Answer: A. To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the probability that his height is less than or equal to 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, we can use the standard normal distribution to find this probability.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the height of a male passenger from the given distribution to the standard normal distribution by using the formula:
$z = \frac{x - \mu}{\sigma}$
where $x$ is the height of the male passenger, $\mu$ is the mean height of 69 inches, and $\sigma$ is the standard deviation of 2.8 inches. Substituting these values into the formula gives us:
$z = \frac{72 - 69}{2.8} = \frac{3}{2.8} = 1.0714$
Since the standard normal distribution is symmetric, the probability that a male passenger's height is less than or equal to 72 inches is the same as the probability that his height is greater than or equal to 72 inches. We can find this probability by looking up the value of $z = 1.0714$ in a standard normal table, which gives us a probability of 0.8413. Therefore, the probability that a male passenger can fit through the doorway without bending is 0.8413.
B. To find the probability that the mean height of the 175 men is less than 72 inches, we need to find the probability that the sample mean is less than 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, the sample mean will also be normally distributed with a mean of 69 inches and a standard deviation of $\frac{2.8}{\sqrt{175}} = 0.32$. We can use the standard normal distribution to find the probability that the sample mean is less than 72 inches.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the sample mean from the given distribution to the standard normal distribution by using the formula:
$z = \frac{x - \mu}{\sigma}$
where $x$ is the sample mean, $\mu$ is the mean of 69 inches, and $\sigma$ is the standard deviation of 0.32. Substituting these values into the formula gives us:
$z = \frac{72 - 69}{0.32} = \frac{3}{0.32} = 9.375$
Since the standard normal distribution is symmetric, the probability that the sample mean is less than 72 inches is the same as the probability that the sample mean is greater than 72 inches. We can find this probability by looking up the value of $z = 9.375$ in a standard normal table, which gives us a probability of 0.0000. Therefore, the probability that the mean height of the 175 men is less than 72 inches is 0.0000.
C. When considering the comfort and safety of passengers, the result from part (a) is more relevant than the result from part (b). This is because part (a) tells us the probability that a randomly selected male passenger can fit through the doorway without bending, which is directly relevant to the comfort and safety of the passengers. In contrast, part (b) tells us the probability that the mean height of the 175 men is less than 72 inches, which is not directly relevant to the comfort
D. Women are ignored in this case because the problem only asks about the heights of men. The problem states that the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, and does not provide any information about the heights of women. Therefore, we cannot use the given information to find the probability that a female passenger can fit through the doorway without bending.
Verify the trig identity and show all expanded steps
We have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.
What are trigonometric identities?
Trigonometric Identities are the equalities that involve trigonometry functions and hold true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.
tan∅ = sin∅/cos∅
cot∅ = cos∅/sin∅
Given:
tanθ.cosθ + cotθ.sinθ = sinθ + cosθ
Now LHS = tanθ.cosθ + cotθ.sinθ
= (sinθ/cosθ)cosθ + (cosθ/sinθ)sinθ
= sinθ + cosθ
LHS = RHS
Hence, we have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.
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what is the solution to 2x^2+x+3=0
The solutions of the quadratic equation are:
x = (-1 + i√23)/4
x = (-1 - i√23)/4
How to solve the quadratic function?For a general quadratic:
a*x^2 + b*x + c = 0
The solutions are given by the quadratic formula
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here we have the quadratic equation:
2x^2 + x + 3 = 0
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}[/tex]
So we will have two complex solutions, these are:
x = (-1 + i√23)/4
x = (-1 - i√23)/4
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on average a customer waits 10 minutes in a queue and customers arrive at the rate of two per minute. how many customers are waiting in the queue on average
The average number of customers waiting in the queue is 20
In this question, we have been given that the customers arrive at the rate of two per minute.
On average a customer waits 10 minutes in a queue.
We need to find the number of customers waiting in the queue on average.
Assume that the average number of customers waiting in the queue is N.
We have the average Rate of Arrival = 2 customers per minute
So, by the formula for average waiting time under the Single-Server Queue Model,
10 = N/2
N = 10 * 2
N = 20
The average number of customers waiting according to the single-server queue model given the above conditions is 20
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What is the value of b?
Enter your answer in the box.
What is the length of segment AC?
By using the property of congruency, it can be calculated that
Length of line segment AC is 26 units
What are congruent triangles?
Two triangles are said to be congruent if their corrosponding sides are equal and the corrosponding angles are equal.
