According to the given information, the terminal side of an angle of 7 radians is in the second quadrant.
What is the terminal angle?
The terminal angle is the angle formed by the terminal side of an angle in standard position (i.e., with its initial side along the positive x-axis) and the nearest x-axis. It is typically measured in a counterclockwise direction from the positive x-axis.
An angle of 7 radians is greater than 2π radians (which is approximately 6.28 radians), so it corresponds to more than one full revolution around the unit circle.
To find the terminal side of an angle of 7 radians, we can subtract 2π radians (or 360 degrees) from 7 radians until the result is between 0 and 2π radians. We have:
[tex]$$7 \text{ radians} - 2\pi \text{ radians} \approx 1.716 \text{ radians}$$[/tex]
Since 1.716 radians is less than π radians (which is approximately 3.14 radians), the terminal side of an angle of 7 radians is in the second quadrant.
The terminal side of an angle of 7 radians is in the second quadrant.
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A coat that costs $72 is marked up by 22%. What is the new price of coat
Answer:87.84$
Step-by-step explanation:
72------100%
x----------122%
x=122*72/100=87.84$
The following system of equations is designed to determine concentrations (the c's in g / (m ^ 3) ) in a series of coupled reactors as a function of the amount of mass input to each rector (right hand sides in g / d * ay ):
10c_{1} + 2c_{2} - c_{3} = 27
- 3c_{1} - 6c_{2} + 2c_{3} = - 61. 5
c_{1} + c_{2} + 5c_{3} = - 21. 5
Solve this problem with the Jacobi's iterative method to epsilon_{s} =5\%
After caculating, a) Matrix is given below, b) C₁ = 65460/193,C₂ = 48480/193, C₃ = 64460/193, c)The mass input to reactor 3 is reduced by 40g/day and d) Change of concentration is Δ C₃ = 2950/193
To solve the system of equations, we can use Gaussian elimination or any other suitable method. Here, we will use Gaussian elimination:
Given:
15C₁-2C₂-C₃=4000
-3C₁+18C₂-6C₃=1500
-4C₁-C₂+12C₃=2400
Therefore:
[tex]A=\left[\begin{array}{ccc}15&-3&-1\\-3&18&-6\\-4&-1&12\end{array}\right][/tex][tex]B=\left[\begin{array}{ccc}4000\\1500\\2400\end{array}\right][/tex]
a) The inverse matrix of A would be
[tex]A^-^1\left[\begin{array}{ccc}14/193&37/2895&12/965\\4/193&176/2895&31/965\\5/193&9/965&87/965\end{array}\right][/tex]
b) For solution of [C] = [A^-1][B]
[tex]C=\left[\begin{array}{ccc}C1\\C2\\C3\end{array}\right] =\left[\begin{array}{ccc}14/193&37/2895&12/965\\4/193&176/2895&31/965\\5/193&9/965&87/965\end{array}\right] \\[/tex]
C₁ = 65460/193
C₂ = 48480/193
C₃ = 64460/193
c) For increasing the concentration [C₁] by 10
C₁ = 65460/193 +10
=67390/193
Now again,
[tex]\left[\begin{array}{ccc}15&-3&-1\\-3&18&-6\\-4&-1&12\end{array}\right] \left[\begin{array}{ccc}67390/193\\48480/193\\64460/193\end{array}\right] =\left[\begin{array}{ccc}4150\\1470\\2360\end{array}\right][/tex]
So from the calculation= 2360 -2400= -40
Therefore the mass input to reactor 3 is reduced by 40g/day
d) Now again reducing mass input
[tex]B=\left[\begin{array}{ccc}4000-500\\1500-250\\2400\end{array}\right] = \left[\begin{array}{ccc}3500\\1250\\2400\end{array}\right] \\\\C=\left[\begin{array}{ccc}C1\\C2\\C3\end{array}\right] = \left[\begin{array}{ccc}173530/579\\130640/579\\61510/193\end{array}\right][/tex]
Δ C₃=C₃-C₃’
=64460-61510/193
= 2950/193
Δ C₃ = 2950/193
Therefore that is the change of concentration.
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Standard postage relates to letters between a weight of 0 to 5 . The letters have a probability distribution for the weight f(x)=(3/125) x2 for 0 < x < 5
What is the probability of getting a score less than 4.3?
