The value of a and b is -5/4. The value describes the value of each digit in relation to its position in the number.
What is meant by real numbers?A quantity in mathematics that can be represented by an infinite decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. The kind of number we typically use, such 1, 15.82, 0.1, 3/4, etc. Real Numbers can be positive or negative, big or tiny, whole values, fractions, or decimal numbers. They are not imaginary numbers, which is why they are termed "Real Numbers." A extremely large actual number is one billion (1,000,000,000). Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.(a) Mean Value = [tex]\frac{1}{3-1} \int_1^3 f(x)=\frac{1}{2}-\frac{5}{2}=\frac{5}{4}[/tex]
b) [tex]} \int_3^5 f(x) d x=\int_1^5 f(x) d x-\int_1^3 f(x) d x=10-\frac{5}{2}=\frac{15}{2} \\[/tex]
[tex]& \left.\int_3^5(2 f(x)+6) d x=2 \int_3^5 f(x) d x+6 \int_3^5 d x=2\left(\frac{15}{2}\right)+6 x\right]_3^5=15+6(2)=27 \\[/tex]
c) [tex]} f(x)=a x+b \\[/tex]
[tex]& \left.\int_1^3(a x+b) d x=\frac{a x^2}{2}+b x\right]_{x=1}^3=\frac{9}{2} a+3 b-\frac{a}{2}-b=4 a+2 b=\frac{5}{2} \\[/tex]
Simplifying,
[tex]\left.\int_1^5(a x+b) d x \cdot \frac{a x^2}{2}+b x\right]_{x=1}^5=\frac{25 a}{2}+5 b-\frac{a}{2}-b=12 a+4 b=10 \\[/tex]
[tex]4 a+2 b=5 / 2 \stackrel{n-3}{\rightarrow}-12 a-6 b=-15 / 2[/tex]
Then we get,
[tex]12 a+4 b=10[/tex]
[tex]$ \frac{12 a+4 b=20/2}{ -2 b=5 / 2} b=\frac{-5}{4}[/tex]
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2+2x[2+2x(2+2:2)]:8=
=
Answer:
2+2×2+2×2+2:2
Step-by-step explanation:
well the answer would be 2×2×2+2+2+2
4×2+2+2
8+2+2
10+2
12:2=8
that's the best that I could solve
I need help Asap!!!!!!!!!
Solve: 9log9(4)=
Answer: 34.3527303398
Step-by-step explanation: hope it is right
What is the Probability.
The value of the conditional Probability is P(A|B) is 1/3.
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The main distinction between a probability and a conditional probability is that a probability is the likelihood of an event, such as A, occurring, whereas a conditional probability assumes that another event, such as B, has already happened in order to define the probability of an event, such as in the conditional probability of A given B.
Conditional probability is the likelihood that any event A will occur in the presence of another event B that is related to A. P(A|B) illustrates it.
By, Conditional Probability :
P (A∩B) =P (A∩B') - P(B)= 4/9 - 1/3 = 1/9
P(A|B) = P (A∩B)/ P(B)
= (1/9)/(1/3) = 1/3
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Find the area of triangle JKL below.
Answer:
Step-by-step explanation:
a/sin A=b/sin B
20/sin90⁰=x/sin60⁰
cross multiply
20sin60⁰=xsin90⁰
17.32=
area=1/2a/bsin∅
=1/2×17.32×20 sin30⁰
86.6square
Fill in the P(X=x) values in the table below give a legitimate probability distribution for the discrete random variable X whose possible values are 0, 3, 4, 5 and 6.
The legitimate probability distribution for the discrete random variable X whose possible values are 0, 3, 4, 5 and 6 is: P(X=0) = 0.2, P(X=3) = 0.2, P(X=4) = 0.3, P(X=5) = 0.2, and P(X=6) = 0.1.
For a probability distribution to be legitimate, the probabilities of all the possible values of a random variable need to add up to 1. So, in this case, the sum of all the probabilities must be equal to 1.