There are six axioms of congruency. They are
AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom
In [tex]\Delta[/tex] ABC and [tex]\Delta[/tex] XYZ,
[tex]\angle[/tex]B = [tex]\angle[/tex]Y [Given]
[tex]\angle[/tex]C = [tex]\angle[/tex]Z [Given]
BC = YZ [Given]
[tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] XYZ [ASA axiom]
AC = XZ [Corrosponding parts of congruent triangles are congruent]
AC = 26 units
Length of line segment AC is 26 units
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Compare the function f(x)=3x-1/2 to the function shown in the graph. Which statements are correct?
Answer: B
Step-by-step explanation:
For [tex]f(x)=3x-\frac{1}{2}[/tex], comparing it with slope-intercept form yields that the slope is [tex]3[/tex] and the [tex]y[/tex]-intercept is [tex]-1/2[/tex].
For the graphed function, the slope is [tex]\frac{-4-0}{-2-6}=\frac{1}{2}[/tex] and the [tex]y[/tex]-intercept is about [tex]-3[/tex].
Since the absolute value of the slope of the graphed function is less than that of [tex]f(x)[/tex], option B is correct.
Please answer with the equation
The perimeter of a rectangle is 80 inches. The width of the rectangle is 5 less than triple the width?
The length is 28.75 inch and width is 11.25 inch.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Perimeter= 80 inches
let the width be x.
length= 3x- 5
Now, perimeter of a rectangle = 2( l+ w)
80= 2( x+ 3x- 5)
40 = 4x -5
45 = 4x
x= 11.25
and, length = 3(11.25)- 5 = 28.75
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Which model represents the equation 6x = 18
Answer:
top right
Step-by-step explanation:
6x3=18
6/22, 3:45 PM
Kris said, "The Rawlings Rockets basketball team does not have any really tall players." These are the players'
heights in inches:
70, 77, 75, 68, 88, 70, and 72.
a. Which number does not seem to fit this set of data? 1
b. Do you agree or disagree with Kris?
2
Answer:
a. 88
b. I disagree with Kris
Step-by-step explanation:
88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.
(3+2)to the power of 2 + 4x8*
Pls help asap
Annie is
picking apples with her sister.
The number of apples in her
basket is described by n =
22t + 12, where t is the number
of minutes Annie spends picking
apples. What do the numbers 22
and 12 tell you about Annie's
apple picking? What is the
domain of this function?
The indications of the numbers in the linear equations that produces the number of apples in Annie's basket, n = 22·t + 12, are as follows;
22 is the number of apples Annie picks each minute12 is the initial number of apples in Annie's basket at the startThe domain of the function n = 22·t + 12 is R⁺ which is the set of positive real numbers, including zero, [0, ∞)
What is a linear equation and what is the domain of a function?A linear equation is a equation of the line of a straight line graph. The domain of a function is the set of the input values of the function.
The equation that describes the number of apples in Annie's basket, n = 22·t + 12
The number of minutes Annie spends picking apples = t
The number of apples in Annie's basket = n
The number 22 which is the coefficient of the variable t in the linear equation, which is the slope or the rate of change of the number of apples in Annie's, which indicates the number of apples Annie picks per minute.
The number 22 indicates that Annie picks 22 apples every minuteThe number 12 is the y-intercept of the equation y = 22·t + 12
The y-intercept is the value of the function where t = 0, which is the initial value of the function.
Therefore;
The number 12 indicates the initial number of apples in Annie's basket.The domain of the function n = 22·t + 12, are the possible values of the independent or input variable, t, which is the set of positive integers including 0
Therefore, the domain of the function is; [0, ∞), or the set of positive real numbers, R⁺ including zero R⁺ ∪ {0}.Learn more about linear equations here:
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Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0. 40. 040, point, 04 liters. Then, he wants to fill the tank with water until it's completely full. If he uses 505050 marbles, he will have to add 333333 liters of water. What is the volume of the tank?.
The total Volume of tank = 35 liters
What is Volume ?In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. Sometimes it is referred to as the
According to the Given information
Volume of each marble = 0.04 liters
Number of marbles to be put in the water tank = 50 marbles
Volume of 50 marbles = 0.04 × 50 = 2 liters
Volume of water added to the tank = 33 liters
Total Volume of tank = 2 liters + 33 liters
= 35 liters
SO,
The total Volume of tank = 35 liters
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Consider Y= F(x) =2- 3x. using the space determine the equation that represents the inverse of f(x) 
Answer: [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
===============================================
Work Shown:
[tex]f(\text{x}) = 2-3\text{x}\\\\\text{y} = 2 - 3\text{x}\\\\\text{x} = 2 - 3\text{y}\\\\\text{x} + 3\text{y} = 2\\\\3\text{y} = 2-\text{x}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
-----------------
Explanation:
The process to find the inverse involves this outline.
