Tickets for the movies are $7 for adults and $4 for children. Fourteen people paid a total of $68 for tickets. How many were adults and how many were children?
how many miles will you go if you ride your bike for t hours at 9 miles per hour?
6. Alice and Alma have to fill a workbook. Alice has already completed 3 pages and can do 7 pages per hour. Alma has completed 11 pages, but can only work at a rate of 3 pages per hour. Eventually Alice will catch up and the two will be working on the same page. How long will that take? How many pages will each of them have finished?
How to find the area under the standard normal curve between z 1.5 and z 2.5?
We have that for the Question, it can be said that the area under the standard normal curve between z 1.5 and z 2.5 is
P(1.5 &2.5) =0.06
From the question we are told
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Generally the equation for the probability is mathematically given as
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
Where
P(Z < 2.5) = 0.99
P(Z < 1.5) = 0.93
From Z Table
Therefore
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
P(1.5 &2.5) =0.06
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^4sqrt6/^5sqrt6 I don't have square root signs
Answer:
6^1/20
Step-by-step explanation:
you multiply the two exponents
Ms. Maple is a teacher whose salary is $22,570 for this school year, which has 185 days. In Ms. Maple’s school district, substitute teachers are paid $80 per day. If Ms. Maple takes a day off without pay and a substitute teacher is paid to teach her classes, how much less does the school district pay in salary by paying a substitute teacher instead of paying Ms. Maple for that day?
Final answer:
The school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple, calculating by comparing Ms. Maple's daily salary to a substitute teacher's daily rate.
Explanation:
To calculate how much less the school district pays by hiring a substitute teacher instead of paying Ms. Maple for a day, we first need to determine Ms. Maple’s daily salary. This is done by dividing her annual salary by the number of working days in the school year.
Ms. Maple’s daily salary = $22,570 / 185 days = $122 per day.Substitute teacher’s daily salary = $80 per day.The difference between what the school district pays Ms. Maple and what it pays a substitute teacher for one day = Ms. Maple’s daily salary - Substitute teacher’s daily salary = $122 - $80 = $42.Therefore, the school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple.
Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually. (Use the tables found in the textbook.)
Using the zero product property to find the solutions to the equation x^2-9=16
Answer:
x=-5, 5
Step-by-step explanation:
To find the solutions, use inverse operations to rearrange the equation to be equal to 0.
[tex]x^2-9-16=16-16\\x^2-25=0[/tex]
Factor the equation and then set each equal to 0 to solve for x.
[tex]x^2-25=0\\(x+5)(x-5)=0[/tex]
x+5=0
x=-5
x-5=0
x=5
Find the slope of the line that passes through (-95, 31) and (-94, 6).
Answer:
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Step-by-step explanation:
The equation of a line has the following format:
[tex]y = ax + b[/tex]
In which a is the slope.
Passes through the point (-95, 31).
When [tex]x = -95, y = 31[/tex]
[tex]y = ax + b[/tex]
[tex]31 = -95a + b[/tex]
Passes through the point (-94, 6).
When [tex]x = -94, y = 6[/tex]
[tex]y = ax + b[/tex]
[tex]6 = -94a + b[/tex]
We have to solve the following system:
[tex]31 = -95a + b[/tex]
[tex]6 = -94a + b[/tex]
We want to find a.
From the first equation
[tex]b = 31 + 95a[/tex]
Replacing in the second equation:
[tex]6 = -94a + 31 + 95a[/tex]
[tex]a = -25[/tex]
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Find the quadratic function whose zeros are 2 and -2 and has maximum value
8 oz of apple juice contains 0.9 milligrams of iron if the RDA for iron is 15 mg what percent of RDA of iron is provided by the apple juice
• Given the function, f(x) = x3 – 5x2 + 9x – 45, determine the number of roots and identify them.
Final answer:
The given function f(x) = x3 – 5x2 + 9x – 45 has rational roots ±1, ±3, ±5, and ±9.
Explanation:
To determine the number of roots and identify them for the function f(x) = x3 – 5x2 + 9x – 45, we can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation, then p must divide the constant term (in this case, 45) and q must divide the leading coefficient (in this case, 1). By trying all possible combinations of p and q, we can find the rational roots of the equation. In this case, the rational roots are ±1, ±3, ±5, and ±9.
The number of real roots is 1, and it is ( x = 5 ).
