Answer: It is not possible that two triangles that are similar and not congruent in spherical geometry.
Step-by-step explanation:
For instance, taking a circle on the sphere whose diameter is equal to the diameter of the sphere and inside is an equilateral triangle, because the sphere is perfect, if we draw a circle (longitudinal or latitudinal lines) to form a circle encompassing an equally shaped triangle at different points of the sphere will definately yield equal size.
in other words, triangles formed in a sphere must be congruent and also similar meaning having the same shape and must definately have the same size.
Therefore, it is not possible for two triangles in a sphere that are similar but not congruent.
Two triangles in sphere that are similar must be congruent.
A sine function has the following key features:
Frequency = 1/4π
Amplitude = 2
Midline: y = 2
y-intercept: (0, 2)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function.
The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
Answer:
I took this test and while it was hard I managed to get this answer correct here is the picture
I know this answers two years late, but it will help those in the future
Good luck, hope you ace the test
To graph the sine function with provided features, we calculate the period from the frequency, acknowledge the midline at y = 2, and recognize the amplitude of 2. The first maximum is at (π, 4), giving us the complete function y = 2 sin(π/2 x) + 2.
Explanation:To graph a sine function with the given features, we first recognize that the frequency of 1/4π means the period (T) of the function is the reciprocal of the frequency, or 4π. The amplitude of 2 indicates the function will oscillate 2 units above and below the midline, which is represented by y = 2. Since the function is not reflected over the x-axis and has a y-intercept of (0, 2), we start at the midline. The graph will reach its first maximum at (T/4, 2 + amplitude) which is (π, 4), since one quarter of the period will place us at a peak of the sine wave. The complete sine function derived from these features would be y = 2 sin(π/2 x) + 2.
One employee of a computer store is paid a base salary of $2,000 a month plus an 8% commission on all sales over $7,000 during the month. How much must the employee sell in one month to earn a total of $4,000 for the month?
Answer: the employee must make sales of $32000
Step-by-step explanation:
Let x represent the total sales that the employee makes in a month.
One employee of a computer store is paid a base salary of $2,000 a month plus an 8% commission on all sales over $7,000 during the month. This means that if the employee makes sales of $x in a month, his total earnings for that month would be
2000 + 8/100(x - 7000)
= 2000 + 0.08(x - 7000)
= 2000 + 0.08x - 560
= 0.08x + 1440
Therefore, for the employee to earn
a total of $4,000 for the month, the amount of sales would be
0.08x + 1440 = 4000
0.08x = 4000 - 1440
0.08x = 2560
x = 2560/0.08
x = $32000
A group of 86 people consist of men women and children. There are twice as many women then there are men. There are 6 more children than there are women. How many men women and children in group
Answer: 16 men
32 women
38 children
Step-by-step explanation:
Let x represent the number of men in the group.
Let y represent the number if women in the group.
Let z represent the number of children in the group.
A group of 86 people consist of men women and children. This means that
x + y + z = 86 - - - - - - - - - - - - 1
There are twice as many women than there are men. It means that
x = y/2
There are 6 more children than there are women. This means that
z = y + 6
Substituting x = y/2 and z = y + 6 into equation 1, it becomes
y/2 + y + y + 6 = 86
multiplying through by 2, it becomes
y + 2y + 2y + 12 = 172
5y = 172 - 12 = 160
y = 160/5 = 32
x = y/2 = 32/2
x = 16
z = y + 6 = 32 + 6
z = 38
There are 16 men, 32 women, and 38 children in the group.
Explanation:Let the number of men be M, the number of women be W, and the number of children be C.
From the given information, we have the following equations:
W = 2M (Twice as many women as men)
C = W + 6 (6 more children than women)
The total number of people is given as 86:
M + W + C = 86
Substituting the values of W and C in terms of M into the third equation, we have:
M + 2M + (2M + 6) = 86
5M + 6 = 86
5M = 80
M = 16
Substituting the value of M in the first equation, we have:
W = 2(16) = 32
Finally, substituting the value of W in the second equation, we have:
C = 32 + 6 = 38
Therefore, there are 16 men, 32 women, and 38 children in the group.
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You are designing a wall Mural that will be composed of squares of different sizes. One of the requirements of your design is that the side length of each square itself is a perfect square. If you represent the side length of the square as x to the power of 2 write an expression for the area of the mural square.