Replace f(x) with y.Swap x and y.Solve for y.This process is followed in the "work shown" portion above.
To confirm the answer, let g(x) be the inverse of f(x).
If they were inverses of each other, then these two properties would hold true:
f( g(x) ) = xg( f(x) ) = xHere's the verification for the first part.
[tex]f(\text{x}) = 2-3\text{x}\\\\f(g(\text{x})) = 2-3*g(\text{x})\\\\f(g(\text{x})) = 2-3*\frac{2-\text{x}}{3}\\\\f(g(\text{x})) = 2-(2-\text{x})\\\\f(g(\text{x})) = 2-2+\text{x}\\\\f(g(\text{x})) = \text{x}\\\\[/tex]
I'll let you do the other confirmation.
f(x) = 3x³ + 4x² - 2x + 8 and g(x) = 2x³+3x²+5x+2. Find f(x) + g(x)
The value of f(x)+g(x) is 5x³+7x²+3x+10
Given that,
f(x)=3x³+4x²-2x+8
g(x)=2x³+3x²+5x+2
f(x)+g(x)=3x³+4x²-2x+8+2x³+3x²+5x+2
=3x³+2x³+4x²+3x²+5x-2x+8+2
=5x³+7x²+3x+10
Step-by-step explanation:
This question is a type of quadratic equation. To solve this type of question first, we have to put the values of f(x) and g(x). Then we have to put similar terms(which have similar coefficients with similar power)together. Then we add the similar term of f(x) with the similar term of g(x) like 3x³+2x³=5x³, 4x²+3x²=7x², 5x-2x=3x and 8+2=10
Therefore the value of f(x)+g(x) is 5x³+7x²+3x+10
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find using distributive property.{[7]\frac{x}{y}[/5]×([-3]\frac{x}{y}[/12])}±{[7]\frac{x}{y}[/5]×[5]\frac{x}{y}[/12]
The value of expression will be;
⇒ 7 / 30
⇒ - 14/15
What is Distributive property?
By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.
Given that;
The expression is,
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
Now,
Since, The expression is,
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
Solve the expression by using distributive property as;
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
⇒ [ 7/5 ] × [ - 3/12 ± 5/12 ]
It gives two solution as;
⇒ 7/5 × [ - 3/12 + 5/12 }
⇒ 7/5 × 2/12
⇒ 7/5 × 1/6
⇒ 7 / 30
And, 7/5 × [ - 3/12 - 5/12 }
⇒ 7/5 × - 8/12
⇒ 7/5 × - 2/3
⇒ - 14 / 15
Thus, The value of expression will be;
⇒ 7 / 30
⇒ - 14/15
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In Japan, the ratio of vending machines to people is 1 to 24. In the city of Osaka there are about 2,400,000 people. How many banding machines are there in Osaka?
From the given ratio, there is a total of 100,000 vending machines in Osaka.
What is the ratio?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.
Given, the ratio of vending machines to people is 1 to 24
That means, for every vending machine, there are 24 people.
In the city of Osaka, there are about 2,400,000 people.
So, the number of vending machines = 2400000/24 = 100000
Hence, there is a total of 100,000 vending machines in Osaka.
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help me please, please write what i put on the sides too and what i put in the bottom right please and thank youuuuu
The values obtained after solving the given equation is x = 6 and y = 10.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
The given equations are,
-5x + 3y = 0 (i)
7x - 4y = 2 (ii)
Multiply equation (i) by -7 and equation (ii) by 5.
35x - 21y = 0 (iii)
35x - 20y = 10 (iv)
Now, solve the equation for y, because 35x in positive and 35x in negative cancel out each other.
-y = -10
y = 10
Substitute y = 10 in equation (i)
-5x + 3(10) = 0
-5x = -30
x = 30/6
x = 5
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Evan drew 8 pictures. Alexa drew p fewer pictures than Evan. Write an expression that shows how many pictures Alexa drew?
An expression or equation that shows how many pictures Alexa drew is 8-p.
What is an equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Given, Evan drew 8 pictures.
Alexa drew p fewer pictures than Evan.
then, Alexa = 8-p
Hence, an expression or equation that shows how many pictures Alexa drew is 8-p.
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Triangle ABC is translated 4 units to the right and 3 units down.
What are the coordinates of the new triangle?
