The linear functions in this problem are given as follows:
1. y = 1/3x + 3.
2. y = 2.
3. y = 3x - 1.
4. x = 1.
How to define the linear functions?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.For item 1, the points are given as follows:
(-6, 1) and (-3,2).
When x increases by 3, increases by 1, hence the slope is given as follows:
m = 1/3.
Then:
y = 1/3x + b.
When x = -3, y = 2, then the intercept b is calculated as follows:
2 = 1/3(-3) + b
b = 3.
Thus the function is:
y = 1/3x + 3.
Then items 2 and 4 are given as follows:
2 -> horizontal line -> y = 2.4 -> vertical line -> x = 1.For item 3, we have an intercept of -1, hence:
y = mx - 1.
When x = 3, y = 8, hence the slope m is calculated as follows:
8 = 3m - 1
3m = 9
m = 3.
Hence the function is:
y = 3x - 1.
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f(x)= -x²+6x-9
find f(7)
Answer:
-16
Step-by-step explanation:
Replace the x values with 7.
Stem and leaf plots
And box
Pls help I have no idea what this is
Answer:
32
Step-by-step explanation:
The end of the box is at 32.
based on the above estimated regression equation, if price is increased by 6 units, then demand is expected to
Therefore demand is "decreased by 100 units".
What is predicted value in regression?
Given the values of X, we can predict the values of Y using the regression line. We go directly up to the line for any given value of X, then move horizontally to the left to get the value of Y. The expected value of Y is abbreviated Y' and is known as the predicted value of Y.
[tex]$$\begin{aligned}& \hat{y}=130-20 x \\& \hat{y}=\text { demand of product } \\& x=\text { price of product }\end{aligned}$$[/tex]
Given [tex]$x$[/tex], increased by 5 units
[tex]$$\begin{aligned}& \hat{y}=130-20(x+5)=130-20 x-100 \\& \hat{y}=30-20 x\end{aligned}$$[/tex]
Therefore demand is "decreased by 100 units"
Complete question: Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained. ŷ = 130 − 20x Based on the above estimated regression equation, if price is increased by 5 units, then demand is expected to: increase by 100 units. decrease by 20 units. increase by 130 units. decrease by 100 units.
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Assume that the mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed.
a. If an individual is selected, find the probability that the individual’s pressure will be between 120 and 121.8 mm Hg.
b. If a sample of 30 adults is randomly selected, find the probability that the sample mean will be between 120 and 121.8 mm Hg.
c. Why is the answer to part a so much smaller than the answer to part b?
(a) The probability that the individual's pressure will be between 120 and 121.8 mm Hg is 0.1255.
(b) The probability that the sample mean will be between 120 and 121.8 mm Hg is 0.4608.
(c) The probability in part a is so much smaller than the probability in part b since, in part a, the probability is calculated for an individual's pressure whereas, in part b, the probability is calculated for a sample of adults.
How to calculate the z-score?The z-score formula in a normal distribution is given by
z = (X - μ)/σ
Here, the mean (μ), standard deviation (σ), and random variable (X) are used for finding the z-score.
With this z-score, from the normal distribution table, we can find the probability of the required random variable.
Calculation:It is given that,
The mean of the pressure of normal adults is μ = 120 mm of Hg
The standard deviation is σ = 5.6
Consider X is a normally distributed variable.
(a) Then, the probability that the individual's pressure will be between 120 and 121.8 mm Hg is calculated by P(120 < X < 121.8).
Here, the z-scores for the given means are:
z-score for the random variable 120 mm Hg is
z = (X - μ)/σ
⇒ z = (120 - 120)/5.6 = 0
z - score for the random variable 121.8 mm Hg is
z = (X - μ)/σ
⇒ z = (121.8 - 120)/5.6 = 0.32
So, the required probability is
P(120 < X < 121.8) = P(0 < z < 0.32)
⇒ P(z < 3.2) - P(z < 0)
From the normal distribution table, we get P(z < 3.2) = 0.6255 and P(z < 0) = 0.5000.
Then, the probability is
P(z < 3.2) - P(z < 0) = 0.625 - 0.5000 = 0.1255
(b) The sample size n = 30 and the random variables are 120 and 121.8 mm Hg.
Since the distribution is for a sample of adults, the sample mean value is
μₓ = μ = 120 and the sample standard deviation is
σₓ = σ/√n = 5.6/√30 = 1.022
Then, the z-scores for the given random variables are:
z-score for the random variable 120 mm Hg is
z = (X - μₓ)/σₓ = (120 - 120)/1.022 = 0
z-score for the random variable 121.8 mm Hg is
z = (X - μₓ)/σₓ = (121.8 - 120)/1.022 = 1.76
So, the required probability is
P(120 < X < 121.8) = P(0 < z < 1.76)
⇒ P(z < 1.76) - P(z < 0)
From the normal distribution table, we get P(z < 1.76) = 0.9608 and P(z < 0) = 0.5000.
Then, the probability is
P(z < 1.76) - P(z < 0) = 0.9608 - 0.5000 = 0.4608.
(c) The answer to part a is so much smaller than the answer to part b. This is because part a is the distribution for an individual and part b is the distribution for a sample of adults.
So, the sample mean and sample standard deviation will get changed in part b.
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A triangle has three angles that measure 80º, 65º, and 35º. How many unique triangles can be drawn that fit that description?
A triangle has three angles that measure 80º, 65º, and 35º will lead to infinite number of triangles
How to know when infinite number of triangles are formedWhen no side is specified, an infinite number of triangles are created.
If side lengths are not given, the three angles will result in an infinite number of triangles that are unique.
The option that provided only angles and no sides, namely angles of 80º, 65º, and 35º are given matches the criterion of formation of unlimited sides of triangle
To build an endless number of triangles, other alternatives have sides or a side is provided but not in accordance with that.
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a line's slope is 0, and it's y intercept is -7. what is its equation in slope intercept form?
At the beginning of the year, Harper had $30 in savings and saved an additional $10 each week thereafter. Stella started the year with $45 and saved $7 every week. Let H represent the amount of money Harper has saved t weeks after the beginning of the year and let S represent the amount of money Stella has saved t weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until Harper and Stella have the same amount of money saved.
S=__
H=___
The number of weeks after the beginning of the year until they have the same amount of money in 5 weeks.
What is a linear equation?
An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent of more than 1. The graph of a linear equation always forms a straight line.
A linear equation can be written as:
y = mx + b, where m is the slope and b is the y-intercept.
Given, the linear equations H and S can be written as follows by defining t as the number of weeks since the beginning of the year:
For Harper, H = 30 + 10t ................ (i)
For Stella, S = 45 + 7t .......... (ii)
To find out how much they had when they had the same amount is our next step.
This means that we must address:
H = S
From eq (i) and (ii), we get
or, 30 + 10t = 45 + 7t
or, 10t - 7t = 45-30
or, 3t = 15
or, t = 5
So they have the same amount of money in week 5.
Hence, H = 30 + 10t and S = 45 + 7t
Answer: 5 weeks
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Plot the complex number on the complex plane and write it in polar form and in exponential form.
19+19i
After solving the equation the complex number 19 + 19i.
What is polar form?
In mathematics, polar form is a way of representing a complex number in terms of its magnitude (the distance from the origin to the point on the complex plane) and its argument (the angle formed by the positive x-axis and the line connecting the origin to the point on the complex plane).
To plot the complex number 19 + 19i on the complex plane, you can represent it as a point with coordinates (19, 19). The complex plane is a two-dimensional coordinate system in which the x-axis represents the real part of a complex number and the y-axis represents the imaginary part.
The complex number 19 + 19i can also be written in polar form and in exponential form.
In polar form, a complex number is represented by its magnitude (the distance from the origin to the point on the complex plane) and its argument (the angle formed by the positive x-axis and the line connecting the origin to the point on the complex plane).
The magnitude of the complex number 19 + 19i is:
magnitude = √(19^2 + 19^2)
= √(361 + 361)
= √(722)
= 27
The argument of the complex number 19 + 19i is:
argument = atan2(19, 19)
= 45°
Therefore, the complex number 19 + 19i can be written in polar form as:
19 + 19i = 27 * cis(45°)
In exponential form, a complex number is represented as the product of its magnitude and the complex exponential cis(θ), where θ is the argument of the complex number.
Therefore, the complex number 19 + 19i
Polar form is usually written as:
r * cis(θ)
where r is the magnitude of the complex number and θ is the argument, expressed in radians.
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A zoo is planning a new building for the penguin exhibit. First, they made a model that was 1.7 meters tall. Then, they made a more detailed model that was 1.5 times as tall as the first model. The building will be 2.5 times as tall as the height of the detailed model.
What will be the height of the building?
The height of the new building in the zoo is calculated to be 6.375 m
How to find the height of the new buildingThe problem is solved by using the scale factor to increase or decrease the model.
When the scale factor is less than it leads to decrease but when above it leads to increasing.
The case in the problem is increasing.
First, they made a model that was 1.7 meters tall
the height of the model = 1.7 m
a more detailed model that was 1.5 times as tall as the first model
the height of the detailed model = 1.7 * 1.5 = 2.55 m
The building will be 2.5 times as tall as the height of the detailed model
= 2.5 * height of the detailed model
= 2.5 * 2.55
= 6.375 m
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Examine the four different companies in the table, which shows their yearly income and their tax rate. Which type of taxation does this table best represent?
A. Indirect
B. Progressive
C. Pegreative
D. Proportional
The type of taxation that this table best represent is B. Progressive
What is a progressive tax?A progressive tax is one in which the tax rate rises (or progresses) as taxable income rises. It imposes a lower tax rate on low-income earners and a higher tax rate on higher-income earners. This is usually accomplished by establishing tax brackets that categorize taxpayers based on their income levels.
A progressive tax is one in which the tax rate rises in proportion to the taxable amount. The term progressive refers to the manner in which the tax rate rises from low to high, resulting in a taxpayer's average tax rate being less than the person's marginal tax rate.
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Answer:
I got c
Step-by-step explanation:
Took the test and that’s what it told me 4nem
A water tank initially contained 55 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 2 minutes? Round answers to the nearest whole liter.
Answer:
50 liters
Step-by-step explanation:
2.5 liters drained per minute x 2 minutes = 5 liters drained total
(2.5 x 2 = 5)
55 liters at the start - the 5 liters drained = 50 liters remaining
(55 - 5)
whole equation would be
55 - (2.5 x 2) = 50
2. WOULD I HAVE COMPETENCES AIMED AT POSITIONING ME IN THE PROFESSIONAL MARKET?
Answer:
In the professional market there is always professional competition, because there are always different professionals competing or looking for the same jobs.
¿What is the labor market?This has been the market where the demand and supply associated with work or labor elements are concentrated.
In a labor market, as in any other market, there are skills, in this context, job skills, because there are always several professionals looking for the same job offers or opportunities.
¡Hope this helped!
Larry is a delivery man.
He has 7 parcels to deliver.
The mean weight of the 7 parcels is 2.7 kg
Larry delivers 3 of the parcels.
Each of these 3 parcels has a weight of W kg
The mean weight of the other 4 parcels is 3.3 kg
Work out the value of W
The value of the W would be 1.9 kg.
What is the mean of numbers?
The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the “average.”
Larry has to deliver 7 parcels.
The mean weight of the 7 parcels is 2.7 kg.
So
mean = sum of all weights of 7 parcels/7
2.7 * 7 = sum of all weights of 7 parcels
Sum of all weights of 7 parcels = 18.9 kg
Now Larry delivers 3 of the parcels each of weight 'W'
now the new weight will be = 18.9 - 3W
Remaining parcels = 7 - 3 = 4
New mean = 3.3
Now again by using the formula of mean, we get
3.3 = (18.9 - 3W)/4
18.9 - 3W = 13.2
3W = 5.7
W = 1.9 kg.
Hence, the value of the W would be 1.9 kg.
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Convert 110 kilograms to pounds. (1 kilogram = 2.204 pounds)
110 kilograms is equal to 242.44 pounds.
To convert kilograms to pounds, you can use the conversion factor:
1 kilogram = 2.204 pounds.
Given that you want to convert 110 kilograms to pounds, you can multiply 110 by the conversion factor:
110 kilograms x 2.204 pounds/kilogram = 242.44 pounds
Therefore, 110 kilograms is equal to 242.44 pounds.
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The following information matrices shows how many of each Video Game Consoles that each
electronics store sold during one weekend and the price that is charged for each gaming console at all
3 stores.
Micro middle sold the least no of different types of consoles.
What are matrices?Matrices represent data in the form of rows and columns together as an array form.
From matrix A we get the data as follows,
A row represents shops and columns represents types of console.
Games Go sold (53 + 21 + 48) = 122 different types of consoles.
Better Buy sold (65 + 34 + 70) = 169 different types of consoles.
Micro middle sold (18 + 11 + 15) = 34 different types of consoles.
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Pls help, I can’t figure this out .
Answer:
Step-by-step explanation:
y = 4×[tex]5^{0}[/tex] y=4
y=4×[tex]5^{2}[/tex] y=100
y=4×[tex]5^{4}[/tex] y=2500
y=4×[tex]5^{6}[/tex] y=62500
y=4×[tex]5^{7}[/tex] y=312500
Find the corresponding z score for each student. Round z scores to two decimal places.
Z-score of college student z=0.725
Z-score of university student z=0.664.
What is z-score?The relationship between a value and the mean of a set of values can be quantified using a Z-score. The Z-score is computed using the standard deviations from the mean. A data point's score is equal to the mean score if the Z-score is 0. The standard score is the value of a raw score in statistics that deviates from or exceeds the mean of the phenomenon being observed or assessed. Positive standard ratings are assigned to raw values above the mean, whereas negative standard ratings are assigned to raw values below the mean.
Given,
For the college student,
X₁=$9935
μ₁=$8581
σ₁=$1867
From the university student,
X₂=$11757
μ₂=$10339
σ₂=$2133
z-score of college student=(X₁-μ₁)/σ₁
z=(9935-8581)/1867
z=0.725
z-score of university student=(X₂-μ₂)/σ₂
z=(11757-10339)/2133
z=0.664
Therefore, z-score of college student=0.725
z-score of university student=0.664
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a meteorologist predicted that there would be 1.0 inches of rainfall from a storm instead there was 2.2 inches of rainfall
The percentage change of the rainfall the meteorologist predict is 55%
How to determine the percentage change of the rainfall the meteorologist predict?From the question, we have the following parameters that can be used in our computation:
Predicted amount of rainfall = 1.0 inches
Actual amount of rainfall = 2.2 inches
The percentage change of the rainfall the meteorologist predict is calculated as
Percentage change = (Actual amount of rainfall - Predicted amount of rainfall)/Actual amount of rainfall * 100%
Substitute the known values in the above equation, so, we have the following representation
Percentage change = (2.2 - 1.0)/2.2 * 100%
Evaluate the difference in the above equation, so, we have the following representation
Percentage change = 1.2/2.2 * 100%
Evaluate
Percentage change = 0.55 * 100%
So, we have
Percentage change = 55%
Hence, the percentage change is 55%
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A softball team is participating in a tournament where the team will spend three nights at a hotel. Each hotel offers a 50%
discount for the third night. The coach wants to keep the total cost for each player at $225 with an absolute deviation of at
most $25. Write an absolute value of inequality. Use x for the variable.
Hotel Price per night
Hotel A
$80
Hotel B
$105
Hotel C
$75
Hotel D $90
12.5x2251>25
The inequality will be;
For Hotel A; 80x + 25 < 225
For Hotel B; 105x + 25 < 225
For Hotel C; 75x + 25 < 225
For Hotel D; 90x + 25 < 225
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The coach wants to keep the total cost for each player at $225 with an absolute deviation of at most $25.
Now,
Since, The coach wants to keep the total cost for each player at $225 with an absolute deviation of at most $25.
Hence, We get;
The inequality will be;
For Hotel A;
⇒ 80x + 25 < 225
For Hotel B;
⇒ 105x + 25 < 225
For Hotel C;
⇒ 75x + 25 < 225
For Hotel D;
⇒ 90x + 25 < 225
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An object is thrown upward at a speed of 109 feet per second by a machine from a height of 7 feet off the ground. The height
h
h
of the object after
t
t
seconds can be found using the equation
h
=
−
16
t
2
+
109
t
+
7
h
=
-
16
t
2
+
109
t
+
7
Write the equation of the line that passes through the points (4, 8) and (5, -1). Put
your answer in fully
line.
simplified point-slope form, unless it is a vertical or horizontal
Slope-intercept form:
y=−9x+44y=-9x+44
Point-slope form:
y−8=−9⋅(x−4)
Find the distance:
Find the distance between 0 and -11
Answer:___
Please help ASAP!!!
Answer:
11
Step-by-step explanation:
If on a number line there would be 11 spaces in between
Find the quotient of x^2-9x+20 and x-5
Answer: x-4
Step-by-step explanation:
[tex]\displaystyle\\\frac{x^2-9x+20}{x-5}=\\\\\frac{x^2-5x-4x+20}{x-5} =\\\\\frac{(x^2-5x)-(4x-20)}{x-5} =\\\\\frac{x(x-5)-4(x-5)}{x-5}=\\\\\frac{(x-5)(x-4)}{x-5} =\\\\x-4[/tex]
Luke is completing a science experiment at home. He bought two hibiscus plants for his experiment. One of the plants was 5 cm tall. Each week he measured and recorded the
height of the plant, H, in cm. After collecting data for several weeks, he determined that the height of the plant, H, in cm, could be represented by the function H (t) = 5 +0.5t,
where t is the number of weeks since he purchased the plant.
Part A
What is the value of H(4)?
Part B
What does H (2) = 10 mean in this situation?
The height of the plant was 2 cm after 10 weeks.
The height of the plant was 7 cm after 4 weeks.
The height of the plant was 4 cm after 7 weeks.
The height of the plant was 10 cm after 2 weeks.
a) The numeric value at t = 4 is of H(4) = 7.
b) The meaning of the numeric value H(2) = 10 is given as follows:
The height of the plant was 10 cm after 2 weeks.
What is the meaning of the function?The function in this problem has the definition presented as follows:
H(t) = 5 + 0.5t.
The variables of the function are given as follows:
t is the number of weeks.H(t) is the height after t weeks.The numeric value at t = 4 is calculated replacing the lone instance of t in the function by 4, as follows:
H(4) = 5 + 0.5(4) = 5 + 2 = 7 cm.
H(2) = 10 means that when t = 2, H(t) = 10, that is, after 2 weeks, the height is of 10 cm, and thus the last option is correct.
(considering the interpretation of each variable).
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Measures of Central Tendency ->
Barry has scores of 93, 84, 86, and 75. He wants to raise the mean to 86.
what is the answer?
Measures of Central Tendency
A central tendency in statistics is a typical or centralised value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most used measurements of A central tendency in statistics is a typical or centralised value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most used measurements of central tendency.
[tex]\text { Mean }=\frac{\text { sum of all the numbers }}{\text { how many numbers there are }}[/tex]
There are 6 numbers and their sum is 525
Therefore, their mean is
[tex]\text { Mean }=\frac{\text { sum of all the numbers }}{\text { how many numbers there are }}[/tex]
Mode is the number with the highest frequency i .e which number appears the most in the sequence
In this case, there is NO mode because each number there appears only once
Median is the middle number when you place the numbers in ascending order
79,85,86,90,92,93
The middle number is between 86 and 90 . So your middle number can be found by [tex]\frac{86+90}{2}=88[/tex]
So your median is 88
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Brad invested $2,500 in an account earning 3.4% annual interest that is compounded semi-annually. How long will it take the investment to triple?
(Round your answer to the nearest hundredth.)
The time needed for the investment to triple is approximately 32.59 years.
What is the time taken for the investment to triple?The compound interest formula can be expressed as;
A = P(1 + r/n)^(n*t)
Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.
Given the data in the question;
Principal P = $2,500Accrued amount A = tripled = 3 × $2,500 = $7,500Interest rate r = 3.4%Compounded semi-annually n = 2Time t = ?Plug the given values into the above formula and solve for t.
A = P(1 + r/n)^(n*t)
t = In( A/P) / n[In( 1 + r/n ) ]
t = In( 7500 / 2500) / (2[In( 1 + 3.4%/2 ) ])
t = In( 7500/2500 ) / ( 2[In( 1 + 0.017 ) ]
t = 32.59 years
Therefore, the required time for the investment to $7,500 is is 32.59 years.
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A like passes the rough the point (-8,-9) and has a slope of 5/4. Write an equation in slope- intercept form for this line
Answer:
y=5/4x+1
Step-by-step explanation:
slope intercept form is y=mx+b
M- slope
B- y intercept
We already know slope
y=5/4x+b
To find b we fill in the coordinates we know (-8,-9)
-9=5/4(-8)+b
-9=-40/4+b
-9=-10+b
+10 +10
1=b
Now. We fill it in
y=5/4x+1
Hopes this helps please mark brainliest
In which direction does the parabola defined by the equation y = -x + 2 open?
Answer:
Downward
Step-by-step explanation:
A parabola is a curve that is shaped like a U. The direction in which a parabola opens depends on the sign of the coefficient of the x^2 term in the equation defining the parabola. If the coefficient is positive, the parabola opens upwards. If the coefficient is negative, the parabola opens downward.
In the equation y = -x + 2, the coefficient of the x^2 term is 0, so the direction of the parabola does not depend on it. However, the coefficient of the x term is -1, which is negative. This means that the parabola defined by this equation opens downward.
Find the distance between the points (6.6, 7.9) and (6.6, 4.7).
Answer:
3.2
Step-by-step explanation:
Compute the Euclidean distance between the following points:
p_1 = (6.6, 7.9) and p_2 = (6.6, 4.7)
The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:
sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)
Substitute (x_1, y_1) = (6.6, 7.9) and (x_2, y_2) = (6.6, 4.7):
= sqrt((6.6 - 6.6)^2 + (7.9 - 4.7)^2)
6.6 - 6.6 = 0:
= sqrt(0^2 + (7.9 - 4.7)^2)
0^2 = 0:
= sqrt(0 + (7.9 - 4.7)^2)
| 7. | 9
- | 4. | 7
| 3. | 2:
= sqrt(3.2^2)
Cancel exponents. sqrt(3.2^2) = 3.2:
Answer: = 3.2
Solve for x . Round to the nearest tenth, if necessary.
Answer:
176.6
Step-by-step explanation:
You can use sine, cosine, or tangent to find x (the trick is determining which to use).
Looking at the 63° angle, its adjacent side is GH, which has a length of 90. The opposite side of the 63° angle is side FG, which has a length of x. You're going to need a ratio that will give you the opposite side knowing the adjacent.
You can use the... acronym?... SOH-CAH-TOA.
SOH - When using sine (S), you get the ratio of the opposite (O) side to the hypotenuse (H).
CAH - When using cosine (C), you get the ratio of the adjacent (A) side to the hypotenuse (H).
TOA - When using tangent (T), you get the ratio of the opposite (O) side to the adjacent (A) side.
Since we're not using the hypotenuse at all, we need to use tangent, which is the ratio of opposite to adjacent. You can set up the equation:
tan(63°) = x/90
Type this into your calculator (make sure it's in degrees and not radians!) and you get:
1.9626 * 90 = x
x = 176.6