Answer: 10) 615° & -105°
12) -440° & 280°
Step-by-step explanation:
Coterminal means it is in the exact same spot on the Unit Circle but one or more rotations clockwise or counterclockwise.
Since one rotation = 360°, add or subtract that from the given angle until you get a positive or negative number.
10) 255° + 360° = 615° (this is a POSITIVE coterminal angle to 255°)
255° - 360° = -105° (this is a Negative coterminal angle to 255°)
12) -800° + 360° = -440° (this is a Negative coterminal angle to -800°)
-440° + 360° = -80° (this is a Negative coterminal angle to -800°)
-80° + 360° = 280° (this is a POSITIVE coterminal angle to -800°)
Final answer:
Coterminal angles for 255° are 615° (positive) and -105° (negative) by adding or subtracting 360° respectively. For -800°, the coterminal angles are -80° (positive) and -1160° (negative).
Explanation:
To find a positive and a negative angle coterminal with the given angle of 255°, we can add or subtract multiples of 360° (the total degrees in a circle). For a positive coterminal angle, we can add 360° to 255°:
255° + 360° = 615°
For a negative coterminal angle, we subtract 360° from 255° until we get a negative result:
255° - 360° = -105°
Similarly, for -800°, to find a positive coterminal angle, we keep adding 360° until we get a positive result:
-800° + 360° = -440°
-440° + 360° = -80°
For a negative coterminal angle, we can subtract 360° from -800°:
-800° - 360° = -1160°
The expression f(x) = 12(1.035)x models the monthly growth of membership in the new drama club at a school. According to the function, what is the monthly growth rate?
A.
0.35%
B.
1.035%
C.
3.5%
D.
12%
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
The expression is defined as
[tex]f(x)=12(1.035)^x------------------------(1)[/tex]
As we know the general form of exponential function:
[tex]f(x)=a(1+r)^x--------------------------(2)[/tex]
Here, a denotes the initial amount.
r denotes the growth rate.
On comparing, we get that
[tex]1+r=1.035\\\\r=1.035-1\\\\r=0.035\\\\r=0.035\times 100\%\\\\r=3.5\%[/tex]
Hence, option 'C' is correct.
Answer:
C) 3.5%
Step-by-step explanation:
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
y – 9 = –6(x – 3)
y + 9 = –6(x + 3)
y – 3 = –6(x – 9)
y + 3 = –6(x + 9)
Answer:
y+3= -6(x+9) is the answer
Step-by-step explanation:
Answer:
[tex]y+3=-6(x+9)[/tex]
Step-by-step explanation:
We are given that
Slope of a line=-6
Given point =(-9,-3)
We have to find the equation which represents the line.
The equation of line passing through the given point [tex](x_1,y_1)[/tex] with slope m is given by
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values then we get
The equation of line passing through the point (-9,-3) with slope -6 is given by
[tex]y-(-3)=-6(x-(-9))[/tex]
[tex]y+3=-6(x+9)[/tex]
Hence, the equation of line that passes through (-9,-3) and has a slope -6 is given by
[tex]y+3=-6(x+9)[/tex]
Find the slope of the line that passes through the pair of points (–1.75, 14.5) and (–1, 4.4). Round to the nearest hundredth if necessary.
