Answer: A van can carry 12 students
A bus can carry 57 students
Explanation:
Let x represent the number of students that a van can carry
Let y represent the number of students that a bus can carry.
The senior class at High school A Rented and Filled 6 vans and 7 buses. This means that
the number of senior class students that the van carried is 6 * x = 6x
the number of senior class students that the bus carried is 7 * y = 7y
If both vehicles were filled with 471 students, it means that
6x + 7y = 471 equation 1
High School B rented and Filled 5 vans and 9 buses. This means that
the number of High School B students that the van carried is 5 * x = 5x
the number of High School B students that the bus carried is 9 * y = 9y
If both vehicles were filled with 573 students, it means that
5x + 9y = 573 equation 2
We would solve both equations by applying the method of elimination. To eliminate x, we would multiply equation 1 by 5 and equation 2 by 6. The new equations are
30x + 35y = 2355 equation 3
30x + 54y = 3438 equation 4
Subtracting equation 3 from equation 4, we have
30x - 30x + 54y - 35y = 3438 - 2355
19y = 1083
y = 1083/19
y = 57
Substituting y = 57 into x equation 1, we have
6x + 7 * 57 = 471
6x + 399 = 471
6x = 471 - 399 = 72
x = 72/6
x = 12
Thus,
A van can carry 12 students
A bus can carry 57 students
The taxes on a house assessed at $71,000 are $1775 a year. If the assessment is raised to $114,000 and the tax rate did not change, how much would thetaxes be now?
Solution:
Given:
[tex]\begin{gathered} \text{House assessed at \$71,000} \\ \text{Tax paid in a year = \$1775} \end{gathered}[/tex]The tax rate paid for the year is;
[tex]\begin{gathered} r=\frac{1775}{71000}\times100 \\ r=2.5\text{ \%} \end{gathered}[/tex]If the assessment is now raised to $114,000 and the tax rate did not change, then the tax paid on the house will be;
[tex]\begin{gathered} \text{Tax}=2.5\text{ \% of \$114,000} \\ \text{Tax}=\frac{2.5}{100}\times114000 \\ \text{Tax}=\text{ \$2,850} \end{gathered}[/tex]Therefore, the tax paid on the house with an assessment of $114,000 is $2,850
Identify the local extrema on the graph below. Type your answer as a coordinate (x,y). If there is not a local maximum/minimum then type "none".positive (opening up) absolute value graph with vertex at (1,-3)Local minimum is at the coordinate AnswerLocal maximum is at the coordinate Answer
The graph is given and local minima from the graph is
[tex](1,-3)[/tex]And the local maxima is none.
Seniors at a high school are allowed to go off campus for lunch if they have a grade of A in all their classes or perfect attendance. An assistant principal in charge of academics knows that the probability of a randomly selected senior having A's in all their classes is 0.1. An assistant principal in charge of attendance knows that the probability of a randomly selected senior having perfect attendance is 0.16. The cafeteria staff know that the probability of a randomly selected senior being allowed to go off campus for lunch is 0.18. Use the addition rule of probability to find the probability that a randomly selected senior has all As and perfect attendance.
Given:
Probability a randomly selected senior has A = 0.1
Probability a randomly selected senior has a perfect attendance = 0.16
Probability a randomly selected senior is being allowed to go offf campus: P(A or B) = 0.18
Let's find the probability that a randomly selected senior has all As and a perfect attendance using addition rule for probability.
Apply the formula below:
P(A or B) = P(A) + P(B) - P(A and B)
Rewrite for P(A and B):
P(A and B) = P(A) + P(B) - P(A or B)
P(A and B) = 0.1 + 0.16 - 0.18
Therefore, the probability that a randomly selected senior has all As and perfect attendance is
The minute hand of a clock extends out to the edge of the clock's face, which is a circle of radius 4 inches. What area does the minute hand sweep out between 9:15 and9:35? Round your answer to the nearest hundredth.
