Answer: False.
Step-by-step explanation:
For any random variable x,
Formula to calculate the z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
, where [tex]\mu[/tex] = Mean
[tex]\sigma[/tex] = Standard deviation
Let x be the data point has a corresponding z-score of -1.5.
Then , we have
[tex]-1.5=\dfrac{x-\mu}{\sigma}[/tex]
[tex]-1.5\sigma=x-\mu[/tex]
[tex]\mu-1.5\sigma=x[/tex]
i.e. x is one and a half standard deviations below the mean value.
( one and a half =[tex]1+\dfrac{1}{2}=1.5[/tex] )
Therefore , the given statement is false.
Can someone please write the equation of hyperbola with vertices (0, -5) and (0, 5) and co-vertices (-2, 0) and (2, 0)?
Thank you so much!
Answer:
y^2/25 -x^2/4 = 1
Step-by-step explanation:
The equation can be written as ...
y^2/a^2 -x^2/b^2 = 1
where the vertices are at (0, ±a) and the co-vertices are at (±b, 0). Filling in the given values (a=5, b=2) gives the equation shown above.
Susan has 5 more pennies than dimes, three times more nickels than dimes and 4 less quarters than pennies. If Susan has 7 dimes, what is the total value of her money?
Three pounds of dried cherries cost $15.90, 5 pounds of dried cherries cost $26.50, and 9 pounds of dried cherries cost $47.70. Which equation gives the total cost y of x pounds of dried cherries?
Final answer:
The equation that gives the total cost of x pounds of dried cherries is y = (10.60/2)x.
Explanation:
Let's create a table to represent the given information:
Pounds of Dried Cherries (x)Total Cost (y)315.90526.50947.70
To find an equation that gives the total cost of x pounds of dried cherries, we need to find a pattern in the data. From the table, we can see that as the pounds of dried cherries increase, the total cost also increases. This suggests a linear relationship between pounds and cost.
Now, let's analyze the changes in cost for each additional pound of dried cherries:
From 3 to 5 pounds: The cost increased by $26.50 - $15.90 = $10.60.From 5 to 9 pounds: The cost increased by $47.70 - $26.50 = $21.20.Based on these changes, the cost increased by $10.60 for every 2 additional pounds of dried cherries. Therefore, the equation that gives the total cost y of x pounds of dried cherries is:
y = (10.60/2)x
At Delia’s company, the purchases are recorded at net amounts. On August 5, $40,000 worth of merchandise was purchased on account for terms of 2/10, n/30. $3,000 of this merchandise was returned, and the account was credited. As of August 31, the balance still had not been paid. What amount will be recorded as the purchase return?
Answer:
$2,940
Step-by-step explanation:
Data provided in the question:
Cost of merchandise purchased = $40,000
Cost of merchandise returned = $3,000
Terms = 2/10, n/30
Now,
The amount that will be recorded as the purchase return
= Cost of merchandise returned - Discount on cost of merchandise
= $3,000 - ( 2% of $3,000 )
= $3,000 - ( 0.02 × $3,000 )
= $3,000 - $60
= $2,940
£980 is divided between Caroline, Sarah & Gavyn so that Caroline gets twice as much as Sarah, and Sarah gets three times as much as Gavyn. How much does Sarah get?
Sarah has received £ 294
Solution:
Given that £980 is divided between Caroline, Sarah & Gavyn
Let "c" be the amount received by caroline
Let "s" be the amount received by sarah
Let "g" be the amount received by gavyn
Caroline gets twice as much as Sarah
amount received by caroline = twice as much as Sarah
amount received by caroline = 2(amount received by sarah)
c = 2s ---- eqn 1
Sarah gets three times as much as Gavyn
amount received by sarah = three times as much as Gavyn
amount received by sarah = 3(amount received by gavyn)
s = 3g ------- eqn 2
Given that total amount is 980
c + s + g = 980 --- eqn 3
Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"
From eqn 2,
[tex]g = \frac{s}{3}[/tex] --- eqn 4
Substitute eqn 1 and eqn 4 in eqn 3
[tex]2s + s + \frac{s}{3} = 980\\\\\frac{6s + 3s + s}{3} = 980\\\\6s + 3s + s = 980 \times 3\\\\10s = 2940\\\\s = 294[/tex]
Thus sarah has received £ 294
Final answer:
To solve for the amount Sarah receives, set up ratios based on the information provided and solve the resulting equation. The total amount divided among them is £980, which when divided by the total parts (10) gives Gavyn's share as £98. Sarah's share is three times Gavyn's share, resulting in £294.
