Step-by-step explanation:
Here is a graph of the given piecewise function:
Graph of f(x)={(1/3 x-1" if " x≤0 -1/2 x+6" if " 0<x≤6
The graph of the given piecewise function is a straight line with two segments. The first segment, which lies between x = 0 and x = 6, has a slope of -1/2 and a y-intercept of 6. The second segment, which lies between x = 0 and x = -∞, has a slope of 1/3 and a y-intercept of -1.
Please help me with the following question.
Step-by-step explanation:
a . median (Q2) =
[tex] \frac{1(n + 1)}{2} [/tex]
[tex] \frac{1(31 + 1)}{2} [/tex]
[tex] \frac{32}{2} = 6[/tex]
therefore the position of the media is the 6th term
6th term =3,11
b. first quartile(Q1)=
[tex] \frac{1(n + 1)}{4} [/tex]
[tex] \frac{1(31+ 1)}{4} [/tex]
[tex] \frac{32}{4} = 8[/tex]
8th term= 2,56
C. third quartile(Q3)=
[tex] \frac{3(n + 1)}{4} [/tex]
[tex] \frac{3(31+ 1)}{4} [/tex]
[tex] \frac{96}{4} = 24[/tex]
24th term = 3,85
D. IQR = Q3 - Q1
= 3,85 - 2,56
= 1,29
e.
[tex]fi = 2.56 - 1.5 \times 1.29 [/tex]
[tex]fi = 0.625[/tex]
[tex]fu = 3.85 + 1.5 \times 1.29[/tex]
[tex]fu = 5.785[/tex]
What matrix equation models the system? Fill in the missing elements in the equation.
Could someone help me? im stuck
The matrix equation that models the system is:
[2 4 0] [ 4 ]
[1 0 -1] = [-3 ]
[4 2 1] [ 7 ]
How to determine what matrix equation models the system?A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.
The given system of equations can be written as:
2x + 4y + 0z = 4
x + 0y -z = -3
4x + 2y + z = 7
Thus, the matrix equation can be written as:
[2 4 0] [ 4 ]
[1 0 -1] = [-3 ]
[4 2 1] [ 7 ]
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Question 1
2
The winner of the 95th annual hotdog eating contest consumed 207 hotdogs (and buns!) in 10 minutes.
You are determined to break this record, so you would have to consume 208 hotdogs and buns in 10 minutes.
How many hotdogs would you have to eat every minute to beat the last winner?
Type the number of hotdogs in the blank below (JUST the number).
Assuming you eat at the average rate needed to win the contest, how many total hotdogs will you consume in two minutes?
Type the number of hotdogs in the blank below (JUST the number).
Assuming you eat at the average rate needed to win the contest, how many total hotdogs will you consume in three minutes?
Type the number of hotdogs in the blank below (JUST the number).
You need to consume 20.8 hotdogs in 1 minute in order to beat the winner. Hotdogs consumed in 2 minutes = 2(20.8) = 41.6. Hotdogs consumed in 3 minutes = 3(20.8) = 62.4.
What is cross multiplication?To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.
Given that:
208 hotdogs = 10 minutes.
x = 1 minute
Using the cross multiplication we have:
x = 208 / 10
x = 20.8 hotdogs.
Hence, you need to consume 20.8 hotdogs in 1 minute in order to bea the winner.
Hotdogs consumed in 2 minutes = 2(20.8) = 41.6.
Hotdogs consumed in 3 minutes = 3(20.8) = 62.4.
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what are the final values of $t0, $t1, $t2, $t3 in the following mips assembly code? (please answer in decimal) g
The final values of $t0, $t1, $t2, and $t3 in the MIPS assembly code are 1, 2, 3, and 4, respectively.
This is because each of the 'addi' instructions adds a constant value to the specified register. The 'addi' instruction in MIPS stands for "add immediate", where the constant value is immediately added to the source register. In this case, each of the 'addi' instructions adds 1, 2, 3, or 4 to the corresponding register.
