A car dealership needs to transport 4,200 cars to an island. If the ferry can hold 60 cars, how many trips will the ferry need to make?
Answer:
700 cars
Step-by-step explanation:
just divide 4200 by 60 to get 700
Answer: 70
Step-by-step explanation:
If you divide 4,200 by 60 you will get 70 and that is how many trips you would need to make.
I need help solving this practiceThe answer options for the three boxes are located at the bottom of the picture One answer option per box
To answer this question we will use the following trigonometric identity:
\(\sin^2\theta+\cos^2\theta=1.\)Solving the first equation for cosθ we get:
\(\begin{gathered} x-2=4\cos\theta+2-2, \\ x-2=4\cos\theta, \\ \frac{x-2}{4}=\frac{4\cos\theta}{4}, \\ \frac{x-2}{4}=\cos\theta. \end{gathered}\)Solving the second equation for sinθ we get:
\(\begin{gathered} y+5=2\sin\theta-5+5, \\ y+5=2\sin\theta, \\ \frac{y+5}{2}=\frac{2\sin\theta}{2} \\ \frac{y+5}{2}=\sin\theta. \end{gathered}\)Substituting
\(\cos\theta=\frac{x-2}{4}\text{ and }\sin\theta=\frac{y+5}{2}\)in the trigonometric identity we get:
\((\frac{x-2}{4})^2+(\frac{y+5}{2})^2=1.\)Simplifying the above result we get:
\(\frac{(x-2)^2}{16}+\frac{(y+5)^2}{4}=1\)Finally, recall that:
\(-1\leq\cos\theta\le1.\)Therefore:
\(\begin{gathered} -4+2\leq4\cos\theta+2\leq4+2, \\ -2\leq4\cos\theta+2\leq6. \end{gathered}\)Therefore x is on the interval:
\([-2,6].\)Answer:
\(\frac{(x-2)^2}{16}+\frac{(y+5)^2}{4}=1\)where x is on the interval
\([-2,6].\)
a ton of recycled paper will save 17 trees. if one bag weighs 2 oz, how many bags are needed to save 68 trees?
Answer:8
Step-by-step explanation:divide 136 with 17 to see how many tons needed
The number of messages that arrive at a Web site is a Poisson distributed random variable with a mean of 5 messages per hour. Round your answers to four decimal places.(a) What is the probability that 5 messages are received in 1 hour?(b) What is the probability that 10 messages are received in 1.5 hours?(c) What is the probability that less than 2 messages are received in 1/2 hour?
The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873
Let X shows the number of messages received per hour. The pdf of X is
\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)
Therefore, the probability that 5 messages are received in a single hour is
\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)
(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is
\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)
(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is
\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)
Learn more about probability
brainly.com/question/30034780
#SPJ4
of a vertain high school graduating class, 75 percent of the students continued their formal education, and 80 percent of those who contined their formal education in the class went four year collages. if 300 students in the class went to four year colleges, how many students were in the graduating class
Answer:
Step-by-step explanation:
The isosceles triangle has a perimeter of 7.5 m.
Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
2 x minus 2.1 equals 7.5
4.2 plus y equals 7.5
y minus 4.2 equals 7.5
2.1 plus 2 x equals 7.5
Olivia picked 482 apples from the orchard’s largest apple tree. She divided
the apples evenly into 4 baskets. How many apples are in each basket? How
many are left over? pls make the solution detailed! :)
There are 120 apples in each basket and 2 leftovers
How to determine the number of apples in each basket?From the question, the given parameters are:
Number of apples = 482
Number of baskets = 4
the number of apples in each basket is calculated as
Apples in each basket = Number of apples/Number of baskets
Substitute the known values in the above equation
So, we have the following equation
Apples in each basket = 482/4
Evaluate
Apples in each basket = 120.5
Remove the decimal
Apples in each basket = 120
The number of leftoverIn (a), we have
Apples in each basket = 120.5
The decimal part is
Decimal = 0.5
The number of leftover is then calculated as
Leftover = Decimal * Baskets
So, we have
Leftover = 0.5 * 4
Evaluate
Leftover = 2
Hence, there are 2 leftovers
Read more about quotients at
https://brainly.com/question/629998
#SPJ1
What is quotient rule with example?
The quotient rule states that the derivative of a quotient of two functions is equal to the derivative of the numerator divided by the denominator minus the numerator multiplied by the derivative of the denominator divided by the denominator squared.
