Let's begin by identifying key information given to us:
Height = 50 m
velocity = 4m/s
The input variable is the number of seconds
The output variable is the theight of the ballon
The equation:
[tex]\begin{gathered} y=4x+50 \\ \text{Comparing this equation with the standard equation,}y=mx+b \\ \Rightarrow m=4,b=50 \\ m=4 \end{gathered}[/tex]Therefore, the rate of change equals 4
If 3x = 21 find the value of x-8
PLEASE HELPPPP
x − 8 = − 10
Explanation: 9x −13 = − 31 Add 13 to each side.
Answer:
-1
Step-by-step explanation:
3x = 21
Divide both sides by the co efficient of x
3x = 21
3 3
x = 21/3
x = 7
Find x - 8
x = 7
7 - 8
= -1
f a 10 percent reduction in price leads to a 20 percent increase in quantity demanded, the coefficient of elasticity of demand would be equal to _______
The coefficient of elasticity of demand would be equal to 2 .
The price elasticity of demand for a good determines how responsive the desired amount is to the price (PED).
When prices rise, demand declines for almost all products, but some products are more negatively impacted than others. When a price increases by 1% while all other factors remain constant, the price elasticity provides the percentage change in quantity required. If the elasticity is 2, a 1% increase in price results in a 2% drop in the amount sought. The effect of changes in other variables on the necessary quantity is measured by various elasticities.We know that the coefficient of elasticity of demand is given by
ED = Change in demand(percent) ÷ change in price (percent)
ED = 20% ÷ 10% = 2
Hence the coefficient of elasticity of demand would be equal to 2 .
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To celebrate its grand opening, a store is giving every 8th customer a 50$ gift certificate and every 5th customer a 10$ gift certificate. Which customer will be the first to receive both?
Find the expected payback for a game in which you bet $10 on any number from 0 to 999. If your number comes up, you get $2000
The expected payback is mathematically given as
$10
This is further explained below.
What is the expected payback?Generally, The formula for calculating the anticipated payback is the product of the likelihood times the value.
E(x) = p(x_1)*x_1 + p(x_2)*x_2 + .....
In this particular scenario, we have two distinct options for repayment.
winning
The payback is $2000-$10 = $1990
x_1 = 1990
The probability of winning is one out of 100 (since the choices are 0 to 99)
p(x_1) = 1/100
Losing
The payback is negative $8 since the individual did not win anything, which makes them lose.
x_2 = -10
Because there is only one number that can win, the other 99 numbers are considered to be losing numbers.
p(x_2) = 99/100
Therefore expected payback is
E(x) = p(x_1)*x_1 + p(x_2)*x_2
= (1/100)* 1990+ (99/100)*(-10)
= $10
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CQ
Find the expected payback for a game in which you bet $10 on any number from 0 to 999. If your number comes up, you get $2000
The expected payback is
what is perpendicular consider of?
Answer: straight line that makes the right angle (90 degrees) with the other
Step-by-step explanation: In other words, if two lines intersect each other at the right angle, then the lines are perpendicular to each other
Differentiate the function f(x)=sinx/(1+tanx)
Differentiation of the given function f(x)=sinx/(1+tanx) is equal to
(cos³x -sin³x) / (cos²x)(1 + tanx)².
As given in the question,
Given function : f(x) = sinx /(1 + tanx )
Let u = sinx , v = ( 1 + tanx)
Differentiate the given function with respect to x
du/dx = cosx
dv/dx = sec²x
= 1/cos²x
(d/dx)(f(x)) = (d/dx)(sinx /(1 + tanx ))
= ( d/dx) (u / v)
= [v (du/dx) -u (dv/dx)] / (v)²
= [(1+tanx)(cosx) -(sinx)(1/cos²x)] / (1 + tanx)²
= [cos²x(cosx + sinx) -sinx]/ (cos²x)(1 + tanx)²
= [cos³x +sinx(cos²x -1)] / (cos²x)(1 + tanx)²
= (cos³x -sin³x) / (cos²x)(1 + tanx)²
Therefore, differentiation of the given function f(x)=sinx/(1+tanx) is equal to
(cos³x -sin³x) / (cos²x)(1 + tanx)².
