Answer:
The number is divisible by 3.
Step-by-step explanation:
The conclusion is what a conditional statement ends with.
find the radius r of the circle if an arc of length 20 cm on the circle subtends a central angle of 40°. (round your answer to two decimal places.)
From the arc length given radius yielded is 22.91 cm.
What is the arc length?
The arc period estimate for a circle equals the radius of the circle. whilst r is in radians, the system for arc length may be written as arc length = r. Arc period = (/180) r, wherein r is the radius and L is the length of an arc.The radius is inversely proportional to the arc period.The length of an arc is the space between its ends measured along a circle (in units like inches or centimeters).The primary angle:
40°
Arc size
20 cm
Recall the arc length formula.
[tex]l=(\frac{Theta}{360} )*(2\pi r)[/tex]
Inserting the values:
20 =[tex]\frac{40}{360} *(2\pi r)[/tex]
[tex]r=\frac{36(20)}{10\pi }[/tex]
=72/π
=22.918cm the radius is.
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dr. aguilera conducts psychological research that examines factors associated with college student academic performance. she administered a survey to 127 participants from her university’s student subject pool. in the survey, she asked students to report their current college grade point average (gpa). dr. aguilera also asked questions about sleeping, eating habits, and social media use.
According to Dr. Aguilera's findings, excessive levels of anxiety are associated with poor academic performance. Sleep duration, on the other hand, is unrelated to excellent or poor academic performance.
we are able to reach this end due to the fact:Dr. Aguilera determined a main significance in the relationship among anxiety and academic success.moreover, this quantity is terrible, indicating a poor dating between these variables.consistent with this bad connection, the greater the value of one variable, the lower the fee of the opposite. As a result, the extra anxiety, the decrease the educational achievement.The phrase "correlation" refers back to the hyperlink between two variables. As a end result, if the adjustment is equal to zero, there may be no link between the two variables.The association among sleep hours and educational fulfillment became nil. this means that those elements have no effect on each other and are unrelated.it is important to word that the operational definition of this test is big since it presentations the measurements utilised to acquire the findings in addition to the general control of the test.nevertheless, the cohort impact is important for averting hurdles to size and research methodologies.To learn more about the cohort effect, visit :
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A line passes through the points (5, 6) and (6, 9). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Submit
Answer:
y = 3 x - 9
Step-by-step explanation:
Find the equation of the line in slope-intercept form with the properties:
point: p_1 = (5, 6)
point: p_2 = (6, 9)
The slope of the line through points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1):
m = (9 - 6)/(6 - 5) = 3
Substitute the slope m = 3 and point (x_1, y_1) = (5, 6) into the point-slope equation y - y_1 = m (x - x_1):
y - 6 = 3 (x - 5)
Add 6 to both sides:
y = 6 + 3 (x - 5)
Distribute: 3 (x - 5) = 3 x - 15:
Answer: y = 3 x - 9
ASAP!!! PLEASE HELPPP!!Write an equation for the following sentence, then solve for the unknown value.
3 times the difference of a number and 8 is less than 15.
Answer:
3(x - 8) < 15
Step-by-step explanation:
3(x - 8) < 15
3x - 24 < 15
3x < 39
x < 13
a hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. the chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
According to given conditions, m+n is equal to 409.
Consider the diagram below.
In the hexagon ABCDEF, let
AB = BC = CD = 3;
DE = EF = FA = 5;
Arc BAF is equal to one-third of the circle's circumference.
Hence, ∠BCF = ∠BEF = 60°;
Similarly, ∠CBE = ∠CFE = 60°;
Let the point of intersection of BE and CF be P, BE and AD be Q and CF and AD be R.
∴ Δ EFP and Δ BCP are equilateral, and so Δ PQR is also equilateral.
Also, ∠ BAD and ∠ BED subtend the same arc and so do ∠ ABE and ∠ ADE.
∴ Δ ABQ is similar to Δ EDQ
[tex]\frac{AQ}{EQ} = \frac{BQ}{DQ} = \frac{AB}{ED} = \frac{3}{5}[/tex]
Also,
[tex]\frac{\frac{AD - PQ}{2} }{PQ + 5} = \frac{3}{5}[/tex]
and [tex]\frac{3 - PQ}{\frac{AD + PQ}{2} } = \frac{3}{5}[/tex]
On solving these simultaneous equations, we get AD = 360/49
∴ m + n = 409.
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please help!
not sure how to solve 6
write the slope intercept form of the equation of the line through the given point with the given slope
Answer: x = 1
Step-by-step explanation:
Since the slope is undefined, that means it will be a vertical line. The equation of a vertical line is: x = h, where h is the x-value/coordinate it runs through. Based on your given point (1, 3), the x-coordinate is 1, so that makes the equation of your line x = 1.
large pies cost $5, and small pies cost $2. if 45 pies were sold for $120, how many small pies were sold ?
