Show solutions please
Answer:
1. Their ages are:
Steve's age = 18
Anne's age = 8
2. Their ages are:
Max's age = 17
Bert's age = 11
3. Their ages are:
Sury's age = 19
Billy's age = 9
4. Their ages are:
The man's age = 30
His son's age = 10
Step-by-step explanation:
1. We make the assumption that:
S = Steve's age
A = Anne's age
In four years, we are going to have:
S + 4 = (A + 4)2 - 2 = 2A + 8 - 2
S + 4 = 2A + 6 .................. (1)
Three years ago, we had:
S - 3 = (A - 3)3
S - 3 = 3A - 9
S = 3A - 9 + 3
S = 3A – 6 …………. (2)
Substitute S from (2) into (1) and solve for A, we have:
3A – 6 + 4 = 2A + 6
3A – 2A = 6 + 6 – 4
A = 8
Substitute A = 8 into (3), we have:
S = (3 * 8) – 6 = 24 – 6
S = 18
Therefore, we have:
Steve's age = 18
Anne's age = 8.
2. We make the assumption that:
M = Max's age
B = Bert's age
Five years ago, we had:
M - 5 = (B - 5)2
M - 5 = 2B - 10 .......................... (3)
A year from now, it will be:
(M + 1) + (B + 1) = 30
M + 1 + B + 1 = 30
M + B + 2 = 30
M = 30 – 2 – B
M = 28 – B …………………… (4)
Substitute M from (4) into (3) and solve for B, we have:
28 – B – 5 = 2B – 10
28 – 5 + 10 = 2B + B
33 = 3B
B = 33 / 3
B = 11
If we substitute B = 11 into equation (4), we will have:
M = 28 – 11
M = 17
Therefore, their ages are:
Max's age = 17
Bert's age = 11.
3. We make the assumption that:
S = Sury's age
B = Billy's age
Now, we have:
S = B + 10 ................................ (5)
Next year, it will be:
S + 1 = (B + 1)2
S + 1 = 2B + 2 .......................... (6)
Substituting S from equation (5) into equation (6) and solve for B, we will have:
B + 10 + 1 = 2B + 2
10 + 1 – 2 = 2B – B
B = 9
Substituting B = 9 into equation (5), we have:
S = 9 + 10
S = 19
Therefore, their ages are:
Sury's age = 19
Billy's age = 9.
4. We make the assumption that:
M = The man's age
S = His son's age
Therefore, now, we have:
M = 3S ................................... (7)
Five years ago, we had:
M - 5 = (S - 5)5
M - 5 = 5S - 25 ................ (8)
Substituting M = 3S from (7) into (8) and solve for S, we have:
3S - 5 = 5S – 25
3S – 5S = - 25 + 5
-2S = - 20
S = -20 / -2
S = 10
Substituting S = 10 into equation (7), we have:
M = 3 * 10 = 30
Therefore, their ages are:
The man's age = 30
His son's age = 10
The slope of a line perpendicular to y = 2x + 1 is -2.
False
True
Answer:
incorrect.
Step-by-step explanation:
the slope of the line perpendicular is the negative reciprocal, which in this case is -1/2
Answer:
False
Step-by-step explanation:
To find the slope of a perpendicular, flip the slope and change the sign.
The slope pf the given line is 2.
The slope of a line perpendicular to y = 2x + 1 is -1/2.
Answer: False
A professor at a university wants to estimate the average number of hours of sleep the students get during exam week. The professor wants to find a sample mean that is within 4.266 hours of the true average for all college students at the university with 99% conconfidence. If the professor knows the standard deviation of the sleep times for all college students is 2.539, what sample size will need to be taken
Answer:
The sample size is [tex]n = 2[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is E =4.266
The standard deviation is [tex]\sigma = 2.539[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
=> [tex]n = [\frac{2.58 * 2.539 }{4.266} ] ^2[/tex]
=> [tex]n = 2[/tex]
please help me!!!!!!! asap
Marsha has 3 rugs. the first rug is 2 meters 87 centimeters long. the second rug has a length 98 centimeters less than the the first. the third rug is 111 centimeters longer than the second rug. what is the difference in centimeters between the length of the first rug and the third?