a.2.52
b.–13.47
c.–1.61
d.–0.07
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Two points are needed through which the line passes:
[tex](x_ {1}, y_ {1}): (- 1.75; 14.5)\\(x_ {2}, y_ {2}}: (- 1; 4.4)[/tex]
Substituting:[tex]m = \frac {4.4-14.5} {- 1 - (- 1.75)}\\m = \frac {-10.1} {0.75}\\m = -13.46666666[/tex]
Rounding:
[tex]m = -13.47[/tex]
Answer:
[tex]m = -13.47[/tex]
Answer:
m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}
Two points are needed through which the line passes:
(x_ {1}, y_ {1}): (- 1.75; 14.5)\\(x_ {2}, y_ {2}}: (- 1; 4.4)
Substituting:m = \frac {4.4-14.5} {- 1 - (- 1.75)}\\m = \frac {-10.1} {0.75}\\m = -13.46666666
Rounding:
m = -13.47
Step-by-step explanation:
solve on the interval [0, 2pi] 2 sec x+5 = 1
Move the 5 to the other side:
[tex]2\sec(x)=1-5=-4[/tex]
Divide both sides by 2:
[tex]\sec(x) = -2[/tex]
Recall the definition:
[tex]\sec(x)=-2 \iff \dfrac{1}{\cos(x)}=-2[/tex]
Invert both sides
[tex]\cos(x) = -\dfrac{1}{2}[/tex]
This is true when
[tex]x=\pm \dfrac{\pi}{3}[/tex]
If you need both angles to be in [0,2pi], you can recall
[tex]\cos\left(-\dfrac{\pi}{3}\right) = \cos\left(-\dfrac{\pi}{3}+2\pi\right) = \cos\left(\dfrac{5\pi}{3}\right)[/tex]
So, the solutions are
[tex]x=\dfrac{\pi}{3},\quad x=\dfrac{5\pi}{3}[/tex]
Answer:
2pi/3 and 4pi/3
Step-by-step explanation:
this is the answer according to apex
100 Points! Please Help Me
Answer:
7. $8123.79
8. 0.012 g
Step-by-step explanation:
It often pays to follow directions. The attachment shows the use of a TI-84 graphing calculator to find the answers.
___
You will notice that the answer to problem 8 does not agree with any of the offered choices. The time period of 22.8 years is 12 times the half-life of the substance, so there will be (1/2)^12 = 1/4096 of the original amount remaining. The time periods corresponding to the amounts shown range from 1.37 years to 16.4 years.
For half-life problems, I find it convenient to use the decay factor (0.5^(1/half-life)) directly, rather than convert it to e^-k. If you do convert it to the form ...
e^(-kt)
the value of k is (ln(2)/half-life), about 0.3648143056.
_____
For multiple choice problems where the choices make no sense, I like to suggest you ask your teacher to show you how to work the problem. (Alternatively, use the "Report this question" or "Ask a tutor" button sometimes provided.)
Answer:
7. 8123.79
8. 0.012
Step-by-step explanation:
Using and Analyzing Regression Lines
The regression line modeling the number of push-ups Juan does each day is y = 0.631x + 0.0357.
Which one doesn't explain the graph correctly?
1. There is a negative correlation between time (in days) and the number of push-ups Juan does.
2. Juan increases the number of push-ups he does by about 0.631 each day.
3. The response variable is the number of push-ups
4. The explanatory variable is time (days)
Answer:
1. There is a negative correlation between time (in days) and the number of push-ups Juan does.
Step-by-step explanation:
The slope of the regression line (0.631) is positive, so the correlation between days and pushups is positive.
You have no more than $65 to spend after paying your bills. You want a drink that costs
$2.25 including tax, and you want to buy a pair of shoes, which will have 7% sales tax.
What is the inequality that represents the amount of money you have to spend?
a. x + 0.07x + 2.25 > 65
b. x + 0.07x + 2.25 ≤ 65
c. x + 0.07x + 2.25 < 65
d. x + 0.07x + 2.25 ≥ 65
Answer: B
Step-by-step explanation: You have no more than $65 which means you will want to spend equal to or less. Since you have $65, you will be able to spend up to that amount but you will not be able to spend any more than that. So, you will need to make sure the final price remains under or equal to your amount.
Each Saturday morning Andy works 4 hours and earns $34 .At that rate,what does Andy earn for each hour he works
Andy earns $8.50 per hour by dividing the total amount he earns ($34).
To find out how much Andy earns for each hour he works, you need to divide the total amount he earns by the number of hours he works on Saturday morning. If Andy earns $34 over 4 hours, his hourly wage is calculated as follows:
Divide $34 by 4 hours.
$34 / 4 hours = $8.50 per hour.
So, Andy earns $8.50 per hour.
Related Scenarios
At an hourly wage of $10 per hour, a similar worker like Marcia Fanning is willing to work 36 hours per week.
With increased hourly wages between $30 and $40, Marcia decides to work 40 hours per week.
When offered $50 per hour, she chooses to reduce her hours to 35 per week, likely to balance her work and leisure time in a way that maximizes her utility.
These examples illustrate how an increase in hourly wage can influence the number of hours a person is willing to work to balance overall life satisfaction and economic benefits
State the y-coordinate of the y-intercept for the function below.
