Using proportions, it is found that:
The class width is of 4.8333.The lower class limits are given as follows: 1, 5.8333, 10.6667, 15.5, 20.3333, 25.1665.The upper class limits are given as follows: 5.8333, 10.6667, 15.5, 20.3333, 25.1665, 30.What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Since the classes have equal width, the width is given as follows:
class width = (max - min)/n
In which n is the number of classes.
Hence, from the data given in this problem, the class width is given as follows:
class width = (30 - 1)/6 = 4.8333.
The lowest class starts at 1, hence, adding 4.8333, we have that:
The lower class limits are given as follows: 1, 5.8333, 10.6667, 15.5, 20.3333, 25.1665
The highest class starts at 30, hence, subtracting 4.8333, we have that:
The upper class limits are given as follows: 5.8333, 10.6667, 15.5, 20.3333, 25.1665, 30.
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PLEASE HELP ASAP!! FULL DETAILED ANSWERS!!!! NO BEGGING FOR BRAINLIEST!!!!!!
The admission fee at an amusement park is $ 3.00 for children and $ 7.00 for adults. On a certain day, 297 people entered the park, and the admission fees collected totaled $ 1551 . How many children and how many adults were admitted?
There were _________________ children admitted.
There were _________________ adults admitted
Answer:
There were 132 children admitted.
There were 165 adults admitted.
Step-by-step explanation:
Given information:
Child admission fee = $3.00Adult admission fee = $7.00Total admissions = 297 peopleTotal admission fees collected = $1,551Define the variables:
Let x = number of children admitted to the park.Let y = number of adults admitted to the park.Create two equations from the given information and defined variables:
[tex]\textsf{Equation 1}: \quad x+y=297[/tex]
[tex]\textsf{Equation 2}: \quad 3x+7y=1551[/tex]
Solve the first equation for y:
[tex]\implies x+y=297[/tex]
[tex]\implies x+y-x=297-x[/tex]
[tex]\implies y=297-x[/tex]
Substitute the found expression for x into the second equation and solve for y:
[tex]\implies 3x+7y=1551[/tex]
[tex]\implies 3x+7(297-x)=1551[/tex]
[tex]\implies 3x+2079-7x=1551[/tex]
[tex]\implies 2079-4x=1551[/tex]
[tex]\implies 2079-1551-4x=1551-1551[/tex]
[tex]\implies 528-4x=0[/tex]
[tex]\implies 528-4x+4x=0 + 4x[/tex]
[tex]\implies 528= 4x[/tex]
[tex]\implies \dfrac{528}{4}= \dfrac{4x}{4}[/tex]
[tex]\implies x=132[/tex]
Substitute the found value of x into the expression for y and solve for y:
[tex]\implies y=297-x[/tex]
[tex]\implies y=297-132[/tex]
[tex]\implies y=165[/tex]
Therefore:
There were 132 children admitted.There were 165 adults admitted.Y= |x-1|-5 find points and graph
Step-by-step explanation:
(-4,0)
(0, -4)
(1, -5)
(6, 0)
Each marble bag sold by bill marble company contains 8 purple marbles for every 5 yellow marbles. If a bag has 64 purple marbles how many yellow marbles does it contain
Answer:
40 yellow marbles
Step-by-step explanation:
1. Divide 64 by 8 (Determine how many sets there are)
64/8 = 8
2. Multiply 8 by 5 (Because for every 8 purple marbles there are 5 yellow ones)
8*5 = 40
18 acres of land is for sale at $11001.
What is the cost per acre?
Answer in units of dollars/acre.
Answer:
$611.17 per acre
Step-by-step explanation:
11001 ÷ 18 = 611.16666...
So, the answer is an infinite decimal, so we round it to the nearest hundredth.
The difference of four times a number and seven is ten more than the number
The number is 5.67
Let the number be 'x'
The difference of four times a number and seven = 4x - 7
Ten more than the number = 10 + x
According to the condition given in the question,
The difference between four times a number and seven is equal to ten more than the number.
4x - 7 = 10 + x
4x - x = 10 + 7
3x = 17
x = 17/3 = 5.67
We can verify the answer,
Consider the LHS,
=> 4x - 7 = 4(5.67) - 7 = 22.68 - 7 = 15.68
Consider the RHS,
=> 10 + x = 5.67 + 10 = 15.67
Both LHS and RHS are equal.
