Answer:
X=1
Step-by-step explanation:
9x -4 = 2x+3 :
9x-4=2x+3
9x -4 + 4= 2x + 3+4
Simplify
subtract 2x from both sides
Simplify
Divide both sides by the same factor
simplify
X=1
g(x)=3/4f(x) graphed
The function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is the following equation-
g(x) = 3/4 f(x)
Since, the functions are not given, we will assume them by ourselves. You can use the same procedure for any pair of functions of the form -g(x) = n f(x)
Assume that -
f(x) = 2x + 1
Now -
g(x) = (3/4) f(x)
g(x) = (3/4)(2x + 1)
g(x) = (3/2)x + 3/4
Now, both the graphs f(x) and g(x) are attached below. In general, g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4).
Therefore, the function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.
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1. consider a lottery with three possible outcomes: $125 will be received with probability 0.25, $100 will be received with probability 0.3 and $50 will be received with probability 0.45. a. what is the expected value of the lottery? b. what is the variance of the outcome? c. what would a risk-neutral person pay (at most) to play the lottery?
The lottery's anticipated worth is $80.
Given that,
The probability of receiving $125 is 0.25; the likelihood of receiving $100 is 0.3; and the likelihood of receiving $50 is 0.45.
A) EV=125*.2+100*.3+50*.5=$80
The lottery's anticipated worth is $80.
The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is what we have: ;;
125(0.2) + 100(0.3) + 50(0.5) (0.5)
= 25 + 30 + 25 = $80
B) This is the formula for variance is shown in figure :
So, we can calculate the variance as follows:
.2*(125-80)^2+.3*(100-80)^2+.5*(50-80)^2=975
C) A risk-neutral person would pay $80 or less to play the lottery.
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Answer:
Step-by-step explanation:
Expected value of the lottery is $83.75.
Variance of the outcome is 909.6.
A risk-neutral person would pay $83.75 or less to play the lottery.
a) The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is,
125(0.25) + 100(0.3) + 50(0.45)
= $83.75
b) we can calculate the variance as follows:
Variance=.25*(125-83.75)^2+.3*(100-83.75)^2+.45*(50-80)^2=909.6
c) A risk-neutral person would pay $83.75 or less to play the lottery.
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The largest angle of a triangle measures 9degrees less than 5 times the measure of the smallest angle. The middle angle measures three times that of the smallest angle. Find the measures of the three angles.
Let the smallest angle be represented as
[tex]=x[/tex]Step 1: The largest angle of a triangle(let the largest angle =z) measures 9degrees less than 5 times the measure of the smallest angle, this statement is represented as
[tex]\begin{gathered} 5\text{ times the smallest angle gives} \\ =5\times x \\ =5x \\ 9\text{ degr}ees\text{ less will give the largest angle to be} \\ \text{largest angle =5x-}9 \\ z=5x-9 \end{gathered}[/tex]Step 2: let's calculate the middle angle (let the middle angle =y)
The middle angle measures three times that of the smallest angle, which means that
[tex]\begin{gathered} y=3\times x \\ \text{middle angle =y= 3x} \\ y=3x \end{gathered}[/tex]Recall that the total angles in a triangle give
[tex]=180^0[/tex]Therefore,
[tex]\begin{gathered} \text{largest angle + middle angle + smallest angle =180}^0 \\ z+y+x=180^0 \end{gathered}[/tex]Substituting we will have
[tex]\begin{gathered} 5x-9+3x+x=180^0 \\ \text{collect the sinmilar terms we will have} \\ 5x+3x+x=180^0+9^0 \\ 9x=189^0 \\ \text{divide both sides by 9} \\ \frac{9x}{9}=\frac{189^0}{9} \\ x=21^0 \end{gathered}[/tex]Hence,
the smallest angle is = 21 degrees
[tex]\begin{gathered} \text{The largest angle =5x-9} \\ =5\times21^0-9 \\ =105^0-9 \\ =96^0 \end{gathered}[/tex]Hence,
The largest angle = 96 degrees
[tex]\begin{gathered} \text{The middle angle=}3x \\ =3\times21^0 \\ =63^0 \end{gathered}[/tex]Hence,
The middle angle = 63 degrees
State the transformation performed on the parent function.
