Answer:
Julie worked 18 hours at Job A and 17 hours at Job B.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Rate per hour at Job A = US$ 6.10
Rate per hour at Job B = US$$ 7.40
Hours at Job A = x
Hours at Job B = 35 - x
Total of hours worked by Julie = 35 hours
Total weekly earnings = US$ 235.60
2. How many hours did she work at each job the week that she made $235.60?
For finding the result, we will use the following formula:
6.10x + 7.4 (35 - x) = 235.60
6.10x + 259 - 7.4x = 235.60
-1.3x = 235.60 - 259 (Subtracting 259 to both sides)
-1.3x = - 23.40
x = -23.4/-1.3 (Dividing by -1.3)
x = 18
Julie worked 18 hours at Job A, so she worked 17 (35 - 18) hours at Job B.
3. Proof that x = 18 is correct.
6.10x + 7.4 (35 - x) = 235.60
6.10 (18) + 7.4 (35 - 18) = 235.60
109.80 + 125.80 = 235.60
235.60 = 235.60
It's proven that x = 18 is correct.
Answer:
Step-by-step explanation:
Let x represent the number of hours worked at Job A and 35-x represent the number of hours worked at Job B.
($6.10 × x) +$7.40 × (35-x) =$235.60
Solving for x
$6.10x + $259 - $7.40x = $235.60
Collect like terms and solve for x
$6.10x-$7.40x=$235.60-$259
-$1.3x=-$23.4
x=18hours for Job A while 35-x=17hours for Job B
I have 3 questions please help me
1) -6(3-6r)= -18+4r
2) -8x-14=7(-2-4x)+4x
3) 5-(8v+5)=-4(1+3v)
4) 3(a-6)= -5a-(7+3a)
Please help me and number it so i don't get confused thank you
Answer:
Please give brainliest :((
1. r = 0
2. x = 0
3. v = -1
4. a = 1
Step-by-step explanation:
1. -18 + 36r = -18 + 4r
-18 + 32r = -18
32r = 0
r = 0
2. -8x - 14 = -14 - 28x + 4x
-8x - 14 = -14 - 24x
16x -14 = -14
16x = 0
x = 0
3. 5 -8v - 5 = -4 - 12v
-8v = -4 - 12v
4v = -4
v = -1
4. 3a - 18 = -5a - 7 - 3a
3a - 18 = -8a - 7
11a = 11
a = 1
Which point is a solution to the linear inequality y < Negative one-halfx + 2?
Answer:
The solution in the attached figure
see the explanation
Step-by-step explanation:
we have
[tex]y < -\frac{1}{2}x+2[/tex]
The solution of the inequality is the shaded area below the dashed line
[tex]y=-\frac{1}{2}x+2[/tex]
The slope of the dashed line is negative [tex]m=-\frac{1}{2}[/tex]
The y-intercept of the dashed line is the point (0,2)
The x-intercept of the dashed line is the point (4,0)
using a graphing tool
The solution in the attached figure
Remember that
Any point that lie on the shaded area is a solution of the inequality and if a point is a solution of the linear inequality, then the point must satisfy the inequality
Answer:
Your answer choices are:
(2, 3)
(2, 1)
(3, –2)
(–1, 3)
Step-by-step explanation:
YOUR ANSWER IS
(3, -2)
I hope this helps!
Plz help 10points Quick
Answer:
First one
Step-by-step explanation:
explain the answer because im stuck
Answer:
The Proof is given below.
Step-by-step explanation:
Given:
[tex]\overline{HF}[/tex] bisect ∠ EHG.i.e
∴ ∠EHF ≅ ∠ GHF
[tex]\overline{EH} \cong \overline{GH}[/tex]
To Prove:
[tex]\overline{EF} \cong \overline{GF}[/tex]
Proof:
In Δ EHF and Δ GHF
EH ≅ GH ………............{Given}
∠ EHF ≅ ∠ GHF …………..{EF bisect ∠ EHG as given above}
HF ≅ HF ………............{Reflexive Property}
Δ EHF ≅ Δ GHF …................{ By Side-Angle-Side test}
∴ EF ≅ GF........{corresponding parts of congruent triangles (c.p.c.t).}
[tex]\overline{EF} \cong \overline{GF}[/tex] ....... PROVED
Evaluate n2+5 when n=3.
Final answer:
To find the value of n² + 5 when n = 3, you substitute 3 for n in the expression to get 3² + 5, which simplifies to 9 + 5, resulting in a final value of 14.
Explanation:
To evaluate the expression n² + 5 when n = 3, we simply substitute the value of n into the expression
1. Substitute 3 for n: (3)² + 5
2. Calculate the square of 3: 3² = 9
3. Add 5 to the result: 9 + 5 = 14
Therefore, the evaluated expression n² + 5 when n = 3 is equal to 14.
What connection may be drawn between the graphs of sin and cos and the signs of both functions relating to the 4 quadrants?
Sin is negative where as cos is positive in the 4th quadrant.
Step-by-step explanation:
Sin, cos and tan are all positive in the 1st quadrant. Sin is only positive in the 2nd quadrant. Tan is only positive in the 3rd quadrant.Cos is only positive in the 4th quadrant.
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The graphs of sin and cos, while similar in shape and period, are shifted horizontally due to their phase difference. This directly affects their signs in different quadrants, revealing their interconnected nature and dependence on the unit circle representation.
Similarities in Graphs:
Shape: Both sine and cosine graphs share the same sinusoidal wave pattern, meaning they oscillate up and down between their maximum and minimum values.
Period: Both functions have the same period of 2π radians or 360 degrees, meaning they complete one full cycle within this interval.
Amplitude: Both have an amplitude of 1, meaning they oscillate between -1 and 1 on the y-axis.
Shift and Relationship between Signs:
Phase Shift: The cosine graph is essentially the sine graph shifted to the left by π/2 radians (or 90 degrees). This explains why their peaks and troughs don't coincide perfectly.
Signs in Quadrants: This phase shift plays a crucial role in determining the signs of sin and cos in different quadrants:
Quadrant I (0° to 90°): Both sin and cos are positive as they increase in value.
Quadrant II (90° to 180°): Sin remains positive as it continues increasing, but cos becomes negative as it decreases.
Quadrant III (180° to 270°): Both sin and cos are negative as they decrease in value.
Quadrant IV (270° to 360°): Sin becomes positive as it increases, but cos remains negative as it continues decreasing.
Underlying Connection:
These relationships can be further explained by their definitions based on the unit circle:
Sine: sin(θ) represents the y-coordinate of a point on the unit circle when the angle θ is measured from the positive x-axis counterclockwise.
Cosine: cos(θ) represents the x-coordinate of the same point.
Therefore, as θ moves around the circle, the signs of sin and cos change based on their positions relative to the axes.
A triangular pyramid with a base area of 15 square inches is congruent to the base area of a hexagonal pyramid. Both pyramids have a height of 5. How do the volumes compare of the two solids? The hexagonal pyramid has a greater volume. The triangular pyramid has a greater volume. The hexagonal pyramid is 5 times the size of the triangular pyramid. The two pyramids have the same volume.
Answer:
The two pyramids have the same volume.
Step-by-step explanation:
What determines the volume of a pyramid is the Base Area, and its height. Since in these two figures, both bases measure the same (congruent) and their respective heights are equal. Then when we compare the volumes of these two solids, the triangular and the Hexagonal pyramid have the same volume, as it follows:
Then:
[tex]\\V=\frac{1}{3}*B*h\\V_{\bigtriangleup \: Triangular\: base}=\frac{1}{3}*15*5\Rightarrow V_{\bigtriangleup \: pyramid}=15 \:in^{3}\\V_{\bigtriangleup \: hexagonal \:base}=\frac{1}{3}*15*5\Rightarrow V_{\bigtriangleup \: hexagonal \:base}=15 \:in^{3}[/tex]
However, each surface area measure differently.
You are making juice from concentrate. The directions on the packaging say to mix
I can of juice with 3 cans of water. A can is 12 fluid ounces.
Answer:
25 can.
Step-by-step explanation:
Here is the complete question: You are making juice from concentrate. The directions on the packaging say to mix 1 can of juice with 3 cans of water to make orange juice. How many 12 fluid ounces cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
Given: Ratio to make juice with concentrate:water is 1:3.
As required we need to prepare 200 6 ounce serving of Orange juice.
∴ [tex]200\times 6= 1200\ ounce[/tex]
Let there be x ounce of concentrate and 3x ounce of water to make 1200 ounce of orange juice.
Now, [tex]x+3x= 1200[/tex]
∴ x= 300 ounce
Next, lets find out how many cans of 12 ounce is required.
[tex]\frac{300}{12} = 25\ cans[/tex]
∴ 25 cans is required to make 1200 ounce of orange juice.
Find the inequality represented by the graph.
Answer:
f(x)<=-1/3x+1
Step-by-step explanation:
so to test this you can do
0<=-1/3(0)+1
0<=1
so it's true
Answer:
y [tex]\leq[/tex] [tex]\frac{-1}{3}x[/tex] + 1
Step-by-step explanation:
To find the inequality represented by the graph, we need to find the linear equation that represents the blue line.
As we can see, the:
y intercept: (0, 1)
x intercept: (3, 0)
So the slope of the equation is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
= [tex]\frac{0-1}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex]
So use the slope and the slope-point formula, we find the linear expression
The standard form is: y = mx+ b
<=> y = [tex]\frac{-1}{3}[/tex] x + b
Substitute the point (0, 1) to find b, we have:
b= y - [tex]\frac{-1}{3}[/tex] x
<=> b= 1 - 0 =1
So the linear equation is: y = [tex]\frac{-1}{3}[/tex] x + 1
After that, we need to take a test point form the shaded area and evaluate the expression. Let the point be: (1, 2), we have:
2 = [tex]\frac{-1}{3} *1[/tex] +1
<=> 2=[tex]\frac{2}{3}[/tex]
We know that 2 > [tex]\frac{-1}{3}[/tex] this means that the left inequality sign is ≥ , so the inequality represented by the graph:
y [tex]\leq[/tex] [tex]\frac{-1}{3}x[/tex] + 1
Can anybody do this sat problem for me? Show your work. (Extra points offered)
Answer:
B) -3Step-by-step explanation:
[tex](4x+4)(ax-1)-x^2+4\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(4x)(ax)+(4x)(-1)+(4)(ax)+(4)(-1)-x^2+4\\\\=4ax^2-4x+4ax-4-x^2+4\qquad\text{combine like terms}\\\\=(4a-1)x^2+(-4+4a)x+(-4+4)\\\\=(4a-1)x^2+(4a-4)x\\\\\text{Given expression is equvalent to}\ bx.[/tex]
[tex](4a-1)x^2+(4a-4)x=bx\\\\(4a-1)x^2+(4a-4)x=0x^2+bx\\\\\text{Therefore}\\\\4a-1=0\ \text{and}\ 4a-4=b\\\\4a-1=0\qquad\text{add 1 to both sides}\\\\4a=1\qquad\text{divide both sides by 4}\\\\a=\dfrac{1}{4}\\\\\text{Substitute to the second equation and solve for}\ b:\\\\4\left(\dfrac{1}{4}\right)-4=b\\\\1-4=b\\\\-3=b\to b=-3[/tex]
5 1/3 + x = 2 1/2. Use least common denominator or easiest common denominator. Please work out
Answer:
The answer is x = -17/6.
Step-by-step explanation:
Given:
5 1/3 + x = 2 1/2 . Using least common denominator.
Now, to solve the equation:
[tex]5\frac{1}{3}+x=2\frac{1}{2}[/tex]
[tex]=\frac{16}{3} +x=\frac{5}{2}[/tex]
Subtracting both sides from 16/3 we get:
[tex]x=\frac{5}{2}- \frac{16}{3}[/tex]
Now, the least common denominator of 2 and 3 is 6.
So, we using this we calculate:
[tex]x=\frac{5\times 3-16\times 2}{6}[/tex]
[tex]x=\frac{15-32}{6}[/tex]
[tex]x=\frac{-17}{6}[/tex]
Therefore, the answer is x = -17/6.
The value of the expression 4 square root of 81^3 is ______.
Choices:
9
27
350
1.4
2.3
Answer:
If its written as the fourth root of (81^3) the answer is 27.
Some numbers can be written as powers of different
bases. For example, 81 = 92 and 81 = 34. Write the number 64 using thr
different bases.
The number 64 can be expressed in the form of base powers as 64=8^2, 64=4^3, and 64=2^6.
Explanation:The number 64 can be expressed as powers of different bases in several ways. The most common notations are as follows: 64 = 8^2, which means that 8 multiplied by itself results in 64. 64 = 4^3, which means 4 multiplied by itself three times equals to 64, and finally, 64 = 2^6, where 2 is multiplied by itself six times to produce 64. Each of these forms express the number 64 in a different base.
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I need help with 5 on the second part.
ammie pays $30 for a bag that she buys at a discount of 50%. What is the price of the bag without the discount? A. $30 B. $45 C. $60 D. $80
This would be C. 60$
This is because if she got the bag for 50% off, 30 divided by 2 is 15$, 45 divided by 2 is 22.5, 60 divided by 2 is 30$ so option C. Would be your answer.
A car's speedometer has a percent error of 5%. The speedometer currently shows that the car is traveling at a speed of 60 mph.
Which statement describes what the actual speed of the car could be?
The actual speed of the car is either 30 mph or 90 mph.
The actual speed of the car is either 55 mph or 65 mph.
The actual speed of the car is either 57 mph or 63 mph.
The actual speed of the car is either 58 mph or 62 mph.
Answer:
The actual speed of the car is either 57 mph or 63 mph
Step-by-step explanation:
Given as :
The measured speed o the car = 60 mph
The percentage error in speedometer = 5 %
Let The actual speed of car = x mph
Now, percentage error = [tex]\dfrac{\textrm actual value - \textrm measured value}{\textrm measured value}[/tex] × 100
So, [tex]\frac{5}{100}[/tex] = [tex]\frac{x - 60}{60}[/tex]
or, [tex]\frac{5}{100}[/tex] × 60 = x - 60
Or, 3 = x - 60
∴ x = 63 mph
Hence The actual speed of the car is either 57 mph or 63 mph . Answer
The correct statement describing the actual speed of the car is: The actual speed of the car is either 57 mph or 63 mph.
To understand why this is the correct answer, let's calculate the range of possible actual speeds given the percent error of the speedometer.
The speedometer shows a speed of 60 mph with a percent error of 5%. The percent error formula is given by:
[tex]\[ \text{Percent Error} = \left( \frac{\text{Error}}{\text{True Value}} \right) \times 100\% \][/tex]
Here, the true value is the actual speed of the car, and the error is the difference between the measured speed (60 mph) and the true value. We can rearrange the formula to solve for the true value:
[tex]\[ \text{True Value} = \frac{\text{Measured Value}}{1 \pm \text{Percent Error}} \][/tex]
Since the percent error is 5%, we have:
[tex]\[ \text{True Value} = \frac{60 \text{ mph}}{1 \pm 0.05} \][/tex]
Now, we calculate the true value for both the lower and upper bounds of the speedometer reading:
For the lower bound (actual speed could be less than the measured speed):
[tex]\[ \text{True Value}_{\text{lower}} = \frac{60 \text{ mph}}{1 + 0.05} = \frac{60 \text{ mph}}{1.05} \approx 57.14 \text{ mph} \][/tex]
For the upper bound (actual speed could be more than the measured speed):
[tex]\[ \text{True Value}_{\text{upper}} = \frac{60 \text{ mph}}{1 - 0.05} = \frac{60 \text{ mph}}{0.95} \approx 63.16 \text{ mph} \][/tex]
Rounding these values to the nearest whole number, we get:
[tex]\[ \text{True Value}_{\text{lower}} \approx 57 \text{ mph} \][/tex]
[tex]\[ \text{True Value}_{\text{upper}} \approx 63 \text{ mph} \][/tex]
Therefore, the actual speed of the car could be either 57 mph or 63 mph, which corresponds to the third option provided in the question.
The cost of our tent rental is $160 for five days at this rate how much does it cost to rent the tent for one day
Answer:
32 Dollars
Step-by-step explanation:
160 divided by 5 equals 32
a teacher is shouting she shuts the door she shuts the windows but forgets to shut something what is it? i know but do you know
Answer:
Her mouth
right ?!
that was not hilarious but okey
Answer:
She forgot to shut her dum dum bubble gum chromosome flip phone no home smash mouth up.
Step-by-step explanation:
Madison says that 579 . 8 × 0 . 001 is the same as 579 . 8 ÷ 10 3 . Is she correct? Explain your answer. 01
Answer:
It is the same answer.
Step-by-step explanation:
579.8 X 0.001= 0.5798
579.8/10^3 (or 1000)=0.5798
If you use a calculator it's easy.
Hope this helped. :D
Following are the calculation to the given expression:
Given:
[tex]\bold{579.8 \times 0.001= 579.8 \div 10^3}[/tex]
To find:
Prove=?
Solution:
[tex]\to \bold{579.8 \times 0.001= 579.8 \div 10^3}[/tex]
Solve L.H.S part:
[tex]\to \bold{579.8 \times 0.001}\\\\\to \bold{0.5798}[/tex]
Solve R.H.S part:
[tex]\to \bold{ 579.8 \div 10^3}\\\\\to \bold{ \frac{579.8}{ 10^3}}\\\\\to \bold{ \frac{579.8}{ 1000}}\\\\\to \bold{ 0.5798}\\[/tex]
Therefore, the L.H.S= R.H.S, so, the answer is the same.
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Gabrielle is 6 years older than Mikhail. The sum of their ages is 64. What is Mikhail's age?
Answer:
59
Step-by-step explanation:
gabrielle is 6 years older than mikhail and gabrielle's age is 64 soooo therefore 64 minus 6 is 59yo
2/3x-7=11
Solve
What is the answer
Answer: 27
Step-by-step explanation:
2/3x-7=11
2/3x=18
1/3x=9
x=27
Essential: Solve the proportions
step by step
Answer:
The value of r=[tex]\frac{-106}{47}[/tex]
The value of x=[tex]\frac{83}{32}[/tex]
Step-by-step explanation:
Given that,
A) [tex]\frac{2r-2}{7r+10} = \frac{9}{8}[/tex]
Now,
[tex]\frac{2r-2}{7r+10} = \frac{9}{8}[/tex]
8(2r-2)=9(7r+10)
16r-16=63r+90
-16-90=63r-16r
-(16+90)=47r
-106=47r
r=[tex]\frac{-106}{47}[/tex]
B) [tex]\frac{x+4}{9} = \frac{3(x-2)-1}{5}[/tex]
Now,
[tex]\frac{x+4}{9} = \frac{3(x-2)-1}{5}[/tex]
5(x+5)=9[3(x-2)-1]
5x+25=9[3x-6-1]
5x+25=9[3x-7]
5x+25=27x-63
25+63=27x+5x
83=32x
x=[tex]\frac{83}{32}[/tex]
Whats 2+2 equal? I need help.
Answer:
The answer is four.
Step-by-step explanation:
II + II= IIII
Answer:
the answer is 4
Step-by-step explanation:
if you have 2 candy bars and are given 2 more you will get 4
A clothes dryer having a wattage of 5000 watts is used for 25 hours each month. How many kilowatt hours of electricity does the dryer use in a months time?
Answer:20000
Step-by-step explanation:
30+1000+4000
Nathan is stocking bathrooms At The hotel Where he works.He has 18 rolls of toilet paper and 9 bars of soap.If he wants all the bathrooms to be stocked identically,With the same combination of supplies and each one and nothing left over,What is the greatest combination of bathrooms Nathan can stock?
Answer:
9 bathrooms
Step-by-step explanation:
9 is their greatest common factor.
give each bathroom 1 bar of soap and 2 toilet paper rolls
Step-by-step explanation:
Since has 9 bars of some and 18 rolls of paper then he can fully stock nine because there are more rolls then bars
a grocery store sells a bag of 4 lemons for $0.79. Which pricing option would result in the same unit price for each lemon
To find a pricing option with the same unit price as 4 lemons for $0.79, we calculated the unit price per lemon as $0.1975. None of the provided pricing options match this unit price, as they are all significantly higher.
We need to determine the equivalent unit price per lemon to match the store's offer of 4 lemons for $0.79. First, we calculate the unit price for one lemon by dividing the total price of the bag by the number of lemons. So, $0.79 divided by 4 gives us a unit price of $0.1975 per lemon.
Now, let's use this unit price to check which pricing option results in the same unit price. We must find a scenario where each lemon costs $0.1975.
An access fee of $4 and a per-unit price of $4 with 2 units bought would have a unit price of $4, which is too high.
An access fee of $9 and a per-unit price of $4 with 3 units bought would also have a unit price of $4, again too high.
An access fee of $24 and a per-unit price of $3 with 4 units bought would have a unit price of $3, which is also higher than $0.1975.
For the bundle size of 4 units with a bundle price of $36, we would have a unit price of $9 ($36 divided by 4), which is much higher.
The scenario with an access fee of $32 and a per-unit price of $16 for 4 units is also incorrect since the unit price is $16.
None of the given pricing options have a per-unit price of $0.1975.
A local hamburger shop sold a combined total of 760 hamburgers and cheeseburgers on Friday. There were 60 more cheeseburgers sold than
hamburgers. How many hamburgers were sold on Friday?
this weekend the hardware store is having a blowout sale, where everything is discounted 40%. A weed eater originially sells for $145. How much will the weed eater cost during the blowout sale?
Answer:
$87
Step-by-step explanation:
to find discounted price, you multiply the original price by the decimal equivalent of the discount. so,
[tex]145 \times .40 = 58[/tex]
so that's 40% of 145 but now you gotta take the 40% off the original price so,
[tex]145 - 58 = 87[/tex]
There are $87 the weed eater cost during the blowout sale.
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.
We have to given that;
This weekend the hardware store is having a blowout sale, where everything is discounted 40%.
And, A weed eater originally sells for $145.
Now, The discounted price is,
⇒ 40% of 145
⇒ 40/100 × 145
⇒ $58
Thus, The weed eater cost during the blowout sale = $145 - $58
= $87
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ASAP answer quickly please
On this necklace the ratio of black beads to white beads is 2:3
How many more black beads do you need to
add to make the ratio of black to white 3:1 ?
Answer:
Add 7 black beads
Step-by-step explanation:
Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.
There are three white beads in the picture.
Total beads we will have (b meaning black) b : 3
Ratio black : white beads 3 : 1
Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.
Find common ratio by dividing total by ratio white beads: 3/1 = 3
Multiply ratio black beads by common ratio. 3 X 3 = 9
We need 9 black beads in total.
Check answer
9 : 3 Both sides divisible by 3; reduce ratio
= 3 : 1 Correct ratio
There will be a total of 9 black beads, but we already have 2 black beads:
(9 total) - (2 original) = (7 to add)
Therefore we need to add 7 black beads.
To make the ratio of black to white beads 3:1, you need to add 1 more black bead.
Explanation:To make the ratio of black to white beads 3:1, we need to determine how many more black beads need to be added. Currently, the ratio is 2:3, which means for every 2 black beads, there are 3 white beads. Let's say we have 2x black beads and 3x white beads. To make the ratio 3:1, we need to have 3 black beads for every 1 white bead. This means we need to add x more black beads. Setting up the equation 2x + x = 3(3x), we can solve for x to find out how many more black beads are needed.
Simplifying the equation, we get 2x + x = 9x. Combining like terms, we have 3x = 9x. Subtracting 3x from both sides, we get 0 = 6x. Dividing both sides by 6, we find that x = 0. Since we need an integer value for x, it means we need to add 1 more black bead to make the ratio 3:1.
Therefore, you need to add 1 more black bead to make the ratio of black to white beads 3:1.
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An estimated 3 out of every 25 men are left handed. What percent of men are left handed
Answer:
12%
Step-by-step explanation:
So we know the ratio of left-handed men to men is 3:25. We also know that percent is out of one hundred, so we can do (ratios are essentially fractions) 3/25*4/4+ 12/100. Converting 12/100 to a percent should be simple and you get an answer of 12%
Please let me know if this was correct