The probability of getting a score less than 4.3 for standard postage is 0.77
In this scenario, f(x) = (3/125) x^2 is a probability density function for the weight of a letter, x, for standard postage where x ∈ (0,5). Thus, the integral of the probability density function between two bounds would give the probability of the event occurring. The probability of getting a score less than 4.3 can be calculated as follows:Pr(X < 4.3) = ∫_0^4.3(3/125) x^2 dx= [(3/125) * (1/3) * 4.3^3] - [(3/125) * (1/3) * 0^3]= 0.77
Thus, the probability of getting a score less than 4.3 for standard postage is 0.77.
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ο Δ Δ Δ Δ 2
A
52. Last month, 200 people each donated between 2 and 5
food items to the Downtown Food Bank, according to the
information in the bar graph below.
Which of the
following statements about the mean, median, and mode
of the data must be true?
F.
G.
H.
1.
K.
Number of Donors
100
80
60
40
20
0
2 3
4 5
Number of Food Items Donated
The mean number of food items donated is equal
to the median number of food items donated.
The mode number of food items donated is equal
to the median number of food items donated.
The median number of food items donated is
greater than the mode number of food items
donated.
The mode number of food items donated is greater
than the median number of food items donated.
The mean number of food items donated is greater
than the median number of food items donated.
Answer:
Step-by-step explanation:
To determine which statement must be true about the mean, median, and mode of the data, we need to analyze the bar graph provided.
We see that the data is not normally distributed, but rather skewed to the right. Therefore, the mean will be greater than the median, as the mean is affected by outliers and extreme values, which in this case will pull it towards the higher end.
Furthermore, since there is no single value that appears more frequently than any other, there is no mode for this data set.
Therefore, the statement that must be true is:
The mean number of food items donated is greater than the median number of food items donated. (Option K)
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Jose's age is 7 years less than 2/3 of his dad's age. If Jose's dad is d years old, write an expression that determines how old Jose is. (No spaces in the expression when typing into solution)
If Jose's dad is 30 years old, how old is Jose?
The expression that determines hοw οld Jose is, in terms of his dad's age, is [tex]\frac{2}{3}d - 7[/tex]
What are Linear equatiοns?Linear equatiοns are equatiοns whοse highest pοwer οf the variables is 1. The graph οf a linear equatiοn is a straight line.Let J be Jοse's age. Accοrding tο the prοblem, Jοse's age is 7 years less than 2/3 οf his dad's age.
We can express this mathematically as:
J = (2/3)d - 7
where d is Jοse's dad's age.
Therefοre, the expressiοn that determines hοw οld Jοse is, in terms οf his dad's age, is [tex]\frac{2}{3}d - 7[/tex]
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There are 4,028 cell phones in a box. 1% of them were broken. 50% of the good phones were sold to another city and the remaining were sold locally. What percent of the phones were sold locally? Round to the nearest one percent.
If 1% of the phones were broken, then the number of good phones is 99% of 4,028:
99/100 x 4,028 = 3,987.72 (rounded to 3,988)
Out of the 3,988 good phones, 50% were sold to another city:
50/100 x 3,988 = 1,994
So, the remaining number of good phones that were sold locally is:
3,988 - 1,994 = 1,994
To find the percentage of phones sold locally, we need to divide the number of phones sold locally by the total number of phones:
1,994 / 4,028 = 0.494
Then, we can convert this decimal to a percentage and round to the nearest one percent:
0.494 x 100 ≈ 49%
Therefore, approximately 49% of the phones were sold locally.
Use the remainder theorem....
NEED HELP PLEASE HELP
Answer:
B. -3/2
Step-by-step explanation:
Plot the Graph, then look for the rise over run. This equation has a rise of -6, and a run of 4. so [tex]\frac{-6}{4}[/tex], or -[tex]\frac{3}{2}[/tex]
simplify the square root of 2 divided by 125
Answer:
20√2
Step-by-step explanation:
20√2 = 28.284...
Raymond works for a pharmaceutical company that is testing the effectiveness of a new medication
The exponential function that gives the amount of medication y in the body after x hours is:
[tex]y = 400(\frac{2}{3} )^x[/tex]
What is an exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. When the input variable x appears as an exponent in the formula f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. A constant serves as the exponent in an exponential function, but not the other way around (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
The complete question is given below.
