Answer:
A = 15t +15
Step-by-step explanation:
The amounts have a common difference of $15, so that is apparently the amount Jasmine is saving each week. Week 1, however, is $15 more than $15×1. The function ...
A = 15t +15 . . . . dollars
seems to fit the data.
Which expression is equivalent to am ÷ an?
Answer:
[tex]\frac{m}{n}[/tex]
Step-by-step explanation:
Setting it up as a fraction will help us see the simplification process a bit easier.
[tex]\frac{am}{an}[/tex]
a/a = 1, so they cancel each other out, leaving us with simply
[tex]\frac{m}{n}[/tex]
Determine the x- and y- intercepts for the graph defined by the given equation.
y = 7x + 3
Answer:
intercept is 3
X intercept is -3/7
For this case we have the following equation:
[tex]y = 7x + 3[/tex]
To find the y-intersection values we do [tex]x = 0[/tex]:
[tex]y = 7 (0) +3\\y = 0 + 3\\y = 3[/tex]
To find the x-intersection values we do[tex]y = 0[/tex]
[tex]0 = 7x + 3[/tex]
Subtracting 3 on both sides:
[tex]-3 = 7x[/tex]
Dividing between 7 on both sides:
[tex]x = - \frac {3} {7}[/tex]
So, we have:
x-intersection: [tex](- \frac {3} {7}, 0)[/tex]
y-intersection: [tex](0,3)[/tex]
Answer:
Option B
Which statements accurately describe Earth’s magnetic field? Check all that apply. The magnetic field lines flow from Antarctica to northern Canada. The magnetic field is created by magnetic rocks on the surface. The magnetic poles line up exactly with Earth’s geographic poles. The magnetic field is generated in Earth’s core. The magnetic field is similar to the magnetic field of a bar magnet.
Answer:
It’s A, D, and E
The magnetic field lines flow from Earth’s geographic South Pole to Earth’s
geographic North Pole.
The magnetic field is generated in Earth’s core.
The magnetic field is similar to the magnetic field of a bar magnet.
thank youhave a good day
Answer:
It’s A, D, and E.
Step-by-step explanation: Try and find out :)
Jk Jk it's right.
Determine whether the graph represents a proportional relationship.
yes, it is a proportional relationship because the graph goes through the origin
No, it is not a proportional relationship because the graph does not go through the origin
Yes, it is a proportional relationship because the graph is a straight line
No, it is not a proportional relationship because the graph is not a straight line
No, it is not a proportional relationship because the graph does not go through the origin. A proportional relationship is supposed to be a straight line, starting from the origin. It starts on the number 4.
The true statement is (b) No, it is not a proportional relationship because the graph does not go through the origin
Proportional relationships are represented with linear equations that begin from the origin.
From the attached figure, we can see that: the graph begins from (0,4)
For the graph to be proportional it must begin from (0,0) as the origin
This means that, the graph does not represent a proportional relationship.
Hence, the true statement is (b)
Read more about proportional relationships at:
https://brainly.com/question/24312388
The graph below shows a system of equations: y = -x + 5 and y = x - 1.
The x-coordinate of the solution to the system of equations is __________. Answer for Blank 1:
Answer:
3
Step-by-step explanation:
I don't see the graph.
So I'm going to do algebra and should be x-coordinate of the intersection you see in front of you.
If y=-x+5 and y=x-1, then -x+5=x-1.
-x+5=x-1
Add x on both sides:
5=2x-1
Add 1 on both sides:
6=2x
Divide 2 on both sides:
6/2=x
Simplify
3=x
You should see them cross when x is 3.
The y there should by 3-1=2.
They should cross at the ordered pair (3,2).
Answer:
3
Step-by-step explanation:
If a graph shows a system of equations: y = -x + 5 and y = x - 1, the x-coordinate of the solution to the system of equations is 3.
y=-x+5
y=x-1
-x+5=x-1
Determine whether the given value is a statistic or a parameter. In a study of all 1580 seniors at a college comma it is found that 40 % own a television. Choose the correct statement below. Parameter because the value is a numerical measurement describing a characteristic of a population. Statistic because the value is a numerical measurement describing a characteristic of a population. Statistic because the value is a numerical measurement describing a characteristic of a sample. Parameter because the value is a numerical measurement describing a characteristic of a sample.