To solve the question, we have to make use of the fact that
A minute hand travels 360 degrees in 60 min
From the question given, we are told that the minute hand sweep out between 9:15 and
9:35, thus
There are 20 minutes in between 9:15 and 9:35
Thus
We can get the area using the formula
[tex]\begin{gathered} Area=\frac{\text{minutes turned}}{60}\times\pi r^2 \\ \text{where} \\ r=4\text{ inches} \end{gathered}[/tex]Area will be
[tex]\begin{gathered} \text{Area}=\frac{20}{60}\times\pi\times4^2 \\ \text{Area}=\frac{1}{3}\times\pi\times16 \\ \text{Area}=16.755 \end{gathered}[/tex]Thus, the area will be 16.76 in²
3. Select all the expressions that will have a remainder. 377 644 74 – 3 96 = 5 56 – 2
To obtain the term that will give a remainder, we will have to check if the dividend is a multiple of the divisor
Dividends and divisors are the two key ingredients that yield the quotient. The dividend is the number being divided, while the divisor is the number by which the dividend is divided. In other words, given a÷b, a is the dividend and b is the divisor
Looking at
37 ÷ 3 = (12 remainder 1), 37 is not a multiple of 3, so this will give a remainder of 1
64 ÷ 4 = (16 remainder 0), 64 is a multiple of 4, so this will not give a remainder
74 ÷ 3 = (24 remainder 2), 74 is not a multiple of 3, so this will give a remainder of 2
96 ÷ 5 = (19 remainder 1), 95 is not a multiple of 5, so this will give a remainder of 1
56 ÷ 2 = (28 remainder 0), 56 is a multiple of 2, so this will not give a remainder
Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets.
Estimate the total cost.
What is the exact cost?
If the family pays $25, what is the exact amount of change they should receive?
The exact cost is $23.75 for the show, and the exact change they should get is $1.25.
An adult ticket to the show costs $5.50
A student ticket to the show costs $4.25.
A family buys two adult tickets and three student tickets. This would imply that the total cost of two adult tickets would be
⇒ 2 × 5.5 = $11
It also implies that the total cost of three student tickets is
3 × 4.25 = $12.75
The total cost of two adult tickets and three student tickets is
⇒ 11 + 12.75 = $23.75
If the family pays $25, the exact change they should get is
⇒ 25 - 23.75 = $1.25
Thus, the exact cost is $23.75 for the show, and the exact change they should get is $1.25.
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Hi, can you help me answer this question please, thank you!
The number of sick days an employee takes per year is believed to be about 12.
The mean purpose of null hypothesis is to verify or disprove the proposed statistical assumptions, also is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.
If you wish to test the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the null hypothesis is "the mean number of sick days an employee takes per year is equal to 12 days".
Then, the correct null hypothesis is:
[tex]H_0\colon\mu=12\text{ days}[/tex]The alternative hypothesis is an alternative to the null hypothesis, then if you want to check the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the alternative hypothesis is "mean number of sick days an employee takes per year is not equal to 12 days".
Then, the correct alternative hypothesis is:
[tex]H_a\colon\mu\ne12\text{ days}[/tex]Hey I need help on this math problem ignore the lines across the answer choices it’s a glitch I can’t change it and the lines don’t mean that the answer choice is wrong
Solution:
Given:
Two box plots for city A and city B.
A box plot with its representations is shown:
From the box plot given:
For City A :
[tex]\begin{gathered} City\text{ A:} \\ Q_3=78 \\ Q_1=76 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-76 \\ IQR=2 \end{gathered}[/tex]For City B :
[tex]\begin{gathered} City\text{ B:} \\ Q_3=78 \\ Q_1=68 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-68 \\ IQR=10 \end{gathered}[/tex]From the IQR calculated, the correct answer is:
The interquartile range for city B is greater.
In Millersburg, the use of landlines has been declining at a rate of 10% every year. If there are 42,000 landlines this year, how many will there be in 7 years?If necessary, round your answer to the nearest whole number.
To calculate how many landlines will be used in 7 years you have to apply the exponential decay
[tex]y=a(1-r)^x[/tex]Where
a is the initial value
r is the decay rate (this value is given as a percentage, you have to use it expressed as a decimal)
x is the time interval that has passed
We know that there are 42000 landlines this year
The declining rate is 10% → expressed as a decimal value r=0.1
The time-lapse is 7 years
[tex]\begin{gathered} y=42000(1-0.1)^7 \\ y=20088.47 \end{gathered}[/tex]In 7 years there will be 20088.47 landlines
Refer to the table which summarizes the results of testing for a certain disease. A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative. Round to three decimal places as needed.Positive Test ResultNegative Test ResultSubject has the disease879Subject does not have the disease27312
Answer: 0.021
First, we will find the total number of results by adding up all the subject results in the table:
[tex]87+9+27+312=435[/tex]Now, we know there are 435 total results. We are asked to find the probability that the subject has the disease given that the test result is negative.
Looking at the table, we can see that the number of subjects that has the disease despite having negative results is 9. We will then divide these results by the total number of subject results to find the probability being asked:
[tex]P=\frac{9}{435}=0.020689\approx0.021[/tex]With this, we know that the probability of the subject having the disease given the results is negative is 0.021.
