The first row of a bank statement shows -
Option D : The account's balance at the beginning of the period.
What is bank statement?
A bank statement, also known as an account statement, is a record that summarises all of an account's transactions for a given month and is normally issued by the bank to the account holder each month.
The transactions for a bank account over a specific time period, typically monthly, are listed in a bank statement.
The statement provides the beginning and ending balances for the period along with deposits, charges, and withdrawals.
Every month, account holders typically analyse their bank statements to assist them keep track of their spending and costs and to check for any erroneous or fraudulent charges.
Therefore, the first row shows the balance at the beginning period.
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Two quantities x and y vary inversely, y=4 when x=7. Identify the value of constant variation, a, for the function.
y= ___/x
I will mark you brainliest!!
Answer:
28
Step-by-step explanation:
The constant variation, a, is equal to the product of x and y when they are both known. In this case, when x = 7 and y = 4, the constant variation is 4 * 7 = 28. So, the equation for the inverse variation is y = 28 / x.
Given f(x) = log x, what transformations are needed to produce g(x) = log (x) - 3?
Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3 transformed .
Define function.Mathematics includes the study of numbers, various variable, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship between the number of inputs and the corresponding outputs for each. Simply explained, a function range is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a realm. The letter f is frequently used to denote functions (x).
Here,
Given :
=> f(x) = log x
=> g(x) = log (x) - 3
So , it is transformed as logx = f(x)
it is transformed as :
=> g(x) = f(x) - 3
Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3 transformed .
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Find the average rate of change of f(x) = 7x² - 6 on the interval [4, b]. Your answer will be an expression involving b
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 7x^2-6 \qquad \begin{cases} x_1=4\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(4)}{b - 4} \\\\\\ \cfrac{(7b^2-6)~~ - ~~(7(4)^2-6)}{b-4}\implies \cfrac{7b^2-6~~ - ~~(112-6)}{b-4} \implies \cfrac{7b^2-112}{b-4}[/tex]
[tex]\cfrac{7(b^2-16)}{b-4}\implies \cfrac{7(b^2-4^2)}{b-4}\implies \cfrac{7~~\begin{matrix} (b-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(b+4)}{~~\begin{matrix} b-4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \boxed{7(b+4)}[/tex]
This expression gives the average rate of change of the function over the interval [4, b].
How is rate of change determined?The average rate of change of a function on an interval is equal to the rise (change in the y-value) divided by the run (change in the x-value) over that interval.
For f(x) = 7x² - 6 on the interval [4, b], the average rate of change can be found by calculating the slope of the secant line connecting the points (4, f(4)) and (b, f(b)).
Therefore, the average rate of change of f(x) = 7x² - 6 on the interval [4, b] is:
(7b² - 6 - (7(4)² - 6)) / (b - 4) = (7b² - 28) / (b - 4)
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2.3.3. 1. Give the rule for translating a point 4 units left and 8 units up. (2 points)
StartFraction 32 Over 8 EndFraction = StartFraction 28 Over x EndFraction
a.
x = 4
c.
x = 8
b.
x = 28
d.
x = 7
Answer:
d. x = 7
Step-by-step explanation:
To find the value of x, you can cross multiply the fractions to get 32 * x = 8 * 28, then simplify:
32x = 224
x = 7.
How many hundredths are in 5/10
There are 50 hundredths in the fraction 5/10.
What is a place value?In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.From the information provided about the numerical value, we have:
5/10 = 0.5.
Note: 1 hundredth is equal to 1/100 = 0.01.
Therefore, by dividing 0.5 by 0.01 we have:
Number of hundredths = 0.5/0.01 = 50.
In conclusion, 5 tenths or 5/10 is equivalent to 50 hundredths.
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which of the following is the shortest distance from a to b
The shortest distance from A to B in the figure is length AB, So Option A is correct
What is displacement ?The smallest (straight line) distance between a body's beginning position and its final location—represented by an arrow pointing from starting position to final position—is referred to as a body's displacement as it moves from one position to another. Being a vector quantity, it.
Given that,
A quadrilateral figure ABCD
and it has one diagonal BD
Shortest distance from A to B =?
Possible paths, For A to B
1. Directly A to B
Distance = AB
2. A to D then D to B
Distance = AD + DB
3. A to D then D to C and then C to A
Distance = AD + DC + CA
It can be seen that distance covered is lesser in case 1 in compare to case 2 & 3
Hence, the shortest distance is AB
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Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
Sample space = lemon-lime, watermelon, grape
Sample space = 1, 2, 3, 4, 5, 6
Sample space = 1, 2, 3
The correct sample space for the gumballs in her bag is;
A: Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
How to find the sample space?The sample space of an experiment is defined as the set of all the possible outcomes. For example, when we toss a coin, the sample space is; {head, tail}.
Now, the parameters for the bag filled with gumballs are;
1 watermelon.
2 lemon-lime.
3 grape gumballs.
Therefore the sample space is the different types of gumballs there and it is; {Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape}
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In a survey of 1.600 people who owned a certain type of car, 880 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
The percent of people satisfied with the survey is 55%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, in a survey of 1,600 people who owned a certain type of car, 880 said they would buy that type of car again, we need to find what percent of the people surveyed were satisfied with the car,
The percent of people satisfied with the survey = 880 / 1600 × 100
= 55%
Hence, the percent of people satisfied with the survey is 55%
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Find the Volume of the following sphere.
A. 1436.03 ft3
B. 58.61 ft3
C. 87.92 ft3
D. 205.15 ft3
Answer:
A. 1436.03 ft³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3)(3.14)(7 ft)³
V = 1436.03 ft³
PLEASE HELP DONT IGNORE.
Bianca is ordering food at a local taco truck. She wants a soda which costs $1.75. Tacos cost $0.75 each.
Write an equation, in slope-intercept form, that represents the total cost (y) for x number of tacos and a drink.
The slope intercept form of the equation is given as y = 0.75x + 1.75
How to write the slope intercept formThe slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is the cost per taco, which is $0.75. The y-intercept (b) is the cost of the drink, which is $1.75.
So, the equation that represents the total cost (y) for x number of tacos and a drink is:
y = 0.75x + 1.75
This equation states that for every taco ordered (x), the cost will increase by $0.75, and the minimum cost will always be $1.75 for the drink.
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The graph below shows a linear function and an exponential function.
x intercept is 1,4 don't have image
What is the minimum y-value after which the exponential function will always be greater than the linear function?
y = 1
y = 3
y = 4
y = 5
y=4 is the minimum y-value after which the exponential function will always be greater than the linear function.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the graph we can see that in the interval [0,1] the value of y is less than 1.
In the interval [1,2] the value of y value is 2 to 4.
In the interval [2,infinity) the graph is going up, and the value of y is greater than or equal to 4.
Therefore, the graph going up after y=4 above the line.
Therefore, the minimum y-value is 4 after which the exponential function will always be greater than the linear function.
Hence, y=4 is the minimum y-value after which the exponential function will always be greater than the linear function.
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Given: P = 56 feet, DC = 16 feet, what is the length of BC?
Answer:
12 feet
Step-by-step explanation:
this is a rectangle! because DC = 16 feet, you know that AB is also equal to 16 feet
therefore, DA + CB = 24
because ABCD is a rectangle, you know that DA = CB and you can use substitution to say that CB + CB = 24
2CB = 24
CB = 12
Ben says that n = 6 is the solution of the equation 7n = 49. Is Ben correct? EXPLAIN.
Answer:
He is incorrect
Step-by-step explanation:
7n = 49
Isolate variable "n" by dividing both sides by 7:
n = 7
Since doing this step makes n to equal 7, [Ben is incorrect to say that n = 6]
In parallelogram EFGH, MLH =
F
Зу
(3x - 15)°
2(y + 1)
H
(7x- 5)°
y + 8
o and HG
＝
The measure of HG is 12
What is a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.
The opposite sides of a parallelogram are equal. This means that 3y = y+8
3y = y+8
3y-y = 8
2y = 8
divide both sides by 2
y = 8/2
y = 4
if y = 4 and HG is y+8
therefore
the measure of HG = 4+8
= 12
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Diana has z gerbils. Jackie has 4 times as many gerbils as Diana.
a) If w stands for the number of gerbils Jackie has, express w in terms of z.
Answer:
Dina =z gerbils
Jacki =4z
W = 4z
Independent:z
Dependeny:w
Step-by-step explanation:
I think it's right
there are two numbers that are twice as far from 5 as from 17
Solving the provided question, we can say that Using quadratic formula, x = 19 or x = 3; Sum of the 2 numbers = 3 + 19 = 22
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
Let x represent a number that is twice as far away from 5 than 17.
|x - 5| = 2|x - 17|
(x - 5)² = 4(x - 17)²
[tex]x^2 + 25 - 10x = 4(x^2 + 49 - 14x)\\x^2 + 25 - 10x = 4x^2 + 196 - 56x\\3x^2 - 46x + 171 = 0\\[/tex]
Using quadratic formula,
x = 19 or x = 3
Sum of the 2 numbers = 3 + 19 = 22
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Ralph has 3/4 gallon of paint. He wants to store all of the paint equally among 5 containers. How much paint, will Ralph store in each container
Answer:
Below
Step-by-step explanation:
He wants to DIVIDE the 3/4 gallon into 5 bux
so divide 3/4 by 5
3/4 / 5 = (3/4) / (5/1) = 3/4 * 1/5 = (3*1) / ( 5*4) = 3/20 gallon per bux
The amount of paint that Ralph store in each container is 3/20 gallon.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Total amount of paint that Ralph has = 3/4 gallon
He wants to store all of the paint equally among 5 containers.
If the paint is stored in 5 containers,
Amount of paint in each container = 3/4 ÷ 5
= 3/4 × 1/5
= 3/20
Hence 3/20 gallon of paint is stored in each container.
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Carlos tried to shade all the factors of 30 on the hundred chart, but he made a mistake.
1 3 5 15
What mistake did Carlos make?
On solving the provided question, we can say that all the factors of 30 on the hundred chart are = 1,2,3,5,6,10,15,30 and mistake he made was he didn't mark = 2,6,10,30
What is factor ?In mathematics, the integer m serves as the divisor (also known as factor n) of an integer n, which may be multiplied by the integers to get n. We may also state that n in this situation is a multiple of m. A number without a residue that divides another number is said to be a factor. In other words, if you multiply two integers to create a product, the numbers you multiply are factors of the product since the result is divisible by the numbers you multiply. Factors can be found using either division or multiplication.
all the factors of 30 on the hundred chart are = 1,2,3,5,6,10,15,30
mistake he made was he didn't mark = 2,6,10,30
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read the question on the paper please
The dimensions for a square that has a perimeter of 14 units and area or 49 units² will be 7 units by 7 units.
How to calculate the sidesThe perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.
In this situation, the square has a perimeter of 14 units and area or 49 units². The dimensions will be 7 units by 7 units.
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The rectangular floor of Ms. Ragan's closet is completely covered with carpet squares. Each carpet square covers 1 square foot of the floor. There are 4 rows and each row has 16 carpet squares. What is the area of the floor of this closet in square feet?
The area of the rectangular closet is given by the equation A = 64 feet²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangular closet be represented as A
Now , the equation will be
The area of 1 carpet square = 1 foot²
The number of rows = 4 rows
The number of carpet square in each row = 16 carpet squares
So , the total number of carpet squares in 4 rows = number of rows x number of carpet square in each row
Substituting the values in the equation , we get
The total number of carpet squares in 4 rows = 16 x 4 = 64 carpet squares
So , the area of 64 carpet squares = 64 x area of 1 carpet square
Substituting the values in the equation , we get
The area of the rectangular closet A = 64 feet²
Hence , the area of the rectangular floor is 64 feet²
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Five percent of the workers in a firm employing a total of 2000 men earn less than Rs 2.00 per hour, 450 earn from Rs.2 to 2.24 per hour, 35 percent earn from Rs.2.25 to Rs.2.49 earn from Rs.2.50 to Rs.2.74 per hour, 12 percent earn from Rs.2.75 to Rs.2.99 per hour and the rest earn Rs.3 or more per hour. What is the median wage?
The median wage of workers in the firm is given as follows:
Rs 2.37 per hour.
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. Hence, the median also represents the 50th percentile of a data-set.
From the data-set in this problem, the median is obtained as follows:
Less than Rs 2 per hour -> 5% -> 5th percentile.450 earn from Rs 2 to Rs 2.24 per hour -> 5 + 22.5 = 27.5th percentile.35% percent earn from Rs 2.25 to Rs 2.49 per hour -> 27.5 + 35 = 62.5%. -> above 50%.Hence the median class is:
Rs 2.25 to Rs 2.49 per hour.
The median is the middle value of the class, hence:
(2.25 + 2.49)/2 = Rs 2.37 per hour.
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Juanita has a hybrid car that averages 44 miles per gallon. Her car has a 12-gallon tank. How far
can she travel on one full tank of gas?
The car can travel 528 miles on a one full tank gas that averages 44 miles per gallon.
What is average?In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data.
Given that, Juanita has a hybrid car that averages 44 miles per gallon.
Her car has a 12-gallon tank.
So, the car travels:
(12) (44) = 528 miles.
Hence, the car can travel 528 miles on a one full tank gas.
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Question
The product of two consecutive positive integers is 42. Find the integers.
Consider the expression 4x² + x + 3.
Complete 2 descriptions of the parts of the expression.
1. The entire expression is a sum with
2. The coefficients are
V
Answer: 4 and 1
Step-by-step explanation:
the expression 4x² + x + 3.
the coefficients are 4 and 1
so the answer is 4 and 1
because 4 is the quadratic coefficient and 1 is the primary term coefficent
Answer:
3 terms
4 and 1 coefficients
Step-by-step explanation:
-2 x (5-3) and found -2 x 2= 4 is that true
Answer: false
Step-by-step explanation:
Ms. Florinda is a kindergarten teacher. She buys 100 pencils and wants to give 2 pencils to each of her students. She has 2 classes, a class with 22 students and a class with 19 students. Part A Write an expression for how many pencils she has left after giving them out to her students. A. 100 − 2 × ( 22 − 19 ) 100 - 2 × ( 22 - 19 ) B. 100 − 2 × 22 − 19 100 - 2 × 22 - 19 C. 100 − 2 × 22 − 2 × 19 100 - 2 × 22 - 2 × 19 D. 100 − 22 − 19 100 - 22 - 19 Part B Does she have enough pencils to give each of her students 2? Choose... , she has Choose... Choose... than she needs.
The expression for the number of pencils she has left will be 100 - 2 × 22 - 2 × 19. Then the correct option is C. And yes, she has enough pencils.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Ms. Florinda is a kindergarten educator. She purchases 100 pencils and needs to give 2 pencils to every one of her understudies. She has 2 classes, a class with 22 understudies and a class with 19 understudies.
Then the expression is given as,
⇒ 100 - 2 × (22 + 19)
⇒ 100 - 2 × 22 - 2 × 19
⇒ 100 - 44 - 38
⇒ 18
The expression for the number of pencils she has left will be 100 - 2 × 22 - 2 × 19. Then the correct option is C. And yes, she has enough pencils.
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What equation of the line which passes through the point (-1, 2) and is parallel to the line y=x+4
Answer:
Thus, the equation of line for point (-1, 2) is y = x + 3.
Step-by-step explanation:
Answer:
The equation of the line is y = x + 3.
Step-by-step explanation:
A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.
y = mx + b
y = 1 * -1 + b
y = -1 + b
b = y + 1
b = 2 + 1
b = 3
Lisa is trying to get her personal finances in order. She does not know how to organize the following information.
Lisa's remaining of her monthly income is $490. Her net worth is $142.980. Her saving ratio is 17%, liquidity ratio is 23% and Debt-to-asset ratio is 63%.
Based on the given data, we can construct Lisa's personal cash flow statement and personal balance sheet as:
Personal Cash Flow Statement
Cash Inflow:
After-tax income = $3.600Cash Outflow:
Debts:
Mortgage Payment = $1,410Car loan Payment = $532Living expenses:
Groceries expense = $288Car maintenance = $280Utilities expense = $120Recreation expense = $480Total cash = $490
Personal Balance Sheet
Assets:
Cash = $600Clothing Owned = $549Car = $18,000Furniture = $14,000House = $350,000Total Assets = $383,140
Liabiities:
Credit Card Balance = $11,160Car loan = $12,000Mortgage = $217,000Total Liabilties = $240,160
Net worth = $142,980
Saving ratio can be calculated by assuming that the amount of Lisa's cash on bank is her saving. Then:
saving ratio = saving : net income
Saving ratio = cash in bank : net income
Saving ratio = $600 : $3,600
Saving ratio = 17%
Liquidity ratio is calculated by comparing Lisa's current assets with her net worth. Hence:
Liquidity ratio = Current assets : Net worth
Liquidity ratio = (Cash in bank + Car + Clothing owned + Furniture) : Net worth
Liquidity ratio = ($600 + $18,000 + $540 + $14,000) : $142,980
Liquidity ratio = 23%
Debt-to-asset ratio = Total Liabilities : Total Assets
Debt-to-asset ratio = $383,140 : $240,160
Debt-to-asset ratio = 63%
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Work out the following sheet
Note that in question 28 above:
X = 56° (Alternative Angles)
Y = 124° (Angles in a straight line)
Z = 81° (Sum of angles in an irregular parallelogram).
in Question 29,
x = 126° (Co-interior angles and Bisector theorem).
Question 28: Note that the sum of angles in an irregular parallelogram always equal 360°. Since X and 56° are alternate angles and are therefore congruent, and Y and 56° are on the same line and therefore sum up to 180°, resulting in Y being equal to 124°, then we have three interior angles of an irregular parallelogram:
∠X = 56°
∠Y = 124°; and
∠99° (As given), which is co-interior with ∠Z
Thus whether by the Co-interior principle where two co-interior angels sum up to 180° or by sum of angles in an irregular parallelogram, we will still obtain a result where:
∠Z = 81°. That is
360° = 56 + 124 + 99 + ∠Z
∠Z = 360 - (56 + 124 + 99)
∠Z = 81°
OR
Using the Co-Interior angles theorem, we can state that:
∠Z = 180 - 99
∠Z = 81°
Question 29:
Recall that an angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.
Thus, we can state that 27° is half of the angle whose Co-interior is x.
Thus ∠x = 180 - (27*2)
∠x = 180 -54
∠x = 126°
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