Answer:
Parameter because the value is a numerical measurement describing a characteristic of a population.
Step-by-step explanation:
A parameter tells you something about the entire population.This means that you will know the "something" after asking every person in that group.In this question, the study was conducted for all 1580 seniors, and it was found that a parameter of 40% own a television.
In the given scenario, the 40% figure is a parameter because it involves a measurement from the entire population of college seniors, not a sample.
Explanation:The value that 40% of all 1580 seniors at a college own a television represents a parameter because it is a numerical measurement that describes a characteristic of a population. Since the study includes all seniors at the college, it is not a sample but the entire population of interest. Therefore, the 40% figure is a fixed value that characterizes that specific group. Had the percentage come from a study of a subset of the college seniors, it would be considered a statistic, as it would be an estimate derived from a sample used to infer about the larger population.
Let's consider another example to clarify the difference. If the U.S. federal government surveyed all high school seniors in the United States concerning their plans for future education and employment and found that 50% were planning to attend a four-year college, that 50% would be a parameter because it includes the entire population. In contrast, if the government only surveyed a sample, such as seniors from a selection of high schools, the result would be a statistic.
Match the items.
a. value of a ratio
b. relationship reciprocal
c. denominator
d. numerator
e. equivalent ratios
f. factor
g. ratio
1. a comparison of two quantities or numbers
2. the quotient of the two values in a ratio
3. ratios with the same meaning or value
4. the number under the fraction line; indicates how many equal parts the whole was broken into
5. a number that divides evenly into another number
6. the number above the fraction line; indicates how many parts of the whole exist
7. two numbers whose product is 1
Answer:
1-a
2-b
3-e
4-c
5-g
6-d
7-f
Step-by-step explanation:
should be this
A baseball team plays in a stadium that holds 58,000 spectators. With ticket prices at $12, the average attendance had been 23,000. When ticket prices were lowered to $10, the average attendance rose to 29,000.
(a) Find the demand function (price p as a function of attendance x), assuming it to be linear.
(b) How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.)
Answer: the lower the price the more people want to come to the baseball game.
Step-by-step explanation:
Answer:
a) p = -x/3000 + 19 2/3
b) $9.83
Step-by-step explanation:
a) The 2-point form of the equation for a line can be used with the two given points. The attendance is said to be the independent variable.
y = (y2 -y1)/(x2 -x1)(x -x1) + y1
Here "y" is the price (p), and "x" is the attendance, so we have ...
p = (10 -12)/(29000 -23000)(x -23000) +12
p = -1/3000(x -23000) +12
p = -x/3000 + 19 2/3 . . . . price as a function of attendance
__
b) Revenue is the product of attendance and price. We can find the attendance associated with maximum revenue, then find the corresponding price.
R(x) = x·p = x(-x/3000 +19 2/3)
This has zeros at x=0 and x=3000(19 2/3) = 59,000. The maximum revenue corresponds to attendance halfway between these values, at x = 29,500. The demand function tells us the ticket price should be ...
p = -29500/3000 +19 2/3 = 9.83 . . . . dollars
_____
Comment on the problem working
I might have written the "demand function" to use price as the independent variable. Then the price is what you know when you find the maximum revenue; you don't have to do an extra step to find it.
x = 3000(19 2/3 -p)
xp = 3000p(19 2/3 -p) is maximized at p = (19 2/3)/2 = 9 5/6 ≈ 9.83
What type of symmetry is shown in this picture (point, line, or rotational)? Explain your answer and identify the line of symmetry or the point of rotation.
Answer:
symmetry about the y-axis is shown
Step-by-step explanation:
Points on the right of the line of symmetry (x=0, the y-axis) are the same distance from that line as the corresponding points on the left. (That is what makes it a line of symmetry.)
There is no point of rotation that will map one figure to the other after rotation, hence no point or rotational symmetry.
Answer:
Step-by-step explanation:
The figure on the right is obtained by reflecting the figure on the left across the y-axis.
The number of times a player has golfed in one’s lifetime is compared to the number of strokes it takes the player to complete 18 holes. The correlation coefficient relating the two variables is –0.26.
