Answer: 7+35j
Step-by-step explanation: First we have to distribute 7 to 1 and 5j. So, (7*1)+(7*5j). So our final answer would be 7+35j
A point is chosen at random in the circle.
What percent of the time will the point be in
the square?
Round to the nearest tenth of a percent.
1 in.
[ ? ]%
Enter
63.64% is the percentage of the area of the square.
What is square?The square is a 4 sided figure, each side of the square is equal and make a right angle.
The area of square having sided a unit can be given by a² square unit.
Given that,
The radius of the circle r = 1 in.
The area of the circle = π r² = π (1)² = π = 22/7 inch.
Also the area of square = 1/2 x (diameter)²
The diameter of the square = 2r = 2
Area = 1/2(2)² = 2 square in.
The required percentage = (2 / (22/7)) x 100 = (7 / 11) x 100 = 700 / 11 = 63.6363.
The percentage of the area of the square is 63.64%.
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The amount of time it takes a student from school A to do a math activity follows the Normal distribution with a mean of 25 minutes and a standard deviation of 5 minutes. Students at school B complete a math activity with a mean time of 20 minutes and have a standard deviation of 8 minutes.
a.) If we take a random student from School A and a random student from School B. What is the expected difference in their minutes?
b.) What is the standard deviation of the difference of their minutes?
Does the graph represent a non-proportional function? How do you know?
The graph attached represents a non proportional function
When does linear graphs give a proportional relationship?Like the name goes, a Linear graph is a straight line graph that represents a linear relationship with the equation of the form
y = mx + c
A relationship is proportionate if its graph is a line or ray that passes through the origin. in this case c = 0
It is not proportional if the line or graph does not go through the origin.
Additionally, if anything is not linear, it is not proportional.
The attached graph passed through point (0, 1) which is not the origin (0, 0) hence the graph is not a proportional relationship
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Solve for X. If m<1=(x+13)
M<2=39
M<3=(5x+4)
Thank you <3
Answer:
x = 9
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles.
<3 = <1 + <2
5x+4 = x+1 + 39
Combine like terms
5x+4=x+40
Subtract x from each side
5x-x+4=x-x+40
4x+4 = 40
Subtract 4 from each side
4x+4-4 = 40-4
4x = 36
Divide by 4
4x/4 = 36/4
x = 9
Answer:
x = 12
Step-by-step explanation:
We know that,
The exterior angle of a triangle equals to the sum of opposite interior angles.
Accordingly,
[tex] \angle \: 1 + \angle \: 2 = \angle \:3[/tex]
That is,
x + 13 + 39 = 5x + 4
Combine like terms.
x + 52 = 5x + 4
Subtract x from both sides.
52 = 5x - x + 4
52 = 4x + 4
Subtract 4 from both sides.
52 - 4 = 4x
48 = 4x
Divide both sides by 4.
12 = x
What is the end behavior of:
1. [tex]\sqrt{6x}[/tex]
2. [tex]\sqrt{x-5}-6[/tex]
3. [tex]-3\sqrt{x+3}+7[/tex]
The end behavior of each function is defined as follows:
1. [tex]\sqrt{6x}[/tex]: as x -> ∞, f(x) -> ∞.
2. [tex]\sqrt{x - 5} - 6[/tex]: as x -> ∞, f(x) -> ∞.
3. [tex]-3\sqrt{x + 3} + 7[/tex]: as x -> ∞, f(x) -> -∞.
How to obtain the end behavior of the functions?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The functions in this problem are all variations of the square root function, which is defined only for non-negative numbers, and thus only the limit when x goes to infinity has to be considered.
As x goes to infinity, the square root goes to infinity, which already define the end behavior for items 1 and 2.
For item 3, the negative leading coefficient means that the function is reflected over the x-axis, assuming a negative value, and thus the end behavior is that the function goes to negative infinity.
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What is the largest 3 even number?
Answer:
Step-by-step explanation:
is that the question? what do you mean by 3
Answer:
998
Step-by-step explanation:
if xy + 9ey = 9e, find the value of y'' at the point where x = 0.
The value of y'' at the point where x=0 is[tex]9 e y^{\prime \prime}=\frac{1}{9 e}$[/tex] ([tex]e^{2}[/tex])
Differentiation is one of the two important concepts apart from integration. Differentiation is a method of finding the derivative of a function. Differentiation is a process, in maths, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity. The opposite of finding a derivative is anti-differentiation.
If x is a variable and y is another variable, then the rate of change of x with respect to y is given by dy/dx. This is the general expression of derivative of a function and is represented as f'(x) = dy/dx, where y = f(x) is any function.
[tex]$x y+9 e^y=9 e$[/tex]
at [tex]x =0[/tex]
[tex]$9 e^y=9 e$[/tex]
[tex]$y=1$[/tex]
[tex]$w \cdot r . t x$[/tex]
[tex]$\left(y+x y^{\prime}\right)+9 e^y y^{\prime}=0[/tex]
at [tex]x=0[/tex]
[tex]$1+9 e y^{\prime}=0$[/tex]
[tex]$y^{\prime}=-\frac{1}{9 e}$[/tex]
[tex]$--------$[/tex]
[tex]$\left(y+x y^{\prime}\right)+9 e^y y^{\prime}=0$[/tex]
[tex]y^{\prime}+x y^{\prime \prime}+y^{\prime}+9 e^y y^{\prime \prime}+9 e^y\left(y^{\prime}\right)^2=0[/tex]
at [tex]x=0[/tex]
[tex]2\left(-\frac{1}{9 e}\right)+9 e y^{\prime \prime}+9 e\left(-\frac{1}{9 e}\right)^2=0[/tex]
[tex]-\frac{2}{9 e}+9 e y^{\prime \prime}+\frac{1}{9 e}=0[/tex]
[tex]9 e y^{\prime \prime}=\frac{1}{9 e}$[/tex][tex]\left(e^2)\right[/tex]
Therefore, the value of y'' at point where x=0 is [tex]9 e y^{\prime \prime}=\frac{1}{9 e}$[/tex] ([tex]e^{2}[/tex])
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Value of x when 48= 3x
Answer:
Step-by-step explanation:
x = 16
Answer:
x = 16
Step-by-step explanation:
If 3 · 16 = 48 Then x = 16
A recipe uses
300 grams of flour for every
200 grams of sugar.
1. Write an equation that represents how many grams of flour we need (f) for some number of grams of sugar (s). 2. How many grams of flour do we need if we use 500 grams of sugar?
we need for 500 grams of sugar, we can plug 500 into the equation for our value of s. This gives us f = 300 * 500/200 = 750 grams.
1. f = 300s/200
2. f = 300 * 500/200 = 750 grams
1. To write the equation, we can set up a ratio that compares the number of grams of flour to the number of grams of sugar. Since the recipe calls for 300 grams of flour for every 200 grams of sugar, we can set up the equation as f = 300s/200, where f is the number of grams of flour and s is the number of grams of sugar.
2. To find out how many grams of flour we need for 500 grams of sugar, we can plug 500 into the equation for our value of s. This gives us f = 300 * 500/200 = 750 grams.
To write the equation, we can set up a ratio that compares the number of grams of flour to the number of grams of sugar. Since the recipe calls for 300 grams of flour for every 200 grams of sugar, we can set up the equation as f = 300s/200, where f is the number of grams of flour and s is the number of grams of sugar.
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Answer:
750
Equation:
f = 3/2s
A local charity is selling seats to a baseball game. Seats cost $32 each, and snacks cost an additional $8
each. The charity needs to raise $640 to consider this event a success.
Use the graph to approximate how many snacks the charity must sell if 10 seats are sold.
32 s +8y=640
By using the graph, the amount of snacks that the charity must sell if 10 seats are sold is equal to 40 snacks.
How to write and solve the equation graphically?In order to graphically solve the equation, we would write an equation that models the situation by assigning variables to the cost of seats and cost of snacks, and then translate the word problem into algebraic equation as follows:
Let the variable s represent the cost of seats.Let the variable y represent the cost of snacks.Since the seats cost $32 each and snacks cost an additional $8 each while the charity needs to raise $640, an equation that models the situation is given by;
32s + 8y = 640
By critically observing the graph, the charity must sell 40 snacks if 10 seats are sold.
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A number is increased by 2/5 to 49. What was the number?
Answer: 35
Step-by-step explanation:
35*140%=49
which angle corresponds to ∠8 ?
The angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.
What are parallel lines ?
parallel lines can be defined as the lines which are equi distant from each other and these lines never interest to each other.
Given ,
from the figure
the parallel lines are l and m.
the angles ∠1,∠2,∠3,∠4,∠5,∠6,∠7,∠8.
∠1,∠2,∠3,∠4. are in one plane
and ∠5,∠6,∠7,∠8. are in another plane.
so the angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.
Hence , the angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.
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I need it done by today.
By algebra properties, the integer 975 is equivalent to rational expression 650 / (2 / 3).
How to simplify a rational expression to a unit rate
Rational numbers are real numbers of the form m / n, where m and n are integers and n is a non-zero integer. In this problem we find a rational expression of the form (a / b) / (c / d), where a, b, c, d are also integers and b and d are non-zero integers.
This expression must be simplified into a rational number of the form m / n, this can be done by the following algebra property:
(a / b) / (c / d) = (a · d) / (b · c)
If we know that a = 6, b = 1, c = 2 and d = 3, then the resulting expression is:
650 / (2 / 3) = (650 / 1) / (2 / 3) = (650 ÷ 1) / (2 ÷ 3) = (650 × 3) / (1 × 2) = 1950 / 2 = 975 / 1 = 975
The rational expression 650 / (2 / 3) is equivalent to integer 975.
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The function, "f" is defined by the following rule. f(x)=3x-1
Answer:
i don't know
Step-by-step explanation:
Lúcia is using energy at a rate of 420420420 kilocalories (\text{kcal})(kcal)left parenthesis, start text, k, c, a, l, end text, right parenthesis per hour (\text{h})(h)left parenthesis, start text, h, end text, right parenthesis ice skating. at what rate is lúcia using energy in calories per minute \left(\dfrac{\text{cal}}{\text{min}}\right)( min cal )left parenthesis, start fraction, start text, c, a, l, end text, divided by, start text, m, i, n, end text, end fraction, right parenthesis?
Answer:
Step-by-step explanation:
lol
One day last week, 6 teachers joined of the members of the chess club for a tournament 5 7 after school. Alan counted a total of 31 people at the tournament that day. How many total members are in the chess club at this school?
The total members of the chess club at the school, given the number of teachers, can be found to be 25 students.
How to find the number of members of the chess club ?When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.
The number of chess club students is therefore :
= Number of people counted by Alan - Number of teachers
= 31 - 6
= 25 members
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6^-10/(6^4)(6^0)
what is the answer
Answer:
6^-14
Step-by-step explanation:
Using laws of indices you'll add the denominators power to account for multiplication
then substract it from the numerators power to get an answer which is 6×10^-14
Ten people are sitting around a round table. Three of them are chosen at random to give a presentation. What is the probability that the three chosen people were sitting in consecutive seats
The possibility of three people being chosen to give a random presentation as calculated from the given data is 1 / 12.
There are 10 possibilities of selecting the required 3 people.
Using combination we can find the required probability as ,
10c3
= 10 ! / 7! x 3 !
= 10 x 9 x 8 / 3 x 2
= 120
Thus, the probability is equal to 10 / 120 = 1 / 12 .
Combination is a way of combining things in the desired manner . Other than probability we also have permutation which tells about the possibility.
Probability refers to the possibility of occurrence of an event. It is used in industries such as weather forecast.
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This morning, Lashonda's car had 13.01 gallons of fuel. Now, 2.6 gallons are left. How much fuel did Lashonda use?
Answer:
10.41
Step-by-step explanation:
Given ,
Lashonda's car had 13.01 gallons of fuel.2.6 gallons are left now.To Find : Number of Fuel used
Let us take the Number of fuel used as 'x'
13.01 = x + 2.60
x = 13.01 - 2.60
x = 10.41
Hence, the fuel used by Lashonda is 10.41
A data set has 10,000 records and 30 predictor variables (columns). Each variablehas 5% of the values missing for that individual variable. The missing values are spread randomly and independently throughout the data set. The analyst uses apredictive model that automatically drops any row (record) that has even a singlemissing values on any of the variables. How many records would be dropped fromthe analysis
10,000 records have 30 predictor variables, each with 5% of the values missing, resulting in 15,000 missing values. The predictive model drops any row with even a single missing value, so 5,000 records would be dropped from the analysis.
1. There are 30 predictor variables.
2. Each variable has 5% of the values missing.
3. 5% of 10,000 records = 500 records.
4. 30 variables x 500 records = 15,000 missing values.
5. 10,000 records - 15,000 missing values = 5,000 records dropped from the analysis.
The data set has 10,000 records and 30 predictor variables. Each variable has 5% of the values missing, so 500 records are missing for each variable. This results in 15,000 missing values spread randomly and independently throughout the data set. The analyst uses a predictive model that drops any row (record) with even a single missing value, so 5,000 records would be dropped from the analysis.
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Explain the error in the work and how you might prevent it.
The error is [tex]12x^2 - 14x = - 26x^2[/tex] because 12x² and 14x are unlike terms, so we can not add them
To prevent it the dividend must be written as [tex]6x^3 + 0x^2 - 14x + 1[/tex]
Now, According to the question:
In the division, you must arrange the dividend according to the greatest power of the variable, and put 0 as a coefficient of the missing term to avoid adding, unlike terms.
Example:
If the dividend is [tex]3x^3 - 2x + 5[/tex], then you must write it as [tex]3x^3 + 0x^2 - 2x + 5[/tex]
Let us solve our question
∵ The dividend is [tex]6x^3[/tex] + 1 - 14x
→ You must arrange it from the greatest power of x
∴ The dividend is [tex]6x^3[/tex] - 14x + 1
∵ The term of x² is missing
→ Write it in the dividend with a coefficient of 0
∴ The dividend is [tex]6x^3 + 0x^2 - 14x + 1[/tex]
The error is the adding of unlike terms
∵ [tex]6x^3[/tex]- 14x + 1 ÷ 3x + 6 = 2x² and [ [tex]6x^3[/tex] - 14x + 1 - [tex]6x^3[/tex] - ( [tex]6x^3[/tex] + [tex]12x^2[/tex])]
∵[tex][6x^3 - 14x + 1 - 6x^3 - (6x^3 + 12x^2)] = 6x^3 - 14x + 1 - 6x^3 - 12x^2[/tex]
∵ [tex]6x^3 - 14x + 1 - 6x^3 - 12x^2 = 0 - 12x^2 - 14x + 1[/tex]
∵[tex]0 - 12x^2 - 14x + 1 = -26x^2 + 1[/tex] ⇒ error
∴ The error is -12x² - 14x = - 26x² because 12x² and 14x are unlike terms,
so we can not add them
→ To prevent it, write 0 as a coefficient of the missing term
∵ The missing term is the term of x²
∴ Add to the dividend the term 0x²
∴ The dividend must be written as [tex]6x^3 + 0x^2 - 14x + 1[/tex]
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24.
Select all polynomials that have a zero located at
(4, 0).
A. fa
B. f(x) = (2x - 8) (x + 5)
C. f(x) = 4x(x - 3)(x - 1)
D. f(x) = (x − 4)(x − 3)(x + 1)
E. f(x) = 2x(4- x)(x + 5)(3x - 4)
Answer:
B
D
E
The first choice A appears to be a typo, so I can't comment on that
Step-by-step explanation:
Substitute x = 4 in each of the polynomials and see which ones end up with a value of 0. Since each of the polynomials is a multiplicative of expressions if any one of the individual expressions is 0 then the whole expression becomes 0
A. Unknown
B. 2x - 8 = 2 · 4 - 8 = 8 - 8 = 0. So this has a zero at (4,0)
C None of the individual expressions will result in 0. So not a correct choice
D x - 4 = 4 - 4 = 0 So this is a correct choice
E. In this case we have a 4-x term which is 4- 4 = 0; so correct choice
111 base 2 to base 5
(111)₂ = (12)₅
What are base of numbers?The base of a number system refers to the total number of digits that are actually used in the given number system. The number system that has the base 'b' consists of its digits in the [0, b-1] range. This base of the number system is also known as the radix of a number system.
Given,
number 111 with base 2
To convert it into base 5 number we need to first convert it into decimal
(111)₂ = 1×2²+1×2¹+1×2⁰
(111)₂ = 4+2+1
(111)₂ = (7)₁₀
Now converting decimal to base 5, converting decimal numbers to base 5 is nearly as simple: just divide by 5.
(111)₂ = (12)₅
Hence, the number becomes (12)₅.
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Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke. 1. 5x – 7 = 4x + 3
2. 6 + 2x = 7x – 9
3. 8x + 1 = -8 – x
4. -5 + 12x = 18x + 7
5. -4x + 3 = 5x – 13 - x
The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1. 5x – 7 = 4x + 3.
To solve for x, we can add 7 to both sides of the equation and subtract 4x from both sides:
5x - 7 + 7 = 4x + 3 + 7
5x = 4x + 10
x = 10
2. 6 + 2x = 7x - 9
To solve for x, we can add 9 to both sides of the equation, subtract 6 from both sides and divide both sides by -1:
6 + 2x + 9 = 7x - 9 + 9
2x = -3
x = -3/2
3. 8x + 1 = -8 - x
To solve for x, we can add x to both sides of the equation and add 8 to both sides:
8x + 1 + x = -8 - x + x + 8
9x + 1 = 0
x = -1/9
4. -5 + 12x = 18x + 7
To solve for x, we can subtract 12x from both sides of the equation and add 5 to both sides:
-5 + 12x - 12x = 18x + 7 - 12x
-5 = 6x + 7
x = -6
5. -4x + 3 = 5x - 13 - x
To solve for x, we can add x to both sides of the equation, subtract 3 from both sides and divide both sides by -1:
-4x + 3 + x = 5x - 13 - x + x + 3
-3x = -10
x = 10/3
The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3
That gives you the letters "joke"
Therefore, The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1. 5x – 7 = 4x + 3.
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help pleaseeeeee urgenttt !!!
The perimeter and area of the image:
(a) 3/2cm²
(b) 2/3cm²
(c) 3/8cm²
What is the perimeter of a trapezoid?
A trapezoid's perimeter is determined by adding the lengths of its four sides. The sum of the lengths of a trapezoid's four sides serves as the formula for the shape's perimeter.
Here,
We have to find the perimeter and area of the image when the trapezoid is dilated by a scale factor of (a) 2, (b) 3, and (c) 4.
(a) Ratio 2: 1 of length
Perimeter = (2 + 5 + 3 +6)/2 = 8cm
Area = (1/2)×3×(6+2)/2×(1/2)² = 3/2cm²
(b) Ratio 3:1
Perimeter = (2 + 5 + 3 +6)/3 = 16/3cm
Area = (1/2)×3×(6+2)/2×(1/3)² = 2/3cm²
(c) Ratio 4:1
Perimeter = (2 + 5 + 3 +6)/4 = 4cm
Area = (1/2)×3×(6+2)/2×(1/4)² = 3/8cm²
Hence, The perimeter and area of the image: (a) 3/2cm², (b) 2/3cm², and (c) 3/8cm²
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amie purchased 78 pieces of candy at the local candy store she kept 24 pieces of candy for herself and gave the rest of the candy to her 3 bestfriends. how many pieces of candy did each friend get?
Answer:
18 pieces
Step-by-step explanation:
78 pieces to start with and she kept 24 to herself which means that she has 54 pieces of candy remaining. Assuming she gave an equal amount to each friend, the answer would be 54/3=18. So she gave 18 pieces to each friend.
Mr. Smith was so pleased with the amount of
homework his students completed that he bought
sandwiches, fries, and drinks for the whole class. The total
cost was $100. The sodas and fries cost $73.27.
If the sandwiches cost $0.99 each, how many sandwiches did he
buy?
The amount of sandwiches purchased in total is 27.
What is system of equations?The term "system of equations" or "equation system" in mathematics refers to a finite set of equations for which common solutions are sought. A set of simultaneous equations is sometimes known as a system of equations or an equation system.
Let the sandwiches be represented as x.
Let the fries be represented as y and drinks be represented as z.
The total cost is given as $100, that is:
x + y + z = 100 (equation 1)
Drinks and fries' cost $73.27, this can be written as:
y + z = 73.27 (equation 2)
Substitute the value of y + z = 73.27 in equation 1:
x + 73.27 = 100
x = 100 - 73.27
x = 26.73
The total amount spent on sandwiches is $26.73.
One sandwich cost $0.99.
The number of sandwiches purchased in $26.73 is:
n = 26.73/ 0.99
n = 27
Hence, the total number of sandwiches purchased is 27.
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Help pleaseeee thanks
Answer:
I'd say A, Adjacent
Step-by-step explanation:
I think its A because adjacent means together/along with, and these angles are next to each other.
Find the slope of a line perpendicular to the line whose equation is x - 6y =24. fully simplfy your answer
Answer:
Step-by-step explanation:
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. To find the slope of the line x - 6y = 24, we can rearrange the equation to the form y = (1/6)x + 4. So the slope of the line is 1/6.
The slope of a line perpendicular to this line would be the negative reciprocal of 1/6 which is -6
if f and g are differentiable and f(x) ≥ g(x) for a < x < b, then f '(x) ≥ g'(x) for a < x < b.
This statement is not always true. It's only true if f(x) and g(x) are both non-decreasing functions.
If f(x) and g(x) are non-decreasing functions, the inequality f(x) ≥ g(x) for a < x < b holds, meaning that the values of f(x) are always greater than or equal to the values of g(x) for x within the interval [a,b]. Since the derivative of a non-decreasing function is non-negative, it follows that f'(x) ≥ 0 and g'(x) ≥ 0 for all x in the interval [a,b], which implies f '(x) ≥ g'(x) for a < x < b.
However, if f(x) and g(x) are not non-decreasing functions, this statement is not true. The inequality f(x) ≥ g(x) for a < x < b does not necessarily imply that the derivatives f '(x) and g'(x) will also be greater than or equal for all x in the interval [a,b].
Therefore, This statement is not always true. It's only true if f(x) and g(x) are both non-decreasing functions.
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