Answer:
1. Area of a square = (x^2)^2 = x^4
(each side is x^2, area of a square = side^2
so (x^2)(x^2) = x^4 )
2. when x = 5
area = 5^4 = 625
3. when x = 10
area = 10^4 = 10000
Step-by-step explanation:
Hope its right!
Final answer:
The area of a square mural where the side length is a perfect square, represented as x², can be expressed as A = x⁴, which simplifies the concept of multiplying the side length by itself twice.
Explanation:
The area of a mural square, where the side length is a perfect square represented as x to the power of 2 (x²), is calculated by squaring the side length. Therefore, if x itself is a perfect square, the area A of the square mural is given by A = x² * x², which simplifies to A = x⁴. Since the side length is a perfect square, x could be expressed as y² where y is an integer, resulting in the area being y⁴, where y⁴ represents the side length squared twice.
Rebecca is three years younger than twice Anthony's age. Write an expression that represents the relationship of Rebecca's age in terms of Anthony's age.
Answer:
X=2y-3
Step-by-step explanation:
Let Rebecca's age be x
Let Anthony's age be y
Twice Anthony =2y
Rebecca's age (x) to be 3 years younger than twice Anthony's =2y-3
So, it's x=2y-3
PLEASEEEEE HELP ASAP!!!
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle
AB represents the hypotenuse of the right angle triangle.
With m∠A as the reference angle,
AC represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine AB, we would apply the Cosine trigonometric ratio
Cos θ = opposite side/hypotenuse. Therefore,
Cos 52 = 10/AB
0.616 = 10/AB
AB = 10/0.616
AB = 16.23
Identify the domain and range of the inverse of f(x) = 0.5^x.
Answer:
Domain (0, ∞) and Range (-∞, ∞).
Step-by-step explanation:
The domain of f(x) = 0.5^x is all values of x and the range is f(x)>0 as 0.5^x cannot be negative or zero.
In interval form this is Domain is (-∞, ∞) and Range is (0, ∞).
So its inverse has Domain (0, ∞) and Range (-∞, ∞).
The requierd domain (0, ∞) and range (-∞, ∞) of the inverse of f(x) = 0.5ˣ.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The exponential function is given in the question, as follows:
f(x) = 0.5ˣ
Here the domain of f(x) = 0.5ˣ is all values of x and the range is f(x) > 0 as f(x) = 0.5ˣ cannot be negative or zero.
In interval form, the Domain is (-∞, ∞) and the Range is (0, ∞).
As a result, its inverse has Domain (0, ∞) and Range (-∞, ∞)
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Mona and Shakira play on a basketball team. In one game, Shakira scored twice as many points as Mona. Together they scored 24 points in that game. How many points did each girl score?
Answer:
Mona = 8, Shakira = 16
Step-by-step explanation:
S = 2m....m = S/2
2S + S = 24
3S = 24
S = 24/3
S = 8
Mona = 8
Shakira = 16
What is the 6th value in the sequence with the explicit formula an=−2n−14?
Answer:
-26
Step-by-step explanation:
a(6)=-2(6)-14
a(6)=-12-14
a(6)=-26
Hope this helped!
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The 6th value in the sequence = an=−2n−14 = -4.3
Take n = 6
⇒ a6 = -2·6 -14 = -12-14 = -26
∴ a= [tex]\frac{-26}{6}[/tex] = -4.3
Explicit formulaThe explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geomrietc, or harmonic sequence.
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In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon. How much cinnamon does the spice mix contain per pound? A. 5/8 B. 9/10 C. 1 1/9 D. 1 3/5
Answer:
option C
Step-by-step explanation:
In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon
The ration of spice mix over Cinnamon is
[tex]\frac{\frac{3}{4} }{\frac{5}{6} } =\frac{3}{4} \cdot \frac{6}{5} =\frac{9}{10}[/tex]
Let x be the spice mix per pound
make a proportion
[tex]\frac{9}{10} =\frac{1}{x}[/tex]
cross multiply
[tex]9x=10\\x=\frac{10}{9}\\x= 1 \frac{1}{9}[/tex]
option C is the answer
What is the value of x? 6.75 + StartFraction 3 Over 8 EndFraction x = 13 and one-fourth 2 and StartFraction 7 Over 16 EndFraction 17 and one-third 18 and two-thirds 53 and one-third
Answer:
the answer is B: 17 and one-third
Step-by-step explanation:
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠H.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠H = °
Answer:
Step-by-step explanation:
Triangle GHI is a right angle triangle.