Which best describes the strength of the correlation, and what is true about the causation between the variables?
A. It is a weak negative correlation, and it is not likely causal.
B. It is a weak negative correlation, and it is likely causal.
C. It is a strong negative correlation, and it is not likely causal.
D. It is a strong negative correlation, and it is likely causal.
its B
Answer:
The option B
Step-by-step explanation:
The weak correlation rank is between 0,25 and 0,5
The correlation is 0,26, which mean that 26 per cent of the variation is caused for set x
Answer: A. It is a weak negative correlation, and it is not likely causal.
Step-by-step explanation:
Given : The number of times a player has golfed in one’s lifetime is compared to the number of strokes it takes the player to complete 18 holes.
It means there is correlation . But there it is not likely causal because one thing is not causing other.
The correlation coefficient relating the two variables is -0.26.
We know that when the absolute value of correlation coefficient lies between 0.1 to 0.3, then it indicates that there is weak association.
The absolute value of given correlation coefficient (0.26) lies between 0.1 to 0.3, therefore, it shows weak correlation.
Also, it has negative sign , so it must indicate a weak negative correlation.
There’s a competition with 6 people. 3 of the 6 advance to the next round. 3 of the 6 are representing the same team. What’s the percentage chance of the previously mentioned team advancing at least one person?
Answer:
The percentage of at least one person of the team advanced is 95%
Step-by-step explanation:
For this exercise is necessary to understand the concept of combination, this is calculate as:
[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]
Where n is the total elements and k is the size of the group that is going to be chosen. This calculation give as the number of ways that is possible to choose a group of k with n elements.
So, the only possibility that there is no one of the same team that advance to the next round is that all of the people chosen were of the other 3 that doesn’t belong to the group mentioned. Then there is only one way to get this case.
On the other hand there are 20 ways to conform a group of 3 from a 6 elements and is calculate as:
[tex]6C3=\frac{6!}{3!(6-3)!}[/tex]
[tex]6C3=20[/tex]
Therefore, the percentage that any of the group mentioned pass to the next round is 1 in 20 or 5%.
So, the percentage that at least one of the group mentioned pass to the next round is the compliment, that’s mean that it is 95%.
Translate the given statement into propositional logic using proposition provided :
You can see the movie only if you are over 18 years old or you have the permission of a parent. Express your answer in terms of m: “You can see the movie,” e: “You are over 18 years old,” and p: “You have the permission of a parent.”
Final answer:
In propositional logic, the statement translates to ‘m → (e ∨ p)’, which denotes that seeing the movie 'm' can happen if the person is over 18 'e' or has parental permission 'p'.
Explanation:
The student is asking to translate a given statement into propositional logic. The statement in question is "You can see the movie only if you are over 18 years old or you have the permission of a parent." Using the propositions provided, where m represents "You can see the movie," e represents "You are over 18 years old," and p represents "You have the permission of a parent," we can express the logical relation in the following way:
In terms of logic, the statement can be written as a conditional: if you can see the movie (m), then you are over 18 years old (e) or you have the permission of a parent (p). This can be expressed as:
m → (e ∨ p)
This states that seeing the movie is the consequence of the condition of being over 18 years old or having parental permission. The conditional statement here establishes a necessary and sufficient relationship, while the use of or indicates that at least one of the conditions (being over 18 or having permission) must be met for the consequence (seeing the movie) to be true.
Identify the polygon with vertices A(5,0), B(2,4), C(−2,1), and D(1,−3), and then find the perimeter and area of the polygon. HELP ASAP!
Answer:
Part 1) The polygon is a square
Part 2) The perimeter is equal to [tex]20\ units[/tex]
Part 3) The area is equal to [tex]25\ units^{2}[/tex]
Step-by-step explanation:
we have
[tex]A(5,0), B(2,4), C(-2,1),D(1,-3)[/tex]
Plot the points
see the attached figure
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
[tex]A(5,0),B(2,4)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-0)^{2}+(2-5)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]AB=5\ units[/tex]
Find the distance BC
[tex]B(2,4), C(-2,1)[/tex]
substitute in the formula
[tex]d=\sqrt{(1-4)^{2}+(-2-2)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]BC=5\ units[/tex]
Find the distance CD
[tex]C(-2,1),D(1,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-1)^{2}+(1+2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]CD=5\ units[/tex]
Find the distance AD
[tex]A(5,0),D(1,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-0)^{2}+(1-5)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]AD=5\ units[/tex]
we have that
AB=BC=CD=AD
Find the distance BD (diagonal)
[tex]B(2,4),D(1,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-4)^{2}+(1-2)^{2}}[/tex]
[tex]d=\sqrt{(-7)^{2}+(-1)^{2}}[/tex]
[tex]BD=\sqrt{50}\ units[/tex]
Verify if the polygon is a square
If the triangle BDA is a right triangle, then the polygon is a square
Applying the Pythagoras theorem
[tex]BD^{2}=AD^{2}+AB^{2}[/tex]
substitute
[tex](\sqrt{50})^{2}=5^{2}+5^{2}[/tex]
[tex]50=50[/tex] -----> is true
so
The triangle BDA is a right triangle
therefore
The polygon is a square
Find the Area of the polygon
The area of a square is equal to
[tex]A=b^{2}[/tex]
we have
[tex]b=5\ units[/tex]
[tex]A=5^{2}=25\ units^{2}[/tex]
Find the perimeter of the polygon
The perimeter of a square is equal to
[tex]P=4b[/tex]
we have
[tex]b=5\ units[/tex]
[tex]P=4(5)=20\ units[/tex]
A newspaper provided a "snapshot" illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as plus or minus 3 percentage points. What important feature of the poll was omitted?
A. Confidence level
B. Point estimate.
C. Sample size
D. Confidence interval
Answer:
A. Confidence level
Step-by-step explanation:
The illustration showed that 26% of applicants said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company.
The margin of error was given as plus or minus 3 percentage points.
The important feature of the poll that was omitted was - confidence level.
The percent of all samples that are included in the true population parameter is given by a confidence level.
Confidence interval defines the probability that the given population parameter will fall within a specific range of values.
Mathematically we can express the scenario as :
Sample size is given as 1910 professionals
Point estimate is 26%
Confidence level is not given.
Confidence interval is plus or minus 3 percent around 26%.
Easy Points if you know math. Please help, question attached in picture.
Answer:
y = 1/2x +6
Step-by-step explanation:
We have a point and a slope. Therefore we can use the point slope form to create a line
y-y1 = m(x-x1)
y-5 = 1/2(x--2)
y-5 = 1/2(x+2)
Distribute the 1/2
y-5 = 1/2x +1
Add 5 to each side
y-5+5 = 1/2x +1+5
y = 1/2x +6
This is in slope intercept form
Please help with this question
Explanation:
1. Sine and Cosine are never greater than 1 because they are the ratio of the leg of a right triangle to the hypotenuse. The hypotenuse is never shorter than one of the legs of a right triangle, so the ratio is at most 1.
__
2. Secant and cosecant are the reciprocals of the cosine and sine (respectively), so are the reciprocals of numbers that are at most 1. Therefore, they can never be less than 1 (in magnitude).
__
3. Tangent and cotangent (and secant and cosecant) are sometimes undefined because they are the ratios of triangle side lengths. The side length used in the denominator may be zero, causing the ratio to be undefined.
Which statements describe a parallelogram that must be a rhombus? parallelogram with four congruent sides parallelogram with opposite sides parallel parallelogram with four congruent angles parallelogram with diagonal that bisects an angle parallelogram with diagonals that bisect each other
Answer:
The correct option is 1.
Step-by-step explanation:
Rhombus is a special case of parallelogram.
The properties of a parallelogram and rhombus:
1. Opposite sides parallel and equal.
2. Diagonals bisect each other.
3. Opposite angles are congruent.
The consecutive sides of a parallelogram may or may not be equal. But a rhombus has four congruent sides.
If a parallelogram has four congruent sides, then that parallelogram is known as rhombus.
The required statement that describe a parallelogram must be a rhombus is "parallelogram with four congruent sides ".
Therefore the correct option is 1.
Answer:
This is what i got
A cone's height is equal to the radius of its base. The area of its base is 1,386 square units. The approximate radius of the cone's base is____ units. The approximate volume of the cone is ____cubic units. Use . Pie= 22/7
Answer:
21 units9702 units³Step-by-step explanation:
The area of the base is given by the formula ...
A = πr²
so the radius is ...
r = √(A/π) = √(1386/(22/7)) = √441 = 21 . . . units
__
The volume is given by ...
V = (1/3)Bh
where B is the area of the base, and h is the height (equal to the radius). Filling in the numbers, we have ...
V = (1/3)(1386)(21) = 9702 . . . . cubic units
Stormer Company reports the following amounts on its statement of cash flow: Net cash provided by operating activities was $37,000; net cash used in investing activities was $13,600 and net cash used in financing activities was $17,400. If the beginning cash balance is $6,800, what is the ending cash balance?
Answer:
The ending cash balance is $12,800
Step-by-step explanation:
This is an addition and subtraction problem. We begin with the initial cash balance of $6,800. Next we are "provided" cash from various activities of $37,000. Based on the word used we can tell that this means we have to add this to our initial balance like so,
[tex]6,800 + 37,000 = 43,800[/tex]
Now our balance is $43,000. Next we are told that Net Cash "used" in investing activities is $13,600 and "used" in financing activities is $17,400. Based on this word we can tell that this money is being subtracted from our balance.
[tex]$43,000 - 13,600 - 17,400 = 12,800[/tex]
Finally, we can see that the ending cash balance is $12,800
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
The ending cash balance for Stormer Company can be calculated by starting with the beginning cash balance, adding the net cash provided by operating activities, and then subtracting the net cash used in investing and financing activities: $6,800 beginning balance + $37,000 provided - $13,600 invested - $17,400 financed = $12,800 ending cash balance.
Explanation:To solve this problem, it's crucial to understand that the ending cash balance is calculated by adding or subtracting the net cash provided or used from the beginning balance. In this scenario, the company has reported net cash provided by operating activities, as well as net cash used in investing and financing activities. To find the ending cash balance, you should follow these steps:
Add the net cash provided by operating activities to the beginning cash balance: $6,800 + $37,000 = $43,800 Subtract the net cash used in investing activities: $43,800 - $13,600 = $30,200 Subtract the net cash used in financing activities: $30,200 - $17,400 = $12,800
So, based on the numbers provided by the Stormer Company, its ending cash balance should be $12,800.
Learn more about Cash Flow here:https://brainly.com/question/34633860
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A person has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of shells. If she has enough shells for a border whose area is 380 square inches, determine the width of the border.
Answer:
so width of border is 10 inches
Step-by-step explanation:
Given data
board size = 12 * 16 inches
border area = 380 square inches
to find out
width of border
solution
let us assume width of border is x
first we find area of board i.e. 12 × 16 = 192 sq inches
and border area is given = 380 square inches
so total area of border and board is 192 + 380 = 572 sq inches
so we can say ( x+ 12 ) (x +16 ) = 572
solve this equation we get
x² +16x + 12x + 192 = 572
x² + 28x + 192 = 572
x² + 28x - 380 = 0
solve this equation and we get two value of x i.e.
x = 10 and x = -38
we will consider positive value here
so width of border is 10 inches
Answer:
The width of the border is 5 inches.
Step-by-step explanation:
Let x be the width of the border,
Given,
The rectangular board has the dimension 12 inches by 16 inches,
Thus, the dimension of the figure by joining the border with the board is,
(12+2x) inches by (16+2x) inches,
= (12+2x)(16+2x)
Hence, the area of the border = area of the figure by joining the border with the board - area of the board
= (12+2x)(16+2x) - 12 × 16
According to the question,
The area of the border = 380 square inches,
[tex](12+2x)(16+2x) - 12\times 16=380[/tex]
[tex]192+24x+32x+4x^2-192=380[/tex]
[tex]4x^2+56x-380=0[/tex]
[tex]4x^2+76x-20x-380=0[/tex]
[tex]4x(x+19)-20(x+19)=0[/tex]
[tex](4x-20)(x+19)=0[/tex]
By zero product property,
[tex]x=5\text{ or }x=-19[/tex]
Since, width can not be negative,
Hence, the width of the border is 5 inches.
