Answer:
19 tables
Step-by-step explanation:
Let X represent the number of tables that have 1 student and 3 seniors
Let Y represent the number of tables that have 2 student2 and 4 seniors
Therefore number students total
1X + 2Y =23 (1)
Number of seniors total
3X + 4Y = 61 (2)
Multiply equation (1) by 2 giving
2X + 4Y = 46 (3)
Subtract (3) from (2)
3X + 4Y - (2X+4y) = 61-46
3X + 4Y - 2X -4Y = 15
3X-2X = 15
X = 15
Plugging this value into equation (1) gives
1(15) + 2Y = 23
15 + 2Y = 23
Subtract 15 from both sides
2Y = 23 - 15
2Y = 8
Divide by 2 both sides
Y = 4
Thus total number of tables used = X +Y = 15+4 = 19
a. Invent two situations that you think would result in distributions with similar measures of variability. Explain your reasoning.
b. Invent two situations that you think would result in distributions with different measures of variability. Explain your reasoning.
Answer:
Step-by-step explanation:
Using measures of variability, it is found that:
a. The situations with constant measures involve constant distributions, such as the number of snow days in Miami each year.
b. The situations with different measures involve constant distributions, such as the number of snow days in Buffalo each year.
What are the measures of variability in a data-set?There are three measures of variability in a data-set: the range, the standard deviation and the variance.
The range is given by the difference between the maximum value and the minimum value of a data-set.
The standard deviation and the variance are described as follows:
The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The variance is the square of the standard deviation.Uniform(constants) data-sets will have similar measures. One example is the number of snow days in Miami each year, which is always of 0, hence the three measures will be of 0.
More disperse data-set will have different measures. Taking the city of Buffalo, in New York, as an example. On average, it should have 40 days of snow each winter, but on colder winters it can have 60 and warmer winters it can have 20. Hence the distribution with the number of snow days in Buffalo over a period of 20 years will have different range, standard deviation and variances.
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Perform the indicated operation & simplify. Express the answer as a complex number. ( 12 − 11 i ) 2
The answer is 24 - 22i
The answer we got is a complex number.
We are asked to find out the multiplication of a complex number and a real number.
The general form of a complex number is a + bi.
If we need to find the product of a complex number and a real number,
then, we need to multiply the real and imaginary parts by the real number and write down the answer.
The real number given is 2.
And the complex number given is 12 - 11i.
The real part of the complex number is 12.
And the imaginary part of the complex number is -11.
When the real part of the complex number is multiplied by the real number, we get 12 × 2 = 24.
When the imaginary part of the complex number is multiplied by the real number, we get (-11) × 2 = -22
Therefore, the required complex number is 24 - 22i
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Help, I don’t know how to solve this
Answer:
a=A/8
Step-by-step explanation:
This MIGHT be the answer, I am 99% sure!
I need help with this please and work out the problem
Answer:The answer is 425
Step-by-step explanation:
Tony buys CDs at a music store. You get 20% off the price of a CD. You still have to add 5% sales tax. But you find the sales tax after the discount. So you save money on taxes, too." How much money does Tony save by getting the discount before adding the sales tax? Explain by using expressions.
Answer:
Lets say a CD costs a 100 dollars (which it obviosly doesn't)
No matter whether we do the discount before or after tax, it'll end up costing 84 dollars to by the CD.
80% of 100 = 80
80 * 1.05 = 84
80% of 105 = 84
The order in which he does the discount and the tax doesn't matter.
Hope this helps.
find the average of 1/8, 1/6, and 3/4
Answer:
Average= [tex]\frac{25}{72}[/tex]
Step-by-step explanation:
o find the average add up the values and divide the sum by the number of values.
Rewriting all values as fractions, rewriting any negatives if necessary and, setting up as an addition problem
= [tex]\frac{1}{8}[/tex] + [tex]\frac{1}{6}[/tex] +[tex]\frac{3}{4}[/tex]The least common denominator (LCD) is: 24.
