A total of 484 tickets we’re sold for the school play. They Either adult or student tickets. There were 66 Fewer student tickets sold than adult tickets . How many adult tickets were sold?
Answers
Answer:
x + 61 = 411
Step-by-step explanation:
Let x = the number of adult tickets sold
Let x + 61 = the number of student tickets sold
x + x + 61 = 761
2x = 700
x = 350
Related Questions
log(0.5) 256 = x
find value of x
Answers
Answer:
[tex]=-8[/tex]
Step-by-step explanation:
[tex]\log _{0.5}\left(256\right)=x\\Switch\:sides\\x=\log _{0.5}\left(256\right)\\\mathrm{Rewrite\:}256\mathrm{\:in\:power-base\:form:}\quad 256=2^8\\x=\log _{0.5}\left(2^8\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\log _{0.5}\left(2^8\right)=8\log _{0.5}\left(2\right)\\x=8\log _{0.5}\left(2\right)\\0.5=2^{-1}\\x=8\log _{2^{-1}}\left(2\right)\\[/tex]
[tex]\mathrm{Apply\:log\:rule\:}\log _{a^b}\left(x\right)=\frac{1}{b}\log _a\left(x\right),\:\quad \mathrm{\:assuming\:}a\:\ge \:0\\x=8\cdot \frac{1}{-1}\log _2\left(2\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\x=8\cdot \frac{1}{-1}\\\mathrm{Simplify}\\8\cdot \frac{1}{-1}\\\frac{1}{-1}=-1\\\frac{1}{-1}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{1}{1}\\\mathrm{Apply\:rule}\:\frac{a}{1}=a\\=-1\\=8\left(-1\right)\\[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\=-8\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:8\cdot \:1=8\\=-8\\[/tex]
The value of x for the expression is, - 8.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ [tex]log_{0.5} ( 256) = x[/tex]
Now, We can solve the expression by the logarithmic for the value of x as;
⇒ [tex]log_{0.5} ( 256) = x[/tex]
⇒ [tex]x = log_{0.5} ( 256)[/tex]
⇒ [tex]x = log_{0.5} ( 2^8)[/tex]
Apply log rule,
⇒ [tex]x =8 log_{0.5} ( 2)[/tex]
⇒ [tex]x = 8 log_{2^{-1} } ( 2)[/tex]
⇒ [tex]x = 8 *\frac{1}{-1} log_{2 } ( 2)[/tex]
⇒ [tex]x = - 8 log_{2 } ( 2)[/tex]
We know that; [tex]log_{2} 2 = 1\\[/tex]
Hence, We get;
⇒ x = - 8 × 1
⇒ x = - 8
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Area of DEF = 6 sq ft
Find the area of ABC. Please help I need BOTH green and grey boxes please .
Answers
Answer:
54 ft^2
(54 in green box; 2 in grey box)
Step-by-step explanation:
We have 2 similar triangles, ABC and DEF.
The area of triangle DEF is given as 6 sq ft.
Side BC of triangle ABC measures 12 ft.
The corresponding side to BC in triangle DEF is EF. It measures 4 ft.
That gives us a scale factor from triangle DEF to triangle ABC.
To find the scale factor between two similar polygons, divide the length of a side of the second polygon by the length of the corresponding side of the first polygon.
scale factor = BC/EF = (12 ft)/(4 ft) = 3
The scale factor of side lengths is 3.
The ratio of the areas is the square of the scale factor.
ratio of areas = 3^2 = 9
Now multiply the area of the first triangle (DEF) by the ratio of areas to get the area of the second triangle (ABC).
area of triangle ABC = 9 * (area of triangle DEF)
area of triangle ABC = 9 * (6 sq ft)
area of triangle ABC = 54 sq ft
Answer: 54 ft^2
(54 in green box; 2 in grey box)
Which statement correctly compares the spreads of the distributions?
Answers
Answer:
b. the ranges of penguin heights are the same.
Step-by-step explanation:
Hello!
Statements:
Which statement correctly compares the spreads of the distributions?
a. the mode of penguin heights at county side zoo is greater than the mode at city view zoo.
b. the ranges of penguin heights are the same.
c. the range of penguin heights is greater at city view zoo than at county side zoo.
d. the range of penguin heights is greater at county side zoo than at city view zoo.
The mode and mean are measurements of central tendency, these indicate the position of a data set but don't show any information concerning the distribution of said data.