Suppose your bank charges a $7 monthly fee and $0.11 per check. If you write 62 checks in a year, how much money in fees would you expect to pay for the year? Type out acalculations and make sure your final answer is clear.
The cost has a monthly fee and a per check fee.
We can write the bank fee as:
[tex]C(m,c)=7m+0.11c[/tex]m: months, c: number of checks.
If, in a year (m=12 months), you write 62 checks (c=62), the total fee is:
[tex]C(12,62)=7\cdot12+0.11\cdot62=84+6.82=90.82[/tex]You expect to pay a yearly fee of $90.82.
Draw the given angles in standard position. 110 degrees, - 80 degrees
Standard Position of Angles
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.
The ray on the x-axis is called the initial side and the other ray is called the terminal side.
Positive angles are measured counterclockwise, negative angles are measured clockwise.
The angle of 110 degrees is positive so it must be measured counterclockwise. The angle -80 will be drawn clockwise.
The following image shows the required angles:
Johanna just returned from a trip to South Africa. She has 7342 rands, the currency of South Africa. She looks up the exchange rate and finds that 1 South African rand = 0.1125 U.S. dollars. What is the value of her money in U.S. dollars
Johanna has 7,342 Rands.
The exchange rate is 1 Rand = 0.1125
To find the value of the money in US dollars, multiply the amount in Rands by 0.1125
[tex]7,342\times0.1125=\$825.975[/tex]Therefore, the value of the money in US dollars is $825.975
Janelle alternates between running and walking. She begins by walking for a short period, and then runsfor the same amount of time. She takes a break before beginning to walk again. Consider the four graphsbelow. Which graph best represents the given situation?
the answer is letter C
letter C best represents a situation in which Janelle starts walking and then running.
We can know this by the slope of the lines.
Trey has bought 10 pounds of dog food. He feeds his dog2/5pounds for each meal. For how many meals will the food last?Write your answer in simplest form
ANSWER
25 meals
EXPLANATION
Trey has 10 pounds of food to give to his dog. To know for how many meals the food will last we have to divide the total amount of food by the amount of food he gives the dog in each meal,
[tex]10\colon\frac{2}{5}[/tex]To divide this we can use the KCF rule:
• K,eep the first fraction. In this case the first number is a whole number, which we can think of as a fraction with denominator 1.
,• C,hange the division sign into a multiplication sign.
,• F,lip the second fraction.
[tex]10\colon\frac{2}{5}=10\times\frac{5}{2}[/tex]And to multiply we just multiply the numerators and the denominators,
[tex]10\times\frac{5}{2}=\frac{10\times5}{1\times2}=\frac{50}{2}[/tex]To write it in simplest form we have to simplify the fraction. Note that 50 is an even number, so it is divisible by 2. 50 divided by 2 is,
[tex]\frac{50}{2}=25[/tex]Hence, the food will last 25 meals
There are 3 consecutive odd integers that sum to –9. What is the least of these integers?
let the three consecutive numbers are,
a , a+ 1 , a+2
sum of the numbers = -9
a + a +1 + a + 2 = -9
3a + 3 = -9
3a = -9 - 3
3a = -12
a = -12/3
a = -4
so the least number is a = -4
thus the answer is -4.
Nora has a coupon for $3 off of a calzone. She orders a beef and olive calzone, and her bill, with the discounted price is $9.49. What is the regular price of the calzone? Make sure to round your answer to the nearest cent. Do not place a dollar sign as it will not be needed for this question.
Explanation
We are given the following information:
• Nora has a coupon for $3.
,• Nora orders a beef and olive calzone.
,• Her bill after the discount is $9.49
We are required to determine the regular price of the calzone.
If we aren’t including tax and we assume that both beef and calzone are the same price then:
[tex]\begin{gathered} Calzone\text{ }price=\frac{9.49+3}{2}=6.245 \\ Calzone\text{ }price\approx6.25 \end{gathered}[/tex]Hence, the price of the calzone is approximately 6.25
independent vs dependent equation5х – Зу = 10 бу = kx - 42
We will assume that we want to know if the system of equations is independent or dependent:
[tex]\begin{cases}5x-3y=10\text{ (1)} \\ 6y=kx-42\text{ (2)}\end{cases}[/tex]where k is a real number. We will try to find the solutions to the system, and we will try to give values to k for which the system becomes independent or dependent.
