There are 15 rows of seats in the theater
How to determine the number of rows?The given parameters are:
Total number of people = 357People per row = 24The number of rows is calculated as:
Rows = Total number of people/People per row
This gives
Rows = 357/24
Evaluate the quotient
Rows = 14.875
Round up the number
Rows = 15
Hence, there are 15 rows of seats in the theater
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Line segment AB is dilated to create line segment A'B' using point Q as the center of dilation.
Point Q is the center of dilation. Line segment A B is dilated to create line segment A prime B prime. The length of Q A is 1.25 and the length of A A prime is 1.25.
The scale factor in the question given above is: 2 See the explanation below.
What is a scale factor?In math, the scale factor is the extent or ratio by which a geometrical shape is enlarged or reduced.
What is the explanation for the above answer?We know that:
The distance from point Q to point A is 1.25The distance from point A to point A' is 1.25Given the above, the distance from point Q to point A' is 2.50. This is double the distance from point Q to point A.
The scale factor is 2.
1.25 + 1.25 = 2.50
2.50 / 1.25 = 2
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Calculate: 1/1x3+1/3x5+…+1/47x49
Answer:
24/49
Step-by-step explanation:
PLEASE ANSWER I'LL GIVE BRAINLIEST. Mrs. Nestler enjoys listening to classical music. She has the following audio CDs by her favorite composers in her collection: 4 by Bach, 6 by Beethoven, 3 by Brahms, and 2 by Handel. If she selects 4 CDs randomly from her collection without replacing them, what is the probability that she will choose one by each composer?
16/455
2/455
16/5625
2/5625
The probability that she will choose one by each composer is 2/455.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability = (number of bach cds / total number of cds) x (number of beethoven cds / total number of cds - 1) x (number of Brahms cds / total number of cds-2) x (number of Handel's cds / total number of cds-3)
= 4/15 x 6/14 x 3/13 x 2/12 = 2/455
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Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
33x+25=33x+2533x+25=33x+2533, x, plus, 25, equals, 33, x, plus, 25
(Choice B)
B
33x-33=33x+2533x−33=33x+2533, x, minus, 33, equals, 33, x, plus, 25
(Choice C)
C
33x-25=33x+2533x−25=33x+2533, x, minus, 25, equals, 33, x, plus, 25
(Choice D)
D
33x+33=33x+2533x+33=33x+25
Answer:
A. 33x-25=33x+25
C. 33x-33=33x+25
D.33x+33=33x+25
A. 33x-25=33x+25
33x-33x=25+25
0 = 50
This is incorrect equality, as it is not equal on both sides.
Therefore this equation has no solutions.
B. 33x+25=33x+25
33x−33x=25−25
0=0
This is correct equality, as it is equal to zero on both sides.
Therefore the equation has an infinite number of solutions.
C. 33x-33=33x+25
33x-33x=33+25
0=58
This is incorrect equality, as it is not equal on both sides.
Therefore this equation has no solution.
D. 33x+33=33x+25
33x−33x=25−33
0=−8
This is incorrect equality, as it is not equal on both sides.
Therefore this equation has no solution.
Hence, the equations which has no solution are;
A. 33x-25=33x+25
C. 33x-33=33x+25
D.33x+33=33x+25
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Which of the following is equivalent to the complex number i^36?
1
i
-1
-i
Answer:
1
Step-by-step explanation:
[tex]i^4=1\\\\i^{36}=(i^{4})^9=(1)^9=1[/tex]
A simple random sample of 81 8th graders at a large suburban middle school indicated that 87% of them are involved with some type of after school activity. Find the 90% confidence interval that estimates the proportion of them that are involved in an after school activity.
The 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).
The confidence interval for a population proportion for a given sample is given by the formula:
[tex](p-Z\sqrt{\frac{p(1-p}{n} } , p+Z\sqrt{\frac{p(1-p}{n} })[/tex],
where p is the population proportion, Z is the Z-score value for the confidence interval, and n is the sample size.
In the question, we are given a random sample of 81 8th graders at a large suburban middle school. This implies that the sample size, n = 81. Also, we are told that they indicated 87% of them were involved with some type of after-school activity. This implies that the population proportion, p = 87% = 0.87.
We are asked to find the 90% confidence interval that estimates the proportion of them that are involved in an after-school activity.
