The expression that represents the total cost of the baseball game will be 5t + 2h.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
An expression or formula is a finite collection of signs and is well thus according to context-dependent norms.
A gathering of 5 companions goes to a ball game. Every individual purchases a ticket for the game and 2 hotdogs. Allow t to address the expense of a ticket and h to address the expense of hotdogs.
Then the expression of the total cost is given as,
⇒ 5t + 2h
The expression that represents the total cost of the baseball game will be 5t + 2h.
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Miles earns a 6% commission on each vehicles he sells. Today he sold a truck for 18500 and a car for 9600. What is the total amount of his commision on these vehicles
Answer:
The total amount of commission on these vehicles is 1686.
Step-by-step explanation:
Given:
Miles earns a 6% commission on each vehicles he sells.
Today he sold a truck for 18500 and a car for 9600.
Now, to get the total amount of his commision on these vehicles.
Percent of commission Miles earns on each vehicles he sells = 6%.
He sold a truck for = 18500.
He sold a car for = 9600.
So, the total amount of vehicles:
[tex]18500+9600=28100.[/tex]
Now, to get the total amount of commission on vehicles:
[tex]6\%\ of\ 28100[/tex]
[tex]=\frac{6}{100} \times 28100[/tex]
[tex]=0.06\times 28100[/tex]
[tex]=1686.[/tex]
Therefore, the total amount of commission on these vehicles is 1686.
i require some assistance :(, please help ASAP. Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents. (b^2)^3
Answer:
My guess is 2b^5
Step-by-step explanation:
This question is kinda tricky. LMK if its correct
Below is the table of values of a function. Write the output when the input is n input 1,5,6,n output 4,8,9
Answer:
output = n+3.
Step-by-step explanation:
input : 1 5 6 n
output: 4 8 9 -
Here , 4= 1+3 , 8= 5+3 ,9 = 6+3
So,
output = input +3
When input =n
Then output = n+3.
Find and equation for the line with the given properties. Express the equation in general form. Slope -6/7; containing the point (10,-9) what is the equation for the line?
Answer:
[tex]6x+7y+3=0[/tex]
Step-by-step explanation:
We are asked to find the equation of the line in general form, which has a of -6/7 and containing the point (10,-9).
We know that genera equation of a line is in form [tex]Ax+By+C=0[/tex], where, A, B and C are real numbers.
First of all, we will write our equation in point-slope form as:
[tex]y-y_1=m(x-x_1)[/tex], where,
m = Slope of line,
[tex](x_1,y_1)[/tex] = Given point on line.
[tex]y-(-9)=-\frac{6}{7}(x-10)[/tex]
[tex]y+9=-\frac{6}{7}x+\frac{60}{7}[/tex]
[tex]y*7+9*7=-\frac{6}{7}x*7+\frac{60}{7}*7[/tex]
[tex]7y+63=-6x+60[/tex]
[tex]6x+7y+63-60=-6x+6x+60-60[/tex]
[tex]6x+7y+3=0[/tex]
Therefore, our required equation would be [tex]6x+7y+3=0[/tex].
Which equation does not support the fact that polynomials are closed under multiplication?
−1⋅−1=1
1/x⋅x=1
1⋅x=x
1/3⋅3=1
Answer:
The second choice:
[tex]\large\boxed{\large\boxed{1/x\cdot x=1}}[/tex]
Explanation:
The closure property on an operation means that the operation between two elements of a set produce one element of the same set.
In this case, the operation is multiplication and the set is the polynomials.
Then, the closrue property is that the multiplication of two polynomials will always produce a polynomial.
Since, [tex]1/x[/tex] is not a polynomial, the equation [tex]1/x\cdot x=1[/tex] does not support the fact that polynomials are closed under multiplication.
The quadratic mean of two real numbers x and y equals p (x 2 y 2)/2. By computing the arithmetic and quadratic means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.?
Answer:
The quadratic mean of 2 real positive numbers is greater than or equal to the arithmetic mean.
Step-by-step explanation:
x and y Quadratic Mean Arithmetic mean
3 and 3 3 3
2 and 3 2.55 2.5
3 and 6 4.74 4.5
2 and 5 3.8 3.5
2 and 17 12.1 9.5
18 and 28 23.5 23
10 and 48 34.7 29
The quadratic mean is always greater than the arithmetic mean except when x and y are the same.
