The real rate of interest is 8 percent.
What is nominal rate of interest?In finance and economics, the nominal interest rate or nominal rate of interest is either of two distinct things: the rate of interest before adjustment for inflation; or, for interest rates "as stated" without adjustment for the full effect of compounding.
Given:
nominal rate of interest= 2%
expected inflation rate = 10 %
We know,
nominal rate = real interest rate + inflation rate
and, real interest rate= nominal rate - inflation rate
then,
real rate interest = 2-10
real rate interest = -8%
Hence, the inflation rate is greater than the nominal interest rate as it is -8%
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which of the following pairs of ratios form a proportion? a. 9 boys to 5 girls and 12 boys to 8 girls
Answer:
12 to 8
Step-by-step explanation:
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What is the decimal number 34.567 written in expanded form?
A: An expression that reads three times ten, plus one times one, plus five times one-tenth, plus seven times one-hundredth, plus four times one-thousandth
B: An expression that reads three times ten, plus three times one, plus six times one-tenth, plus seven times one-hundredth, plus five times one-thousandth
C: An expression that reads three times ten, plus four times one, plus five times one-tenth, plus six times one-hundredth, plus seven times one-thousandth
D: An expression that reads three times ten, plus seven times one, plus five times one- tenth, plus four times one-hundredth, plus six times one-thousandth
Answer:
option 3
Step-by-step explanation:
C: An expression that reads three times ten, plus four times one, plus five times one-tenth, plus six times one-hundredth, plus seven times one-thousandth
which expressions below equal a rational number? select all that apply.
The expressions that are equal to a rational number are [(2/3)+(4/5)], [(√3) - (√3)], and [(√49)(√1)].
A rational number is one that can be stated as the ratio of two numbers, with the denominator not equal to zero.All real numbers that are not rational numbers are referred to as irrational numbers. The ratio of two integers cannot be used to express irrational values.(a) π√4π√4 is equal to 2π, which is an irrational number.(b) (2/3)+(4/5)(2/3)+(4/5) = (22/15), which is a rational number.(c) (√36)-(√5)(√36)-(√5) = 6-√5, which is an irrational number.(d) (√3)-(√3)(√3)-(√3) = 0, which is a rational number.(e) (√49)(√1)(√49)(√1) = 7*1 = 7, which is a rational number.To learn more about real numbers, visit :
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If f ( x ) = 3 x + 2 and g ( x ) = x 2 − x , find the value. f ( 4 )
-1/2 is equivalent to 1/2
Answer: No
Step-by-step explanation:
No because its off by 1 point, -1/2, 0, 1/2
<6 and <7 form a linear pair. Twice the measurement of <6 is twelve more than four times the measurement of <7. Find the measurement of each angle.
A linear pair , m∠7 = 58°, m∠6 = 122° are the measurement of each angle.
What is Linear Pair?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Linear Pairs add up to equal 180°.
Step 1: Define
m∠6 + m∠7 = 180°
2m∠6 = 4m∠7 + 12
Step 2: Rewrite systems of equations
I will set m∠6 = x and m∠7 to y
x + y = 180°
2x = 4y + 12
Step 3: Rewrite 2nd equation
2x = 2(2y + 6)
x = 2y + 6
Step 4: Use Substitution
2y + 6 + y = 180
3y + 6 = 180
3y = 174
y = 58°
Step 5: Find x by plugging y back into an original equation
x + 58 = 180
x = 122°
Step 6: Rewrite
x = m∠6
y = m∠7
m∠6 = 122°
m∠7 = 58°
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Chose the step below that correctly uses the distributive property to begin solving the equation: 2(x + 1) + 4 = 8 O 2x+5=8 Ox+1+2 = 4 O 2x + 2 + 4 = 8 O 2x + 1 + 4 = 8
2(x+1)+4
Distributive property : According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
solve equation by using distributive property we should use laws of this property that are as follows:
Expand the equation. Multiply (distribute) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set. Combine like terms.
2(x + 1) + 4 = 8
2(x)+2(1)+4=8
2x+2+4=8
2x+6=8
2x=8-6
2x=2
x=2/2
x=1
so final conclusion is Option A 2(x+1)+4=8 is the right answer
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Help please for algebra
in slope intercept form:
y=mx+b.
slope of line:
-3/4
y intercept:
(0, 5/2)
The length of a rectangle is three more than double the width. if the perimeter is 78 inches, find the dimensions.
The length of a rectangle is 27 inches and the width of a rectangle is 12 inches.
Given that, the length of a rectangle is three more than double the width and the perimeter of a rectangle = 78 inches.
We need to find the dimensions of the rectangle.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Let the width of the rectangle be x.
Then, length=2x+3
Now, perimeter=2(2x+3+x)
⇒ 78=2(3x+3)
⇒ 3x+3= 39
⇒ 3x=36
⇒ x=12 inches
So, width=12 inches and length=2x+3=27 inches
Therefore, the length of a rectangle is 27 inches and the width of a rectangle is 12 inches.
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Reasoning true or false: if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution. explain your reasoning.
False, if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution.
A square matrix with a row of zeroes means that one variable can be written as a linear combination of the other variables.What does the term "echelon form" mean?
If a matrix in linear algebra has the shape that comes from a Gaussian elimination, it is said to be in echelon form. When a matrix is in row echelon form, Gaussian elimination has been applied to the rows, and when it is in column echelon form, Gaussian elimination has been applied to the columns.What purpose does echelon matrix serve?
By reducing a complex matrix to a simple matrix, the Echelon Form of a matrix can be utilized to solve a linear equation. If a matrix meets certain criteria, which we'll go over in this post, it is said to be in an echelon form.Learn more about echelon form
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For which value of a does 4 = a +| x – 4| have no solution?
-6
0
4
6
Answer:
a = 6
Step-by-step explanation:
Hello!
First, let's isolate the Absolute Value bracket.
4 = a + |x - 4|4 - a = |x - 4|Based on the definition of Absolute value, the outcome should always be a positive number. Therefore, if the product, 4 - a, is a negative number, it will have no solutions.
That means a has to be greater than 4 for it to be negative. a should be 6.
a = 6
Multiply:
-2x(3x - 4)
Enter the correct answer
Answer:
- 6x² + 8x
Step-by-step explanation:
- 2x(3x - 4) ← multiply each term in the parenthesis by - 2x
= - 6x² + 8x
What is the area of this tile?
6 in.
8in.
Answer:that would be 24
Step-by-step explanation: A triangle is a three side shape so after you multiply 6 and 8 thats 48 but then you multiply by 1/2 which is the same as dividing by 2 so (48/2)=24 and thats your answer hope this helps
Please help me! I am so confused
Theoretical probability is what might happen, but the experimental probability is definitely happens in trials. The probability in these cases is 0.25.
What is the difference between theoretical and experimental probability?Theoretical probability is based on the total outcomes vs the desired outcomes; due to this, this is just the expectation of what will hapen. However, as this is mainly based on expectations, it is not completely accurate.
On the other hand, the experimental probability is based on the observation of reality as the probability is tested, which makes it more accurate.
What are the probabilites in the cases presented?Desired outcomes /total outcomes
Probability of getting red in the spinner:
4/10 0.25 or 25%Probability of getting a 4 in a dice
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8+
49
6-
5
Based on the graph above, estimate (to one decimal place) the average rate of change from x = 1 to
x = 5.
The Average Rate of change of a function f on the interval [a , b] is given by
[tex]r=\frac{f(b) - f(a)}{b-a}[/tex]
Now, the given interval is [1, 5]
⇒ b=5 and a = 1
Since, the graph passes through (1, 3) and (5, 5)
⇒ f(1) = 3 and f(5) = 5
Thus,
[tex]r=\frac{f(5) - f(1)}{5-1}[/tex]
[tex]r=\frac{5- 3}{4}[/tex]
[tex]r=\frac{2}{4}[/tex]
[tex]r=\frac{1}{2}[/tex]
[tex]r=0.5[/tex]
∴ The Average Rate of change of the graph is equal to 0.5
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6. The value of a car is gradually declining in such a way that at the end of each year it is worth in January 2002 6 of its value at the beginning .it was worth 36000,000 in January 2000. What was its worth in January 2002?
Answer:
the value of a car is gradually declining in such a way that at the end
Step-by-step explanation:
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Eight families live on abbie's street. she asks each family how many pets they have. abbie's data set is: 0, 0, 1, 1, 2, 2, 2, 5. the modal number of family pets on abbie's street is:__________
Answer:
Step-by-step explanation:
It is asking for the "mode" which is the data element you see the most, therefore it is 2.
greg is 5yr. older than randy, who is 3yr. older than Wilson. the sum of their ages is 32. how old is greg
The ages of Wilson, Randy and Greg given their total ages is 7, 10 and 15 years respectively.
This means that the total ages of Wilson, Randy and Greg is 7 years, 10 years and 15 years.
AlgebraLet's represent the information above as follows:
Wilson's age = xRandy's age = (x + 3)Greg = (x + 3) + 5Total ages = 32The total ages = Wilson + Randy + Greg
That is, Wilson's age, Randy's age and Greg's ages is given as:
32 = x + (x + 3) + (x + 3) + 5
32 = x + x + 3 + x + 3 + 5
32 = 3x + 11
32 - 11 = 3x
21 = 3x
x = 21/3
x = 7 years
Therefore, from the calculations above,
Wilson's age = x
= 7 years
Randy's age = (x + 3)
= 7 + 3
= 10 years
Greg = (x + 3) + 5
= (10) + 5
= 15 years
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Evaluate
4(x+3)(x+1)
(x+5)(x-5)
for x = 3.
Answer: -1536
Step-by-step explanation:
1: 4(3+3) (3+1) (3+5) (3-5)
2: 4(6) (4) (8) (-2)
3: 24 (4) (8) (-2)
4: 96 (8) (-2)
5: 768 (-2)
= -1536
Write an algebraic expression to represent how much money Max has saved.
Max is saving to buy a car. He already has $700 saved. He will continue to earn money by cutting lawns; he earns $15 for each lawn. Let x represent the number of lawns Max cuts.
Answer: x=700+15
Step-by-step explanation: an educated guess
Answer:
y = 15x + 700
Explanation:
In this sentence said Max already has $700 which means it should be constant value in the equation. Max earns $15 for each lawn he cuts.
Linear equation:
y = mx + bwhere 'm' is rate of change, 'b' is constant value
So, the equation should be (for total money Max saved):
y = 15x + 700where y represents total money Max saved and x = number of lawns cut.
6. You just had surgery on your knee. As part of rehabilitation your physical
therapist wants you to walk 1 minute on day 1 and double your time every day. How
many minutes will you be walking on day 7?
64 minutes
Step-by-step explanation:
1x2=2 it day one
2x2=4 it day two
and more
32x2=64 it day 7
Which one is correct
All rhombus are parallelograms, parallelogram have exactly two pairs of parallel lines, therefore all rhombus have exactly two pairs of parallel lines, so option A is correct.
What is parallelogram?
A unique kind of quadrilateral created by parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but for it to be a parallelogram, its opposite sides must be parallel.
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. Every rhombus is a parallelogram because its opposite sides are all parallel. But all parallelograms cannot be rhombus as a rhombus have all sides equal.
Both a square and a rhombus have equal numbers of sides. The square's diagonals are also perpendicular to one another and divide the opposing angles. A square is a rhombus as a result.
Thus, all rhombus are parallelograms as they have one pair of parallel sides.
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A is the midpoint of segment ST. Point A is located at (7,-1) and point S is located at (5,0). What are the coordinates of point T?
The coordinates of point T is (9,-2)
Given that A is the midpoint of segment ST. midpoint A has coordinates (7,-1) and point S has coordinates ( 5,0 ) and asked to find the coordinates of the point T
Let's assume the coordinates of the point T as(a,b)
Midpoint formula for a line segment having endpoints (x1,y1) and (x2,y2)
Let's assume the midpoint as (X,Y)
(X,Y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
Here the endpoints of the linesegment ST are S(5,0) and T(a,b) and the midpoint of the linesegment ST is A and has coordinates (7,-1).
⇒(7,-1)=([tex]\frac{5+a}{2}[/tex],[tex]\frac{b}{2}[/tex])
⇒7=[tex]\frac{5+a}{2}[/tex]⇒14=5+a⇒a=9
⇒-1=[tex]\frac{b}{2}[/tex]⇒b=-2
Therefore,The coordinates of point T is (9,-2)
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x^5y^5z^3 =?
A. bases are different, so this can't be done.
B. xy5z3
C. (xy)5z3
To simplify the indices expression x⁵y⁵z³, we can conclude that; A. bases are different, so this can't be done.
How to simplify Indices?We want to simplify the indices given as;
x⁵y⁵z³
Now, we can see that the bases are different and as such it means they cannot be simplified using laws of indices on the exponents.
This is because when the bases are different, the expression cannot be factored with the exponents being added, subtracted, divided or multiplied.
Thus, we will conclude that the bases are different, so this can't be done.
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x + 4y= 15
2x-y=-15
Solve for X and Y
Step-by-step explanation:
work is shown and pictured
(3x-5)/4 is less than or equal to -1
How to solve for x?
Step-by-step explanation:
[tex] \frac{3x - 5}{4} \leq1[/tex]
[tex]3x - 5 \leq1 .4[/tex]
[tex]3x - 5 \leq4[/tex]
[tex]3x \leq4 + 5[/tex]
[tex]3x \leq9[/tex]
[tex]x \leq \frac{9}{3} [/tex]
[tex]x \leq3[/tex]
x = {3,2,1,0,...}
Graph y=0.2x use the graph to find the value of x when y=-2,0,2
By graphing the equation y = 0.2x, we find that x is equal to -10 when y is -2, x is equal to 0 when y is 0, and x is equal to 10 when y is 2.
To graph the equation y = 0.2x, we can plot a few points and then connect them to create the line.
Let's calculate the corresponding values of x when y takes on the values of -2, 0, and 2:
When y = -2:
-2 = 0.2x
x = -2 / 0.2
x = -10
When y = 0:
0 = 0.2x
x = 0 / 0.2
x = 0
When y = 2:
2 = 0.2x
x = 2 / 0.2
x = 10
Using these values, we can plot the points (-10, -2), (0, 0), and (10, 2) on the coordinate plane. Drawing a line passing through these points, we obtain the graph of the equation y = 0.2x.
The graph will be a straight line that passes through the points (-10, -2), (0, 0), and (10, 2). The line will have a positive slope, indicating that as x increases, y increases at a slower rate.
The graph visually represents the relationship between x and y according to the equation y = 0.2x. It shows that for every increase of 1 unit in x, y increases by 0.2 units.
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What is the slope of the line that passes through the points (-4,5) and (-7,8) ? write your answr in the simplest form
∠A and angle B∠B are complementary angles. If m angle A=(x+13)m∠A=(x+13)
and m angle B=(7x+13)^∠B=(7x+13) then find the measure of angle B∠B
The value of angle B is 69°.
How to calculate the angle?It should be noted that the sum of a complementary angle is 90°.
Therefore, the value will be:
x + 13 + 7x + 13 = 90
8x + 26 = 90
Collect like terms
6
8x = 90 - 26
8x = 64
Divide
x = 64/8
x = 8
Angle B = 7x + 13
= 7(8) + 13
= 56 + 13
= 69
Angle B is 69°.
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TASK 2-Percentages (34 Marks)
Topic: Finding Percentages
1. Suppose you have a grandmother who gives you one cent on your first birthday. The
next year she gives you 3 cents, the following year 9 cents. Each year she triples the
amount she gave the year before until you are 13.
How much money would you have on your 12 birthday? you would have
$154
72
(a) Complete the table below (BMarks)
Birthday
1
2
3
4
5
6
7
8
9
10
11
12
13
Total
Money
1c
3c
9c
27c
81c
$2.43
34 86
39 72
$19 34
338 68
377 36
$154 72
Percentage
3309-44
$309 44
(b) What percentage is the amount of money on your 12th birthday to the total money
given by your grandmother. Your percentage need to be corrected to two decimal
places. You need to show all the steps for your percentage calculation.
Answer:
1; 1
2:3
3:9
4:27
5:81
6:243
7:729
8:2,187
9:6,561
10:19,683
11:59,049
12:177,147