ASAP someone please help me out please
Answer:
0
Step-by-step explanation:
If you think in degrees easier than in radians, then make this conversion.
pi = 180 degrees
(3/2)*pi = (3/2) * 180 = 180 * 3/2 = 270
Sin(270) = -1
cos(270) = 0
==========
sin(270) * cos(270) = -1 * 0 = 0
DOES ANYONE KNOW HOW TO DO THIS??????????
Donna's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Donna $4.20 per pound, and type B coffee costs $5.30 per pound. This month, Donna made 145 pounds of the blend, for a total cost of $659.90. How many pounds of type B coffee did she use?
Answer:
She used 49 of type B
Step-by-step explanation:
4.20 x 96 = 403.25.3 x 49 = 259.7403.2 + 259.7 = 659.9Step-by-step explanation:
Same steps, different problem.
x - pounds of type A coffee for current month
y - pounds of type B coffee for current month
x+y=145
4.2x+5.3y=659.9
x+y=145 -> multiply both sides by 4.2
4.2x+5.3y=659.9
4.2x+4.2y=609
1.1y=50.9
Find the area of the circle.
Use 3.14 for t.
Help Resources
d = 4 m
A = [?] m2
A=Tr2
Answer:
The area of the circle is A = 12.56 m²
Step-by-step explanation:
* Lets explain how to solve the problem
- The area of any circle is A = π r² , where r is the radius of the circle
- In any circle the length of the radius is half the length of its diameter
* Lets solve the problem
- The diameter of the circle is 4 meters
∵ The radius of the circle = 1/2 diameter
∵ The diameter = 4 meters
∴ The radius = 1/2 × 4 = 2 meters
- The area of the circle is A = π r²
∵ The value of π = 3.14
∵ The length of r = 2 meters
- Substitute the value of r in the rule of the area
∵ A = π r²
∴ A = 3.14 × (2)²
∴ A = 3.14 × 4 = 12.56 meters²
* The area of the circle is A = 12.56 m²
Find the volume of the cylinder.
Answer:
502.7
Step-by-step explanation:
I'm not sure on this! but this is what I think its supposed to be, I'm sorry if that's wrong
At what point is the maximum value found in the system of inequalities graphed below for the function f(x, y) = 4x - 3y?
A(5, 0)
B(4, 6)
C(7, 5)
D(8, 2)
Answer:
D.
Step-by-step explanation:
Just see which point yields the highest value.
f(x,y)=4x-3y
Checking choice A:
(x,y)=(5,0)
f(5,0)=4(5)-3(0)=20-0=20.
Checking choice B:
(x,y)=(4,6)
f(4,6)=4(4)-3(6)=16-18=-2.
Checking choice C:
(x,y)=(7,5)
f(7,5)=4(7)-3(5)=28-15=13.
Checking choice D:
(x,y)=(8,2)
f(8,2)=4(8)-3(2)=32-6=26
Choice D yields the highest value of the points given for our relation f(x,y)=4x-3y.
If it took Carlos an hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile = 5,280 feet)
(1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
(2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.
Answer:
Option 2 is the correct answer.
Step-by-step explanation:
We know that
[tex]Speed=\frac{Distance}{time}[/tex]
We have 1 mile = 5280 feet thus 6 miles = 31680 feet
Similarly 1 hour = 3600 seconds
Applying values in the equation above we get
[tex]Speed=\frac{31680feet}{3600sec}\\\\Speed=8.8feet/sec[/tex]
Thus his average speed is less than 18feet/sec
The heights of a group of boys and girls at a local middle school are shown on the dot plots below.
When comparing the shapes of the two sets of data, what conclusion can someone draw?
A) The shortest boy is taller than the shortest girl.
B) The range for the girls is greater than the range for the boys.
C) There is an outlier in the data for the boys, but not for the girls.
D) The girls are generally taller than the boys.
Answer:
The most appropriate answer option is D) The girls are generally taller than the boys.
Step-by-step explanation:
A) The shortest boy is taller than the shortest girl:
The shortest guy is not taller than the girl so its false.
B) The range for the girls is greater than the range for the boys:
Range for girls = 56 - 44 = 12
Range for boys = 54 - 41 = 13
C) There is an outlier in the data for the boys, but not for the girls:
It is present in both.