The personal assets and liabilities of a carpenter are listed below.
What is the carpenter's net worth?
$139,450
$145,228
$281,313
$284,678
$139,450
==========================================================
Explanation:
asset = an item that is either cash or can be turned into cash
liability = something that needs to be paid back (eg: truck loan)
A = total assets
A = (homeValue) + (workEquipment) + (carValue) + (investments)
A = ( $175,742 ) + ($3,365) + ($44,346) + ($61,225)
A = $284,678
B = total liabilities
B = (mortgage)+(credit card balance)+(truck loan)
B = ($76,765)+($2,055)+($66,408)
B = $145,228
C = net worth
C = A - B
C = ($284,678) - ($145,228)
C = $139,450 which points us to choice A as the final answer.
The net worth of the carpenter is $144,633.
Given that, Home value = $175,742, Mortgage = $76,765, Credit card balance = $2,055, Owned work equipment = $3,365 and Car value = $44,346.
What is the net worth?Net worth is the value of all the non-financial and financial assets owned by an individual or institution minus the value of all its outstanding liabilities.
Here,
Net worth = Financial assets - Liabilities
= (175,742+3,365+44,346) - (76,765+2,055)
= 223,453 - 78,820
= $144,633
Therefore, the net worth of the carpenter is $144,633.
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What's the circumference of a circle with a diameter of 31 inches
Answer:
C≈97.39in
Step-by-step explanation:
Answer:97.39
Step-by-step explanation:
Ms. Gartland bought x number of shirts for the new members of her chorus. The cost for x number of shirts, including $3.99 shipping, was $77.49. Each shirt cost $12.25. There was no sales tax on this purchase. Which equation could be used to find x?A. 3.99(+12.25)=77.49B. 3.99+12.25=77.49C. 12.25(+3.99)=77.49D. 12.25+3.99=77.49
the expression for the given situation is given as follows,
12.25x + 3.99 = 77.49 $
here, x = no. of shirt
so the correct answer is option D
10
-90+30+(−10)+ +... n = 16
3
in a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices
The probability that the randomly selected sample is vulnerable or critically endangered is equal to 0.76
The probability can be determined using the following formula;
probability = number of desired events or outcomes ÷ total number of events or outcomes
The total is known to be 45, the favorable or desired outcomes can be calculated as follows;
number of desired outcomes = number of vulnerable species + number of critically endangered species
number of desired outcomes = 12 + 22
number of desired outcomes = 34
Now we calculate the probability by using the above formula;
probability = 34 ÷ 45
probability = 0.76
Therefore, 0.76 is the probability that the randomly selected species is vulnerable or critically endangered.
Although a part of your question is missing, you might be referring to this question:
In a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices
11/45
0.24
0.83
0.76
12/45
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4 Given the table below, which student wrote a correct equation between the number of horses, x, and the cost of boarding, y? # of Horses Cost O C. Tori only 37 4 99 TORI 31x - 2y = 74 J A. Both Laquita and Tori go to 6 go to 1 8 161 10 192 12 223 LAQUITA y = 15.5x +37 B. Neither Laquita nor Tori D. Laquita only go to 9 go to 8
Both Laquita and Tori wrote a correct equation which is the correct answer would be an option (A).
Let the required line would be as
⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )
Here x₁ = 0 and y₁ = 37
x₂ = 4 and y₂ = 99
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 37 = (62/4)x
⇒ y - 37 = 15.5x
⇒ y = 15.5x +37
This equation is written by Laquita.
Multiply by 2 both sides of the equation,
⇒ 2y = 31x + 74
⇒ 31x - 2y = 74
This equation is written by Tori.
Therefore, both Laquita and Tori wrote a correct equation.
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Need to find the mean, median, mode, and midrange.
The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.
Explain about mean median mode?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The value that appears the most frequently on the list is the mode.
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1. How many ways can you flip a coin and roll four-sided tetrahedron dice?
Draw the tree diagram in the space provided below.
Answer:
Step-by-step explanation: I cant do the tree Diagram, however, I will help if you flip a coin (Heads or tails) The chances of it landing on heads will divide by 2 every time its heads or tails again and vise versa .
HELP ASAP
You are working as a car salesperson. You make $13.25 per hour. You are paid biweekly (two weeks of work). Your boss encourages competition between employees by letting you know that you will receive a commission of $150 for each new car you sell.
