The quarterly interest rate is equal to 2.25%. This implies that Gavin is correct.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this formula:A(t) = P(1 + r/n)^{nt}
Where:A represents the future value.
r represents the interest rate.
n represents the number of times compounded.
P represents the principal.
T represents the time measured in years.
In this scenario, Gavin's savings account is compounded annually at an interest rate of 9%. This ultimately implies that, the equivalent quarterly interest rate would be calculated by dividing the annual interest rate of 9% by 4 as follows:
Quarterly interest rate = 9/4
Quarterly interest rate = 2.25%
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Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
Sandy earn 306.9 dollars in commission and 1739.1 dollars in hourly wages.
How to find Sandy hour wages and commission?Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales.
She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
The amount she will earn in her hourly wages and commission is as follows:
amount earn in commission = 15% of 2046
amount earn in commission = 15 / 100 × 2046
amount earn in commission = 30690 / 100
amount earn in commission = 306.9 dollars
Therefore,
amount earn in hourly wages = 2046 - 306.9
amount earn in hourly wages = 1739.1 dollars.
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The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2
What is the mean, and what does it tell you in terms of the problem?
The mean is 38.5. It tell us that the average distance a heavy ball was thrown is 38.5 feet.
What is the mean?A stem-and-leaf plot is table that displays a data set in ascending order. used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. In this stem-and-leaf plot, the stem is the tens digit and the leaf is the units digit. For example, in the number 32, 3 is the stem 2 is the leaf.
The mean is a measure of the center of a dataset that is used to determine the average of a set of numbers
Mean = sum of numbers / total numbers in the data set
(20 + 21 + 24 + 31 + 32 + 36 + 41 + 43 + 47 + 51 + 51 + 65) / 12
462 / 12 = 38.5
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Write an equation for line L in point-slope form and slope-intercept form?
L is perpendicular to y=5x
Write an equation for the line L in point - slope form
The linear equation in the slope-intercept is:
y = (-1/5)*x - 26/5
And it can be written as:
y = (-1/5)*(x + 1) - 5
How to find the equation for line L?
We can write the equation for line L as:
y = a*x +b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular if the product between the slopes is equal to -1.
So if we want our line to be perpendicular to y= 5x, then we must have:
a*5 = -1
a = -1/5
So our line is something like:
y = (-1/5)*x + b
And the line passes through (-1, -5), replacing these values:
-5 = (-1/5)*-1 + b
-5 = 1/5 + b
-5 - 1/5 = b
-26/5 = b
The linear equation is:
y = (-1/5)*x - 26/5
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The function g(x)=3x^3+x is an odd function.Which transformation of g(x) would result in odd functions?Check all that apply
The transformations of g(x) that would result in odd functions are (a)-g(x) , (b)g(2x) and (d)g(–x) ,
In the question ,
it is given that,
the function is g(x) = 3x³ + x
We know that the function f(x) is called an odd function if f(-x) = -f(x) .
Option(a)
the transformation is given as -g(x)
-g(x) = -(3x³ + x) = -3x³ - x
g(-x) = 3(-x)³ + (-x) = -3x³ - x
so , this is odd function .
Option (b)
the transformation is given as g(2x)
g(-2x) = 3(-2x)³ + (-2x) = -24x³ - 2x
-g(2x) = -{3(2x)³ + (2x)} = -( 24x³ + 2x ) = -24x³ - 2x
so , this is odd function .
Option (c)
the transformation is given as g(x)-3
(g(-x) - 3) = 3(-x)³ + (-x) - 3 = -3x³-x-3
-(g(x) - 3) = -{(3x³ + x) -3} = -3x³ - x +3
So, so , this is not an odd function
Option (d)
the transformation is given as g(-x)
g(-(-x)) = g(x) = 3x³+x
-g(-x) = -(3(-x)³ + (-x)) = -(-3x³ - x) = 3x³+x
so , this is odd function .
