Answer:
Thaddeus: 7 hIan: 9 hStep-by-step explanation:
If Thaddeus drives the whole 16 hours, the distance between them is ...
distance = speed · time
distance = 20 mi/h · 16 h
distance = 320 miles.
It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...
(45 mi)/(5 mi/h) = 9 h
The rest of the 16 hours is the time that Thaddeus drove: 7 hours.
___
Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...
distance = speed · time
365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)
45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms
(45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x
_____
Comment on the solution
You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.
To solve the problem, we need to set up two equations based on the information given in the problem. Solving the equations simultaneously gives Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.
Explanation:First, we'll define the variables. Let's say the time Thaddeus has been driving is T hours, and the time Ian has been driving is I hours. The total distance they covered is the sum of the distances each one traveled, which is 365 miles. Thaddeus travels at a rate of 20 mph, while Ian travels at 25 mph. This is represented by the equation 20T + 25I = 365.
Next, we know that the total time they have been driving is 16 hours, which gives us another equation, T + I = 16. Now we have a system of linear equations that we can solve simultaneously to find the values of T and I. The solution gives T = 7 hours and I = 9 hours. Hence, Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.
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14. Simplify 3! (1 point) 2 5 3 6
Answer: the answer is 6
Step-by-step explanation: 3 times 2 is 6 then 6 times 1 is still 6
Answer: [tex]3!=6[/tex]
Step-by-step explanation:
The factorial function has the following symbol: "!" (As you can observe, it is an exclamation mark).
The factorial functions are applied to the numbers greater than zero. Then, the factorial of a positive integer "n" is representend as:
[tex]n![/tex]
Since you need to simplify 3!, you has to multiply all the positive integer numbers that are between the number 3 and and the number 1.
Therefore, for 3! you get the following result:
[tex]3!=3*2*1\\3!=6[/tex]
A computer company produced this graph to show how many computers it expects to sell based on
how much the company spends on Internet advertising. The company expects to sell 40 million
computers, spending $5 million on Internet advertising. Which set of units and scales are appropriate
for the two axes?
Answer: Hence, Fourth option is correct.
Step-by-step explanation:
Since we have given that
Number of computers expected to sell = 40 millions
Cost price of internet advertising = $5 million
According to the graph, we can see that
40 millions is the y-coordinate and $5 million is the x-coordinate.
so, Horizontal axis - y- axis is the "Number of computers".
Vertical axis - x- axis is the "Advertising cost ":
Hence, Fourth option is correct.
Horizontal axis will have number of computers in millions and vertical axis will have advertising dollars in millions.
Given information:
The graph of computer production and advertising amount spent is given in the question.
Total number of computer sell = 40 millions
Cost of internet advertising = $5 million
Now , by looking the graph one can conclude that, Y coordinate of the graph is 40 million and the X coordinate of the graph is $5 million.
Hence, from the above conclusion one can write as:
Horizontal axis (X-axis) is the number of computers and the Vertical axis is (Y-axis) the advertising cost of computers.
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What is Mean Absolute Deviation (MAD)? How do I do it? (Please have an example to show.)
Explanation:
It is the average (mean) of the absolute values of the differences between a set of numbers and their mean.
Example: consider the set {1, 2, 4}. The mean is computed in the usual way: the sum divided by the number of contributors —
mean = (1 + 2 + 4)/3 = 7/3 = 2 1/3
Then the deviations are ...
1 -2 1/3 = -1 1/3 . . . . the absolute value of this is 1 1/3
2 -2 1/3 = -1/3 . . . . . the absolute value of this is 1/3
4 -2 1/3 = 1 2/3 . . . . the absolute value of this is 1 2/3
The mean of these absolute values is their sum divided by the number of them:
(1 1/3 +1/3 +1 2/3)/3 = (3 1/3)/3 = 1 1/9
The MAD of {1, 2, 4} is 1 1/9.
_____
Your graphing calculator or spreadsheet program may have a function that will calculate this for you.
Members at a yoga school pay $10 per class plus a one time $100 membership fee.non members pay $15 per class.how many classes would a member have to take to save money compared to taking classes as a non-member?
Show work Plz!!
Answer:
21 classes
Step-by-step explanation:
Let’s set up equations for both memebers and non-members!
Let c = classes
To find how many classes it would take to make the two things even, we set them equal.
10c+100 = 15c
Solving for c,
5c = 100
So c = 20.
Since you need 20 classes to break even, to save money as a member, you need 21 classes.
A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. The quarterly rate of growth is 0.03 or 3%. The growth rate is 1.03. The growth factor is represented by 1.03. The compound periods multiplied by the number of years is 4t. 920(1.03) is the number of cars multiplied by 1.03. The initial number of cars serviced is 920. Coefficient arrowRight Exponent arrowRight Rate arrowRight Base arrowRight
Answer:
N=920 (1+0.03)^4t
where N=number of cars serviced after t years
Step-by-step explanation:
Apply the compound interest equation
N=P( 1+r/n)^nt
where N ending number of cars serviced , P is the number of cars serviced in 2012, r is the interest rate, n is the number of compoundings per year, and t is the total number of years.
Matching parts of the exponential function
Initial number of cars serviced=920
The quarterly rate of growth = if interest is compounded quarterly, n=4
r=12% ÷ 4 = 0.03 or 3%
The growth rate is given by (1 +r/n) = 1+0.03 = 1.03
number of compoundings for t years= nt= 4t
The compound period multiplied by the number of years = 920(1.03)^4t
a weight lifter uses both 2 kg blocks as well as 5 kg blocks to set up his bar. he has a total of 30 blocks if the total weight of the bar is observed to be 120 kg then calculate the number of 5 kg blocks and 2 kg blocks
Answer:
The number of the 2 kg blocks is 10
The number of the 5 kg blocks is 20
Step-by-step explanation:
Let the number of the 2 kg blocks be x and the number of the 5 kg blocks be y.
The total number of blocks in terms of x and y is;
x + y
We are informed that he has a total of 30 blocks, implying that;
x + y = 30
The total weight of the bar in terms of x and y will be;
2x + 5y
We are also informed that the total weight of the bar is observed to be 120, implying that;
2x + 5y = 120
We therefore have two equations in two unknowns.;
x + y = 30
2x + 5y = 120
We can solve these equations simultaneously via elimination method;
multiply the first equation by 2;
2x + 2y = 60
2x + 5y = 120
Subtracting the first equation from the second one yields;
5y - 2y = 120 - 60
3y = 60
y = 20
But x + y = 30, implying that;
x = 30 - 20
x = 10
What are the solution(s) to the quadratic equation 50 – x2 = 0?
x = ±2
x = ±6
x = ±5
no real solution
Answer:
x = ±[tex]5\sqrt{2}[/tex]
Step-by-step explanation:
We have been given the quadratic equation;
[tex]50-x^{2}=0[/tex]
The first step is to subtract 50 from both sides of the equation;
[tex]50-x^{2}-50=0-50[/tex]
[tex]-x^{2}=-50[/tex]
Multiplying both sides by -1 yields;
[tex]x^{2}=50[/tex]
The final step is to obtain square roots on both sides;
[tex]\sqrt{x^{2} }=\sqrt{50}\\x=+/-\sqrt{50}[/tex]
Therefore, x = ±[tex]5\sqrt{2}[/tex]
*help please* What is the amplitude of the function graphed?
So amplitude is the length from the highest (or lowest) point from the mid-line of the function
In this case the mid-line is y = 1
The highest point, which has a y of 3 is 2 units away from the mid-line. This means that the amplitude is 2!
Hope this helped!
The amplitude of the function graphed will be 2.
What is amplitude ?The amplitude of a function is the amount by which the graph of the function travels above and below its midline, i.e. it is the height from the mean value of the function to its maximum or minimum.
We have,
A graph,
The highest value = 3,
Lowest value = -1
So,
From the definition mentioned above,
Amplitude [tex]=\frac{3+|-1|}{2}[/tex]
We get,
Amplitude = 2
Hence, we can say that the amplitude of the function graphed will be 2.
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Write an equation for the line below.
Answer:
x = 3
Step-by-step explanation:
A vertical line has the form x = constant. The graph shows the constant you want is 3.
PLEASE HELP!!!!! TIMED!!! Will give brainliest!! 70 POINTS!!!!!
Matteo wants to write a statement that can be represented by the inequality P<9 Which describes the correct method to write a statement to match this inequality?
Use the inequality symbol to determine the relationship between the variable and the constant. Decide what the variable will represent. Decide what the constant will represent. Write a statement using the same relationship. An example is “Alva spent more than $9.”
Decide what the variable will represent. Decide what the constant will represent. Write a statement using the same relationship. An example is “Alva spent less than $9.” Use the inequality symbol to determine the relationship between the variable and the constant.
Decide what the variable will represent. Decide what the constant will represent. Use the inequality symbol to determine the relationship between the variable and the constant. Write a statement using the same relationship. An example is “Alva spent less than $9.”