[tex]f(x)=x^{3} -x^2-x+1[/tex]
Answer:
1
Step-by-step explanation:
y-intercept is defined as the point where the graph crosses the y-axis. The value of x coordinate at this point is zero, as along entire y-axis, the value of x coordinate is always zero. So substituting x = 0 in the function will give us the y-coordinate of the y-intercept of the given function.
[tex]f(x)=x^{3}-x^{2} -x+1[/tex]
Substituting x = 0 in this function, we get:
[tex]f(0)=0^{3}-0^{2}-0+1=1[/tex]
Thus, the y-coordinate of the y-intercept is 1. Therefore the y-intercept of the function in ordered pair will be: (0, 1)
Rectangle A has a length of 2x + 6 and a width of 3x. Rectangle B has a length of x + 2 and an area of 12 square units greater than Rectangle A's area. What is a simplified expression for the width of Rectangle B? x + 2 x + 1 6x + 6 6(x + 2)(x + 1)
Answer: So the final answer would be width is 6x + 6
Step-by-step explanation: The formula for Area is Length x width.
So A = (2x + 6)(3x) and the result is: 6x^2 + 18x
Now, let y be the width of rectangle B.
(x+2) (y) = 6x^2 + 18x + 12
(x+2) y = 6(x+1)(x+2)
y = 6(x+1)
Use the diagram to complete the statements.
The measure of angle EJB is (equal to, one-half, twice, 180 minus) the measure of angle BOE.
The measure of angle BDE is (equal to, one-half, twice, 180 minus) the measure of angle BOE.
The measure of angle OED is (equal to, one-half, twice, 180 minus) the measure of angle OBD.
Answer:
m < EJB = half of m < OBE.
m < BDE = 180 minus m < BOE.
m < OED = m<OBD.
Step-by-step explanation:
First part : Because angled subtended by an arc at the circumference = half of angle at the center.
Second: Because The 2 angles OBD and OED = 90 degrees.
Third: DB and DE are both tangents to the circle, and OE and OB are both radii. So m < OED = m<OBD = 90 degrees.
Answer:
1. B. one-half
2. D. 180 minus
3. A. equal to
Fill in the blank to complete the following sentence.
The two roots a+√b and a-√b are called _______ radicals.
Answer:
Conjugate radicals.
Step-by-step explanation:
The two roots a+√b and a-√b are called Conjugate radicals.
Just like in the complex number system where we have complex conjugates such as of 4+7i and 4 - 7i, the radicals also have their conjugate radicals. The conjugate radical of a+√b is simply obtained by changing the sign of the radical part of the expression to obtain a-√b. Therefore, the two expressions given are conjugate radicals
Answer:
Conjugate.
Step-by-step explanation:
The difference is in the signs. They are conjugate radicals.
Kai bought 120 shares of stock for $68.24 per share. He sold them nine months later for $85.89 per share. What was his capital gain?
Answer:
2118 dollars
Step-by-step explanation:
His capital gain is the difference in the (sell - buy) prices multiplied by the number of shares (120).
120 * (85.89 - 68.24) = 120 * 17.65 = 2118
The capital gain is a short term gain (held under a year)
The amount is 2118 dollars.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A football coach wants to see how many laps his players can run in 15 minutes. During a non-mandatory meeting, the coach asks for volunteers on his team to do the experiment.
Which sentences explain how randomization is not applied in this situation?
Select EACH correct answer.
Answer:
It's answers 1 and 3
Step-by-step explanation:
The meeting is not mandatory and only volunteers are participating in the task he wanted, this shows bias and doesn't correctly represent the whole team.
SOMEONE HELP MEEEEEE 75 POINTS TO THE PERSON THAT HELPS
1. Indicate the equation of the given line in standard form.
The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).
2. Indicate the equation of the given line in standard form.
The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).
3. Indicate the equation of the given line in standard form.
The line containing the midpoints of the legs of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.
4. Indicate the equation of the given line in standard form.
The line containing the hypotenuse of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.
5. Indicate the equation of the given line in standard form.
The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
6. Indicate the equation of the given line in standard form.
The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).