The initial value of the medication = 400 mg
This is the value of a.
a = 400
b is the growth or decay factor in the exponential function formula.
In this question, it is the decay factor.
b = 1-r
where r is the decay rate = 1/3
b = 1-1/3 = 2/3
The exponential function is given by the formula:
y = abˣ
[tex]y = 400(\frac{2}{3} )^x[/tex]
Therefore the exponential function that gives the amount of medication y in the body after x hours is:
[tex]y = 400(\frac{2}{3} )^x[/tex]
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Please answer
Determine the common difference of the arithemetic sequence in which a1=3 and a4=15
Check the picture below.
The common difference of the arithmetic sequence in which a1=3 and a4=15 is d = 4
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is [tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference is [tex]T_{n+1} - T_n[/tex]
for all positive integer values of n
Given that a1=3 and a4=15
nth term of G.P is ;
Calculation:
[tex]T_n = a + (n-1)d[/tex]
a1 = 3
a2 = 3+ d
a3 = 3+ d
a4=15
3 + 3d = 15
d =4
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Which symbol will make this statement true?
|-6| ______ 2
>
<
=
Answer:
The > (Greater Than) symbol
Step-by-step explanation:
The absolute value symbol makes the value inside positive by calculating the inside's distance from 0. -6 is 6 units away from zero.
|-6| = 6, and 6 is greater than 2
You purchased a used car for $12,000 and have agreed to pay off
the car in 48 monthly payments of $365 each. What will be the total
sum of your payments?
Answer:
$17,520
Step-by-step explanation:
The total can be found using multiplication.
48 x 365
Use long multiplication to solve this.
After solving, you should get $17,520.
A spinner has three sections which are coloured red, green and blue.
Chris spun the spinner 100 times in total.
The frequency of spins that landed on green was 35.
The ratio of the frequency of red to the frequency of green was 4 : 7.
What is the estimated probability of the spinner landing on blue?
Give your answer as a decimal.
The estimated probability of the spinner landing on blue is 0. This means the spinner will not land on blue.
What is probability?Probability is the measure of how likely an event is to occur out of the number of possible outcomes. It is expressed in terms of a number between 0 and 1, where 0 means that the event is impossible and 1 means the event is certain. Probability is used to calculate the likelihood of an event or outcome in a variety of situations, from predicting the weather to playing the lottery.
The estimated probability of the spinner landing on blue can be calculated by using the ratio of the frequency of red to the frequency of green.
As the ratio is 4 : 7, the frequency of red is 4/11 of the total frequency of 100 spins. The frequency of green is 7/11 of the total frequency of 100. Therefore, the frequency of blue is 100-(4/11+7/11) which is 1 – (11/11) = 0.
Therefore, the estimated probability of the spinner landing on blue is 0. This means the spinner will not land on blue.
To calculate the estimated probability, first we need to calculate the total frequency of all the sections. This is done by adding all the frequencies of the sections together. In this case, the total frequency is 100. Then using the ratio of the frequency of red to the frequency of green, calculate the frequency of red and the frequency of green. Subtract the total frequency and the total frequency of red and green from the total frequency, to get the frequency of blue. Finally, divide the frequency of blue by the total frequency and convert it into a decimal. This will give us the estimated probability of the spinner landing on blue.
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The lines represented by the equations +
the same line
O parallel
neither parallel nor perpendicular
+²1²x=4 and 3x+6y= 12 are
perpendicular
Answer:
on dividing both side of the second eqn by 6 you get
y+1/2x=2
so they are parallel to each other
[
keep in mind that:
any two equations are parallel if they have same coefficient for x and y but different constant values.
]
Answer:
slope(m1)= -coeff.of x/coeff.of y
:.m1= -1/2
slope(m2)= -coeff.of x/coeff.of y
:.m2= -1/2
so it is parallel to each other......
Solve, (x + 2) (x +3) – (x + 2) (x – 3) = 0
Answer:
The value of x is -2.
