7. All 231 students at DORS went on a field trip. Some students rode in vanswhich hold 7 students each and some students rode in buses which hold 25students each. There was a total of 15 vans and buses that went on the fieldtrip.7a. Write a system of equations to represent this situation.
Answers
Solution:
Given:
\(\begin{gathered} \text{Total students that went for the field trip= 231 students} \\ \text{Vans can hold 7 stduents each} \\ \text{Buses can hold 25 students each} \\ \text{Total buses and vans =15} \end{gathered}\)Question 7a:
Let
\(\begin{gathered} v\text{ represent vans} \\ b\text{ represent buses} \end{gathered}\)The following equations can be deduced from the question;
\(\begin{gathered} \text{Total students that the total number of vans can hold is;} \\ 7\times v=7v \\ \\ \text{Total students that the total number of buses can hold is;} \\ 25\times b=25b \\ \\ \text{Total students on the trip is 231, hence,} \\ 7v+25b=231\ldots\ldots\ldots\ldots\ldots.(1) \\ \\ \\ \text{Also,} \\ \text{Total vans and buses is 15. This means;} \\ v+b=15\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}\)Therefore, the system of equations to represent this situation is;
\(\begin{gathered} 7v+25b=231 \\ v+b=15 \end{gathered}\)Ha
Question 7b.
Solving equations (1) and (2) simultaneously,
\(\begin{gathered} 7v+25b=231\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ v+b=15\ldots\ldots\ldots\ldots\ldots\text{.}(2)\times7 \\ 7v+7b=105\ldots\ldots\ldots\ldots(3) \\ \\ \text{Subtracting equation (3) from (1),} \\ equation(1)-equation(3); \\ 7v-7v+25b-7b=231-105 \\ 18b=126 \\ \text{Dividing both sides by 18 to get b,} \\ b=\frac{126}{18} \\ b=7 \\ \\ \\ To\text{ get v, substitute b in euqation (2)} \\ v+b=15 \\ v+7=15 \\ v=15-7 \\ v=8 \\ \\ \\ \text{Hence, } \\ 7\text{buses and 8 vans went on the field trip} \end{gathered}\)Therefore, DORS needs 7 buses for the field trip.
Related Questions
Bandhan Bank employee salary after 10 years
Answers
Answer:
- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries
A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answers
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
\(f(x) = \lambda e^{-\lambda x}\)
And the cumulative distribution function (CDF) is,
\(CDF = 1 - e^{-\lambda x}\)
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
A line segment has end points at (3, -5) and (4, 1) What is its length?
a. 9 units
b. 6.9 units
c. 9.2 units
d. 5 units
need an explanation if possible please.
Answers
Answer:
6.08units
Step-by-step explanation:
The distance between two points of a line is expressed as;
D = √(y2-y1)²+(x2-x1)²
Given the coordinates (3, -5) and (4, 1);
D = √(1+5)²+(4-3)²
D = √(6)²+(1)²
D = √36+1
D = √37
D = 6.08 units
Hence its length is 6.08units
Answer the questions below.
(a) The perimeter of a rectangular field is 276 m.
If the length of the field is 75 m, what is its width?
Width of the field: /m
Answers
Answer:
63 m
Step-by-step explanation:
Perimeter is 276, 2L + 2W = 276, so L + W = 138
L = 75
138 - 75 = W
63 m
What is another way to write the compound inequality y + 3 ≥ 2 and y + 3 ≤ 6 ?
Answers
Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer
How to write a compound inequality in another way?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Given: y + 3 ≥ 2 and y + 3 < 6
To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:
y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:
2 ≤ y+3 and y + 3 < 6
Combine the two:
2 ≤ y+3 < 6
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Compute the following using a calculator.
csc(203∘)
Round your answer to the nearest thousandth, and only include the numerical value in your answer - do not write cscθ= in your response.
Answers
Using a calculator, the value of csc (203°) is -1.086
How to compute csc (203°) using a calculator?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Since csc (203°) = 1/[sin (203°)]
Press 1/ [sin (203°)] and then the equal to button on your calculator. We have:
1/[sin (203°)] = -1.086
Note: If you calculator have "cosec" or "csc" button, you can simply press cosec (203°) or csc (203°) to get the answer.
Thus, the value of csc (203°) is -1.086
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The model below represents the equation 3x+2=2x-5,
Х
х
x
TAN
х
What is the value of x?
