Answer: C - 3a - 27
Step-by-step explanation:
We start with 2.5 + 3a - 20 - 9.5, and first solve for variables:
3a
Then we solve for constants:
2.5 - 20 - 9.5 = 2.5 - 29.5 = -27
Add the two together:
3a - 27
1
2 3
5
1
Jared takes 10 minutes to wash dishes and 20
minutes to write a paper. Jason takes 10 minutes to
wash dishes and 30 minutes to write a paper. Which
of the following statements is correct?
Summary
O Jared has a comparative advantage in washing
dishes.
O Jared has absolute advantage in writing the
paper.
Back
O Jared has absolute advantage in washing the
dishes.
O Jared has a comparative advantage in writing a
paper.
Next
The correct answer is Jared has absolute advantage in washing the dishes.
what is the quotient and remainder of 39 divided by 8
Answer:
39 divided by 8 is equal to 4 with a remainder of 7.
The quotient is the number of times the divisor goes into the dividend. In this case, 8 goes into 39 4 times with a remainder of 7.
The remainder is the number that is left over after the divisor has been divided into the dividend. In this case, 7 is left over after 8 has been divided into 39.
Here is the long division of 39 by 8:
```
39 / 8
4
32
7
```
Step-by-step explanation:
The quotient of 39 divided by 8 is 4, and the remainder is 7.
We have,
When performing long division, we divide the dividend (39) by the divisor (8) to find the quotient and remainder.
4
--------
8 | 39
- 32
---
7
Here's how the long division process works for 39 divided by 8:
-We start by dividing the first digit of the dividend (3) by the divisor (8). Since 3 is less than 8, we can't divide it evenly, so we move to the next digit (9).
- We now have 39 as the remaining portion of the dividend. We divide 39 by 8. The largest multiple of 8 that fits into 39 is 4. We place the quotient, which is 4, above the line.
- We multiply the quotient (4) by the divisor (8), which gives us 32. We subtract 32 from 39, which leaves us with a remainder of 7.
- Since there are no more digits to bring down from the dividend, and the remainder (7) is less than the divisor (8), we stop the division process.
Therefore,
The quotient of 39 divided by 8 is 4, and the remainder is 7.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
Can you find X? Show how did u find
Answer:
x=90°
Step-by-step explanation:
As in the angle, there is a box giving us info that x has to be 90°.
But to be sure that there is no mistake we have to do the following:
Look at all the other angles (see what kind of angles they are).Add all the angles up to 360°( in this case as the angle we are looking for is on a straight line which gives straight line=180°).Checking and comparing the two answers.So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.
The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).
Therefore the answer is:
x=90°
A housewife along with group of ladies sold bags of different sizes. She earns a profit of 25 rupees on a purce and incures a loss of Rs 20 on a vanity bag sold
how many purces must she sell to have neither profit nor loss if the number of vanity bags sold is 750
pls answer quickly
whoever answers first will be marked brainliest
In linear equation, Her profit is rupees 4000.
No. of purses she must sell to have neither profit nor loss is 600 nos.
She made loss of rupees 2135.
What is a linear equation in mathematics?
A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.
The housewife earns,
Profit on 1 purse = 25 rupees
Loss on 1 vanity bag = 20 rupees
So,
Profit on 1000 purses = 25*1000 rupees
= 25000 rupees
Loss on 1050 purses = 20*1050 rupees
= 21000 rupees
Here, Profit > Loss
So,
Total profit = 25000-21000 rupees
= 4000 rupees
i) Her profit is 4000 rupees.
If no. of vanity bags sold = 750 nos.
She made loss of = 750*20 rupees
= 15000 rupees
ii) No. of purses she must sell to have neither profit nor loss
= 15000/25 nos.
= 600 nos.
Profit on selling 325 purses = 325*25 rupees
= 8125 rupees
Loss on selling 513 vanity bags = 513*20 rupees
=10260 rupees
Here, Profit < Loss
So,
iii) She made loss of = 10260-8125 rupees
= 2135 rupees
Learn more about linear equation
brainly.com/question/11897796
#SPJ1
The complete question is -
A housewife along with a group of ladies sold bags of different sizes. She earns a profit of 25 on a purse and a loss of 20 on a vanity bag sold. i. She received an order of 1050 vanity bags and 1000 purses. What is her profit or loss? ii. How many purses must she sell to have neither profit nor loss, if the number of vanity bags sold is 750? iii. How much profit/loss did she make in selling 325 purses and 513 vanity bags?
Prove that
sin 2x
1+ cos2x
= tan x
The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.
How to prove the mathematical statement ?To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.
(sin 2x) / (1 + cos 2x)
(2sin x × cos x) / (1 + (cos²x - sin²x))
(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)
We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:
(2sin x × cos x) / (1 + 2sin x × cos x)
(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)
((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)
(2sin x - 4sin²x) / (1/cos²x - 4sin²x)
Since tan x = sin x / cos x, we can rewrite the expression:
(2tan x - 4tan²x) / (sec²x - 4tan²x)
(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)
(2tan x - 4tan²x) / (1 - 3tan²x)
2tan x × (1 - 2tan²x) / (1 - 3tan²x)
tan x
So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.
Find out more on proof at https://brainly.com/question/17029275
#SPJ1
what is the range of the function in the graph?
A. 6≤e≤12
B. 40≤f≤100
C. 6≤f≤12
D. 40≤e≤100
The range of the function in the graph is 6≤e≤12. So correct option is A.
Describe Range?In mathematics, range is a term used to refer to the set of all possible output values of a function. It is the set of values that the function can take as its input varies over its entire domain. In other words, the range of a function is the set of all output values that can be obtained by evaluating the function for all possible input values.
For example, consider the function f(x) = x². The domain of this function is all real numbers, but the range is only non-negative real numbers, since x² is always non-negative for any real number x.
The range of a function can be determined by analyzing its graph, which is a visual representation of the function. The range corresponds to the set of all y-values that appear on the graph. For instance, the range of the function f(x) = sin(x) is the closed interval [-1, 1], since the sine function oscillates between -1 and 1 as its input varies over all real numbers.
Sometimes, it is useful to restrict the domain of a function in order to obtain a specific range. This process is called domain restriction or range selection. For example, the inverse function of f(x) = x² can be obtained by restricting the domain of f to non-negative real numbers, which ensures that the inverse function is also a function. The resulting function is f^-1(x) = √x, whose domain is non-negative real numbers and range is the same as the domain of f.
The range of the function in the graph is 6≤e≤12. So correct option is A.
To know more about function visit:
https://brainly.com/question/2709928
#SPJ1
What are the trig ratios for the angle 7π/4 rad?
Sin 7π/4 is the value of sine trigonometric function for an angle equal to 7π/4 radians. The value of sin 7π/4 is -(1/√2) or -0.7071 (approx).
How many degrees does 74 radians equal?
315° is comparable to 7 / 4 radians. In general, we multiply the angle measurement in radians by 180/ to translate an angle measurement given in radians to degrees. Therefore, we multiply 7 / 4 by 180 / to convert to radians. We discover that 7/4 radians equals 315 degrees.
We can first convert the angle to degrees as follows:
7π/4 radians = (7/4) × 180 degrees/π ≈ 315 degrees
The trigonometric ratios for 315 degrees (or 7/4 radians) can therefore be calculated using the reference angle of 45 degrees (which is /4 radians), as shown below.
sin(7π/4) = -sin(π/4) = -1/√2
cos(7π/4) = -cos(π/4) = -1/√2
tan(7π/4) = tan(π/4) = 1
csc(7π/4) = csc(-π/4) = -√2/2
sec(7π/4) = sec(-π/4) = -√2/2
cot(7π/4) = cot(-π/4) = 1
Therefore, the trigonometric ratios for the angle 7π/4 radians are:
sin(7π/4) = -1/√2
cos(7π/4) = -1/√2
tan(7π/4) = 1
csc(7π/4) = -√2/2
sec(7π/4) = -√2/2
cot(7π/4) = 1
To know more about trigonometric function visit:-
https://brainly.com/question/6904750
#SPJ1
Find the number that makes the ratio equivalent to 36:84?
Answer: 3:7
Step-by-step explanation: since the simplest form of the fraction 36/84 is 3/7 that means 36:84 in simplest form is 3:7.
Write the following expression without negative exponents.
[tex]\cfrac{5^7}{5^{-13}}\times\left( \cfrac{4^3}{7^{-2}} \right)^{-2}\implies 5^7\cdot 5^{13}\times \left( \cfrac{7^{-2}}{4^3} \right)^{+2}\implies 5^7\cdot 5^{13}\times\left( \cfrac{7^{-4}}{4^6} \right) \\\\\\ 5^{7+13}\times\left( \cfrac{1}{4^6\cdot 7^4} \right)\implies \cfrac{5^{20}}{4^6\cdot 7^4}\implies \cfrac{95367431640625}{9834496}[/tex]
2À candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 200 jelly beans. What is the probability that a bag will contain more than 20% blue jelly beans?
We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The probability that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.
Define probability?The probability of an event is the ratio of good outcomes to all other potential outcomes. The number of successful outcomes for an experiment with 'n' outcomes can be expressed using the symbol x.
Here in the question,
We can utilise the binomial distribution formula to resolve this issue. In a bag of 200 jelly beans, let X represent the proportion of blue jelly beans. Following that, X exhibits a binomial distribution with parameters of n = 200 and p = 0.15, where p is the likelihood of drawing a blue jellybean.
The formula for determining the likelihood of finding more than 20% blue jellybeans in a bag is:
P (X > 0.2 × 200) = P (X > 40)
Since n is large (200) and p is not too near to 0 or 1, we can utilise the usual approximation to the binomial distribution. We may determine the equivalent mean and standard deviation of the normal distribution by using the mean and variance of the binomial distribution:
μ = np = 200 × 0.15 = 30
σ = √ (np(1-p)) = √ (200 × 0.15 × (1-0.15)) = 4.07
Then, we can standardize the random variable X as:
Z = (X - μ) / σ
So, we have:
P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)
= P(Z > (40 - 30) / 4.07)
= P(Z > 2.46)
We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The likelihood that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.
To know more about probability, visit:
https://brainly.com/question/16484393
#SPJ1
Jackson had $104,292.12 in a savings account with simple interest. He had opened the
account with $80,040 exactly 3 years earlier. What was the interest rate?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years.
Answer: Using the formula i = prt, we have:
i = (104292.12 - 80040) = 24252.12
p = 80040
t = 3
Substituting these values, we get:
24252.12 = 80040 * r * 3
Solving for r, we get:
r = 0.101 or 10.1%
Therefore, the interest rate is 10.1%.
Step-by-step explanation:
Can someone help me with this problem? I need to find x and y
Answer:
x = √17
y = 10.1
Step-by-step explanation:
x² + 8² = 9²
x² = 81 - 64 = 17
x = √17
sin∅ = √17/9
∅ = 27.27°
9/y = cos(27.27)
y = 9/cos(27.27) = 10.13
y = 10.1
Translate in two ways each of these statements into logical expressions using predcates quantifiers and logical connective first let the domain consist of the students in your class and second let it consist of all people a) everyone in your class has a cellular phone
For all x, P(x) (using universal quantifier ∀) and It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
1. For all x in S, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
For all x, P(x) (using universal quantifier ∀)
It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
For all x in S, P(x) (using universal quantifier ∀)
It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
1. For all x, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
To learn more about probability from the given link:
https://brainly.com/question/30034780
#SPJ1
Problem 1: Find the Area and round to the nearest tenth.
Answer:
39.96
Step-by-step explanation:
the shape is a parallelogram ao the formula is base x height
A=10.8 x 3.7
A=39.97
Which choice is NOT equal to the others? Responses A −[[2/5]]−[[2/5]] B [[2/−5]][[2/−5]] C [[−2/5]][[−2/5]] D [[2/5]]
Answer:
B is the answer
Step-by-step explanation:
The expression that is not equal to the others is B [[2/−5]] The other expressions are A −[[2/5]], C [[−2/5]], and D [[2/5]].
2. center (5, -6), radius 4
Answer:
(x - 5)² + (y + 6)² = 16
Step-by-step explanation:
assuming you require the equation of the circle
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (5, - 6 ) and r = 4 , then
(x - 5)² + (y - (- 6) )² = 4² , that is
(x - 5)² + (y + 6)² = 16
lisa ran 1/2 of a mile.jan ran 3/6 of a mile.which girl ran further
The fraction that has been given illustrates that the person who ran further is Lisa and Jane.
