1. On a journey from Dover to Sheffield, Liam drove at an average speed of 40mph
for the first three hours of his journey.
The remaining 120miles of his journey were completed at an average speed of
30mph.
According to the given statement Liam is incorrect because average speed is 34.28 miles per hour.
Why do people use average speed?The average scores of a body's speed over a duration of time is its average speed. Because a moving body's speed is not constant over time and fluctuates, the average speed formula is required.
What does "average speed" actually mean?The overall distance the thing travels in a given amount of time is its average speed. A scalar value symbolizes the average speed. It has no direction and therefore is indicated by the magnitude.
Distance covered in first three hours = 40 × 3 = 120 miles
Time taking to covered remaining 120 miles = 120/30
= 4 hours
Total time = 4 hours + 3 hours = 7 hours
Total distance = 120 miles + 120 miles
= 240 miles
Average speed = total distance / total time
Average speed = 240 miles / 7 hours = 34.28 miles per hour
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Solve the simultaneous equation 4x+6y=21;7x-3y=3
The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equation is given below.
4x + 6y = 21 ...1
7x - 3y = 3 ...2
From equation 2, then we have
7x - 3y = 3
3y = 7x - 3
y = (7/3)x - 1
Put in equation 1, then we have
4x + 6[(7/3)x - 1] = 21
4x + 14x - 6 = 21
18x = 27
x = 3/2
x = 1.5
Then the value of the variable 'y' is calculated as,
y = (7/3)(3/2) - 1
y = 7/2 - 1
y = 3.5 - 1
y = 2.5
The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).
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At the beginning of the year, Juan had $60 in savings and saved an additional $15
each week thereafter. Mila started the year with $40 and saved $20 every week. Let J
represent the amount of money Juan has saved t weeks after the beginning of the
year and let M represent the amount of money Mila has saved t weeks after the
beginning of the year. Graph each function and determine the number of weeks after
the beginning of the year until Juan and Mila have the same amount of money saved.
Answer: They both meet up at $160
Step-by-step explanation:
40 + 20= 60 + 20 = 80 + 20 = 100 + 20 = 120 + 20 = 140 + 20 = 160
60 + 15 = 75 + 15 = 90 + 15 = 115 + 15 = 130 + 15 = 145+ 15 = 160
Daphne wants to buy some apples. An advertisement says that she can get $2$ apples for $1.24$. What is the price of $5$ apples?
Answer:
The price of 5$ worth of apples will be $3.10.
Step-by-step explanation:
5 dollars worth of apples would be 2 and a half apples. So, you would multiply 1.24 by 2.5. that gives you 3.1. Then, change those into change and you have your answer. Hope this helps!
15. Every year in Delaware there is a contest where people create cannons and catapults designed
to launch pumpkins as far in the air as possible. The equation y = 12 + 105x-16x² can be
used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the
pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How
many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the
ground, its height is 0 feet.)
(1 point)
To find the maximum height that the pumpkin reaches, we can set the derivative of the equation equal to 0 and solve for x. The derivative of y = 12 + 105x - 16x^2 is y' = 105 - 32x. Setting y' = 0, we get:
0 = 105 - 32x
32x = 105
x = 105/32
The maximum height is reached when x = 105/32 seconds. To find the maximum height, we can plug this value of x into the original equation:
y = 12 + 105(105/32) - 16(105/32)^2
= 12 + 1053.28125 - 163.28125^2
= 12 + 342.8125 - 106.25
= 248.5625
The maximum height that the pumpkin reaches is 248.5625 feet.
To find the number of seconds it takes for the pumpkin to hit the ground (when its height is 0), we can set y = 0 in the original equation and solve for x:
0 = 12 + 105x - 16x^2
16x^2 - 105x + 12 = 0
(4x - 3)(4x - 4) = 0
The solutions to this equation are x = 3/4 and x = 4/4. The second solution is extraneous, since it represents the time at which the pumpkin was launched (when x=0, y would be 12 feet, not 0 feet). Therefore, the number of seconds it takes for the pumpkin to hit the ground is x = 3/4 seconds.
a researcher studying malnutrition among children in a developing country collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight. which statement best describes this situation? measurement error has not occurred, and the researcher is not guilty of unethical statistical practice. measurement error has occurred, and the researcher is guilty of unethical statistical practice. measurement error has occurred, but the researcher is not guilty of unethical statistical practice. measurement error has not occurred, but the researcher is guilty of unethical statistical practice.