Therefore the number that satisfies the given condition is 5.67
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Solve the following system of equations using either Gaussian elimination or a matrix. Write your answer as a point and explain how you would check your work:
By using Matrix method it denotes that the equations are consistent and have a single solution.
Matrix method, we will use the formula, [tex]X=A^{-1} B[/tex] where,
[tex]\[{\rm{X}} = \left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\][/tex]
[tex]\[{A^{ - 1}} = \frac{{adjA}}{{|A|}}\][/tex]
[tex]\[{\rm{B}} = \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right]\][/tex]
So, we will have to find [tex]A^{-1}[/tex], for that, we will first find the determinant of matrix A, that is |A|, then we will find the cofactors of matrix A, take its transpose, and that will be Adj A.
Therefore, we will be able to get the inverse of matrix A using
[tex]A^{-1}[/tex] =Adj A|A|
and hence We then substitute all the obtained values of [tex]A^{-1}[/tex] and B in the main formula and do necessary calculations to get the value of x, y and z accordingly.
Complete step-by-step answer:
It is given in the question that, we have to solve the system of equations,
2x-y+4z=33
X+2y-3z=−26
-5x−3y+5z=23
Applying the matrix approach.
Therefore, the first step is to convert the supplied equations into matrix form. Thus, it can be expressed as follows.
[tex]\[\left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\]\[[/tex][tex]= \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right][/tex]
[tex]\[|{\rm{A}}| = \left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\][/tex]
= 2(10+9) + 1(5-15) + 4(-3+10)
= 38-10+28
=56
Since we have |A|≠0.
Hence, it denotes that the equations are consistent and have a single solution.
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100000000000000000000000000000000000000000000 x 22222222222222 =
Scientific e Notation: 2.2222222e+57
Scientific Notation: 2.2222222 x 10^57
Answer:
I am pretty sure the answer is 2.2222222e+57.
find the measures of the labeled angles :)
3x =
second answer =
simplified =
please help im struggling !! this is my last question :) ill mark brainliest
Answer: 54
Step-by-step explanation:
3x=72-x ==> 3x and 72-x are both congruent angles, so they're equal
3x+x=72-x+x
4x=72
x=18
3x=
3(18)=54 degrees
Please help ASAP! Help greatly appreciated with step by step solutions
The nth terms of the arithmetic sequences;
I. Tn = 3 + √2 + ( n - 1) √2
ii. Tn = 2/ √3 + ( n - 1) 1/ √3
How to determine the nth termThe formula for the nth term of an arithmetic sequence is expressed as;
Tn = a + ( n - 1)d
Where;
Tn is the nth terma is the first term n is the number of termsd is the common differencei. a = 3 + √2
d = √2
Substitute the values, we have;
Tn = 3 + √2 + ( n - 1) √2
ii. a = 2/ √3
d = 1/ √3
Substitute the value, we have;
Tn = 2/ √3 + ( n - 1) 1/ √3
Thus, the nth terms of the arithmetic sequences are Tn = 3 + √2 + ( n - 1) √2 and Tn = 2/ √3 + ( n - 1) 1/ √3 respectively
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Four brothers have ages that are consecutive even integers. From youngest to oldest, their names are Matt, Pat, Dave, and Dan. If Dan's age is 36 years less than twice Pat's age, then what are the ages of all four brothers?
Answer:
Matt is 38, Pat is 40, Dave is 42 and Dan is 44.
Step-by-step explanation:
Let Matt's age be x.
Then Pat is x + 2, Dave is x + 4 and Dan is x + 6.
Dan's age is 36 years less than twice Pat's age:
x + 6 = 2(x + 2) - 36Solve it for x:
x + 6 = 2x + 4 - 36x + 6 = 2x - 322x - x= 6 + 32x = 38So Matt is 38, Pat is 40, Dave is 42 and Dan is 44.
A used car dealership reduced the price of a used compact car by 10%. If the price of the car before
discount was $18,500, find the discount and the new price.
The discount in price is $
Hint: Discount = Original Price x Percentage
Answer:1/1850
Step-by-step explanation: Davide 10% from 18500
Help me am I correct?
Answer: Yes
Step-by-step explanation:
All you had/have to do is 19-11 and get 8
Answer:
Yes, you're correct.
Step-by-step explanation:
Because since the bases are the same you can set the exponents equal. Then move the constant to the right hand side and it changes the sign. Then you calculate the difference. Finally you change the signs on both sides of the equation. x = 8
Aubrey has 64 m of fencingEli has 44 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 120 square meters. Solve for the dimensions (length and width) of the field. to build a four-sided fence around a rectangular plot of land. The area of the land is 255 square meters. Solve for the dimensions (length and width) of the field.
The dimensions of the rectangular field with area 120 square meters is 10 meters by 12 meters.
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given perimeter of the rectangular plot is 44 meters.
let the length is x , and width = y
Therefore perimeter = 2 (x + y)
or, 2 (x + y) = 44
or, x + y = 22
or, y = 22 - x
Now the area of the field is given as 120 square meters.
Area of the fields in terms of x is given by:
x ( 22 - x ) = 22 x - x²
Therefore 22 x - x² = 120
or, x² -22x +120 = 0
or, x² - 10x - 12x + 120 = 0
or, x (x -10) -12(x-10)=0
or, (x-10)(x-12) = 0
Now either the value of x is 10m or the value of x is 12m
Therefore the dimensions of the rectangular field is 10 meters by 12 meters.
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Louisa made a purchase at her local convenience store for $6.65. She wanted to use up her change so she used
quarters and dimes to pay the clerk. If she used a total of 29 coins, how many fewer dimes than quarters did she
use?
Louisa used Number
fewer dimes.
Answer:
25 quarters and 4 dimes. Louisa used 21 more quarters than she did dimes.
Step-by-step explanation:
q=number of quarters
d=number of dimes
6.65=.25q+.10d 6.65 (the total) is equivalent to the amount of quarters times .25 (the value of a quarter) plus the amount of dimes times .10 (the value of a dime)
Now divide 6.65 by .25.
26 quarters can be used.
26 times .25 = 6.50
26 quarters is $6.50
29-26=3
3 times .10 = .30
.30+6.50=6.80
This is too much. Let's try taking off one quarter.
Now we have 25 quarters. .25 times 25 = 6.25
29-25=4 (This means there will be 4 dimes if she used 25 quarters, but let's see)
4 times .10 = .40
.40 + 6.25=6.65
6.65 is the total amount she had to pay, so we did it. Solving this showed us that she used 25 quarters and 4 dimes. This equals $6.65, the amount she paid, uses only quarters and dimes, and uses a total of 29 coins.
I hope this helps you! Please mark as Brainliest answer! I worked really hard to type all of this out for you.
Multiply the numbers.
Answer:
[tex] \: \: \: \: \: { \rm{2 \: \: \: 3 \: \: \: 4}} \\ { \underline{ \times \: \: 0. \: \: 3 \: \: 5}} \\ { \rm{ 1 \: \: 1 \: \: 7\: \: 0}} \\ { \underline{ + 7\: \: 0\: \: 2 \: \: 0 }} \\ { \underline{ \: \boxed{ 8\: \: 1 \: .\: \: 9 \: \: 0}}}[/tex]
Answer: 81.9
In ΔXYZ, ∠Y=90° and ∠X=60°. ∠ZWY=83° and XW=1.5. Find the length of ZY to the nearest 100th.
Applying the law of sines, the length of ZY to the nearest hundredth is: 3.30 units.
How to Apply the Law of Sines?sin X/x = sin W/w = sin Z/z [according to the law of sines].
Given:
Measure of angle X = 60°
Measure of angle Z (∠XZW) = 180 - 60 - (180 - 83) = 23°
x = WZ = ?
z = XW = 1.5
Plug in the values into sin X/x = sin Z/z
sin 60/WZ = sin 23/1.5
WZ = (sin 60 × 1.5)/sin 23
WZ = 3.32
Find ZY using the sine ratio;
sin ∅ = opp/hyp = ZY/WZ
sin 83 = ZY/3.32
ZY = (sin 83)(3.32)
ZY = 3.30
Therefore, applying the law of sines, the length of ZY to the nearest hundredth is: 3.30 units.
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If the price of gas was on average $3.20 per gallon, and this was $1.43 cheaper than a year before, what is the percent of decrease in price? (Round to the nearest percent.)
Based on the current price of gas per gallon, and the fact that it was cheaper the year before, the percent decrease in price is 31%
How to find the percentage decrease?First, find the price of gas last year:
=Current price of gas + Decrease in price
= 3.20 + 1.43
= $4.63
The percent of decrease in price can be found by the formula:
= Change in gas price / Price of gas last year x 100%
= 1.43 / 4.63 x 100%
= 0.30885529157667386609071274298056 x 100%
= 31%
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The following trial balance of Reese Corp. at December 31, 2014 has been properly adjusted except for the income tax expense adjustment. Reese Corp. Trial Balance December 31, 2014 Dr. Cr. Cash $ 775,000 Accounts receivable (net) 2,695,000 Inventory 2,085,000 Property, plant, and equipment (net) 7,566,000 Accounts payable and accrued liabilities $ 1,701,000 Income taxes payable 654,000 Deferred income tax liability 85,000 Common stock 2,350,000 Additional paid-in capital 3,680,000 Retained earnings, 1/1/14 3,450,000 Net sales and other revenues 13,560,000 Costs and expenses 11,180,000 Income tax expenses 1,179,000 $25,480,000 $25,480,000 07. The current assets total is: A. $6,080,000 C. $5,405,000 B. $5,555,000 D. $4,955,000
Based on the balances in Reese Corp's trial balance, the current assets total can be found to be B. $5,555,000
What is the total current assets?The total of the current assets can be found by the formula:
= Inventory + Accounts Receivable + Cash
Solving then gives:
= 775,000 + 2,695,000 + 2,085,000
= $5,555,000
In conclusion, the current assets for Reese Corp is $5,555,000 .
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please help
please hurry
Answer:
-22 I arrived as fast as I could
For the season, a basketball player made 279 free throws out of 313 attempts. What percent is this?
Answer:
89.14%
Step-by-step explanation:
279 Out of 313 is 89.14%. Follow the below steps to calculate what percent is 279 out of 313 or how to write 279/313 as a percentage.
Step 1: Percentage Formula = Number 1/Number 2 x 100
Step 2: plugin the 279 and 313 to the percentage formula and we get 279/313 x 100 = 89.14%
Macy jogs 27 miles a month.
Part A
Explain how to use compensation to find how many miles Macy jogs in 6 months.
Part C
Which investment would you choose if you were Sam or Julia?
In two to three sentences, state your choice of investment and the reasoning for your decision using concepts you've
learned in this lesson.
Answer:
i would choose investment A
Step-by-step explanation:
A is simply the best anwser choice
Answer:
If I were Sam, I would buy the bond with a 3% interest rate since selling at any time is not a priority. The bond would provide a steady income from the investment, which is what he his needing.If I were Julia, I would invest in the stock, which has long-term growth potential. This would allow her to sell the investment at any time in the future.
Step-by-step explanation:
SAMPLE ANSWER!!!
(3x^-4)6/9x^-12 can you please solve? I’ll give brainly
The answer to this given simplification (3x^-4)6/9x^-12 is 2 x^8.
What are exponents?
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. In this essay, let's study more about exponents.
given:
(3x^-4)6/9x^-12
=x^-4 . 3 . 6 / 9 . x^-12
= 2. x^-4 / x^-12
=2 x^8
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−13,9,9,−13,5,−13,9
Calculate the value of the sample standard deviation. Round your answer to one decimal place.
Step-by-step explanation:
first we need the mean value. this is the sum of all data points divided by the number of data points :
(3×9 + 5 - 3×13)/7 = -7/7 = -1
next, for the standard deviation, we need to sum the squares of the differences of the data points to the mean value, divide that by the number of data points again, and then pull the square root :
(3(-13 - -1)² + 3(9 - -1)² + (5 - -1)²)/7 =
= (3×196 + 3×100 + 36)/7 = (588 + 300 + 36)/7 =
= 924/7 = 132
the standard deviation is now the square root of 132 :
sqrt(132) = 11.48912529... ≈ 11.5
so, yes, as we can see, the numbers vary/deviate rather strongly from the mean value.
A triangle has a perimeter of 13. If it has
sides of x/2,( x – 5), and (x - 2) lengths,
then:
a) find the value of x
b)find the length of the longest side
[tex]\stackrel{\textit{\LARGE sides}}{\cfrac{x}{2}+(x-5)+(x-2)~}~ = ~~13\implies \cfrac{x}{2}+2x-7=13 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{x}{2}+2x-7 \right)=2(13)}\implies x+4x-14=26\implies 5x-14=26 \\\\\\ 5x=40\implies x=\cfrac{40}{5}\implies \boxed{x=8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(8)}{2}\implies 4\hspace{5em}(8)-5\implies 3\hspace{5em}\underset{Longest}{(8)-2\implies 6}[/tex]
how many terms are in the sequence given of the following d=5,a1=-9 and an=141
The number of terms in the sequence with d=5 , a₁ = -9 and aₙ=141 is 31 terms.
Arithmetic Sequence
The nth term of the sequence { a , a+d , a+2d , ... , a+(n-1)d } is given by
aₙ=a+(n-1)d ...(i)
where , a = first term ,
d = common difference ,
n = number of terms ,
aₙ = nth term of the sequence .
It is given in the question that
first term (a) = -9
common difference (d) = 5
and nth term (aₙ) = 141
Substituting the values in equation (i) we get ,
141 = -9 + (n-1)5
simplifying further we get
141+9=(n-1)5
150 = 5n - 5
150+5 = 5n
155 = 5n
n=155/5
n=31.
Therefore , There are 31 terms in the sequence with d=5 , a1 = -9 and aₙ=141 .
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Input
0
1
6
Output = Input x Itself + (-5) Output
95
59
76
We are given a table for input and output values and the relation between them.
Consider the table,
Input Output = Input × itself + (-5) Output
0
1
6
95
59
76
For Input = 0 :
Output = Input × itself + (-5)
Output = 0 × 0 - 5
Output = -5
Now, for Input = 1,
Output = Input x Itself + (-5)
Output = (1) × 1 + (-5)
Output = 1 - 5
Output = - 4
For Input = 6,
Output = Input x Itself + (-5)
Output = (6) × 6 + (-5)
Output = 36 - 5
Output = 31
For Output = 95,
Output = Input x Itself + (-5)
95 = (Input)²+ (-5)
95 + 5 = (Input)²
(Input)² = 100
Input = √100
Input = 10
For Output = 59,
Output = Input x Itself + (-5)
59 = (Input)²+ (-5)
59 + 5 = (Input)²
(Input)² = 64
Input = √64
Input = 8
For Output = 76,
Output = Input x Itself + (-5)
76 = (Input)²+ (-5)
76 + 5 = (Input)²
(Input)² = 81
Input = √81
Input = 9
Therefore the complete table will be:
Input Output = Input × itself + (-5) Output
0 Output = 0 × 0 + (-5) -5
1 Output = 1 × 1 + (-5) -4
6 Output = 6 × 6 + (-5) 31
10 95 = Input × itself + (-5) 95
8 59 = Input x Itself + (-5) 59
9 76 = Input x Itself + (-5) 76
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Please help! Brainliest to whoever correct first!!! THANK YOU!
An equivalent expression for 4d⁻³/22d⁹ is: B. 2d⁻³/11d⁻⁹
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is an exponent?An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
Next, we would write the equation as a quotient:
Expression = 4d⁻³/22d⁹
Expression = 2d⁻³/11d⁹
By applying the law of indices, we have:
Expression = 2 × 1/11d(⁹ ⁻ ⁽⁻³⁾)
Expression = 2/11d¹²
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BD bisects AC at point E. if AE is 2x²- 8 and AC is 5x^2-25
find the length of EC
The length of EC will be 154 units.
We have the data that:
BD is the bisector of AC at point E.
This means that AE = EC
Also, AE + EC = AC
AE + AE = AC
2 AE = AC
Now,
AE = 2x² - 8 and AC is 5x² - 25
Substituting the values, we get that:
2 (2x² - 8) = 5x² - 25
4x² - 16 = 5x² - 25
5 x² - 4 x² = 25 - 16
x² = 9
x = 3 ( as length cannot be negative)
AE = EC = 2x² - 8
EC = 2 (9)² - 8
EC = 162 - 8
EC = 154 units.
Therefore, we get that, the length of EC will be 154 units.
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3x^2+7-6+1+3+7 add , sub, mult, what is the answer
Answer:
If just combining like terms: 3x^2 + 12
If solving for x: 2i, -2i
Step-by-step explanation: Combine like terms, so 3x^2 + 12 = 0; move the 12 to the other side by subtracting (3x^2 = -12), then divide both sides by 3, which gives x^2 = -4. Then get the square root of both sides to cancel out the power on the x. Since -4 is negative, use imaginary numbers, which makes x = 2i and x = -2i