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13. Highlight the answer choice that represents the distance between the two points below. Round to the nearest hundredth if necessary. You may use a calculator.
A. 10
B. 28
C. 3100
D. 10
E. 310
F. 3.16
Supposing that the two points are (2,4) and (10,10), the distance between them is given by:
A. 10.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
For this problem, the two points are (2,4) and (10,10), hence the distance between them is given as follows:
[tex]D = \sqrt{(10 - 2)^2+(10 - 4)^2} = \sqrt{100} = 10[/tex]
Hence the distance is of 10 units and option A is correct.
What is the missing information?This problem is incomplete, and I could not find it on any search engine, hence we are going to suppose that the two points are (2,4) and (10,10).
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I need answer for this question
The probability that the aircraft is overloaded is 97.98%, which means the pilot should take the action.
In a Normal distribution with mean ц and standard deviation σ, the z-score of a measure x is given by:
Z = X-ц / σ
· It measures how many standard deviations the measure is from the mean.
· After finding Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
· By the Central Limit Theorem, the sampling distribution of sample means of the size n has standard deviation σ
σ = σ / [tex]\sqrt{n}[/tex]
σ is standard deviation
n is the sample size.
Given that the mean and the standard deviation of the population is 176.1 lb and 35.4 respectively.
⇒ ц = 176.1 and σ = 35.4
For a sample of 43 passengers, we have
n = 43
σ = [tex]\frac{35.4}{\sqrt{43}}[/tex]
σ = 5.398
Z = X-ц / σ
Z = [tex]\frac{165-176.1}{5.398}[/tex]
Z = -2.05 has p- value of 0.9798
The probability that the aircraft is loaded is
1 - p-value of Z
1 - 0.0202 = 0.9798
The probability that the aircraft is overloaded is 97.98%
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Find the area of the triangle:
Answer:30
Step-by-step explanation:
The sum of two numbers is 96. The difference of the two numbers is 42. What are the two numbers.
Let
x
be the larger number and
y
be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 96."
Correct
Write an equation that expresses the information in the sentence "The difference of the two numbers is 42."
Correct
Solve the system you have written above.
The larger number,
x
is
Correct. The smaller number,
y
is
Correct.
Question HelpQuestion 1: Message Message instructor
Submit QuestionQuestion 1
Using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27
Consider the largest number as x and the smallest number as y
The sum of two numbers is 96
The equation will be
x+y = 96
x = 96-y
The difference of the two numbers 42
x-y = 42
Use the substitution method here
Substitute the value of x in the second equation
x-y =42
(96-y)-y =42
96-2y = 42
-2y = 42-96
-2y = -54
y = 27
Substitute the value of y in the first equation
x+y = 96
x+27 = 96
x = 96-27
x = 69
Hence, using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27
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Find the equation of the linear function represented by the table below in slope-intercept form.X1234y-3-7-11-15
Answer:
The equation of the linear function represented in the table is y = -4x + 1.
Explanation:
Since the values in the x-variable are consecutive, let's take a look at the y-values.
Let's determine the common difference of the y-values.
[tex]\begin{gathered} -15-(-11)=-4 \\ -11-(-7)=-4 \\ -7-(-3)=-4 \end{gathered}[/tex]As we can see, the common difference between the y-values is -4. Therefore, the slope of the equation is -4.
To determine the y-intercept, let's subtract -4 from -3 to determine the y-value at x = 0.
[tex]-3-(-4)=1[/tex]Hence, the y-intercept is 1.
Therefore, the equation is y = -4x + 1.
Mean of 20 observations is 17. If in the observations, observation 40 is replaced
by 12, find the new mean.
Please help
The new mean is 18.4
According to the question,
The mean of 20 observations is 17
So the total value of all the observations = 20*17
= 340
The new value will be = 340 +40-12
= 368
Then,
The new mean of 20 observations will be= 368÷20
= 18.4
Hence, the new mean is 18.4
Mean is the average of a set of two or more numbers. It is of two types; arithmetic mean and geometric mean. It is part of statistics.
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Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
3 answers for this problem.
CORRECT ANSWERS ONLY!!!
Annie is selling chocolate bars for school. The cost of 12 bars is $18.
