = 321.8 ÷0.34
x = 946.470588235
To the nearest whole number will be 946 as 4 rounds it down
So our final answer will be 946
Hope this helped and have a good day
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{34}{100} \sdot x = 321.8[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{(321.8) \sdot(100)}{34} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 946.47[/tex]
Round off to nearest whole number :
[tex]\qquad \sf \dashrightarrow \: x = 946[/tex]