When the difference between the pairs is small the difference in the means is also small. As that difference increases the difference in the means also increases.
So we conjecture that the quadratic mean is always greater than or equal to the arithmetic mean.
Proof.
Suppose it is true then:
√(x^2 + y^2) / 2) ≥ (x + y)/2 Squaring both sides:
(x ^2 + y^2) / 2 ≥ (x + y)^2 / 4 Multiply through by 4:
2x^2 +2y^2 ≥ (x + y)^2
2x^2 +2y^2 >= x^2 + 2xy + y^2
x^2 + y^2 >= 2xy.
x^2 - 2xy + y^2 ≥ 0
(x - y)^2 ≥ 0
This is true because the square of any real number is positive so the original inequality must also be true.
The quadratic mean of two real numbers, x and y, is given by the formula sqrt((x^2 + y^2)/2). A conjecture can be made that the quadratic mean is greater than or equal to the arithmetic mean for positive real numbers. This conjecture can be proved using the AM-QM inequality and algebraic manipulations.
The quadratic mean of two real numbers, x and y, is given by the formula:
Q(x, y) = sqrt((x^2 + y^2)/2)
To formulate a conjecture about the relative sizes of the arithmetic and quadratic means of different pairs of positive real numbers, we can compare the two means for various pairs of numbers. Based on observations, it can be conjectured that the quadratic mean is always greater than or equal to the arithmetic mean for positive real numbers.
To prove the conjecture, we can use the AM-QM inequality, which states that the quadratic mean is greater than or equal to the arithmetic mean:
Q(x, y) >= A(x, y)
Where Q(x, y) is the quadratic mean and A(x, y) is the arithmetic mean.
Let's consider two positive real numbers, a and b:
Q(a, b) = sqrt((a^2 + b^2)/2)
A(a, b) = (a + b)/2
Now, we need to prove that Q(a, b) >= A(a, b):
Start with the inequality:(a^2 + b^2)/2 >= (a + b)/2
Multiply both sides of the inequality by 2:a^2 + b^2 >= a + bCombine like terms:a^2 - a + b^2 - b >= 0
Factor the expression:(a^2 - a) + (b^2 - b) >= 0
Factor out 'a' and 'b':a(a - 1) + b(b - 1) >= 0
Since 'a' and 'b' are positive numbers, both terms on the left side of the inequality are non-negative.a(a - 1) >= 0
The above inequality is true for all positive 'a' values, and the same holds for 'b'.Therefore, Q(a, b) >= A(a, b), which confirms the conjecture that the quadratic mean is always greater than or equal to the arithmetic mean for positive real numbers.
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Describe how to solve any equation in the form ax + b = c for the variable x.
Subtract b from both sides: ax=c-b
Divide both sides by a: x=(c-b)/a
Hope this helped
Explanation:
To solve any equation that is linear in the variable of interest, you first look at what is done to the variable, using the Order of Operations as your guide.
Here, the variable is ...
multiplied by "a"the product has "b" added to it.You find the value of the variable by reversing these steps, starting from the last one on the list and working up the list.
To "undo" the addition of "b", we add its opposite (-b) to the equation. The rules of equality tell you that anything you do to one side of the equation must also be done to the other side, so we add -b to both sides:
ax +b -b = c -b
ax = c -b . . . . . . . . simplify
To "undo" the multiplication by "a", we multiply by its reciprocal. That is, we multiply by 1/a, or, equivalently, divide by "a". Again, we must do this to both sides of the equation:
(1/a)ax = (1/a)(c -b)
x = (c -b)/a . . . . . . . simplify
__
In short, we subtract the added constant (b) and divide by the multiplier (a).
The following data reflect the number of customers who return merchandise for a refund on Monday. Note these data reflect the population of all 10 Mondays for which data are available. 40 12 17 25 9 46 13 22 16 7Based on these data, what is the standard deviation?
Answer:
The standard deviation of given data is 12.36
Step-by-step explanation:
We are given the following data in the question:
40, 12, 17, 25, 9, 46, 13, 22, 16,7
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{207}{10} = 20.7[/tex]
Sum of squares of differences =
372.49 + 75.69 + 13.69 + 18.49 + 136.89 + 640.09 + 59.29 + 1.69 + 22.09 + 187.69 = 1528.1
[tex]\sigma = \sqrt{\dfrac{1528.1}{10}} = 12.36[/tex]
Thus, the standard deviation of given data is 12.36
Final answer:
The standard deviation of the provided data set (number of merchandise returns on Mondays) is approximately 14.8.
