The rate at which the angle between the sides of the triangle is changing is 4/9 radians per second.
Explanation:In this problem, we are given that one side of the triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. We need to find the rate at which the angle between the sides is changing.
To solve this, we can use the formula:
angle_rate = (-side2_rate/side1)*(cos(angle))/(sin(angle))
Substituting the given values:
angle_rate = (-(-2)/9)*(cos(π/6))/(sin(π/6))
Simplifying, we get:
angle_rate = 4/9
Therefore, the rate at which the angle between the sides is changing is 4/9 radians per second.
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A student taking a math class needs 6 minutes to solve each algebra problem. How many problems can the student solve in 72 minutes?
Final answer:
By dividing the total minutes (72) by the minutes per problem (6), we find that the student can solve 12 algebra problems in 72 minutes.
Explanation:
The student asking how many algebra problems can be solved in 72 minutes if each problem takes 6 minutes can be answered with a simple division operation. You divide the total available time by the time taken for each problem to find the number of problems that can be solved. In this case, 72 minutes ÷ 6 minutes per problem equals 12 problems.
common factor for 4x+8
I need help ASAP Please and thank you
Write an equation or inequality that best represents each statement below
6 times a number, x, is at least 22
A cake decorator rolls a piece of stiff paper to form a cone. She cuts off the tip of the cone and uses it as a funnel to pour decorative sprinkles into small containers. The cone has a radius of 666 cm and a height of 181818 cm. What is the volume of the cone before the end is cut off? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Answer:
V = 216 pi cm^3.
Step-by-step explanation:
Which is the standard form of the equation of the parabola that has a vertex of (–4, –6) and a directrix of y = 3?
Answer:
The required equation is [tex](x+4)^2=-36(y+6)[/tex].
Step-by-step explanation:
The standard form of the equation of the parabola is
[tex](x-h)^2=4p(y-k)[/tex] .... (1)
where, (h, k) is vertex and y = k - p is directrix.
It is given that vertex of parabola is (–4, –6) and the directrix is y = 3.
[tex](-4,-6)=(h,k)[/tex]
On comparing both the sides, we get
[tex]h=-4,k=-6[/tex]
Directrix of the parabola is
[tex]y=k-p[/tex]
Put y=3 and k=-6 in the above equation.
[tex]3=-6-p[/tex]
[tex]3+6=-p[/tex]
[tex]9=-p[/tex]
[tex]-9=p[/tex]
Substitute h=-4,p=-9 and k=-6 in equation (1).
[tex](x-(-4))^2=4(-9)(y-(-6))[/tex]
[tex](x+4)^2=-36(y+6)[/tex]
Therefore the required equation is [tex](x+4)^2=-36(y+6)[/tex].
Determine whether it is possible to circumscribe a circle about the quadrilateral.
80 POINTS
In the equation x=8y , what is the unit rate?
Trig: Use a half angle formula to find the exact value of the expression?
cos(5pi/12)
The correct answer is [tex]\frac{1}{2}[/tex].
To find the exact value of [tex]\cos(5\pi/12)[/tex] using a half-angle formula, we can follow these steps:
[tex]\cos(2\theta) = 2\cos^2(\theta/2) - 1[/tex]
Substituting [tex]\theta = 5\pi/6[/tex], we get:
[tex]\cos(5\pi/3) = 2\cos^2(5\pi/12) - 1[/tex]
[tex]\cos^2(5\pi/12) = \frac{\cos(5\pi/3) + 1}{2}[/tex]
[tex]\cos(5\pi/3) = \cos(\pi/3 + \pi) = -\cos(\pi/3)[/tex]
[tex]\cos(\pi/3) = \frac{1}{2}[/tex]
[tex]\cos(5\pi/3) = -\frac{1}{2}[/tex]
[tex]\cos^2(5\pi/12) = \frac{-\frac{1}{2} + 1}{2} = \frac{1}{4}[/tex]
[tex]\cos(5\pi/12) = \pm\sqrt{\frac{1}{4}} = \pm\frac{1}{2}[/tex]
Since cosine is an even function, we take the positive value.
[tex]\cos(5\pi/12) = \frac{1}{2}[/tex]
Therefore, the exact value of [tex]\cos(5\pi/12)$ is $\frac{1}{2}[/tex].
Complete question:
Use a half angle formula to find the exact value of the expression?
[tex]\cos(5\pi/12)[/tex]
A basketball player made 57 out of 100 attempted free throws. What percent of free throws was made?
ashley measure the shell she collect she records the measurements in the chart
15% of the school parking spaces are handicap spaces. The school has 18 handicap spaces. How many parking spaces are there?
Answer:
The answer is "120"
Step-by-step explanation:
I did it myself, and this is the answer i got :) I made sure it was correct but let me know if you have problems!
3x - 12 + 6x + 9?/ Help Please
The third side of an isosceles triangle is 2 inches shorter than each of the other two sides. if the perimeter of this triangle is 67 inches find the length of each side.
A random sample of size n = 64 is taken from a population with mean μ = −12.2 and standard deviation σ = 5.
a. calculate the expected value and the standard error for the sampling distribution of the sample mean. (negative values should be indicated by a minus sign. round "expected value" to 1 decimal place and "standard error" to 4 decimal places.)
The expected value for the sampling distribution of the sample mean is -12.2. The standard error for the sampling distribution of the sample mean is 0.6250.
Explanation:The expected value for the sampling distribution of the sample mean can be calculated using the formula µx = μ = -12.2. So, the expected value is -12.2.
The standard error for the sampling distribution of the sample mean can be calculated using the formula σx = σ/√n, where σ is the population standard deviation and n is the sample size.
Substituting the given values, we get σx = 5/√64 = 0.6250 (rounded to four decimal places).
The expected value and the standard error for the sampling distribution of the sample mean is 0.6250.
Expected Value: -12.2
Standard Error: 0.6250
1. The expected value (mean) of the sampling distribution of the sample mean is equal to the population mean, which is given as -12.2. Therefore, the expected value of the sampling distribution is also -12.2.
2. The standard error (SE) of the sampling distribution of the sample mean is calculated using the formula:
[tex]\[ SE = \frac{\sigma}{\sqrt{n}} \][/tex]
where [tex]\sigma[/tex] is the population standard deviation and n is the sample size.
Given [tex]\sigma[/tex] = 5 and n = 64, we can calculate the standard error as follows:
[tex]\[ SE = \frac{5}{\sqrt{64}} = \frac{5}{8} = 0.625 \][/tex]
Rounded to four decimal places, the standard error is 0.6250.
the initial population was 50 thousand people and the population increased by 12% each year. Determine the function rule for this definition.
A scale drawn on the map shows that 1 inch represents 24 miles. Of two cities are 2.25 inches apart on the map, what is the distance between them in real life?
About 12% of men and 10% of women are left-handed. if we select a person at random, are the event that the person is male and the event that the person is left-handed independt or associated?
The correct option is A. Gender and handedness are associated because men are more likely to be left-handed than women. This conclusion is drawn from the different probabilities of being left-handed based on gender, indicating an association rather than independence.
A. Gender and handedness are associated because men are more likely to be left-handed than women - - This statement is correct based on the given information. Men have a [tex]12\%[/tex] likelihood of being left-handed compared to women who have a [tex]10\%[/tex] likelihood. This difference shows an association between gender and handedness.
The other incorrect options are:
B. Gender and handedness are independent because all of the possible combinations of each exist - This option is incorrect because independence between two events means that the occurrence of one event does not affect the occurrence of the other. In this case, the probability of being left-handed depends on whether the person is male or female ([tex]12\%[/tex] for men and [tex]10\%[/tex] for women), indicating an association rather than independence.
C. Gender and handedness are associated because the percentage is an estimate - This option is incorrect because the percentages given ([tex]12\%[/tex]for men and [tex]10\%[/tex] for women) are specific probabilities based on data, not estimates. The difference in these probabilities reflects an association between gender and handedness.
D. Gender and handedness are independent because they are both comprised of mutually exclusive events - This option is incorrect because being male or female (gender) and being left-handed (handedness) are not mutually exclusive events. One can be male or female and still be left-handed or right-handed. Independence would require that the probability of being left-handed is the same regardless of gender, which is not the case here.
The complete Question is
About 12% of men and 10% of women are left-handed. If a person is selected at random, are the event that the person is male and the event that the person is handed independent or associated?
Choose the correct answer below.
A. Gender and handedness are associated because men are more likely to be left handed than women
B. Gender and handedness are independent because all of the possible combinations of each exist
C. Gender and handedness are associated because the percentage is an estimate
D. Gender and handedness are independent because they are both comprised of mutually exclusive events
Kylie writes an equation to solve for the diameter, d, of the circle shown. Solve Kylie’s equation to find the diameter of the circle. 4 (d + 4) = 72 What is the diameter? 7.5 in. 8.25 in. 11.25 in. 13.25 in.
Answer:
8.25 in.
Step-by-step explanation:
In order to solve this you just have to clear the equation that Kylie created to calcuate the diameter of the circle for diameter, in this case, you just need to do the next steps:
[tex]4(d+4)=7^{2} \\4(d+4)=49\\d+4=\frac{49}{4} \\d+4=12.25\\d=12.25-4\\d=8.25[/tex]
Now we know that the diameter of the circle is 8.25 inches.
Last week,you finished level 2 of a video gamr in 32 minutes. Today, you finish level 2 in 28 minutes. What is your percent change
What are the slope and the y intercept of the graph of the liner function shown on the grid
The population of a particular town is given by the function P(t) = 920(1.06)2t, where t is the time in years and P(t) is the population after t years. What is the current population, the percentage growth rate, and the population size (rounded to the nearest whole person) in 4 years?
A: 920, 6% annually, and 1,161
B:920, 6% semiannually, and 1,466
C: 920, 0.6% per year, and 7,801
D:920, 60% semiannually, and 4,135
Katie has 16 3/4 hours to finish 3 school projects. How much time may sge spend in each project if she plans to spend the same amount of time on each.
Without overlapping, how many college basketball courts 94ft x 50ft would fit into a football field 360ft x 160ft?
The sum of two numbers is 45. One number is 4 times as large as the other. What are the numbers?
The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The sum of the two numbers is 45. One number is 4 times as large as the other.
Let the two numbers be x and y. Then the equation is given as,
x + y = 45 ...1
y = 4x ...2
From equations 1 and 2, then we have
x + 4x = 45
5x = 45
x = 9
Then the value of y will be
y = 4(9)
y = 36
The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.
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Fill in the blank. The number pi relates the diameter of a circle to its_____ a.circumference b.center c.radius d.chord
The number pi relates the diameter of a circle to its circumference. Therefore, the correct option to fill in the blank is:
a. circumference
how do u estimate 8.36
Find z such that 6.8% of the standard normal curve lies to the left of z. (round your answer to two decimal places.)
Answer with explanation:
it is given that ,6.8% of standard normal curve lies to left of z.
6.8% [tex]=\frac{6.8}{100}\\\\=0.068[/tex]
We will use z table to calculate the value of z.
First we will go on y axis in z table to see value of 0.06 and then on 0.08 on x axis.Their point of intersection will give value of z at 0.068, which is equal to 0.2483.
Value of Z ,at 6.8% ,when the curve is normal = 0.25
⇒0.25 represents area in the left of ,z=0.068.
The z-score corresponding to 6.8% in the standard normal distribution is approximately -1.48, rounding to two decimal places, ensuring 6.8% lies to the left.
To find the z-score such that 6.8% of the standard normal curve lies to the left of it,
use a standard normal distribution calculator.
For the z-score corresponding to the cumulative probability of 0.068 (6.8%).
Using a standard normal distribution calculator:
The cumulative probability of 0.068 (or 6.8%) in the standard normal distribution calculator.
find the z-score associated with this probability.
The z-score corresponding to a cumulative probability of 0.068 is approximately -1.48 (rounded to two decimal places).
Therefore, the z-score z such that 6.8% of the standard normal curve lies to the left of it is approximately -1.48.
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What is the y-value when x equals -11?
y = -200 – 12(x).
Real Question:
You Make A Table To Use AS A Quick Reference Guide. [tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]
Use The Table Tool To Answer The Question:
[tex]\left[\begin{array}{ccc}-8&-104\\-9&-92\\-10&-80\\-11&-68\\-12&-56\end{array}\right][/tex]
What is the y-value when x equals -11?
[tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]
Step-By-Step Explanation:
Plug In The X-Value [tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\end{array}\right][/tex]
Then You'll Multiply [tex]\left[\begin{array}{ccc}-12(x) Or -12(-11)\\132\end{array}\right][/tex]
To Find The Y-Value Simplify [tex]\left[\begin{array}{ccc}y=-200+132\\y=-68\end{array}\right][/tex]
Answer:
[tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\\y=-200+132\\ y=-68\end{array}\right][/tex]
Choose the right answer. Two hundred fifty tickets are sold at a church fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is .
Answer:
Her probability to win the prize quilt is 0.06, or she has a 6% probability of winning it.
Step-by-step explanation:
In statistics, a probability of 100% is represented with a 1. In this case, if Sarah would have bought the 250 tickets, she would have a probability of 1 to win the prize, as
[tex]\frac{250}{250}=1[/tex]
then, if this expression is multiplied by 100, we could say that the precentage of probability would have been 100%...
But Sarah didn't buy the 250 tickets, instead she bought 15, therefore
[tex]\frac{15}{250}=\frac{3}{50}=0.06[/tex]
which means that the probability of her winning the prize quilt is 0.06, or, if multiplied by 100, she has a 6% probability of winning the prize quilt.