Answer:
35 small pies
Step-by-step explanation:
Framing system of linear equations and solving:Let the number of large pies be 'l' and
The number of small pies be 's'.
Total pies sold = 45
⇒ l + s = 45 ------------(I)
l = 45 - s -------(II)
Cost of 45 pies = $120
Cost of 1 large pie = $5
Cost of 'l' large pies = 5*l = 5l
Cost of 1 small pie = $2
Cost of 's' small pie = 2*s = 2s
5l + 2s = 120 --------------(III)
Solving : substitution method
Substitute l = 45 -s in equation (III)
5*(45 - s) + 2s = 120
5*45 - 5*s + 2s = 120
225 - 5s + 2s = 120 {Combine like terms}
225 - 3s = 120
-3s = 120 - 225 {Subtract 225 from both sides}
-3s = -105
s = -105 ÷ (-3) {Divide both sides by (-3)}
s = 35
Substitute s = 35 in equation (II),
l = 45 - s
= 45 - 35
l = 10
[tex]\sf \boxed{\text{\bf 35 small pies were sold}}[/tex]
mrs. temple has just finished grading a quiz for a class of 26 students and has calculated measures of center and spread on the scores. while writing the grades on the quizzes, she realizes she made a mistake, and the highest grade should be 10 points higher. which one of the following sets of measurements will he have to recalculate?
Measures of central tendency assist in the discovery of a data set's middle, or average. The mean is the only set of measurements that will have to recalculate.
What is the measure of central tendency?Measures of central tendency assist in the discovery of a data set's middle, or average. The mode, median, and mean are the three most popular metrics of central tendency.
Mode: It is the most common value in a given data set.Median: In an ordered data set, the median is the number in the middle.Mean: It is the total number of values divided by the sum of all values.Given that Mrs. temple has just finished grading a quiz for a class of 26 students and has calculated measures of center and spread on the scores. Now, if she made a mistake, the highest grade should be 10 points higher. Therefore, there will be no change in the median because the median is measured by the center value or is affected by the center value.
Also, the mode will not change because it is the most common value in a given data set. Therefore, the one that is repeating a lot of time.
Further, the only value that will change is the mean, because it is the sum of the observations divided by the number of observations, now since the sum is changed, therefore, the mean will be changed.
Hence, the mean is the only set of measurements that will have to recalculate.
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15 blank CDs for $5; 45 blank CDs for $15
The cost of 45 blank CD's will be equal to $ 14.85.
It is given that 15 blank CD's costs $5.
We have to find out what will be the cost of 45 blank CD's.
What is the unitary method?
The unitary method is a method in which we find the value of a unit and then the value of the required number of units.
As per the question ;
Cost of 15 blank CD's = $5
So ;
The cost of 1 blank CD will be ;
= 5 ÷ 15
= $ 0.33
And
The cost of 45 blank CD's will be ;
= 45 × $0.33
= $ 14.85
Thus , the cost of 45 blank CD's will be equal to $ 14.85.
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can anyone help me solve this (-5z)³
Answer:
-125z³
Step-by-step explanation:
cube each value
(-)³x(5)³x(z)³
negative sign multiplied by three is negative
- x - x - = -
5 x 5 x 5 = 125
z x z x z = z³
answer = -125z³
I really need help with these and they are due tomorrow... 100 points if you could please answer all
1) The time taken is 2.47 s
2) The time taken is 21.4 s
3) The time taken is 1.2 s
4) The time taken is 81 s
5) The time taken is 5.7 s
What is the time taken for the free fall?Using the equation of kinematics under gravity we knw that;
h = ut + 1/2 gt^2
h = height from which it fell
u = initial velocity
g = acceleration due to gravity
t = time taken
Given the fact that the objects were dropped from a height u = 0 m/s
h = 1/2 gt^2
t = √2h/g
1) √2 * 30/9.8
t =2.47 s
2) t = √2 * 2250/9.8
t = 21.4 s
3) t = √2 * 7/9.8
t = 1.2 s
4) t = √2 * 32000/9.8
t = 81 s
5) t = √2 * 160/9.8
t = 5.7 s
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The sum of 3 consecutive even numbers is 60. What are they?
Answer:
18, 20 and 22.
Step-by-step explanation:
Let the lowest number be n, then:
n + n + 2 + n + 4 = 60
3n + 6 = 60
3n = 54
n = 18.
So the other 2 are 20 and 22.