Z-score (Z) corresponding to a 90% confidence interval is 1.645.
Thus, we can find the confidence interval as follows:
(0.87 - 1.645√{(0.87(1 - 0.87))/81},0.87 + 1.645√{(0.87(1 - 0.87))/81})
= (0.87 - 0.061469,0.87 + 0.061469)
= (0.80853,0.93147).
Thus, the 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).
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Please answer urgently
Consider these functions:
f(x)= 3x - 7
g(x) = + = 1
What is the value of f(g(3))?
OA. -1
О в.
о
OC. 3
OD. 5
The value of the composition of functions f(g(3)) is given by (A) -1.
Here given that the functions are,
f(x) = 3x-7
g(x) = (x+1)/(x-1)
To find the value of g(3) we have to first substitute the value x = 3 in the given function g(x), doing that we get,
g(3) = (3+1)/(3-1) = 4/2 =2
Thus the value of g(3) = 2
Now in order to find the value of composition of functions f(g(3)) we have to substitute the value of x = g(3) = 2 in the given function f(x), doing that we get,
f(g(3)) = f(x = g(3)) = f(x = 2) = f(2) = 3*2-7 = 6-7 = -1
Thus the value of the required composition of functions f(g(3)) is given by -1.
Hence the correct option is given by (A).
The question is incomplete. Find the full content below.
Consider these functions:
f(x) = 3x-7
g(x) = (x+1)/(x-1)
What the value of f(g(3))?
(A) -1
(B) 0
(C) 3
(D) 5
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What is the range of the function f(x) = |x| + 5?
Answer:
[tex][0, \infty)[/tex]
Colin found 22 more mushrooms that sophie did while they were out picking them in the forest. On the way home Sophie asked Colin to give her mushrooms so they have equal amounts. How many mushrooms did Colin give to Sophie?
Answer:
11 mushrooms
Step-by-step explanation:
Let's take two sets of numbers that fulfill the requirements (2 and 24 | 5 and 27)
In the first case, there are 26 mushrooms, and to have an equal amount they each need 13. Collin had to give 11 mushrooms to Sophie.
In the second case, there are 32 mushrooms, and they both need 16 each. So in this case, Collin also had to give 11 to Sophie.
The answer is 11 mushrooms.
GEOMETRY)
Find the area in square miles, of the sector shown below. Round your answer to the nearest whole number. (Enter only a number for your answer.)
(Picture is below) Thank you!
SOLUTION :-
AREA of sector = ( ∆/360° ) × πr²
∆ = given angle , r = radius
hence ,
AREA of sector for given angle
= ( 120°/360° ) × π 12² mi²
= ⅓ × π × 144 = 150.79 mi² = 151 mi² ( rounded off )
________________________________
HOPE IT HELPS
MARK BRAINLIEST!
FOLLOW ME!
Answer:
Sector area = 151 mi²
Step-by-step explanation:
We can use the formula for sector area:
Area = [tex]\frac{\theta}{360} \pi\ r^2[/tex]
where:
θ = central angle (120°),
r = radius of circle (12 mi) .
Substituting these values into the formula:
Area = [tex]\frac{120}{360} \pi\ \times (12)^2[/tex]
⇒ 48 π
⇒ 150.796
≈ 151 mi² (rounded to the nearest whole number)
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
326. (5k + 6)(5k − 6)
Answer:
The product is the difference of squares is [tex]$$\left(5k+6\right)\left(5k-6\right)=25{{k}^2}-36$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (5 k+6)(5 k-6).We have to multiply the given expression.Square the first term 5k. Square the last term 6 .[tex]$$\begin{aligned}&(5 k+6)(5 k-6)=(5 k)^{2}-(6)^{2} \\&(5 k+6)(5 k-6)=25 k^{2}-36\end{aligned}$$[/tex]
I need help with this geometry question, matching the right ones to each other.
The transformations and their respective descriptions are:
A. (x, y) ⇒ (3x, y) implies horizontal stretch by a scale factor of 3
B. (x, y) ⇒ (x+3, y) implies translation 3 units right
C. (x, y) ⇒ (x, 3y) implies vertical stretch by a factor of 3
D. (x, y) ⇒ (x, y+3) implies implies translation 3 units up
E. (x, y) ⇒ (3x, 3y) implies dilation with a scale factor 3
What is Translation?Translation is an algebraic transformation of a shape by moving the vertices some units along the x or y axis.