D) The girls are generally taller than the boys:
Average height of boys = [tex]\frac{(41)+(44\times3)+(46\times3)+(48\times2)+(50\times3)+(52\times)+(54\times4)}{20}[/tex] = 49.05
Average height of girls = [tex]\frac{(44\times2)+(46\times2)+(48)+(50\times3)+(52\times4)+(54\times3)+(56\times4)}{20}[/tex] = 50.9
Therefore, the correct answer option is D) The girls are generally taller than the boys.
Answer:
D) The girls are generally taller than the boys.
Step-by-step explanation:
The heights of a group of boys and girls at a local middle school are shown on the dot plots. When comparing the shapes of the two sets of data, the girls are generally taller than the boys.
I am having difficulty with these initial investment losses.
[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=4000(1-0.10)^t\implies A=4000(0.9)^t \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=100(1-0.08)^t\implies A=100(0.92)^t[/tex]
Can someone help me with this math question it involves transformation
Answer:
ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])
Step-by-step explanation:
* Lets explain the reflection and the translation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is (x , y - k)
* Now lets solve the problem
∵ The vertices of ABCD are:
A = (-5 , 2) , B = (-3 , 4) , C = (-2 , 4) , D = (-1 , 2)
- If ABCD reflected over the y-axis we will change the sign of the
x-coordinate of all the points
∴ The image of A = (5 , 2)
∴ The image of B = (3 , 4)
∴ The image of C = (2 , 4)
∴ The image of D = (1 , 2)
∴ The image of ABCD after reflection over the y-axis will be at
the first quadrant
- The figure EHGF is left and down the image of ABCD after
the reflection over the y-axis
∴ The image is translate to the left and down
∵ E = (1 , -2) and E is the image of A after reflection and translation
∵ The image of a after reflection is (5 , 2)
- That means 5 became 1 and 2 became -2
∵ 1 - 5 = -4
∴ The image of A after reflection translate 4 units to the left
∵ -2 - 2 = -4
∴ The image of A after reflection translate 4 units down
∴ ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])
* You can check the rest of points
# B with H
∵ B = (-3 , 4) after reflection over y-axis is (3 , 4) after translation is
(3 + [-4] , 4 + [-4]) = (-1 , 0) the same with point H = (-1 , 0)
# C with G
∵ C = (-2 , 4) after reflection over y-axis is (2 , 4) after translation is
(2 + [-4] , 4 + [-4]) = (-2 , 0) the same with point G = (-2 , 0)
# D with F
∵ D = (-1 , 2) after reflection over y-axis is (1 , 2) after translation is
(1 + [-4] , 2 + [-4]) = (-3 , -2) the same with point F = (-3 , -2)
Certainly! In order to assist you effectively with your math question involving transformation, please provide me with the specific details or instructions regarding the transformation problem you're facing.
Are you looking to translate, rotate, reflect, or dilate a geometric figure? Please provide the specifics such as the type of transformation, the figure involved, and any parameters (like the direction and distance of a translation, the angle and direction of a rotation, the line of reflection, or the scale factor and center of dilation for a dilation).
Once you provide these details, I'll be able to guide you through the mathematical process to solve your transformation problem step by step.
A 50-foot ladder leans against a wall 15 feet from the base of the wall. What is the measure of the angle formed by the ladder and the wall? Please show all work.
Answer:
72.5°
Step-by-step explanation:
This is a right triangle problem. The ladder is the hypotenuse, and we have a length for that of 50 feet. We also have the distance along the ground that the ladder's base is from the wall against which it is leaning. This is the side adjacent to the angle for which we are seeking, so it the side adjacent to the angle, and it measures 15 feet.
We need a trig ratio that relates the side adjacent to the hypotenuse. That will be the cosine. Setting up:
[tex]cos\theta =\frac{adjacent}{hypotenuse}[/tex] and then filling in:
[tex]cos\theta=\frac{15}{50}[/tex]
Use the 2nd button on your calculator, and then press cos and you will get a display on your screen that looks like this:
[tex]cos^{-1}([/tex]
After that open parenthesis enter the fraction 15/50 and hit enter and you'll get the angle of 72.5 degrees, rounded.
just an addition to that superb reply above by @Luv2Teach
to the risk of sounding redundant.
Check the picture below.
make sure your calculator is in Degree mode.