[tex]$t0 = 0 + 1 = 1$$t1 = 0 + 2 = 2$$t2 = 0 + 3 = 3$$t3 = 0 + 4 = 4$[/tex][tex]$[/tex]
Assuming that the initial values of the registers are 0, the final values of $t0, $t1, $t2, and $t3 would be the sum of the constant value and the initial value of the corresponding register. Thus, the final values of $t0, $t1, $t2, and $t3 would be 1, 2, 3, and 4, respectively.
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The complete question is-
What are the final values of $t0, $t1, $t2, and $t3 in the following MIPS assembly code after its execution is completed, assuming that the initial values of the registers are 0?
Don and Ana are driving to their vacation destination. Upon entering the freeway they began driving at a constant rate of 80 miles an hour. Don noticed that 4 hours into the trip they were 675 miles from the destination.
Answer: 830 Miles
Step-by-step explanation:
Distance = Speed x Time
60 x 3 = 180 Mi
3 hours = 180
Total Distance from their destination
= Distance traveled by them in 3 hours + 650 miles
= 180 miles + 650 miles
= 830 miles
Edit: 180 Miles*
Two systems of equations
For each system, choose t
If applicable, give the solu
System A
x+3y=6
-x-3y=-6
For the given system t is not application. There is no solution for the system.
What do you understand by solution ?In mathematics, the phrase "solution" refers to a particular value or set of values that satisfies a given equation or set of equations. Finding a solution to the problem is a necessary step in solving a system of equations.
A value for the unsolved variable that makes the equation true is referred to as the solution.
The solutions are all the values of x in the domain such that f(x) = g if we have two functions f and g that both map to the same co-domain (x).
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.
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Use the properties of logarithms to expand the logarithm as much as possible. rewrite the expression as a sum, difference, or product of logs. log √(x^7y^-4) = can you explain it?
The logarithm is expanded as much as possible to, log √(x^7y^-4) = (7/2) log (x) + (-2) log(y).
Simplifying the given logarithmic expression, log √(x^7y^-4).
Use the power rule of logarithms, log(a^x) = x log a.
Say, x= 1/2 and a = (x^7y^-4).
log √(x^7y^-4) = (1/2) log (x^7y^-4)
Now, use the multiplication property of the logarithms, log (ab) = log(a) + log(b). Consider a = x^7 and b = y^-4.
log √(x^7y^-4) = (1/2) log (x^7) + (1/2) log(y^-4)
Now, again use the power rule in both the terms,
log √(x^7y^-4) = (7/2) log (x) + (-4/2) log(y)
log √(x^7y^-4) = (7/2) log (x) + (-2) log(y)
This is the simplified expression.
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What is the scale factor? Question 4 options: 6 3 1/3 1/6
The scale factor is discussed below.
What is scaling? How is it done?Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. Similarly, if the initial coordinates are (x, y) then after scaling the coordinates would be {Kx, Ky}.Given is the scale factor.
Scale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities. In case of length scaling, we can write -
K = L{final}/L{initial}
Therefore, the scale factor is discussed above.
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All 12 kids from Mrs. Appleton's class that went to the beach went swimming, but only 3/9 of hem wanted to go surfing. How many kids wanted to go surfing?
Answer
3 kids wanted to go surfing.
Find the area (in square inches) of the shape shown below.
On the beach, 3/5 of the sand castles David and his friends were building were gigantic. 2/9 of the gigantic ones were washed away when the tide came in that evening. What fraction of the castles were washed away?
PLEASE HELP THANK YOU SO MUCH
To successfully escape a planet's gravity, a spaceship must achieve escape velocity. The escape velocity from planet Earth is 672 km per minute. Convert this speed to miles per hour, round your answer to the nearest whole number.
Answer:
The escape velocity from Earth is approximately 415.9 miles per hour.
17p = 34 = - 10 + 196
The value of the expression is p = -8.94.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
We have an expression,
17p = 34 = - 10 + 196.
Simplifying,
17p = 34 = 186
17p = 34 - 186
17p = -152
p = -8.94
Therefore, the value is -8.94.
