The hours worked at the babysitting job is 6 hours.
The hours worked at the barber shop is 3 hours.
What are the hours worked at the babysitting job?
Given the two linear equations:
x + y = 9 equation 1
15x + 9y = 117 equation 2
Multiply equation 1 by 9
9x + 9y = 81 equation 3
Subtract equation 3 from 1
36 = 6x
x = 6
What are the hours worked at the barber shop?
Substitute for x in equation 1
6 + y = 9
y = 9 - 6
y = 3 hours
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please help, have to turn in in 30 mins
Please attach some form of question first, thank you!
A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass for the herd, the pasture must contain 18 square meters. No fencing is required along the river. What dimensions will use the least amount of fencing?
Answer:
390 m (perpendicular to river) x 780 m (parallel to river)
Step-by-step explanation:
Let y be the length of the side parallel to the river, and let x be the length of the sides perpendicular to the river.
The total area and length of fence required are given by:
Rewriting the length of fence as a function of only x:
The value of x for which the derivate of L(x) is zero is the length of x that uses the least amount of fencing:
If x = 390 m, then:
The dimensions that will use the least amount of fencing are 390 m x 780 m
Tony saw 6 birds in a tree. 1/6 of them flew away. How many were left?
Answer:
5 birds flew away
Step-by-step explanation:
1/6x6=1
( 1 bird flew away)
so, 6-1=5
Answer:
[tex]\huge\boxed{\bf\:5\:\:birds}[/tex]
Step-by-step explanation:
Number of birds Tony saw = 6Fraction that flew away = ⅙Number of birds that flew away = ?
Number of birds that flew away = Number of birds × Fraction that leftNumber of birds that flew away = 6 × ⅙Number of birds that flew away = 1Number of birds remaining = ?
Number of birds remaining = Total number of birds - Number of birds that flew awayNumber of birds remaining = 6 - 1Number of birds remaining = 5[tex]\rule{150pt}{2pt}[/tex]
A farmer ploughts his lands in 12 days if he use 5 tractors ow long will it if he uses 3 tractors?
Answer:
Step-by-step explanation:
By proportion it will be (5/3) * 12
= 60/3
= 20 days.
Fill in the missing term on each line. Simplify any fractions.
4t + 11 = 19
4t =
Subtract 11 from both sides
t =
Divide both sides by 4
Answer:
Step-by-step explanation:
4t + 11 = 19
Subtract 11 from both sides
4t = 19 - 11
4t = 8
Divide both sides by 4
t = 8/4
t = 2
Suppose you budgeted $2800 for fuel expenses for the year. How many miles could you drive if gas were $2.70 per gallon and your vehicle averaged 28 mi/gal?
Answer:
29037.036 miles
Step-by-step explanation
There are two possible ways to solve this problem.
The first option starts with the $2800 dollars for the years. You first want to divide this by $2.70, because it will give you the amount of gallons of gas you can buy with that money.
2800/2.70 = 1037.037
This means you can buy 1037.037 gallons of gas in the year. Now you need to convert this to miles by multiplying by the amount of miles per gallon.
1037.037 x 28 = 29037.036 gallons
The second way to look at this is dimensional analysis. If you have learned this, then continue on reading this, but if you haven't I might only confuse you. I only suggest this because it can make it a little easier.
For the dimensional analysis, you need to start with what you are given and move to what you need to know, so you will start with the $2800 dollars and move to gallons. $2.70 per gallon and 28 miles per gallon are your conversion factors.
Set it up like this:
[tex]2800 dollars * \frac{1 gallon}{2.70 dollars} * \frac{28 miles}{1 gallon} = 29037.036 miles[/tex]
This allows the equation to be more organized, and you can check your work by canceling the units.
Hope this helps.
The selling price for a classic speedboat is $20,000, which is $2000 less than two times its original price. What was the original price of the speedboat?
Answer:
$11,000
Step-by-step explanation:
let x = original price.
2x-2000=20000
2x=22000
x=11000
Find the mean median and range of the data 0,1,1,2,2,3,3,3,4,4,4,4,5,5,5,5,6,6,7,7,7,8,8,9,9,17
Answer:
Mean: 5.19 or 5.2
Median: 5
Range: 17
Step-by-step explanation:
Range: Q3 - Q1
0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 17
Here, we have 26 numbers
Minimum: 0
Maximum: 17
Median: 5 + 5 = 10/2 = 5
Lower quartile (Q1): 3
Upper quartile (Q3): 7
Range (biggest # - the smallest #): 17 - 0 = 17
Mean (add up all the numbers, and divide it by 26): 135/26 = 5.19 or 5.2
Hope this helps!
At the beginning of the summer,
Shay had $27 in her savings
account. Shay worked as a
lifeguard and by the end of the
summer had a total of $575 in
her savings account. How much
did Shay save over the summer?