We will use substitution, we solve for the variable x on the first equation to obtain:
[tex]\begin{gathered} 5x-3y=10 \\ 5x=10+3y \\ x=\frac{10+3y}{5} \end{gathered}[/tex]And now we replace it onto the second equation:
[tex]\begin{gathered} 6y=k(\frac{10+3y}{5})-42 \\ 6y=\frac{10k+3ky}{5}-42 \\ 6y=\frac{10k+3ky-210}{5} \\ 30y=10k+3ky-210 \\ 30y-3ky=10k-210 \\ y(30-3k)=10k-210 \\ y=\frac{10k-210}{30-3k} \end{gathered}[/tex]And the value of x will be:
[tex]\begin{gathered} x=\frac{10+3(\frac{10k-210}{30-3k})}{5}=\frac{10+\frac{10k-210}{10-k}}{5} \\ =\frac{10(10-k)+10k-210}{5(10-k)} \\ =\frac{100-10k+10k-210}{50-5k} \\ =-\frac{110}{50-5k} \\ =-\frac{22}{10-k} \end{gathered}[/tex]This means that a solution of the system will be:
[tex]\begin{cases}x=-\frac{55}{10-k} \\ y=\frac{10k-210}{30-3k}\end{cases}[/tex]Now, for finding the values which make the system dependent. This happens when the lines have the same slope, this is, when:
[tex]\begin{gathered} \frac{-5}{-3}=\frac{k}{6} \\ \frac{5}{3}=\frac{k}{6} \\ 30=3k \\ 10=k \end{gathered}[/tex]We did the division of the opposite of the coefficient of x, over the coefficient of y. This means that the system will be independent for each value of k different than 10, and will be dependent for k=10.
How many 1 hour days is 240 hours?
Answer:
The answer to your question is,
10 days in 240 hours
I hope this helps :)
Answer:
`10 days are in 240 hours
Step-by-step explanation:
We know 1 day is 24 hours. So if we divide 240 by 24, we get 12.
Use the two-way table on left and right-handed people to create a two-way table that shows the joint and marginal relative frequencies. Drag and drop the numbers to complete the table. Dominant Hand left. right. totalfemale 11. 104. 115Male. 24. 92. 116total. 35. 196. 231 Dominante hand left. rigth. totalfemale maletotalBank:0.0480.1520.1670.3760.3980.4500.4980.5020.5260.84810.104
1st Row (Female)
[tex]\begin{gathered} \frac{11}{231}=0.048 \\ \frac{104}{231}=0.450 \\ \frac{115}{231}=0.498 \end{gathered}[/tex]2nd Row (Male)
[tex]\begin{gathered} \frac{24}{231}=0.104 \\ \frac{92}{231}=0.398 \\ \frac{116}{231}=0.502 \end{gathered}[/tex]Third Row (Total)
[tex]\begin{gathered} \frac{35}{231}=0.156 \\ \frac{196}{231}=0.848 \\ \frac{231}{231}=1 \end{gathered}[/tex]The completed table is given below:
1. A taxi driver records the time required to complete various trips and the distance for each trip. time (minutes) The equation for the line of best fit is y=0.50x + 0.40. Which of the following statements BEST interprets the slope of the line of best file A. For every 0.50 minute increase in time, the distance increases by 1 mile. B. For every 1 minute increase in time, the distance increases by 0.50 miles. C. For every 0.54 ninute increase in time, the distance decreases by 1 mile. . D. For every 1 minute increase in time, the distance decreases by 0.50 miles.
Given
Equation
y = 0.5x + 0.4
Procedure
Slope = 0.5
Intercept = 0.4
B. For every 1 minute increase in time, the distance increases by 0.50 miles.
20. Damilola wrote the equation h = 2d + 1 to represent the height of hisplant, h, after a certain number of days. In this relationship, he identified has the dependent variable, and d as the independent variable. Do youagree? Why or why not?*
As we can see we have the next equation
[tex]h=2d+1[/tex]where h is the dependent variable and d is the independent variable
So we agree, because d does not depend on the height, but the height depends on the days
In order words
An independent variable is a variable that represents a quantity that is modified in an experiment. In this case d
A dependent variable represents a quantity whose value depends on how the independent variable is modified. In this case h
find each unit rate. round to the nearest hundredth if necessary 325 meters in 25 seconds
325 meters in 25 seconds
To find out the unit rate divide the total meters by the total seconds
so
325/25=13 m/sec
therefore
the answer is
13 m/secor 13 m per one secondThe ratio of the number of oranges to the number of apples is 1 : 3.21 oranges were added and the ratio became 4 : 5. How many fruitswere there initially?
Answer
There were 15 oranges initially.
There were 45 apples initially.
Hence, there were (15 + 45) = 60 fruits there initially.