Rewriting as equivalent fractions with the LCD:
= [tex]\frac{3}{24\\}[/tex] + [tex]\frac{4}{24}[/tex] + [tex]\frac{18}{24}[/tex]Rewriting numerators over the common denominator,
= [tex]\frac{3 + 4 + 18}{24}[/tex]Totaling the numerator:
= [tex]\frac{25}{24}[/tex]
Dividing by the number of values: 3
[tex]\frac{25}{24}[/tex] ÷3 =[tex]\frac{25}{24}[/tex] ×[tex]\frac{1}{3}[/tex] = [tex]\frac{25}{72}[/tex]
Average of the fractions is:
Average= [tex]\frac{25}{72}[/tex]
Compare the fractions -14/21, -3/9
Answer:
It's answer is..-2/7 and -1/3
Simplify the expression √48
-3x+6=-24bwhat is the value of 2x-17
The value of the expression 2x - 17 is 3
How to evaluate the expression?The expression is given as
-3x + 6 = -24
Subtract 6 from both sides
-3x = -30
Divide both sides by -3
x = 10
Multiply by 2
2x = 20
Subtract 17 from the sides
2x - 17 = 3
Hence, the value of the expression 2x - 17 is 3
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Mia has 7 boxes of cherry tarts. Each box has 8 cherry tarts. Explain how to use an open number line to solve.
Use of open number line is
7 boxes of cherry tarts
Each box has 8 cherry tarts.
Total cheny tarts is
[tex]$$7 \times 8=7+7+7+7+7+7+7+7$$[/tex]
A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and drop as we move to the left.
A number line is a visual depiction of numbers on a straight line drawn either horizontally or vertically. It is simple for humans to compare numbers and carry out simple arithmetic operations on them when they are written down on a number line. A number line is said to begin at zero (0). Left of zero, there are only negative numbers, and right of zero, there are only positive numbers. So, on a number line, we may say that the value of numbers grows as we travel to the right. This indicates that there are more numbers on the right than on the left.
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Using the scale found on the number line, how would the number 1 be best represented?
A 0/8. B 4/8. C 8/1. D 7/8. E 8/8
PLEASE I NEED HELP
Based on the given scale, the number, 1, on the number line would best be represented by the number A. 8/8.
What is the scale?Based on the first number given which is 1/8, we know that the scale is such that the denominator would be 8.
The best way to write 1 would therefore be to express it in terms of a ratio with 8 being the denominator.
That would mean that 1 would be 8/8 which results in 1.
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Graph the numbers -0.2, 7/10, -1, √2, and -4 on a number line.
-8 -7, -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Answer:
Step-by-step explanation:
The student council is selling popsicles to raise money for prom. Each box contains 10
popsicles and each box costs $4.50. How much does the school need to charge per
popsicle to make a profit of $6 per box?
Answer:
1.05 dollars per popsicle
Step-by-step explanation:
x is the price per popsicle. In order for you to make 6 dollars of profit, each box is going to cost 10.50 dollars because 4.50 is your amount of expenses.
Profie= revenue-expenses
6= revenue-4.5
revenue=10.5
If you charge 10.5 per box, and each box has 10 popsicles, then one popsicle is 10.5/10=1.05 dollars per popsicle.
There are 100 marbles in a bag. 21 are green, 26 are blue, 17 are red, 19 are yellow, and 17 are orange. True or False: 17% of the
marbles are orange and red.
Answer:
False
Step-by-step explanation:
there are total 17+17=34 orange and red marbles
34/100 is 34%, not 17%
Help me with this problem please
The Lopez family buys 4 dinners at the market. The total cost is $5 above or below $50. Write an equation that models the cost x, in dollars of a single dinner?
answer: |_-_x|-_=0
==================================================
Explanation:
x = cost of one dinner
4x = cost of four dinners
50-4x = the difference in the cost of $50 vs 4x dollars
To ensure this difference is never negative, we use absolute value to form the expression |50-4x|
Set this equal to 5 since we want this distance or difference to be 5 units above or below 50
|50-4x| = 5
|50 - 4x| - 5 = 0
Answer:
l 50 - 4x l - 5 = 0
Step-by-step explanation:
How much must be the last repayment be made if the loan is terminated after 5 year for which a loan of K10,000 is taken at 12% p.a. flat, where the loan is repaid by equal quarterly repayments for 9 years?
Answer:
Step-by-step explanation:
Financial Goals: Tutorial
Part C
? Question
Diego's cash flow is the difference of his monthly income, $3,000, and his total expenses, $2,715. Which equation
correctly represents Diego's cash flow?
O cash flow = $2,715 - $3,000
O cash flow = $3,000-$2,715
O $3,000 = $2,715 - cash flow
$3,000 = cash flow-$2,715
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The equation that represents Diego's cash flow is cash flow = $3,000-$2,715.
What is the cash flow?Cash flow is the difference between cash inflows and cash outflows. Cash inflow are additions to the cash flow. An example of cash inflow is monthly income. Cash outflow would reduce the cash flow. An example of cash inflow is expenses.
Cash inflow = income - expense
$3,000 - $2,715
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Find the perimeter of the rectangle. Then, find the area of the rectangle. Round your
answer to the nearest tenth, if necessary.
(Lesson 2-3)
Solution :
solve by considering data :
The perimeter of a rectangular pool is 56 meters. If the length of the pool is 16 meters, then find its width.
Here the perimeter and the length of the rectangular pool are given. We have to find the width of the pool.
The perimeter P of a rectangle is given by the formula, P=2l+2w, where l is the length and w is the width of the rectangle.
Given that, the perimeter is 56 meters and the length is 16 meters. So, substitute these values into the formula.
56=2(16)+2w
Simplify.
56=32+2w
Subtract 32 from both sides.
24=2w
Divide each side by 2 .
12=w
Therefore, the width of the rectangular pool is 12 meters.
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Which sequence of transformations on preimage ∆ABC will NOT produce the image ∆A'B'C'?
Graph shows 2 triangles plotted on a coordinate plane. First triangle is at A(minus 3, 0), B(minus 2, 3), C(minus 1, 1). Second triangle is at A prime (0, minus 3), B prime (3, minus 2), C prime (1, minus 1).
A.
reflection across the line y = x
B.
reflection across the x-axis followed by a reflection across the y-axis
C.
reflection across the line y = -x followed by a rotation 180° counterclockwise about the origin
D.
reflection across the y-axis followed by a rotation 90° clockwise about the origin
E.
rotation 180° clockwise about the origin followed by a reflection across the line y = -x
The geometric transformation which will not produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis
In this question, we have been given a triangle ABC and the transformed triangle A'B'C'
Also, in the graph the first triangle is at A(-3, 0), B(-2, 3), C(- 1, 1) and the Second triangle is at A prime (0, -3), B prime (3, -2), C prime (1, -1).
Consider the graph as shown below.
From the coordinates of vertex of triangle ABC and triangle A'B'C' we can observe that,
A(-3, 0) -> A'(0, -3)
B(-2, 3) -> B'(3, -2)
C(-1, 1) -> C'(1, -1)
For each vertex,
x coordinate of triangle ABC = y coordinate of triangle A'B'C'
and y coordinate of triangle ABC = x coordinate of triangle A'B'C'
This means, the geometric transformation of triangle ABC is reflection across the line y = x
But the reflection across the x-axis followed by a reflection across the y-axis.
Therefore, the geometric transformation which will not produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis
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Brainliest, 5 star, & thanks.
The coordinates of the vertices of △PQR are P(4, −2) , Q(6, −4) , and R(8, 0) .
The coordinates of the vertices of △P′Q′R′ are P′(−4, 3) , Q′(−6, 5) , and R′(−8, 1) .
A large water container has a leak. It loses 40 drops of water every minute. If 50 drops of water is equivalent to half of a teaspoon. At what rate
Is the water leaking?
O 48 teaspoons per hour
24 teaspoons per hour
O 80 teaspoons per hour
O 12 teaspoons per hour
O 20 teaspoons per hour
4. — 1+4= + 12 10 1 2 3 4 5 can you answer this?
Answer:
7=37
Step-by-step explanation:
no solution problem
Rs=3x st=6x-5 rt=58 find st
The value of st is 30.4
As S is the point in RT, it implies that RS+st=Rt. Therefore according to the question,
3x+6x-5=58
⟹9x=58-5
or
9x=53
⟹x=5.9
RS = 3×5.9=17.7
st=(6×5.9)-5=35.4-5=30.4
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If the perimeter of the irregular figure is 35 2/3 cm, then what is the missing side length?
The two numbers on top are 4 3/4 and 3 1/2
the ones inside left to right is 1 1/3 1 1/3 again and 3 1/2
Then the one in the outside bottom is 9.25 cm
The one at the right outside is 6.6 cm
Left outside is the missing one
srry for bad photo quality
The missing side of the figure if the perimeter is 35 2/3 cm, is calculated as: 10.9 cm.
How to Find the Perimeter of a Figure?The perimeter of a figure is the total length surrounding the figure.
We are given that the figure shown below has a perimeter of 35 2/3 cm, which means all the total length of all its sides equals 35 2/3 cm.
To find the missing length, sum all the given lengths and subtract it from the perimeter of the figure.
Sum of all the given lengths = 4 3/4 + 3 1/2 + 1 1/3 + 1 1/3 + 3 1/2 + 9.25 + 6.6 = 4.75 + 2.3 + 1.3 + 1.3 + 2.3 + 9.25 + 6.6
Sum of all the given lengths = 27.8 cm
The missing side = 38 2/3 - 27.8 = 38.7 - 27.8
The missing side = 10.9 cm.
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A company is designing boxes to ship their product to stores. The design team decides that the width of the box should be five feet shorter than the length, and the height of the box should be three feet longer than the width. Due to shipping constraints, the length of the box can be no greater than six feet.
The volume of the box, V(x), can be modeled by a polynomial function, where x is the length of the box. Which of the following correctly models the situation above and gives the correct domain?
The polynomial function is V(x) = x^3 - 7x^2 + 10x and domain of x is (5,6]
Here we are given that the length of the box is x
Also, the width of the box should be 5 feet shorter than the length
Thus, width = x - 5
and the height should be 3 feet longer than the width
Thus, height = x - 5 + 3
= x - 2
Now the volume of the box = length × width × height
Volume = x (x-5) (x-2)
V(x) = (x^2 - 5x) (x-2)
V(x) = x^3 - 2x^2 - 5x^2 + 10x
V(x) = x^3 - 7x^2 + 10x
Now, looking at the options, we see that option C is eliminated.
Now, let us look at the domain of x
Since width cannot be negative (x-5) > 0
⇒ x > 5
Now in option A domain is (0, 6], but x cannot take values from (0,5). Thus, option A is eliminated.
Similarly, we can eliminate option B also since x cannot take values from (0, 2)
Thus, option 4 is the correct answer.
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Your question was incomplete. Check for the missing options below, in the figure attached.
step by step explanation
The sum of the given infinite geometric series is; 32
What is the sum of the geometric series?The general formula for finding the sum of an infinite geometric series is s = a₁/(1 - r)
where;
s is the sum
a₁ is the first term of the series
r is the common ratio.
To find the common ratio, use the formula: r = a2⁄a1
where a2 is the second term in the series and a1 is the first term in the series.
Thus;
r = 2²/4²
r = 1/2
Thus;
S = 4²/(1 - 1/2)
S = 16/(1/2)
S = 32
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Which inequality does this graph match?
−19 + 7k< −6(−4−k)
−7 (4−x) + 4 > −18 + 7x
−4 (4+7x) + x < −6x + 5
−2n − 40 < 5 (6+n) + 7n
Answer:
I think it is -5
Step-by-step explanation:
Help me plsss this is my last oneeeree
Answer:
For the first question:
The fraction that comes after 0/3 is 1/3The fraction that comes after 1/3 is 2/3For the second question:
The fraction that comes after 0/6 is 1/6The fraction that comes after 1/6 is 2/6The fraction that comes after 2/6 is 3/6The fraction that comes after 3/6 is 4/6The fraction that comes after 4/6 is 5/6Step-by-step explanation:
Hope it helps! =D
HELP ASAP I WILL GIVE 30 points to whoever can show their work!
Answer:
Step-by-step explanation:
sin(A)=2/5
[tex]cos^2(A) +sin^2(A)=1\\cos^2(A)+[\frac{2}{5}]^2=1\\cos^2(A)+\frac{4}{25}=1\\ cos^2(A)=1-\frac{4}{25}\\ cos^2(A)=\frac{21}{25}\\ cosA=\frac{\sqrt{21} }{5}[/tex]