Responses
(−2,3),(3,1),(−2,1)
( − 2 , 3 ) , ( 3 , 1 ) , ( − 2 , 1 )
(−2,0),(3,−2),(−2,−2)
( − 2 , 0 ) , ( 3 , − 2 ) , ( − 2 , − 2 )
(0,−2),(−2,3),(2,−2)
( 0 , − 2 ) , ( − 2 , 3 ) , ( 2 , − 2 )
(−6,0),(−6,−2),(−1,−2)
Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].
What is the coordinates?
A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by [tex](x,y)[/tex] the x-value and y-value.
Here given coordinates are
[tex](-2,3),(3,1),(-2,1)\\\\(-2,0),(3,-2),(-2,-2)\\\\( - 2 , 0 ) , ( 3 , - 2 ) , ( - 2 , -2 )[/tex]
Suppose [tex]a[/tex] units on the horizontal and [tex]b[/tex] units on the vertical. Then, the new coordinate become
[tex]A(x,y)=A(x+a,y+b)[/tex]
As per the question triangle [tex]ABC[/tex] is translated [tex]4[/tex] units to the right and [tex]-3[/tex]units down.
So, [tex]a=4,b=-3[/tex] and the coordinates are
[tex]A(-2,3),B(3,1),C(-2,1)\\\\[/tex]
Then,
[tex]A(-2+a,3+b)=A(-2+4,3-3)=A(2,0)\\\\B(3+a,1+b)=B(3+4,1-3)=B(7,-2)\\\\C(-2+a,1+b)=C(-2+4,1-3)=C(2,-2)[/tex]
Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].
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Fred deposits $6,500 in a saving account that pays 0.5% interest, compounded quarterly. Round each answer to the nearest cent.
a. Find the first quarter's interest.
b. Find the first quarter's ending balance.
c. Find the second quarter's interest.
d. Find the second quarter's ending balance.
e. Find the third quarter's interest.
f. Find the third quarter's ending balance.
g. Find the fourth quarter's interest.
h. What is the balance at the end of one year?
i. How much interest does the account earn in the first year?
The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;
a. Interest for the first quarter = $8.125
b. First quarter ending balance = $6,508.125
c. Interest for the second quarter = $8.13515625
d. Second quarter ending balance = $6,516.26015625
e. Interest for the third quarter = $8.1432520325
f. Third quarter closing balance = $6,524.40548145
g. Interest for the fourth quarter = $8.15550685975
h. The amount of interest earned in a year is about $32.56
What is an interest earned on an amount?
An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.
The amount Fred deposited, P = $6,500
The interest paid by the account, r = 0.5% compounded quarterly
a. The first quarter interest can be found by the formula;
C.I. = P[tex](1+ r/4)^{4 . 1/4}[/tex] - P
Therefore
C.I. = 6500 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6500 = 8.125
b. The first quarter ending balance is therefore;
A = P + C.I.
A = $6,500 + $8.125 = $6,508.125
c. The second quarter's interest can be found from the formula;
C.I. = 6508.125 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6508.125 = 8.13515625
The second quarter's interest is $8.13515625
d. The second quarter ending balance is therefore;
A = $6,508.125 + $8.13515625 = $6,516.26015625
The second quarter ending balance is $6,516.26015625
e. The third quarters interest is therefore;
C.I. = 6516.26015625 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6516.26015625 = 8.1432520325
The third quarter's interest is about $8.1433
f. The third quarter's ending balance is therefore;
A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145
The third quarter's ending balance is $6,524.40548145
g. The fourth quarter's interest can be found as follows;
C.I. = 6524.40548145 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6524.40548145 = 8.15550685975
The fourth quarter's interest is; $8.15550685975
h. The balance at the end of one year is therefore;
Balance = C.I. fourth quarter + Principal for the fourth quarter
Therefore;
Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831
i. The interest the account earns in a year is therefore;
$6,532.56098831 - $6,500 = $32.5609883
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Angles x and y are supplementary. angle x measures 132.54°, and angle y measures (m − 15)°. find m∠y. 47.46° 62.46° 85.08° 117.54°
The value of the angle y will be equal to 47.46. The correct option is A.
What is a supplementary angle?Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles because the sum of 130° and 50° equals 180°.
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Given that the angle x is equal to 132.54°. The value of the angle y will be calculated as,
x + y = 180
132.54 + y = 180
y = 180 - 132.54
y = 47.46
Therefore, the value of the angle y will be equal to 47.46. The correct option is A.
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solve for x and y y=6x+12 y=x+47
The value of x = 7 and y = 54.