The range on the other had is a measurement of variance, it shows the difference between the maximum and minimum values of the data set and indicates its total dispersion.
City view Zoo R= 44-37= 7 cm
County side Zoo: R= 45-38= 7 cm
Both ranges are the same.
I hope this helps!
Given
Principal 1500
Intrest 6%
Time 240 days
Partial payments for 100th day 7,000
For 180th day 4,000
A. Use the u.s rule to solve for total intrest cost
B. Use the u.s rule to solve the balance after payments for the 100th and 180th
C use the u.s rules to solve final payment
Answers
The Tip Top Tennis Balls manufacturing company makes and sells tennis balls. The revenue (in dollars) that the company receives in selling x cases (12 cans per case, three balls per can) of tennis balls in one week is given by The cost (in dollars) is given by All of the following questions refer to a one-week period, and only full cases of balls are sold. Write an equation for the profit P the company makes in producing and selling x cases. (Remember the profit = revenue – cost.) How many tennis balls need to produced and sold for the profit to be greater than zero? Choose the correct answer.
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
A circle has a circumference of 452.16. What is the radius of the circle
Answers
Formula: r = C/2π
Solve with the given values.
r = 452.16/2(3.14)
r = 452.16/6.28
r = 72
Therefore, the radius is approximately 72 units.
Best of Luck!
There are 4 dogs at each corner. They each see three dogs. How many dogs are there?
Answers
Step-by-step explanation:
there are four dogs because each dog at a corner will see the other three dogs at the other corners
The graph shows equivalent ratios. Khalid plots a point to show a fourth equivalent ratio. If the x-value of Khalid’s point is 35, what is the y-value? 20 25 28 35
Answers
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
Which set of numbers is arranged in increasing order?
Answers
Answer:
Hey mate, I think you forgot to attach photo of sets. Check it.
**10 POINTS PLEASE HELP!!**
A cube is dilated by a factor of 4. By what factor does its volume increase? Complete the explanation of your reasoning.
The volume increases by a factor of ____. When the cube is dilated, each side length is increased by (select), so the volume is increased by (select) the dilation factor.
Answers
Answer:
The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64.
Step-by-step explanation:
Let L represents the Length of the cube before it's dilated.
Volume, V1 = Length * Length * Length
Volume, V1 = L * L * L
Volume, V1 = L³
When the cube is dilated by a factor of 4.
The new Length becomes 4L.
The new volume is calculated as thus.
New Volume, V2 = 4L * 4L * 4L
New Volume, V2 = 64L³
Dividing the new volume by the old volume gives the increment factor.
Factor = New Volume ÷ Old Volume
Factor = V2/V1
Factor = 64L³/L³
Factor = 64.
Hence, when the sides of the cube is dilated by 4, the volume increases by a factor of 64.
Filling the gap of the given sentence;
"The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64"
Will give brainliest for answer
Answers
Answer:
y > -x -3
Step-by-step explanation:
The graph is shaded above the dashed line, indicating y-values in the solution are greater than those on the line, so your inequality will start with ...
y >
The y-intercept of the line is (0, -3), so the "b" value in ...
y > mx +b
will be -3.
The line has a rise of -3 for a run of 3 (between the marked points), so the slope is ...
m = rise/run = -3/3 = -1
Then the inequality you want is ...
y > -x -3
A study conducted by Harvard Business School recorded the amount of time CEOs devoted to various activities during the workweek. Meetings were the single largest activity averaging 18 hours per week. Assume that the standard deviation for the time spent in meetings is 5.2 hours. To confirm these results, a random sample of 35 CEOs was selected This sample averaged 16.8 hours per week in meetings. Which of the following statements is correct? A) The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School. B) The interval that contains 95% of the sample means is 17.1 and 18.9 hours. Because the sample mean is not between these two values, we do not have support for the results of the CEO study by the Harvard Business School C) The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School D) The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we do not have support for the results of the CEO study by the Harvard Business School
Answers
Answer:
The correct option is A
Step-by-step explanation:
From the question we are told that
The average number of meetings hours per week is [tex]\mu= 18 \ hours[/tex]
The standard deviation is [tex]\sigma = 5.2 \ hours[/tex]
The sample size is n= 35
The sample average per week is [tex]p = 16.8 \ hours[/tex]
From each solution statement we can deduce that the confidence level is
[tex]t = 95[/tex]%
Thus the significance level is [tex]\alpha = 0.05[/tex]= 5%
The z value for the significance level is gotten as 1.96 from the z-table
The confidence level interval for the sample mean is mathematically evaluated as
[tex]\= x = \mu \pm (1.96 * \frac{\sigma }{\sqrt{n} } )[/tex]
Sustituting values
[tex]\= x = 18 \pm (1.96 * \frac{5.2 }{\sqrt{35} } )[/tex]
[tex]\= x = 18 \pm1.7[/tex]
=> [tex]18 - 1.7 < \= x < 18 +1.7[/tex]
[tex]16.3 < \= x < 19.7[/tex]
Point R is at (4, 1.5) and Point T is at (4, 2.9) on a coordinate grid. The distance between the two points is ____. (Input numbers and decimal point only, such as 8.2.)
Answers
Answer:
1.4
Step-by-step explanation:
Both points are on the vertical line x=4, so the distance between them is the difference of their y-coordinates:
2.9 -1.5 = 1.4
The points are 1.4 units apart.
peter surveyed a random sample of adults and a random sample of teenagers about the number of hours that they exercise in a typical week. What comparative inference can Peter make from the data sets?
Answers
Answer:
Step-by-step explanation:
Hello!
Peter is interested in comparing the number of hours adults and teenagers exercise per week, for this selected one random group of adults and a random group of teenagers and surveyed them on their weekly exercise times.
To compare the weekly exercise time of both populations, the best is to use a measure central tendency, so you can compare their positions and see if they are significantly similar or not.
The most common parameters to use for comparing two populations are its population means. So the analysis to do is a two independent sample test.
I hope this helps!
(Easy question, plz answer) Roberto made fruit punch. He used 3 quarts of mango juice and 1 pint of pomegranate juice. He used 1 quart more cranberry juice than mango juice, How many cups of fruit punch did Roberto make?
Answers
Answer:
30 cups
Step-by-step explanation:
mango: 16 cups x 3/4 = 12 cups
pomegranate: 1 pint = 2 cups
cranberry: 1 gallon= 16 cups
Cups of fruit punch: 12+2+16= 30
Roberto made 30 cups of Fruit punch( Hopefully this helped )
Solve plzzzz As attached
Answers
Answer:
Step-by-step explanation:
Basically, we're solving for a.
w = 3(2a + b) - 4
w = 6a + 3b - 4
-6a + w = 3b - 4
-6a = -w + 3b - 4
a = (w - 3b + 4)/6
Hope this helps!
What’s the correct answer for this?
Answers
Answer:
Second option is the correct answer
[tex](x+11)^2+(y+6)^2 = 324[/tex]
Step-by-step explanation:
[tex]x^{2} +12y+22x+y^2-167=0\\x^{2}+22x +y^2 +12y-167=0\\(x^{2}+22x +121)-121 +(y^2 +12y+36)-36-167=0\\(x+11)^2+(y+6)^2-324 = 0\\\huge\red{\boxed{(x+11)^2+(y+6)^2 = 324}}\\[/tex]
Answer:
[tex](x+11)^2+(y+6)^2=324[/tex]
Step-by-step explanation:
[tex]x^2+12y+22x+y^2-167=0\\\mathrm{Circle\:Equation}\\\left(x-a\right)^2+\left(y-b\right)^2=r^2\:\:\mathrm{is\:the\:circle\:equation\:with\:a\:radius\:r,\:centered\:at}\:\left(a,\:b\right)\\\mathrm{Rewrite}\:x^2+12y+22x+y^2-167=0\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}\\x^2+12y+22x+y^2-167=0\\\mathrm{Move\:the\:loose\:number\:to\:the\:right\:side}\\x^2+22x+y^2+12y=167\\Group\:x-variables\:and\:y-variables\:together\\\left(x^2+22x\right)+\left(y^2+12y\right)=167[/tex]
[tex]\mathrm{Convert}\:x\:\mathrm{to\:square\:form}\\\left(x^2+22x+121\right)+\left(y^2+12y\right)=167+12\\Convert\:to\:square\:form\\\left(x+11\right)^2+\left(y^2+12y\right)=167+121\\\mathrm{Convert}\:y\:\mathrm{to\:square\:form}\\\left(x+11\right)^2+\left(y^2+12y+36\right)=167+121+36\\Convert\:to\:square\:form\\\left(x+11\right)^2+\left(y+6\right)^2=167+121+36\\\mathrm{Refine\:}167+121+36\\\left(x+11\right)^2+\left(y+6\right)^2=324\\Rewrite\:in\:standard\:form[/tex]
[tex]\left(x-\left(-11\right)\right)^2+\left(y-\left(-6\right)\right)^2=18^2\\\mathrm{Therefore\:the\:circle\:properties\:are:}\\\left(a,\:b\right)=\left(-11,\:-6\right),\:r=18[/tex]
Twelve and sixty-eighty thousandths
Answers
Answer:
12,60800000
hope it is not help full
Answer:
12 80000 I hope this helps buddy
Step-by-step explanation:
good luck
Solve 56 - 10x20 + 8x.
O A. xs-2
O B. X2-2
O c. x52
O D.x22
Answers
The value of the given equation is 2 and -10.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Given is an equation, x²+8x-20 = 0, we need to solve for x,
x²+8x-20 = 0
Solving for x, by using factorization,
x²+8x-20 = 0
Splitting the middle term,
x²+10x-2x-20 = 0
x(x+10)-2(x+10) = 0
(x-2)(x+10) = 0
x = 2 and x = -10
Hence, the value of the given equation is 2 and -10.
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The complete question is attached
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT PLEASE EXPLAIN WHY YOU ARE CORRECT
Answers
Answer:
AB is mid-segment of this trapezoid, then we have:
2 x AB = DG + EF
=> 2 x 12 = 5x - 4 + 8x + 2
=> 24 = 13x - 2
=>13x = 26
=> x = 2
=> Option A is correct
Hope this helps!
:)
The number of visitors to a town increases by 2.5% each year. If the first year the town recorded visitors, there were 575,
which function represents the total number of visitors in terms of the years since they were first counted?
Answers
Answer:
575(1+2.5)^x
Step-by-step explanation:
X represents the number of years since they were first counted.
Solve: -(1/4)m + 5 = 16
Answers
Answer:
m=-44
Explanation: distribute the negative and add -1/4 to m and then take the 5 away from 16 and then multiply both sides
Answer:
M = - 44
Step-by-step explanation:
You will start by subtracting 5 on both sides of the equation.
- (1/4)m + 5 =16
-5 -5
Simplify
- 1/4 m =11
Multiple both sides by - 4
(-1/4m)(-4)= 11 (- 4)
The final result is m equals negitive 4.
M = -44
Colin invests £3900 into his bank account.
He receives 4% per year compound interest.
How much will Colin have after 2 years?
Give your answer to the nearest penny where appropriate.
Answers
Answer:
Colin will have 421824 pennies after 2 years
Step-by-step explanation:
Given:
Amount invested in bank by Colin (P) = £3900
Rate of interest (r) = 4%
Time period (n) = 2 years
To find: Amount after 2 years (A)
Solution:
Formula for amount (A) is [tex]A=P\left ( 1+\frac{r}{100} \right )^n[/tex]
[tex]A=3900\left ( 1+\frac{4}{100} \right )^2\\=3900\left ( 1+\frac{1}{25} \right )^2\\=3900\times \frac{26}{25}\times \frac{26}{25}\\=4218.24[/tex]
As 1 pound = 100 pennies,
4218.24 pounds = 4218.24 × 100 = 421824 pennies
So,
Colin will have 421824 pennies after 2 years.
In ΔIJK, k = 7.7 cm, i = 3.4 cm and ∠J=30°. Find the length of j, to the nearest 10th of a centimeter.
Answers
Answer:
To the nearest tenth = 10.8cm
Step-by-step explanation:
Using the cosine rule
J² = i² + k² + 2ikcosj
J² = 3.4² + 7.7² + 2(3.4)(7.7) cos 30
J² = 11.56 + 59.29 + 52.36cos30
J² = 11.56 + 59.29 + 52.36(0.8660)
J² = 11.56 + 59.29 + 45.35
J² = 116.2
J=√116.2
J= 10.78 cm
To the nearest tenth = 10.8cm
Answer:
its 5.1
Step-by-step explanation:
\text{S.A.S.}\rightarrow \text{Law of Cosines}
S.A.S.→Law of Cosines
a^2=b^2+c^2-2bc\cos A
a
2
=b
2
+c
2
−2bccosA
From reference sheet.
j^2 = 7.7^2+3.4^2-2(7.7)(3.4)\cos 30
j
2
=7.7
2
+3.4
2
−2(7.7)(3.4)cos30
Plug in values.
j^2 = 59.29+11.56-2(7.7)(3.4)(0.866025)
j
2
=59.29+11.56−2(7.7)(3.4)(0.866025)
Square and find cosine.
j^2 = 59.29+11.56-45.34509
j
2
=59.29+11.56−45.34509
Multiply.
j^2 = 25.50491
j
2
=25.50491
Add.
j=\sqrt{25.50491} \approx5.05 \approx5.1
j=
25.50491
≈5.05≈5.1
Square root and round.
54,36,24 whats the next term in the geometric sequence
Answers
Answer:
16
Step-by-step explanation:
The common ratio is 36/54 = 2/3.
So the next term is 2/3 (24) = 16.
Answer:
16
Step-by-step explanation:
sorry no step by step explanation because I was in a rush anyway I did the quiz and here u go anyway have a great day I hope this helps :D
Gale makes two gallons of a punch solution that contains 25% orange juice. How many gallons of orange juice should gayle add to make the solution 40% orange juice
Answers
Answer:
0.5 gallons
Step-by-step explanation:
Let x represent the amount of orange juice (in gallons) Gayle must add to the mix. Then the total amount of orange in the mix is ...
0.25(2) +x = 0.40(2+x)
0.50 +x = 0.80 +0.40x . . . . eliminate parentheses
0.60x = 0.30 . . . . . . . . . . . . subtract 0.50+0.40x
x = 0.5 . . . . . . . . . . . . . . . . . divide by 0.60
Gayle should add 0.5 gallons of orange juice to make a 40% solution.
compare and contrast perfect squares and imperfect squares. explain your reasoning by talking about square roots and the process of finding perfect square roots and imperfect square roots.
Answers
Answer: perfect squares are the squares of the whole numbers: 1, 4, 9,25,36,49,64,81,100...... For example, 9 is a squared number because it can be written as 3x3. However, imperfect squares are numbers whose square roots contain fractions or decimals. For example square root of 20 = 4 1/2
The square number, sometimes known as a perfect square, is an integer that is the square of another integer and numbers with fractional or decimal square roots are considered imperfect squares.
We need to compare and contrast perfect squares and imperfect squares.
Perfect squares: When you multiply an integer by itself, you get a perfect square, which is a positive integer. Perfect squares are sums that are the products of integers multiplied by themselves, to put it simply. A perfect square is typically expressed as x², where x is an integer and x²'s value is a perfect square.
Imperfect squares: Numbers with fractional or decimal square roots are considered imperfect squares.
Therefore, the square number, sometimes known as a perfect square, is an integer that is the square of another integer and numbers with fractional or decimal square roots are considered imperfect squares.
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Wesson Company sold 10,000 units of its only product in the first half of the year. If sales increase by 12% in the second half of the year, which cost will increase?
Answers
Answer:
Direct materials
Step-by-step explanation:
In this case we must bear in mind that as more products are sold, more material is needed to manufacture those additional final products
.
Therefore, in this case the cost would be related mainly to the materials, mainly the direct materials, since they are essential in the production of the product.
You're choosing between two car rental companies. Company A charges an initial fee of $15 with $.25 per mile, while Company B only charges $.50 per mile. How many miles will it take for both companies to have the same service price? What's this price amount? Use the following systems of linear equations to solve by graphing. Company A: y = 0.25x + 15 Company B: y = 0.50x
Answers
The price amount is $16
Joe went to the bank and withdrew $358 from his checkings account and his balance is now at -$96. He later deposited ¾ of his $800 check and put the rest in his savings account. How much money does he have in his checking account?
Answers
Answer:
$504
Step-by-step explanation:
In this case you're solving for his checking account. In the beginning due to him withdrawing $358 he was left with -$96, assuming that he grabbed more than he could take. But later, he deposited 3/4 of $800 into his checking account.
So you need to find what 3/4 of 800 is first to see how much money he put into his checking account
3/4x800/1=600
But thats not the answer since thats only how much he put into his checking account, not how much he has.
So according to the question he had -96 left in the checking account. Therefore, you have to add the 600 in.
600+-96=504
In case you are wondering why there was a lower number when adding, it was a negative number which causes you to start from -96, but go more right into the number line 600 times.
If you have any questions please ask and I hope this helped! :)