7. Indicate the equation of the given line in standard form.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
8. Indicate the equation of the given line in standard form.
The line containing the diagonal of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
Answer:
Part 1) [tex]9x-7y=-25[/tex]
Part 2) [tex]2x-y=2[/tex]
Part 3) [tex]x+8y=22[/tex]
Part 4) [tex]x+8y=35[/tex]
Part 5) [tex]3x-4y=2[/tex]
Part 6) [tex]10x+6y=39[/tex]
Part 7) [tex]x-5y=-6[/tex]
Part 8)
case A) The equation of the diagonal AC is [tex]x+y=0[/tex]
case B) The equation of the diagonal BD is [tex]x-y=0[/tex]
Step-by-step explanation:
Part 1)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{2-6}{2},\frac{-3+5}{2})[/tex]
[tex]M=(-2,1)[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-1=\frac{9}{7}(x+2)\\ \\y=\frac{9}{7}x+\frac{18}{7}+1\\ \\y=\frac{9}{7}x+\frac{25}{7}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=\frac{9}{7}x+\frac{25}{7}[/tex]
Multiply by 7 both sides
[tex]7y=9x+25[/tex]
[tex]9x-7y=-25[/tex]
Part 2)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{1+5}{2},\frac{0-2}{2})[/tex]
[tex]M=(3,-1)[/tex]
step 2
Find the slope
The slope between two points is equal to
[tex]m=\frac{-2-0}{5-1}=-\frac{1}{2}[/tex]
step 3
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
Find the slope of the line perpendicular to the segment joining the given points
[tex]m1=-\frac{1}{2}[/tex]
[tex]m1*m2=-1[/tex]
therefore
[tex]m2=2[/tex]
step 4
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=2[/tex] and point [tex](1,0)[/tex]
[tex]y-0=2(x-1)\\ \\y=2x-2[/tex]
step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=2x-2[/tex]
[tex]2x-y=2[/tex]
Part 3)
In this problem AB and BC are the legs of the right triangle (plot the figure)
step 1
Find the midpoint AB
[tex]M1=(\frac{-5+1}{2},\frac{5+1}{2})[/tex]
[tex]M1=(-2,3)[/tex]
step 2
Find the midpoint BC
[tex]M2=(\frac{1+3}{2},\frac{1+4}{2})[/tex]
[tex]M2=(2,2.5)[/tex]
step 3
Find the slope M1M2
The slope between two points is equal to
[tex]m=\frac{2.5-3}{2+2}=-\frac{1}{8}[/tex]
step 4
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{8}[/tex] and point [tex](-2,3)[/tex]
[tex]y-3=-\frac{1}{8}(x+2)\\ \\y=-\frac{1}{8}x-\frac{1}{4}+3\\ \\y=-\frac{1}{8}x+\frac{11}{4}[/tex]
step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=-\frac{1}{8}x+\frac{11}{4}[/tex]
Multiply by 8 both sides
[tex]8y=-x+22[/tex]
[tex]x+8y=22[/tex]
Part 4)
In this problem the hypotenuse is AC (plot the figure)
step 1
Find the slope AC
The slope between two points is equal to
[tex]m=\frac{4-5}{3+5}=-\frac{1}{8}[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{8}[/tex] and point [tex](3,4)[/tex]
[tex]y-4=-\frac{1}{8}(x-3)[/tex]
[tex]y=-\frac{1}{8}x+\frac{3}{8}+4[/tex]
[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]
Multiply by 8 both sides
[tex]8y=-x+35[/tex]
[tex]x+8y=35[/tex]
Part 5)
The longer diagonal is the segment BD (plot the figure)
step 1
Find the slope BD
The slope between two points is equal to
[tex]m=\frac{4+2}{6+2}=\frac{3}{4}[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex] and point [tex](-2,-2)[/tex]
[tex]y+2=\frac{3}{4}(x+2)[/tex]
[tex]y=\frac{3}{4}x+\frac{6}{4}-2[/tex]
[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]
Multiply by 4 both sides
[tex]4y=3x-2[/tex]
[tex]3x-4y=2[/tex]
Note The complete answers in the attached file
For a standard normal distribution, find the approximate value of P(z>-1.25) Use the portion of the standard normal table below to help answer the question. z Probability
Z Probability
0.00 | 0.5000
0.25 | 0.5987
1.00 | 0.8413
1.25 | 0.8944
1.50 | 0.9332
1.75 | 0.9599
a. 11% b. 39% c. 61% d. 89%
The approximate value of P(z>-1.25) from the normal table is 0.8944
What is z score?