07
0 -7
O 3
O2
Answers
Step-by-step explanation:
Hey there!
The equation is;
\(3x + 2 = 2x - 5\)
Shifting "2x" to left side and "2" to right side.
\(3x - 2x = - 5 - 2\)
Simplify them to get answer.
\(x = - 7\)
Therefore the value of x is -7.
Check;
3 × -7 + 2 = 2 × -7 -5
-19 = -19 ( True ).
So, your answer is option B.
Hope it helps..
This is the question that im stuck on
Answers
If a graph has 20 vertices with odd degree (valence), what is the smallest number of edges that would need be duplicated to eulerize the graph?
Answers
The smallest number of edges that would need be duplicated to eulerize the graph is 10.
Given that a graph has 20 vertices.
In order for a graph to be eulerized, it has to added an edge to each vertex having odd valence.
Here total number of vertices = 20
So, the smallest number of edges that would need be duplicated to eulerize the graph is half of the total number of vertices.
Number of edges = 20/2 = 10
Hence it is needed 10 edges to eulerize the graph.
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What is the volume of the shape below
Answers
The volume of the given figure is 1176 cubic cm.
The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).
The volume of the figure is calculated as,
Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )
Volume = 1176 Cubic cm
Hence, the volume of the figure will be equal to 1176 Cubic cm.
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Help llllllllllliiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Answers
Answer:
Help with what? I do not see your question But it says there's something attached
Step-by-step explanation:
A convex polyhedron has 18 edges and 4 more vertices than faces. How many faces does the polyhedron have?
Euler’s formula: V + F = E + 2
8
12
14
16
Answers
Answer:
8 faces
Step-by-step explanation:
F = # faces
4 + F + F = 18 + 2
2F + 4 = 20
2F = 16
F = 8
Answer:
8
Step-by-step explanation:
got it right on test
Please help me with this problem, I've been trying for more than twenty minutes. pls help.
Answers
Answer:
The inequality has two prime solutions. To determine the number of prime solutions that the inequality has, we need to first solve the inequality to find its solutions. Since the inequality involves a polynomial, we can use the techniques of algebraic manipulation and factoring to solve it.
We begin by multiplying out the left-hand side of the inequality to obtain:
(n²-17)(n²-100)≤0
This expression can be further simplified by multiplying out the terms in the brackets, which gives us:
n⁴ - 117n² + 1700 ≤ 0
To solve this inequality, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting the expression equal to zero and then factoring it to obtain:
n⁴ - 117n² + 1700 = 0
n² (n² - 117) + 1700 = 0
(n² - 19)(n² - 90) + 1700 = 0
(n² - 19)(n² - 90) = -1700
To find the solutions of this equation, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting each factor equal to zero and solving for n:
n² - 19 = 0 or n² - 90 = 0
n² = 19 or n² = 90
n = ±√19 or n = ±√90
Since the problem states that n is a prime number, we need to consider only the solutions where n is a prime number. Of the solutions above, only n = ±√19 and n = ±√90 are prime numbers, so these are the only solutions that we need to consider. Since there are two such solutions, the inequality has two prime
Finding the derivative of a function at a point x gives
A.) The slope of the secant line of the function at x
B.) A line parallel to the function
C.) The slope of the tangent line of the function at x
D.)None of the above
Answers
Answer:
C.)
Step-by-step explanation:
that is exactly the definition of the derivative.
the derivative is the limit of
(f(x+h) - f(x))/((x+h) - x) = (f(x+h) - f(x))/h
with h going to 0.
this is the limit of the standard rate of change concentrated on a single point = the slope of the tangent at that point.
can somebody please help me with my language arts please?
Answers
Answer: alright
Step-by-step explanation:
Two of the statements are true; one is a lie.
Select the one that is a lie.
Then explain your reasoning.
∠GAF ≌ ∠TAE.
∠TAE and ∠FAH are complementary.
∠TAF is obtuse.
Answers
Answer: Choice A
angle GAF = angle TAE is the lie (aka false statement)
========================================================
Explanation:
Let's go through each answer choice to see which is true or which is false.
-----------------------------
Choice A
The markers for angles GAF and TAE are different. Both would need to have a single angle marker, or a double angle marker. The differing markers indicates the angles aren't the same.
Also, note that angle TAG isn't a 180 degree angle, or that point G isn't on line TA. We need this to be the the case, so that two vertical angles form. However, such a thing doesn't happen.
So that's why angles TAE and GAF aren't the same measure.
Choice A is the answer. You can stop here if you wanted.
-------------------------------
Choice B
Let
x = measure of angle TAE
y = measure of angle TAH
z = measure of angle HAF
We can see that x+y+z = 180, since angle EAF is a straight angle. The diagram gives y = 90 and z = 50, so,
x+y+z = 180
x+90+50 = 180
x+140 = 180
x = 180-140
x = 40
Angle TAE is 40 degrees. It adds with angle FAH to get 40+50 = 90, showing that the two angles are indeed complementary.
Choice B is a true statement, so we can rule it out.
-------------------------------
Choice C
Angle TAF is composed of angles TAH and HAF
Adding the two angles gets us 90+50 = 140, which is larger than 90.
Therefore angle TAF is obtuse.
Choice C is a true statement, and it can be ruled out as well.
Technically you could have stopped at choice A once you found the lie, but I figured to show why choices B and C could be ruled out.
Please help me with this homework
Answers
Answer:
4, 2, 0, -2
Step-by-step explanation:
just plug the x value into y=-2x
Entering 38.00 into the Price of Sneakers field Entering 6.00 into the Price field Entering 3.00 into the Price of Leather field True or False: You will no
Answers
Answer:
This question seems incorrect.
Kindly take a look again and re-state it properly to enable me give the most accurate answer.
Thank you
The American Population is living longer. Along with the longevity of life comes additional challenges with both medical and Psychiatric problems. Your patient is about to be discharged from a short-tern rehab center. You overhear the daughter confiding in the nursing student that she cannot handle her mother and will be looking for a Memory care unit to put her mother in. You also hear the student nurse who was raised in a foreign country state, " I would NEVER put my mother in a home. I would take care of her woth my two sisters junti she dies.
what considerations might you make withthis students. Address the cultural differneces in elder care and adress the conself od "Role Strain" in caring for special populations.
Answers
Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.
What is the cultural Strain?Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.
Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.
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I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.4 years with a standard deviation of 0.8 years. Step 1 of 2: If a sampling distribution is created using samples of the ages at which 38 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
According to the Central Limit Theorem, the sampling distribution of sample means would have a mean of 5.4 years.
Step-by-step explanation:
For a normally distributed random variable X, with mean and standard deviation, the sampling distribution of sample means with size n can be approximated to a normal distribution with mean and standard deviation.
As long as n is at least 30, the Central Limit Theorem can also be applied to skewed variables.
We have the following problem:
5.4 years is the average age for the entire population.Based on the Central Limit Theorem, 5.4 years would be the mean of the sampling distribution of sample means.Answer:
Step-by-step explanation:
The mean of the sampling distribution of sample means can be calculated using the formula:
μM = μ
where μ is the population mean and M is the sample mean.
Thus, μM = μ = 5.4 years.
Therefore, the mean of the sampling distribution of sample means would also be 5.4 years.
pls help I will fail 10th grade
Answers
Answer:
B) -6
Step-by-step explanation:
Placing a minus sign outside absolute value bars gives you a negative result For example, –|6| = –6, and –|–6| = –6.
Caroline packs 12 jars of jam in a box . She has 50 boxes. She has 665 jars of jam. How many jars of jam will she have left when all the boxes are full?
Answers
Answer:
62 is the answer
Step-by-step explanation:
Hope that helps!
Parallelogram HIJK with vertices H(-1,3),I(-1,-1),J(2,-2),and K(2,2) over the y-axis.
Answers
The coordinates of the image of the reflection of the parallelogram, HIJK, over the y-axis are;
H'(1, 3), I'(1, - 1), J'( -2, -2), K'( -2, 2)
How can the resulting image of a reflection transformation be found?The reflection of a pre-image, (x, y), over the y-axis gives an image at the point (-x, y), on the coordinate plane.
The given vertices of the parallelogram HIJK are;
H(-1, 3), I(-1, -1), J(2, -2), and K(2, 2)
The coordinates of the image are therefore;
\(H(-1, 3) \: \underrightarrow{ R_{ y-axis}} \: H ' (1, 3)\)
\( I (-1, - 1) \: \underrightarrow{ R_{ y-axis}} \: I ' (1, - 1)\)
\( J (2, -2) \: \underrightarrow{ R_{ y-axis}} \: J'( -2, -2)\)
\( K (2, 2) \: \underrightarrow{ R_{ y-axis}} \: K'( -2, 2)\)
The coordinates of the image, H'I'J'K' are therefore;
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On the basis of a survey of 25 random typists, a confidence interval for the mean time needed to complete typing a page was (5.588; 6.412). Knowing that the distribution of the time needed to type a page is normal, and the sample standard deviation was equal to 1, determine the confidence level used for the calculations
Answers
Answer:
95%
Step-by-step explanation:
Confidence interval:
Mean (m) ± Tcrit * s/sqrt (n)
s = standard deviation = 1
Lower boundary = m - Tcrit * s/sqrt (n) - - - (1)
Upper boundary = m + Tcrit * s/sqrt (n) - - - (2)
m - Tcrit * s/sqrt (n) = 5.588 - - - (1)
m + Tcrit * s/sqrt (n) = 6.412 - - (2)
Subtracting (1) and (2)
-2Tcrit * s/sqrt (n) = - 0.824
Tcrit = [0.824 * sqrt(n)] / 2 * s
Recall:
s = 1
[0.824 * sqrt(n)] / 2 * 1
Sample size = n = 25
[0.824 * sqrt(25)] / 2
[0.824 * 5] ÷ 2
Tcrit = 2.06
Hence, we use the t table to obtain the significance level which gives a t value of 2.06 at (n-1) = (25 - 1) = 24 degrees of freedom.
Significance level α = 0.05
(1 - 0.05) * 100%
0.95 * 100% = 95%
Question 1
Is V8 a rational or irrational number?
A
irrational, because its decimal expansion does not repeat
B
rational because all radicals are rational
D
rational because its decimal expansion eventually repeats
D
irrational, because all radicals are ichtional
©2021 Illuminate Education TM, Inc.
Answers
9514 1404 393
Answer:
A irrational, because its decimal expansion does not repeat
Step-by-step explanation:
8 is not a perfect square integer. The closest ones are 2² = 4 ad 3² = 9. The square root of an integer that is not a perfect square is irrational. That is, the decimal expansion does not end and does not repeat.
√8 is irrational
Which value for k makes the equation 42 ÷ k = 14 true? Select all that apply. A. 588 B. 62 C. 1452 D. 3 E. 23
Answers
3 is the value of k in the Linear equation .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
equation 42 ÷ k = 14
42/k = 14
42 = 14 * k
k = 42/14
k = 3
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Solve the following algebraic expression.
\(\text {2a + 3b + 10r + 4r =}\)
Please help me out.
Answers
Answer:
2a + 3b + 14r
Please give me brainliest
thanks
7th grade math help me please :).
Answers
Answer:
a
Step-by-step explanation:
divide each price by the number of juice packs they got, then subtract the smaller number from the larger one. you get 0.15
Twenty four blood samples were selected by taking every seventh blood sample from racks holding 199 blood samples from the morning draw at a medical center ANSWER BOTH A AND B
Answers
a. FPCF for this sample is FPCF = √(199/24) = 2.89.
b. The population cannot be considered effectively infinite, so the answer is no.
What is FPCF?When the sample size is significant compared to the size of the community, the Finite Population Correction Factor, also known as the FPC factor, is applied. The population in most cases is so vast that typical sample sizes are insufficient to raise concerns about the need for the FPC.
The recommendation is to use the FPC when the sample size to population size ratio is higher than 5%. The FPCF must be used, for instance, if the population number is 300 and the sample size is 30, which results in a ratio of 10%.
a. To calculate the FPCF (finite population correction factor) for this sample, we can use the formula:
FPCF = √(N/n)
where N is the population size, and n is the sample size.
In this case, N = 199 (the number of blood samples in the racks), and n = 24 (the number of samples selected every seventh blood sample).
FPCF = √(199/24) = 2.89 (rounded to two decimal places)
b. To determine whether the population should be considered effectively infinite, we need to compare the sample size to the population size. A general rule of thumb is that the population can be considered effectively infinite if the sample size is less than 5-10% of the population size.
In this case, the sample size is 24, which is approximately 12% of the population size of 199. Therefore, the population cannot be considered effectively infinite, and the FPCF should be applied to adjust for the finite population size.
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