When a shape is translated it may move to a new position depending on the orientation of the translation.
Analysis:
For A, the x coordinate was transformed three times its initial value stretching it horizontally.
For B, the x coordinate moved 3 units further away from its initial value making the new value x+3 and y remaining the same.
For C, the y coordinated was transformed to a value three times what it was, making it to be stretched vertically, since the y-axis is a vertical axis.
For D, the y coordinate was moves 3 units away from its initial position making it to be translated up, since 3 is positive.
For E, both coordinates were stretched 3 units as much as their original value making the shape to dilate.
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Help pleaseeeeeeeeeeeee
Answer:
no because it would be flipped
Complete the proof.
The options are substitution property of equality, multiplication property of equality, distributive property, and definition of property bisector.
The blanks can be filled with definitions of property bisector, Substitution property of equality, and Distributive property, respectively.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The given blanks can be filled as,
The first blank is needed to be filled with the definition of property bisector.The second blank will be filled by the Substitution property of equality.The third blank can be filled with the Distributive property.Hence, the blanks can be filled with definitions of property bisector, Substitution property of equality, and Distributive property, respectively.
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The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
u = 0.25
u = 0.75
u = 1.1
u = 2.5
The value of u, number of hours walking up a hill based on the equation is 2.5
Equation9(u – 2) + 1.5u = 8.25
where,
u = number of hours walking up a hill (u - 2) = number of hours sledding down the hill9(u – 2) + 1.5u = 8.25
9u - 18 + 1.5u = 8.25
9u + 1.5u = 8.25 + 18
10.5u = 26.25
u = 26.25/10.5
u = 2.5
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7. If 1 || m and n || q, identify any of the following
angles congruent to 6
The angle congruent to ∠6 are ∠8, ∠3, ∠9 and ∠14
How to find congruent angles?When parallel lines are cut by a transversal, angle relationships are formed. They include corresponding , alternate and many more.
L║m
n ║ q
Therefore, the angles congruent to ∠6 by alternate or corresponding relationship are as follows:
∠6≅∠8≅∠3≅∠9≅∠14
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The original price of a book is x dollars. The book is sold for 10% discount. After that, the increased by 25%
Answer:
assume X dollar is $100
If so then,
$100-10% =$90
Thus,
$90x125%=$112.5
If the numerator and denominator of a fraction are increased and decreased by 1 respectively, then it becomes 12/11 if the numerator and denominator are increased and decreased by 3 respectively then it becomes 14/9 find the fraction.
Answer needed.
Let the numerator be x & denominator be y then,
ATQ,
x+1/y-1=12/11
11x+11=12y-12
11x-12y+11+12=0
11x-12y+23=0....(1)
&
x+3/y-3=14/9
9x+27=14y-42
9x-14y+27+42=0
9x-14y+69=0....(2)
Multiplying eq . 1 by 9 & eq. 2 by 11
We get,
99x-108y+207=0....(3)
99x-154y+759=0....(4)
Subtracting eq. 4 by eq. 3
99x-108y+207=0
99x-154y+759=0
______________
0 + 46y - 552 =0
______________
46y= 552
________
y=552/46
________
y=12
____
putting the value of y in eq. 1,
11x-12y+23=0
11x-12*12+23=0
11x-144+23=0
11x-121=0
11x=121
x=121/11
x=11
So, y = 12 & x = 11 & the fraction is 11/12
ㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤ
-lyricalblues
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 15 ft high
The height is increasing at the rate of (6/5π) ft/min.
It is given that Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min. Also, its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.
For this, we need to find the volume of a cone. Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
The volume of a cone is - V=1/3hπr²
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help trigonometry
cccccc
Answer:
D
Step-by-step explanation:
Trigonometry ratios:[tex]\sf Sin \ \theta =\dfrac{opposite \ side }{hypotenuse} =\dfrac{12}{37}[/tex]
To find the adjacent side use Pythagorean theorem.
Opposite side² + adjacent side² = hypotenuse²
adjacent side² = hypotenuse² - opposite side²
= 37² - 12²
= 1369 - 144
= 1225
adjacent side = √1225
= 35
[tex]\sf tan \ \theta =\dfrac{Opposite \ side }{adjacent \ side}\\\\tan \ \theta = \dfrac{12}{35}[/tex]
Match the average rates of change of f(x) to the corresponding intervals.
The intervals [-5,-1], [-4,-1], [-3,1],[-2,1] match with -8,-7,4,-3.
Given the value of function at x=-5 is 35, at x=-4 is 24, at x=-3 is 15,at x=-2 is 8,at x=-2 is 8,at x=-1 is 3, at x=0 is 0, at x=1 is -1.
Average rate of change of values refers to the average of differences in the values divided by the difference of values of x.
First finding the average rate of change of interval [-5,-1]
Average rate of change={f(-1)-f(-5)}/(-1+5)
=(3-35)/4
=-32/4
=-8
Finding the average rate of change of interval [-4,-1]
Average rate of change={f(-1)-f(-4)}/(-1+4)
=(3-24)/3
=-21/3
=-7
Finding the average rate of change of interval [-3,1]
Average rate of change={f(1)-f(-3)}/(-3-1)
=(-1-15)/-3-1
=-16/-4
=4
Finding the average rate of change of interval [-2,1]
Average rate of change={f(1)-f(-2)}/(1+2)
=(-1-8)/3
=-9/3
=-3
Hence the values which are to be filled in the boxes are -8,-7,4,-3.
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Simplify 2x + x. pleaseeee help
Answer:
3x
Step-by-step explanation:
2x is the name, there are 2 x's, you are adding an x to the 2 x's therefore making 3 x's or 3x
A grocery store sells 1 gallon containers of milk for 3.99. The store also sells orange juice in a 6 pack of 5.5 fluid ounce bottles for $1.79. Suppose the store wants to sell its orange juice in gallon containers instead. To the nearest dollar, how much more would a gallon of orange juice cost than a gallon of milk?
The a gallon of orange juice will cost $ 3.0 more than a gallon of milk.
Size of the orange juiceThe size of the orange juice in gallon is calculated as follows;
1 ounce = 0.0078125 gal
5.5 ounce = ?
= 0.043 gallon
Total volume of 6 pack = 6 x 0.043 gal = 0.258 gal
0.258 gal = $1.79
1 gal = ?
= $ 6.94
Difference between cost of gallon of milk and orange juice= $ 6.94 - $ 3.99
= $2.95
≈ $ 3.0
Thus, the a gallon of orange juice will cost $ 3.0 more than a gallon of milk.
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Please help me out :P
cos θ = [tex]\frac{-4\sqrt{65} }{65}[/tex], sin θ = [tex]\frac{-7\sqrt{65} }{65}[/tex], cot θ = 4/7, sec θ = [tex]\frac{-\sqrt{65} }{4}[/tex], cosec θ = [tex]\frac{-\sqrt{65} }{7}[/tex]
What are trigonometric ratios?Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin θ: Opposite Side to θ/Hypotenuse
Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos
Cos θ: Adjacent Side to θ/Hypotenuse
Sec θ: Hypotenuse/Adjacent Side & 1/cos θ
Analysis:
tan θ = opposite/adjacent = 7/4
opposite = 7, adjacent = 4.
we now look for the hypotenuse of the right angled triangle
hypotenuse = [tex]\sqrt{7^{2} + 4^{2} }[/tex] = [tex]\sqrt{49+16}[/tex] = [tex]\sqrt{65}[/tex]
sin θ = opposite/ hyp = [tex]\frac{7}{\sqrt{65} }[/tex]
Rationalize, [tex]\frac{7}{\sqrt{65} }[/tex] x [tex]\frac{\sqrt{65} }{\sqrt{65} }[/tex] = [tex]\frac{7\sqrt{65} }{65}[/tex]
But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.
Therefore, sin θ = - [tex]\frac{7\sqrt{65} }{65}[/tex]
cos θ = adj/hyp = [tex]\frac{4}{\sqrt{65} }[/tex]
By rationalizing and knowing that cos θ is negative, cos θ = -[tex]\frac{-4\sqrt{65} }{65}[/tex]
cot θ = 1/tan θ = 1/7/4 = 4/7
sec θ = 1/cos θ = 1/[tex]\frac{4}{\sqrt{65} }[/tex] = -[tex]\frac{-\sqrt{65} }{4}[/tex]
cosec θ = 1/sin θ = 1/[tex]\frac{\sqrt{65} }{7}[/tex] = [tex]\frac{-\sqrt{65} }{7}[/tex]
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8. In February 2018, a newspaper reported that the total land area of Singapore is expected to reach 76 600 hectares by 2030. This is an increase of about 6.4% from the total land area in 2017. Find the total land area in 2017, giving your answer correct to 4 significant figures.
Answer:
The answer is 7.199 x 10^4 hectares
Step-by-step explanation:
Let's set x as the total land area in 2017.
x * (1 + 6.4%) = 76,600
x * (1 + 0.064) = 76,600
x * 1.064 = 76,600
x = 76,600 / 1.064
x = 71,992.48
x = 7.199 * 10^4 hectares
Solve this please.
• Log 2 + log(3/2) + log (4/3) + log (5/4)+ log(6/5) + log (7/6) + log (8/7)
Answer:
[tex]3 \log 2[/tex]
Step-by-step explanation:
Given expression:
[tex]\log 2 + \log \left(\dfrac{3}{2}\right)+\log \left(\dfrac{4}{3}\right)+\log \left(\dfrac{5}{4}\right)+\log \left(\dfrac{6}{5}\right)+\log \left(\dfrac{7}{6}\right)+\log \left(\dfrac{8}{7}\right)[/tex]
[tex]\textsf{Apply the \underline{Log Product Law}}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log \left(2 \cdot \dfrac{3}{2} \cdot \dfrac{4}{3} \cdot \dfrac{5}{4} \cdot \dfrac{6}{5} \cdot \dfrac{7}{6} \cdot \dfrac{8}{7}\right)[/tex]
Cross out common factors:
[tex]\implies \log \left(\diagup\!\!\!\!2 \cdot \dfrac{\diagup\!\!\!\!3}{\diagup\!\!\!\!2} \cdot \dfrac{\diagup\!\!\!\!4}{\diagup\!\!\!\!3} \cdot \dfrac{\diagup\!\!\!\!5}{\diagup\!\!\!\!4} \cdot \dfrac{\diagup\!\!\!\!6}{\diagup\!\!\!\!5} \cdot \dfrac{\diagup\!\!\!\!7}{\diagup\!\!\!\!6} \cdot \dfrac{8}{\diagup\!\!\!\!7}\right)[/tex]
Therefore:
[tex]\implies \log 8[/tex]
Factor the number: 8 = 2³
[tex]\implies \log 2^3[/tex]
[tex]\textsf{Apply the \underline{Log Power Law}}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies 3 \log 2[/tex]
If two triangles are congruent, then they can be moved so fast they line up perfectly
Answer:
This is true.
Step-by-step explanation:
Congruence means the same shape and size. So if they line up, they will line up perfectly.
By the way, is there any question you need help with, or do you just need to see if this is true or false?
Shota invests $2000 in a certificate of deposit that earns 2%, percent in interest each year.
Write a function that gives the total value V(t) in dollars, of the investment t years from now.
Answer:
[tex]2 * 10^3 * 1,02^t[/tex]
Step-by-step explanation:
Let [tex]S = 2000 = 2 * 10^3[/tex] dollars be our investment, [tex]r = 2\%[/tex] - our interest rate. In order to simplify things, I suggest bringing the variable [tex]p[/tex] into play: [tex]p = 1 + \frac{r}{100}[/tex]. So, after year [tex]1[/tex] we will have [tex]S_{1} = S + \frac{r}{100}S = S(1 + \frac{r}{100} ) = Sp[/tex]. After year [tex]2[/tex]: [tex]S_{2} = S_{1}p = Sp * p = Sp^2[/tex]. After year [tex]t[/tex]: [tex]S_{t} = S_{t - 1}p = Sp^t[/tex]. Besides, we can count [tex]p[/tex]. Indeed, [tex]p = 1 + \frac{r}{100} = 1 + \frac{2}{100} = \frac{100}{100} + \frac{2}{100} = \frac{102}{100} = 1,02[/tex]. Therefore, [tex]V(t) = Sp^t = 2 * 10^3 * 1,02^t[/tex].
which of the following are equivalent to 55%? (Check all that apply.)
5.5
13/25
0.55
11/20
Answer:
The answer is 0.55
Step-by-step explanation:
Because 55% = [tex]\frac{55}{100}[/tex] = 0.55