Z score is used to determine by how many standard deviations the raw score is above or below the mean.
It is given by:
z = (raw score - mean) / standard deviation
P(z > -1.25) = 1 - P(z < -1.25) = 1 - 0.1057 = 0.8944
The approximate value of P(z>-1.25) from the normal table is 0.8944
Find out more on z score at: https://brainly.com/question/25638875
which of the following equations will produce the graph below?
The answer is:
The equation D will produce the shown circle.
[tex]6x^{2}+6y^{2}=144[/tex]
Why?Since the graph is showing a circle, we need to find the equation of a circle that has a radius which is between 0 and 5 units, and has a center located at the origen (0,0).
Also, we need to remember the standard form of a circle:
[tex](x+h)^{2} +(y+k)^{2}=r^{2}[/tex]
Where,
x, is the x-coordinate of the x-intercept point
y, is the y-coordinate of the y-intercept point
h, is the x-coordinate of the center.
k, is the y-coordinate of the center.
r, is the radius of the circle.
So, discarding each of the given options, we have:
First option:
A.
[tex]\frac{x^{2} }{20}+ \frac{y^{2} }{20}=1\\\\\frac{1}{20}(x^{2}+y^{2})=1\\\\x^{2}+y^{2}=20*1\\\\x^{2}+y^{2}=20[/tex]
Where,
[tex]radius=\sqrt{20}=4.47=4.5[/tex]
Now, can see that even the center is located at the point (0,0), the radius of the circle is equal to 4.5 units and from the graph we can see that the radius of the circle is more than 4.5 units but less than 5 units, the option A is not the equation that produces the shown circle.
Second option:
B.
[tex]20x^{2} -20y^{2}=400\\\\\frac{1}{20}(x^{2} -y{2})=400\\\\x^{2} -y{2}=400*20[/tex]
Where,
[tex]radius=\sqrt{8000}=89.44units[/tex]
We can see that even the center is located at the point (0,0), the radius of the circle is 89.44 units, so, the option B is not the equation that produces the shown circle.
Third option:
C.
[tex]x^{2}+y^{2}=16[/tex]
Where,
[tex]radius=\sqrt{16}=4units[/tex]
We can see that even the center is located at the point (0,0), the radius of the circle is 4 units, which is less than the radius of the circle shown in the graph, so, the option C is not the equation that produces the shown circle.
D.
[tex]6x^{2}+6y^{2}=144\\\\6(x^{2} +y^{2})=144\\\\x^{2} +y^{2}=\frac{144}{6}=24\\\\[/tex]
Where,
[tex]radius=\sqrt{24}=4.89units[/tex]
Now, we have that the radius of the circle is 4.89 units, which is approximated equal to 0, also, the center of the circle is located at (0,0) so, the equation D will produce the shown circle.
[tex]6x^{2}+6y^{2}=144[/tex]
Have a nice day!
The equation that represents the given graph is:
[tex]6x^2+6y^2=144[/tex]
Step-by-step explanation:By looking at the given graph we observe that the graph is a circle with center at (0,0) and the radius is close to 5.
Now, we know that:
The general equation of a circle with center (h,k) and radius r is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k)=(0,0)
Hence, the equation of the circle is:
[tex]x^2+y^2=r^2[/tex]
A)
[tex]\dfrac{x^2}{20}+\dfrac{y^2}{20}=1\\\\i.e.\\\\x^2+y^2=20[/tex]
i.e.
[tex]x^2+y^2=(2\sqrt{5})^2[/tex]
This equation is a equation of a circle with center at (0,0)
and radius is: [tex]2\sqrt{5}\ units[/tex]
i.e. the radius is approximately equal to 4.5 units.
But the radius is close to 5.
Hence, option: A is incorrect.
B)
[tex]20x^2-20y^2=400\\\\i.e.\\\\x^2-y^2=20[/tex]
This is not a equation of a circle.
This equation represents a hyperbola.
Hence, option: B is incorrect.
C)
[tex]x^2+y^2=16[/tex]
which could be represented by:
[tex]x^2+y^2=4^2[/tex]
i.e. the radius of circle is: 4 units
which is not close to 5.