Therefore the the best statement that describes this situation is Measurement error has occurred, and the researcher is guilty of unethical statistical practice.
As per the details share in the above question are as follow,
A researcher collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight.
We have to determine the best statement that describes this situation?
It measured precisely 2.5 kg less, which is a systematic inaccuracy, thus there has been a measuring error.
The statistician was guilty because she purposefully gave them less weight in order to support her argument.
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If a coil of cable ,50m in length has a conductor resistance of 0. 275W,calculate the value for 800m of the same cable
If a coil of cable ,50m in length has a conductor resistance of 0. 275W,then the value of resistance for 800m of the same cable will be 4.4 ohms.
What is resistance?The opposition to current flow in an electrical circuit is measured by resistance. The Greek letter omega represents the unit of measurement for resistance, known as ohms. Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance.
what is conductance?the ratio of a conductor's current to potential difference, which measures how well a thing conducts electricity. This is the resistance' inverse, and it is measured in siemens.
as we are given with;
Length=50m
Resistance=0.275W
we got Formula;
Resistance=pL/A
p/A=R/A
p/A=0.275/50
=0.0055
Now for 800m wire
R= p/A(800)
R=0.0055x800
R=4.4 ohms
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juliet has 9 cups of orange syrup. she adds 32 fluid ounces of water to the syrup in order to prepare juice. find the total number of cups in the mixture.
Juliet will have 13 cups mixture of the orange juice and water .
Given :-
Juliet already has 9 cups of orange juice , and she adds 32 fluid ounces of water into the cup of orange uice syrup.
So, we have to find that how much cups of syrup does Juliet had ,
So, we know that
1 cup = 8 ounces
but she adds 32 ounces of water which means
= No. of ounces added / no. of ounces in a glass
= 32 / 8
= 4
therefore ,
9 + 4 = 13 glasses.
which means she has 13 glasses of the syrup made up of water and orange juice .
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Find the y-intercept of the line y=10x+ 7/13
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
Answer: 7/13 is the y intercept
Two ladders are leaning against a wall at the same angle, as shown. How long is the short ladder?
Answer:
15 ft
Step-by-step explanation:
60 divide by 40 equal 1.5
1.5 x 10 = 15
Please help me respond this question.
Answer:
Apples are least preferred
75% don’t prefer oranges
40 people prefer bananas
Answer:
Step-by-step explanation:
a) apples
b)
(40+ 20 + 15)
75% do not prefer oranges
c)
20% prefer bananas
20% as decimal is 0.2
0.2 * 200 =
40 people prefer bananas
Given the following data calculate the correlation coefficient. Then describe the correlation based on the correlation coefficient.
0 11
3 26
9 17
4 22
6 18
The correlation coefficient is -7.44, which shows a strong negative correlation.
To calculate the correlation coefficient, you can use the following formula:
r = (n Σ(xy) - Σ(x) Σ(y)) / √((n Σ(x²) - (Σ(x))²) (n Σ(y²) - (Σ(y))²))
Where n is the number of data points, x is the variable on the x-axis, y is the variable on the y-axis, Σ(xy) is the sum of the products of x and y, Σ(x) is the sum of x, Σ(y) is the sum of y, Σ(x²) is the sum of the squares of x, and Σ(y²) is the sum of the squares of y.
Plugging in the values from the data, we get:
r = (5 x 198 - 39 x 91) / √((5 x 114 - 39²) x (5 x 187 - 91²))
Simplifying this equation gives us:
r = (-179) / √((-97) x (-6))
r = (-179) / √(582)
r = (-179) / 24.07
r = -7.44
The correlation coefficient is -7.44, which indicates a strong negative correlation. This means that as the value of x increases, the value of y decreases. Conversely, as the value of x decreases, the value of y increases.
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a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank.
The work done to empty the tank by pumping the water out of the top of the tank is 3.4 * 10^6 .
