Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?
Answers
line l is the orange line, intersecting the positive x-axis and the positive y axis.
The angle with measure ∅ is the angle made by the line and the positive x-axis. It is the obtuse (>90° angle) shown in the picture.
the slope of the line l is tan∅
Related Questions
How many solutions to 15x+11=8x
Answers
15x+11=8x
collecting like terms we get:
11=8x-15x
11=-7x dividing both sides by -7 we get:
x=-7/11
therefore we conclude that the number of solutions is one
PLEASE HELP?? EASY 5 POINTS!!! The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.
Answers
36 in³ + 12 in³ = 48 in³
Volume of the Blue Prism in Model 1:
48 in³ - 16 in³ = 32 in³
An apartment has 1026 square feet of carpeting. How much is this in square meters? Use the following conversion: 1 square meter is 10.8 square feet.
Answers
answer this plz
14 students are surveyed about the clothes they are wearing.
8 students are wearing a t-shirt.
2 students aren't wearing jeans or a t-shirt.
3 students are wearing jeans and a t-shirt.
How many students are wearing jeans, but not a t-shirt?
2
3
4
5
Answers
Answer:
its
Step-by-step explanation:
The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 40.4 meters, how wide must it be?
Answers
solve for "w".
Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.
Answers
The dependent variable is the additional charge applied for each hour whereas the independent variable is the charge to be applied on the first hour
The dependent variable would be $1.45 for each additional hour. The cost depends on every hour so we can't really calculate it unless we have the hours given.
$3 is independent since it's only charged on the first hour. It doesn't depend on any other information.
Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.
John's goal is to have more than -7 dollars in his bank account by the end of the month. The variable d is the number of dollars in John's bank account at the end of the month. Write an inequality in terms of d that is true only if John meets his monthly goal.
Answers
Answer:
d > - 7
Step-by-step explanation:
Here, d represents the number of dollars in John's bank account at the end of the month.
As per statement,
In John's account,
The balance must be more than -7 dollars,
That is, Number of dollars at the end of each month > - 7 ( '>' is used for more than )
⇒ d > - 7
Which is the required inequality.
A basketball player makes 39% of her shots from the free throw line. suppose that each of her shots can be considered independent and that she takes 5 shots. let x = the number of shots that she makes. what is the standard deviation for x?
Answers
Answer: 1.09
Step-by-step explanation:
Given : A basketball player makes 39% of her shots from the free throw line.
i.e. Proportion of her shots from the free throw line: p= 0.39
We assume that each of her shots can be considered independent .
She takes 5 shots.
i.e. Number of trials : n= 5
Let x = the number of shots that she makes.
Then , the standard deviation for x will be :-
[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{5(0.39)(1-0.39)}\\\\=\sqrt{1.1895}=1.09064201276\approx1.09064201276\approx1.09[/tex]
Hence, the standard deviation for x= 1.09
Final answer:
The standard deviation for the number of shots made by a basketball player who has a 39% success rate and takes 5 shots is approximately 1.09 shots, calculated using the binomial distribution formula.
Explanation:
To find the standard deviation for the number of shots made by a basketball player who makes 39% of her shots, we use the concept of a binomial distribution.
Given that each shot is independent and that she takes 5 shots, with x representing the number of shots made, we can calculate the standard deviation using the formula for a binomial distribution.
The formula for the standard deviation (σ) in a binomial distribution is σ = √[n × p × (1 - p)], where n is the number of trials (in this case, 5 shots), and p is the success probability per trial (in this case, 0.39 for making a shot).
Plugging in the values, we get σ = √[5 × 0.39 × (1 - 0.39)] = √[5 × 0.39 × 0.61] = √[1.1885] ≈ 1.09 shots.
Therefore, the standard deviation for the number of shots made is approximately 1.09 shots.
Suppose your average, after taking 4 quizzes, is 73(out of 100). What must your average be on the next 5 quizzes to increase your average to 88 out of 100?
Answers
x = average of next 5 quizzes
4 * 73 = first 4 quizzes
There will be a total of 4 +5 = 9 quizzes
Average of all quizzes = 88 = (4*73+5x)/9
9*88 = 9*(292 +5x)/9
792 = 292 + 5x
500 = 5x
X = 500/5 = 100
Next 5 quizzes need to average 100
Which of the following is not one of the three ways to express ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4
Answers
Find the circumference and the area of a circle with diameter
2ft
Answers
The circumference of a circle with diameter 2ft is 2π ft and the area is π ft².
Explanation:To find the circumference of a circle, you can use the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 2ft, so the circumference would be C = π(2) = 2π ft. To find the area of a circle, you can use the formula A = πr², where A is the area and r is the radius. Since the radius is half the diameter, the radius would be 2ft/2 = 1ft. Therefore, the area would be A = π(1)² = π ft².
Final answer:
The circumference of a circle with a diameter of 2 feet is approximately 6.28 feet, and the area is approximately 3.14 square feet using the formulas C = πd and A = πr².
Explanation:
To find the circumference and the area of a circle with a diameter of 2 feet, we can use the formulas for circumference and area. The diameter of the circle is given as 2 feet. Therefore, the radius (r) is half of the diameter, which is 1 foot.
The formula for the circumference of a circle is C = πd where C is the circumference, π (pi) is approximately 3.14159, and d is the diameter. Since the diameter (d) is 2 feet, the circumference is:
C = π × 2 feet ≈ 3.14159 × 2 feet ≈ 6.28318 feet
So the circumference is approximately 6.28 feet.
The formula for the area of a circle is A = πr² where A is the area and r is the radius of the circle. Using the radius 1 foot, we find the area as follows:
A = π × (1 foot)² ≈ 3.14159 × 1 foot × 1 foot ≈ 3.14159 square feet
So the area of the circle is approximately 3.14 square feet.
The histogram shows the duration, in minutes, of movies in theaters.
What relationship between the median and mean is shown by the histogram?
A) The mean is less than the median.
B) The median is less than the mean.
C) The mean is equal to the median.
D) The median and mean cannot be compared from a histogram.
Answers
The mean of these data is (2+4+5+4+3+3+2+2)/8 = 3.125
The median is the middle data when the frequency is arranged from least to greatest. Thus, the median in the data set 2, 2, 2, 3, 3, 4, 4, 5 is 3. Therefore, the mean is greater than the median.
The answer is: the median is less than the mean
Noel reads 90 minutes a day for six days. Tyra reads 60 minutes for eight days. what is the diffrence , in minutes , between the total amount of time Noel read and the total amount Tyra read.
A. 30
B. 40
C.60
D. 80
Answers
Tyra : 60 minutes a day for 8 days....60 * 8 = 480 minutes
difference of : 540 - 480 = 60 <==
The difference between the total reading times of Noel and Tyra is 60 minutes. Therefore, the correct option is option C.
The difference in minutes between the total time Noel read and Tyra read can be calculated by adding up the individual reading times for each and then finding the difference.
Calculate Noel's total reading time: 90 minutes/day * 6 days = 540 minutes.Calculate Tyra's total reading time: 60 minutes/day * 8 days = 480 minutes.Find the difference: 540 minutes (Noel) - 480 minutes (Tyra) = 60 minutes.Perform the operation and reduce the answer fully.
frac{1}{12}+\frac{5}{9}
Answers
To solve this manually, you must find first the greatest common factor of the denominators. To do this, simply multiply 12×9 = 108. Now, you know that the final answer would have a denominator of 108.
1 5 [(108/12)*1] + [(108/9)*5]
--- + --- = -----------------------------------
12 9 108
Now for the numerator, you divide the denominator, 108, to each of the addends, 12 and 9. Then, multiply it with their respective numerators. The answer would then be 69/108. Both numerator and denominator are multiples of 3, so you can simplify them further by diving each with 3. The final answer is 23/36.
HELP PLEASE
Evaluate the expression.
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
v ⋅ w
a) -41
b) <-20, -36, 15>
c) <-28, 18, -35>
d) -9
Answers
Note-x means multiply.
Answer:
v . w = <-20, -36, 15>
Step-by-step explanation:
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
To find the dot product of vectors we multiply the numbers
We need to multiply v and w
vectors is in the form of <x,y,z>
Multiply all the x values
4 times -5= -20
6 times -6 = -36
-5 times -3 = 15
So v . w = <-20, -36, 15>
for the function y=-2+5sin(pi/12)(x-2)), what is the minimum value
Answers
[tex]y=-2+5\sin\left(\dfrac\pi{12}(x-2)\right)[/tex]
recall that [tex]-1\le\sin x\le1[/tex], which means
[tex]-1\le\sin\left(\dfrac\pi{12}(x-2)\right)\le1[/tex]
[tex]\implies-5\le5\sin\left(\dfrac\pi{12}(x-2)\right)\le5[/tex]
[tex]\implies-7\le-2+5\sin\left(\dfrac\pi{12}(x-2)\right)\le3[/tex]
and so the minimum value is -7.
Answer:
-7
Step-by-step explanation:
We are given that a function
[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]
We have to find the minimum value of y.
We know that range of sin x is [-1,1].
[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]
[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]
[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]
[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]
[tex]-7\leq y\leq 3[/tex]
Maximum value of y=3
Minimum value of y=-7
Hence, the minimum value of given function =-7
How many different three digit numbers can be written using digits 1,2,3,4,5 without any repeating digits? Thank you.
Answers
The 1st digit can be written in 5 ways
The 2nd digit can be written in 4 ways (since 1 already gone and no repetition)
The 3rd digit can be written in 3 ways (since 2 already gone and no repetition)
Total number of ways = 5x4x3 = 60 ways
2nd Method : Permutation (since ORDER MATTERS) of 3 digits chosen among 5 (with no repetition)
⁵P₃ = (5!)/(5-3)! = (5!)/(2!) = 60 ways
We can use the principles of permutation to find out that there are 60 different three-digit numbers that could be formed using the digits 1,2,3,4,5 without repetition.
Explanation:In order to find out how many different three-digit numbers can be formed using the digits 1,2,3,4,5 without repetition, we use the principles of permutation. Firstly, we should determine how many options we have for each digit place in the three-digit number.
There are 5 possible digits for the first place (since none has been used yet).There are 4 remaining digits for the second place.Finally, there are only 3 digits left to fill the third place.We then multiply these options together (5 x 4 x 3) which equals to 60 different three-digit numbers.
Learn more about Permutations here:https://brainly.com/question/23283166
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what is 475% of 9.2?
Answers
Explain how you can use place value patterns to describe how 50 and 5000 compare
Answers
The place values in the pattern are: ones, tens (10*ones), hundreds (10*tens), thousands (10*hundreds),...
So, 50 = 5 tens
5000= 5 thousands, 0 hundreds, 0 tens, 0 ones
So, 5000 > 50
What is the total amount in an account that has had $35 per month added into it for 30 years and grew with an annual interest rate of 7%?
Answers
Fv=pmt [(1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT monthly payment 35
R interest rate 0.07
K compounded monthly 12 because the payment is monthly
N time 30 years
Fv=35×(((1+0.07÷12)^(12×30)
−1)÷(0.07÷12))
=42,698.98
Which expression is the greatest common factor (GCF) of the terms of trinomial 12x^7y^9 + 6x^4y^7 - 10x^3y^5
Answers
Answer: 2. [tex]\mathbf{2x^3y^5}[/tex]
Step-by-step explanation:
Greatest common factor of any two or more expression is the largest common expression that divides them.The given expression : [tex]12x^7y^9 + 6x^4y^7 - 10x^3y^5[/tex]
Term 1 : [tex]12x^7y^9[/tex]
Term 2 : [tex]6x^4y^7[/tex]
Term 3: [tex]- 10x^3y^5[/tex]
Lowest power of x = 3
Thus , The highest common power of x = [tex]x^3[/tex] (i)
Lowest power of y = 5
The highest common power of y =[tex]y^5[/tex] (ii)
Greatest common factor of 12, 6 , -10= 2 [Because 2 is the largest number that divides all of them] (iii)
From (i) , (ii) , (iii) , we have
Greatest common expression : [tex]2x^3y^5[/tex]
Hence, the correct answer is 2. [tex]\mathbf{2x^3y^5}[/tex]
Plastic storage bins are designed so they can be nested. The picture shows how each one fits inside another, leaving only the top part showing. The 4 stacked 10-gallon bins shown here measure 29 inches high. The height of the stack grows at the rate of 4 inches for each added bin. Write an equation in the form y = mx + b to describe the relationship between x, the number of nested bins, and y, the height of the stack.
Answers
so for every added bin, the stack grows by 4 inches. rise/run, the run is 1, the rise is 4, 4/1 = m = slope
now.... in the picture not shown hehee, the 10-gallon bins, 4 of them measure up to 29 inches high.... wait a second.. I thought the rise was only 4?
well, there are 4 bins, like in this case, so the rise should be 4*4, or 16, but there are 29 inches, that means, the slack leftover is the "initial value", or y-intercept, which should be 29 - 16, or 13.
[tex]\bf slope=m=\cfrac{rise}{run}\implies \cfrac{4}{1}\implies 4 \\\\\\ y-intercept\implies 13 \\\\\\ y=mx+b\implies y=4x+13[/tex]
The points A(12,7)A12,7, B(12,-3)B12,-3, C(-2,-3)C-2,-3, and D(-2,7)D-2,7 form rectangle ABCDABCD. Which point is halfway between AA and BB?
Answers
A (12, 7)
B (12, -3)
Mid point ([tex] \frac{12+12}{2} [/tex], [tex] \frac{7+-3}{2} [/tex])
Mid point ([tex] \frac{24}{2} [/tex], [tex] \frac{4}{2} [/tex]}
Mid point (12, 2)
The table shows how an elevator 500 feet above the ground is descending at a steady rate. Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending? h(t) = 5t + 500 h(t) = 5t – 500 h(t) = –5t + 500 h(t) = –5t – 500
Answers
h(t)=-5t+500.
The correct answer is h(t)=-5t+500
A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?
Answers
the rate going south is 13, the rate going east is 10
it took a total amount of 6hours and 72miles for the whole travel
so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles
so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours
thus [tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ South&d&13&t\\ East&72-d&10&6-t \end{array} \\\\\\ \begin{cases} \boxed{d}=13t\\ 72-d=10(6-t)\\ ----------\\ 72-\boxed{13t}=10(6-t) \end{cases}[/tex]
solve for "t"
so, it travelled East for 6-t hours
Suppose we select, without looking, one marbles from a bag containing 4 red marbles and 10 green marbles.what is the probability of selecting a green marbles? cours hero
Answers
Similarly, the probability of selecting a red marble would be 4/14.
Answer: 0.714
Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (3x + 1) / (x + 1)^3(x^2 + 8)^2
Answers
can be expanded as
[tex]\dfrac a{x+1}+\dfrac b{(x+1)^2}+\dfrac c{(x+1)^3}+\dfrac{dx+e}{x^2+8}+\dfrac{fx+g}{(x^2+8)^2}[/tex]
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before the customer adds the toppings. After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces. Which of the following graphs represents the acceptable weights for the frozen yogurt options?
Answers
So the answer will be the 3rd graph
Answer: Third graph represents the acceptable weights for the frozen yogurt options.
Step-by-step explanation:
Since we have given that
Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4
After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.
So, it means the weight should be lie between 4 ounces and 7 ounces.
So, it can be written as [4,7].
4≤ x ≤7, here, x is the weight of frozen yogurt.
So, third graph represents the acceptable weights for the frozen yogurt options.
The data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. Which of the numbers below is the best measure of the central tendency of the data? {3, 3, 4, 4, 4, 5, 5, 5, 5, 30}
Answers
find the solution x-4y=9 and x-y=-9
Answers
see picture for solution