Please help asap! :)
Answer:
x= 11.57017697
x= 41.2
x=16.50849765
Step-by-step explanation:
sin40=x/18
=> x= sin40 *18
tan x = 14/16
=> x= 41.2
cos 32 = 14/x
=> x= 14/ cos32
Probability Practice: Cass is interested in figuring out how many customers have applied for a home mortgage recently.
Review the data and calicut are the probability that if Cass runs into one of the financial institutions customers at random, that person has applied for a home mortgage this year.
What is the total number of customers?
How many customers applied for a home mortgage?
The data given relating to the probability shows that the total number of customers will be 27300.
How to calculate probability?The total number of customers will be:
= 24300 + 3000
= 27300
The number of customers that applied for a home mortgage will be:
= 2430 + 150
= 2580
In conclusion, the total number of customers will be 27300.
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(+1) + (-5) - (+5) + (+9)
Answer:
The answer is 0
Hope that helps!
Answer: Your answer is 0-
Which number is a common multiple of 3 and 4?
A) 8
B) 14
C) 32
D) 48
Answer:
LCM of 3 and 4 is 12
Step-by-step explanation:
This is your answer
Answer:
The answer is D.
Step-by-step explanation:
To find the common multiple you would divide each answer choice by both numbers & if the are whole numbers then there is your answer. If it is a number with a decimal somewhere then that is not the answer.
the functionary f is such that f(x)=7x-6 a)work out the value of f(4) b)hence, or otherwise,work out the value of f^-1(22)
Answer:
Step-by-step explanation:
a) f(4)=7(4)-6=22.
b) This is equal to 4. Since [tex]f^{-1}(x)=y \implies f(y)=x[/tex], we get that since f(4)=22, [tex]f^{-1}(22)=4[/tex].
PLS HELP ME PLSS AND SHOW HOW YOU GOT YOUR ANSWER
Answer:
Step-by-step explanation:
A student draws several cards from a deck of 10 unique cards.
Which of these statements are true?
Select all that apply.
There are 252 different ways that 5 cards can be drawn.
There are 120 different ways that 7 cards can be drawn.
There are 210 different ways that 4 cards can be drawn.
There are 240 different ways that 6 cards can be drawn.
There are 90 different ways that 8 cards can be drawn.
Answer:
There are 210 different ways that 4 cards can be drawn.
There are 252 different ways that 5 cards can be drawn.
There are 120 different ways that 7 cards can be drawn.
Step-by-step explanation:
Use the combination formula
10C4 =210
10C5 = 252
10C7 = 120
The loudness (L) of sound in decibels is related to intensity (I)measured in watts per square centimeter by the equation: L = 10log( I 10-16 ). Find the loudness of a whisper at 10-12 W/cm2. A) 35 decibels B) 40 decibels C) 45 decibels D) 50 decibels
The function L= 10 log(I/10^-16) is a logarithmic equation
The loudness of the whisper is 40 decibels
How to determine the loudness?The function of the loudness is given as:
L= 10 log(I/10^-16)
When the intensity is 10^-12, the equation becomes
L= 10 log(10^-12/10^-16)
Evaluate the quotient
L= 10 log(10^4)
Apply the rule of logarithm
L= 10 * 4
Evaluate the product
L = 40
Hence, the loudness of the whisper is 40 decibels
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In a survey of 1,372 office workers, 4.2% said that they do not make personal phone calls. Find the actual number of respondents corresponding to the given percentage.
The actual number of respondents corresponding to the given percentage is 57.
What do percentages mean?Percentage is the fraction of an amount expressed as a number out of 100. The sign used to rerepresnt percentages is %. Percentages are a measure of frequency.
What is the number of respondents?4.2% x 1372 = 57
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3x + 5
it should be equal to 65 i just need to know how to do it
Answer:
x = 20
Step-by-step explanation:
to make 3x + 5 = 65, first you can subtract 5 from 65, then divide. 60/3, which equals 20, so x = 20
Nine people were asked, "How many times have you been on an airplane?" Their responses are listed below. 6,9,1,19,1,6,8,1 find the range and the mode for the data
pleaseeee helpppp
Step-by-step explanation: Range is where you put the numbers from greatest to least, I believe you can also do least to greatest. Mode is whenever you have your numbers in order form greatest to least the number that shows up the most is the mode. HOPE THIS HELPED !!!
Betsy, a recent retiree, requires $5,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $5,000 in interest per year?
A. The amount of money invested at 13% = ___
B. The amount of money invested at 5% = ___
A. The amount of money that Betsy should invest n B-rated bonds at 13% is $20,000.
B. The amount of money that Betsy should invest in a certificate of deposit (CD) at 5% is $50,000.
How are CDs different from Bonds?Certificates of deposit (CDs) are short-term investments in financial institutions (money market) while Bonds are long-term investments in the stock exchange (capital market).
CDs pay reduced interest rates when compared to bonds'.