Decide what the variable will represent. Decide what the constant will represent. Use the inequality symbol to determine the relationship between the variable and the constant. Write a statement using the same relationship. An example is “Alva spent more than $9.”
Answer:C
Step-by-step explanation:
The constant and the variable relationship is p<9.That means it is "Alva spent less than 9%"
Answer:
it is c
Step-by-step explanation:
Factor and Simplify the expression sin^2x+sin^2xcot^2x
[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)+sin^2(x)cot^2(x)\implies sin^2(x)+\underline{sin^2(x)}\cdot \cfrac{cos^2(x)}{\underline{sin^2(x)}} \\\\\\ sin^2(x)+cos^2(x)\implies 1[/tex]
Given: m EH =85°, m∠EYV=35°. Find: m EV .
Answer:
155°
Step-by-step explanation:
∠EYV is half the difference of arcs EV and EH
(1/2)(EV -EH) = ∠EYV
(1/2)(EV -85°) = 35° . . . . fill in the given values
EV -85° = 70° . . . . . . . . .multiply by 2
EV = 155° . . . . . . . . . . . . add 85°
______ of symmetry- ALine that divides an object into two congruent halves.
Answer:
"A line"
Step-by-step explanation:
A line of symmetry is a line that divides an object into two congruent halves.
_____
However, not every line that does so is a line of symmetry. The vertical line in the attached diagram divides both figures into congruent halves. It is only a line of symmetry for the green figure.
Answer:
Axis of symmetry
Step-by-step explanation:
That's the "axis of symmetry." It's most often associated with parabolas.
HELP. See attached for question and choices.
Answer: Second Option
{m| [tex]m\leq-0.48[/tex]}
Step-by-step explanation:
We have the following equation
[tex]10(10m+6)\leq12[/tex]
To solve this equation apply the distributive property
[tex]10(10m+6)\leq12[/tex]
[tex]10*10m+6*10\leq12[/tex]
[tex]100m+60\leq12[/tex]
Subtract 60 on both sides of the inequality
[tex]100m+60-60\leq12-60[/tex]
[tex]100m\leq12-60[/tex]
[tex]100m\leq-48[/tex]
Divide between 100 both sides of the inequality
[tex]m\leq-\frac{48}{100}[/tex]
[tex]m\leq-0.48[/tex]
The solution is
{m| [tex]m\leq-0.48[/tex]}
Given: AB ≅ BC BD − median of ΔABC, m∠ABD = 40° Find: m∠ABC, m∠BDC
Answer:
m∠ABC= 80°, m∠BDC= 90°
Step-by-step explanation:
If m∠ABD = 40°, then add 40°+40° to get m∠ABC because AB ≅ BC, meaning their angles would be congruent.
For m∠BDC, just look at the picture and deduce that it's a 90 degree angle.
Answer:
m∠ABC=80° and m∠BDC=90°
Step-by-step explanation:
Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is median of ΔABC.
we have to find the measure of angle ∠ABC and ∠BDC.
As the median of isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD
⇒ [tex]\angle ABC=2\angle ABD[/tex]
[tex]\angle ABC=2\times 40=80^{\circ}[/tex]
Also the median of isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC
⇒ ∠BDC=90°
Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.
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Answer:
x = 21
Step-by-step explanation:
From the rules of secants (and tangents), you know that ...
x^2 = 7·(7 +56)
x = √(7·63) = √441 = 21
_____
When secant lines intersect, the product of distances from the point of intersection to the two points on the circle is a constant. The tangent line is a degenerate case where the two points of intersection are the same point (hence the product of distances is x^2). For the other secant, the near distance is 7, and the far distance is 7+56 = 63.
Interestingly, this property holds whether the secants intersect inside the circle or outside (as here). That makes it easier to remember, since there's really only one rule, not three.
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. C cos(y) dx + x2 sin(y) dy C is the rectangle with vertices (0, 0), (5, 0), (5, 4), (0, 4)
By Green's theorem,
[tex]\displaystyle\int_C\cos y\,\mathrm dx+x^2\sin y\,\mathrm dy=\iint_D\left(\frac{\partial(x^2\sin y)}{\partial x}-\frac{\partial(\cos y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
where [tex]D[/tex] is the region with boundary [tex]C[/tex], so we have
[tex]\displaystyle\iint_D(2x+1)\sin y\,\mathrm dx\,\mathrm dy=\int_0^5\int_0^4(2x+1)\sin y\,\mathrm dy\,\mathrm dx=\boxed{60\sin^22}[/tex]