In the first week, you work 25 hours and sell 3 cars.
In the second week, you work 18 hours and sell 2 cars.
How much will your total pay be at the end of these two weeks?
Total pay be the at the end of the two weeks with rate of $13.25 per hour and commission of $150 for selling each new car is $1319.75.
As given,
Rate of salesperson per hour pay = $13.25
Commission on selling each new car =$150
Amount of the pay earned by salesperson:
First week :
25 (13.25) + 3 (150)
= 331.25 + 450
= $781.25
Second week:
18 (13.25) + 2(150)
= 238.5 +300
= $538.50
Total pay of salesperson at the end of two weeks
=$(781.25 +538.5)
=$1319.75
Therefore, total pay be the at the end of the two weeks with rate of $13.25 per hour and commission of $150 for selling each new car is $1319.75.
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Explain in detail with at least two sentences how to represent the difference of z1 and z2 geometrically, given that z1= −7i and z2 = 4+3i. Then, give the difference z1 − z2 in rectangular form.
Given that z₁= −7i and z₂ = 4+3i, the difference z₁ − z₂ in rectangular form is; -4 - 10i
What is the Vector in rectangular form?Addition of complex numbers is basically the same thing as adding two-dimensional vectors that are located on the x-y Cartesian plane.
Now, it is pertinent to note that when doing vector addition, we denote the x-component with i^ and y-component with j^.
We should also not that when adding complex numbers, the x-component is the real part and y-component is the imaginary part.
Geometrically, we can say that the addition of complex numbers can be equated to the addition of vectors in x-y plane.
Thus by the the parallelogram law of vector addition, we will be able to find the resultant vector.
In rectangular coordinates,
z₁ = -7i
z₂ = 4 + 3i
Then, z₁ - z₂ = -7i - (4 + 3i)
= -7i - 4 - 3i
= -4 - 10i
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En una circunferencia señalamos diez puntos. ¿Cuál es la diferencia entre el número de heptágonos y el de triángulos cuyos vértices son algunos de esos puntos?
Answer:
ok wirrudi 123 alf8 434 21 3dis w
Find the values of x and y that maximize the objective function
Answer: D
Step-by-step explanation:
A. [tex]P=2(4)-3=5[/tex]
B. [tex]P=2(0)-3=-3[/tex]
C. [tex]P=2(0)-0=0[/tex]
D. [tex]P=2(4)-0=8[/tex]
Plot the intercepts to graph the equation
8x-3y=-24
Answer:
Step-by-step explanation:
Use the values In 8 ≈ 2.08 and In 1000≈6.91 to find the approximate value of log8 1000
The approximate value of log₈1000 is 0.30.
What are logarithms?The inverse of power is a logarithm. When you take the log of a number, you reverse the exponent.Logarithms normally use a base of 10 (but a different value can be provided), whereas natural logs always use a base of e. Use the following calculation to convert between logarithms and natural logs.[tex]log_{10}x[/tex] [tex]= ln(x) / ln(10)[/tex]
The given values are:
In 8 ≈ 2.08 and In 1000 ≈ 6.91
To find the approximate value of log₈1000,
log₈1000 = In 8/In 1000
= 2.08/6.91
≅ 0.30
Therefore, the approximate value of log₈1000 is 0.30.
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Write the equation for the line that passes through the given point and is perpendicular to the given line (1,7); x - 4y = 8
The equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3
Given : x - 4y = 8
4y = x- 8
On dividing by 4 we get;
y= x/4 - 2
This is of the form y = mx + c
Thus m in this case on comparing we get m= 1/4
We know the formula of the slope ;
y - y₁ =m ( x - x₁ )
y - 1 = 1/4 ( x- 7)
On cross multiplying we get ;
x- 4y = 3
Thus the equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3 .
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write a real world situation for which the rate of change is -15
The most appropriate choice for velocity and accleration will be given by- Deacceleration of a car of 15 [tex]m/s^2[/tex] is a real world situation for which the rate of change is -15
What is velocity and acceleration?
Velocity
The distance travelled by a body per unit interval of time where the direction of the motion of a body is taken into account is known as velocity.
Velocity is a vector quantity as direction of motion of body is taken into account.