For the given values, we can assign the probability of 0.2 to the values 0 and 3, 0.3 to the value 4 and 0.1 to the value 6, so that the sum of all the probabilities is 1.
Therefore, the legitimate probability distribution for the given discrete random variable X is as follows:
| Value (x) | P(X=x) |
|---|---|
| 0 | 0.2 |
| 3 | 0.2 |
| 4 | 0.3 |
| 5 | 0.2 |
| 6 | 0.1 |
The legitimate probability distribution for the discrete random variable X whose possible values are 0, 3, 4, 5 and 6 is: P(X=0) = 0.2, P(X=3) = 0.2, P(X=4) = 0.3, P(X=5) = 0.2, and P(X=6) = 0.1.
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large circle contains six small circles, each of which is tangent to two other small circles and the large circle, as shown. if each small circle has a radius of 4 cm, what is the area of the large circle? express your answer as a decimal to the nearest tenth.
The area of a large circle contains six small circles (radius = 4cm ) each of which is tangent to the two other small circles and the large circle is [tex]452.2[/tex] [tex]cm^{2}[/tex].
Given,
A large circle contains six circles having tangents with a large circle and two small circles as shown in the attached figure.
The radius of a small circle = 4cm
we know that,
The radius of a large circle [tex]= \frac{8+8+8}{2}[/tex]
[tex]= \frac{24}{2}[/tex]
[tex]= 12 cm[/tex]
Area of Large circle [tex]= \pi R^{2}[/tex]
[tex]= 3.14* 12^{2}[/tex]
[tex]= 3.14 * 144[/tex]
[tex]= 452.2[/tex]
Therefore, the Area of the large circle is approx [tex]452.2[/tex] [tex]cm^{2}[/tex] .
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A is the set of integers greater than -9 and less than -2
B = {a, i, j, y}
(a) Find the cardinalities of A and B.
n(A) =
n (B) = 4
Answer:
n(A) = 6
n(B) = 4
Step-by-step explanation:
The integers greater than -9 but less than -2 are
-8, -7, -6, -5, -4, -3
There are 6 integers and the set A = {-8, -7, -6, -5, -4, -3}
Cardinality of a set is the number of elements in that set
n(A) = 6
n(B) = 4 since there are 4 elements - this seems to have been answered
Drag the tiles to the correct boxes to complete the pairs.
Match each data set with the value that best describes its center.
6
2
4
9
Data set A: 2, 3, 1, 4, 2, 0, 0
arrowRight
Data set B: 6, 4, 5, 6, 5, 7, 8, 7
arrowRight
Data set C: 1, 4, 0, 2, 4, 4, 6, 7
arrowRight
Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11
arrowRight
The measure of center that best describes each data-set is given as follows:
Data set A: 2.Data set B: 6.Data set C: 4.Data set D: 9.How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
The median is usually considered the best measure of center of a data-set, as it is not affected by outliers.
Each of the data-sets in this problem have 7 elements, which is an even cardinality, hence the median is given by the fourth element of the ordered data-set.
The ordered data-set A is given as follows:
0, 0, 1, 2, 2, 3, 4.
The fourth element is of 2, which is the median, and the same procedure is applied for all the other data-sets.
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Insert <, >, or in the space provided to make a true statement.
=
|-7-3
|-7|| |-3|
Answer:
<
Step-by-step explanation:
-3 is greater than -7 since its more closer to the 0 then -7.
Pls answer ASAP.
Select all the true statements.
24 ÷ 8 > 24 ÷ 6
12 ÷ 12 = 7 ÷ 7
6 ÷ 1 < 9 ÷ 1
12 ÷ 3 > 12 ÷ 6
10 ÷ 5 < 10 ÷ 1
The true statements are;
a) 12 ÷ 12 = 7 ÷ 7 (both side are equal to 1)
b) 6 ÷ 1 < 9 ÷ 1 ( The left quotient is less than the right)
c) 12 ÷ 3 > 12 ÷ 6 (The left quotient is greater than the right)
d) 10 ÷ 5 < 10 ÷ 1 ( The left quotient is less than the right)
What are the true statements?We have to note that the true statements have to be the statements that satisfy the in equality that have been written in the question. We would have to look at the inequality in the question and then decide whether or not it is true.
Let us note that the in equality must take into account the expressions that are on both sides and then know if it holds true under all the circumstances that are possible mathematically.
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last digit of 2 to the power of 47
Answer:
2^1 = 2 -> last digit is 2
2^2 = 4 -> last digit is 4
2^3 = 8 -> last digit is 8
2^4 = 16 -> last digit is 6
2^5 = 32 -> last digit is 2
2^6 = 64 -> last digit is 4
2^7 = 128 -> last digit is 8
We can observe that the last digit follows a pattern of 2,4,8,6,2,4,8 and repeat.
Therefore, 2 to the power of 47 will have the same last digit as 2 to the power of (47 modulo 4) + 3
(47 mod 4) + 3 = 51 mod 4 = 3
The last digit of 2 to the power of 3 is 8
Therefore, the last digit of 2 to the power of 47 is 8.
In a flower bed, there are 51 plants in first row 48 plants in the second row 45 Plants in the third row and so on there are 12 plants in the last row. How many rows are there in the flower bed?
Answer:
14 rows.
Step-by-step explanation:
It could be any amount, but there is a clear pattern that follows "-3". Starting from 51 and ending at 12, let's subtract by 3.
51, 48, 45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, and 12.
There are 14 numbers; therefore, there are 14 rows.
Please hurry
The number of hours of sick leave, s, an
employee of a company earns varies
directly with the number of weeks, t,
he or she works. An employee of the
company who works 4 weeks earns
9 hours of sick leave. Which equation
represents the relation between s and t?
A S= 9t
B S = 4t - 9
C S = 4t + 9
D t = 8-4
E t = 9s - 4
The equation represents the relation between s and t is s = 9t
What is Direct Variation?This question is an example of Direct Variation, which is a type of proportional relationship between two variables. In direct variation when one variable increases, so does the other, and when one variable decreases, so does the other.
This relationship can be expressed mathematically by the equation
y = k x
where k is the constant of variation. In the given problems is the dependent variable, and t is the independent variable.
Since we know that when t = 4, s = 9, we can substitute these values into the equation and solve for k.
9 = k(4)
k = 9/4
Therefore, the equation for this direct variation is s = (9/4)t.
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Part B
? Question
Complete the statements.
The vertex of the equation modeling the bird's flight path is a
point
The vertex reveals
k
and is located at the
Y = 2(x-2)²+2 is the equation used to model the bird's vertex form journey.
Vertex form: What is it?A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the points A, B, C, D, and E in the aforementioned figures are vertices.
Formula for the general vertex form: f(x) = a(x − h) ² + k
where the vertex is (h,k).
This equation can be used to represent a bird's flight path:
y = 2x² - 8x+10
Vertex form equation conversion
Filling in the square:
y = 2(x² - 4x+5)
y=2
(x²-4x+5+ (2)2- (2)2)
y=2(x²-4x+5+ (2)²-4) y=2((x-2)2-4+5)
y=2((x-2)²+1)
y = 2(x-2) (x-2)²+2
Where:
(h,k)=(2,2)
a=2
Consequently, the vertex form equation for the bird's journey is Y = 2(x-2)²+2
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Complete Question -
Flight Path of a Bird
In this activity, you'll use quadratic equations to model situations and interpret the solutions to the equation
The flight path of a bird can be represented by this equation, where x represents the horizontal distance, in feet, from a tree
branch and y represents the height, in feet, relative to the ground.
y = 2x2 - 8x + 10
Part A
Question
Rewrite the equation modeling the path of the bird in vertex form by completing the square,
Substitute the values of a, h, and k to complete the equation.
The logarithmic functions, f(x) and g(x), are shown on the graph.
What is the equation that represents g(x)? Explain your reasoning.
The image of the function after the translation is g(x) = log(x + 1) + 4
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
f(x)=logx
How to determine the equation of g(x)?
From the graph, the given parameters are:
f(x) = log(x)
From the graph, we can see that:
The graph of f(x) is translated left by 1 unit
The graph of f(x) is translated up by 4 units
This transformation is given as
g(x) = f(x + 1) + 4
Mathematically, this transformation can be represented as
(x, y) = (x + 1, y + 4)
When represented as a function, we have
g(x) = f(x + 1) + 4
Substitute the equation f(x) = log(x)
f(x + 1) = log(x + 1) + 4
So, we have the following equation
g(x) = log(x + 1) + 4
Hence, the equation of g(x) is g(x) = log(x + 1) + 4
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Prove divisibility
thanks!
The prove that the given expression is divisible by 43 is explained below.
Divisibility of numbers.A number is said to be divisible by a given number when it leaves no remainder after the division. Example; show that 7^7 is divisible by 49.
7^7 = 823543
So that;
823543/ 49 = 16807
To prove that the expression is divisible by 43, we have;
7^8 = 5764801
7^7 = 823543
7^6 = 117649
Then,
7^8 - 7^7 + 7^6 = 5764801 - 823543 + 117649
= 4941258 + 117649
= 5058907
Then,
5058907/ 43 = 117649
Thus the expression is divisible by 43.
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Each marble bag sold by Lena's Marble Company contains 5 red marbles for every 8 blue marbles. If a bag has 40 blue marbles, how many red marbles does it contain?
Answer:25
Step-by-step explanation:
40 multiple by 5 over 8 cross multiplication
Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm^3. She painted the entire surface of the cylinder purple. How many square centimeters of the cylinder
did Mariah paint in terms of π?
Enter the correct answer in the box in terms of π.
answer: _______ cm squared
The number of square centimeters of the cylinder that Mariah painted is given as follows:
36π cm².
How to obtain the volume and the surface area of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm^3, hence the height of the cylinder is obtained as follows:
36πh = 72π
h = 2.
The surface area of a cylinder is obtained as follows:
S = 2π r h + 2π r
Hence it's value is of:
S = 2π x (2 x 6 + 6)
S = 36π cm².
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please i need help with steps
The total distance ran by the wide receiver is given as follows:
195.6 yd.
How to obtain the distance between two points?Suppose that we have two points with coordinates given as follows:
[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
Then the formula for the distance between these two points is given as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For the out route, the distance is given as follows:
[tex]D = \sqrt{(60 - 30)^2+(50 - 20)^2} = 42.43[/tex]
To the end zone, the distance is given as follows:
[tex]D = \sqrt{(60 - 80)^2+(50 + 30)^2} = 82.46[/tex]
From the end zone back to the huddle, the distance is given as follows:
[tex]D = \sqrt{(80 - 30)^2+(-30 - 20)^2} = 70.71[/tex]
Hence the total distance is of:
42.43 + 82.46 + 70.71 = 195.6 yd.
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Write the expression in exponential form. 9×9×9×9x9x9x9=|
its 9 of the 7th power
its also 9^7
Answer:
(9)^7
Step-by-step explanation:
All you have to do is count how many 9's you have, and the number you get will be the (power)
Put (9) as the base and then add the power
Which gives us (9)^7
[tex] {9}^{7} [/tex]
Purchases Transactions
Rolfes Company purchased merchandise on account
from Springhill Company for $12,200, terms 1/10, n/30.
Rolfes returned merchandise with an invoice amount of
$2,400 and received full credit.
a. If Rolfes Company pays the invoice within the
discount period, what is the amount of cash required for
the payment? If required, round the answer to the
nearest dollar.
b. What account is debited by Rolfes Company to record
the return?
?
Therefore , the solution of the given problem of percentage comes out to be the sum of money needed to complete the transaction is $7,722.
A percentage is defined.A percentage is mathematics is a figure or number that is stated as a proportion of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. However, the symbol "%" used to denote it is frequently used. The percentage amount is flat; there are no dimensions. Given that their numerator is 100, percentages are basically fractions.
Here,
According to the clauses 1/10, n/30, the buyer would receive a 1% reduction if the discount was applied within 10 days.
The consumer would be required to pay the whole amount in 30 days if the payment was not completed within this time frame.
Considering this and the fact that Nieman invoiced $2,400 for the returned goods, you must deduct this sum from their original purchase:
=> $12,200-$2,400= $7,800
Then, you must figure out the discount at 1% of $7,800 and deduct it from $7,800:
=> $7,800*1%= $78
=> $7,800-$78= $7,722
This means that, in the event Nieman Company settles the invoice during in the buy the product, the sum of money needed to complete the transaction is $7,722.
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-25 POINTS-
What is the equation?
[?]n+[?]
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. Answer is y = -2x + 9.
What is the equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
Fundamental Equations and Ideas:
Operational hierarchy: BPEMDAS
Form of the Slope-Intercept: y = mx + b
meter slope
y-intercept of b
Define variables first
Degree (Slope m) = -2
Random thought (1, 7)
Step 2: Locate b's y-intercept
Equation to be written down is y = -2x + b.
Substitute: 7 = -2(1) + b
Add the following factors together to multiply: 7 = -2 + b
2 more on either side:
9 = b
Write a linear equation in step 3
Replace with our freshly discovered b.
y = -2x + 9
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-1/5x-2>4
solve pls show work!
Step-by-step explanation:
-1/5x - 2 > 4
-1/5x - 2 + 2> 4 +2
first you subtract 2. The two cancels out into 0 making the equation this
↓
-1/5x x -1/5> 6 x -1/5
you multiply both sides by the -1/5 and if you divide or multiply a number over the inequality you must change the sign to the opposite one.
ANSWER:
x< -30
Answer:
x < -30
Step-by-step explanation:
-1 / 5 * x – 2 > 4
-1 / 5 * x > 6
We divide both parts of the inequality by (-1 / 5). It must be remembered that when dividing or multiplying both sides of the inequality by a negative number, the sign changes to the opposite:
x < 6 / (-1 / 5)
x < 6 * 5 / -1
x < -30
Сheck:
for -29 (> then -30):
-1 / 5 * -29 – 2 > 4
3.8 > 4? - No
for -31 (< then -30):
-1 / 5 * -31 – 2 > 4
4.2 > 4? – Yes
The solution is right!
Find the average/mean of following numbers:
6,11,7,13,3
Answer:
8
Step-by-step explanation:
[tex]mean = \frac{sum \: of \: numbers}{how \: many \: numbers \: there \: are} [/tex]
[tex]mean = \frac{6 + 11 + 7 + 13 + 3}{5} [/tex]
[tex] mean = \frac{40}{5} = 8[/tex]
The plane with normal vector <-6, 3, -3> containing the point (7, -4, 5) has equation Ax + By + Cz = D. If A= - 6 find what B, C, and D equals.
Step-by-step explanation:
for a plane defined as
Ax + By + Cz + D = 0
(A, B, C) is the normal vector (90° with the plane).
so, we know with the given normal vector (-6, 3, -3) that
A = -6
B = 3
C = -3
we are only missing D.
for that we use the given point (7, -4, 5) :
-6×7 + 3×-4 + -3×5 = D
-42 - 12 - 15 = D
-69 = D
A moving truck can carry no more than 1,480 pounds of cargo. Brian loaded x640 pounds into the truck already. He is loading boxes that weigh 70 pounds. How many boxes can he put into the truck?
The number of boxes that he can put into the truck will be 12.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
From the information, the moving truck can carry no more than 1,480 pounds of cargo. Brian loaded x640 pounds into the truck already. He is loading boxes that weigh 70 pounds.
Let the number of boxes that he can put into the truck will be represented as x.
640 + 70x = 1480
Collect the like terms
70x = 1480 - 640
70x = 840
Divide
x = 12
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let e be the amount in dollars that jacques spends on salad and pizza. if jacques buys s bowls of salad and p slices of pizza, then the total amount of money he spends (e) can be represented by the equation
The total amount of money (e) spent can be represented by the equation E = ($3.00S) + ($5.00P).
The total amount of money spent will be the sum of money sent of salad and pizza.
The total amount of salad = number of bowls of salad × cost of each bowl of salad
Similarly, the total amount of pizza = number of slices of pizza × cost of each slice of pizza
So, the combined equation will be -
Total money spent = number of bowls of salad × cost of each bowl of salad + number of slices of pizza × cost of each slice of pizza
Keep the values in above mentioned equation -
E = (S × 5) + (P × 3)
Performing multiplication of constant and variable on Right Hand Side of the equation
E = 5S + 3P
Thus, third option is correct.
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Find the least common denominator of 1/2x-6 and 2x/7x-21.
The least common denominator of the fractions 1/2x-6 and 2x/7x-21 is (2x-6)(7x-21)
What is a fraction?A fraction can be described as the part of a whole variable or number.
Some types of fractions in mathematics are;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsWhat is the least common denominator?The least common denominator of a fraction can be defined as the smallest number of all the common multiples of the denominators given.
From the information given, we have the fractions as;
1/2x-6 and 2x/7x-21
Note that the denominator of both fractions are
(2x-6)(7x-21)
Since they are in form of expression, the least common denominator is their product.
Hence, the LCD is (2x-6)(7x-21)
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It takes 29 pounds of seed to completely plant a 5-acre field. How many acres can be planted per pound of seed?
0.17 acres can be planted per pound of seed.
What is Ratio ?
In mathematics, the term "ratio" is used to compare two or more numbers. It is used to show how big or little an amount is in relation to another. Two quantities are compared using division for calculating a ratio.
Given, It takes 29 pounds of seed to completely plant a 5-acre field.
So, Acres per pound of seed = 5 Acres ÷ 29 pounds of seed
= 0.17 acres (approx).
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According to the given statement, 0.17 acres can be planted per pound of seed.
What is Ratio?In mathematics, the term "ratio" is used to compare two or more numbers. It is used to show how big or little an amount is in relation to another. Two quantities are compared using division for calculating a ratio.Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare one piece of data (A) to some other data point (B).
Given, It takes 29 pounds of seed to completely plant a 5-acre field.
So, Acres per pound of seed = 5 Acres ÷ 29 pounds of seed
= 0.17 acres (approx).
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Majka Company was started on January 1, Year 1. During Year 1, the company experienced the following accounting events: (1) Issued 52,500 worth of common stock (2) earned cash revenues of $33,400, (3) paid cash expenses of $14,800, and (4) paid a $3,100 cash dividend to its stockholders. These were the only events that affected the company during Year 1.
The cash from financing activities for Majka Company, can be found to be
How to find the cash from financing activities ?The net amount of financing a business generates during a specific time period is called cash flow from financing activities. The issuing and repayment of equities, the payment of dividends, the issuance and repayment of debt, and capital lease obligations are all examples of financial activity.
The cash from Financing activities for Majka Company is therefore:
= Common stock issued - Cash dividends
= 52, 500 - 3, 100
= $ 49, 400
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The full question is:
Majka Company was started on January 1, Year 1. During Year 1, the company experienced the following accounting events: (1) Issued 52,500 worth of common stock (2) earned cash revenues of $33,400, (3) paid cash expenses of $14,800, and (4) paid a $3,100 cash dividend to its stockholders. These were the only events that affected the company during Year 1.
What were the cash flows from financing for the year?