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
Here, we have
Given: y = 6x+12 and y = x+47
We have to solve this equation and find the value of x and y.
y = 6x+12....(1)
y = x+47.....(2)
We put the value of y in equation (1) and we get
x + 47 = 6x + 12
6x -x = 47 -12
5x = 35
x = 7
Now, we put the value of x in equation(2) and we get
y = 7 + 47
y = 54
Hence, the value of x = 7 and y = 54.
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PLS HELP Which function has the same slope as the graph of the function represented by the table.
The slope of the given function is 0.25. The function that has the same slope is y = 0.25x + 5. Option B is the correct option.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given table is
x 0 1 2 3
y -0.5 -0.25 0 0.25
The slope of a function that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁)
Assume that x₁ = 0, y₁ = -0.5, x₂ = 1, y₂ = -0.25
The slope of the function is [-0.25 - (-0.50)]/(1 - 0) = 0.25
Now compare the equation y = -0.25x - 2 with y = mx + c
m = -0.25
The slope of the function is -0.25.
Now compare the equation y = 0.25x + 5 with y = mx + c
m = 0.25
The slope of the function is 0.25.
Now compare the equation y = 4x - 5 with y = mx + c
m = 4
The slope of the function is 4.
Now compare the equation y = -4x + 34 with y = mx + c
m = -4
The slope of the function is -4.
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Consider the line -7x-3y = 1.
Find the equation of the line that is perpendicular to this line and passes through the point (-7, 4).
Find the equation of the line that is parallel to this line and passes through the point (-7, 4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line:
Equation of parallel line:
0
X
0=0
S
Answer:
Parallel: Y= -7/3x - 37/3
Perpendicular: Y=3/7x + 7
Step-by-step explanation:
Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.
Remember when the slope is parallel it's always the same slope in this case -7/3
When perpendicular flip it and change the sign 3/7
Does anyone know the answer?
Answer:
d = 5m
Step-by-step explanation:
Look at point (1, 5).
When the number of months is 1, the amount in dollars is 5.
The amount in dollars is always 5 times the number of months.
d = 5m
which age group has more variable finish times
Answer:
l
v
Step-by-step explanation:
80, 5, 30, 7, and 3,
You have two exponential functions. One has the formula h(x) = 3x – 2. The other function, g(x), has the graph shown below.
Which inequality below is true for all points on the indicated interval?
A g( x) ≥ h( x) on the interval –3 ≤ x ≤ 3
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2
C g( x) ≤ h( x) on the interval –3 ≤ x ≤ 3
D g( x) ≤ h( x) on the interval –2 ≤ x ≤ 2
The correct statement regarding the exponential functions g(x) and h(x) is given as follows:
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.
What is an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients of the function are described as follows:
a is the y-intercept, the value of y at which the function crosses the y-axis.b is the rate of change of the exponential function.Function h(x) is defined as follows:
h(x) = 3^x - 2.
For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:
a = 4.
When x = 1, y = 5, hence the rate of change of the function is obtained as follows:
b = 5/4.
b = 1.25.
Then function g(x) is given as follows:
g(x) = 4(1.25)^x.
Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.
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pls help!
select the row of Pascal's triangle that is used to expand the binomial expression (2x^3+3y^2)^7
Row one: 1
Row two: 1 1
Row three: 1 2 1
Row four: 1 3 3 1
Row five: 1 4 6 4 1
Row six: 1 5 10 10 5 1
Row seven: 1 6 15 20 15 6 1
Row eight: 1 7 21 35 35 21 7 1
Row nine: 1 8 28 56 70 56 28 8 1
The row of Pascal's triangle that is used to expand the binomial expression (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.
What is a binomial expression?A binomial expression is an expression that contains only two terms.
What is Pascal's triangle?Pascal's triangle is an algorithm for finding the coefficients of a binomial expansion.
How to find the row that is used to expand the binomial expression (2x³ +3y³)⁷?Since we require the expansion of the binomial expression (2x³ +3y³)⁷ using Pascal's triangle, we note that, the power of the binomial expression is always equal to the second and second to the last coefficient of the terms in the Pascal's triangle.
So, we see that the Row eight: 1 7 21 35 35 21 7 1, satisfies this condition.
So, the row of Pascal's triangle that is used to expand the binomial expression (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.
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The starting salary for a new employee is 25,000. The salary for this employee increases by 8% per year. what is the salary after 1 year?
Answer: $27,000
Step-by-step explanation:
1) In the figure below Zy Zz and segment
AB I CD.
What is the length of AE?
F. 18
G. 20
H. 24
J. 30
Answer:
F
Step-by-step explanation:
15/10 = x+12/12
180=10x+120
x=6
x+12=18=AE