Hence,option: C is incorrect.
D)
[tex]6x^2+6y^2=144[/tex]
On dividing both side of the equation by 6 we get:
[tex]x^2+y^2=24[/tex]
i.e.
[tex]x^2+y^2=(\sqrt{24})^2[/tex]
i.e.
Radius is: [tex]\sqrt{24}\ units[/tex]
which is approximately equal to 4.9 units which is close to 5 units.
(20 points to correct answer)
Find the area of sector GHJ given that θ=65°. Use 3.14 for π and round to the nearest tenth. Show your work and do not forget to include units in your final answer.
Answer:
The area of a sector GHJ is [tex]36.3\ cm^{2}[/tex]
Step-by-step explanation:
step 1
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=8\ cm[/tex]
substitute
[tex]A=\pi (8)^{2}[/tex]
[tex]A=64\pi\ cm^{2}[/tex]
step 2
Remember that the area of a complete circle subtends a central angle of 360 degrees
so
by proportion find the area of a sector by a central angle of 65 degrees
[tex]\frac{64\pi}{360}=\frac{x}{65}\\ \\x=64\pi (65)/360[/tex]
Use [tex]\pi =3.14[/tex]
[tex]x=64(3.14)(65)/360=36.3\ cm^{2}[/tex]
Using the quadratic formula to solve 2x^2 = 4x - 7, what are the values of x?
Explaining the quadratic formula application in solving an equation.
The quadratic formula:
Given equation: [tex]2x^2 = 4x - 7[/tex]Rearrange into a quadratic equation: [tex]2x^2 - 4x + 7 = 0[/tex]Using the quadratic formula, a=2, b=-4, c=7Substitute into the formula to get x = 1 or x = -3/2Researchers in a local area found that the population of rabbits with an initial population of 20 grew continuously at the rate of 5% per month the fox population had an initial value of 30 and grew continuously at the rate of 3% per month. Find, to the nearest tenth of a month, how long it takes for these populations to be equal
The answer is:
It will take 20.5 months to the populations to be equal.
Why?Since from the statement we know that both populations are growing, we need to use the formula to calculate the exponential growth.
The exponential growth is defined by the following equation:
[tex]P(t)=StartPopulation*e^{\frac{growthpercent}{100}*t}[/tex]
Now,
Calculating for the rabbits, we have:
[tex]StartPopulation=20\\GrowthPercent=5\\[/tex]
So, writing the equation for the rabbits, we have:
[tex]P(t)=20*e^{\frac{5}{100}*t}[/tex]
[tex]P(t)=20*e{0.05}*t}[/tex]
Calculating for the fox, we have:
[tex]StartPopulation=30\\GrowthPercent=3\\[/tex]
So, writing the equation for the fox, we have:
[tex]P(t)=30*e{\frac{3}{100}*t}[/tex]
[tex]P(t)=30*e^{0.03}*t}[/tex]
Then, if we want to calculate how long does it takes for these populations to be equal, we need to make their equations equal, so:
[tex]20*e^{0.05}*{t}=30*e^{0.03}*{t}\\\\\frac{20}{30}=\frac{e^{0.03}*{t}}{e^{0.05}*t}}\\\\0.66=e^{0.03t-0.05t}=e^{-0.02t}\\\\0.66=e^{-0.02t}\\\\ln(0.66)=ln(e^{-0.02t})\\\\-0.41=-0.02t\\\\t=\frac{-0.41}{-0.02}=20.5[/tex]
Hence, we have that it will take 20.5 months to the populations to be equal.
To find out how long it takes for the populations to be equal, set up and solve an equation using the growth rates of the rabbit and fox populations.
Explanation:To find out how long it takes for the rabbit population and the fox population to be equal, we can set up and solve an equation. Let's start by setting up an equation for each population growth:
Rabbit population: P(t) = 20 * (1 + 0.05)^t
Fox population: P(t) = 30 * (1 + 0.03)^t
We want to find the value of t when the two populations are equal, so we set the equations equal to each other and solve for t:
20 * (1 + 0.05)^t = 30 * (1 + 0.03)^t
Divide both sides by 20:
(1 + 0.05)^t = 1.5 * (1 + 0.03)^t
Now take the natural logarithm of both sides:
t * ln(1 + 0.05) = ln(1.5 * (1 + 0.03)^t)
Divide both sides by ln(1 + 0.05):
t = ln(1.5 * (1 + 0.03)^t) / ln(1 + 0.05)
Using a calculator, we can approximate the value of t to the nearest tenth of a month.