Explanation:
The problem described is a classic division in ratio mathematics question where £980 is being divided among Caroline, Sarah, and Gavyn following certain rules.
According to the problem, Caroline receives twice the amount that Sarah receives and Sarah receives triple the amount that Gavyn receives.
We can set up the following ratios: C = 2S and S = 3G, where C stands for Caroline's amount, S for Sarah's, and G for Gavyn's. If we denote Gavyn's amount as G, then Sarah's amount is 3G and Caroline's is 2 × 3G which is 6G.
To find the value of G, we can write the equation G + 3G + 6G = £980 or 10G = £980. Solving for G gives us G = £98.
Therefore, Sarah, receiving three times as much as Gavyn, gets 3 × £98 = £294.
21. What is the exact volume of a sphere whose diameter is 14 cm? Show your work.
Answer:
The exact volume of a sphere is [tex]V=1437cm^3[/tex]
Step-by-step explanation:
Given that the diameter of a sphere is 14cm.
That is d=14
First find the radius of the sphere with diameter
[tex]r=\frac{d}{2}[/tex]
[tex]r=\frac{14}{2}[/tex]
Therefore r=7cm
Now to find the volume of the sphere:
[tex]V=\frac{4}{3}\pi r^3cm^3[/tex]
[tex]V=\frac{4}{3}\frac{22}{7}(7)^3[/tex] (here[tex]\pi=\frac{22}{7}[/tex] and r=7)
[tex]V=\frac{4}{3}(22)(7)^2[/tex]
[tex]V=\frac{4}{3}(22)(49)[/tex]
[tex]V=\frac{4}{3}(1078)[/tex]
[tex]V=\frac{4312}{3}[/tex]
[tex]V=1437.33cm^3[/tex]
Therefore the volume of the given sphere is [tex]V=1437.33cm^3[/tex]
The exact volume of a sphere is [tex]V=1437cm^3[/tex]
Find the m∠p.
pls and thanks <3
Answer:
36°
Step-by-step explanation:
Like your other question, the angles of the triangle must add up to 180. The tangent line is perpendicular to the center, so the angle must be 90°.
90° + 54° + 36° = 180°
In an arcade game, a 0.13 kg disk is shot across a frictionless horizontal surface by being compressed against a spring and then released. The spring has a spring constant of 242 N/m and is compressed from its equilibrium position by 5.2 cm. What is the magnitude of the spring force on the disk at the moment it is released?
Answer:
12.584 N
Step-by-step explanation:
To solve this problem you need to use Hokke's law, this is a physics lar which states the force (F) you need to compress a spring for some distance (x) can be easily calculated with the equation F=kx. The constant k (the stiffness of the spring) is the value of 242 N/m and x is the distance 5.2 cm = 0.052 m. So if you multiply 242 N/m by 0.052 m you will obtain 12.584 N, which is the necessary force to compress the spring 5.2 cm. The mass of the spring is a nonrelevant data in this problem.
7600 people were surveyed about their favorite type of milkshake what percentage of the people like vanilla how many of the people like chocolate how many of the total people like vanilla or strawberry
Answer:
Lack of information
Step-by-step explanation:
I can't find what percent or whatever information about the flavour,so I guess you need to give more information. If you give me more information, I will try to reply in the comments.
Hope this helps!!! ;)
HELPPPPP
(Attaching the pic now)
Explanation:
1. BF bisects ∠CBA. Given
2. ∠CBF ≅ ∠ABF. Definition of angle bisector
3. BF ≅ BF. Reflexive property
4. ∠CFB ≅ ∠AFB. Given
5. ΔCBF ≅ ∆ABF. ASA congruence postulate
6. CF ≅ FA. Corresponding parts of congruent triangles are congruent (CPCTC)
_____
Comment on the problem
It appears as though all of the congruence symbols have gone missing.
Sketch the graph of the given function. Then state the function’s domain and range. f(x)= 1/2(5)^x+3
Answer:
Graph of the following function is attached with the answer.
Domain : ( - ∞ , + ∞ )
Range : ( 3 , + ∞ )
Step-by-step explanation:
[tex]f(x)=\frac{1}{2}x^{2}+3[/tex]
Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.
So, Domain : ( - ∞ , + ∞ )
The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:
Range of x : ( - ∞ , + ∞ )Range of [tex]\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as every square number is more than or equal to zero.Range of [tex]\frac{1}{2}\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as 0/2 = 0 and ∞/2 = ∞.Range of [tex]\frac{1}{2}\textrm{x}^{2}+3[/tex] : [ 3 , + ∞ ) as 0 + 3 = 3 and ∞ + 3 = ∞.Therefore the Range of [tex]\mathbf{f(x)\boldsymbol=\frac{1}{2}x^{2}\boldsymbol+3}[/tex] is [ 3 , + ∞ )
(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.
(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.
(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.
[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.
{a,b} means only 'a' and 'b'.
{a,b] or (a,b} doesn't mean anything. )
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.
To calculate the interest that Rich will accrue during the 4.5-year nonpayment period on his federal unsubsidized student loan, we can use the formula for simple interest:
Interest = Principal (loan amount) x Rate x Time
Where:
Principal (loan amount) = $7,900
Rate = 4.29% (0.0429 as a decimal)
Time = 4.5 years
Now, plug these values into the formula:
Interest = $7,900 x 0.0429 x 4.5
Interest = $7,900 x 0.19205
Interest ≈ $1,518.45
So, Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.
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Rich has been approved for a federal unsubsidized student loan and wants to know the interest that will accrue during his 4.5 years as a freshman in college. Calculating the interest using the formula, the total accrued interest is $1,146.75.
Explanation:Rich is attending a 4-year college and has been approved for a 10-year federal unsubsidized student loan of $7,900 at an interest rate of 4.29%. During his 4 years as a freshman, he has the option to start repaying the loan after 4.5 years. However, interest will continue to accrue at a rate of 4.29% during this non-payment period.
To calculate the interest that will accrue during the 4.5 years, we can use the formula:
Interest Accrued = Principal x Interest Rate x Time
Substituting the values, we get:
Interest Accrued = $7,900 x 0.0429 x 4.5 = $1,146.75
Therefore, the interest that will accrue during the non-payment time is $1,146.75.
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Which of the following is the simple interest paid on a loan of $354 at 6% for six months?
$10.62
$10.26
$12.47
$12.74
Answer: interest at the end of 6 months is $10.62
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 6 months = 6/12 = 0.5 years
P = $354
R = 6%
Therefore
I = (354 × 6 × 0.5)/100
I = 1062/100
I = 10.62
Jake, a varsity swimmer, is training for his upcoming season and needs to accelerate his post-exercise recovery rates. He trains intensely for 2 hours, 5 days a week. If he weighs 155-lb (70.45 kg), which of the following nutritional strategies would BEST replenish his glycogen stores?
Answer:
high glycemic carb with some protein
Step-by-step explanation:
Food like white bread made from dextrose supplement and chocolate milk that contains some protein for muscle repair.
Due to the spongelike characteristic of the muscle would make it soak up glucose from high glycemic carb.
Match the square root with its perfect square: 1 . √4 1 2 . √144 2 3 . √9 3 4 . √121 4 5 . √64 5 6 . √169 6 7 . √100 7 8 . √25 8 9 . √1 9 10 . √36 10 11 . √81 11 12 . √16 12 13 . √49 13
Answer:
√1 1
√4 2
√9 3
√16 4
√25 5
√36 6
√49 7
√64 8
√81 9
√100 10
√121 11
√144 12
√169 13
Step-by-step explanation:
1. = 49
2. = 169
3. = 81
4. = 100
5. = 441
6. = 36
I just finished the assignment, trust me.
2. Jenna Ford purchased a compact stereo that regularly sells for $229.99 at a markdown rate of 53%. In California, where Jenna lives, the sales tax rate on this item is 7%. Find the final price of the item.
Answer:
$115.67
Step-by-step explanation:
given that the markdown rate is 53%, that means that the markdown is 53% of the original price, or,
markdown = 53% of $229.99 = 0.53 x 229.99 = $121.89
sale price before tax = Original Price - Markdown
= 229.99 - 121.89
= $108.10
sales tax = 7% of sale price before tax
= 0.07 x 108.10
= $7.57
Final price = price before tax + tax
= 108.1 + 7.57
= $115.67
Calculate the simple interest paid on a loan of $544 at 3% for three months.
$48.96
$4.80
$4.90
$4.08
Answer:
4.08
Step-by-step explanation:
Interest I =Pnr
3 months =3/12 year = n
r = 3%
and, P = 544$
Therefore,
[tex]i = 544 \times (3 \div 100) \times (3 \div 12) \\ \: \: \: = 4.08[/tex]
please answer soon Which expression is equivalent to − 7 x + 6 ( x − 8 2 ) − 2 ( x + 3 ) + 10 ? A. − 3 x + 40 B. − 15 x − 20 C. − 3 x − 20 D. 15 x + 40
Multiply the parenthesis by 6:
-7x+6x-492-2(x+3)+10
Multiply the parenthesis by -2:
-7x+6x-492-2x-6+10
Calculate the sum of similar terms:
-3x-492-6+10
Calculate the sum or difference:
-3x-488
If an integer n is to be selected at random from the integers 1 to 100, inclusive, what is the probability that n(n 1) will be divisible by 4
Answer:
Step-by-step explanation:
total integers=100 (1,2,3,...,98,99,100)
numbers divisible by 4 =25 (4,8,12,...,96,100)
P=25/100=1/4
math question in the attached text
Answer:
A 1.44 cm cubed
Step-by-step explanation:
Just multiply all the numbers to get the area of the block
Answer:
A 1.44 cm cubed
Step-by-step explanation:
A 20 kg sphere is at the origin and a 10 kg sphere is at x = 20 cm. At what position on the x-axis could you place a small mass such that the net gravitational force on it due to the spheres is zero?
Step-by-step explanation:
Let the small mass be m and position on x axis be y.
A 20 kg sphere is at the origin.
Distance to 20 kg mass = y
A 10 kg sphere is at x = 20 cm
Distance to 10 kg sphere = 20 - y
We have forces between them are equal
We have gravitational force
[tex]F=\frac{GMm}{r^2}[/tex]
Where G = 6.67 x 10⁻¹¹ N m²/kg²
M = Mass of body 1
M = Mass of body 2
r = Distance between them
Here we have
[tex]\frac{G\times 20\times m}{y^2}=\frac{G\times 10\times m}{(20-y)^2}\\\\800-80y+2y^2=y^2\\\\y^2-80y+800=0\\\\y=68.28cm\texttt{ or }y=11.72cm[/tex]
So the small mass should be placed at x = 11.72 cm or x = 68.28 cm
The positions on the x-axis obtained using quadratic equation such that net gravitational force is zero are 68.28 and 11.72 cm respectively.
Recall the force of universal gravitational attraction :
[tex] \frac{Gm_{1}m_{2}}{r^{2}}[/tex]Sphere 1 :
Mass = 20 kg Distance of 20kg sphere = dSphere 2 :
Mass = 10kgDistance of 10kg sphere = 20 - dGravitational force ; sphere 1 :
[tex] \frac{G \times 20 \times m_{2}}{d^{2}}[/tex] --(1)Gravitational force ; sphere 2 :
[tex] \frac{G \times 10 \times m_{2}}{(20 - d)^{2}}[/tex] - - (2)Equate (1) and (2)
[tex] \frac{G \times 20 \times m_{2}}{d^{2}} = \frac{G \times 10 \times m_{2}}{(20 - d)^{2}} [/tex]
[tex] 20(20 - d)^{2} = 10 \times d^{2} [tex]
20(400 - 40d + d²) = 10d²
8000 - 800d + 20d² = 10d²
10d² - 800d + 8000 = 0
Divide through by 10
d² - 80d + 800 = 0
Using a quadratic equation solver :
d = 68.28 cm or d = 11.72 cm
The possible positions are 68.28 cm and 11.72 cm
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What is the measure of a°?
Answer:
The correct answer is C. 129.
Step-by-step explanation:
Let's recall that the Inscribed Quadrilateral Theorem states that a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.
In the case of the inscribed quadrilateral ABCD in the graph attached, we have that:
m∠C= 51°, therefore its supplementary angle, ∠A, should be the difference between 180° and m∠C.
m∠C= 180° - m∠A
Replacing with the real values:
51 = 180 - m∠A
m∠A = 129°
The correct answer is C. 129.
1/4 + 1/8= I know it should be easy but my teacher told me that we can't add fractions if they have different denominators. Now if you are going to explain the to me I am in 5th grade so please don't make it to complicated.Thank you.
Match the key aspect of a function's graph with its meaning.
f(x) > 0
intervals of the domain where the
graph is above the x-axis
f(x) < 0
location on graph where input is zero
x-intercept
location on graph where output is
zero
y-intercept
intervals of the domain where the
graph is below the x-axis
Answer:
Part 1) Intervals of the domain where the graph is above the x-axis (f(x) > 0)
Part 2) location on graph where input is zero (y-intercept)
Part 3) location on graph where output is zero (x-intercept)
Part 4) Intervals of the domain where the graph is below the x-axis (f(x) < 0)
Step-by-step explanation:
Verify each case
Part 1) we have
Intervals of the domain where the graph is above the x-axis
we know that
If the graph is above the x-axis, then the value of f(x) is positive
therefore
f(x) > 0
Part 2) we have
location on graph where input is zero
Let
x ---> the independent variable or input value
f(x) ---> the dependent variable or output value
we know that
The y-intercept is the value of f(x) (output value) when the value of x (input value) is zero
therefore
y-intercept
Part 3) we have
location on graph where output is zero
Let
x ---> the independent variable or input value
f(x) ---> the dependent variable or output value
we know that
The x-intercept is the value of x (input value) when the value of the function f(x) (output value) is zero
therefore
x-intercept
Part 4) we have
Intervals of the domain where the graph is below the x-axis
we know that
If the graph is below the x-axis, then the value of f(x) is negative
therefore
f(x) < 0
Answer:
Intervals of the domain where the graph is above the x-axis (f(x) > 0)
location on graph where input is zero (y-intercept)
location on graph where output is zero (x-intercept)
Intervals of the domain where the graph is below the x-axis (f(x) < 0)
Step-by-step explanation:
answer edge 2020
The measures of one acute angle in a right triangle is four times the measure of the other acute
angle. Write and solve a system of equations to find the measures of the acute angles.
Help with this exercise
[tex]A_2[/tex] = 18°
[tex]A_3[/tex] = 4(18°) = 72°
Step-by-step explanation:Given:
One angle in the triangle is 90°One angle that isn't 90° is 4 times larger than another angle that isn't 90°Angles:
[tex]A_1[/tex] = 90°
[tex]A_2[/tex] = x
[tex]A_3[/tex] = 4x
Solution Pathway:
Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:
sum of the interior angles = 180°90° + x + 4x = 180°Now let's solve for x.
90 +x + 4x = 18090 + 5x = 1805x = 90x = 18°Now that we know x is 18°, lets plug this value into the two unknown acute angles.
[tex]A_2[/tex] = 18°[tex]A_3[/tex] = 4(18°) = 72°Answer:
72 degrees and 18 degrees.
Step-by-step explanation:
If the 2 angles are x and y, we have the system:
x + y = 90 (as it is a right triangle)
x = 4y (given).
Substitute x =- 4y in the first equation:
4y + y = 90
5y = 90
y = 18.
So x + 18 = 90
x = 90 - 18
x = 72.
Find f(2) if f(x) = 2x + 1.
A) 3
B) 5
C) 7
D) 9
Answer:
The answer to your question is letter B
Step-by-step explanation:
Process
1.- Write the equation
f(x) = 2x + 1
find f(2)
2.- Substitute x for 2
f(2) = 2(2) + 1
3.- Simplify
f(2) = 4 + 1
f(2) = 5
Answer:
5
Step-by-step explanation:
2(2) + 1 = 5
If you have a lowest score of 21 and a range of 47, your highest score will be:________
Answer: 68
Step-by-step explanation:
range=47 lowest score = 21 let highest score =x
Range=highest score - lowest score
47 = x - 21
x = 47 + 21
x = 68
Therefore the highest score is 68
The highest score is 68.
Range = Highest Score - Lowest Score
In this case,
the lowest score is 21 and
the range is 47.
So, we can rearrange the formula to solve for the highest score:
Highest Score = Range + Lowest Score
Substituting in the given values:
Highest Score = 47 + 21
Thus, the highest score will be 68.
Your grandmother always has a jar of cookies on her counter. One day while you are visiting, you eat 555 cookies from the jar. In the equation below, ccc is the number of cookies remaining in the jar and bbb is the number of cookies in the jar before your visit.
Answer:
For 1 How does grandma have so many cookies??? For 2 if i eat 555 cookies then imma have diabetes. and for 3 there really is no way to find this out. The only way to find out how many cookies there is now it to see how much cookies there were before and you cant do that without seeing how much is in there now. Its a catch 22.
Step-by-step explanation:
Judy bought her tent on sale .The same price was $70 off the original price . Judy also used a coupon for an extra $15 off if Judy paid $125 for the tent , what was it's original price
Answer:210
Step-by-step explanation:
175+70+15=210
Answer:the original price is $210
Step-by-step explanation:
Let x represent the original price of the tent. She bought it at price that is $70 off the original price. This means that $70 was taken off the original price.The amount after the discount has been removed would be
x - 70
Judy also used a coupon for an extra $15 off. This means that the amount the Judy finally paid for the tent would be
x - 70 - 15
if Judy paid $125 for the tent, it means that
x - 70 - 15 = 125
x = 125 + 70 + 15
x = $210
Prove that if f is one-to-one, then f(X) ∩ f(Y ) = f(X ∩ Y ) for all X, Y ⊆ A. Is the converse true?
Answer:
See proof below, the converse is true
Step-by-step explanation:
Let f be a function whose domain is the set A, and X,Y be arbitrary subsets of A. One way to prove the equality of sets f(X)∩f(Y)=f(X∩Y) is, by definition, to prove the inclusions f(X)∩f(Y) ⊆ f(X∩Y) and f(X)∩f(Y )⊇f(X∩Y).
First, let a∈f(X)∩f(Y). Then a∈f(X) and a∈f(Y) by definition of intersection. Thus, a=f(t) for some t∈X (because a is an element of the direct image of X) and a=f(s) for some s∈Y. Then a=f(t)=f(s). We know that f is 1-1, so the previous equality implies that t=s. Now, t∈X and t=s∈Y, thus t∈X∩Y. Therefore, a=f(t) for some t∈X∩Y, which means that a is an element of the direct image of X∩Y, that is, a∈f(X∩Y). This holds for all a, thus f(X)∩f(Y) ⊆ f(X∩Y).
For the second inclusion, let b∈f(X∩Y), then there exists some z∈X∩Y such that b=f(z). Since z∈X∩Y, we have that z∈X and z∈Y. Thus, b=f(z) for some z∈X, that is, b∈f(X). Similarly, b∈f(Y) because b=f(z) and z∈Y. Therefore b∈f(X)∩f(Y) for all b∈f(X∩Y), then f(X)∩f(Y )⊇f(X∩Y). Note that this holds for any function f, as we did not use that f is 1-1.
To prove the converse, suppose that f(X)∩f(Y)=f(X∩Y) for all X, Y⊆ A. We will prove that f is 1-1, that is, for all a,b∈A if f(a)=f(b) then a=b.
Define the sets X:={a} and Y:={b}. Then f(X)={f(a)} and f(Y)={f(b)}. Assuming that f(a)=f(b), we obtain f(X)=f(Y). We know that f(X)∩f(Y)=f(X∩Y), which means {f(a)}=f(X∩Y). Then, there exists some s∈X∩Y such that f(s)=f(a), thus X∩Y is a non-empty set, which implies that a∈Y. But Y has only one element, b, therefore a=b which shows that f is 1-1.