Data and Calculations:The amount required per year in interest = $5,000
Total investible funds = $70,000
Interest rate of B-rated bonds = 13%
Interest rate in CD = 5%
Since Betsy is not interested in realizing more than $5,000 in interest per year, she should invest $50,000 in the CD and $20,000 in the B-rated bonds.
The interest in CD = $2,500 ($50,000 x 5%)
The interest in bonds = $2,600 ($20,000 x 13%)
Total interest in CD and bonds = $5,100 ($2,500 + $2,600)
Thus, Betsy should invest $50,000 in the CD and $20,000 in the B-rated bonds.
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-1 (1 + 7x) - 6(-7 -x) = 36
Answer: x = 5
Step-by-step explanation:
If you need to solve for x,
Given:
-1 (1 + 7x) - 6(-7 -x) = 36
Distribute:
-1 - 7x + 42 + 6x = 36
Combine like terms:
- x + 41 = 36
Subtract 41 from both sides of the equation:
- x = -5
Divide both sides by -1:
x = 5
Find the exact value or type
"undefined"
tan(-315)
[?]
Answer:
the exact value of tan(-315) is 1
Answer:
The tangent of -315 is opp/adj = 1/1 = 1
Step-by-step explanation:
The angle -315 is in the 1st quadrant, in which we see a 45-45-90 triangle. Thus, this triangle has 'opposite side' = 1, 'adjacent side' = 1, and hypotenuse √2. The tangent of -315 is thus opp/adj = 1/1 = 1
please someone help me! I’m not accepting any links or files.
:)
Answer:
400
Step-by-step explanation:
48 is 12% of x
12/100 = 48/x
3/25 = 48/x
1/25 = 16/x
x = 25 × 16
x = 400
Answer: 400
Answer:
400
Step-by-step explanation:
(48 x 100) / 12 = 400
What is the value of x?
Enter your answer in the box.
X
8 2
X=
30°
452
The length οf the perpendicular is 2√2.
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It includes the study οf trigοnοmetric functiοns such as sine, cοsine, and tangent, which are used tο sοlve prοblems in fields such as engineering, physics, and navigatiοn.
Step 1:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 8√2 and the angle at the base is 30 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(30°) = p/8√2
We can simplify this expressiοn by nοting that sin(30°) = 1/2 and 8√2 = 8√(2/2) = 8√(1/√2) = 8/√2. Substituting these values, we get:
1/2 = p/(8/√2)
Simplifying further, we can multiply bοth sides by 8/√2:
4/√2 = p
Tο express the result in simplest radical fοrm, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by √2:
p = 4/√2 * √2/√2 = 4√2
Therefοre, the length οf the perpendicular is 4√2.
Step 2:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 4√2 and the angle at the base is 45 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(45°) = p/4√2
We can simplify this expressiοn by nοting that sin(45°) = √2/2 and 4√2 = 4√(2/2) = 4√(1/√2) = 4/√2. Substituting these values, we get:
√2/2 = p/(4/√2)
Simplifying further, we can multiply bοth sides by 4/√2:
2√2 = p
Therefοre, the length οf the perpendicular is 2√2.
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In drawing a circle,what instrument is used to ensure that its radius is 6 cm?
Answer:
That would be a compass.
Step-by-step explanation:
This allows you to draw circles with great accuracy.
Help help help! Lateral area means total surface area I believe!
Thanks!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:lateral \: surface \: area = \pi rl[/tex]
[tex]\qquad \sf \dashrightarrow \:la = \pi12 \times 15[/tex]
[tex]\qquad \sf \dashrightarrow \:la =180 \pi[/tex]
Therefore, the lateral surface area of cone = 180 pi in²
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The questionnnnnnnnn
Answer:
C
Step-by-step explanation:
C because 25% + 10% = 35% and 10% + 25% is also 35%
The sum of 3 times a number and 7 equals 4.
Answer: x = -1
Step-by-step explanation:
The problem is asking you the sum (+) of 3 times of a unknown number (let the unknown number be x) and 7, as in 3x + 7
According to the problem this expression is equal to 4,
3x + 7 = 4
1. Subtract 7 from both sides
3x = -3
2. Divide 3 on both sides
x = -1
Your final answer would be negative 1
Figure ABCD is a parallelogram.
Parallelogram A B C D is shown. The length of A B is 4 y minus 2, the length of B C is 2 x + 2, the length of D C is 2 y + 6, and the length of A D is 3 x minus 1.
What is the perimeter of ABCD?
14 units
38 units
44 units
49 units
Answer: 44 units
Step-by-step explanation:
Opposite sides of a parallelogram are equal, hence sides
AB = DC
4y-2 = 2y+6
2y=8
y=4
and
BC = AD
2x+2=3x-1
x=3
AB = 4Y-2
y=4
AB=14
BC=2x+2
x=3
BC=8
Perimeter = 2 X (AB + BC)
= 2 X (14+8)
= 44
Answer:
44 units
Step-by-step explanation: