The average cost of weekly groceries exists at $124.50." The statistical measurement exists they most probably claim exists mean.
What is mean?The arithmetic mean of a given data exists as the totality of all observations divided by the number of observations.
For instance, a cricketer's scores in five ODI matches exist as follows:
12, 34, 45, 50, 24.
To estimate his average score in a match, we compute the arithmetic mean of data utilizing the mean formula:
Mean = Sum of all observations/Number of observations
Median
The value of the middlemost observation, acquired after organizing the data in ascending or descending order, exists named the median of the data.
For instance, consider the data: 4, 4, 6, 3, 2. Let's organize this data in ascending order: 2, 3, 4, 4, 6. There exist 5 observations.
Therefore, median = middle value i.e. 4.
Mode
The value which occurs most often in the provided data i.e. the observation with the highest frequency exists named a mode of data.
As per the circumstances we have given the average cost of groceries.
The mean exists also the average sum of data divided by the total number of data.
Therefore, the statistical measurement exists as the mean.
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The graph below shows the results of a survey of vacations. Which explanation below can be used to explain the point (1,1400)?
please help Tragize towels to the correct boxes to complete the pairs. Match the pairs of values
The results of the division of polynomials are given as follows:
h(x) = x + 3 for f(x) = x² - 9 and g(x) = x - 3.h(x) = x + 4 for f(x) = x² - 16 and g(x) = x - 4.h(x) = x - 1 for f(x) = x² - 4x + 3 and g(x) = x - 3.h(x) = x + 5 for f(x) = x² + 4x - 5 and g(x) = x - 1.What is the division of x² - 9 by x - 3?Considering that x² - 9 is the subtraction of perfect squares, we have that:
x² - 9 = (x - 3)(x + 3)
Hence the division is:
h(x) = (x - 3)(x + 3)/(x - 3) = x + 3.
What is the division of x² - 16 by x - 4?Considering that x² - 16 is the subtraction of perfect squares, we have that:
x² - 16 = (x - 4)(x + 4)
Hence the division is:
h(x) = (x - 4)(x + 4)/(x - 4) = x + 4.
What is the division of x² - 4x + 3 by x - 3?Considering that the roots of x² - 4x + 3 are x = 1 and x = 3, we have that:
x² - 4x + 3 = (x - 1)(x - 3).
Hence the division is:
h(x) = (x - 1)(x - 3)/(x - 3) = x - 1.
What is the division of x² + 4x - 5 by x - 1?Considering that the roots of x² + 4x - 5 are x = -5 and x = 1, we have that:
x² + 4x - 3 = (x + 5)(x - 1).
Hence the division is:
h(x) = (x + 5)(x - 1)/(x - 1) = x + 5.
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What is the value of x in the equation7x+2y=48 , when y = 3?
Answer:
x = 6
Step-by-step explanation:
put '3' in where 'y' is :
7x + 2(3) = 48
7x + 6 = 48 subtract 6 from both sides of the equation
7x = 42 divide both sides by 7
x = 6
Simplify the expression below.
2^3 x 2^2
A.46
B. 45
C. 25
D. 26
Answer: 32 is the answer to the expression you provided.
Step-by-step explanation:
[tex]2^3\times2^2\\2\times2\times2\times2\times2\\4\times4\times2\\16\times2\\\rightarrow32[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{E}\textsf{quation:}[/tex]
[tex]\mathsf{2^3 \times 2^2}[/tex]
[tex]\huge\boxed{S}\textsf{olving:}[/tex]
[tex]\mathsf{2^3 \times 2^2}[/tex]
[tex]\mathsf{= 2\times2\times2 \times2\times2}[/tex]
[tex]\mathsf{= 4\times4\times2}[/tex]
[tex]\mathsf{= 16\times2}[/tex]
[tex]\mathsf{= 32}[/tex]
[tex]\huge\boxed{T}\textsf{herefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{32}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
If A c B and A N B= • then which of the following can be concluded about the sets A and B!
Step-by-step explanation:
Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)
The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets
so, the answer for the question would be "both the Sets A and B are the empty sets"
In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.
Step-by-step explanation:
3over4 which is 75percentAn unfair coin is flipped. if a head turns up you win $1. the probability of a head is. 54 and the probability of a tail is 0. 46. what is the expected value of the game?
Answer:
if you end up landing on a heads you should walk away with a $1.46
How much work can a 500 w Electric mixer do in 2.5 minutes
Answer:
Work(W)=7.5*10⁴J
Step-by-step explanation:
Greetings !
[tex]firstly \: recall \: the \: work \: power \: equation \\ w = pt \\ substitute \: known \: variables \: to \: the \: equation \\ w = (500)(150) \\ change \: 2.5min \: to \: second = 150second \\ solve \: for \: work \\ w = 7.5 \times 10 {}^{4} j[/tex]
Which linear inequality is represented by the graph
Answer:
y > 3x + 2
Step-by-step explanation:
The slope is 3. slope = (-7 - 2)/(-3 - 0) = -9/(-3) = 3
The y-intercept is 2.
The equation of the line is y = 3x + 2
The shading is "above" the line.
Answer: y > 3x + 2
x(x-5) (x+5) - (x+2) (x^2 - 2x +4) = 17
x[x²-25] - [x³+8] = 17
x³- 25x - x³- 8 = 17
-25x = 17 + 8
-25x = 25
x = -1
There are two numbers between 30 and 40 that have just two factors.
What are they?
Answer:
31 and 37
Step-by-step explanation:
Those are the only two numbers
Answer:
The two numbers between 30 and 40 which have only 2 factors are -
31 and 37
Hope it helps you.
Why is APR an important tool for consumers?
a. It allows consumers to borrow from more than one lender at the same time.
b. It allows consumers to compare the full cost of loans from different lenders.
c. It allows consumers to choose their level of down payment.
d. It provides an opportunity for consumers to become familiar with various interest calculators.
e. It provides consumers with negotiating skills to get lenders to reduce rates.
The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.
According to the statement
we have to explain all about the APR and tel that why it is important for the consumers.
So, For this purpose,
We know that the
The term annual percentage rate of charge, corresponding sometimes to a nominal APR and sometimes to an effective APR.
It is the interest rate for a whole year, applied on the loan etc. It is a finance charge expressed as an annual rate
APR is the important tool for the consumers because of some reasons which are written below:
APR is important because it can give you a good idea of how much you'll pay to take out a loan.
APR helps a customer determine the true cost of the loan, allowing them to compare many loans and choose the most advantageous one.
So, The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.
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A semi-circle window can be used above a doorway or as an accent window
in a room to allow more light in large rooms. The semi-circle window in your
home theater room lets too much light in so that the movie experience is not
optimal at any time of the day.
You research and find there are “room darkening” blinds and shades for
semi-circle windows. You can’t quite reach the semi-circle window to
measure but you are able to measure the window beneath. The height of the
rectangle window below is 85 in and the width of the window below the semi-circle is 50 in.
What is the area of the semi-circle window so that you can start your search for the correct size?
Be sure to show and explain your work.
A semicircle is a part of a circle, and it is referred to as half of a given circle. Thud the area of the semi-circle window is 982 [tex]in^{2}[/tex].
A circle is a shape that is bounded by a curved path which is referred to as the circumference. Some parts of a circle are radius, diameter, sector, arc, semi-circle, circumference, etc.
A semicircle is a part of a circle, and it is referred to as half of a given circle.
such that:
Area of a circle = [tex]\pi[/tex] [tex]r^{2}[/tex]
and
area of a semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]
where: r is the radius of the circle, and [tex]\pi[/tex] is a constant with a value of [tex]\frac{22}{7}[/tex].
Thus from the given question, it can be inferred that;
r = [tex]\frac{50}{2}[/tex]
= 25
r = 25 in
Thus, the area of the semi-circle can be determined as;
area of the semi-circle = [tex]\frac{1}{2}[/tex] * [tex]\frac{22}{7}[/tex] * [tex]25^{2}[/tex]
= 982.1429
area of the semi-circle = 982.14 [tex]in^{2}[/tex]
The area of the semi-circle window is approximately 982 [tex]in^{2}[/tex].
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Let ABCD be an isosceles trapezoid (AB//CD). Draw AE, BF perpendicular to CD (E, F belong to CD), Let AB = 8cm, CD = 18cm, AD = 13cm.
a) Prove that triangle ADE = triangle BCF
b) Calculate DE, CF.
c) Calculate AE.
Thanks for solving the homework
A trapezoid is a plane figure bounded by four sides. Therefore, the required answers are given below;
a) ΔADE = ΔBCF (Side-Angle-Side congruent property)
b) DE = 5 cm and CF = 5 cm
c) AE = 12 cm
Plane figures are shapes that are formed by straight boundaries referred to as sides. Examples include; square, rectangle, trapezium, etc.
A trapezoid is a family of quadrilaterals., these are figures that have four straight sides.
In the given question, the required answers are:
a) To prove that ΔADE = ΔBCF
Thus,
AE ⊥ DC (given)
BC ⊥ DC (given)
<AED = <BFC = [tex]90^{o}[/tex]
AE = BF (height of the trapozoid)
<ADE ≅ <BCF (congruent property of two triangles)
Therefore, it can be concluded that;
ΔADE = ΔBCF (Side-Angle-Side congruent property)
b) Given that AB = 8 cm, and DC = 18 cm.
Then,
CD = DE + EF + FC
18 = DE + 8 + FC (since EF = AB)
18 - 8 = 2 DE (since DE = FC)
DE = 5 cm
Thus, DE = 5 cm and CF = 5 cm
c) To determine the value of AE, we have to apply the Pythagoras theorem. So that;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]13^{2}[/tex] = [tex]AE^{2}[/tex] + [tex]5^{2}[/tex]
169 - 25 = [tex]AE^{2}[/tex]
[tex]AE^{2}[/tex] = 144
AE = [tex]\sqrt{144}[/tex]
= 12
AE = 12 cm
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Marcus had $50 in the bank and deposited
$x a week. At the end of 15 weeks, he had
$1,010 in the bank. Write and solve an
equation to determine how much money he
deposited each week.
13)
Answer:
$64
Step-by-step explanation:
Equation: 50 + 15x = 1010
x = (1010 - 50) ÷ 15 = 64
Since x is the total amount of money deposited in the bank per week, the answer is $64.
Sumalee and Julio are selling cheesecakes for a school fundraiser. Customers can buy pecan
cheesecakes and apple cheesecakes. Sumalee sold 6 pecan cheesecakes and 12 apple
cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a
total of $285. Find the cost each of one pecan cheesecake and one apple cheesecake.
The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.
According to the statement
we have given that the Sumalee sold 6 pecan cheesecakes and 12 apple
cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a
total of $285.
And we have to find that the cost each of one pecan cheesecake and one apple cheesecake.
So, for this purpose,
Let x be the cost of each pecan cheesecake.
and y be the cost of each one apple cheesecake.
Then The equation become
6x + 12y = 270 -(1)
12x + 9y = 285 -(2)
From elimination method
multiply (1) by 12 and (2) by 6 then
72x + 144y = 3240
72x + 54y = 1710
Now eliminate x from them then the equation become
90y = 1530
here y = 17
then the x become
6x + 12y = 270
6x + 12(17) = 270
6x = 270-204
6x = 66
and x become 11.
So, The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.
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Write 2^8 * 8^2 * 4^-4 in the form 2^n
The given expression 2^8 * 8^2 * 4^-4 can be written in the exponential form 2^n as 2^6.
What are exponential forms?The exponential form is a more convenient way to write repetitive multiplication of the same integer by using the base and its exponents.
For example:
If we have a*a*a*a, it can be written in exponential form as:
=a^4
where
a is the base, and4 is the power.The power in this format reflects the number of times we multiply the base by itself. The exponent is also known as the index or power.
From the information given:
We can write 2^8 * 8^2 * 4^-4 in form of 2^n as follows:
[tex]\mathbf{= 2^8\times (2^3)^2 \times (2^2)^{-4} }[/tex]
[tex]\mathbf{= 2^8\times (2^6) \times (2^{-8}) }[/tex]
[tex]\mathbf{= 2^{8+6+(-8)}}[/tex]
[tex]\mathbf{= 2^{6}}[/tex]
Therefore, we can conclude that by using the exponential form, the given expression 2^8 * 8^2 * 4^-4 in the form 2^n is 2^6.
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Select the correct answer. if function g has the factors (x − 7) and (x 6), what are the zeros of function g? a. -7 and 6 b. -6 and 7 c. 6 and 7 d. -7 and -6
Option (b) -6 and 7 is the correct option.
The zeroes of the function f and g are x=7 and x=-6 respectively.
What are the zeroes of a polynomial?The values of x that satisfy the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Put x-7=0
X=7
Now, put x+6=0
So, x=-6
The zeroes of the function f and g are 7 and -6 respectively.
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Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. if he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings? a. $40 b. $60 c. $74 d. $55
The total amount he puts towards emergency savings is $74
The correct option is C.
According to the given information:His total weekly deposits are as follows: 219+115+40+20+10+40+15 = 459
Now
that we are aware, his weekly deposits total $459 in total.
His total remuneration is $498 due to an error in his addition of the numbers.
The amount he has each week will be determined by deducting his deposits from his paycheck:
498-459 = 39
He contributes two equal payments of $20 and $15 to his emergency fund.
His entire contribution to emergency savings is = 20 + 15 = 35.
Only need to add the additional $39
To determine how much he can set aside each week for emergency savings, multiply his total emergency savings by 35 dollars:
39+35 = 74
the total per week that he can put towards emergency savings = $74
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I understand that the question you are looking for is:
Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Pictable) Education investment fund $10 Other (Pictable) Retirement investment fund $40 Other (Pictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?
a. $40
b. $60
c. $74
d. $55
Answer: C. $74
Step-by-step explanation: C. $74.00
Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the bird reaches Bob, it turns around immediately and starts flying toward Alice at the same speed, turning around immediately when it reaches Alice, and repeating this procedure until Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
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which graph below shows the solutions for the linear inequality y>- 1/3x + 1
The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.
How to Find the Graph of a Linear Inequality?The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.
On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.
Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.
Graph A has a slope of -1/3 and the shaded part is above the boundary line.
Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.
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Can someone pls help me get the anwser for this question
Answer: [tex]\Large\boxed{x=6.5}[/tex]
Step-by-step explanation:
Given equation
-9 - (x + 1) = -2 - (3x - 5)
Expand the parenthesis
-9 - x - 1 = -2 - 3x + 5
Combine like terms
-9 - 1 - x = -2 + 5 - 3x
-10 - x = 3 - 3x
Add 3x on both sides
-10 - x + 3x = 3 - 3x + 3x
-10 + 2x = 3
Add 10 on both sides
-10 + 2x + 10 = 3 + 10
2x = 13
Divide 2 on both sides
2x / 2 = 13 / 2
[tex]\Large\boxed{x=6.5}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Evaluate |2 5/6 + y for y = 7/4
O A. 2 2/5
O B. 3 1/5
O C. 3 4/5
O D. 4 8/12
Answer:
D) 4 8/12
Step-by-step explanation:
To first start this, let's make 2 5/6 an in-proper fraction by adding 12 and removing the whole 2. =17/6. Then let's get a common denominator by multiplying both the denominators by each other...6x4 and 4x6, but we also multiply the numerators by the same thing that the denominators are getting multiplied by... 17x4 and 7x6. We will then get 68/24 and 42/24. And then we can add both numerators with eachother and keep the denominator to get, 110/24... and making this into a propor fraction would equal 4 16/24... and dividing by 2 would equal 4 8/12
A dealer marked the price of a digital watch as Rs 6,000. She then allowed 20% discount to make 20% profit. If she increased the discount to 25%, by how much was the profit percent decreased?
Profit decreased by 7.5%
Answer:
Solution Given:
Marked Price= Rs 6,000
discount =20%
Selling Price =M.P- discount% of M.P
=M.P(1-discount%)
=6000(1-20%)
= Rs 4,800
Again
Profit = 20%
Cost Price=(S.P*100)/(100+profit%)
= (4800*100)/(100+20%)
= Rs 4,000
For discount 25%
Marked Price =Rs 6,000
Selling Price =M.P - discount% of M.P
=M.P(1-discount%)
=6000(1-25%)
=Rs 4,500
Profit = S.P- C.P= Rs 4,500- Rs 4,000=Rs 500
Profit %=Profit/C.P* 100%= 500/4000*100 = 12.5%
Profit % decreased from 20% to 12.5%
Profit decreased by 7.5%
Answer:
7.5%
Step-by-step explanation:
Marked Price
Rs 6,000
Discounted Price
If the price is discounted by 20%, then the discounted price is 80% of the marked price:
[tex]\implies \sf Discounted\:Price =80\% \textsf{ of marked price}[/tex]
[tex]\implies \sf Discounted\:Price =0.8 \times 6000[/tex]
[tex]\implies \sf Discounted\:Price = 4800\:Rs[/tex]
Cost Price
If the dealer makes 20% when selling the watch at the discounted price, then the cost price is:
[tex]\implies \sf Cost\:Price=\dfrac{100\%}{120\%} \times 4800[/tex]
[tex]\implies \sf Cost\:Price=\dfrac{4800}{1.2}[/tex]
[tex]\implies \sf Cost\:Price=4000\:Rs[/tex]
Discount of 25%
If the price is discounted by 25%, then the discounted price is 75% of the marked price:
[tex]\implies \sf Discounted\:Price =75\% \textsf{ of marked price}[/tex]
[tex]\implies \sf Discounted\:Price =0.75\times 6000[/tex]
[tex]\implies \sf Discounted\:Price = 4500\:Rs[/tex]
Profit after 25% discount
[tex]\implies \sf Profit=\dfrac{discounted\:price}{cost\:price}-1 \times 100[/tex]
[tex]\implies \sf Profit=\dfrac{4500}{4000}-1 \times 100[/tex]
[tex]\implies \sf Profit=12.5\%[/tex]
Therefore, the profit decreased from 20% to 12.5% which means the profit percent decreased by 7.5%.
Select the order in which the operations should be performed
(L20) 5 – 3(4)
Subtract 3 from 5, then multiply that number by 4.
Multiply 3 and 4, then subtract that total from 5.
Subtract 4 from 5, then multiply that number by 3.
Multiply 5 and 4, then subtract 3 from that total.
Answer:
Multiply 3 and 4, then subtract that total from 5.
Step-by-step explanation:
You would need to follow P.E.M.D.A.S.
Parentheses, Exponents, Multiply & Divide, Add & Subtract
Hope that helps! Let me know if you need more help. Please mark me as brainliest!
(3-4^2)^2+8
Bdhdhdhsjsjsj
Answer: 177
Step-by-step explanation:
1. 4x4=16
(3-16)^2+8
2. 3-16=-13
(-13)^2+8
3. -13x-13=169
169+8
4.169+8=177
177
Answer:
177
Step-by-step explanation:
PEMDAS
The PEMDAS rule is an acronym representing the order of operations in math:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)Given expression:
[tex](3-4^2)^2+8[/tex]
Parentheses
Begin by calculating the part inside the parentheses.
Following PEMDAS, calculate the exponent first:
[tex]\implies (3-4^2)^2+8=(3-16)^2+8[/tex]
Then carry out the subtraction:
[tex]\implies (3-16)^2+8=(-13)^2+8[/tex]
Exponents
[tex]\textsf{Apply the exponent rule}: \quad (-a)^n=a^n, \quad \textsf{if }n \textsf{ is even}[/tex]
[tex]\implies (-13)^2+8=169+8[/tex]
Addition
[tex]\implies 169+8=177[/tex]
Therefore:
[tex]\implies (3-4^2)^2+8=177[/tex]
A bag with 6 marbles has 2 yellow marbles, 1 blue marble, and 3 red marbles. A marble is chosen from the bag at random. What is the probability that is yellow?
Answer:
P = 1/3
P = 0.333
Step-by-step explanation:
There are 6 marbles in the pack, two of them are yellow.
[tex]P=\frac{2}{6} =\frac{1}{3}[/tex]
Hope this helps
if 1+sin² =3sin *cos, prove that tan = 1 or 1/2
Step-by-step explanation:
hif 1+sin² =3sin *cos, prove that tan = 1 or 1/2pls help me with this
Answer:
Step-by-step explanation:
9. the set containing all objects or elements and of which all other sets are subsets.
10. complement --> the amount in only one of teh sets
intersection --> the amount in both sets
11. 14 or -14
13. 46 1/2
14. 2 31/120
15. 1100% profit
16. 1200 gm
17. cube root of 7?
18. 6000 per year
If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]
▪ [tex] \sf{Area = 72 yd^2}[/tex]
▪ [tex] \sf{BD = 6yd}[/tex]
[tex]\leadsto[/tex] Substitute the values:
[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]
[tex]\leadsto[/tex] Solve for AC:
[tex]\longrightarrow \sf{72=8\times AC}[/tex]
[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]
[tex]\longrightarrow \sf{AC=9}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large \bm{AC= \: 9 yd}[/tex]
BD = 16 yd
Area of ABCD = 72 yd²
AC = ?
Area of rhombus, using diagonal:
[tex] \frac{1}{2} \times d1 \times d2[/tex]
Therefore:
[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]
Then:
[tex] \frac{16ac}{2} = 72[/tex]
Cross multiply the above into:
[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]
Divide by the coefficient of AC:
[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]
Final answer is 9 yd