How to solve fractionYour information isn't complete. Therefore, an overview of the fraction will given.
Let's assume that Lisa ran 1/2 of a mile and Jane ran 3/6 of a mile. In order to know who ran more, you can convert the fraction to percentage.
This will be
[tex]\text{Lisa} = \dfrac{1}{2} \times 100 = \bold{50\%}[/tex]
[tex]\text{Jane} = \dfrac{3}{6} \times 100 = \bold{50\%}[/tex]
Therefore, both Lisa and Jane ran more.
Learn more about fractions on:
brainly.com/question/78672
help with statistics
Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.
What is statistics?In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.
Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.
Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.
Learn more about statistic on;
https://brainly.com/question/15525560
#SPJ1
find the value for each variable in simplest radical form
The values are;
1. x = 6 ,y = 6√2
2. x = 9√2, y = 18
3. x = y = 9
4. x = 12, y = 12√2
5. x = y = 4√2
6. x = y =( 3√2)/2
What trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
There are some special angles , in which 45 is part of them.
sin 45 = 1/√2
cos 45 = 1/√2
tan 45 = 1
1. x = 6 ( isosceles triangle)
y = 6 × √2 = 6√2
2. x = 9√2 ( isosceles triangle)
y = 9√2 × √2 = 9×2 = 18
3. x = 9√2/√2 = 9
x = y = 9 ( isosceles triangle)
4. x = 12 ( isosceles triangle)
y = 12×√2 = 12√2
5. x = 8/√2 = 8√2/2 = 4√2
x = y = 4√2( isosceles triangle)
6. x = 3/√2 = (3√2)/2
x = y =( 3√2)/2 ( isosceles triangle)
Learn more about trigonometric ratio from
https://brainly.com/question/24349828
#SPJ1
Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5
a. i. The function f(x)/g(x) = (2x - 1)/√(3x - 5)
ii. The domain is x > 5/3
b. i. The function f(x) - g(x) = (2x - 1) - √(3x - 5)
ii. The domain is x > 5/3
What is a function?A function is a mathematical relation ship between two variables.
Since we have the functions f and g defined as follows
f(x) = 2x-1
g(x) = √3x-5
a. i To find f/g we note that
(f/g)(x) = f(x)/g(x)
So, substituting the values of the variables into the equation, we have that
f(x)/g(x) = (2x - 1)/√(3x - 5)
ii. The domain of f(x)/g(x) = (2x - 1)/√(3x - 5) is the value for which the denominator g(x) > 0.
So,g(x) > 0
⇒ √(3x - 5) > 0
⇒ 3x - 5 > 0²
⇒ 3x > 5
⇒ x > 5/3
So, the domain is x > 5/3
b. i. to find f - g, we note that
f - g = f(x) - g(x)
So, substituting the values of the variables into the equation, we have that
f(x) - g(x) = (2x - 1) - √(3x - 5)
ii. The domain of f(x) - g(x) is the value of x at which g(x) > 0
So. g(x) > 0
⇒ √(3x - 5) > 0
⇒ [√(3x - 5)]² > 0
⇒ 3x - 5 > 0
⇒ 3x > 5
⇒ x > 5/3
So, the domain is x > 5/3
Learn more about function here:
https://brainly.com/question/24779057
#SPJ1
"The quotient of 30 and a number is decreased by 2." please help
This sentence relating to the quotient can be expressed mathematically as:
(30 / x) - 2
What is the explanation for the above response?
This sentence can be expressed mathematically as:
(30 / x) - 2
where x represents the unknown number.
The word "quotient" indicates that we are dividing 30 by the unknown number x. The phrase "is decreased by 2" means that we need to subtract 2 from the quotient.
Learn more about quotient at:
https://brainly.com/question/16134410
#SPJ1
Create a Truth Table for
(A ⋀ B) → C
The truth table is given above for (A ⋀ B) → C.
What is the logical statement?
A logical statement, also known as a proposition or a statement of fact, is a declarative sentence that is either true or false, but not both. It is a statement that can be evaluated based on the available information or evidence to determine its truth value. In other words, a logical statement is a statement that can be either true or false, but not both.
To create a truth table for the logical statement (A ⋀ B) → C, we need to consider all possible combinations of truth values for propositions A, B, and C.
