A relationship between two definitions can be seen through the idea of magnitude or distance.
How do these two definitions connect?Finding an absolute value of a number requires us to inspect the difference between that figure and zero on a number line; this amount is always positive regardless of whether the initial number was negative or positive. To illustrate, the absolute value of -5 is 5 since there is only five units separating it from zero.
The absolute value primarily entails a totality- recognizing the entirety of someone's peculiarity independent of their direction. It serves as a method of measuring the scope or size of a number without any external parameters or assessment.
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[4x2+(5+1)] devide 2 =
Answer:
7
Step-by-step explanation:
[4x2+(5+1)] ÷ 2
[8+(6)] ÷ 2
14 ÷ 2
7
Please Help Quickly ASAP Hurry Geometry
Questions in the picture
The area of the figure, given the vertices on the coordinate plane, is 14 square units.
How to find the area ?The shoelace formula can be used to find the area. First, find the sum of the products :
= ( - 1 × 2 ) + ( -2 × - 3 ) + ( 4 × 2 ) + ( 4 × 4 ) + (1 × -2)
= 2 + 6 + 8 + 16 - 2
= 26
Then the products of the y coordinate and the x coordinates :
= ( -2 × - 2 ) + (2 × 4 ) + ( - 3 × 4 ) + ( 2 × 1) + ( 4 × -1 )
= - 2
We can then find the absolute value to be:
= | Sum 1 - Sum 2 | = | 26 - (- 2 ) | = | 26 + 2 | = 28
The area is then:
= 28 / 2
= 14 square units
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How many gallons of a 80% alcohol solution and a 20% alcohol solution must be mixed to get 9 gallons of 60% alcohol solution?
In linear equation, x = 6 gallons (of 80% alcohol)
y = 3 gallons (of 20% alcohol)
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Let
x = liters of 80% alcohol
y = liters of 20% alcohol
There are two unknowns, we need two equations
x + y = 9. (1)
0.80x + 0.20y = 0.60(x+y) (2)
From (1)
x + y = 9
y = 9-x
Substitute the value of y into (2) and solve for x:
0.80x + 0.20y = 0.60(x+y)
0.80x + 0.20(9-x) = 0.60(x+9-x)
0.80x + 1.8 - 0.20x = 0.60(9)
0.80x + 1.8 - 0.20x = 5.4
0.6x = 3.6
x = 6 gallons (of 30% alcohol)
Substitute x=6 into (1) and solve for y:
x + y = 9
6 + y = 9
y = 3 gallons (of 60% alcohol)
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Physicians at a clinic gave what they thought were drugs to 820
patients. Although the doctors later learned that the drugs were really placebos,
52% of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patient's condition improving is .48
Test the hypotheses that the proportion of patients improving is >
.48
We reject the null hypothesis since the p-value is less than the significance level of 0.05.
what is null hypothesis ?The null hypothesis in statistics is a claim that presupposes there is no statistically significant distinction among the two or even more variables be compared. The antithesis of the alternative hypothesis, it is frequently denoted as H0 (Ha). While conducting statistical studies, the null is often evaluated to see if there is sufficient proof against it or not. The default assumption is typically the null hypothesis, and it serves as a benchmark for comparison of the statistical analysis's findings. A statistically significant distinction between the variables under comparison is said to exist if the statistical analysis yields sufficient data to refute a null hypothesis.
given
To test the hypothesis, we can utilise a z-test. This is the test statistic:
[tex]z = (x - E) / σ[/tex]
where x is the observed percentage of patients whose conditions are getting better. x = 820 * 0.52 = 426.4 is the result. Therefore:
z = (426.4 - 393.6) / 0.026 = 1245.98
P(Z > z) = 1 - P(Z z) is the p-value for this one-tailed test, where Z is a normal standard variable. By using a typical table or calculator, we discover:
P(Z > 1245.98) < 0.0001
We reject the null hypothesis since the p-value is less than the significance level of 0.05.
We have enough data to draw the conclusion that the percentage of patients whose conditions are improving is more than 0.48.
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(x- 4 8/11) + 1 9/11 = 7 3/11 what is x?
Thus, the value of x for the given expression containing the mixed fractions is found as: x = 8/11.
Explain about the mixed fractions:A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls in between two whole numbers.
Multiply the whole integer by the denominator, then add the numerator to create an incorrect fraction out of a mixed number. The response here becomes the new numerator, while the denominator stays the same.