From the given right angle triangle,
HI represents the hypotenuse of the right angle triangle.
With m∠H as the reference angle,
GH represents the adjacent side of the right angle triangle.
GI represents the opposite side of the right angle triangle.
To determine m∠H, we would apply
the Sine trigonometric ratio.
Sine θ = opposite side/hypotenuse. Therefore,
Sin H = 9/10 = 0.9
m∠H = Sin^-1(0.9)
m∠H = 64.2° to the nearest tenth.
What is the near or exact matching of the left and right sides of a three-dimensional for or a two-dimensional composition?
Answer:
Im pretty sure it is symmetrical-balance
Step-by-step explanation:
Answer:
symmetrical-balance.
Step-by-step explanation:
In design, the near or exact matching of left and right sides of a three-dimensional form or a two-dimensional composition.
You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall
is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an
arithmetic sequence. What is the total distance the object will fall in 6 seconds?
Answer: the total distance that the object will fall after 6 seconds is 576 feet.
Step-by-step explanation:
The formula for determining the sum of n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
n represents the number of terms in the arithmetic sequence.
d represents the common difference of the terms in the arithmetic sequence.
a represents the first term of the arithmetic sequence.
From the information given,
n = 6 seconds
a = 16 feet
d = 80 - 48 = 48 - 16 = 32
Therefore, the total distance the object will fall in 6 seconds is the sum of the first 6 terms, S6. It becomes
S6 = 6/2[2 × 16 + (6 - 1)32]
S6 = 3[32 + 32 × 5]
S6 = 3 × 192 = 576 feet
Final answer:
The total distance the penny falls in 6 seconds, according to the arithmetic sequence provided (16 feet the first second, 48 feet the second, and so on), is 576 feet.
Explanation:
The question involves calculating the total distance an object falls in a given number of seconds, according to an arithmetic sequence. In this case, the penny falls 16 feet in the first second, 48 feet in the second, and the distance increases by a constant amount each second. This is an arithmetic sequence where each term increases by 32 feet (48 - 16 = 32). To find the total distance, we sum the first six terms of the sequence.
The general formula for the nth term of an arithmetic sequence is a_n = a_1 + (n - 1) * d, where a_1 is the first term and d is the common difference. We can calculate the distance for each second and then add them up.
Here is how you calculate it:
First second: 16 feet
Second second: 16 + 32 = 48 feet
Third second: 48 + 32 = 80 feet
Fourth second: 80 + 32 = 112 feet
Fifth second: 112 + 32 = 144 feet
Sixth second: 144 + 32 = 176 feet
To find the total distance, add these values together:
Total distance = 16 + 48 + 80 + 112 + 144 + 176 = 576 feet.
PLZ HURRY IT'S URGENT!!
What is the ratio of m to n in simplest form given 10m = 5n?
2/5
1/2
2/1
10/1
Answer:
1/2.
Step-by-step explanation:
10m = 5n
m = 5n/10
m = n/2
m/n = n/2 * 1/n
m/n = 1/2.
Answer:1/2
Step-by-step explanation:
10m=5n
Divide both sides by 5n
10m/5n=5n/5n
2m/n=1
Therefore m/n=1/2
BRAINLIEST !! Pls at least take a look , answer all or don't answer
Answer:
1) 706.86
2) 726 cm^3
3) V= 792 km^3
4) 209.4 ft^3
Step-by-step explanation:
#4: V=πr2h
3.14 times the radius, then the height divided by 3
#3 V=lwh
V=lwh3 length times width times height divided by 3
#2 ^same as #3 steps
#1 A=πr2
pi times the radius squared
Answer:
1. 706.5
2. 726
3. 396
4. 130.8
Step-by-step explanation:
1. Area = pi × r²
= 3.14 × 15²
= 706.5 ft²
2. Volume = ⅓ × base area × height
= ⅓ × 11² × 18
= 726 cm³
3. Volume = ⅓ × base area × height
= ⅓ × ½ × 9 × 12 × 22
= 396 km³
4. radius = 10/2 = 5
Volume = ⅓ × base area × height
= ⅓ × 3.14 × 5² × 5
= 130.83333 ft³
If Alex and Brandon work together, they will clean the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself?
Answer:
I think it is 5 but don't take my word for it
Step-by-step explanation:
I think you minus 20 - 15 which equals to 5 so 20 - 15 = 5 hopefully i was a little helpful just try that if its not correct i'm so sorry i will practice my math and answer this question again thank you for being so understanding
Answer:
Correct answer: Alex can finish the same job in 60 hours
Step-by-step explanation:
The appropriate equation for this situation is:
1/20 + 1/x = 1/15 => (x + 20) / 20x = 1/15 => 15 · (x + 20) = 20x =>
15x + 300 = 20x => 5x = 300 => x = 300/5 = 60 hours
x = 60 hours
God is with you!!!
Estimate the solution to the graph shown below.
5,-3)
(4,-3)
(-3,4)
Solve the following linear system any way you like.
x+ y= 4
x - y= 2
(2, 0)
(2, 4)
No solution
(0, 6)
(0, 4)
(-6,0)
Answer:
The answer to your question is 1.- (-3, 4) 2.- (3, 1) None of the choices
Step-by-step explanation:
1.- The solution of a system of equation by the graph method is the point in which the lines cross. In this graph we observe that this point is approximately
(-3, 4).
2.-
Equation 1 x + y = 4
Equation 2 x - y = 2
Solve by the combination method
x + y = 4
x - y = 2
2x 0 = 6
2x = 6
Solve for x
x = 6/2
x = 3
Substitute x in equation 1 to find y
3 + y = 4
Solve for y
y = 4 - 3
y = 1
Solution (3, 1)
Josie combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. She pours the paint equally into 2 containers, and has 1.56 liters of paint left over. How many liters of paint are in each container?
Answer: each container has 6.68 liters.
Step-by-step explanation:
Josie combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. This means that the total number of liters of paint in the mixture(purple paint) is
8.27 + 6.65 = 14.92 liters
She pours the paint equally into 2 containers, and has 1.56 liters of paint left over. This means that the amount of paint that she poured inside the 2 containers is
14.92 - 1.56 = 13.36 liters.
Therefore, the number of liters of paint in each container is
13.36/2 = 6.68 liters
Which of the following describe the function
g(x) = log2 (x - 2) – 3.
Choose ALL that apply.
The domain is the set of all real number greater than 2.
The x-intercept = ( 10,0) and there is no y-intercept
Avertical asymptote at x = 2.
There is no x-intercept and the y-intercept = (0,10 ).
The domain is the set of all real numbers less than 2
The graph of g(x) is symmetric to its inverse exponential function over the line y = 0
The graph of g(x) is symmetric to its inverse exponential function I’ve ether like y = x
A vertical asymptote at x = 10
Answer:
The domain is the set of all real number greater than 2.
The x-intercept = ( 10,0) and there is no y-intercept
A vertical asymptote at x = 2.
The graph of g(x) is symmetric to its inverse exponential function over the line y = x
Step-by-step explanation:
Final answer:
The correct descriptions of the function g(x) = log2 (x - 2) – 3 are: the domain is all real numbers greater than 2, there is a vertical asymptote at x = 2, and the graph is symmetric over the line y = x with relation to its exponential inverse. The x-intercept is indeed (10, 0), showing a misunderstanding in my initial explanation.
Explanation:
The question involves analyzing the properties of the function g(x) = log2 (x - 2) – 3. Let's address each statement:
The domain is the set of all real numbers greater than 2. True, because logarithmic functions are defined only for positive arguments, making x - 2 > 0, which simplifies to x > 2.A vertical asymptote at x = 2. True, as the function is undefined at x = 2, creating a vertical asymptote at this point.The graph of g(x) is symmetric to its inverse exponential function over the line y = x. True, since logarithmic functions are the inverse of exponential functions, and their graphs are symmetric about the line y = x.The x-intercept is (10, 0). This statement is false. To find the x-intercept, set g(x) = 0 and solve for x. Thus, log2(x - 2) = 3, and solving for x yields x = 10, making the statement true. My mistake.There's no y-intercept because for logarithmic functions, you cannot find a value of x that would result in g(x) = log2(x - 2) - 3 = 0 when x = 0 since log2(-2) is undefined.Which equation describes a linear function? a) y = 3x + 5, b) y = -x^2 -5 , c) y = 3/x, d) y = x^3
Answer:
A Linear function is an equation whose graph is a straight line. It has the following form; y = a + bx.
A linear function contains one independent variable and one dependent variable. X is the independent variable and y is the dependent variable.
The answer is a) y = 3x + 5
Let us first concentrate on the central value. take f0 = n and 0 = . find the central value of fx, in n
Answer:
Fx=N177.007
Step-by-step explanation:
Let us first concentrate on the central value. Take F0 = 325 and theta 0 = 57 degrees. Find the central value of Fx, in N
can be pu as thus from an online resource
To resolve forces into the horizontal component , we have
Fx=fCosФ
Fx=325Cos57
Fx=N177.007
Take Note that a force is that which tends to change a body's state of rest or uniform motion in a straight line.
Which 2 statements are correct regarding reconciling a bank account in QuickBooks Online? (Select all that apply) You can only undo a bank reconciliation via a link in the Accountant Toolbox To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement Reconciliations must only be run at period end to estimate tax owed To see the Reconciliation report, select View report after you've successfully reconciled the account
Answer:
The correct statements are:
To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement
To see the Reconciliation report, select View report after you've successfully reconciled the account.
EXPLANATION:
The steps to reconciling a bank account using QuickBooks Online include:
1. Click on the Gear button, then on “Tools” and then “Reconcile.”
2. Click on the drop-down menu under “Accounts” and select the account you want to reconcile.
3. Enter the “Ending balance” and “Ending date” based on your bank statement information.
4. Match transactions to your bank statement and check them off one by one.
5. Apply filters so transactions are easier to find.
6. Keep going until the “Difference” field is zero and you see the Success! page.
7. Select "View Report" from the Report period drop-down arrow to view your reconciliation report.
The two options that are correct regarding bank account reconciliation QuickBooks online are:
Quickbooks is an Accounting Application that aids in the collection, processing, analyses, and reporting of Accounting and Financial Information for organizations.
It is a tool that is very useful for business owners.
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Three fair dice are rolled, one red, one green and one blue. What is the probability that the upturned faces of the three dice are all of different numbers?
Answer: [tex]\dfrac{5}{9}[/tex]
Step-by-step explanation:
When we throw a die , Total outcomes =6
When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]
Given : Three fair dice are rolled, one red, one green and one blue.
Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed
By Permutations , the number of favorable outcomes = [tex]^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120[/tex]
The probability that the upturned faces of the three dice are all of different numbers = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{120}{216}=\dfrac{5}{9}[/tex]
The probability that the upturned faces of the three dice are all of different numbers is [tex]\dfrac{5}{9}[/tex] .
A triangle has sides with lengths a,b,and c.The longest side is b.Write An Equation or inequality that shows the relationships of the lengths of the three sides
the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
In a right triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. So, we have:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
This equation represents the relationship among the side lengths of a right triangle.
Therefore, the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
This completes the three relations among a, b, andc.
The complete Question is given below:
A right triangle has side lengths of a,b , and c units. The longest side has a length of c units. Complete each equation show three relations among a,b , and c .
Type the answers in the boxes below.
c^(2)= _____
a^(2)= _____
b^(2)= _____
Find the x- and y-intercepts of 3/5x + 1/3y = 1/15
Answer: X-intercept: 1/9
Y-intercept: 1/5
Step-by-step explanation:
Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives. Black olives cost three dollars a pound. Green olives cost five dollars a pound. She spends $15.50. How many pounds of each type of olives does she buy? Write and solve a system of equations. Give the answer to in context of the problem.
Answer:
She buy 0.5 pounds of black olives and 3.5 pounds of green olives.
Step-by-step explanation:
Given:
Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives.
Black olives cost three dollars a pound. Green olives cost five dollars a pound.
She spends $15.50.
Now, to find the pounds of olives she buy.
Let the pounds of black olives be [tex]x.[/tex]
And the pounds of green olives be [tex]y.[/tex]
So, total pounds of olives:
[tex]x+y=4[/tex]
[tex]x=4-y[/tex] ........( 1 )
As, given the cost of black olives $3 a pound.
And cost of green olives $4 a pound.