There are 2 possible truth values (true or false) for each proposition, so there are 2³ = 8 possible combinations.
We can organize these combinations into a table as follows:
| A | B | C | (A ⋀ B) | (A ⋀ B) → C |
|---|---|---|---------|-------------|
| T | T | T | T | T |
| T | T | F | T | F |
| T | F | T | F | T |
| T | F | F | F | T |
| F | T | T | F | T |
| F | T | F | F | T |
| F | F | T | F | T |
| F | F | F | F | T |
In this table, the column labeled (A ⋀ B) represents the truth value of the conjunction of A and B (i.e., A AND B), and the column labeled (A ⋀ B) → C represents the truth value of the conditional statement (A ⋀ B) → C.
The symbol "T" represents "true" and the symbol "F" represents "false".
Hence, The truth table is given above for (A ⋀ B) → C.
To learn more about the logical statement visit:
https://brainly.com/question/29021787
#SPJ1
Jasper's aunt gave him a big bin of 500 beads made out of assorted materials to use for the wind chimes he makes. Jasper takes out a handful of beads, looks at the types of beads, then puts them back. Here are the materials of the handful he selected: glass, clay, wood, glass, wood, clay, metal, clay, wood, glass, wood, clay, metal, wood, clay Based on the data, estimate how many glass beads are in the bin. If necessary, round your answer to the nearest whole number.
We can estimate that there are approximately 134 glass beads in the bin.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.
There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:
4/15 ≈ 0.267
We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as
0.267 x 500 ≈ 134
Therefore, we can estimate that there are approximately 134 glass beads in the bin.
To learn more about probability from the given link:
https://brainly.com/question/30034780
#SPJ1
2. Violet is baking cupcakes for a bakesale. The equation for her profit, p, based on the
number of cupcakes she sells, c, is based on the equation p = 2.75c-24. What is the best
nterpretation of the number -24.
A. How many cupcakes she sold.
B. How much it cost to buy the ingredients for the cupcakes.
C. How much each cupcake cost.
D. What her profit is.
Answer: The best interpretation of the number -24 in the equation p = 2.75c-24 is option D: What her profit is.
The equation is in slope-intercept form, where the coefficient of c (2.75) represents the profit per cupcake and the constant term (-24) represents the fixed costs or expenses that Violet incurs regardless of how many cupcakes she sells.
In this case, the constant term of -24 represents the fixed costs such as the cost of ingredients, supplies, and other expenses that Violet incurs to make the cupcakes. This cost is subtracted from the total revenue generated by selling cupcakes to determine the profit. Therefore, the number -24 represents the fixed costs or expenses and its inclusion in the equation allows us to determine Violet's profit as a function of the number of cupcakes sold.
Step-by-step explanation:
12×(3+2²)÷2-10 what is the answer
Answer:
32 I hope this helps please make me a brianlist that would help :)
Find the volume of this sphere.
Use 3 for TT.
-d=6in
V ≈ [?] in ³
V = πr³
Enter
Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.
If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.
(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)
Step-by-step explanation:
The numbers of students in the 9 schools in a district are given below.
(Note that these are already ordered from least to greatest.)
164, 225, 227, 250, 261, 268, 277, 379, 523
Send data to calculator
Suppose that the number 523 from this list changes to 424. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
It decreases by
O It increases by 0.
It stays the same.
O It decreases by 0.
It increases by
It stays the same.,
X
5
if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.
How to calculate the mean?
To calculate the mean, we add up all the numbers in the list and divide by the total number of values. Before the change, the sum of the numbers is:
164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 523 = 2494
And there are 9 numbers in the list. So the mean is:
2494 / 9 ≈ 277.11
If we change the value of 523 to 424, then the sum becomes:
164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 424 = 2465
And there are still 9 numbers in the list. So the new mean is:
2465 / 9 ≈ 273.89
So the mean decreases by approximately 3.22.
To calculate the median, we find the middle value of the list. If the list has an odd number of values, then the median is the middle value. If the list has an even number of values, then the median is the average of the two middle values. In this case, the list has an odd number of values, so the median is:
261
If we change the value of 523 to 424, then the list becomes:
164, 225, 227, 250, 261, 268, 277, 379, 424
And the median is still:
261
So the median stays the same.
In summary, if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.