A) What is the unit rate of 1 candy bar?
B)How many bars must Annie sell to make $75?
Answer:
A) $1.5
B)50 bars
Step-by-step explanation:
A) First find out how much money one bar costs: 18/12= 1.5
$1.5 is how much one costs
B) Now that you know how much one bar costs, divide 75 by 1.5 to determine how many bars you need to get to $75.
75/1.5=50
50 bars to get to $75
Answer:$1.50 per bar and she would have to sell 50 bars to get 75
Step-by-step explanation: brainliest please? i could really use it
A president of a company wants to know if his employees think he is doing a good job. Which descriptions represents a sample? Select all that apply.
the president of the company’s family and relatives
the 5,000 residents of the town
25% of the workers at the company
the 1,000 total employees of the company
50% of the retirees from the company
The sample can be 25% of the workers of the company and 50% of the retirees.
Sampling is the practice of selecting a small group of individuals (a statistical sample) from a statistical population in order to make an educated guess about the characteristics of the full population.
It is utilized in survey methodology, quality control, and statistics. The goal of statisticians is to obtain samples that are representative of the population being studied. Sampling provides insights and is more economical and expedient than assessing the entire population when it is not practicable to do so.Each sample provides a numerical value for one or more properties of certain objects or individuals, such as their size, location, color, or weight. Weights can be applied to the data in survey sampling, particularly in stratified sampling, to account for the sample design.Now of the given options sample can only be selected from the groups that directly affect the president of the company.
Therefore the options will be :
25% of the workers at the company
50% of the retirees from the company
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what is the permiter in feet of a rectangle with height 4 1/6 feet and width 3 1/3
The perimeter in feet of a rectangle with height 4 1/6 feet and width 3 1/3 is 15 feet.
How to calculate the perimeter?It should be noted that the perimeter of a rectangle is calculated thus:
Perimeter = 2(Length + Width).
Based on the information, the following can be deduced:
Length = 4 1/6 feet
Width = 3 1/3 feet
Perimeter = 2(Length + Width).
Perimeter = 2(4 1/6 + 3 1/3)
Perimeter = 2(7 1/2)
Perimeter = 15 feet
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I don’t understand how to do this i need all the help i can get. thank you.
The sum of the angles on a straight line is 180 degrees. This means that
angle MJO + angle NJO = 180
From the information given,
angle MJO = 131
angle NJO = 15x + 4
Thus,
131 + 15x + 4 = 180
135 + 15x = 180
15x = 180 - 135 = 45
x = 45/15
x = 3
We would substitute x = 3 into angle NJO = 15x + 4
angle NJO = 15 * 3 + 4 = 45 + 4
angle NJO = 49
The following relations describe monthly demand and supply relations for dry cleaning
services in the metropolitan area?
Qd = 500000 – 50000P
Qs = -100000 + 100000P
A, Calculate the market equilibrium price/output combination, show graphically
B, Calculate the surplus or shortage when P=3 and P= 6
C, Calculate price elasticity of demand at equilibrium price
It is to be noted that at the equilibrium level, the Equilibrium price/output combination is $4 and 300,000 units respectively. See further calculations and answer below.
What is the Equilibrium level?Recall that the equilibrium level of the national income is defined as that point where the aggregate supply (QS) and the aggregate demand (AQD) are the same.
To calculate the market equilibrium price/output combination (EQL:
Step I - Recall the given data
Recall that at EQL, QD = QS
Where:
Qd = 500000 – 50000P; and ....................1
Qs = -100000 + 100000P. ...........................2
Hence, at EQL,
500000 – 50000P = -100000 + 100000P
⇒ 150,000P = 600,000 [divide both sides by 150,000
⇒ P = 600,000/150,000
⇒P = $4
Step II
To get Q, substitute P into (1)
thus, we have:
500,000 – 50000 (4)
500,000 – 200,000
= 300,000 units.
Hence, at EQL, P = $4 and Q = 300,000 units.
B)i What is P = $3?
Recall Step II above,
Simply substitute $3 into (1)
⇒ 500,000 – 50,000 (3)
= 500,000 – 150,000
= 350,000 units
ii) what is P = $6, just repeat the above steps to get
200,000 units.
C) Price Elasticity of Demand (PED) at Equilibrium Price
The PED is the percentage change in the quantity requested as a result of a 1% change in price. The PED coefficient is often negative, although economists frequently overlook the sign. If the PED coefficient is less than one, demand for an item is generally inelastic (in absolute value).
The formula for demand (PED) at P = 6 is determined using the formula:
PED = %Δ in QD / %Δ in Price..................1
%Δ in QD = (200,000-300,000)/300,000 ..............2
With 300,000 beings (Original Unit at Equilibrium)
Hence %Δ in QD = -0.333
%Δ in Price = (6-4)/4
= 1/2j or 0.5
PED = -0.333/0.5
PED = |-0.666|
Given that the PED is < 1, we can conclude that the demand for dry cleaning is inelastic.
In a situation where it is greater than 1, then the demand is elastic.
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cos 20-2 cos0=-1
Find all solutions of the equation in the interval [0,2pie).
The solutions for the trigonometric cosine equation are [0, 90,2pi].
What is trigonometric cosine function?
Trigonometric is one of the branch in mathematics which is used to study the relationship between the length and angles. Its angle is categorized into six form depending upon their sides.
To calculate the solution of the given equation in the interval of [0, 2 pi].
Therefore, the given equation in the form of the trigonometric function is as written below:
[tex]cos^{2} 0 - 2cos0 +1 = 0\\(cos0-1)^{2} =0[/tex]
Hence, the solutions for the trigonometric cosine equation are [0, 90,2pi].
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Solve for c.
a(c+b) = d
Answer: C=D\A-B THAT IS THE ANSWER
Step-by-step explanation:
Sentences to Algebraic EquationsTranslate the following sentence into equations and solve them.1. The quotient of a number and six is five. Find the number.
1. The quotient of a number and six is five.
he algebraic expression ifor the previous sentence is:
x/6 = 5
multiply by 6 to solve for x:
x = 5(6)
x = 30
. Eight decreased by twice a number is four.
- 2x = 4 subtract 8 both sides
-2x = 4 - 8
2x = -4 divide by -2 both sides
x = 2
3. Three less than the division of a number to seven is one.
3 - x/7 = 1 subtract 3 both sidesa
-x/7 = 1 - 3
x/7 = -2 multiply by -7 both sides
x = 2
4. Seven times the difference of 15 and a number equals - 56.
7(15 - x) = -56 a
7(15) - 7x = -56
105 - 7x = -56 subtract 105 both sides
-7x = -56 - 105
7x = -161 divide by -7 both sides
x = 23
5 (x² − 2) + 2x − 3x (x − 7)?
I just need help with the working it out step.
Answer:
[tex]2x^2+23x-10[/tex]
Step-by-step explanation:
1) distribute the parenthesis by multiplying 5 into (x^2 - 2) and -3x into (x - 7)
[tex]5x^2-10 +2x-3x^2+21x\\[/tex]
2) simplify by adding and subtracting like terms
[tex]2x^2+23x-10[/tex]
Consider the equation 6 – x = 3 – x. The picture shows the graphs of y = 6 – x and y = 3 – x. Which statement is true?
The two lines never intersect (are parallel lines) thus the equation:
6 - x = 3 - x
Has no solutions.
What can we say about the equation?
Here we have the equation:
6 - x = 3 - x
And (supposedly) a graph of the two lines:
y = 6 - x
y = 3 - x
Notice that the part on the linear equations that depens of x is equal to the ones in the equation above.
So basically we have a system of equations:
y = 6 - x
y = 3 - x
Because "y" is the same thing in both equations, we can rewrite:
6 - x = y = 3 - x
If we remove the part in the middle, we return to the original equation:
6 - x = 3 - x
Now, the solution of that equation is given by the point where the two graphs of the linear equations intersect, it will never happen, because both linear equations are parallel (have the same slope) which means that the equation:
6 - x = 3 - x
Has no solutions.
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Answer:
its smthing about no solutions. Just pick the answer that says no solution satifies it
Step-by-step explanation:
i got it right on imagine math :))) (i dont have the screen shot)
one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x
The value of the expression one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x is 2 - 2/15x.