Explanation:
To calculate the standard deviation of the provided data set (40, 12, 17, 25, 9, 46, 13, 22, 16, 7), we will follow these steps:
Find the mean of the data set.Subtract the mean from each data point and square the result.Calculate the sum of the squared differences.Divide this sum by the number of data points (since we have the population standard deviation).Take the square root of the result from step 4.Let's apply these steps:
The mean (average) is (40 + 12 + 17 + 25 + 9 + 46 + 13 + 22 + 16 + 7) / 10 = 20.7Squared differences (rounded to two decimal places) would be: (40 - 20.7)², (12 - 20.7)², (17 - 20.7)², and so on.The sum of these squared differences is approximately 2190.1Divide by the number of points, 2190.1 / 10 = 219.01The square root of 219.01 is approximately 14.8Therefore, the standard deviation is about 14.8.
what is 5x -2=38
A 36
B 8
C 7
D 13
A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than it's maximum capacity. What is the percent of its capacity is the large container filled?
Answer:
87.5%
Step-by-step explanation:
64:64-8
64:56
56/64 *100 = 87.5%
Jordy looked at a package of M&M's.He realized 1/3 of the M&M's is blue 1/4 were red and 1/8 were yellow. What color M&M's did Jordy have the most?
Answer:
Blue M&M's
Step-by-step explanation:
Let the total M&M's bought be 100%.
If 1/3 of the M&M's is blue this means we have 1/3 of 100 of blue M&M's i.e 33.3% are blue.
If 1/4 were red, then we have 1/4 of 100 of red M&M's i.e 25% of reds
If 1/8 of the M&M's were yellow, this means there are 1/8 of 100% M&M's i.e 12.5% of yellow.
According to the results, Jordy have more of blue M&M's
The addition law is potentially helpful when we are interested in computing the probability of
Answer:
The union of two event
Step-by-step explanation:
Addition law of probability define that probability of two event is total sum of probability of any event subtract the probability of both events
There are two rules in addition law:
Addition law 1 - when both event are mutually exclusive, then probability of either event is the sum of each event probability.
P( A or B) = P(A) +P(B)
Addition law 2 - when both events are non mutually exclusive then there in addition to the individual probability there is some overlap .
P( A or B) = P(A) +P(B) - P(A and B)
It should be noted that addition law is potentially helpful when we are interested in computing the probability of The union of two event.
According to this question, we are to discuss about Addition law of probability.
As a result of this we can see that Addition law of probability explain about probability for either of two mutually exclusive events which is occurring and also the probability of two non-mutually exclusive events that is occurring.
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Suppose triangle DEF = triangle WXY. Which choice below shows corresponding parts to congruent triangles that are congruent? Explain your answer. (A) angle E = angle X; DF = XY (B) angle D = angle Y; EF = XY ( C) angle E = angle X; DF = XY; (D) angle F = angle X; DE = WX
Answer:
(C ) angle E = angle X; DF = XY
Step-by-step explanation:
a triangle is said to be congruent if SAS(two sides and included angle)
SSS (all the sides are equal), ASA (two angles and an included sides).
therefore, if angle E and angle X are equal
line DF and line XY are also equal.
Let f ( x ) = x 2 + 6 x + 6 f ( x ) = x 2 + 6 x + 6 , and g ( x ) = 1 g ( x ) = 1 . Find all values for the variable x x , for which f ( x ) = g ( x ) f ( x ) = g ( x ) .
Answer:
Therefore the value of x are = -1 and -5 for which f(x)=g(x).
Step-by-step explanation:
Given,
f(x)=x²+6x+6 and g(x)=1
f(x)=g(x)
⇒x²+6x+6=1
⇒x²+6x+6-1=0
⇒x²+6x+5=0
⇒x²+5x+x+5=0
⇒x(x+5)+1(x+5)=0
⇒(x+5)(x+1)=0
⇒x+5=0 or x+1=0
⇒x=-5 x=-1
Therefore the value of x are = -1 and -5.
To find the values of x for which f(x) equals g(x), we set the equations x² + 6x + 6 equal to 1 and solve. The quadratic equation factors to yield x = -1 and x = -5 as solutions.
To find the values of x for which f(x) equals g(x), we need to set the functions equal to each other and solve for x:
Given:
f(x) = x² + 6x + 6
g(x) = 1
We need to solve for x when:
x² + 6x + 6 = 1
Subtract 1 from both sides to set the equation to zero:
x² + 6x + 5 = 0
Next, we factor the quadratic equation:
(x + 1)(x + 5) = 0
Set each factor to zero and solve for x:
x + 1 = 0
x = -1
x + 5 = 0
x = -5
Thus, the values of x for which f(x) = g(x) are x = -1 and x = -5.
What is the slope of this line?
Slope of this line is -2.5
Step-by-step explanation:
Step 1: Slope of the line, m = (y2 - y1)/(x2 - x1)Here, from the graph, x1 = -2, x2 = -4, y1 = 3, y2 = 8
⇒ m = (8 - 3)/(-4 - -2) = 5/-2 = -2.5
What is the 6th term in the sequence described by the following recursive formula?
a1=9
an=an−1−4
Answer:
[tex] a_{6} = - 11[/tex]
Final answer:
The 6th term in the recursive sequence with the first term 9 and each subsequent term decreasing by 4 from the previous term is -11.
Explanation:
To find the 6th term in the sequence described by the recursive formula given:
a1=9
an=an-1−4
We will apply the formula recursively to determine each term up to the 6th term.
First term (a1): 9
Second term (a2): a1 − 4 = 9 − 4 = 5
Third term (a3): a2 − 4 = 5 − 4 = 1
Fourth term (a4): a3 − 4 = 1 − 4 = -3
Fifth term (a5): a4 − 4 = -3 − 4 = -7
Sixth term (a6): a5 − 4 = -7 − 4 = -11
Therefore, the 6th term in the sequence is -11.
What is the surface area of a cube that has a side length of 2.2 meters? Use the formula S A = 6 s squared, where SA is the surface area of the cube and s is the length of each side
Answer:
Step-by-step explanation:
surface area=6*2.2²=6×4.84=29.04 m²
Answer:
29.04
Step-by-step explanation:
just took the test
Tesha withdrew $22.75 each weak for four weeks from her savings account to pay for her piano lessons. By how much did these lessons change her savings account balance
Final answer:
Tesha's savings account balance was decreased by $91.00 after withdrawing $22.75 each week for four weeks to pay for piano lessons.
Explanation:
To calculate the change in Tesha's savings account balance due to payment for her piano lessons, we need to multiply the weekly withdrawal amount by the number of weeks. Tesha withdrew $22.75 each week for four weeks.
Multiply the weekly withdrawal amount by the number of weeks: $22.75 × 4.This results in a total withdrawal of $91.00 over the four weeks ($22.75 × 4 = $91.00).Therefore, Tesha's lessons decreased her savings account balance by $91.00 after four weeks.Angie has some red and blue beads. 40% of her beads were red. When she lost 50 blue beads, the number of blue beads was reduced by 1/3 its original number of beads. How many beads did Angie have in the end?
Answer:
Step-by-step explanation:
Let x represent the total number of red and blue beads
Angie has some red and blue beads. 40% of her beads were red. This means that the total number of red beads is
40/100 × x = 0.4x
The number of blue beads would be
x - 0.4x = 0.6x
When she lost 50 blue beads, the number of blue beads was reduced by 1/3 its original number of beads. This means that
0.6x - 50 = 0.6x - 0.6x/3
0.6x - 50 = 0.6x - 0.2x = 0.4x
0.6x - 0.4x = 50
0.2x = 50
x = 50/0.2 = 250
The number of blue beads that Angie had initially is
0.6 × 250 = 150
The number of blue beads that Angie has left is
150 - 50 = 100 beads
The number of beads that Angie has in the end is
250 - 50 = 200 beads
1) A family consisting of three persons—A, B, and C—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that
(a) All three family members are assigned to the same station? (Round your answer to three decimal places.)
(b) At most two family members are assigned to the same station? (Round your answer to three decimal places.)
(c) Every family member is assigned to a different station? (Round your answer to three decimal places.)
Answer:
Step-by-step explanation:
Let us record the station number 1, 2 or 3 for each family member A, B or C.