The quotient rule, also known as the "rule of quotients", is a fundamental concept in calculus that allows us to differentiate functions that are the ratio of two other functions. It states that if we have two functions, f(x) and g(x), then the derivative of their quotient, f(x)/g(x), can be found using the formula:
(d/dx)(f(x)/g(x)) = (g(x) * df/dx - f(x) * dg/dx) / g(x)^2
In other words, the derivative of the quotient of two functions is equal to the derivative of the numerator divided by the denominator minus the numerator multiplied by the derivative of the denominator divided by the denominator squared.
For example, consider the function h(x) = sin(x) / x. To find the derivative of h(x), we can use the quotient rule:
(d/dx)h(x) = (x * cos(x) - sin(x)) / x^2.
The quotient rule is a fundamental tool in calculus and is used in many real-world applications, including optimization, control theory, and the analysis of physical phenomena.
To know more about derivative on the link below:
https://brainly.com/question/25324584#
#SPJ11
solve pls brainliest
Answer:
2/5 > 1/4
Step-by-step explanation:
First convert the denominators to the LCM which will be 20
2/5 will convert to 8/20 because 5 x 4 = 20 so 2 x 4 = 8 and 1/4 will convert to 5/20 because 4 x 5 = 20 so 1 x 5 = 5
1.Suppose a chef ices and decorates cupcakes in batches of 100. Each batch requires 40 minutes to setup the equipment, and each cupcake in the batch takes 1.25 minutes to process. Each unit in the batch must wait for the entire batch to be processed before moving on to packaging. What is the throughput capacity (in cupcakes and/or minutes) of the icing stage? Pick the closest answer.
.6
.8
1
1.25
1.65
2
2. Refer to the previous question. What is the throughput time for a batch of cookies, in minutes? Pick the closest answer.
1.25
2.5
40
125
140
The closest answer is 80 cupcakes per minute, so the correct option is .8. The closest answer is 165 minutes, so the correct option is 165.
The throughput capacity of the icing stage can be calculated by dividing the number of cupcakes in a batch (100) by the time required to process each cupcake (1.25 minutes).
Throughput capacity = Number of cupcakes in a batch / Time to process each cupcake
Throughput capacity = 100 cupcakes / 1.25 minutes
Throughput capacity = 80 cupcakes per minute
The closest answer is 80 cupcakes per minute, so the correct option is .8.
The throughput time for a batch of cupcakes is the time required to process the entire batch, including the setup time.
Throughput time = Time for setup + (Number of cupcakes in a batch * Time to process each cupcake)
Throughput time = 40 minutes + (100 cupcakes * 1.25 minutes per cupcake)
Throughput time = 40 minutes + 125 minutes
Throughput time = 165 minutes
The closest answer is 165 minutes, so the correct option is 165.
Learn more about cupcakes from
https://brainly.com/question/1955459
#SPJ11
can someone PLEASE help me with this!?! its due tonight
explaining your answer = brainliest
what is the perimeter of the square?
Answer:
24
Step-by-step explanation:
6*4
What is the value of a in the equation 3 a+b = 54, when b = 9?
15
18
21
27
can someone help me with this?
Answer:
15
Step-by-step explanation:
3a+b=54
3a+9=54
54-9=45
45 ÷ 3= 15
3 × 15 - 9=54
45 + 9=54
3
Select the correct answer from the drop-down menu.
Consider this system of linear equations:
y- x = -13
-4x + 3y = -51
The solution of the system of equations is
Reset
Next
Answer:
x = 12, y = 1
Step-by-step explanation:
y - x = -13
-4x + 3y = -51
Find y.
y = -13 + x
Plug y into 2nd equation
-4x + 3y = -51
-4x + 3(-13 + x) = -51
-4x + -39 + 3x = -51
-x = -12
x = 12
y = -13 + 12
y = -1
Solve sin(5x)cos(10x)−cos(5x)sin(10x)=−0.25 for the smallest positive solution. x= Give your answer accurate to two decimal places.
The smallest positive solution to the equation is \(x \approx 0.05\) (rounded to two decimal places).
To solve the equation \(\sin(5x)\cos(10x) - \cos(5x)\sin(10x) = -0.25\) for the smallest positive solution, we can use trigonometric identities to simplify the equation and then solve for \(x\).
Using the identity \(\sin(A - B) = \sin A \cos B - \cos A \sin B\), we can rewrite the equation as follows:
\(\sin(5x - 10x) = -0.25\)
Simplifying the angle, we have:
\(\sin(-5x) = -0.25\)
Since \(\sin(-\theta) = -\sin(\theta)\), we can rewrite the equation as:
\(-\sin(5x) = -0.25\)
Dividing both sides by -1, we get:
\(\sin(5x) = 0.25\)
To find the smallest positive solution, we can use the inverse sine function (also known as arcsine or sin^(-1)). Applying the inverse sine to both sides, we have:
\(5x = \sin^(-1)(0.25)\)
Using a calculator, we find that \(\sin^(-1)(0.25) \approx 0.2527\) (rounded to four decimal places).
Dividing both sides by 5, we obtain:
\(x = \frac{0.2527}{5}\)
Calculating the result, we find that \(x \approx 0.0505\) (rounded to four decimal places).
Therefore, the smallest positive solution to the equation is \(x \approx 0.05\) (rounded to two decimal places).
Learn more about equation here
https://brainly.com/question/17145398
#SPJ11
a worker A finishes a project on his own in 12 days. the worker completes the same work alone in 16 days. the two workers started working together, but after 3 days A leaves and B. continues on his own. How many days will B need to finish the rest of the work?
Answer:
Worker B needs 9 days to finish the rest of the work
Step-by-step explanation:
Proportions
Worker A finishes a project on his own in 12 days and worker B does the same in 16 days.
Worker A does 1/12 of the project in one day and worker B does 1/16 of the project in one day. When working together, they do
\(\frac{1}{12}+\frac{1}{16}=\frac{7}{48}\)
After 3 days they have completed:
\(3*\frac{7}{48}=\frac{7}{16}\)
parts of the project, this means it still remains:
\(1-\frac{7}{16}=\frac{9}{16}\)
parts of the project and it is done by B alone. Since B does \(\frac{1}{16}\) per day, he now takes
\(\displaystyle \frac{\frac{9}{16}}{\frac{1}{16}}=9\)
days to complete the project.
Worker B needs 9 days to finish the rest of the work
Are the two shapes similar?
Answer:
Yes they are same shape but different size
Step-by-step explanation:
if 7(2x-5)-2(2x-5)=4(x+ 5) what is the value of x
1
15/2
65/6
65
Option B is correct -The value of x is 15/2
EquationAn equation is a mathematical statement that is made up of two expressions connected by an equal sign.
the given expression is,
7( 2x - 5) -2(2x - 5) = 4(x + 5)
now ,open all the brackets of the equation,
14x - 35 - 4x + 10 = 4x + 20
now , add all the like terms of this expression,
10x -25 = 4x + 20
arrange all the like terms on one side and rest on the other side,
10x - 4x = 20 +25
6x = 45
x = 45/6
x = 15/2
so, 15/2 is the value of x in this expression.
Learn more about equation here :-
https://brainly.com/question/10413253
#SPJ4
(Pre-cal polynomial functions) When I'm finding the zeros of x^4 + 2x^2 - 3, how do I know when to implement imaginary numbers for the answer? ( +- [root3] vs. +- i[root3] ).
Given:
\(x^4+2x^2-3=0\)We will find the zeros of the function:
Factor the given function:
\(\begin{gathered} (x^2+3)(x^2-1)=0 \\ x^2-1=0\rightarrow x^2=1\rightarrow x=\pm1 \\ x^2+3=0\rightarrow x^2=-3\rightarrow x=\pm i\sqrt[]{3} \end{gathered}\)So, there are four zeros
So, the answer will be:
\(x=\mleft\lbrace-1,1,i\sqrt[]{3},-i\sqrt[]{3}\mright\rbrace\)The quadratic function f(x) has a vertex at (1, 6) and opens downward.
If g(x) = (x - 7)2 + 1, which statement is true?
A.
The axis of symmetry of f(x) is x = 1, and the axis of symmetry of g(x) is x = 7.
B.
The axis of symmetry of f(x) is x = 1, and the axis of symmetry of g(x) is x = -7.
C.
The axis of symmetry of f(x) is x = -1, and the axis of symmetry of g(x) is x = -7.
D.
The axis of symmetry of f(x) is x = -1, and the axis of symmetry of g(x) is x = 7.
The statement A is correct option.
What is the vertex of a quadratic function?The vertex of a quadratic equation is the minimum or maximum point of the equation.
Given that, the quadratic function f(x) has a vertex at (1, 6) and opens downward and g(x) = (x - 7)² + 1,
The vertex of f(x) is at (1, 6), we know that a vertical line passing through the vertex is called the axis of symmetry for the parabola.
That mean, axis of symmetry will pass through (1, 6)
Therefore, the axis of symmetry for f(x) is x = 1
And, g(x) = (x - 7)² + 1
= x²+49-14x+1
= x²-14x+50
Vertex = -b / 2a
here, b = -14 and a = 1
Vertex (h, k) = 14 / 2 = 7
To find k, put x = 7 in the equation,
(7-7)²+1 = 1
Therefore, point of the vertex = (7, 1)
That mean axis of the symmetry will pass through (7, 1)
Therefore, axis of the symmetry for g(x) = 7
Hence, the statement A is correct option.
Learn more about vertex of a quadratic function, click;
https://brainly.com/question/11258039
#SPJ1
What is the area of triangle ABC if a = 7, c = 11, and B = 55°?
Round the answer to the nearest hundredth.
The area of the triangle is 31.54 square units
How to determine the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
We have the following values
a = 7 units
c = 11 units
B = 55 degrees
The area of the triangle is calculated using the following area formula
Area = 1/2absin(C)
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 7 * 11 * sin(55 degrees)
Evaluate
Area = 31.54
Hence, the area is 31.54 square units
Read more about area at
brainly.com/question/25292087
#SPJ1
There are 30 students in a class. 12 of the students are boys. a) Write the amountof boys in the class as a fraction in its simplest form. b) Write the amount of girls in the class as a fraction in its simplest form.
Answer:
a)2/5
b)3/5
Step-by-step explanation:
a) 12 are boys and 30 is the whole class so 12/30=6/15=2/5
b)if 12 are boys then 30-12=18 girls
18/30=3/5
Use the Pythagorean Theorem to find the missing length and then round the
result to the nearest tenth.
a = 8, b = 3, c =
Answer:
~8.5
Step-by-step explanation:
Knowledge Needed
Pythagorean Theorem:
\(a^2+b^2 = c^2\)
Plug in 2 known values to solve.
Question
\(a^2+b^2 = c^2\\(8)^2 + (3)^2 = c^2\)
64 + 9 = c^2
c^2 = 73
Find the square root of both sides.
\(\sqrt{c^2} = \sqrt{73}\)
c = \(\sqrt{73}\)
~8.5
Answer:
c = 8.5
Step-by-step explanation:
The Pythagorean theorem is
\(a^{2} +b^{2} =c^{2}\)
Since we know a and be, we simply square them, then add those values together, and take the square root of the final value
\(8^{2} = 64\)
\(3^{2} = 9\)
\(64 + 9 = 73\)
\(\sqrt{73} = 8.5\)
c = 8.5
Can you help me cause I’ve been struggling
Answer:
-8
Step-by-step explanation:
Hope it helps you.
Can you mark my answer as a Brainliest Please
how many 4 digit numbers have at least 1 even digit
Answer: I hope this is helpful
Step-by-step explanation:
A 4-digit number contains at least one even digit. To find:How many such numbers are there?Solution:Digits are 0,1,2,3,4,5,6,7,8,9.Number of odd digits = 5Number of even digits = 54-digit numbers are from 1000 to 9999.Total number of 4-digit numbers = 9000Possible ways to get odd digits on all the 4 places isIt means 625 numbers are their in which all 4 digits are odd.To find total 4-digit number that contains at least one even digit, subtract the numbers which contains only odd numbers from the total 4-digit numbers.Therefore, total 4-digit number that contains at least one even digit is 8375.
5. A theater wants to take in at least $2000 for the matinee. Children's
tickets cost $5 each and adult tickets cost $10 each. The theater can seat
up to 350 people. Select all the combinations of children and adult tickets
that will make the $2000 goal.
There are several possible answers.
A- (80, 150)
B- (40, 200)
C- (60, 150)
D- (70, 160)
E- (90, 200)
F- (200, 100)
The required number of children and adults for sitting in the theater are 300 and 50 respectively.
Explain linear equation of two variable.A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.
According to question:Let be consider number of children be x and that of adults is y.
We have,
x + y = 350-------(1)
y = 350 - x
And 5x + 10y = 2000------------------(2)
Put value of y in equation (2)
5x + 10( 350 - x) = 2000
5x + 3500 - 10x = 2000
-5x = -1500
x = 300
Then
y = 350 - x = 350 - 300 = 50
Thus, There will be 300 children and 50 adults in the theater .
To know more about equation of two variable visit:
brainly.com/question/29209545
#SPJ1
Select the correct answer from each drop-down menu.
A deli owner has determined that his revenue, y, from selling sandwiches each day is at most -0.05r2 + 6x where x represents the number
of sandwiches he sells. To make a gprofit, his revenue must be greater than his costs, represented by the expression 1.5x + 45.
Write a system of inequalities to represent the values of x and ywhere the deli owner makes a profit. Then complete the statements.
The point (30,90) is
The point (60,160) is
of this system.
of this system.
The system of inequalities is:
y ≤ -0.05*x^2 + 6x
y > 1.5x + 45
(30, 90) is not a solution of that system, while (60, 160) is a solution.
How to get the system of inequalities?
We know that the revenue y is given by:
y ≤ -0.05x^2 + 6x
And we know that the costs are 1.5x + 45, and the revenue must be larger than that, so we also have the inequality:
y > 1.5x + 45
So the system is:
y ≤ -0.05*x^2 + 6x
y > 1.5x + 45
Now, the point (30, 90) means that we need to replace x by 30 and y by 90, replacing that in the second inequality, we will get:
90 > 1.5*30 + 45 = 90
90 > 90
This is false, so the point is not a solution of this inequality, meaning that the point is not a solution of the system.
For the second point we do the same: x= 60, y = 160, replacing that in the second inequality we get:
160 > 1.5*60 + 45 = 135
160 > 135
This is true, now we need to check with the other inequality.
160 ≤ -0.05*60^2 + 6*60 = 180
This is also true.
So the point (60, 160) is a solution to the system.
If you want to learn more about systems of inequalities, you can read:
https://brainly.com/question/9774970
Answer:
30,90= not a solution
60,160= a viable solution
Step-by-step explanation:
On your trip, you are travelling approximately 8,400,000 m. You estimate the cost of your gas as 72 cents per 1 km. The trip costs you $6,405. Is your estimate correct? What is the difference in costs?
The difference in costs is $357.
To determine if estimate of the gas cost is correct?To determine if your estimate of the gas cost is correct, we need to calculate the actual cost of the gas for the trip and compare it with the estimated cost.
Since you traveled 8,400,000 m, which is equivalent to 8,400 km, we can find the actual cost of gas for the trip as follows:
Actual cost = 8,400 km * $0.72/km = $6,048
Now we can compare the estimated cost with the actual cost:
Difference in costs = Actual cost - Estimated cost
Difference in costs = $6,048 - $6,405
Difference in costs = -$357
The negative difference in costs indicates that the estimated cost was higher than the actual cost.
In other words, the actual cost of gas for the trip was less than what was estimated. The difference in costs is $357 less than the estimated cost.
Learn more about difference in costs
brainly.com/question/17196993
#SPJ11
Someone please walk me through how to solve this LOL THANKS
Answer:
ok it would be the answer on the bottom right which is \(x^{4} \sqrt[7]{x^{6} }\)
Step-by-step explanation:
So basically you just divide 34 by 7 to see how many times 7 goes into 34 which is 4 times. 7 times 4 gives you 28 and now you need to find the remainder, which is what's left inside the square root symbol. You put the x to the 4th power outside. So subtract 28 from 34 and that gives you 6 so you're left with x to the power of 6th inside the square root.
Please please please help meee
Calculate the Distance between the ordered pairs (-2, 3) and (4, -7). Use graph paper if necessary.
if firms receive an economic forecast predicting future increases in the growth of real GDP, they are likely to respond by Quizlet
If firms receive an economic forecast predicting future increases in the growth of real GDP, they are likely to respond by adjusting their business strategies and decisions in several ways.
1. Investment: Firms may increase their investment in capital goods and expand their production capacity. The expectation of higher economic growth signals increased demand for goods and services, encouraging firms to invest in new equipment, technology, and infrastructure to meet future demand.
2. Hiring and Expansion: With anticipated economic growth, firms may increase their workforce by hiring more employees. Additionally, they may expand their operations by opening new branches or facilities to take advantage of the expanding market opportunities.
3. Research and Development: Firms may allocate more resources towards research and development activities to innovate and develop new products or services. Anticipated economic growth creates a favourable environment for firms to invest in research and technology-driven initiatives, aiming to gain a competitive edge and capture a larger market share.
4. Marketing and Advertising: Firms may intensify their marketing and advertising efforts to promote their products and services in anticipation of increased consumer demand. This could involve increasing advertising budgets, launching new marketing campaigns, or exploring new market segments.
5. Strategic Planning: Firms may review and adjust their strategic plans, taking into account the forecasted economic growth. They may set higher revenue targets, revise sales forecasts, and reassess their market positioning to align with the expected economic conditions.
Overall, the response of firms to an economic forecast indicating future increases in the growth of real GDP will depend on their specific industry, market conditions, and internal capabilities. However, in general, they are likely to adapt their strategies to capitalize on the projected economic expansion and position themselves for growth.
To learn more about GDP from the given link
https://brainly.com/question/1383956
#SPJ4