How to illustrate the information?It should be noted that expressions are simply used to show the relationship that exists between the variables that are given.
In this case, one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x will be illustrated as:
= 1/5(3x + 10) - (11/15x)
= 3/5x + 2 - 11/15x
= 9/15x + 2 - 11/15x
= 2 - 2/15x
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Write a function(x) that calculates the cost of learning the machine for x months
The question provides that an initial fee of $1000 and a monthly fee of $115 is paid.
Since the initial fee is a one-time payment and the monthly fee is a recurring payment, over x months, the fee that would have been paid is given o be:
[tex]C(x)=1000+115x[/tex]After 1 year, 12months would have passed. This means that we can scalculate the cost using x = 12 in the equation:
[tex]\begin{gathered} x=12 \\ \therefore \\ C(x)=1000+115(12)=1000+1380 \\ C(x)=2380 \end{gathered}[/tex]ANSERS
(a) The function is:
[tex]C(x)=1000+115x[/tex](b) At the end of one year, he would have paid $2,380.
Simplify and write your answer with a positive exponent
Write an equation of the line.
Vertical; through (-3,-5)
Equation of the vertical line passing through point (-3, -5) is given by x = -3.
As given in the question,
Line passes through the point (-3, -5)
It represents the x- coordinate is equal to -3
And y- coordinate is equal to -5.
Condition for the line is given as vertical line.
Vertical line represent the value of x- coordinate remain constant.
It represent x-intercept
x = -3
x-intercept represents the equation of the vertical line.
Therefore, equation of the vertical line passing through point (-3, -5) is given by x = -3.
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A computer password is required to be 7 characters long. How many passwords are possible if the password requires 2 lowercase letter(s) followed by 5 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
We will see that there are 19,656,000 different passwords that can be made with the given characters.
How many passwords are possible?We need to find the number of possible options for each character of the password.
The first character is a letter, so we have 26 options.
The second character is another letter, so we have 25 options (because we can't repeat).
Then we have 5 digits, for each digit we have 10 options (removing one for each subsequent one)
First digit: 10 options.Second digit: 9 options.Third digit: 8 options.Fourth digit: 7 options.Fifth digit: 6 optionsThe total number of passwords is given by the product between the numbers of options.
P = 26*25*10*9*8*7*6 = 19,656,000
There are 19,656,000 different passwords that can be made.
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I don’t know how to do these
The area, A, of the regular polygons found their side lengths, s and the length of their apothem, are;
4. A ≈ 2144.5 cm²
6. A = 12080 in²
8. A ≈ 1168.5 m²
What is a regular polygon?A regular polygon is a polygon that have sides of the same length and that the sides are symmetric about a common central point.
The area of a regular polygon is given by the formula;
[tex] \displaystyle{A = \frac{n \times s\times a}{2} }[/tex]
Therefore, we have;
4. The area of a regular pentagon is given by the formula;
[tex]\displaystyle{A = \frac{5 \times s\times a}{2} }[/tex]
Where;
a = 24.3 cm, s = 35.3 cm, we have;
[tex]\displaystyle{A = \frac{5 \times 35.3 \times 24.3}{2} \approx 2144.5}[/tex]
The area of the pentagon is therefore; A ≈ 2144.5 cm²6. The area of a regular octagon is given by the formula;
[tex]\displaystyle{A = \frac{8 \cdot s\cdot a}{2} }[/tex]
Where;
a = 60.4 in,
s = 50 in
Which gives;
[tex]\displaystyle{A = \frac{8 \times 50\times 60.4}{2} = 12080 }[/tex]
The area of the octagon is A = 12080 in²8. The area of a regular decagon is given by the formula;
[tex]\displaystyle{A = \frac{10 \times s\times a}{2} }[/tex]
Where;
a = 19 m
s = 12.3 m
Which gives;
[tex]\displaystyle{A = \frac{10 \times 12.3\times 19}{2} = 1168.5}[/tex]
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REDUCING RATIOS
1. 55:33
2. 1,000:100
3. 560:80
4. 20:340
Answer:
Step-by-step explanation:
1. 5:3
2. 10:1
3. 7:1
4. 1:17