If d is the displacement of body and t is the time,
Velocity = [tex]\frac{d}{t}[/tex]
Acceleration
The rate of change of velocity of a body is called acceleration.
Acceleration is a vector quantity as direction of motion of a body is taken into account.
If [tex]\Delta[/tex]v is the change of velocity and t is the time,
Acceleration = [tex]\frac{\Delta v}{t}[/tex]
If velocity decreases then it is called Deacceleration
Here
Deacceleration of a car is 15 [tex]m/s^2[/tex]
That means rate of change of velocity of a car is -15 [tex]m/s^2[/tex]
This is a real world situation for which the rate of change is -15
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Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Correct option are C,D, E. g(x) > h(x) for x = -1, For positive values of x, g(x) > h(x), For negative values of x, g(x) > h(x).
What are functions?A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
They have the same value if x=0.
The first and second choices are not viable
for x=-1
g(-1)=1
h(-1)=-1
3. is accurate
4th , false G(x)>H for all values other than zero (x)
the proper ones are
For x=-1, g(x) exceeds h(x).
G(x) > h for positive values of x. (x).
G(x) > h for negative values of x (x).
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(20pts, 5pts each) The median of AMND from vertex N of the
isosceles trapezoid MNFD is 5cm. The diagonal ND is
perpendicular to the leg MN. The shorter base NF = 6cm and the
32cm².
A
MNFD
=
Find: MD, the altitude of the trapezoid h, the length of the
legs of the trapezoid and the ratio between the areas of AMND and
ANFD.
Answer:
MD = 10 cmh = 4 cmMN = FD = 2√5 cm ≈ 4.47 cmarea ratio = 5 : 3Step-by-step explanation:
Given isosceles trapezoid MNFD with short base NF = 6 cm, diagonal ND perpendicular to leg MN, and triangle MND median NX = 5 cm, you want ...
length MDaltitude h of the trapezoidlengths of MN and FDratio of areas of ∆MND and ∆NFDMDMD is the hypotenuse of right triangle MND. The median from the right angle of a right triangle is half the length of the hypotenuse, so ...
MD = 2·NX = 2·(5 cm)
MD = 10 cm
AltitudeIn the attached diagram, we see that right triangle XYN has side XY = 3 (half of NF), and hypotenuse NX = 5 (given). These are two sides of a 3-4-5 right triangle, so the remaining side, altitude h, is 4.
h = 4 cm
Side lengthsThe attache diagram shows congruent side lengths MN and FD are the hypotenuse of a right triangle with sides YM = 2 and YN = 4. The Pythagorean theorem tells us the length of side MN is ...
MN² = MY² +NY²
MN² = 2² +4² = 4 +16 = 20
MN = √20
MN = FD = 2√5 ≈ 4.47
Area ratioTriangle MND has a base length MD = 10 and a height h = 4. Triangle NFD has a base length NF = 6 and a height h = 4. The ratio of the areas of these two triangles is ...
[tex]\dfrac{A_{MND}}{A_{NFD}}=\dfrac{\frac{1}{2}\cdot10\cdot4}{\frac{1}{2}\cdot6\cdot4}=\dfrac{10}{6}=\boxed{\dfrac{5}{3}}[/tex]
The ratio between the areas is 5 : 3.
__
Additional comment
We are also given the area of the trapezoid as 32 cm². That can be used to find the longer base and/or the altitude, or to check the answers we have for those values. It is redundant information.
The midpoint X of MD is the center of the circumscribing circle of the trapezoid and right triangles MND and MFD. The midpoint of the hypotenuse of a right triangle is always the circumcenter, so knowing the length NX tells us the radius of that circle, hence MX and XD.
The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons is 9 to 11. There are 55 gallons of gasoline. How many ounces of oil are there?
Given:
Ratio of ounces of oil to gallons of gasoline = 9 : 11
Gallons of gasoline = 55 gallons
Let's find the ounces of oil.
To find the ounces of oil, we have the equation:
[tex]\begin{gathered} \frac{\text{Ratio of ounces of oil}}{Ratios\text{ of gallons of gasoline}}=\frac{\text{Ounces of oil}}{\text{Gallons of gasoline}} \\ \\ \end{gathered}[/tex]Thus, we have:
[tex]\frac{9}{11}=\frac{x}{55}[/tex]Let x represent the ounces of oil.
Cross multiply:
[tex]\begin{gathered} 11x=9(55) \\ \\ 11x=495 \\ \\ \text{Divide both sides by 11:} \\ \frac{11x}{11}=\frac{495}{11} \\ \\ x=45 \end{gathered}[/tex]Therefore, there are 45 ounces of oil.
ANSWER:
45 ounces of oil
A pump fills a pool at a constant rate. At the end of 1 minute, it has filled 10 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
A
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
22 2020
44 4040
66 6060
B
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
11 1010
22 3030
44 5050
C
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
22 2020
44 2222
66 2424
D
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
11 1010
22 1111
44 1313
I'm sorry this is confusing :\
The answer is A, because if one minute corresponds to 10 gallons of water, then the amount of gallons is the minutes times 10.
ill give brainliest!!!!
Answer:
(f ⋅ g)(x) = f(g(x)) = 5·√(9 - x^2)
The domain is: -3 ≤ x ≤ 3
(g ⋅ f)(x) = g(f(x)) = √(9 - (5·x)^2)
The domain is: -0.6 ≤ x ≤ 0.6
Springfield Mini Golf offers its customers a
25-round pass for $84, or they can pay
$3.25 per round. Which option has the
lesser price per round?
Evaluate (-3)^8 and (-3)^9
The evaluation of the numbers (-3)^8 and (-3)^9 will be (-3)^17.
How to calculate the value?Based on the information given, it should be noted that this illustrates that the numbers are raised to power.
In this case, it should be noted that we want to multiply the powers, this illustrates that we gave to add the powers. This will be:
Evaluate (-3)^8 × (-3)^9
Note that 8 + 9 = 17. Therefore,
Evaluate (-3)^8 and (-3)^9
= -3^17.
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Evaluate (-3)^8 × (-3)^9
The product of 8 and n decreased by 5 is _________________ 25. less than greater than less than or equal to greater than or equal to
The statement that represents the given inequality is:
The product of 8 and n decreased by 5 is less than 25.
Which sentence represents the inequality?The inequality is defined as follows:
8(n - 5) < 25.
The meaning of the expression n - 5 is given as follows:
n decreased by 5. (n is an unknown number).
The meaning of the expression 8(n - 5) is given as follows:
The product of 8 and n decreased by 5. (multiplication of two numbers is also called product).
The symbol of the inequality is given as follows:
<
Which represents the expression less than.
Considering the 25 on the other side of the inequality, the complete sentence is given as follows:
The product of 8 and n decreased by 5 is less than 25.
Missing informationThe complete problem is:
Sal wrote the statement below to represent the inequality 8(n - 5) < 25. Which words should Sal use to complete the verbal statement? The product of 8 and n decreased by 5 is ___________
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if you want to just give me the answer that would be fine. i just want to make sure i’m correct.
Okay, here we have this:
Considering that if the graph of the line rises from left to right, then it means that the slope is positive. On the other hand, if the graph of the line falls from left to right, the slope will be negative.
So, according with this finally we obtain that the correct answer is that the slope is negative.
Answer:
Negative
Step-by-step explanation:
Because MATH
Form a polynomial whose zeros and degree are given.
Zeros: -7, multiplicity 1; -2, multiplicity 2; degree 3
MODE
Type a polynomial with integer coefficients and a leading coefficient of
f(x) = (Simplify your answer.)
Let p(x) be the required polynomial.
we are given that p(x) has a zero 1 with multiplicity 2
in other word, this means that (x-1) occurs twice as a factor of p(x).
How Do Polynomial Functions Work?Expressions with polynomial functions include variables with various degrees, non-zero coefficients, positive exponents (of variables), and constants. A polynomial in "b" of degree 2 is, for instance, f(b) = 4b2 - 6.
Likewise, (x-3) appears as a factor of p(x) once.
we are also given that the degree of p(x) is 3.
So, p(x) can not have more than 3 linear factors.
Altogether,
p(x) = k(x-1)^2 (x-3), where constant k ∈ R - {0}.
We may take k = 1 and get the desired polynomial,
p(x) = ( x-1)^2 ( x-3) = x^3 - 5x^2 +7x -3
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