Given expression:
(x- 4 8/11) + 1 9/11 = 7 3/11
Solving all the mixed fractions in proper fractions:
4 8/11 = (4*11 + 8) / 11 = (44 + 8) /11 = 52/11
1 9/11 = (1*11 + 9) /11 = (11 + 9)/ 11 = 20/11
7 3/11 = (7*11 + 3) /11 = (77 + 3)/11 = 80/ 11
Put the obtained results in expression:
(x- 52/11) + 20/11 = 80/11
x - 52/11 = 80/11 - 20/11
x - 52/11 = (80 - 20)/11
x - 52/11 = 60/11
x = 60/11 - 52/11
x = (60 - 52) / 11
x = 8/ 11
Thus, the value of x for the given expression containing the mixed fractions is found as: x = 8/11.
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The number of customers, y, queueing at the payment counter at a given time t, is given by equation:
y=t^3-14t^2+50t,where 0≤t≤8.5,
t is the number of hours after the shop opens at 9 am
Required:
1. Advise the management of the shop as to when they can deploy more cashiers and the number of customers queueing at that time. (6 Marks)
2. Determine the number of man-hours spent per day by shoppers queueing
Answer: 1. To find the time when the management should deploy more cashiers, we need to find the time when the number of customers queueing is the highest. We can find the maximum value of y by taking the derivative of the equation and setting it equal to zero:
dy/dt = 3t^2 - 28t + 50 = 0
Solving for t, we get:
t = (28 ± sqrt(28^2 - 4350)) / (2*3) = 4.67 or 9.33
Since the time has to be between 0 and 8.5 hours, the maximum occurs at t = 4.67 hours. Therefore, the management should deploy more cashiers around 1:40 pm (9:00 am + 4.67 hours). At this time, the number of customers queueing is:
y = 4.67^3 - 14(4.67)^2 + 50(4.67) = 51.64
So, there will be approximately 52 customers queueing at that time.
2. To find the number of man-hours spent per day by shoppers queueing, we need to integrate the equation for y over the range 0 ≤ t ≤ 8.5:
∫(0 to 8.5) y dt = ∫(0 to 8.5) (t^3 - 14t^2 + 50t) dt
Evaluating the integral, we get:
= [(1/4)t^4 - (14/3)t^3 + 25t^2] from 0 to 8.5
= (1/4)(8.5)^4 - (14/3)(8.5)^3 + 25(8.5)^2
= 1907.81
Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 1908.
Step-by-step explanation:
To determine when the shop should deploy more cashiers, we need to find the maximum point of the function y(t), which corresponds to the peak of the queue. The maximum point of a cubic function is found at its turning point, which is where its derivative equals zero. Therefore, we can find the turning point by taking the derivative of y(t) and setting it equal to zero:
y'(t) = 3t^2 - 28t + 50
0 = 3t^2 - 28t + 50
Using the quadratic formula, we get t = 4.47 or t = 3.19.
However, we need to make sure that the maximum point lies within the given range of 0 ≤ t ≤ 8.5. Since 3.19 is within this range and 4.47 is not, the maximum point occurs at t = 3.19 hours after the shop opens.
What is the number of man-hours spent per day by shoppers queueing?To find the number of customers queueing at that time, we simply plug in t = 3.19 into the original equation:
y(3.19) = (3.19)^3 - 14(3.19)^2 + 50(3.19) ≈ 30.8
Therefore, the management of the shop should deploy more cashiers at 12:11 pm (9 am + 3.19 hours) when there are approximately 30.8 customers queueing.
To determine the number of man-hours spent per day by shoppers queueing, we need to find the total area under the curve of y(t) from t = 0 to t = 8.5. This area represents the total number of customers queueing during the day.
Using integration, we get:
∫(t^3 - 14t^2 + 50t)dt = (t^4/4) - (14t^3/3) + (25t^2) + C
where C is the constant of integration.
Evaluating this expression at t = 8.5 and t = 0, and subtracting the latter from the former, we get:
(8.5^4/4) - (14(8.5)^3/3) + (25(8.5)^2) - (0^4/4) + (14(0)^3/3) - (25(0)^2) ≈ 2233.1
Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 2233.1. Note that this assumes that each customer spends exactly one hour in the queue, which may not be realistic, but provides a rough estimate of the total time spent.
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You want to place stone pavers around the edges of your concrete patio. The patio is 12ft wide by 14ft long and each stone paver is 14 inches long. How many stone pavers will you need to go around the patio ( not counting the side against the house which is 14ft long)? Round to the nearest whole number
You will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.
Explain whole numbers
Whole numbers are a set of numbers that includes all natural numbers (positive integers) and zero. They are represented by the symbol "W" and do not include any fractions or decimals. Whole numbers are used in counting, measuring, and representing quantities of discrete objects or entities, and are a fundamental concept in mathematics.