Step-by-step explanation:
(x+2) (x+3) - (x+2) (x-3) =0
Multiplying
x(x+3) +2(x+3) - [x(x-3) +2(x-3) =0
x² +3x +2x +6 -[x²-3x +2x -6] =0
Opening the bracket
x²+3x +2x +6 -x²+3x-2x+6=0
Adding the like terms
6x+12=0. [x²-x²=0]
6x = -12
x = -12 ÷6
x = -2
complete the steps to solve the equation -16x - 13= -157
Answer: no
Step-by-step explanation:
Can anyone help with this question? I’m stumped.
The fewest number of cards you will have to look at the back of to know what color the back of each card is 2
How to determine the number of cardsTo determine the color of the back of each card, we need to observe the color of the opposite side.
We can start by looking at the two-sided white card.
Since both sides of the card are white, no matter which side we look at, we can't determine the color of the back of the card.
So, we have to move on to the other cards.
Next, we can look at the two-sided black card. If we look at either side of this card, we know that the back of the card must also be black.
So, we have determined the color of the back of this card by looking at just one side.
The above means that, in the worst-case scenario, we will have to look at three cards, but we only need to look at two sides of each card
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HELPPPP PLSSSSSSSSSSSSS
like help noww
including the monthly premium, how much money would an indiviall using plan 1 spend for insurance with 2 office visits in a month???
Including the monthly premium the total money spent using plan 1 spend for insurance with 2 office visits in a month is $230.
What is insurance?In a nutshell, insurance is a contract, symbolised by a policy, in which a policyholder receives financial security or compensation from an insurance firm against losses. In order to make payments to the insured more manageable, the firm combines the risks of its clients.
Insurance policies are intended to protect against the possibility of monetary losses, large and little, that may be brought on by harm to the insured or their property or by liability for harm or injury given to a third party.
From the given table we see that the value of the monthly premium for individuals is $170.
Now, the value of office visit is: $30.
There are 2 office visits thus, 2(30) = 60.
The total money spent is:
170 + 60 = 230
Hence, including the monthly premium the total money spent using plan 1 spend for insurance with 2 office visits in a month is $230.
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Reuben and his wife are each starting a saving plan. Reuben will initially set aside $50 and then add $50. 85 every week to the savings. The amount A (in dollars) saved this way is given by the function =A+50. 85N50, where N is the number of weeks he has been saving.
His wife will not set an initial amount aside but will add $70. 55 to the savings every week. The amount B (in dollars) saved using this plan is given by the function =B70. 55N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible
Answer:
T=50+86.49N
Step-by-step explanation:
you just have to combine A and B.
Total (T)=A(50+30.65N)+B(55.85N) thank just open the prentices and add 30.65N and 55.85N=86.49N. so total is initial savings+ weekly savings by both.
Three friends are eating enormous freeze pops on a hot summer day. Benjamin has a strawberry freeze pop that has a density of 0.8 pounds per cubic inch. His freeze pop is shaped like a square pyramid with a 1.5 inch side and a height of 2 inches. Kendra has a giant grape freeze pop which has a density of 0.2 pounds per cubic inch. The freeze pop is a cylinder which has a radius of 1 inch and a height of 4 inches. Luke has a giant cherry freeze pop, which has a density of 0.05 pounds per cubic inch and is also shaped like a cylinder which has a radius of 1.5 inches and a height of 3 inches. Answer the following questions.
1. Who is eating the largest mass of freeze pop? Round to the nearest tenth of a pound.
2. How many more pounds of freeze pop does Kendra have compared to Luke? Round your answer to the nearest tenth.
3. If all three freeze pops were the same size, which flavor would you prefer, based on the densities? Explain why.
Hence, in answering the stated question, we may say that As a result, cylinder Kendra has approximately 1.45 pounds more freeze pop than Luke.
what is cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most basic curved geometric forms. In elementary geometry, it is called a prism with a circle as its basis. A cylinder is also defined as an infinitely curved surface in several modern domains of geometry and topology. A "cylinder" is a three-dimensional object with curved sides and round tops and bottoms. A cylinder is a three-dimensional solid figure with two identical circle bases linked by a curving surface at the cylinder's height, which is determined by the distance between the bases from the centre. Cold beverage cans and toilet paper wicks are both examples of cylinders.
1.5 cubic inches = 1/3 * 2.25 * 2
1.5 * 0.8 = 1.2 lbs.
* radius2 * height = * 12 * 4 = 4 cubic in.
Kendra's freeze pop has the following mass:
4 * 0.2 = 0.8 lbs.
