A total of $1680 is to be given as cash prizes to 7 students of a school for their
overall academic performances. If each price is $30 less than its preceding prize, find
the value of each prize.
Answers
Answer: the values of each prize are
$330,$300,$270,$240,$210,$180,$150.
Given: sum of total prize money=$1680number of students=7each prize is $30 less than the preceding prizeThe above conditions are in the form of an Arithmetic Progression(AP)
with sum of series(\(S_{n}\)) 1680 , 7 terms(n) in the AP and common ratio(d)=30
Let the first term of the AP be 'a'.
\(S_{n}=\frac{n}{2}[2a+(n-1)*d]\)
\(1680=\frac{7}{2}[2a+(7-1)*30] \\1680=\frac{7}{2} [2a+180]\\1680*2=7*(2a+180)\\3360=14a+1260\\14a=3360-1260\\14a=2100\\a=2100/14\\a=150\)
The 7th award is $150
The 6th award is $(150+30)=$180
The 5th award is $(180+30)=$210
The 4th award is $(210+30)=$240
The 3rd award is $(240+30)=$270
The 2nd award is $(270+30)=$300
The 1st award is $(300+30)=$330
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Related Questions
Students at Sunnyvale Middle School volunteered to work a 2-hour shift at a
car wash fundraiser. The table shows the number of people who worked each
shift and how many cars they washed.
Is the relationship between the number of
cars washed and the number of workers
proportional? Complete the statement.
The number of cars washed per person
?
of workers, so the relationship is
the same for each number
?
People Working
4
6
8
10
Cars Washed
8
12
20
25
Answers
The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The ratios between the output and the inputs are given as follows:
8/4 = 2.12/6 = 2.20/8 = 2.5.25/10 = 2.5.Different ratios, hence the relationship is not proportional.
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Please help me right now!
Thank you so much
Answers
The length of the arc KL in the given circle is 3.49 units
How to find the length of the arc KL?In a circle whose radius is R, the length of an arc defined by an angle x is given by:
Length = (x/360)*2*3.14*R
Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:
Length = (100/360)*2*3.14*2
Lenght = 3.49 units.
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A random sample of a specific brand of snack bar is tested for calorie count, with the following results:
149 145 140 160 149 153 131 134 153
Assume the population standard deviation is ı = 24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars.
Answers
Answer:
iddiduududjdhdhdjdhdjr
Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
Answers
Step-by-step explanation:
this isn't much I think so this isn't plus how come everything in March
A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
Complete the table to show the relationship between the amounts of salt and water in the stew recipe. Enter a number in each box.
Can someone please help me quickly!! And also let me know if I got the first 2 correct
Answers
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
What is the amount of salt?A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
There is a ratio issue here.
As X is to three, 3 is to 4.
3 : 4 :: X : 3
To eliminate the fractions, multiply each integer in the ratio by 12.
9 : 12 :: 9X : 12
This is a portion of what is
9 / 12 = 9X / 12
to obtain, cross-multiply.
9 / 12 = 3 teaspoons of salt,
Check: 3 cup of flour yields 3 cups, which is a 4x increase.
The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
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Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Since corresponding parts of
congruent triangles are congruent, angle ZWY is congruent to angle XWY and angle ZYW is congruent to angle XYW.
True or False: Mai can now conclude that diagonal WY bisects angles ZWX and ZYX.
True
O False
Answers
It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX
Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:
Diagonal WY bisects angles ZWX and ZYX because:
all corresponding parts of both triangles are congruent. (Option A).
If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.
Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.
If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).
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I need an answer for this question please :)
Answers
69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 696 969
Determine whether each statement about the solid is TRUE or FALSE.
1)?
2)?
3)?
4)?
Answers
Answer:
1.False(It is a cube)
2.True(Cubes have 6 faces)
3.False(Its base is a square)
4.False(It has 12 edges)
Step-by-step explanation:
1 is subtracted from the square of a number.
Represent the following sentence as an algebraic expression. Where “ a number” is the letter X. You don’t need to simplify. Please help.
Answers
The sentence represented as an algebraic expression is x² - 1
What are algebraic expression?Algebraic expressions can be defined as a mathematical expression that consists of terms, variables, constants, coefficients and fractions.
Also, these algebraic expressions are identified with arithmetic or mathematical operations. These operations are;
AdditionMultiplicationSubtractionBracketParenthesesDivisionFrom the information given, we have that;
Let the number be x
If 1 is then subtracted from the square of a number.
Fiirst, the square of the number is x²
This is represented as;
x² - 1
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Find the circumference of a circle with a radius of 6 cm.
Hi besties i need. help ASAP please and. ty
Answers
Answer:
37.7
Step-by-step explanation:
Circumference = \(2\pi r\)
Circumference = \((2)(\pi )(6)\)
Circumference = 37.69911184 / 37.7
Therefore, circumference of the circle with the radius 6 cm is 37.7.
Answer:
37.7
Step-by-step explanation:
formula for circumference of a circle=2πr
2×π×6=37.7cm
PLEASE HELP 11 POINTS!!
find the composition of transformations that map ∆PQR to ∆P'Q'R. Rotate 90 counterclockwise about the origin and then reflect over the ___?
Answers
Answer:
x-axis
Step-by-step explanation:
Two forces, F1 and F2, are acting on a body, as shown in the figure. The resultant force, R, is
newtons.
Answers
Answer:
R ,is the Resultant of two forces,
∠ACB +50°=180°
∠ACB=180° -50°
∠ACB=130°
→Cos(130°)=Cos (180°-50°)= -cos 50°= -0.6427
Magnitude of resultant force =70.70 Newtons(Approx)
Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
Answers
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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Steven’s cat drinks water from a bowl. The following function represents the ounces of water left in the bowl in terms of hours since it was filled. y= -1/2x + 4 Which variable represents the number of hours since the bowl was filled
Answers
Considering the given linear function, variable x represents the number of hours since the bowl was filled.
What is a linear function?A linear function is modeled by:
\(y = mx + b\)
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the number of ounces of water left in the bown after x hours is given by:
y = -0.5x + 4.
Variable x is the input, hence, it represents the number of hours since the bowl was filled.
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Answer:
Part A: The number of ounces of water left in the bowl depends on the number of hours since the bowl was filled. So the number of ounces is the dependent quantity. The y-variable represents the dependent quantity. So, the y-variable represents the ounces of water left in the bowl.
Part B: The number of hours since the bowl was filled is the independent quantity. The x-variable represents an independent quantity. So, the x-variable represents the number of hours since the bowl was filled.
Part C: The value 4 is the initial value of the function. It represents the ounces of water in the bowl immediately after the bowl was filled and before the cat drank any water from the bowl.
Part D: The value -1/2 is the function’s rate of change. It represents the change in ounces of water in the bowl with every hour.
Step-by-step explanation:
I took the Edmentum test.
An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location in the sea. It then flies 483 miles from the sea at a bearing of S 55° W to another location. Finally, the aircraft flies straight back from the second location to its base. What is the total distance it flies, rounded to the nearest mile?
A.
550 miles
B.
1,033 miles
C.
1,583 miles
D.
1,692 miles
E.
2,210 miles
Answers
============================================
Explanation:
A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram
Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.Plot the points E and F, which are north and south of point B.Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.The diagram below shows all of this visually summarized. We have the segments
AB = 550 milesBC = 483 milesAC = x milesAnd we have these angles
Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)Angle ABC = 79 degrees (red)Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.
------------------------------
Once the diagram is set up, we'll use the law of cosines to find x.
Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.
The interior angles of triangle ABC are
A = 46 degreesB = 79 degreesC = 55 degreesThe sides opposite the angles are
a = 483 (opposite angle A)b = x (opposite angle B)c = 550 (opposite angle C)Now we can apply the law of cosines
b^2 = a^2 + c^2 - 2*a*c*cos(B)
x^2 = 483^2 + 550^2 - 2*483*550*cos(79)
x^2 = 434412.180756441
x = sqrt(434412.180756441)
x = 659.099522649229
x = 659
Side AC, or CA, is roughly 659 miles long.
------------
To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)
Distance Traveled = AB + BC + CA
Distance Traveled = 550 + 483 + 659
Distance Traveled = 1692 miles
The triangle above has the following measures.
s = 29 m
r= 63 m
Find the m/Q.
Round to the nearest tenth and include correct units.
Show all your work.
Answers
The value of m∠Q as shown in the right-angled triangle below is 62.59°.
The Formula used is:
m∠Q = cos⁻¹(s/r)........................ (1)
Where:
s = 29 m
r = 63 m
Now, Substitute these values into equation 1
m∠Q = cos⁻¹(29/63)
m∠Q = cos⁻¹(0.46)
m∠Q = 62.59°
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Look at these calculations.
1301 + 287 = ?
1499 + 287 = ?
1545 + 287 = ?
Which calculation is the odd one out? Why?
Answers
Answer:
None or 1499 + 287 I assume
Answer:
1545 + 287
odd man out
Step-by-step explanation:
-20 greater than or equal to 5w
Answers
Answer:
It depends is w is a negative or positive number
Step-by-step explanation:
5w could = 5 x 4 = 20 this is greater than -20
5w could = 5 x -4 = -20 this is equal to -20
hope this helps...
what is -7 + 3x = 8 - 2x
Answers
Answer: x = 3
Step-by-step explanation: -7 + 9 = 8 - 6
Abena wanted to buy a bag and had saved for eight consecutive weeks. She saved $2.00 im the first week,$4.00 in the second week,$6.00 in the third week,$8.00 in the fourth week,and so on until the 8th week. How much did the bag cost if her entire savings at the end of the eighth week was spent on buying the bag?
Answers
Answer: 88 dollars
Step-by-step explanation: We will follow the pattern of 2s, so 2 4 6 8 10 12 14 16 is how much she saved over the course of all 8 weeks. 2 plus 4 equals 6. 6 plus 8 equals 14. 10 plus 12 is 22. 14 plus 16 is 30. 6 plus 14 is 30 and 22 plus 36 is 58. Last of all, 58 plus 30 is 88
Add. Write your answer as a fraction in simplest form.
-4/9+-23/18
Answers
Answer:
-1 13/18
Step-by-step explanation:
There is a ratio of 9 kangaroos to 7 emus. If there are 49 emus, how many total animals are there
Answers
The total number of animals are 112 if the ratio of kangaroos to emus is 9:7 and the number of emus are 49.
What is meant by ratio?A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3).
A ratio can have any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values.
Given,
The ratio of kangaroos to emus is 9:7
And also given that the number of emus=49
Since, the ratio is 9:7
The number of kangaroos=63
63:49
9:7
Total number of animals=63+49
=112
Therefore, the total number of animals are 112 if the ratio of kangaroos to emus is 9:7 and the number of emus are 49.
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Question content area top
Part 1
A particular country has 60 total states. If the areas of all 60 states are added and the sum is divided by 60, the result is 194,473 square kilometers. Determine whether this result is a statistic or a parameter.
Question content area bottom
Part 1
Choose the correct answer below.
A.
The result is a parameter because it describes some characteristic of a sample.
B.
The result is a statistic because it describes some characteristic of a population.
C.
The result is a parameter because it describes some characteristic of a population. D.
The result is a statistic because it describes some characteristic of a sample
Answers
The result is a statistic because it describes some characteristic of a sample (the 60 states).
what is statistics?
Statistics is the study of collecting, analyzing, and interpreting numerical data to make inferences and decisions. It involves techniques such as sampling, probability, hypothesis testing, and regression analysis to extract meaningful insights from data and make informed decisions based on them.
Solution:
The result is a statistic because it describes some characteristic of a sample (the 60 states).
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solve each equation if there is no solution write no solution if every number works write all real numbers.1. 6x-16=14x+82. 9y+21=3y-53. 5n+7+3n=-8+3n 4. 6d-1=-d+ 205. 3b+8-5b= 2 (4-b)6. -11 - 2p= 6p+5 (p+3)7. 7w-3 (w+6) = 6w+ 148. 6(n+3)=2 (3n-9)9. -(3b-15)=6 (2b+5)10. h+3 (h-2)=2 (2h-3)11. 5m+6-3m-9=4 (m-3)12. 4(x-2)= 8 (x-3)- 12
Answers
1.
6x - 16 = 14x + 8
the question above can be solved by simply collecting like terms and solve for x
step 1
collect like terms by carrying 6x to the right hand side and taking 8 to the left hand side
however, note that the sign changes when they cross equality sign
\(\begin{gathered} 6x-16=14x+8 \\ \text{collect like terms} \\ -16-8=14x-6x \\ -24=8x \end{gathered}\)proceed to divide both sides by 8 to solve for x
\(\begin{gathered} 8x=-24 \\ \frac{8x}{8}=\frac{-24}{8} \\ x=-3 \end{gathered}\)2.
9y + 21 = 3y - 5
step 1
collect like terms
\(\begin{gathered} 9y+21=3y-5 \\ 9y-3y=-5+21 \\ 6y=16 \\ \end{gathered}\)step 2
divide both sides by 6
\(\begin{gathered} \frac{6y}{6}=\frac{16}{6} \\ y=\frac{8}{3} \end{gathered}\)3
5n + 7 + 3n = -8 + 3n
step 1
\(\begin{gathered} 5n+3n-3n=-8-7 \\ 5n=-15 \\ n=\frac{-15}{5} \\ n=-3 \end{gathered}\)4
6d - 1 = -d + 20
\(\begin{gathered} 6d+d=20+1 \\ 7d=21 \\ \frac{7d}{7}=\frac{21}{7} \\ d=3 \end{gathered}\)5
3b + 8 - 5b = 2(4 - b)
step 1
open the bracket on the right hand side and collect like terms
\(\begin{gathered} 3b+8-5b=8-2b \\ 8-8=-2b+5b-3b \\ 0=0 \end{gathered}\)6
-11 - 2p = 6p + 5(p + 3)
-11 - 2p = 6p + 5p + 15
\(\begin{gathered} -11-15=6p+5p+2p \\ -26=13p \\ \frac{13p}{13}=\frac{-26}{13} \\ p=-2 \end{gathered}\)10
h + 3(h - 2) = 2(2h -3)
step 1
simplify by opening the bracket
\(\begin{gathered} h+3(h-2)=2(2h-3) \\ h+3h-6=4h-6 \\ 4h-4h=-6+6 \\ 0=0 \end{gathered}\)7
7w - 3(
Drew has a job that pays $34,000 the first year with a guaranteed raise of 2% per year. How much money will Drew earn in 9 years? Round
to the nearest thousand.
In 9 years, Drew will earn $
Answers
Answer:
KONO DIO DA
Step-by-step explanation:
When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
Answers
When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.
How should you construct the first statement in a proof?When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.
It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.
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9. Use the graph of the function f(x) = x³ – 7x² + 10x to
x`
identify its relative maximum and minimum.
da
-4
8
8
2
K
T
2
da
y
8
+w
8
maximum = 4.1, minimum = -8.2
maximum = 0.9, minimum = 3.8
Answers
The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:
Relative maximum: (0.88, 4.061).Relative minimum: (3.786, -8.209).What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing, that is, where the function curves down.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing, that is, where the function curves up.More can be learned about extremas of a function at https://brainly.com/question/9839310
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Which inequality is graphed below
Answers
Answer:
wheres it at?
Step-by-step explanation:
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A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests.
The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.
First, place a point on the graph representing the solution to the system of equations. Notice that one of the equations in the system has already been graphed.
Then, determine the approximate number of guests that were children and the approximate number of guests that were adults for that day.
Answers
The approximate number of guests that were children are 172 and adults are 278
How to determine the approximate number of guests that were children and adults for that day?From the complete question, we have the following system of equations
25x + 12y = 9014
x + y = 450
Make y the subject in x + y = 450
y = 450 -x
Substitute y = 450 - x in 25x + 12y = 9014
25x + 12(450 - x) = 9014
Expand the expression
25x + 5400 - 12x = 9014
Evaluate the like terms
13x = 3614
Divide both sides by 12
x = 278
Substitute x = 278 in y = 450 -x
y = 450 - 278
Evaluate
y = 172
Hence, the approximate number of guests that were children are 172 and adults are 278
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Answer this for 5 star! Need explanation
Answers
Answer: 6
Step-by-step explanation: To solve we first start by adding like terms in our equation which is 30 + 54 = x(5+9) which becomes 84=x(14). Now we need to isolate the x variable by dividing both sides by 14.
x(14) ÷ 14 = x, 84 ÷ 14 = 6
This leaves us with the answer x = 6