Answer:
330 day passes, 367 tournament passes
Step-by-step explanation:
The number of day passes sold is 330, while the number of tournament passes sold is 367.
What is a System of equations?A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.
Let the number of day passes sold be represented by x, while the number of tournament passes sold is y.
Given that on the first day of a water polo tournament, the total value of tickets sold was $17,610.
y = x + 37
Also, The number of tournament passes sold was 37 more than the number of days passes sold.
20x + 30y = 17610
20x + 30(x + 37) = 17610
20x + 30(x+ 37) = 17610
20x + 30x + 1110 = 17610
50x = 16,500
x = 16,500 / 50
x = 330
y = x + 37
y = 330 + 37
y = 367
Hence, the number of day passes sold is 330, while the number of tournament passes sold is 367.
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_____13. Public opinion polls are only estimates because (A) random digit dialing has replaced person-to-person interviewing. (B) all surveys have a sampling error. (D) samples of fewer than one million people are too small. (E) opinion polls have been deemed ineffective by political candidates.
Answer:
(B) all surveys have a sampling error.
Step-by-step explanation:
46.6 is what percent of 67?
Answer:
46.6 is 69.5522% of 67
Step-by-step explanation:
brainliest plz
I really need help finding the solution!!
Answer:
-0.5 is not a solution
2 is a solution
Step-by-step explanation:
To check if something is a solution of the equation, you need to substitute the value in place of the variable
15 + 2y = -12 - 4y
15 + 2(-0.5) = -12 - 4(-0.5)
15 - 1 = -12 + 2
14 ≠ -10 ∴ -0.5 is not a solution
5 - 2(3x + 5) = 3 - 10x
5 - 2[3(2) + 5] = 3 - 10(2)
5 - 2(6 + 5) = 3 - 10(2)
5 - 12 - 10 = 3 - 120
-17 = -17 ∴ 2 is a solution
HELP PLEASE
Write each number as a logarthm with base 3.
0
1
-2
4
Answer:
See belowStep-by-step explanation:
Let the number is x in each case.
Use the property below:
logₐc = b ⇒ aᵇ = c or vice versaWe have:
[tex]log_3x = 0 -->x = 3^0=1 -->log_31=0[/tex][tex]log_3x = 1 -->x = 3^1=3 -->log_33=1[/tex][tex]log_3x = -2 -->x = 3^{-2}=1/9 -->log_3(1/9)=-2[/tex][tex]log_3x = 4 -->x = 3^4=81 -->log_381=4[/tex]Answer:
[tex]\log_31=0[/tex]
[tex]\log_33=1[/tex]
[tex]\log_3\left(\frac{1}{9}\right)=-2[/tex]
[tex]\log_{3}81=4[/tex]
Step-by-step explanation:
[tex]\textsf{Apply log law}: \quad \log_ax=c \iff x=a^c[/tex]
Therefore:
[tex]\log_3x=0 \implies x=3^0=1[/tex]
[tex]\log_3x=1 \implies x=3^1=3[/tex]
[tex]\log_3x=-2\implies x=3^{-2}=\dfrac{1}{3^2}=\dfrac{1}{9}[/tex]
[tex]\log_3x=4 \implies x=3^4=81[/tex]
Additionally, the logarithm of 1 with any base is always zero:
[tex]\log_a1=0[/tex]
The logarithm of the same number as the base is always 1:
[tex]\log_aa=1[/tex]
show that P(x)=x³-6x²+11x-6 is divisible by x-1.
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Hello haohaoxNienie!
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
[tex] \huge \boxed{\mathfrak{Explanation} \downarrow}[/tex]
To show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1, we must divide the polynomial by x - 1. If we get the remainder as 0, then we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
So, let's do the division (steps in the attached picture).
__________________
We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
More steps :-x² - 5x + 6
= (x - 3) (x - 2) [use the splitting the middle term method].
So, the zeroes are,
(x - 3)
x - 3 = 0
x = 3 ⇨ 1st zero.
(x - 2)
x - 2 = 0
x = 2 ⇨ 2nd zero.
Now, use the values of x on the equation. If we get 0 as the solution of the equation then we can prove that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
p(x) = x³ - 6x² + 11x - 6
p(3) = 3³ - 6(3)² + 11 (3) - 6
p(3) = 27 - 54 + 33 - 6
p(3) = 0.
p(x) = x³ - 6x² + 11x - 6
p(2) = 2³ - 6(2)² + 11 (2) - 6
p(2) = 8 - 24 + 22 - 6
p(2) = 0
Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
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Plsss help me with this question!!!
pls answer ASAPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
46, 57 , 67
Step-by-step explanation:
Acute scalene triangle : A triangle in which all three angles are less then 90 degrees and all three angles are different measurements .
have a good day
The product of four and a number C is decreased by five?
plss help me for with this math..
Answer:
Step-by-step explanation:
3. x^2 +3x=54
x^2 +3x -54 = 0
(x-9)(x+6) = 0
x = 9 and x = -6
4. X^2 - 10x + 21 [(x - 7)(x - 3)
WILL GIVE BRAILIST TO PERSON WHO ANSWERS CORRECTLY!!
For FHG find the measure of the smallest angle ∠HFG, if m∠GHF = 92° and m∠HGF =72°
Answer:
The Answer is 16
Step-by-step explanation:
The three angles enclosed in a triangle, made by its sides, are called its internal angles. The sum of internal angles of a triangle is
180
o
. Based on its internal angles, a triangle can be classified as acute angled, right angled and obtuse angled.
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The sum of the measure of angle of a triangle = 180° .
Given two angles = 92° and 72°
_________________________
92° + 72° = 164°
180° - 164° = 16° (Ans)
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Answer:
2436 cubic centimeters
Step-by-step explanation:
11 * 14 = 154
14 * 7 / 2 = 49
154 + 49 = 203
203 * 12 = 2436
eight times the difference of a number and 7. write in algebraic expression.
Answer:
8(n - 7)
Step-by-step explanation:
let the number be n then the difference of n and 7 is n-7
8 times this difference is
8(n - 7)
Answer: 8(n-7)
Step-by-step explanation:
it should be that <3
Here's a question ~
p1 and p2 are points on either of the two lines
[tex]y - \sqrt{3} |x| = 2[/tex]
at a distance of 5 units from their point of point of intersection. Find the coordinates of the foot of perpendiculars drawn from p1 , p2 on the bisector of the Angle between the given lines.
Answer:
(0, 5√3/2 + 2)Step-by-step explanation:
Given is the absolute value function.
Observations:
It has a slope of ±√3 and the y- intercept of 2.There is no horizontal shift, so the the y-axis is the line of symmetry.The y-axis is also an angle bisector of the two lines.The foot P₁P₂ is parallel to the x-axis since it's perpendicular to the y- axis.We need to find the coordinates of intersection of the line P₁P₂ with the y- axis (the point Y in the picture).
Consider the triangle AYP₂.
We know AP₂ = 5.
The angle YAP₂ is:
arctan (1/√3) = 30°The distance AY is:
AY = AP₂ cos 30° = 5*√3/2The distance from the x-axis to the point Y is:
5√3/2 + 2, added the y- intercept of the graphed linesThe coordinates of the point Y:
(0, 5√3/2 + 2)In the given figure ABCD is a tripepizeum with AB||CD. If AO = x-1, CO = BO = x+1 and CD = x+4. Find the value of x.
[tex]\longmapsto[/tex]The value of "x" is 5.
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
A trapezium ABCD in which AB || CD such that
AO = x - 1CO = BO = x + 1OD = x + 4Now,
[tex]\rm In \: \triangle \: AOB \: and \: \triangle \: COD[/tex]
[tex]\rm \: \angle \: AOB \: and \: \angle \: COD \: \: \{vertically \: opposite \: angles \}[/tex]
[tex]\rm \: \angle \:ABO \: and \: \angle \: CDO \: \: \{alternate \: interior \: angles \}[/tex]
[tex]\bf \: \triangle \: AOB \: \sim \: \triangle \: COD \: \: \: \{AA \: similarity \}[/tex]
[tex]\bf\longmapsto\:\dfrac{AO}{CO} = \dfrac{BO}{DO} [/tex]
[tex]\rm \longmapsto\:\dfrac{x - 1}{x + 1} = \dfrac{x + 1}{x + 4} [/tex]
[tex]\rm \longmapsto\:(x - 1)(x + 4) = {(x + 1)}^{2} [/tex]
[tex]\rm \longmapsto\: {x}^{2} - x + 4x - 4 = {x}^{2} + 1 + 2x[/tex]
[tex]\rm \longmapsto\: 3x - 4 = 1 + 2x[/tex]
[tex]\rm \longmapsto\: 3x - 2x= 1 +4[/tex]
[tex]\bf\longmapsto \:x = 5[/tex]
3.5m/min = how manny miles/hour
Answer:
[tex]\sf\longmapsto0.13 miles/hour[/tex]
Step-by-step explanation:
Firstly we have to use the formula to find the miles/hour
[tex]\sf\longmapsto \: Formula:Divide \: the \: speed \: value \: by \: 26.822.[/tex]
[tex]\sf\longmapsto \: 3.5 \div 26.822[/tex]
[tex]\sf\longmapsto \: 0.13 miles/hour[/tex]
If the original quantity is 10 and the new quantity is 14, what is the percent increase?
Answer:
40% increase
Step-by-step explanation:
10 is you 100%
if it increased to 14, then that means your 100% = 10 increased +4 which is the 40%
how do you use subsitution for5x+2y=4
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5*x+2*y-(4)=0
Equation of a Straight Line
1.1 Solve 5x+2y-4 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5x+2y-4 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 2/1 so this line "cuts" the y axis at y= 2.00000
y-intercept = 4/2 = 2
Calculate the X-Intercept :
When y = 0 the value of x is 4/5 Our line therefore "cuts" the x axis at x= 0.80000
x-intercept = 4/5 = 0.80000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.000 and for x=2.000, the value of y is -3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -3.000 - 2.000 = -5.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -5.000/2.000 = -2.500
Geometric figure: Straight Line
Slope = -5.000/2.000 = -2.500
x-intercept = 4/5 = 0.80000
y-intercept = 4/2 = 2
HELP ASAP 100 POINTS!
Functions can be defined using graphs, tables, and ordered pairs. What is the range of a function?
The range is the input.
The range is all numbers.
The range is the output.
The range is any x-value.
Answer:
the range is the set of possible output of values
Step-by-step explanation:
The range is the set of y-values (OUTPUT) that map to the set of x-values (INPUT).
Find the GCF for the pair of numbers. 9,4
The GCF of numbers is the greatest common factor of the numbers.
The numbers are given as: 4 and 9.
Factorize both:
[tex]\mathbf{4 = 1 \times 2 \times 2}[/tex]
[tex]\mathbf{9 = 1 \times 3 \times 3}[/tex]
The common factor between both is 1.
So, we have:
[tex]\mathbf{GCF = 1 }[/tex]
Hence, the GCF of 4 and 9 is 1
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May I please receive help?
Answer:
Parallel: y=2x+3
Perpendicular= 1/2x+6
If two acute angles of a right angled triangle are in the ratio 1:2, Find them.
Answer:
30°,60°,90°
Step-by-step explanation:
Let :-
Ratio = 1x : 2xAs we know :-
Sum of all angles = 180°So that ,
x + 2x + 90 = 180 3x = 90 x = 90/3 x = 30Angles ,
90° x = 30° 2x = 60°Answer:
Let the angles be x and 2x.
We know that the sum of all interior angles of a triangle is 180°.
Therefore,
x+2x+90 = 1803x+90 = 1803x = 180-90x = 90/3x = 30Angles,
90°x = 30°2x = 2×30 = 60°60% of all bald eagles survived their first flight. If 25 randomly selected bald eagles are observed, what is the probability that at least 15 of them will survive their first flight.
a) Use the binomial distribution to approximate the probability.
Answer:
[tex]100%[/tex][tex]\%[/tex]
write the equation of the line perpendicular to the given line y - 2 = 1/4 (x+2)
Help me please Asap
Answer:
it is the last one {-4, -1, 0, 1, 2}
Step-by-step explanation:
Sienna, Rhys, and Micah are all reading the same book for school. Sienna has read 40% as far as Rhys has, and Rhys has read 40% as far as Micah has. If Sienna has read 60 pages, how many pages has Micah read?
Based on the fact that Sienna has read 60 pages, we can infer that Micha has read 375 pages of the book.
Sienna has read 40% of what Rhys has read and that corresponds to 60 pages. The number of pages read by Rhys is therefore:
= Number of pages / Percentage read
= 60 / 40%
= 150 pages
The 150 pages read by Rhys is 40% of what Micah has read. Micah has therefore read:
= 150 / 40%
= 375 pages
In conclusion, Micah has read 375 pages.
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which value of n makes the value of the expression 4n + 3 a composite number
Answer:
3
Step-by-step explanation:
Given expression :-
4n + 3It will be composite if it will has more than 2 factors ( other than 1 and itself )
If n = 1 :-
4*1 + 3 4+ 3 7 ( prime )If n = 2 :-
4*2 + 3 8 + 3 11 ( prime )If n = 3 :-
4*3+312+3 15 ( composite )Please could I have some help with this question? Thanks
Answer: 270
Step-by-step explanation:
1) Find DE
1 : 6
17 : x
Cross multiply
x = 17 * 6
x = 102
DE = 102
2) Compare the two triangles
1st (ABC)
side = 45
base = 17
2nd (ADE)
side = x
base = 102
[tex]\frac{x}{45} = \frac{102}{17}[/tex]
Cross multiply
17x = 102 x 45
17x = 4590
x = 4590/17
x = 270
AD = 270
parallelogram ABCD with vertices A(6,8) B(10,9) C(9,3) and D(5,2): 90 counterclockwise rotation about P(4,1)
A ( , )
B ( , )
C ( , )
D ( , )
Answer:
A(-3 , 3) B(-4 , 7) C(2 , 6) D(3 , 2)
Step-by-step explanation:
Rotation of the parallelogram about the point P(4, 1), is done by taking
point P as the origin, and using relative coordinates for the rotation.
[tex]\underline{A(-3, \, 3)}[/tex][tex]\underline{B(-4, \, 7)}[/tex][tex]\underline{C(2, \, 6)}[/tex][tex]\underline{D(3, \, 2)}[/tex]Reasons:
The given parameters are;
Vertices of the parallelogram ABCD are;
A(6, 8), B(10, 9), C(9, 3) and D(5, 2)
Point about the parallelogram is rotated = P(4, 1)
Angle of rotation = 90°
Direction of rotation = Counterclockwise
90° rotation counterclockwise of (x, y) about the origin gives → (-y, x)
Therefore, we have;
The given points relative to the point P are;
A'(6-4, 8 - 1) = A'(2, 7)
B'(10 - 4, 9 - 1) = B'(6, 8)
C'(9 - 4, 3 - 1) = C'(5, 2)
D'(5 - 4, 2 - 1) = D'(1, 1)
Therefore, we get;
A'(2, 7) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] A''(-7, 2)
B'(6, 8) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] B''(-8, 6)
C'(5, 2) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] C''(-2, 5)
D'(1, 1) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] D''(-1, 1)
Which then gives;
The image location are;
A(-7 + 4, 2 + 1) = A(-3, 3)
B''(-8 + 4, 6 + 1) = B(-4, 7)
C''(-2 + 4, 5 + 1) = C(2, 6)
D''(-1 + 4, 1 + 1) = D(3, 2)
Therefore, we have;
A(-3, 3), B(-4, 7), C(2, 6), and D(3, 2)
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PLEASE HELP!!!!! You are given an isosceles trapezoid ABCD with median XY. Complete the following.
m
Steve leaves the corner of First and Maple on his bicycle and travels an average speed of 9 mi/hr. Two hours later,his brother leaves from First and Maple, following him on a moped traveling 27 mi/hr. How long will it take him to catch up with steve?
Answer:
Two hours later his brother leaves from first and maple and comes after him on a moped travelling 27 mph, His uphill speed was 8 miles per hour slower than his downhill speed.
Step-by-step explanation:
