Answer:
8 students
Step-by-step explanation:
Let's say there are x students in the theater club. We can set up the following equations to represent the information given in the problem:
2/7 * x = number of students in the second show3/5 * x = number of students in the third showx - (2/7 * x + 3/5 * x) = number of students in the first showWe are told that there are 70 students in the theater club, so we can substitute 70 for x in the equations above to find the number of students in each show:
2/7 * 70 = 20 students in the second show3/5 * 70 = 42 students in the third show70 - (2/7 * 70 + 3/5 * 70) = 8 students in the first showTherefore, there will be 8 students in the first show.
find the exact length of the curve. y = 4 + 6x3/2, 0 ≤ x ≤ 1
[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex] is the required length of the curve y = 4 + 6[tex]x^\frac{3}{2}[/tex]
Given equation of curve:
y = 4 + 6[tex]x^\frac{3}{2}[/tex]
length of the curve is given by L= [tex]\int\limits^a_b {\sqrt{1+(y^')^2} } \, dx[/tex]
where [tex]y^'[/tex] is derivative of y with respect to x
so [tex]y^'[/tex] = 6*(3/2) * [tex]\sqrt{x}[/tex]
=> 9 [tex]\sqrt{x}[/tex]
given a=1 and b=0
so L= [tex]\int\limits^1_0 {\sqrt{1+(9\sqrt{x})^2 } } \, dx[/tex]
L= [tex]\int\limits^1_0 {\sqrt{1+81x } } \, dx[/tex]
let 1+81x be t
81dx = dt
as the value of x changes after the substitution of the value.
so now the L changes as:
L= 1/81 [tex]\int\limits{\sqrt{t } } \, dt[/tex]
L=1/81* [tex]\left \{ {{t=82} \atop {t=1}} \right.[/tex] [tex]\frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]
the min value of t=1 and max value of t=82
L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]
so the exact length of the curve is given by L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]
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Solve the equation: logsx + 3logsx = 1.
{-√5, √5)
{√5)
(-√5)
Ø
14. 8:14
16. There are 16 pints in 2 gallons. Complete the
table to write three ratios of pints to gallons.
Number of
Pints
Number of
Gallons
16
2
I don’t understand what to do
Answer:
Step-by-step explanation:
Number of pints | 16 | 32| 48|
Number of galll. | 2 | 4 | 6 |
Those are 3 ratios
16:2
32:4
and 48:6
You multiply by 2 to get 3 ratios
suppose that the series cn xn has radius of convergence 13 and the series dn xn has radius of convergence 14. what is the radius of convergence of series (cn dn)xn ?
The radius of convergence of the series sigma cnx9n will be R raised to the power 1/9.
Radius=a straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter. the length of such a line.
The radius of convergence of the sum of the two series will be 5.
sigma (cnxn + dnxn) = sigma cnxn + sigma dnxn, and if both the series on the right-hand side converge.
The LHS converges for values of x on which both the series on the RHS converge. Hence, the LHS will converge on the intersection of the convergence of the two RHS series.
( if 5 < |x| < 6, the second series will converge, but the first will not.)
The series sigma cnx9n has radius of convergence R raised to the power 1/9.The series sigma cnxn has radius of convergence R. This means that it converges for |x| < R.The series sigma cnx9n can be written as sigma cn(x9)n
This means that the series converges for |x9| < R.
Therefore, the radius of convergence of the series sigma cnx9n will be R raised to the power 1/9.
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Complete the square-
x^2-1/2x=8/16
thank you :)))
Answer: (x- 1/4)^2=9/16
Step-by-step explanation:
x^2 -1/2x =8/16
(x^2-1/2x +1/16)^2= 8/16+1/16)
(x- 1/4)^2=9/16
Simplify the expression: (6 − 2i)(4 − 5i). a. 34 − 17i b. 14 − 17i c. 34 − 38i d. 14 − 38i
misha increased her test score from 60% to 80%. what was the approximate percent increase of misha's test score? 66% 75%
Answer:
the approximate percent increase of Misha's test score is 33% !
Step-by-step explanation:
Answer: 33.3333%
Step-by-step explanation:
Percent Increase Formula
c = x2-x1/x1
x2- final value
x1- initial value
c= 80-60/60 = 33.3333%
The profit function, P(x), for a tamale cart is shown below, where a represents the number of
tamales sold. What is P¹(x) for this situation?
P(x) = 5x² 100; x ≥ 0
TAMALES
Tamales
P¹(x)=√(x+20); -∞
P-¹ (2)=√ ;-100
(z + 100)
P-¹(x)
P-¹ (x) =
2+100
10
(+100)
5
·∞<*<∞
; x>-100
The inverse function for this problem is defined as follows:
P^(-1)(x) = square root of (x + 100/5), x ≥ -100.
How to obtain the inverse function?The function in this problem is defined as follows:
P(x) = 5x² - 100, x ≥ 0.
In which P(x) is the profit earned when x tamales are sold.
To obtain the inverse function, first we exchange the variable y = P(x) and x are follows:
x = 5y² - 100
Then the variable y must be isolated as follows:
5y² = x + 100
y² = (x + 100)/5
y = square root of (x + 100/5).
The domain must be the same domain of the square root function, that does not accept negative values hence:
P^(-1)(x) = square root of (x + 100/5), x ≥ -100.
This means that the first option is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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There are x melons and y oranges. The product of integers x and y is
539. The number of melons is 11 times of that of oranges, How many
melon(s) is / are there?
Answer:
77 melons
Step-by-step explanation:
[tex]11x \times x = 539 \\ 11 {x}^{2} = 539 \\ \frac{11x}{11} = \frac{539}{49} \\ {x}^{2} = 49 \\ \sqrt{ {x}^{2} } = \sqrt{49} \\ x = 7[/tex]
The oranges are 7
And the melons are 11 times the number of the oranges hence
11 x 7= 77
Answer:
There are 77 melons
Step-by-step explanation:
See picture below :)
Tommy i buying ued book the price of the book are 180. He ue the 30% off tudent dicount and there i a 4 % ale tax. What i the total price
Using percentages we know that the total price of the book that Tommy will pay is $131.04.
What is the percentage?
In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A% is a number that has neither dimensions nor a defined unit of measurement.
For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, we know that the price of the book is 180.
Sales tax is 4%. So, the total price:
180/100 * 4 = 7.2$ ⇒ $187.2
Now, there is a 30% discount:
187.2/100 * 30 = $56.16
⇒ 187.2 - 56.16 = $131.04
Therefore, using percentages we know that the total price of the book that Tommy will pay is $131.04.
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what is the simple linear regression model for the response variable of annual salary (as) and explanatory variable of years of education (ed)? multiple choice question.
The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.
Variables used to explain or predict a response variable are called explanatory variables.
The students want to predict age using their height, so the explanatory variable is height and the response variable is age.
The values of an ordinal variable have a meaningful order. For example, an education level (with possible values of high school, bachelor's degree, and graduate degree) can be an ordinal variable.
"Hand" belongs to "Clock". "Experience" also belongs to "Year". So if he has 10 years of experience in the industry, no apostrophes are needed. An apostrophe is required if you have more than 10 years of experience.
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the equation is given: a^2x-a=ax. for some values of a this equation has a unique solution. Solve the equation for these values of a
The solution of the equation for values of a is 1/(x - 1)
How to solve the equation for these values of aFrom the question, we have the following parameters that can be used in our computation:
a^2x - a = ax
Rewrite properly as
a²x - a = ax
Divide through by a
So, we have
ax - 1 = x
Collect the like terms
ax - x = 1
Factor out x
This gives
a(x - 1) = 1
Divide both sides by x - 1
a = 1/(x - 1)
Hence, the solution is 1/(x - 1)
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proof: fill in the reasons for the proof
∠1≅∠2 if RECT is the rectangle and M is the midpoint of EC.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
RECT is the rectangle and M is the midpoint of EC.
we need to prove angle one is congruent to angle two.
By given,RECT is the rectangle and M is the midpoint of EC.
∠E≅∠C
In the rectangle all the angles are 90 degrees.
∠EM≅∠MC.
As M is midpoint, it has equidistant from E and C.
ER≅CT both sides are congruent.
ΔERM≅ΔCTM both are similar triangles.
RM≅TM both sides are congruent.
∠1≅∠2 by SAS postulate.
Hence, RECT is the rectangle and M is the midpoint of EC then ∠1≅∠2
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Given: AB = CD
Prove: AC = BD
What reason can be used to justify statement 4 in the proof above?
the reflexive property the symmetric property the transitive property the segment addition property
Step-by-step explanation:
To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.
In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.
Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.
ethan plants a 8-inch tomato plant in his garden. the plant grows by about 14% per week for several months. which formula represents the height h of the tomato plant (in inches) as a function of the time t in weeks since it was planted?
The formula that represents the height h of the tomato plant as a function of the time t in weeks since it was planted is h=8(1.14)^t inches.
The height of a plant is considered to be "h".
The increase percentage per week =14
Compound interest is the interest you earn on interest. This may be illustrated via way of means of the usage of primary math: in case you have $one hundred and it earns 5% interest every year, you may have $one hundred and five on the cease of the primary year. At the cease of the second one year, you may have $110.25.
Now,
h=8(1+r/100)^t
h=8(1+14/100)^t
h=8(114/100)^t
h=8(1.14)^t inches
Therefore, the formula that represents the height h of the tomato plant as a function of the time t in weeks since it was planted is h=8(1.14)^t inches.
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3-quart carton of milk costs $4.92. What is the price per cup?
Answer:
The price per cup would be 0.41 cents.
Step-by step explaination:
Answer:
$0.41
Step-by-step explanation:
To find the price per cup of milk, we first need to know how many cups are in a 3-quart carton.
1 quart is equivalent to 4 cups, so a 3-quart carton contains:
[tex]\sf 3\;quarts=3 \times 4 \;cups= 12\;cups[/tex]
Now, we can calculate the price per cup by dividing the total price by the number of cups:
[tex]\begin{aligned}\textsf{Price per cup} &= \dfrac{\textsf{Total price}}{\textsf{Number of cups}} \\\\&=\sf \dfrac{\$4.92}{12}\\\\&=\sf \$0.41\end{aligned}[/tex]
Therefore, the price per cup of milk is $0.41.
discuss the continuity of the function. f(x, y) = sin(xy) xy , xy ≠ 0 1, xy = 0
The function f(x,y) is at origin [tex]\left|\frac{\sin x y}{x y}-1\right| < \varepsilon[/tex].
We can treat this function as h=xy and then it will looks like sin h/h because if we choose any path passing through original it will always continuous so above f(x,y) is continuous
[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]
Choose y=mx path y→0, x→0
[tex]$$\begin{aligned}\lim _{\substack{x \rightarrow 0 \\y=\infty}} f(x, x) & =\lim _{x \rightarrow 0} \frac{\sin m x^2}{m x^2} \\& =\lim _{x \rightarrow 0} \frac{\cos m x^2 \cdot 2 m x}{2 m x}=1\end{aligned}$$[/tex]
Now consider,
[tex]$|f(n, y)-L 1=| \frac{\sin x-1}{n y}-1 \mid < \varepsilon$[/tex]
[tex]$$$\forall \varepsilon > 0$, and $|n| < \delta,|y| < d$$$=\left|\frac{\sin x y}{x y}-1\right| < \varepsilon$$[/tex]
Hence f(x,y) is continues at origin.
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Discuss the continuity of the function:
[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]
The perimeter of a regular pentagon is 100 centimeters. how long is each side?
a. 100 cm
b. 40 cm
c. 20 cm
d. 80 cm
The correct option c. 20 cm, is the length of each sides of the regular pentagon.
Explain the term regular pentagon?Every side of a regular pentagon has the same length, and its five angles are all the same size. A pentagon is said to as irregular if its side length as well as angle measurement are not equal.A quadrilateral with five equal sides is known as a regular Pentagon.
Regular pentagon perimeter equals 5*side
Since we already know that a normal pentagon's perimeter is 100 cm.
Hence, 100 = 5*side
Side = 20 cm
Each side is 20 cm long.
As a result, the side of a regular pentagon is 20 cm long.
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Identify the measure of angle x please show work because I have too !!
Answer:
145 degrees
Step-by-step explanation:
the 2 angles are on a flat line so added together they equal 180 degrees
so we can subtract from 35 from 180 to find x
180-35
145
hopes this helps
Please help with questions 1 2 3 5
An integer to represent the situation, the temperature was 3° below zero is -3.
What is an Integer?Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.
1) The stock market increased 75 points
Integer to represent the given situation is +75 or 75.
2) A loss of 15 yards
Integer to represent the given situation is -15
3) Nancy owes her friend $10
Integer to represent the given situation is -10
4) Frederick is located 290 feet above sea level
Integer to represent the given situation is 290 or +290
5) The temperature was 3° below zero
Integer to represent the given situation is -3.
Therefore, an integer to represent the situation, the temperature was 3° below zero is -3.
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In the entence, the author want to ue alliteration. Which choice provide the bet example of thi?
Ted abolutely aced hi teaching exam
The choice that provides the best example of alliteration for the given sentence is tested terrifically on teaching. (Option C)
Alliteration is a literary device in which there is a noticeable repetition of initial consonant sounds in consecutive or nearby words in a phrase. It refers to the occurrence of the same sound or letter at the beginning of adjacent or closely connected words. Alliteration is created by repeated sound at the start of the words and not the repeated letter. For example, the phrase “kids’ coats” is alliterative, and the phrase “phony people” is not alliterative. In the given sentence, author can create alliteration by using tested terrifically in place was absolutely aced.
Note: The question is incomplete. The complete question probably is: In the sentence, the author wants to use alliteration. Which choice provides the best example of this? Ted absolutely aced his teaching exam. A) NO CHANGE B) was astounded at how well he did on C) tested terrifically on teaching.
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Wanda sews small and large gloves. It takes her 45 minutes to sew a small pair of gloves and 120 minutes to sew a large pair of gloves. The costs of producing the gloves are $2 for a small pair and $4 for a large pair. Wanda has 16 hours available to sew gloves. The materials to make the gloves must cost at most $40. The system of linear inequalities represents this situation. {45x+120y≤9602x+4y≤40 What does the solution (16, 2) represent?
At Lara' party, 4 gallon of fruit punch are hared equally among 18 friend. How much fruit punch will each peron get?
Answer: About 0.2 gallons
Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.
Each of her friend will get 4 and a half gallons of juice.
What is division?Division is one of the four main arithmetical operations by which we find the equal distribution of something.
Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.
To find how much each of them got, we will divide total amount of punch by total number friends
Amount of juice each of them gets, = 18/4 = 4.5
Hence, Each of her friend will get 4 and a half gallons of juice.
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[tex]evaluate 2^{-1}(\alpha +\beta)^{2} if \alpha and \beta are the roots of the quadratic equaton x^{2}-4x+1=0[/tex]
The value of α + β is 4. Then the value of the expression 2⁻¹ x (α + β)² will be 8.
What are the sum and product of the roots?Let the equation be ax² + bx + c = 0 and the roots are α and β.
Then the sum of the roots will be
α + β = - b / a
And the product of the roots will be
α · β = c / a
The quadratic equation is given below.
x² - 4x + 1 = 0
The sum of the roots of the equation is given as,
α + β = - (-4) / 1
α + β = 4
Then the value of the expression will be given as,
⇒ 2⁻¹ x (α + β)²
⇒ 2⁻¹ x (4)²
⇒ 16 / 2
⇒ 8
The value of the expression 2⁻¹ x (α + β)² will be 8.
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what is the probability of having at least 2 collisions within the next 3 insertions using linear probing
The probability is that this is least 2 collisions within the next 3 insertions using linear probing is 0.7.
Required probability
= 1 - (There isn't anyt any collision in subsequent 2 insertions)Now, for no collisions :The 1st insertion have to hash to one of the final empty 6/10 cells.The second new release have to then hash to one of the final empty 5/10 cells.Thus, the desired probability= 1-610*510= 13010070100= 0.7Read more about probability;
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Resolver:
|3x − 4| = 9 - 5x
—
Answer:
Step-by-step explanation:
suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. how large of a survey would you recommend? a survey should include at least
If we want the margin of error for the 90% confidence level to be about 1.5%, then a sample of 3002 is recommended.
In this problem, we want to find n for which the margin of error for the 90% confidence level to be about 1.5%
From part (a), the 90% confidence interval is (0.435, 0.525)
the margin of error M = 0.015
0.015 = 1.645√(0.48 * 0.52)/n
(√n) ² = (0.015)²
n = 3001.9
n ≈ 3002
Therefore, a sample of 3002 is recommended.
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The complete question is:
Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot a ord it. (a) Calculate a 90% con dence interval for the proportion of Americans who decide to not go to college because they cannot a ord it, and interpret the interval in context. (b) Suppose we wanted the margin of error for the 90% con dence level to be about 1.5%. How large of a survey would you recommend?
The tens digit of a certain two-digit number is 1/3 of the units digit. When the digits
are reversed, the new number exceeds twice the original number by 2 more than the
sum of the digits. Find the original number
Answer:
Step-by-step explanation
The tens digit of a certain two-digit number is 1/3 of the units digit. When the digits are reversed, the new number exceeds twice the original number by 2 more than the sum of the digits. Find the original number.
Angie borrowed 20 dollars from victor. She already paid him back d of the dollars. Choose the expression that shows how many dollars Angie still owes victor
The expression that shows that Angie still owes victor is 20-d.
What is meant by an expression?In algebra, an expression can be used to represent a value that may or may not be dependent on the values given to the variables that appear in the expression. The semantics associated with the expression's symbols are used to determine its value. The expression's context affects the semantic choice. Depending on the presumed order of operations by the context.
When an expression involves division by 0, for example, the semantic rules may state that it does not indicate any value; yet, despite having an undefined value, these expressions are still well-formed. Expressions generally have a wide range of meanings.
Given,
The number of dollars borrowed by Angie from victor is 20 dollars
And also given that Angie paid d dollars back to victor.
The expression that shows that Angie still owes victor is 20-d.
Therefore, the expression that shows Angie still owes victor is 20-d.
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Enter the value of x below.
x+6=9
Answer:
x = 3
Step-by-step explanation:
x + 6 = 9
Subtract 6 from both sides :
x = 9 - 6
x = 3
Hope this helped and have a good day
Answer:
x = 3
Step-by-step explanation:
x + 6 = 9 Subtract from both sides of the equation
x + 6 - 6 += 9 - 6
x = 3
Check:
x + 6 = 9
3 + 6 = 9
9 = 9 Checks