Explanation
Let the number of oranges be x
Let the number of apples be y
The ratio of the number of oranges to the number of apples is 1 : 3 implies:
[tex]\begin{gathered} x\colon y=1\colon3 \\ \frac{x}{y}=\frac{1}{3} \\ \text{Cross multiply} \\ y\times1=x\times3 \\ y=3x----i \end{gathered}[/tex]If 21 oranges were added and the ratio became 4 : 5, this implies:
[tex]\begin{gathered} (x+21)\colon y=4\colon5 \\ \frac{x+21}{y}=\frac{4}{5} \\ \text{Cross multiply} \\ 5(x+21)=4\times y \\ 5x+105=4y----ii \end{gathered}[/tex]To know how many fruits were there initially, solve the system of the equations:
[tex]\begin{gathered} \text{Substitute }y=3x\text{ into }ii \\ 5x+105=4(3x) \\ 5x+105=12x \\ \text{Combine the like terms} \\ 12x-5x=105 \\ 7x=105 \\ \text{Divide both sides by 7} \\ \frac{7x}{7}=\frac{105}{7} \\ x=15 \end{gathered}[/tex]x = 15 implies there were 15 oranges initially.
To get y, substitute x = 15 into equation (i):
[tex]\begin{gathered} y=3x----i \\ y=3\times15 \\ y=45 \end{gathered}[/tex]y = 45 implies there were 45 apples initially.
Hence, there were (15 + 45) = 60 fruits there initially.
Can I Plss get help on this homework number 1
1.
given the equation
[tex]y=0.32x-20.53[/tex]where
x= number of times at bat
y=number of hits
y=? when x=175
then
[tex]y=0.32(175)-20.53[/tex][tex]y=56-20.53[/tex][tex]y=35.49[/tex]then
Correct answer is option A
A player who is at bat 175 times should expect 35 hits
DiaporamGiven the diagram below and the following statements. GliProve that mZHIW90".HEZGIW and ZHW are supplementaryReasonmZGIH+mZHIW-180°ReasonEnter the unknown statements and reasons to complete theflow chart proof. You can click the Organize button at anytime to have the tutor automatically organize the nodes inthe flow chart .StatementSubtraction Property ofConclusion
Step 1
Perpendicular lines are lines that meet at right-angles or 90°
Step 2
First statement: Definition of right angles
Second statement:
Find the area of the triangle below.9.9 m5.6 m4.4 m7.8 m
the Answer
Step by Step Explanation
The area of the triangle formula is
[tex]A=\frac{h_b\cdot b}{2}[/tex]where
[tex]\begin{gathered} h_b=4.4m \\ b=9.9m \end{gathered}[/tex]Subs, the value in above equation
[tex]\begin{gathered} A=\frac{h_b\cdot b}{2} \\ A=\frac{4.4_{}\cdot21.78}{2} \\ A=21.78 \end{gathered}[/tex]The area of the triangle is 21.78 cm^2
Which normal distribution has a wider spread: distribution A with a mean of one and a standard deviation of two, or distribution B with a mean of two and a standard deviation of one?
The normal distribution with mean of one and standard deviation of two has the wider spread.
Normal distribution:
Normal distribution defines a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Given,
Here we have the distributions,
Distribution A with a mean of one and a standard deviation of two, or Distribution B with a mean of two and a standard deviation of one
Now, we have to identify the normal distribution has a wider spread.
Here the normal distribution with a mean of 1 and standard deviation of 2 will be wider than a distribution with a mean of 2 and standard deviation of 2.
Because, the distributions with greater standard deviations indicate greater variability/spread of its variables around the mean.
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -16x2 + 261x + 130
Answer
The highest height attained by the rocket = 1194.4 feet
Explanation
The height of the rocket, y, in feet as a function of the time, x in seconds as
y = -16x² + 261x + 130
We are then asked to find the maximum height reached by the rocket
To do this, we would use the differentiation analysis to obtain the maximum of this function.
At maximum point for any function,
The first derivative = (dy/dx) = 0
The second derivative = (d²y/dx²) < 0
y = -16x² + 261x + 130
First derivative
(dy/dx) = -32x + 261 = 0
32x = 261
Divide both sides by 32
(32x/32) = (261/32)
x = 8.15625 s
We can then substitute this value of x (time) into the equation to get the maximum height (y)
y = -16x² + 261x + 130
At x = 8.15625 s,
y = -16 (8.15625)² + 261 (8.15625) + 130
= -1064.39 + 2128.78 + 130
= 1194.39
= 1194.4 feet to the nearest tenth.
Hope this Helps!!!
the fraction of 1 yard that is 4 inches is?
We need to remember
1 yard= 36 inches
x yard = 4 inches
x is the fraction of the yard that is 4 inches
[tex]x=\frac{4}{36}=\frac{1}{9}[/tex]1/9 of yard is 4 inches