I am attaching a table containing total outcomes. Outcomes are presented along rows while the assigned station to each member is written along columns. For ease of understanding, 1 3 2 in the table should be interpreted as family member A being assigned to station 1, member B to station 3 and member C to station number 2, respectively.
From table it is clear that the total outcomes possible are 27.
We know that, probability can be defined as,
[tex]PROBABITILY = \frac{NUMBER\;OF\;DESIRED\;OUTCOMES}{TOTAL\;NUMBER\;OF\;OUTCOMES}[/tex]
a) All Members Assigned to the Same Station.
Cases for all members being assigned to same station are as follows:
[1 1 1], [2 2 2], [3 3 3] (outcome number 1, 14 and 27 in the table).
Therefore,
[tex]PROBABILITY\;(Case\;a) = \frac{3}{27}\\\\PROBABILITY\;(Case\;a) = 0.111[/tex]
b) At Most Two Members Assigned to the Same Station.
It means that maximum of 2 members can have the same station. Cases for this situation are as follows:
[1 1 2], [1 1 3], [1 2 1], [1 2 2], [1 3 1], [1 3 3], [2 1 1], [2 1 2], [2 2 1], [2 2 3], [2 3 2],
[2 3 3], [3 1 1], [3 1 3], [3 2 2], [3 2 3], [3 3 1], [3 3 2]
(outcome number 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 25 and 26 in the table).
Therefore,
[tex]PROBABILITY\;(Case\;b) = \frac{18}{27}\\\\PROBABILITY\;(Case\;b) = 0.666[/tex]
c) All Members Assigned to a Different Station.
For this scenario, we have the following results:
[1 2 3], [1 3 2], [2 1 3], [2 3 1], [3 1 2], [3 2 1] (outcome number 6, 8, 12, 16, 20 and 22 in the table).
Therefore,
[tex]PROBABILITY\;(Case\;c) = \frac{6}{27}\\\\PROBABILITY\;(Case\;c) = 0.222[/tex]
Sonya, who is paid time and a half for hours worked in excess of 40 hours, had gross weekly wages $725 for 52 hours worked. What is her regular hourly rate?
Answer: her regular hourly rate is $12.5
Step-by-step explanation:
Let x represent the regular payment that Sonya receives per hour for the first 40 hours of work. This means that her total pay for the first 40 hours of work is
40 × x = $40x
Sonya is paid time and a half for hours worked in excess of 40 hours. This means that her hourly pay for working more than 40 hours would be x + 0.5x = $1.5x
She worked for 52 hours. This means that the extra hours that she worked is
52 - 40 = 12 hours
Total pay for 12 extra hours is
12 × 1.5x = 18x
If she had gross weekly wages of $725, then
40x + 18x = 725
58x = 725
x = 725/58 = $12.5
To find Sonya's regular hourly rate, we need to calculate her overtime pay and then subtract it from her total weekly wages.
Explanation:To find Sonya's regular hourly rate, we need to calculate her overtime pay and then subtract it from her total weekly wages. Sonya earned $725 for 52 hours worked. Since she is paid time and a half for hours worked more than 40, she worked 12 overtime hours (52 - 40 = 12).
Her overtime pay is calculated by multiplying her regular hourly rate by 1.5, so her overtime pay is 1.5 * regular hourly rate * 12 hours. Subtracting her overtime pay from her total wages gives us her regular wages, so we have the equation: $725 - (1.5 * regular hourly rate * 12) = regular wages. Solving for regular hourly rate will give us the answer.
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use a property to write an equivalent expression 6x7
Answer:
Step-by-step explanation:
6 X 7 = 42
This is simply the sum of 6 in seven places or 7 in six places.
The build a dream construction company has plans for two models of the homes they build, model a and model b. The model a home requires 18 single windows and 3 double windows. The model b home requires 20 single windows and 5 double windows. A total of 1,800 single windows and 375 double windows have been ordered for the developments. Write and solve a system of equations to represent this situation. Define your variables. Interpet the solution of the linear system in terms of the problem situation
Answer:
a = 50 houses
b = 45 houses
Step-by-step explanation:
Given
Number of houses called Model A = a
Number of houses called Model B = b
Total of single windows = 1800
Total of double windows = 375
then we have the system of equations
18a + 20b = 1800 (I)
3a + 5b = 375 (II)
Solving the system by whatever method we prefer, we obtain
(I) a = (1800 - 20b)/18
then (II)
3((1800 - 20b)/18) + 5b = 375
⇒ 300 - (10/3)*b + 5b = 375
⇒ (5/3)*b = 75
⇒ b = 45 houses
then
a = (1800 - 20*45)/18
⇒ a = 50 houses
50 model A homes and 45 model B homes will be built.
To solve the problem, let's define our variables:
A = number of model A homesB = number of model B homesWe then create the following system of equations based on the given information:
1. For single windows:
18A + 20B = 1800
2. For double windows:
3A + 5B = 375
We can solve this system using the substitution or elimination method.
Step-by-Step Solution:
Multiply the second equation by 4 to align the coefficients of A:12A + 20B = 1500Subtract the modified second equation from the first equation:(18A + 20B) - (12A + 20B) = 1800 - 15006A = 300A = 50Substitute A = 50 back into the second original equation:3(50) + 5B = 375150 + 5B = 3755B = 225B = 45The solution to the system is A = 50 and B = 45, meaning that the construction company plans to build 50 model A homes and 45 model B homes.
what is the length of the missing side of the triangle? 24,66 29.15 26.5 30.6
Answer:
24.66
Step-by-step explanation:
You use the Pythagorean Theorem and do 27^2 -11^2= x
Brandon eats half the amount of pie that Mollie eats.Yuki eats four times as much pie as Brandon. Mollie eats 1/4 of the pie. How much pie does Anna eat?
Answer: Anna eats 1/8 of pie
Step-by-step explanation: Let total pie =1
Mollie eats 1/4 of pie
Brandon eats half the amount of pie that Mollie eats i.e 1/2 of (1/4)
⇒1/8
Yuki eats 4 times as much as pie as Brandon i.e 4*(1/8)
⇒1/2
Total pie eaten by Mollie +Brandon+Yuki = 1/4+1/8+1/2
⇒7/8
Therefore Anna eats (1-7/8)
⇒ 1/8 of pie
The army bus has 12 seats on one side. Two soldiers can sit in each seat. If five seats are reserved for equipment, how many buses will they need for 1120 soldiers
Answer:
80 buses will be required for 1120 soldiers.
Step-by-step explanation:
Given:
Number of seats on One side = 12 seats.
Now Given:
five seats are reserved for equipment.
So we can say that;
Number of seats used by soldiers = [tex]12-5=7\ seats[/tex]
Number of soldiers on Each seat =2
So we will now find number of soldiers on each bus.
number of soldiers on each bus is equal to Number of seats used by soldiers multiplied by Number of soldiers on Each seat.
framing in equation form we get;
number of soldiers on each bus = [tex]7\times2 = 14\ soldiers[/tex]
Now we know that;
For 14 soldiers = 1 bus
So 1120 soldiers = Number of buses required for 1120 soldiers.
By Using Unitary method we get;
Number of buses required for 1120 soldiers = [tex]\frac{1120}{14} =80[/tex]
Hence 80 buses will be required for 1120 soldiers.
The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.)
A sine function is written to represent the data.
What is the amplitude, period, and vertical shift of this equation?
Drag a value into each box to correctly complete the statements.
Answer:
Part A) The amplitude = 24
Part B) The period = 24
Part C) Vertical shift = 36
Step-by-step explanation:
The general equation of the sine function:
y = A sin (Bx) + C
Where A is the amplitude and B = 360°/Period and C is the vertical shift
See the attached figure which represents the graph of m and f(m)
So,
Part A:
The function has minimum at 12 and maximum at 60
The difference is = 60 - 12 = 48
So, The amplitude = 48/2 = 24
Part B:
Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.
We can deduce that the function completes one cycle within 24 months
So, the period = 24
Part C:
Vertical shift is obtained at m = 0
So, f(m) = 36
36 = A sin (0) + C
C = 36 ⇒ Vertical shift
So, The amplitude = 24
The period = 24
Vertical shift = 36
Answer:
Answer:
Part A) The amplitude = 24
Part B) The period = 24
Part C) Vertical shift = 36
Step-by-step explanation:
The general equation of the sine function:
y = A sin (Bx) + C
Where A is the amplitude and B = 360°/Period and C is the vertical shift
See the attached figure which represents the graph of m and f(m)
So,
Part A:
The function has minimum at 12 and maximum at 60
The difference is = 60 - 12 = 48
So, The amplitude = 48/2 = 24
Part B:
Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.
We can deduce that the function completes one cycle within 24 months
So, the period = 24
Part C:
Vertical shift is obtained at m = 0
So, f(m) = 36
36 = A sin (0) + C
C = 36 ⇒ Vertical shift
So, The amplitude = 24
The period = 24
Vertical shift = 36
Step-by-step explanation:
HELP!! i dont understand this math question and need help
Answer:
52.2 ft
Step-by-step explanation:
Triangle JSV is similar to triangle HTV so you have the proportion ...
JS/SV = HT/TV
JS/(36 ft) = (5.8 ft)/(4 ft) . . . . . . . fill in the given values
JS = (36 ft)(5.8/4) = 52.2 ft . . . . multiply by 36 ft
The height of the wall is 52.2 ft.
We know that m<HVT = m<JVS because the mirror projects equal angles. We can claim this about the angle theta.
tan(θ) = 5.8/4
θ = [tex]tan^{-1}(5.8/4)=55.4[/tex] degrees approx.
So, we want sin theta in the other triangle. Luckily, we also know that...
cos(55.4°) x hypotenuse = 36
hypotenuse = 63.4 ft approx.
So we can find the height by evaluating...
sin(55.4°) x 63.4 = 52.2 ft
answer: 52.2 ft
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A woman is selected by a marketing company to participate in a paid focus group. The company says that the woman was selected because everyone in five randomly selected towns was being selected. Which type of sampling did the marketing company use?
A) Stratified sampling
B) Systematic sampling
C) Random sampling
D) Convenience sampling
E) Cluster sampling
Stratified sampling method - where population were divided into different groups called strata and the sample is then drawn from EACH group.
Systematic sampling method - sampling method using probability where elements are chosen from a target population.
Random sampling - each sample chosen has equal probability to be chosen.
Convenience sampling method - Not a random sampling method where the sample is being chosen as per ease of access.
Cluster sampling method - population were divided into different groups as known as clusters. The clusters were then chosen randomly as the samples. Each individuals in the clusters chosen are used as the samples.
Answer: E. Cluster sampling where selected towns refer to the clusters and were chosen randomly.
The type of sampling used by the researcher is cluster sampling.
What is cluster sampling?Cluster sampling is a technique used when it becomes difficult to study the target population spread across a wide area and simple random sampling cannot be applied.
The researcher divides the entire population into sections or clusters. Then the researcher randomly selects a few clusters from the total clusters for the research.
In this case, the clusters are the five randomly selected towns. Everyone in these selected towns is included in the sample. This makes it a cluster sample.
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Researchers randomly divide participants into groups. Each group takes a different amount of omega-3 fatty acid supplements daily for a month. One group receives a placebo. The researchers measure the impact on cholesterol levels in the blood. What is the purpose of random assignment in this experiment? Check all that apply. To ensure that all people with high cholesterol have an equal chance of being selected for the study To increase the accuracy of the research results and prevent skewness in the data To produce treatment groups with similar characteristics To control confounding
Answer: To produce treatment groups with similar characteristics
Step-by-step explanation:
The purpose of this experiment is to determine that the treatments groups with similar characteristics are produced. Every groups is taking different amount of the supplement so this study ensures that by randomly assigning the supplements, we can check the cholesterol level in the blood. In this way, similar characteristics in groups are imparted so we can then make treatment groups of same characteristics.
The purpose of random assignment in experiments is to avoid bias, increase the research results' accuracy, help in producing treatment groups with similar characteristics, and control confounding variables. In this case, it ensures that all participants have an equal chance of receiving any level of omega-3 fatty acid or placebo.
Explanation:The purpose of random assignment in this experiment is multifold. Firstly, it ensures all participants, regardless of their cholesterol levels, have an equal chance of being selected. This prevents bias in the sample selection. Secondly, it increases the accuracy of the research results by preventing skewness in the data. The random assignment ensures that every participant has an equal chance of receiving any level of the omega-3 fatty acid supplement or the placebo. This helps produce treatment groups with similar characteristics, which in turn allows for fair comparisons to be made. Finally, it aids in controlling confounding variables. These are factors other than the independent variable (in this case, omega-3 fatty acid supplements) that may affect the dependent variable (cholesterol level), and random assignment helps to equalize these among the groups.
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