The volume for Luke's freeze pop is:
*1.52 x 3 = 6.75 cubic inches
And the majority is:
6.75 * 0.05 = 0.3375 lbs
1.2 pound Benjamin
Kendra weighs 0.8 2.51 pounds.
Luke: 0.3375 1.06 lbs.
As a result, Kendra is consuming the most freeze pop, weighing around 2.51 pounds.
We may deduct Luke's mass from Kendra's to figure out how many more pounds of freeze pop Kendra has than Luke:
2.51 - 1.06 1.45 lbs.
As a result, Kendra has approximately 1.45 pounds more freeze pop than Luke.
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How many 3 digit numbers can be formed using numerals in the set 3,2,7, and 9 if repetition is not allowed?
There are 24 possible 3 digit numbers that can be formed using numerals 3,2,7 and 9 without repetition.
Since repetition is not allowed, the first digit can only be 3, 2, 7 or 9. Each of the four digits can be chosen in 4 ways.
For the second digit, the choices are now reduced to 3, 2 or 7 (since 9 has already been used). There can be 3 ways to pick the second digit.
For the third digit, the choices are now reduced to 2 or 7 (since 3 and 9 have already been used). There can be 2 ways to pick the third digit.
Therefore, there are 4 x 3 x 2 = 24 possible 3 digit numbers that can be formed using numerals 3,2,7 and 9 without repetition.
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Please help asap! thanks!
Answer:
it could be either A or D
SLAP ME IF I AM WRONG!
Step-by-step explanation:
Please Answer the question.
Which of the fractions below is closest to zero? OA) 1/2 O B) 1/6 OC) 1/9 OD) 1/12
Answer:
1/12
Step-by-step explanation:
Lets look at all of the answers:
1/2
1/6
1/9
1/12
1/12 is closest to 0 because a higher denominator means a lower number that is closer to 0.
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The measure of ∠N is (15x +47) °. If x=8, find the measure of∠N, then classify the angle
line bm bisects angle abc if angle mbc is 32 degrees what is the measure of anble abc
The measure of angle abc is 64 degrees.
What is the measure of angle abc?An angle bisector is simply a line or ray that divides an angle into two equal parts.
Given that;
Line bm bisects angle abc.
Angle mbc = 32 degreesAngle abc = ?First, we determine the measure of angle abm.
Since line bm bisects angle abc, it divides the angle into two equal parts.
Hence;
Angle mbc = angle abm
Angle abc = angle mbc + abm
Plug in the value
Angle abc = 32 degrees + 32 degrees
Angle abc = 64 degrees.
Therefore, 64 degrees is the measure of ∠b.
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Can someone help me with this
Answer: f(x)=90
Step-by-step explanation:
f(x)=-(-9)^2-(9) substitute -9 for x
f(x)=9^2+9 simplify negatives
f(x)=81+9 simplify exponents
f(x)=90 add
1. A rectangle is 10cm long and its perimeter is 26 cm. Find the breadth of the rectangle
If a rectangle is 10cm long and its perimeter is 26 cm, then the breadth of the rectangle is 3 cm
Let's assume the breadth of the rectangle to be 'b' cm.
We know that the perimeter of a rectangle is the sum of the lengths of all four sides.
Therefore, the perimeter of the given rectangle = 2(length + breadth)
Given, the length of the rectangle = 10 cm and the perimeter = 26 cm.
So, 2(10 + b) = 26
Simplifying this equation, we get:
20 + 2b = 26
Move 20 to right hand side of the equation
2b = 26 - 20
2b = 6
b = 6/2
b = 3 cm
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the angle of the elevation from a park bench is 778 feet from the base of the getaway arch in St. Louis Missouri is 39 degrees how tall is the getaway arch
By trignometric property, The 630 .18 feet tall is the gateway arch .
What is the definition of trigonometry?
Trigonometry is a discipline of mathematics that examines certain functions of angles and how to use them in computations. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc).
As given
The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.
Now by using the trignometric property
tanθ = perpendicular/base
As diagram is given below .
θ = 39
tan39° = AB/CB
CB = 778 feet
tan39° = 0.81 (approx)
0.81 = AB/778
AB = 0.81 × 778
AB = 630 .18 feet
Therefore, the 630 .18 feet tall is the gateway arch .
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