Someone Help please
Answer:
is B espero que esto te ayude yo también estoy nececicando ayuda con mis trabajos
solve the following quadratic equation by extracting the square root.
4(m-1)²-4=0
thank u!!!
Step-by-step explanation:
[tex] \sqrt{} 4(m - 1) ^{2} = \sqrt{} 4 [/tex]
Answer:
4(m-1)^2=4
(2(m-1))^2=2^2
2(m-1)=2
2m-2=2
2m=4
m=2
Using the diagram and the given angle measure to find the other three angle measures
Based on the given.
If [tex]m∠2 = 59°[/tex]
Then, [tex]m∠4 = 59 °[/tex]
(reason: vertically opposite angles are equal)
If [tex]m∠4 = 59 °[/tex]
Then, [tex]m∠1⟹ 180 - 59 = 121 °[/tex]
(reason: angles on a straight line = 180°)
If [tex]m∠1 = 121°[/tex]
Then, [tex]m∠3 = 121°[/tex]
(reason: vertically opposite angles are equal)
Therefore:
[tex]m∠1 = 121°[/tex]
[tex]m∠3 = 121°[/tex]
[tex]m∠4 = 59 °[/tex]
See attached image for the placement of the values.
A recipe calls for of a cup of milk for 12 cookies. How many cups of milk are needed to make 72 cookies?
Answer: 6 cups of milk
Step-by-step explanation:
Set-up proportion
[tex]\frac{1}{12} =\frac{x}{72}[/tex]
1*72=72/12=6
6 cups of milk
1. The distance between Earth and Mars is approximately 4.35 × 107 miles.
What is this distance in standard form?
A 435,000 miles
B 4,350,000 miles
C43,500,000 miles
D 435,000,000 miles.
The distance between Earth and Mars in the standard form is 43, 500, 000 miles.
The correct answer is an option (C)
In this question we have been given the distance between Earth and Mars.
The distance between Earth and Mars is approximately 4.35 × 10^7 miles.
We need to write above distance between Earth and Mars in the standard form.
So, we get an expression,
4.35 × 10^7 miles
= 435 × 10^5 miles
= 435 × 100, 000 miles
= 43, 500, 000 miles
Therefore, the distance between Earth and Mars in the standard form is 43, 500, 000 miles.
The correct answer is an option (C)
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in the eight-term sequence $a$, $b$, $c$, $d$, $e$, $f$, $g$, $h$, the value of $c$ is 5 and the sum of any three consecutive terms is 30. what is $a h$?
The value of A + H is 25 for the given sequence.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
Given that sum of any three consecutive terms is 30
Since c = 5
So a + b + c = 30
a + b = 25
⇒ (a+b)+(c+d+e)+(f+g+h)
⇒ 25 + 30 + 30 = 85
Now,
a+b+c+d+e+f+g+h = 85
a + h +(b+c+d)+(e+f+g) = 85
a + h + 30 + 30 = 85
a + h = 25
Hence "The value of A + H is 25 for the given sequence".
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62 + 14 ÷ 2 - 8
Which operation appears first in the given expression?
Which operation did you select first in order to evaluate the expression?
Which operation is not included in the expression?
(the number problom goes with all questions)
The addition is the operation that appears first, the division is the operation that is selected first in order to evaluate and multiplication is the operation that is not included in the given expression.
The given expression can be evaluated using the BODMAS rule which tells the order of priority to give to solve an equation with multiple operations
BO stands for Bracket off means to solve the bracket first
D stands for division
M stands for multiplication
Stands for addition
S stands for subtraction
Now we should look at the expression given which is 62 + 14 ÷ 2 - 8
Although the addition operation appears first in the given expression, we would select the division operation first that can be bracketed because of BODMAS rule and then addition and then Subtraction at last which results
62 +( 14 ÷ 2) - 8
62 + 7 -8
69 -8
61
Hence, Using the BODMAS rule the expression is solved and the result is 61
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please answer this its due by 12
Answer:
4. 4(x+1)
5. 7(d+4)
6. y(y+3)
Answer:
I could be totally wrong but ill tr7
Step-by-step explanation:
4. 12 OR 4x+4
5. 56 (28+28)
6. y^2 + 3y
The midpoint of overline AB is M(3, 0) If the coordinates of A are (2, 4) what are the coordinates of B?
Answer: B(4,-4)
Step-by-step explanation:
M(3,0) A(2,4) B(x,y)=?
[tex]\displaystyle\\x_M=\frac{x_A+x_B}{2} \\\\Multiply\ both\ parts\ of\ the\ equation\ by \ 2:\\2x_M=x_A+x_B\\2x_M-x_A=x_A+x_B-x_A\\2x_M-x_A=x_B\\x_M=3\ \ \ \ \ x_A=2\\Hence,\\2*3-2=x_B\\6-2=x_B\\4=x_B\\Similarly:\\2y_M-y_A=y_B\\y_m=0\ \ \ \ \ y_A=4\\Hence,\\2*0-4=y_B\\0-4=y_B\\-4=y_B\\Thus,\ B(4,-4)[/tex]
4 ÷ 2/5
Help (( 15 points ))
[tex]4 \div \frac{2}{5} [/tex]
[tex]4 \times \frac{5}{2} [/tex]
[tex]2 \times 5[/tex]
[tex]10[/tex]
Answer:10
Step-by-step explanation:
first step 4× 5/2
second step 4x5
2
third step is to simplify 20/2 which is
10
Solve the equation. Check the solution
11-10x-7-4x=6
X= =(Type an integer or a
(Type an integer or a simplified fraction.)
Answer: x=-1/7
Step-by-step explanation:
11-10x-7-4x=6
11-7-10x-4x=6
4-14x=6
-14x=2
x=-1/7
with show work please!
the figure, ray OJ is perpendicular to ray OE. If ∠JOL=6x+10 and ∠LOE=x+10, find the measure of ∠LOE.
Answer:
∠ LOE = 20°
Step-by-step explanation:
since OJ is perpendicular to OE then ∠ JOE = 90°
from the diagram
∠ JOL + ∠ LOE = ∠ JOE ( substitute values )
6x + 10 + x + 10 = 90
7x + 20 = 90 ( subtract 20 from both sides )
7x = 70 ( divide both sides by 7 )
x = 10
Then
∠ JOE = x + 10 = 10 + 10 = 20°
60 is what percent of 180?
Answer:
about 33%
Step-by-step explanation:
Answer:e
Step-by-step explanation:
e
A stack of one dozen cookies with diameter of 5in. exactly fits in a cylindrical container of volume 176.715 in^3. which is the thickness of each cookie?
The thickness of each cookie is 0.75 inch.
The cookies are in cylindrical container, hence, the shape of cookies will also be cylindrical. Now, the volume of cylinder is given by the formula : V = πr²h, where V refers to volume, r refers to radius and h represents height.
So, volume of 12 cookies will be equal to the cylindrical container.
Radius of cookies = Diameter÷2
Radius of cookies = 5÷2
Radius of cookies = 2.5 inches
Taking π as 3.14
Volume of a stack of cookies = 3.14×2.5²×h
Volume of a stack of cookies = 19.625h
Relating both the volumes to find the value of h
19.625h = 176.715
h = 176.715 ÷ 19.625
Performing division to find the height
h = 9 inches
So, height of 12 cookies is 9 inches
Height of 1 cookie = 9 ÷ 12
Height of 1 cookie = 0.75 inch
Thus, the thickness of each cookie is 0.75 inch.
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What is an equivalent form of 12(p + 5) − 11(3q + 4)?
−21pq + 1
60p − 77q
12p − 33q + 16
12p − 33q + 9
Answer:
12p − 33q + 16
Step-by-step explanation:
Let's simplify step-by-step.
12(p+5)−11(3q+4)
Distribute:
=(12)(p)+(12)(5)+(−11)(3q)+(−11)(4)
=12p+60+−33q+−44
Combine Like Terms:
=12p+60+−33q+−44
=(12p)+(−33q)+(60+−44)
=12p+−33q+16
=12p−33q+16
if the rate of inflation is 3.9% per year, the future price pt (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today.
The current price of the item = 400 dollars
The price in 8 years from today = 543.23 dollars
Given the rate of inflation = 3.9%
The exponential function modelling the future price, p(t) in t years for a certain item is, [tex]p(t)=400(1.039^t)[/tex]
We have to find the current price of the item. This is given by substituting t = 0 in p(t).
That is, p(0) = 400 x 1 = 400 dollars
Therefore current price = 400 dollars
To find the price of the product in 8 years, substitute t = 8 in p(t).
That is, p(8) = [tex]400(1.039^8)[/tex] = 543.23 dollars
Therefore, the future price of the item in 8 years = 543.23 dollars
The question is incomplete. Find out the complete question below:
If the rate of inflation is 3.9% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)= 400(1.039^t).Find the current price of the item and the price 8 years from today.
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x-4 1/3=9 2/3 ive been trying to find the answer to this for hours someone please help
Answer:
x = 14
Step-by-step explanation:
1. Change the equation to x + -4 1/3 = 9 2/3
2. Add 4 1/3 to each side of the equation to get rid of the -4 1/3
3. You will be left with x = 14