Answer:
13 cm
Step-by-step explanation:
rug 1= 2.87 meters or 287 cm
rug 2= 287-98 or 189 cm
rug 3= 189+111 or 300 cm or 3m
300-287=13cm or 0.13m
Graph the equation .
y = 4x + 1
Answer:
-Picture attached-
Step-by-step explanation:
The gradient would be 4, with a rising graph and the y-intercept would be 1. I attached a picture of the graph, hope it helps.
-3/5a=2
a= ___ please help
Answer:
a=-3 1/3
Step-by-step explanation:
Jill paid a sales tax of $1.40 when she bought a vest.What was the price of the vest not including the tax?
Answer:
Price of tne Vest + $40 - 1.40 = $38.6
Step-by-step explanation:
3.5% * n = $1.40
0.035 * n = $1.40
0.035/0.035 * n = $1.40/0.035
n = $40
The price of the vest not including the tax is, $40
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Since, Tax is a sum levied by the government or an agency of the government on goods and services. taxes increases the price of products
Now,
Let p = price of a vest
Hence, from the question, this equation can be formed,
⇒ 35% of p = $1.40
⇒ 0.035 x p = $1.4
divide both sides of the equation by 0.035;
⇒ p = $40
Thus, The price of the vest not including the tax is, $40
Learn more about the percent visit:
https://brainly.com/question/24877689
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Complete question is this;
Jill paid a sales tax of $1.40 when she bought a vest. What was price of vest not including tax? Sales tax = 3.5%
What is the common ratio between successive terms in the sequence? 27,9,3,1, 1/3, 1/9, 1/27
Answer:
not sure if this is correct but is it 3??
Step-by-step explanation:
If there are 4 quarts in a gallon and 2 pints in a quart, how many pints are in 6 gallons?
Answer:
48 pints
Step-by-step explanation:
please help me im very behind
Answer:
y=1/3x-2
Remeber the slope intecpet form is y=mx+b
Hope this helps :)
Step-by-step explanation:
PLZ MARK ME BRAINIIEST THANK YOU
Please help me find out if there congruent
Chanel rolls a 6-sided die {1,2,3,4,5,6), and then flips a coin {H,T}
Which outcome is in the sample space of this experiment?
A.5H
B. T3
C. 24
D.TH
Answer:
5H
Step-by-step explanation:
Given
A roll of die followed by a flip of coin.
Required
Determine possible outcome in the sample space
Taking the experiment one at a time.
A roll of die will either give any of 1 to 6 as its outcome.
A flip of coin will either give any of H or T as its outcome.
So, the possible outcomes of a roll of die followed by a flip of coin is:
{1H,2H,3H,4H,5H,6H,1T,2T,3T,4T,5T,6T}
Note that numbers came first because the question stated that the die is rolled first.
Comparing the list of given options with the sample space above.
Option (A) i.e. 5H answers the question.
Chuck made $13.90 per hour, gets a 12% raise, and works 40 hours per week.
Answer:
40 times 9 equals 299
Step-by-step explanation:
Sean has a beginning balance of $328.15 in his account. He writes checks for the following amounts: $20.75, $43.58, $30.45, and $29.72. What is the new balance in Sean’s account?
Answer:
20.75+43.58+30.45+29.72= 124.5
328.15-124.5=
203.65.Answer:
198
Step-by-step explanation:
whats 93, −76, 102, −101, 83, −48 least to greatest
Answer:
it iss -101, -76, -48, 83, 93
Answer:
-101, -76, -48, 83 ,93, 102
I’ll make you brainliest:Which shows the equation 12x + 4y = 480
in general form?
Answer:
y = -3x + 120
Step-by-step explanation:
Hope this helps!
The price of a 40-inch television is $268 plus 8% sales tax rate. What is the amount of the sales tax for the television, in dollars and cents?
If 14 gallon of paint covers 112 of a wall, then how many quarts of paint are needed for the entire wall?
Answer:
168 gallons
Step-by-step explanation:
Correct question;
If 14 gallon of paint covers 1/12 of a wall, then how many quarts of paint are needed for the entire wall?
If 14 gallon of paint covers 112 of a wall, this can be expressed as;
14 gallons = 1/12 of the wall
x gallons = entire wall (1 wall)
Cross multiply
1/12 * x = 14
x/12 = 14
Multiply both sides by 12
x/12 * 12 = 14*12
x = 168 gallons
Hence 168galons of paints are needed for the entire wall
LGS 2.5.052.MI.
A fax machine that regularly sells for $227.88 is on sale for
off the regular price. Find the sale price.
$
Answer:
I’m sorry but I can’t see how much it’s on sale for so just tell me and I’ll answer.
Step-by-step explanation:
The equation of the line that has a slope of 3 and passes through the point (2, 1) is y = 3x - 5.
True
ОО
False
Answer:
True
Step-by-step explanation:
y = 3x - 5 does have slope 3.
Let's test point (2, 1).
y = 3x - 5
1 = 3(2) - 5
1 = 6 - 5
1 = 1
Point (2, 1) does work in the equation.
Answer: True
Please help me with the attachment below, will give brainlest
Answer:
D.
Step-by-step explanation:
9+x=12 Can you guys please tell me the answer
Answer:
X=3
Step-by-step explanation:
9+x=12
x=12-9
so x is 3
Answer:
3
Step-by-step explanation:
Let's go through this together.
Step 1) Rearrange Terms (Optional)
9 + x = 12
x + 9 =12
Step 2) Subtract 9 from both sides of the equation
x + 9 = 12
-9 -9
Step 3) Simplify
If we subtract 9 on both sides, we end up with:
x + 0 = 3
Since 0 no longer has any part in the equation, we can conclude that:
x = 3
How do I turn 93.75 into a fraction? :)
Answer:
Say it out loud like 93/and 75 hundrenths you count the denominators place and since it has two you say hundrenths.
Answer:
93 3/4
Step-by-step explanation:
93.75 = 93.75/1
93.75/1 × 100/100 = 9375/100
9375 ÷ 25 / 100 ÷ 25 = 37/54
93 3/4
93.75 = 93 3/4
Consider the line y=5x-3.
Find the equation of the line that is parallel to this line and passes through the point (2, -5).
Find the equation of the line that is perpendicular to this line and passes through the point (2, -5).
Answer:
y=5x-15, y=-1/5x-23/5
Step-by-step explanation:
Parallel lines have the same slope, so we know the line that is parallel to y=5x-3 must have slope 5.
We now have y=5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=5x+b
-5=5(2)+b
-5=10+b
b=-15
So the equation of the parallel line is y=5x-15.
Perpendicular lines must have slopes that multiply to -1, so we know the line perpendicular to y=5x-3 must have slope -1/5.
We now have y=-1/5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=-1/5x+b
-5=-1/5(2)+b
-5=-2/5+b
b=-23/5
So the equation of the perpendicular line is y=-1/5x-23/5.
Solve: with full workings
(32/243)^-4/5
Answer:
[tex](\frac{32}{243})^{-\frac{4}{5}}=39.0625[/tex]
Step-by-step explanation:
Given
[tex](\frac{32}{243})^{-\frac{4}{5}}[/tex]
Required
Solve
[tex](\frac{32}{243})^{-\frac{4}{5}}[/tex]
Express 32 as 2^5 and 243 as 3^5
[tex](\frac{2^5}{3^5})^{-\frac{4}{5}}[/tex]
The exponent can be expressed as 1\5 * -4
So we have:
[tex](\frac{2^5}{3^5})^{\frac{1}{5} * -4}[/tex]
Apply law of indices:
[tex](\frac{2^{5*1/5}}{5^{5*1/5}})^{-4}[/tex]
[tex](\frac{2}{5})^{-4}[/tex]
In indices:
[tex](\frac{a}{b})^{-c} = (\frac{b}{a})^{c}[/tex]
So, the expression becomes
[tex](\frac{5}{2})^{4}[/tex]
[tex](\frac{5^{4}}{2^{4}})[/tex]
[tex]\frac{625}{16}[/tex]
[tex]39.0625[/tex]
Hence:
[tex](\frac{32}{243})^{-\frac{4}{5}}=39.0625[/tex]
PLEASE HELP ME FAST!
Which graph represents y=⌈x⌉ over the domain −4≤x≤−1 ?
Answer:
4th one
Step-by-step explanation:
Please helppp!
Solve the system using elimination
-5x+5y=5
5x-4y=-4
A. (1,0)
B. (0,1)
C. (-1,1)
D. (1,-1)
Answer:
a
Step-by-step explanation:
look i need the answer quick
Answer:
Step-by-step explanation:
division