Now, the total money spends:
[tex]3x+4y=15.50[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]3(4-y)+4y=15.50[/tex]
[tex]12-3y+4y=15.50[/tex]
[tex]12+y=15.50[/tex]
Subtracting both sides by 12 we get:
[tex]y=3.5[/tex]
The green olives = 3.5 pounds.
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=4-y\\x=4-3.5\\x=0.5\ pounds.[/tex]
The black olives = 0.5 pounds.
Therefore, she buy 0.5 pounds of black olives and 3.5 pounds of green olives.
Final answer:
Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party, determined by solving a system of equations representing the total weight and cost of the olives.
Explanation:
How Many Pounds of Black and Green Olives did Susan Buy?
To determine how many pounds of black and green olives Susan bought, we need to create a system of equations based on the information provided:
Let x be the number of pounds of black olives Susan bought, and let y be the number of pounds of green olives.
The first equation will represent the total weight of olives:
1. x + y = 4 (since Susan bought 4 pounds of olives in total)
The second equation will represent the total cost of olives:
2. 3x + 5y = 15.50 (because black olives cost $3 per pound and green olives cost $5 per pound)
Now, let's solve this system of equations:
Multiplying the first equation by 3 gives us a new equation:
3x + 3y = 12
Now, we subtract this new equation from the second equation to find y:
(3x + 5y = 15.50) - (3x + 3y = 12)
2y = 3.50
y = 1.75
So, Susan bought 1.75 pounds of green olives. We can now substitute y into the first equation to find x:
x + 1.75 = 4
x = 4 - 1.75
x = 2.25
Therefore, Susan bought 2.25 pounds of black olives.
In conclusion, Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party.
Which equation could be used to solve for the length of XY? XY = (22) sin (41°) XY = (22) cos (41°) XY = Start Fraction 22 Over cosine (41 degrees) End Fraction XY = Start Fraction 22 Over sine (41 degrees) End Fraction
Answer:
Pythagorean's theorem: a²+ b²= c²
Sines: sin A = a/c, sin B = b/c.
Cosines: cos A = b/c, cos B = a/c.
Tangents: tan A = a/b, tan B = b/a.
Step-by-step explanation:
For example, if the side a = 22 and the angle A = 41°, we can use a sine and a tangent to find the hypotenuse and the other side. Since sin A = a/c, therefore c = a/sin A = 22/sin 41. Using a calculator, this is 22/0.6561 = 33.5314. Also, tan A = a/b, so b = a/tan A = 22/tan 41 = 22/0.8693 = 25.307.
Leah had 50 stickers. Leah gave 1/2 of the stickers to her sister. Of the amount left, she gave 2/5 to her friend.How many does Leah have left for herself?
Answer: Leah has 15 stickers left for herself.
Step-by-step explanation:
Total number of stickers that Leah had initially is 50. Leah gave 1/2 of the stickers to her sister. This means that the number of stickers that Leah gave to her sister is
1/2 × 50 = 25 stickers
Of the amount left, she gave 2/5 to her friend. This means that the number of stickers that Leah gave to her friend is
2/5 × 25 = 10 stickers
Therefore, the number of stickers that Leah have left for herself is
50 - (25 + 15)
= 50 - 35
= 15
After giving away some of her stickers to her sister and friend, Leah has 15 stickers left for herself.
Explanation:Leah initially had 50 stickers. She gave half of them to her sister, which left her with 50/2 = 25 stickers. Then, she gave away 2/5 of these remaining stickers to her friend.
To calculate how many she gave her friend, we multiply 25 * 2/5 = 10 stickers.
To find out how many Leah has left for herself, we subtract this from the number she had after giving stickers to her sister: 25 - 10 = 15 stickers.
So, Leah has 15 stickers left for herself.
Learn more about Fraction and Subtraction Calculation here:
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Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this information, what interval of prices would we expect at least 89% of new car prices to fall within?
Answer:
($13,300,$46,900)
Step-by-step explanation:
We are given the following in he question:
Mean, μ = $30,100
Standard Deviation, σ = $5,600
Chebyshev's Theorem:
According to theorem atleast [tex]1 - \dfrac{1}{k^2}[/tex] percent of data lies within 2 standard deviations of mean.For k = 3,[tex]1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%[/tex]
Thus, 89% of data lies within three standard deviation of mean.
[tex]\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900[/tex]
Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)