To determine the number of roots and identify them for the function[tex]\( f(x) = x^3 - 5x^2 + 9x - 45 \)[/tex], we can use various methods such as the Rational Root Theorem, Descartes' Rule of Signs, or graphing techniques. In this case, since the degree of the polynomial is 3, we know that there will be 3 roots in total.
We'll start by checking for rational roots using the Rational Root Theorem. According to this theorem, if a rational root [tex]\( \frac{p}{q} \)[/tex] exists for the polynomial [tex]\( f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 \), then \( p \)[/tex] is a factor of the constant term [tex]\( a_0 \) and \( q \)[/tex] is a factor of the leading coefficient [tex]\( a_n \)[/tex].
The constant term of [tex]\( f(x) \) is \( -45 \)[/tex]and the leading coefficient is ( 1 ). The factors of ( -45 ) are [tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]. The factors of \( 1 \) are \( \pm 1 \)[tex]\( 1 \) are \( \pm 1 \)[/tex].
By trying all possible combinations of these factors, we can find the rational roots of the polynomial. We'll then use synthetic division or polynomial long division to check if these roots are actually roots of the polynomial.
Let's proceed with the calculations:
1. Possible rational roots:
[tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]
2. Testing these roots using synthetic division or polynomial long division:
Testing [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = (1)^3 - 5(1)^2 + 9(1) - 45 = 1 - 5 + 9 - 45 = -40 \][/tex]
Testing [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = (-1)^3 - 5(-1)^2 + 9(-1) - 45 = -1 - 5 - 9 - 45 = -60 \][/tex]
Testing [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = (3)^3 - 5(3)^2 + 9(3) - 45 = 27 - 45 + 27 - 45 = -36 \][/tex]
Testing [tex]\( x = -3 \)[/tex]:
[tex]\[ f(-3) = (-3)^3 - 5(-3)^2 + 9(-3) - 45 = -27 - 45 - 27 - 45 = -144 \][/tex]
Testing ( x = 5 ):
[tex]\[ f(5) = (5)^3 - 5(5)^2 + 9(5) - 45 = 125 - 125 + 45 - 45 = 0 \][/tex]
[tex]\[ \Rightarrow \text{Root: } x = 5 \][/tex]
Testing ( x = -5 ):
[tex]\[ f(-5) = (-5)^3 - 5(-5)^2 + 9(-5) - 45 = -125 - 125 - 45 - 45 = -340 \][/tex]
Testing ( x = 9 ):
[tex]\[ f(9) = (9)^3 - 5(9)^2 + 9(9) - 45 = 729 - 405 + 81 - 45 = 360 \][/tex]
Testing ( x = -9 ):
[tex]\[ f(-9) = (-9)^3 - 5(-9)^2 + 9(-9) - 45 = -729 - 405 - 81 - 45 = -1260 \][/tex]
Testing ( x = 15 ):
[tex]\[ f(15) = (15)^3 - 5(15)^2 + 9(15) - 45 = 3375 - 1125 + 135 - 45 = 2340 \][/tex]
Testing ( x = -15 ):
[tex]\[ f(-15) = (-15)^3 - 5(-15)^2 + 9(-15) - 45 = -3375 - 1125 - 135 - 45 = -4680 \][/tex]
Testing ( x = 45 ):
[tex]\[ f(45) = (45)^3 - 5(45)^2 + 9(45) - 45 = 91125 - 10125 + 405 - 45 = 81060 \][/tex]
Testing ( x = -45 ):
[tex]\[ f(-45) = (-45)^3 - 5(-45)^2 + 9(-45) - 45 = -91125 - 10125 - 405 - 45 = -102705 \][/tex]
From these tests, we see that ( x = 5 ) is a root of the polynomial. The other roots are irrational or complex.
So, the number of real roots is 1, and it is ( x = 5 ).
A company sells brass and steel machine parts.One shipment contains 3 brass and 10 steel parts and costs $48. A second shipment contains 7 brass and 4 steel parts and costs $54. Find the cost of each type of machine part.
A university is trying to determine what price to charge for tickets to football games. At a price of $18 per ticket, attendance averages 40,000 people per game. Every decrease of $3 adds 10,000 people to the average number. Every person at the game spends an average of $4.50 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?
Final answer:
To maximize revenue from football game ticket sales and concessions, we create a revenue function based on ticket price adjustments and evaluate changes in quantity demanded. The optimal price and attendance are found by analyzing the combined revenue function, deriving it with respect to the number of price decreases, and finding the maximum value of this function.
Explanation:
To determine the ticket price that should be charged by the university to maximize revenue from football game attendance, we need to analyze the effect of price changes on the quantity demanded. We can create a revenue function based on the given figures and the assumptions that a decrease of $3 in ticket price increases attendance by 10,000 people, and each person spends an average of $4.50 on concessions.
Let x represent the number of $3 decreases in price from the original $18. The ticket price can then be expressed as P = 18 - 3x, and attendance as A = 40000 + 10000x. The revenue from ticket sales is R1 = P × A, which gives us R1 = (18 - 3x) × (40000 + 10000x). The concession revenue per person is $4.50, so total concession revenue is R2 = 4.50 × A, which gives us R2 = 4.50 × (40000 + 10000x).
To maximize total revenue R = R1 + R2, we need to find the maximum of the function R = (18 - 3x) × (40000 + 10000x) + 4.50 × (40000 + 10000x). To find this, we can use calculus to take the derivative of R with respect to x and find the value of x that makes this derivative zero. This will be the critical point which we can then test to confirm it provides a maximum.
What is the volume of a right circular cylinder with a radius of 3in and a height of 10in
Answer:
282.6 inches cubed
Step-by-step explanation:
The volume of the cylinder with radius 3 in and height 10 in is
[tex]V=\pi (3^2)(10)= \pi (9)(10)= 90\pi = 90(3.14) = 282.6 in^3[/tex]
Answer:
90 in3
Step-by-step explanation:
Which multiplication expression that does not belong based on scaling. Explain.
Choose an expression
6 x 2 1/2
6 x 3 3/5
1/2 x 6
2 2/5 x 6
How can you tell if the rule you have written for a set of points is correct?
For any value of n, list the numbers ln, rn, mn, tn and i in increasing order. (enter your answers as a comma-separated list. enter your answer using the variables rather than numerical values.)
The correct order is [tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex].
To list the values ln, rn, mn, tn and i in increasing order for any value of n, we need to understand the relationship between these variables.
The variables ln, rn, mn, and tn likely represent different measures, such as left endpoint, right endpoint, midpoint, and trapezoid point in numerical methods, while i often represents the imaginary unit iota in mathematics.
Commonly, if we assume these have increasing values when ordered, they would be listed as:
[tex]l_n[/tex][tex]m_n[/tex][tex]t_n[/tex][tex]r_n[/tex]iTherefore, the values in increasing order are:
[tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex]
NEED HELP ASAP What is the simplified form of the following expression? 4 sqrt 3/2x Assume x>0
Answer:
[tex]\frac{4\sqrt{6x}}{2x}[/tex]
Explanation:
The problem we are given is
[tex]4\sqrt{\frac{3}{2x}}[/tex]
We can write the square root of a fraction as a fraction with a separate radical for the numerator and denominator; this gives us
[tex]4\times \frac{\sqrt{3}}{\sqrt{2x}}[/tex]
We can write the whole number 4 as the fraction 4/1; this gives us
[tex]\frac{4}{1}\times \frac{\sqrt{3}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}}{\sqrt{2x}}[/tex]
We now need to "rationalize the denominator." This means we need to cancel the square root in the denominator. In order to do this, we multiply both numerator and denominator by √(2x); this is because squaring a square root will cancel it:
[tex]\frac{4\sqrt{3}}{\sqrt{2x}}\times \frac{\sqrt{2x}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}\times \sqrt{2x}}{2x}[/tex]
When multiplying radicals, we can extend the radical over both factors:
[tex]\frac{4\sqrt{3} \times \sqrt{2x}}{2x}\\\\=\frac{4\sqrt{3\times 2x}}{2x}\\\\=\frac{4\sqrt{6x}}{2x}[/tex]
Answer:
The correct answer is ^4sqrt24x^3/2x or B on edge.
Step-by-step explanation:
they knew that they could 3 miles in 20 minutes. how far can they ride in 45 minutes?
To find out how far the student can ride in 45 minutes, we calculate the speed of 0.15 miles per minute from the given 3 miles in 20 minutes, then multiply this speed by 45 minutes, resulting in a distance of 6.75 miles.
Explanation:The student has stated that they can travel 3 miles in 20 minutes. To find out how far they can ride in 45 minutes, we need to calculate their riding speed and then apply it to the longer time period.
Step 1: Calculate the riding speed
The speed can be calculated by dividing the distance (3 miles) by the time (20 minutes), which gives us a speed of 0.15 miles per minute.
Step 2: Use the speed to determine the distance in 45 minutes
Now that we know the speed, we can multiply it by the new time period (45 minutes) to find the distance they can ride. That calculation is 0.15 miles/minute × 45 minutes = 6.75 miles.
When we check whether the answer is reasonable, we can notice that 45 minutes is a little more than twice 20 minutes, and since they can ride 3 miles in 20 minutes, it makes sense that they could ride more than twice that distance in 45 minutes, so our answer of 6.75 miles seems reasonable.
They can ride 6.75 miles in 45 minutes.
Explanation:To find how far they can ride in 45 minutes, we can use the concept of average speed.
Given that they can ride 3 miles in 20 minutes, we can calculate their average speed as:
Average Speed = Distance / Time
Average Speed = 3 miles / 20 minutes
Average Speed = 0.15 miles per minute
Now, we can find how far they can ride in 45 minutes:
Distance = Average Speed x Time
Distance = 0.15 miles per minute x 45 minutes
Distance = 6.75 miles
Therefore, they can ride 6.75 miles in 45 minutes.
A polynomial that is written as a product has been ______.
A polynomial that is written as a product has been "factored completely."
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
In the expression Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Since we know that factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
A polynomial which can be written as a product has been "factored completely."
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Mike drew a quadrilateral with four right angles. What shape could be drawn?
Use the diagram of the right triangle above and round your answer to the nearest hundredth. If m
Answer choices:
A) 17.32 m
B) 6.83 m
C) 14 m
D) 9.99 m
Answer:
b. 6.93 m.
Step-by-step explanation:
We have been given triangle ABC and we are asked to find the measure of a.
We will use law of sines to solve our given problem.
[tex]\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are opposite sides of angle A, B and C respectively.
First of all, we will find the measure of angle B using angle sum property.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]30^{\circ}+\angle B+90^{\circ}=180^{\circ}[/tex]
[tex]\angle B+120^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-120^{\circ}[/tex]
[tex]\angle B=60^{\circ}[/tex]
Upon substituting our given values in law of sines we will get,
[tex]\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}[/tex]
[tex]\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}[/tex]
[tex]\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5[/tex]
[tex]a=\frac{12}{\sqrt{3}}[/tex]
[tex]a=6.9282032302755\approx 6.93[/tex]
Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.
Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that the average salary of a group of 16 randomly selected ph.d. students is more than $13,000.
in fifteen minutes greg sailboat went 3/6 miles, gina sailboat went 6/6 miles, and stuart sailboat went 4/6 miles. whose sailboat went the longest distance in fifteen minutes?
A fourth as much as the product of two thirds and 0.8
A fourth as much as the product of two thirds and 0.8 is ²/₁₅
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
First, we will translate this word problem into a mathematical equation.
The product of two thirds and 0.8
[tex]\frac{2}{3} \times 0.8[/tex]
A fourth as much as the product of two thirds and 0.8
[tex]\frac{1}{4} (\frac{2}{3} \times 0.8)[/tex]
[tex]= \frac{1}{4} (\frac{2}{3} \times \frac{4}{5})[/tex]
[tex]= \frac{1}{4} (\frac{2 \times 4}{3 \times 5})[/tex]
[tex]= \frac{1}{4} (\frac{8}{15})[/tex]
[tex]= \frac{1}{4} \times \frac{8}{15}[/tex]
[tex]= \frac{1 \times 8}{4 \times 15}[/tex]
[tex]= \frac{8}{60}[/tex]
[tex]= \frac{8 \div 4}{60 \div 4}[/tex]
[tex]= \boxed {\frac{2}{15}}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
seth made 4 quarts of fruit punch for a birthday party. How many cups of fruit punch did he make
What is f(2) if the linearization of f(x) at a = 2 is l(x) = 12x + 4?
Donte simplified the expression below. mc024-1.jpg What mistake did Donte make? He did not apply the distributive property correctly for 4(1 + 3i). He did not distribute the subtraction sign correctly for 8 – 5i. He added the real number and coefficient of i in 4(1 + 3i). He added the two complex numbers instead of subtracted.
Find the fifth term of A n = 2n