To know more about mean visit :-
https://brainly.com/question/26177250
#SPJ1
Trangle ABC has an area 25 square feet and perimeter of 65.5 feet of triangle ABC is dilated by a factor of 5/2 to create now calculate the area of trangle DEF using the scale factor
So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.
What is dilation?the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.
In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.
For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.
Let's start by using the formula for the perimeter of a triangle:
[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]
We can also use Heron's formula to find the area of triangle ABC:
[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
where s is the semi perimeter of the triangle:
[tex]s = (AB + BC + AC) / 2[/tex]
We can use these equations to solve for the side lengths of triangle ABC:
[tex]AB + BC + AC = 65.5[/tex]
[tex]s = (AB + BC + AC) / 2[/tex]
[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
Solving for AB, BC, and AC gives us:
AB = 15
BC = 20
AC = 30.5
Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.
DE = AB * (5/2) = 37.5
EF = BC * (5/2) = 50
DF = AC * (5/2) = 76.25
Now we can use Heron's formula again to find the area of triangle DEF:
s = (DE + EF + DF) / 2 = 81.875
Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet
To know more about triangle, visit:
https://brainly.com/question/2773823
#SPJ1
Which of the following is an even function?
f(x) = (x - 1)^2
f(x) = 8x
f(x) = x^2-x
f(x) = 7
Answer: An even function is a function that satisfies the condition:
f(-x) = f(x)
Let's check which of the given functions satisfies this condition:
f(x) = (x - 1)^2
f(-x) = (-x - 1)^2 = x^2 + 2x + 1
f(x) = (x - 1)^2
The two expressions are not equal, so f(x) is not an even function.
f(x) = 8x
f(-x) = -8x = -f(x)
f(x) = 8x
The two expressions are equal with opposite signs, so f(x) is an odd function.
f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
f(x) = x^2 - x
The two expressions are not equal, so f(x) is not an even function.
f(x) = 7
f(-x) = 7 = f(x)
f(x) = 7
The two expressions are equal, so f(x) is an even function.
Therefore, the only even function among the given functions is:
f(x) = 7.
Step-by-step explanation:
Owen has two options for buying a car. Option A is 1.3 % APR financing over 36 months and Option B is 5.2 % APR over 36 months with $1500 cash back, which he
would use as part of the down payment. The price of the car is $32,020 and Owen has saved $3200 for the down payment. Find the total amount Owen will spend on the
car for each option if he plans to make monthly payments. Round your answers to the nearest cent, if necessary.
Option A:
Option B:
Answer: Option A:
To calculate the total amount Owen will spend on Option A, we need to calculate the monthly payment and then multiply it by the number of months:
First, we need to calculate the total amount of the loan. Owen is making a down payment of $3200, so he will be borrowing $28,820 (the price of the car minus the down payment).
Next, we can use the formula for calculating the monthly payment for a loan:
P = (r * A) / (1 - (1 + r)^(-n))
where P is the monthly payment, r is the monthly interest rate, A is the total amount of the loan, and n is the number of months.
For Option A, the monthly interest rate is 1.3% / 12 = 0.01083, the total amount of the loan is $28,820, and the number of months is 36. Plugging these values into the formula, we get:
P = (0.01083 * 28,820) / (1 - (1 + 0.01083)^(-36)) = $860.45
Therefore, the total amount Owen will spend on Option A is:
36 * $860.45 = $30,975.98
Option B:
For Option B, we need to take into account the $1500 cash back that Owen will receive as part of the down payment. This means that the total amount of the loan will be $32,020 - $3200 - $1500 = $27,320.
To calculate the monthly payment, we can use the same formula as before:
P = (r * A) / (1 - (1 + r)^(-n))
For Option B, the monthly interest rate is 5.2% / 12 = 0.04333, the total amount of the loan is $27,320, and the number of months is 36. Plugging these values into the formula, we get:
P = (0.04333 * 27,320) / (1 - (1 + 0.04333)^(-36)) = $825.53
Therefore, the total amount Owen will spend on Option B is:
36 * $825.53 + $1500 = $30,316.08
Therefore, Option A will cost Owen a total of $30,975.98, and Option B will cost him a total of $30,316.08. Therefore, Option B is the cheaper option for Owen.
Step-by-step explanation: