Answer:
To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.
From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:
Number of stories: 5
Number of cards used: 40
To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).
Ratio = Number of stories / Number of cards used
Ratio = 5 / 40
Now, we can use this ratio to calculate the number of cards needed for 100 stories:
Number of cards for 100 stories = Ratio * Number of stories
Number of cards for 100 stories = (5 / 40) * 100
Calculating the result:
Number of cards for 100 stories = (0.125) * 100
Number of cards for 100 stories = 12.5
Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.
Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.
What the meaning of statement this?
The statement means that an n-ary operation on set X takes n inputs and produces a single output, with the operation defined by the function f:[tex]X^n[/tex] -> X.
The statement "An n-ary operation on x is functions f:X^n -> X" can be understood as follows:
In mathematics, an n-ary operation refers to an operation that takes n inputs and produces a single output. In this case, the operation is defined on a set X, and the inputs are elements from X. The result of the operation is also an element from X.
The symbol "f" represents the function that performs the n-ary operation. The function f takes n arguments, which are elements from the set X. The notation [tex]X^n[/tex] indicates the Cartesian product of X with itself n times, meaning that the inputs are taken from X and repeated n times as ordered tuples. The arrow "->" signifies that the function f maps the n-tuple of inputs to a single element in X.
To put it simply, the statement is describing a mathematical operation that takes n elements from a set X and combines them in some way to produce a single element, where the combination is determined by the function f. This function f can be defined explicitly based on the specific operation being considered.
for such more question on function
https://brainly.com/question/14723549
#SPJ8
Find the 5th term in the expansion of (3x + 1)7 in simplest form.
The 5th term in the expansion of [tex](3x + 1)^7[/tex] would be [tex]945x^3[/tex].
Binomial expansionTo find the 5th term in the expansion of [tex](3x + 1)^7[/tex], we use the binomial theorem formula:
[tex](a + b)^n = nC0 a^n b^0 + nC1 a^(n-1) b^1 + nC2 a^(n-2) b^2 + ... + nCn-1 a^1 b^(n-1) + nCn a^0 b^n[/tex]
where nCk represents the binomial coefficient, given by the formula:
nCk = n! / (k!(n-k)!)
In this case, a = 3x and b = 1, so we have:
[tex](3x + 1)^7 = 7C0 (3x)^7 1^0 + 7C1 (3x)^6 1^1 + 7C2 (3x)^5 1^2 + 7C3 (3x)^4 1^3 + 7C4 (3x)^3 1^4 + 7C5 (3x)^2 1^5 + 7C6 (3x)^1 1^6 + 7C7 (3x)^0 1^7[/tex]
To find the 5th term, we need to look at the term with k = 4, which is:
[tex]7C4 (3x)^3 1^4[/tex] = [tex]35 (3x)^3[/tex]
= [tex]35 (3x)^3[/tex]
= [tex]35 (27x^3)[/tex]
Therefore, the 5th term in the expansion of [tex](3x + 1)^7[/tex] is [tex]945x^3[/tex].
More on Binomial expansions can be found here: https://brainly.com/question/29260188
#SPJ1
Solve 2(2x-5)=3x+x-2x
Answer:
5=x
Step-by-step explanation:
Q=2(2x-5)=3x+x-2x
SOLUTION:
4x-10=4x-2x
-10=2x-4x
-10= -2x
(-+-=+ so 10 and 2 are positive now)
10/2=x
5=x
Flip a half a day league table in her kitchen, the lacewings from one corner of the table to the middle of the far side of the table. How long is the gateleg table?
The length of gateleg of the table whose leg swings from one corner of the table to the middle of the far side of the table top is 53 inches long.
The shape forms a trapezoid
The length of the parallel side = is 56 in
The length of the base = is 45 in
To the length of the triangle formed when the base of the gateleg is connected with the middle of the table
The length of the side when connected with the midpoint = 56/2 = 28
The length of gateleg = hypotenuse
Using Pythagorean theorem :
(hypotenuse)² = (base)² + (perpendicular)²
(hypotenuse)² = (45)² + (28)²
(hypotenuse)² = 2025 + 784
(hypotenuse)² = 2809
hypotenuse = 53
Know more about length click here :
https://brainly.com/question/9461061
#SPJ1
The question is incomplete the complete question is :
Philippa has a gateleg table in her kitchen. The leg swings from one corner of the table to the middle of the far side of the tabletop, as shown in the sketch below.
Note: The figure is not drawn to scale.
How long is the gateleg of the table?
A.) 53 inches
B.) 49 inches
C.) 73 inches
D.) 72 inches
Nancy flew home from vacation with a heavy bag. With the first airline she flew, Nancy had to pay $20 to check her bag, plus $5 for every pound that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Nancy had to pay $4 per pound that her bag was over the weight limit, in addition to the checked bag fee of $25. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag? Write a system of equations, graph them, and type the solution.
Nancy's bag was 0.2kg over the weight limit.
What weight in which Nancy's bag exceeded limit?Let's denote the weight limit as x.
The total cost for the first airline can be expressed as:
Cost1 = 20x + 5
The total cost for the second airline is given by:
Cost2 = 25x + 4
As fees were same with both airlines, we will set up equation to find the weight difference:
20x + 5 = 25x + 4
20x-25x = 4-5
-5x = -1
x = -1/-5
x = 0.2kg
Read more about weight
brainly.com/question/28571689
#SPJ1
Find the inverse of the function.
f-¹(x) =
+
f(x) =
1
x - 2
X # 2
, X = 0
Answer:
The given function is:
f(x) = 1/(x - 2), x ≠ 2
0, x = 2
To find the inverse of the function, we need to solve for x in terms of f(x).
Let y = f(x)
Case 1: When y = 0
If y = 0, then x = 2 as per the definition of the function.
Case 2: When y ≠ 0
y = 1/(x - 2)
1/y = x - 2
x = 1/y + 2
So, the inverse function is:
f-¹(x) = 2, x = 0
1/(x - 2), x ≠ 0 and x ≠ 2
Step-by-step explanation:
LUUK al uit grapii velow.
Part B
-4
Part A
-3-2
Part C
3
2
-2
-3
Part D
Which part of the graph best represents the solution set to the system of
inequalities y ≥x+1 and y + x>-1? (5 points)
The solution set of given inequalities are represented by Part A.
The given inequalities are
⇒ y ≥ x + 1 and y + x > -1
Hence, The related equations of both inequalities are
y = x + 1
Put x=0, to find the y-intercept and put y=0, to find x intercept.
y = 0 + 1
y = 1
And, 0 = x + 1
x = - 1
Therefore, x-intercept of the equation is (-1,0) and y-intercept is (0,1).
Similarly, for the second related equation
y + x = - 1
y + 0 = - 1
y = - 1
0 + x = - 1
x = - 1
Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).
Now, join the x and y-intercepts of both lines to draw the line.
Now check the given inequalities by (0,0).
0 ≥ 0 + 1
0 ≥ 1
It is a false statement, therefore the shaded region is in the opposite side of origin.
0 + 0 ≥ - 1
0 ≥ - 1
It is a true statement, therefore the shaded region is about the origin.
Hence, From the below figure we can say that the solution set of given inequalities are represented by Part A.
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ1
brainly hates me!!!!!!!!!!!
Answer:
1. x = 13.75
2. 17 degrees
3. a = 4, b = 2√2
Step-by-step explanation:
1. cos(37) = 11/x
since cos(37) = 4/5
4/5 = 11/x
4x = 55
x = 13.75
2. tan(0) = opp/adj
tan(0) = 4/13 = 0.30769
=> (0) = 17.1 degrees or 17 degrees
3. since the triangle is right triangle with 2 angles of 45 degress
=> isosceles right triangle
then b = 2√2
a^2 = (2√2)^2 + (2√2)^2
a^2 = = 8 + 8 = 16
a = √16= 4
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
A.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
hope it helps you
The radius of a circle is 14 yards. What is the circle's circumference?
Use 3.14 for .
pls help
Answer:
Circumference = 87.92 yd
Step-by-step explanation:
We know that formula for circumference (C) of a circle is
C = πd, where d is the diameter.
We know that the diameter is twice the measure of the radius, so we can find the diameter of the circle by multiplying the radius by 2:
d = 2r
d = 2 * 14
d = 28 yd
Now, we can find circumference, remembering to use 3.14 for π
C = 3.14 * 28
C = 87.92 yd
need help urgently, don’t think the answers i have are right and i don’t know how to do it!!!
Answer:
See attached graphy-intercepts = [tex]\dfrac{3}{2}[/tex]Roots: x = - 3Step-by-step explanation:
Given function is
[tex]f(x) = \dfrac{\left(x^2-9\right)}{\left(x^2-x-6\right)}[/tex]
Part 1
Graph attached
y-intercepts can be found by finding f(0) ie the value of f(x) at x = 0
[tex]f(0) = \dfrac{\left(0^2-9\right)}{\left(0^2-0-6\right)} = \dfrac{-9}{-6} = \dfrac{3}{2}[/tex]
Roots of a function can be found by setting f(x) = 0 and solving for x
Setting f(x) = 0
==> [tex]\dfrac{x^2-9}{x^2-x-6} = 0\\\\[/tex]
We can factor the numerator as follows:
x² - 9 = (x + 3) (x -3) since (a + b)(a-b) = a² - b²
Denominator can be factored as follows
x² - x - 6 = (x-3)(x+2)
So
[tex]f(x) = \dfrac{(x + 3)(x-3)}{(x-3)(x+2)}\\\\[/tex]
The (x-3) term cancels leaving
[tex]f(x) = \dfrac{x+3}{x+2}[/tex]
Setting this equal to 0 gives
[tex]\dfrac{x+3}{x+2} = 0[/tex]
This is 0 when x + 3 = 0 or x = -3
So there is only one root and that is x = -3
Asymptotes
The vertical asymptote occurs when at a value of x when the denominator becomes 0
The given function has been factored as
[tex]f(x) = \dfrac{x + 3}{x + 2}[/tex]
The denominator becomes 0 at x = -2
Vertical asymptote is x = - 2
To find the horizontal asymptote use the fact that when the degrees of the numerator and denominator are equal, the horizontal asymptote is given by
[tex]y=\dfrac{\mathrm{numerator's\:leading\:coefficient}}{\mathrm{denominator's\:leading\:coefficient}}[/tex]
The degree of the numerator x + 3 is 1 and the degree of the denominator x + 2 is also 1
So the horizontal asymptote is y = 1/1 = 1
y = 1 is the horizontal asymptote
End behavior is the behavior of the function as x → ±∞
This is determined by examining the leading term of the function and determining what its behavior is as x → ±∞
In the function
[tex]f(x) = \dfrac{x + 3}{x + 2}[/tex]
which is the factored form of the originally given function
the domain of x = all real numbers with the exception of -2 since at x = -2, the function is undefined
The end behavior can be determined by finding the limit of f(x) as x tends to infinity
[tex]\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right)\\\\\dfrac{x+3}{x+2} \text{ can be transformed by dividing by x both numerator and denomiator :}\\\\\\=\dfrac{\dfrac{x}{x}+\dfrac{3}{x}}{\dfrac{x}{x}+\dfrac{2}{x}}\\\\\\=\dfrac{1+\frac{3}{x}}{1+\dfrac{2}{x}}[/tex]
[tex]\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right) \\\\\\\\=\lim _{x\to \infty \:}\left(\dfrac{1+\dfrac{3}{x}}{1+\dfrac{2}{x}}\right)\\\\\\\\=\dfrac{\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right)}{\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right)}[/tex]
[tex]\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right) = 1\\\\\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right) = 1[/tex]
[tex]\lim _{x\to \:-\infty \:}\left(\dfrac{x+3}{x+2}\right) = 1[/tex]
End behavior
[tex]\mathrm{as}\:x\to \:+\infty \:,\:y\to \:1,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:y\to \:1[/tex]
Table:
x y
-4 1/2
- 3 0
-1 2
0 3/2
1 4/3
2 5/4
3 6/5
Note that the function is undefined at x = -2
Simplify (4x5y³)(-3x³y²).
O-12x85
Ox³y5
O-12x³y6
O-12x¹5,6
Answer:
-12x⁸y⁵
Step-by-step explanation:
Exponent law:
xᵃ * xᵇ = xᵃ ⁺ ᵇ
In exponent multiplication, if bases are same, add the exponents.
Multiply the co-efficient.Multiply the variable using the exponent law.(4x⁵y³) (-3x³y²) = 4*(-3) * x⁵⁺³ * y³⁺²
= -12x⁸y⁵
At the beginning of the week, James has 8 quarts of milk. At the end of the week there are 412 cups of milk left.
How many cups of milk did James drink during the week?
James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week
To determine how many cups of milk James drank during the week, we need to find the difference between the initial amount of milk and the amount of milk left at the end of the week. The initial amount of milk: 8 quarts = [tex]$8 \times 4 = 32$[/tex] cupsThe remaining amount of milk: [tex]$4 \frac{1}{2}$[/tex] cupsTo find the amount of milk James drank, we subtract the remaining amount from the initial amount: [tex]$32 \text{ cups} - 4 \frac{1}{2} \text{ cups} = 27 \frac{1}{2}$[/tex] cupsThe concept used in this problem is subtraction. By subtracting the amount of milk left at the end of the week from the initial amount of milk, we can determine how much milk James consumed during the week. The difference between these two values represents the amount of milk that James drank.Therefore, James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week.
NOTE: The given question has wrong information. The correct question is:
"At the beginning of the week, James has 8 quarts of milk. At the end of the week, there are [tex]$4 \frac{1}{2}$[/tex] cups of milk left. How many cups of milk did James drink during the week?"
For more questions on cups of milk:
https://brainly.com/question/21469890
#SPJ8
What is the slope of a line passing through the points (2,3)
and (5,3)?
Enter your answer as a number, like this: 42
Or, if the slope is undefined, enter a lowercase letter "u," like this: u
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 3 ) and (x₂, y₂ ) = (5, 3 )
m = [tex]\frac{3-3}{5-2}[/tex] = [tex]\frac{0}{3}[/tex] = 0
a line with a slope of zero is a horizontal line parallel to the x- axis
Convert
24 in = ___________ ft
700 cm. =__________m
Answer:
0.24ft
7m
Step-by-step explanation:
Simplify the expression
log₂8³x
Answer:
We can simplify the expression log₂8³x using the following logarithmic rule:
logₐb^c = c * logₐb
Using this rule, we can rewrite the expression as:
log₂8³x = 3log₂8 + log₂x
We can further simplify by recognizing that 8 can be expressed as a power of 2:
8 = 2³
Substituting this in, we get:
3log₂8 + log₂x = 3log₂(2³) + log₂x = 3 * 3 + log₂x = 9 + log₂x
Therefore, the simplified expression is:
log₂8³x = 9 + log₂x
Step-by-step explanation:
2 A car dealer, at a year-end clearance, reduces the price of last year's models by a certain amount. If a certain four-door model has been sold at a discounted price of Birr 51,000, with a discount of Birr 9,000, what is the percentage of discount?
The four-door model is sold at 15% discount.
Discount is the difference between list price and selling price.
List price is the original price of the product set by the seller.
Selling price is the price at which the product is actually sold.
We know that percentage of discount is:
Discount % = (Discount/ List price) * 100
where Discount= List price- Selling price
⇒ List price= Discount + Selling Price
⇒ List price = 9000 + 51000 = Birr 60,000
Calculating the discount percentage based on above mentioned results:
Discount % = (Discount/ list price)*100
⇒ (9,000/60,000)*100 = 15%
Therefore the percentage of discount for the four-door model sold at discounted price of Birr 51,000 with discount of Birr 9,000 is 15%.
Read more about discounts :
https://brainly.com/question/30366937?referrer=searchResults
https://brainly.com/question/32602544?referrer=searchResults
The athletic department spent $1,204 on airline tickets and $600 on hotel costs for the 4 members of the tennis team. How much was spent for each member of the tennis team?
HELP ME ASAP PLEASE
Answer:
451$
Step-by-step explanation:
$1,204 + $600 = 1804$
Since there are 4 members on the team, we divide the total sum of costs by 4.
$1804/4 = 451$.
Answer:
The athletic department spent $1,204 on airline tickets and $600 on hotel costs for the 4 members of the tennis team. To find out how much was spent for each member of the tennis team, you can add the cost of airline tickets and hotel costs and then divide by the number of members.
So, the total cost for airline tickets and hotel costs is $1,204 + $600 = $1,804. Since there are 4 members on the tennis team, the cost per member is $1,804 ÷ 4 = $451.
Therefore, $451 was spent for each member of the tennis team.
MARK AS BRAINLIEST!!!
4. Higher Order Thinking A national TV
news show conducted an online poll to find
the nation's favorite
comedian. The
website showed
the pictures of
5 comedians and
asked visitors of the
site to vote. The news
show inferred that
the comedian with
the most votes was
the funniest comedian
in the nation.
a. Is the inference valid? Explain.
b. How could you improve the poll? Explain.
No, the inference is not valid because it excluded those who were not online and so did not see the poll.
To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds
How to improve the poll ?The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.
To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.
Find out more on polls at https://brainly.com/question/29829313
#SPJ1
Need help, show work please
Using the first two points we can get an exponential model:
[tex]y = (225/23)*(23/15)^x[/tex]
How to find the exponential equation?
The general exponential equation can be written as:
[tex]y = A*(b)^x[/tex]
We can replace any two values of the table to get the system of eqautions:
[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]
Taking the quotient between the second and the first equation we get:
[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]
Replacing that on the first equation we will get:
[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]
Then an exponential model is:
[tex]y = (225/23)*(23/15)^x[/tex]
LEarn more about exponential equations at:
https://brainly.com/question/11464095
#SPJ1
Show that the partition of G into left cosets of H is different from its partition into right cosets?
It is shown below that the partition of G into left cosets of H is different from its partition into right cosets when n ≥ 3.
How to prove right cosets?Let us first find the left cosets of H in G:
H = {1, s₀}
s₁H = {s₁, s₁s₀}
s₂H = {s₂, s₂s₀}
s₃H = {s₃, s₃s₀, s₂s₁, s₂s₁s₀}...
Now, find the right cosets of H in G:
H = {1, s₀}
Hs₁ = {s₁, s₀s₁}
Hs₂ = {s₂, s₀s₂}
Hs₃ = {s₃, s₀s₃, s₁s₂, s₀s₁s₂}...
Observe that the left cosets of H in G and the right cosets of H in G are not the same when n≥3. This is because s₁s₀ is not in H, but s₀s₁ is in H.
Therefore, the left coset s₁H is not the same as the right coset Hs₁. Similarly, s₂s₁s₀ is not in H, but s₀s₁s₂ is in H, so the left coset s₃H is not the same as the right coset Hs₃.
Thus, it is shown that the partition of G into left cosets of H is different from its partition into right cosets when n≥3.
Find out more on cosets here: https://brainly.com/question/31416446
#SPJ1
Haleigh decides that instead of throwing away old candles, she can use the last bit of wax combined together to make new candles. Each candle has 10% of it's original wax left. How many 5 ounce candles can she make if she has five 20 oz candles, 5 five ounce candles, and twenty-five one-ounce candles?
Answer:she can make three 5 ounce candles. she had 15 ounces left over , 15/5=3 .
Step-by-step explanation: 5 of 10% of 20 ounces is 10 ounces, and both the 5 five ounce candles and the twenty five one ounce candles are each 2.5 extra ounces left. (5 for both), making a totalm of 15 ounces left to put into new candles.
A car travels for 10minutes.
At the beginning of the trip, the car traveled at a speed
of 13 m/s. At the end of the trip the car was traveling at a speed of 6 m/s. What is
the acceleration of the car?
Answer:
0.01167 m/s^2
Step-by-step explanation:
Acceleration is chage in velocity with respect to time. Another way to think of acceleration is in the units: m/s^2, or as I like to say, (m/s) /s.
The strategy to solve this kind of problem is to find the change in velocity (which will be in units of m/s)... and then divide that by the time passed.
In this case:
Change in Velocity = (13 m/s) - (6 m/s) = 6 m/s
Time passed = 10 min
Converting units of time: 10 min * (60 s / 1 m) = 600 sec
Acceleration = Change in Velocity / Time Passed
Acceleration = (6 m/s) / (600 s)
Acceleration = 0.01167 m/s^2
P(R) = 1/3 P(R & W) = 2/19
What is P(W|R)?
Group of answer choices
9/16
19/51
6/19
51/19
The probability of event W occurring given that event R has occurred is 6/19. Among the given answer choices, the correct probability is 6/19.
To find P(W|R), we can use the conditional probability formula:
P(W|R) = P(W & R) / P(R)
Given that P(R) = 1/3 and P(R & W) = 2/19, we can substitute these values into the formula:
P(W|R) = (P(R & W)) / P(R) = (2/19) / (1/3)
To divide by a fraction, we can multiply by its reciprocal
P(W|R) = (2/19) * (3/1) = 6/19
Therefore, the probability of event W occurring given that event R has occurred is 6/19.
Among the given answer choices, the correct probability is 6/19.
To learn more about probability :
https://brainly.com/question/24756209
#SPJ11
Write an expression to show how much it will cost if Kenny buys x number of hotdogs and each hot dog costs $2.
The expression to show how much it will cost if Kenny buys x number of hotdogs is x * $2.
To find the total cost if Kenny buys x number of hotdogs, we can multiply the number of hotdogs (x) by the cost per hotdog ($2). The expression to calculate the cost would be:
Total Cost = x * $2
In this expression, x represents the number of hotdogs Kenny wants to buy, and $2 represents the cost per hotdog.
For example, if Kenny wants to buy 5 hotdogs, we can substitute x with 5 in the expression:
Total Cost = 5 * $2
Simplifying the expression:
Total Cost = $10
So, if Kenny buys 5 hotdogs, it will cost him $10 in total.
Similarly, if Kenny buys any other number of hotdogs, we can substitute that value for x in the expression to calculate the corresponding total cost.
In summary, the expression to show how much it will cost if Kenny buys x number of hotdogs is x * $2.
For more questions on expression
https://brainly.com/question/1859113
#SPJ8
Help Quickly! Which line in the graph contains the point (4,3) and has a slope of 2/5?
*Giving Brainlyest if correct*
A. line r
B. line p
C. line s
D. line t
x + 2y = 2 y = −2x − 2
The solution of the system of equations is (-2, 2).
How to solve the system of equations?Here we want to find the solution of the system of equations:
x + 2y = 2
y = -2x- 2
To solve this, we can replace the second equation into the first one, then we will get:
x + 2*(-2x - 2) = 2
Now we can solve that for x:
x - 4x - 4 = 2
-3x = 2 + 4
-3x = 6
x = 6/-3 = -2
Thus, the value of y is:
y = -2*-2 - 2
y = 4 - 2 = 2
The solution of the system is (-2, 2)
Learn more about systems of equations at:
https://brainly.com/question/13729904
#SPJ1
Complete question:
"Which is the solution of the system of equations?
x + 2y = 2
y = -2x- 2"
The distribution for the life of refrigerators is approximately normal with a mean of 14 years and a standard deviation of 2.5 years. What percentage of refrigerators have lives between 11 years and 18 years?
The percentage of refrigerators that have lives between 11 years and 18 years is approximately 83.01%.
The values of 11 years and 18 years using the given mean and standard deviation, and then find the area under the standard normal curve between those two standardized values.
First, we standardize the value of 11 years:
z1 = (11 - 14) / 2.5 = -1.2
Next, we standardize the value of 18 years:
z2 = (18 - 14) / 2.5 = 1.6
Now we need to find the area under the standard normal curve between these two standardized values.
We can use a standard normal table or calculator to find this area.
Using a standard normal table, we can find the area between z = -1.2 and z = 1.6 by finding the area to the left of z = 1.6 and subtracting the area to the left of z = -1.2:
Area = P(-1.2 < z < 1.6) = P(z < 1.6) - P(z < -1.2)
Looking up these values in the standard normal table, we find:
P(z < 1.6) = 0.9452
P(z < -1.2) = 0.1151
Substituting these values, we get:
Area = 0.9452 - 0.1151 = 0.8301
For similar questions on percentage of refrigerators
https://brainly.com/question/27234494
#SPJ11
WORTH 25 points
Find the area of the parallelogram with given points.
(7,4)
(3,0)
(-4,9)
(13,0)
Question 14 of 15
Which number line shows the solutions to x+8 > 15?
A number line that shows the solutions to x+8 > 15 include the following: B. number line B.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Based on the information provided above, we have the following equation (inequality);
x + 8 > 15
By subtracting 8 from both sides of the equation (inequality), we have;
x + 8 - 8 > 15 - 8
x > 7
This ultimately implies that, the inequality must be shaded to the right with an open dot because the inequality symbol is greater than (>).
Read more on inequality here: https://brainly.com/question/30665021
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.