Learn more about Population Growth here:https://brainly.com/question/18415071
#SPJ11
99. Gretchen needs to bake 3 pies. Each pie takes
10 minutes to bake. She needs to let the oven
reheat for 5 minutes between each pie. She
begins baking at 8:05 a.m. Use the number line
to show when each pie is finished baking.
Answer: she will be done by 8:50
Step-by-step explanation:
45 minutes
A department store is haveing 30% off sale on all pair of jeans. If you have an coupon for an additional 15% off any items price, how much will a $60.00 pair of Jeans cost? (hint: first find the scale price of the jeans and then take the coupon discount off the sale price)
then jeans will cost $38.25
Answer:
the answer would be $35.70
Step-by-step explanation:
0.70 x $60 = $42
0.85 x $42 = $35.70
This is using multipliers so the amount off will be taken away from 1 and that answer times amount needed to found from will give the answer you are looking for
Lily takes a train each day to work that averages 35 miles per hour . On her way home her train ride follows the same path and averages 45 miles per hour . If the total trip takes 2.5 hours , what equation can be used to find n, the number of miles Lilly's homes is for work
Answer:
49.2 miles
Step-by-step explanation:
The distance remains the same. d
The time spent on the outbound trip is t1 = -------------
35 mph
and that on the inbound (return) trip is
d
t2 = -------------
45 mph
We combine these two fractions and set the sum = to 2.5 hours:
d(1/35 + 1/45) = 5/2
We wish to solve for d, the distance between home and work.
The LCD of 35, 45 and 2 is 630.
1/35 becomes 18/630; 1/45 becomes 14/630, and 5/2 becomes 1575/630. Then we have the simpler equation d(18 + 14) = 1575, or
d(32) = 1575, and d is then
d = 1575/32 = 49.2 miles
In the triangle below
Answer: first option.
Step-by-step explanation:
Given the right triangle shown in the figure, to calculate the measure of the angle m∠C, you can use the inverse function of the cosine:
[tex]\alpha=arccos(\frac{adjacent}{hypotenuse})[/tex]
You can identify in the figure, that, for the angle ∠C:
[tex]\alpha=\angle C\\adjacent=7\\hypotenuse=15[/tex]
Then, since you know the lenght of the adjacent side and the lenght of the hypotenuse, you can substitute these values into [tex]\alpha=arccos(\frac{adjacent}{hypotenuse})[/tex].
Therefore, the measure of the angle ∠C is:
[tex]\angle C=arccos(\frac{7}{15})\\\\\angle C=62.2\°[/tex]
List price of article = $2,150 Percentage discount = 18% Retail price = _____.
Answer:
18% reduction leaves 82% remaining. 82% of $2150 = .82(2150) = $1763.
Answer:
Retail Price = $1763
Step-by-step explanation:
List price of article = $2150
Percentage discount given = 18%
Then value of discount on the list price = 18% of $2150
= [tex]\frac{(2150)(18)}{100}[/tex]
= $387
Now the retail price of the article = List price - discount given
= $2150 - $387
= $1763
Therefore, Retail price of the article will be $1763
Math please help ???
Answer: Option B
[tex]y=0.5x +0.75[/tex]
Step-by-step explanation:
The equation modeling this situation is a linear equation of the form
[tex]y = mx + b[/tex]
Where x is the slope and b is the intercept with the y axis.
To find the equation of a line we need two points that belong to the line.
We know that when it is empty the jug weighs 0.75 lib.
This is:
When x = 0, y = 0.75
Then when the jug contains 3 cups of water it weighs 2.25 pounds.
This is:
When x = 3, y = 2.25
We already have the two points
Then we find the slope of the straight
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_2 = 2.25\\\\y_1=0.75\\\\x_2=3\\\\x_1=0[/tex]
[tex]m=\frac{2.25-0.75}{3-0}[/tex]
[tex]m = 0.5[/tex]
The equation is:
[tex]y=0.5x +b[/tex]
We substitute the point (0, 0.75) in the equation and solve for b
[tex]0.75=0.5(0) +b[/tex]
[tex]b=0.75[/tex]
Finally the equation is:
[tex]y=0.5x +0.75[/tex]
Answer:
no freaking way, is the state test? because if it is, then wow, you need to do your work
Step-by-step explanation:
omae wa sinderou nani (questions in the image btw)
Let [tex]a[/tex] be the number of hours worked at Job A and [tex]b[/tex] the number of hours at Job B. Then
[tex]a+b=30[/tex]
and
[tex]7.5a+8b=234.50[/tex]
From the first equation,
[tex]b=30-a[/tex]
and substituting this into the second gives
[tex]7.5a+8(30-a)=234.50\implies-0.5a+240=234.50[/tex]
[tex]\implies0.5a=5.50[/tex]
[tex]\implies\boxed{a=11}[/tex]
Answer:
Its called Omae Wa Mou Shindeiru.....then NANI?!
Step-by-step explanation:
and 11 is your answer....
A car purchased for $10,000 depreciates under a straight-line method in the amount of $750 each year. Which equation below best models this depreciation? A. y = 10000x + 750 B. y = 10000 + 750x C. y = 10000x - 750 D. y = 10000 - 750x
Answer:
D. y = 10000 - 750x
Step-by-step explanation:
The answer is D. y = 10000 - 750x, where:
y = the current value of the car,
10000 is the initial value of the car
750 is the depreciation it has every year
x is the number of years.
The 10000 has to be fixed and not multiplied by anything (unlike answer A or C) because that's the initial value of the car. Then it has to be reduced (meaning we take value of out it, so a subtraction), so that excludes A and B. The devaluation occurs every year, so it has to be multiplied by the number of years (excluding answers A and C again). So, only answer D remains.
Final answer:
The equation that best models the depreciation of the car is: y = 10000 - 750x. This equation represents the value of the car decreasing by $750 each year.
Explanation:
The equation that best models the depreciation of the car is: y = 10000 - 750x.
This equation is derived from the given information that the car depreciates by $750 each year, which is a constant amount. The equation represents the value of the car, denoted by 'y', decreasing by $750 for each year, denoted by 'x'.
For example, if we plug in x = 1 into the equation, we get y = 10000 - 750(1) = 9250, which means the car is worth $9250 after the first year.
In a video game player can choose a character from for animal characters in three human characters players can also let the computer randomly select a character for them to player will have the computer randomly selected character what is the probability it will pick a human character
____________________________________________________
Answer:
Your answer would be 3/7 or [tex]\frac{3}{7}[/tex]
____________________________________________________
Step-by-step explanation:
In this type of question, we would need to find out the chances of getting something as an outcome, and that would be expressed as a fraction.
In order to find out the chance (or likeliness) of an outcome, we would need o use the information provided in the question.
Let's give you some key information that was given to us.
Key information:
4 animal characters
3 Human characters
With the information above, we can figure out what would be the probability of an outcome.
The question is saying "what is the probability of the computer picking a human character." That means that the amount of human characters would go on our numerator.
There's not only human characters, but there are 4 animal characters too, so that would be used to give us our total. the "4" will be added to our denominator.
Now, let's write it in a fraction.
Fraction: [tex]\frac{numerator}{denominator}[/tex]
We know that we are trying to find the probability of getting a human character, so "3" would go on our numerator.
For our denominator, we would add up both numb ers since it would have to be the total amount of options in order to find the probability, and that would be "7" since 4 + 3 = 7.
When you put those into a fraction. Your FINAL answer would be:
3/7 or [tex]\frac{3}{7}[/tex]
____________________________________________________
PLEASE HELP SOLVE! FIRST TO SOLVE RIGHT WILL GET BRAINIEST
Answer:
40π/3 cm^2
Step-by-step explanation:
The centerline of the shaded region has a radius of 3 +4/2 = 5 cm. Its length is 1/3 of a circle with that radius, so is ...
length of centerline = (1/3)(2π·5 cm) = (10/3)π cm
The shaded region is 4 cm wide, so the area is the product of that width and the centerline length:
(4 cm)(10/3 π cm) = 40π/3 cm^2