Therefore, the odd transformations are -g(x) , g(2x) and g(–x) ,
The given question is incomplete , the complete question is
The function g(x)=3x³+x is an odd function. Which transformation of g(x) would result in odd functions? Check all that apply
(a) -g(x)
(b) g(2x)
(c) g(x) − 3
(d) g(–x)
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What value of k will translate the graph of f(x) = 5x + 6 down by 1 when replaced by f(x) + k?
Step-by-step explanation:
"down by one" means that the y values (the function result values) are all decreased by 1.
so, k = -1
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5.
A car service charges $2.40 for driving 1 mile. How much does the company charge for
driving 12.45 miles?
) (
$14.85
$24.85
$27.48
$29.88
Show Your Work
Answer:
Step-by-step explanation:
$2.40 12.45 mi
___ * ___ = ? ;
1 mi. 1
The units of miles— "mi" —cancel out to "1" ;
since: " mi/ mi = 1 "
and we have:
$2.40 * 12.45 = ? ;
= $29. 88 ; {using a calculator};
⇒ which corresponds to: Answer choice: [D]: $29.88 .
_____
Hope this is helpful!
Best wishes!
_____
Anna makes a round pizza. She wants to put a cheese layer on the pizza. If the
pizza is 11 in in diameter, how many square cm of cheese layer does she need
to put on the pizza?
The number of square cm of cheese layers that Anna needs to put on the pizza is 30.25π square cm.
What is the area of a circle?
In geometry, the area of a circle is the space occupied by the circle.
To find the area of a circle having radius "r", we can use the formula.
Area of a circle = π×r².
In the given question, the diameter of the pizza is 11 cm.
so the radius will be = 11/2 = 5.5 cm.
Area of the pizza = π×r²
= π×(5.5)²
= 30.25π square cm.
Hence, the number of square cm of cheese layers that need to be put on the pizza is 30.25π square cm.
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a. Use the points (5, 1273) and (10, 2546) to write an equation for the line.
Type an equation in y=mx form
(Type an equation: Use integers or fractions for any numbers in the equation.)
Using the points (5, 1273) and (10, 2546), equation for the line is 5y = 1273x.
Define equation.There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Given,
Coordinates (5, 1273) and (10,2546)
For slope, m
m = y₂ - y₁/ x₂ - x₁
m = 2546 - 1273/10 -5
m = 1273/5
Equation in y = mx form,
y = 1273/5 x
Cross multiplying,
5y = 1273x
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The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given that the graph of the function has increased and decreasing orders on the coordinate plane.
The interval in which the given graph of the function is increasing is,
(-∞,-6)
(-4,-1)
(3,6)
(8,∞)
Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).
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Fin the measurement of the angle
A=
B=
C=
D=
E=
F=
G=
45°
Answer:
Step-by-step explanation:
A=60
B=75
C=45
D=60
E=75
F=45
G=90
a certain washing machine uses 29 gallons of water for each load of laundry washed. How many gallons of water would the washing machine use for 156 loads of laundry?
Answer:156
Step-by-step explanation:
Hayley's fuel bills for her house increased from £76 a month in 2021
to £89 a month in 2022. Calculate the percentage increase in Hayley's
fuel bills from 2021 to 2022.
Give your answer correct to three significant figures.
The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.
What is a Percentage Increase?
The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.
Steps to Calculate Percentage Increase?
The formula to calculate Increase (I) is given by, [tex]I=Y-X[/tex], where [tex]X[/tex] is the original value and [tex]Y[/tex] is the new value.The percentage increase formula is given by, [tex]\%I=\frac{I}{X} \times 100[/tex]Here, in the question, it is given that,
The original amount (X) or the fuel bill in 2021 is £76.
The new amount (Y) or the fuel bill in 2022 is £89.
So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,
[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]
Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,
[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]
Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.
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(PLEASE OPEN) Need help with triangle proofs.
The missing terms in the two column proof are;
Reason 1; Perpendicular bisector
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Reason 4; Reflexive Property of Congruence
Reason 5; Definition of Isosceles Triangle
Reason 6; AAS Congruency Postulate
How to carry out two column proof of triangles?From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC
Now, we have the two column proof as follows;
Statement 1; AO ⊥ BC
Reason 1; Perpendicular bisector
Statement 2; ∠AOB and ∠AOC are right angles
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Statement 4; AO ≅ AO
Reason 4; Reflexive Property of Congruence
Statement 5; AB ≅ AC
Reason 5; Definition of Isosceles Triangle
Statement 6; ΔAOB ≅ ΔAOC
Reason 6; AAS Congruency Postulate
The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.
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Only 9 people can be in a roller coaster cart. How many people can fit in nine train carts
Answer:
81 people
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Find(f-g)(x)if f(x)=/4x and g(x)=/16x
The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x
How to evaluate the composite function?The definitions of the functions are given as
f(x) = √4x and g(x) = √16x
Evaluate the square roots in the above equations
This gives
f(x) = 2√x and g(x) = 4√x
To find the composition (f - g)(x), we make use of
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation So, we have the following equation
(f - g)(x) = 2√x - 4√x
Evaluate the like terms
This gives
(f - g)(x) = -2√x
Hence, the value of the composition is (c) (f - g)(x) = -2√x
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18. How does the
product change when one of the factors in
a multiplication problem is doubled? Give
two examples to support your conclusion.
The product doubles when one of the factors in a multiplication problem is doubled
What is a product?A product in mathematics is the result of multiplication, or an expression that identifies the objects to be multiplied, known as factors. For instance, 30 is the sum of 6 and 5.
In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product.
For example, 2 × 3 = 6. When 2 is doubled, it becomes 4 and the product will be:
= 4 × 3 = 12
Therefore, the product doubles too.
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A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1487 and the standard deviation was 314. The test scores of four students selected at randon
1870, 1250, 2170, and 1390. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
If a standardized exam's scores are normally distributed. The z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.
How to find the z-score?mu = population mean = 1487
sigma = population standard deviation = 314
x =1870
z = (x - mu)/σ
z = (1870-1487)/314
z = 1.22 (approximately)
x =1250
z = (x - mu)/σ
z = (1250-1487)/314
z = -0.75
x =2170
z = (x - mu)/σ
z = (2170-1487)/314
z = 2.18 (approximately)
x =1390
z = (x - mu)/σ
z = (1390-1487)/314
z = -0.31 (approximately)
Therefore the z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.
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What does “more than” mean in math?
Means if a number is bigger than other number.
Simplify the experession
6²-3³)÷7
Answer:
9/7 or 1.285714
Step-by-step explanation:
Answer:9/7
Step-by-step explanation:
Differentiate the function with respect to x.
When we differentiate the given function with respect to x we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
what is Differentiation?
Differentiate is used for calculating rates of change.
How to Differentiate function?
Some of the formulas are; Power Rule: (d/dx) (xn ) = nxn⁻¹. Derivative of a constant, a: (d/dx) (a) = 0.
Here, we have
y = 2x⁵ + 2x⁴ / 5x² -3
when we differentiate a given function with respect to x, we get
dy/dx = {(5x² -3)(10x⁴ + 8x³)} - {(2x⁵ + 2x⁴)(10x -3)}/(5x -3)²
dy/dx = (30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
Hence, after differentiating the given function with respect to x, we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
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Which graph represents the solution of -3m < 15?
Question 9 of 10
Solve (x-3)² = 5.
A. x=-3+√√5
B. x=3+√5
C. x = 8 and x = -2
OD. x=5± √√3
Answer:
B (x = 3 + √5)
Explanation:
x² + 9 = 5
Take square root of both sides
x + 3 = ± √5
Add 3 to both sides
x = 3 + √5 or x = 3 - √5
What is the range of f(x)=−3x−1?
Answer:
(−∞,1/3)∪(1/3,∞),{yly≠1/3}
Step-by-step explanation:
1. What is the missing number 56/7=?-5
Answer:
13
Step-by-step explanation:
56/7 = 8
13 - 5 = 8
15/7 = 13 - 5
The missing number in the expression is 13.
We have,
To find the missing number in the equation 56 / 7 =? - 5, solve for the unknown value.
Unknown value = x
Starting with the equation 56 / 7 = x - 5, simplify the left side:
56 / 7 = x - 5
8 = x - 5
x = 8 + 5
x = 13
Thus,
The missing number in the expression is 13.
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what is the inequality of the length of a rectangle is 1 unit more than its width.the width of the rectangle is 2 units and the length of the wire that is used to make this rectangle is a maximum of 57 units. what represent this situation using an inequality
Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives
Perimeter = 2(L + W) ≤ 57 units How to determine the inequality that shows the length and width of a rectangleThe perimeter of a rectangle, P is given by the formula
P = 2(L + W) ≤ 57 units of wire
width, W = 2 units
length, L = 1 + W
= 1 + 2
= 3
The perimeter of the rectangle is given by
P = 2(L + W)
plugging the values of L and W
P = 2 (3 + 1)
P = 2 (4 )
P = 8 units
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Write each number as a product using gcf as a factor sipping distributive property the numbers are 28 49 77 and 3 gcf
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
Define GCF.The biggest number that both numbers can be divided by to get the two numbers' largest common factor. The smallest number that is a multiple of both numbers is the least common multiple of the two numbers. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF). This is also sometimes referred to as the highest common factor (HCF) or the greatest common divisor (GCD).
Given,
Factor sipping distributive property,
For the numbers 28 and 49
GCF:
28 + 49
7(4) + 7(7)
7(4+7)
7(11)
77
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
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estimate each sum or difference.
74/10+42/5
The sum of the fraction 74/10 + 42/5 is 15 4/5.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the fraction will be illustrated as:
= 74/10 + 42/5
Change to mixed numbers
= 7 4/10 + 8 2/5
= 7 4/10 + 8 4/10
= 15 8/10
= 15 4/5
The value is 15 4/5.
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6x-5=6x-5 pls help fast
Answer:
0=0
Step-by-step explanation:
Answer: Infinite Solutions
Step-by-step explanation:
Hello! Let's solve this equation.
[tex]\textbf{First, add 5 to both sides.}[/tex][tex]\sf{6x-5=6x-5}[/tex]
↓
[tex]\sf{6x=6x-5+5}[/tex]
↓
[tex]\sf{6x=6x}[/tex]
[tex]\textbf{Next, subtract 6x from both sides.}[/tex][tex]\sf{6x-6x}[/tex]
↓
[tex]\sf{0}[/tex]
[tex]\textbf{So as you see, all the terms \textit{cancel out.}}\\\textbf{The \textsf{given equation} has \textit{\underline{infinite solutions.}}}\\\textbf{The equation is true for any x-value.}[/tex]
[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]
Use the compound interest formula to compute the total amount accumulated and the interest earned.
$3000 for 3 years at %4 compounded semiannually.
The amount in the account is ____.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The amount in the account is $3499. 2
How to determine the compound interestThe formula for determining compound interest is given as;
A = P ( 1 + r/ n) ^nt
Given that;
A is the final amountP is the principal amountr is the ratet is the time taken n is the number of times interest applied per periodSubstitute the values into the formula, we have;
A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)
Find the exponential value
A = $3000 ( 1 + 0. 04 / 0. 5) ^2
A = $3000( 1+ 0. 08)^2
Expand the bracket, we get;
A = $3000 (1. 08)^2
A = $3000(1. 17)
multiply through
A = $3499. 2
Hence, the value is $3499. 2
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