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Try This question out and I’ll give you brainliest
Answer:
See below
Step-by-step explanation:
The U.S has more people under 18 than China does: correct
There are more people under 18 than age 45-60 in the US: correct
The population of China is more than four times of the US: You can't tell given the graph
There are more people age 19-44 than any other age group in the US: correct
College math need help
C-3 30-5
Which expression is equivalent to g^2h√5g?
Answer:
B
Step-by-step explanation:
every factor you want to bring inside a square root has to be squared first.
so,
g²h×sqrt(5g) = sqrt((g²)²×h²×5g) = sqrt(g⁴×h²×5g) =
= sqrt(5g⁵h²)
A ball is thrown into the air. Its height (in feet) t seconds later is given by h ( t ) = 64 t − 16 t 2 Based on the two equivalent forms of the function h ( t ) = 64 t − 16 t 2 = t ( 64 − 16 t ) , answer the following questions: a) What is the height of the ball 1 second after it has been thrown? (Include units) b) After how many seconds does the ball hit the ground? (Include units) c) At what time(s) is the ball 50 feet above the ground?
After 1 second, the height of the ball will be 48 feet above the ground, and if the ball lands after 4 seconds of being thrown into the air the ball is 50 feet above the ground after 4.66 seconds.
So we have the function:
h(t)=64t-16t²
height h(t) is measured as the ball after t seconds.
A) To find the height of the ball after 1 second if it has been thrown, then substitute 1 for t. Thus:
h(1)=64(1)-16(1)²
Simplify:
h(1)=64-16
Subtract:
h(1)=48
Thus, after 1 second, the height of the ball is 48 feet above the ground.
B) To know how many seconds after being thrown the ball hit the ground, we have to set h(t) to 0. 0 can be defined as that it will be 0 feet above ground level: in another word, on the ground. So:
0=64t-16t²
Solve for t. Factor out a 16t
0=16t(4-t)
Zero Product Property:
16t=0, 4-t=0
Solve for t:
t=0 or t=4.
We have to ignore the first zero. So, the value of t is 4 and the ball lands after 4 seconds of being thrown into the air.
C) To calculate at what time(s) the ball is 50 feet above the ground, set h(t) to 50 and solve for t:
50=64t-16t²
First, we have to divide everything in 2 to simplify things:
25=32t-8t²
Subtract 15 from both sides:
-8t²+32t-10=0
Now, to find the zeros, we can use the quadratic formula. a=-8, b=32, and c=-10. Thus:
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
Substitute:
[tex]x=\frac{-32+\sqrt{(32)^2-4(-8)(-10)} }{2(-10)}[/tex]
Simplify:
[tex]x=\frac{32+\sqrt{704} }{20}[/tex]
Use a calculator. Approximate:
x=4.6647
Therefore, the ball is 50 feet above the ground after 4.66 seconds.
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Question
A data set is summarized in the frequency table
below. The data set contains a total of 40 data
values. What is the missing frequency?
Value
1
2
3
4
Cr
5
6
7
8
Frequency
2
4
9
[]
6
8
2
4
The required Missing Frequency is 3.
What is frequency ?Frequency is a measure of the number of occurrences of a given event within a specified period of time. It can refer to the number of times a particular event happens in a unit of time.
Such as the number of times a wave or vibration occurs in a second, or the number of times an action occurs in a given period. In physics, frequency is measured in hertz (Hz); in electrical engineering, it is measured in cycles per second (cps). Frequency is also used in mathematics, music, and sound engineering.
Value Frequency
1 2
2 4
3 9
4 ?
5 6
6 8
7 2
8 4
Total 40
We have to find the Missing frequency:
Computation:
Missing frequency = Total frequency - Counted
Missing frequency = 40 - 37
Missing frequency = 3
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when the significance level is small enough in the f-test, we can reject the null hypothesis that there is no linear relationship.
Correct, in a hypothesis test using an F-test, the significance level refers to the probability of rejecting the null hypothesis when it is actually true.
The F-test is a statistical test used to determine if there is a significant linear relationship between two variables.
In the F-test, the null hypothesis is that there is no linear relationship between the variables, while the alternative hypothesis is that there is a linear relationship. When the significance level (usually denoted by alpha) is set to a small value, such as 0.05, we can use the F-test to determine if the observed relationship between the variables is likely due to chance or if it is a real, significant relationship.
If the calculated F-value is greater than the critical value for the given significance level, we reject the null hypothesis and conclude that there is a significant linear relationship between the variables.
On the other hand, if the calculated F-value is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant linear relationship between the variables.
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Please help if you can, this is due in two days.
Note that the statement that verified that ST || to QR is the converse of the Triangle Proportionality Theorem and the ratios given in Option A.
What is the converse of the Triangle Proportionality Theorem?According to the converse of the Triangle Proportionality Theorem, If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
The Theorem of Proportionality states that a line drawn parallel to one side of a triangle and cutting the other two sides splits the other two sides in equal proportion. The reverse of the Basic Proportionality Theorem - A line drawn to cut two sides of a triangle in equal proportion is parallel to the third side.
Since 4.5/7.5 = 7.5/12.5, then the converse of the Triangle proportionality theorem holds true.
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Tennis starts moving at 4m/s to the left. for 5s he is accelerating at a constant rate of 3m/s^2. what is his final velocity
The final velocity of the Tennis for the condition is 19 m/s.
What is acceleration?acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.
Given Tennis starts moving at 4m/s to the left,
initial speed = 4 m/s
for 5s he is accelerating at a constant rate of 3m/s^2
time = t = 5 s
acceleration = 3 m/s²
to find the final velocity,
velocity is given by,
v = u + at
u = initial speed, t = time, and a = acceleration
v = 4 + 3(5)
v = 4 + 15
v = 19 m/s
Hence velocity is 19 m/s.
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Suppose that a country has approximately 2,900 cellular phones per 1,000 people. Express the number of phones per person as a whole or mixed number
The country has approximately 3 cellular phones per person.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity.
Given that a country has approximately 2,900 cellular phones per 1,000 people.
Number of cell phones for 1000 people = 2900
Number of cell phones for 1 person = 2900 / 1000 = 2.9 ≈ 3
Hence there are approximately 3 cellular phones per person.
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Aiguo places 6 circular biscuits, each with the same diameter, on a baking sheet as shown below. What is the
approximate area in inches squared of the baking sheet left uncovered? Use 3.14 for pi
8 in.
12 in.
A. 20.64
B. 301.44
C. 75.36
D.72
Therefore , the solution of the given problem of rectangle comes out to be about 46cm2 of the baking sheet are left uncovered.
What is a rectangle?A rectangle is just a cube with quartet right angles in the Euclidean plane. It is also known as a quadrant that appears to have equal angles, or an equiangular quadrilateral. A straight angle is an additional alternative for the parallelogram. A square has four sides that are the same length. A quadrilateral with four 90° vertices and four equal sides is rectangular in shape. Due of this, it is occasionally referred to as a "equirectangular rectangle".
Here,
Given :
Size: 12 cm
Size = 18 cm
Rectangle's area is equal to 12*18.
Rectangle's surface area is 216 cm2.
One circle's diameter is equal to Length/3.
One circle's diameter is equal to 18/3, or 6 cm.
Circle area is equal to d2/4.
Circle area equals (6)2/4
Circles have an area of 364.
A circle's area is 9 cm2.
The six circular biscuits' surface area is 6 (9), or 54 cm2.
The six circular biscuits' surface area is 54 (3.14), or 169.56 cm2.
Amount of the baking sheet still exposed is equal to 216 - 169.56
46.44 cm2 of the baking sheet were left uncovered.
About 46cm2 of the baking sheet are left uncovered.
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An experiment conducted at Pennsylvania State University was designed to evaluate the effectiveness of irrigation and fertilizers on colorado blue spruce trees growth. Fertilizer is used with one group of colorado blue spruce trees in a moist region, and irrigation is used with colorado blue spruce trees in a dry region. What are the confounding variables and why?
It's important to control for these confounding variables to ensure that the results of the experiment accurately reflect the impact of the independent variables (irrigation and fertilizers) on the dependent variable (growth of Colorado blue spruce trees).