Given :
a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank .
Formula :
[tex]W=\int_a^bpA(y)D(y)dy[/tex]
Using the base radius of 4, I found the equation of the line which was y = 5x / 2 and by solving for x gives us x = 2y / 5 .
Work = [tex]9.8*1000\int_0^{8} (\pi(\frac{2y} 5)^2)(10-y)dy[/tex]
= 3.4 * 10^6
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Please help NOWWW!!!
Write y=2/3x+7 in standard form using integers.
A. -2x+3y=7
B. -2x+3y=21
C. 3x-2y=21
D. -2x-3y=21
Conider the algebraic expreion
32pq2−4p2q12pq−7
Find term that are not contant. A) 32p2q,−4p2q,12pq, 7
b) 32, -4, 12, 7
c) 32pq2,4pq2,12pq
d) 32pq2, −4p2q, 12pq
The correct part is (d) i.e. 32pq2, -4p2q and 12pq are not constants in the given algebraic expression.
What is a constant?
A constant is a value or number that is consistently the same, regardless of how it is expressed.
The algebraic expression given is 32pq2−4p2q + 12pq−7.
A constant is that term which does not any variable portion or which is fixed.
Here, all terms have variables in the form of p and q but The last term does not have any variable.
So, The terms which have variables are the terms which are not constant.
Hence, 32pq2, -4p2q and 12pq are not constant in the given expression.
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Attachment 1 is answer options, attachment 2 is questions, answer all please 30 points
Any quality that pertains to a certain set is referred to in mathematics as a property. A property p that is rigorously specified for every component of a set X is typically defined as a function p: X → {true, false}.
What are the 4 properties of equality?The four properties of equality addition, subtraction, multiplication, and division can be used to solve an equation. To get the value of an equation's unknown variable, we can easily add, subtract, multiply, or divide the two sides of the equation.
The qualities of equality are those characteristics that have no effect on an equation's truth value, i.e., those characteristics that do not affect the equality of two or more values. These equality-related qualities enable us to define an equivalence relation and solve a number of algebraic equations.
9/2 x - 3 = 1/2 x + 2 Addition property of equality
9/2 x - 1/2 x - 3 = 1/2 x - 1/2 x + 2 Addition property of equality
1/4 * 4x = 1/4 * 5 Multiplication property of equality
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PLEASE HELP! much thanks to who ever does answer !
Answer:
-x+4 [tex]\leq[/tex]y
Step-by-step explanation:
You in-line skate from an elevation of 720 feet to an elevation of 750 feet in 30 minutes. Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour. Compare your rates of change in elevation.
Please help im stuck on this problem
Your friend's rate of change in elevation is 0.5 feet per minute more than your rate.
What is the formula for the rate of change in elevation?To find the height of the building (QR), we can use the angle of elevation formula tan θ=QR/PR.If you're looking for an exact number, use an altimeter, computer, or smartphone to calculate your current position above sea level. If you're trying to find a difference in elevation between 2 points of land, use tie a length of string between two posts and use a level to determine the difference.Let the area of the triangle be xy/2 and dA/dt becomes dA/dt= (xy' +yx')/2. To find y' use the Pythagorean theorem x2 +y2 =z2 where z is constant. So xx' +yy' =0 and y'=-xx'/y and substituting this into dA/dt gives dA/dt =(-x2x'/y +x'y)/2 = x'(y2 -x2)/2y.An angle of elevation is an angle with one horizontal arm, and one arm above horizontal. Usually an angle of elevation is less than or equal to 90°.Rate of change in elevation = elevation of distance/time
The elevation of 720 feet to an elevation of 750 feet in 30 minutes.
Your rate of change in elevation = 750 - 720 / 30
Your rate of change in elevation = 30 / 30
Your rate of change in elevation = 1 foot per minute
Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour.
Your friend's rate of change in elevation = 690 - 600 / 60
Your friend's rate of change in elevation = 90 / 60
Your friend's rate of change in elevation = 1.5 feet per minute
The difference in rate of change in elevation = 1.5 - 1 = 0.5 feet per minute
Thus, your friend's rate of change in elevation is 0.5 feet per minute more than your rate.
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statisticians have been able to show that the normal bell curve property also occurs when the sample size is 30 observations or fewer. true false
statisticians have been able to show that the normal bell curve property also occurs when the sample size is 30 observations or fewer: False.
Where in a normal curve can most observations be found?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.
The normal distribution is a continuous probability distribution with symmetry around its mean, a central peak around which the majority of observations cluster, and a tapering off of probabilities in both directions for values that are farther from the mean.
When a result is significant, it simply implies that you may be certain that it is true, not that you merely got fortunate (or unlucky) in the sample selection.
Thus, the statement given in the question is false.
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can someone help me out here,im a little confused.
Three vertices of a square are A(1,2), B(4,2), and C(4,−1).
Plot all four vertices of the square.
Using a graphing calculator to plot the vertices, the points plotted gave a triangle
Vertices of a SquareThis can be said to be the location of the endpoints in a given square. The vertices of a square must be equidistant from one another. This is a place in geometry where common endpoints of two or more rays or line segments meet. Thus, in a square, the vertex is the point where two sides meet. It is each corner of a square. Thus, each square has 4 vertices.
In this problem, we have to use a graphing calculator and plot each points
In doing so, we have A(1, 2), B(4, 2) and C(4, -1)
Plotting the points, it gives a triangle instead of a square;
The point A and B are located in the first quadrant and point C is located in the second quadrant.
Kindly find the attached graph below
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Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old. Ava adopted her pig when it was 1 year old, and she has had it for x years.
Write a one-step inequality to represent the situation, where x is the time, in years, since Ava adopted her pet pig.
Enter the correct answers in the boxes in the form of x+p ? q, where p and q are rational numbers and ? is replaced by >, ≥, <, or ≤.
The inequality that represents this situation is, (1 + x) > 2.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old.
Ava adopted her pig when it was 1 year old, and she has had it for x years.
∴ The inequality that represents this situation is,
(1 + x) > 2.
x > 2 - 1.
x > 1.
Ava adopted her pig for more than one year.
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Let f(x)=x3 and g(x)=13x.
Use the composition of functions to determine if f(x) and g(x) are inverse functions.
Drag and drop the answers into the boxes to correctly complete each statement.
The functions f(g(x)) and g(f(x)) are not inverse functions
How to determine if the functions are inverse functions?From the question, we have the following parameters that can be used in our computation:
f(x) = x³
g(x) = 1/3x
Calculate the composite function f(g(x)).
So, we have
f(g(x)) = (1/3x)³
This gives
f(g(x)) = 1/27x³
Calculate the composite function g(f(x)).
So, we have
g(f(x)) = 1/3(x³)
This gives
g(f(x)) = 1/3x³
The functions f(g(x)) and g(f(x)) are not the same
Hence, they are not inverse functions
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HELP!!! a wooden block in a set of building blocks is a rectangular prism with a volume of 168 cubic centimeters. the block is x2 centimeters tall, (x-3) centimeters long, and (x-4) centimeters wide. find the dimensions of the block.
The dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.
What is prism?In three dimensional space prism is a polyhedron where two ends are similar.
Given that volume of rectangular prism is 168 cubic centimeters.
And the wooden block is 2x cm tall, (x-4) cm wide and (x-3) cm long.
And also given that a wooden block in a set of building blocks is a rectangular prism.
That means,
Volume of wooden block = Volume of rectangular prism = 168 cm³
Volume of wooden block ;
length × width × height = 168 cm³
Substituting given values in above expression,
2x (x-3) (x-4) = 168 cm³
2x (x²-7x + 12) = 168 cm³
2x³ - 14x²+ 24x = 168 cm³
Simplifying the above equation;
2x³ - 14x²+ 24x- 168 = 0
x³ - 7x²+ 12x- 84 = 0
The factor of above cubic equation is x = 7.
Now the 2x = 14 , x-3 = 4, x-4 = 3.
Therefore the dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.
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pleaseee help me ill give brainliest IM BEING TIMED
-STATISTICS question!!!-
Answer:
The data given from the graph proves that Catherine and Ana's suspicions were correct and the athletes at their school do indeed have a quicker reaction time than other students at their school. The average reaction time for the athletes ranges from 240 - 300, while the normal student's reaction time ranges from 260 - 330. There still should be more experiments to test this theory to get more detailed and accurate results because there are still athletes that have the same reaction time as normal students and the dot away from the boxes shows that there is a athlete that has a slower reaction rate than all of the normal students. So it is safe to say there is indeed a difference in reaction times, but not a drastic one.
The legs of a right triangle are 3 units and 5 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. (5 points)
Question 4 options:
1)
4.00 units
2)
2.83 units
3)
5.83 units
4)
8.00 units
Answer:
bom é a soma dos algarismos se for matemática
This one is confusing please someone help:
1. give another name for plane p
2. name a line that intersects the plane
3. name two rays
4. name 3 points in plane p
1.You can find another name for plane P by using any three points in the
plane that are not on the same line. Hence, the another name for plane P is the plane GAC .
2. The line intersects the plane is EF
3. The two rays in the plane are CB , DB
4. A,B,C are three points in the plane p.
What is meant by plane?Spanned by two linearly independent vectors, a plane is a doubly ruled surface in two dimensions. Hyperplanes are the result of extending the plane to higher dimensions. The dihedral angle is the angle at which two planes intersect.
Using any three points on the plane that are not on the same line, you can come up with another name for plane P. Therefore, another name for plane P is GAC. The plane is intersected by the line at EF. CB and DB are the two rays in the plane. There are three points in the plane p, A, B, and C.
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A new club sent out 192 coupons to boost sales for next year's memberships. They provided 5 times as many to potential members than to existing members. How many coupons did they send to existing members? A. 37 B. 6 C. 32 D. 5
They send 32 coupons to existing members. Option C is correct.
What is a linear equation in two variables?
A Linear equation in two variables x and y is of the form
Ax + By = C.
Given,
They provide 5 times as many to potential members than existing members.
Let, there are y potential members and x existing members.
Therefore, x + 5y = 192
Also, x and y are whole numbers.
Hence, x=32 satisfy the equation.
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18. Higher Order Thinking The student council was
preparing for the school bake sale. The members divided
each type of donated item equally on plates. Each plate
contained only one type of item, and every plate had
exactly the same number of items. There were no leftovers.
What is the greatest number of items that could have been
placed on each plate?
Bake Sale Donations
Muffins
Breadsticks
Rolls
96
48
84
3-2 Find Greatest Common Factor and Least Common M
We need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.
What are the denominator and numerator?
A fraction's top digit is always referred to as the numerator. It displays the number of our parts. A fraction's numerator—the lowest digit—is referred to as the denominator. It displays the overall number of pieces that something can be broken down into.
we have to divide each item in a way that gives us equal groups on each plate,
we have to find a divisor for each item that gives us the same result.
Muffins.
96/2=48
96/3=32
96/4=24
96/8=12
That is, by dividing all muffins into 8 plates we would have 12 muffins per plate.
Breadsticks.
48/2=24
48/4=12
That is, by dividing all breadsticks into 4 plates we would have 12 breadsticks per plate.
Rolls.
84/2=42
84/3=28
84/4=21
84/6=16
84/7=12
By dividing all rolls in 7 plates, we would have 12 rolls per plate.
Therefore, we need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.
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PLEASE HURRY!!
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 9 feet.
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 18 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Approximate new height QR of the scaffold would be 11.31 Fee
What is Pythagoras theorem?
The pythagorean theorem or Pythagoras' theorem may be a elementary relation in geometry between the 3 sides of a triangle.
Main Body:
A) Here, We'll use "Pythagoras Theorem" which tells:
a² + b² = c²
So, PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
In short, approximate length of rod PR would be 16.64 Feet.
B) Again, Use the Pythagoras Theorem,
c² - a² = b²
18² - 14² = b²
b² = 324 - 196
b = √128
b = 11.31
Hence , approximate new height QR of the scaffold would be 11.31 Feet
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evaluate 2n if n = 9
Answer:
18
Step-by-step explanation:
If n=9, then plug in 9 for n in the equation and solve. You should get 2•9, which is 18 when you simplify. Hope this helps and please mark brainliest!