What are confounding variables?Confounding variables are extraneous variables that can influence the relationship between the independent variable (irrigation and fertilizer) and the dependent variable (growth of Colorado blue spruce trees).
In this experiment, some confounding variables that might be present include:
Soil quality: Soil quality can affect the growth of the Colorado blue spruce trees and may differ between the moist and dry regions.
Climate: Climate, including temperature, humidity, and precipitation, can affect the growth of the trees and may differ between the two regions.
Sun exposure: The amount of sunlight the trees receive can affect their growth and may differ between the two regions.
Pest and disease pressure: The presence of pests and diseases can affect the growth of the trees and may differ between the two regions.
Genetic variability: There may be genetic variability between the Colorado blue spruce trees in the moist and dry regions, which could affect their growth.
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Convert the following equations from standard form to slope-intercept form. 1-x-2y=-6
Answer:
The given equation 1 - x - 2y = -6 is in standard form, and can be converted to slope-intercept form (y = mx + b) by solving for y.
To do this, we first add x and 2y to both sides of the equation to get:
1 + x + 2y = -6
Next, we divide both sides of the equation by 2 to get:
(1/2) + (1/2)x + y = -3
Finally, we rearrange the equation to get:
y = -(1/2)x - 3
Therefore, the equation in slope-intercept form is y = -(1/2)x - 3.
could someone help me out?
The inequality equation is x ≤ 7 and represented as ←. with number 7 included
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
x - 1 ≤ 6 be equation (1)
On simplifying the equation , we get
Adding 1 on both sides of the equation , we get
x ≤ 7
Therefore , the value of x is less than or equal to 7
Hence , the inequality is x ≤ 7
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A data set has 24 data points. Enter values to answer each of the questions below. I Will Give Brainist
The number of data points above the median is 12, number of data points below the 1st quartile is 6 and the number of data points between 1st and 3rd quartile is 12.
What is Median?Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.
There are 24 data points in a data set.
Let x₁, x₂, .........., x₂₄ be the data points arranged in an increasing order.
Since the number of elements are even, median is the average of middle two elements.
Median = (x₁₂ + x₁₃) / 2, which will be in the middle of x₁₂ and x₁₃.
Number of elements above median = number of elements from x₁₃ to x₂₄ = 12
First quartile range is the average of the first part of elements which has been divided by the median.
Average of x₁, x₂, ......., x₁₂
1st quartile, Q₁ = (x₆ + x₇) / 2, which is located in the middle of x₆ and x₇.
Number of data points below 1st quartile = 6
Third quartile is the average of the second part of elements which has been divided by the median.
Average of x₁₃, x₁₄, ......., x₂₄
3rd quartile = (x₁₈ + x₁₉) / 2, which is located in the middle of x₁₈ and x₁₉.
Number of elements between 1st and 3rd quartile = 12
Hence the number of elements in each of the range is found.
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Two identical moving balls of mass 6 kg have clastic collisioa where the first ball was moving at $ m/s before collition. Find the initial velocity of the second ball if the kinetic energy of the system after collision is 75 j.
A-200 m/s
B-4m/s
C-6m/s
D-3 m/s
Answer: The correct answer is D-3 m/s.
Step-by-step explanation: To find the velocity of the second ball, we need to use the principle of conservation of kinetic energy.
The total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Initial kinetic energy = $\frac{1}{2} * 6 * v^2$
Final kinetic energy = $\frac{1}{2} * 6 * 6 + \frac{1}{2} * 6 * v^2 = 75$
Solving for v, we get v = 3 m/s.
Find all solutions of the equation that lie in the interval [0,π]. State each answer correct to two decimal places.
cos(x)=0.4
The solutions of the equation that lie in the interval [0,π] is 1.1592 and 1.98239.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
cos(x)=0.4
Take cos inverse on both side
[tex]cos^{-1[/tex] (cos(x)) = [tex]cos^{-1[/tex] (0.4)
x = [tex]cos^{-1[/tex] (0.4)
x= 1.1592
and, the second solution
x = π - 1.1592
x = π - 1.1592
x= 1.98239
Hence, the solutions are 1.1592 and 1.98239.
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