According to the given information
First, let’s convert the length of the stone paver from inches to feet: 14 inches = 14/12 feet = 1.17 feet.
The perimeter of the patio is (12 + 14 + 12) feet = 38 feet. Since each stone paver is 1.17 feet long, you will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.
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You are trying to determine if a router you’re thinking of purchasing will give off a strong enough wifi signal to cover the area in your house. The router you have selected will cover an area of 850 ft^2.
The wi-fi router shall not be strong enough to cover the area of the house.
How to determine whether a wi-fi router can cover a given area
According to the statement, we must determine if a wi-fi router can cover all the area of a house, described by a rectangle. The area formula of rectangle is introduced below:
A = b · h
Where:
A - Area, in square feet.b - Base, in feet.h - Height, in feet.Now we proceed to determine the area of the house:
A = (50 ft) · (50 ft)
A = 2500 ft²
The wi-fi router shall not cover the entire area of the house.
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suppose that a and b are positive for which log9(a) = log15(b) = log25(a + 2b). What is the value of b over a
Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.
Explain about the logarithmic function:The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent with which b must be raised in order to obtain a number x is the logarithm of x to the base b.
A base must still be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bˣ = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.
Given that:
log9(a) = log15(b) = log25(a + 2b)
Let , log9(a) = log15(b) = log25(a + 2b) = x
Then,
log9(a) = x (taking antilog)
log3²(a) = x
a = 3²ˣ
log15(b) = x (taking antilog)
log(3*5)(b) = x
b = 3ˣ.5ˣ
log25(a + 2b) = x (taking antilog)
log5²(a + 2b) = x
a + 2b = 5²ˣ
Now,
b²/a = a + 2b
(b/a)² = 1 + 2*(b/a)
If t = b/a, then t² - 2t -1 = 0
On factorization:
t = 1 ± √2 ( a and b are positive integer)
b/a = 1 + √2
Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.
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Which of the following equations will produce the graph shown below? A. x²/20 + y²/20 = 1 B. 20x² - 20y² = 400 C. 6x² + 6y² = 144 D. 5x² + 5y² = 80
An equation that will produce the graph shown above include the following: D. 5x² + 5y² = 80.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Based on the information provided above, we have the following parameters:
Radius, r = √16 = √80/5
Center, (h, k) = (0, 0).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 0)² = (√80/5)²
5x² + 5y² = 80.
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please answer and explain how to get it.
The value of x is given as follows:
x = 21 cm.
How to obtain the value of x?The value of x is obtained applying the proportions in the context of the problem.
The ratio between the volumes is given as follows:
2430/90 = 27.
The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:
x/7 = cubic root of 27
x/7 = 3
x = 21.
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the area of a circle is 144m2 What is the diameter of the circle
Step-by-step explanation:
AREA = pi r^2
144 = pi r^2 shows r = 6.77 m ( or sqrt ( 144/pi) )
then diameter = 2 * r = 13.54 m (or 2 sqrt (144/pi) )
Answer:
7.64
Step-by-step explanation
This is what I did so I take the root of 144 = 12 and 12/3.14 = roughly 3.82 thats the radius and that times 2 = 7.64 have a great day success to homework yay! Have a great day!!! :D
You paid $6.99 for a shirt that was 70% off; what was the original price of the shirt?
Answer:
$23.30
Step-by-step explanation:
We Know
You paid $6.99
The shirt was 70% off
$6.99 = 30%
What was the original price of the shirt?
We Take
(6.99 ÷ 30) x 100 = $23.30
So, the original price is $23.30
How many total mangement are there in the organization if 40 have a technical degree and 100 have a non technical degree
The total number of employees in the organization will be 140.
Given that:
There are 40 employees who have a technical degree
There are 100 employees who have a non-technical degree
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The total number of employees are calculated as,
Total = Employees who have a technical and non-technical degree
Total = 40 + 100
Total = 140
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Pattern A starts at 1 and uses the rule add 5." Pattern B starts at 28 and uses the rule "subtract 4."
What are the next four terms in each pattern?
Enter your answers in the boxes.
For the pattern A, the terms are 6, 11, 16 and 21
For the pattern B, the terms are 24, 20, 16, 12
How to determine the termsTo determine the consecutive terms of the sequence, we need to take note of the rule of each.
From the information given, we have that;
For the Pattern A
Each term is the previous term plus 5
This is represented as;
Pattern A = a + 5,
The first term = 1
Second term = 1 + 5 = 6
Third term = 6 + 5 = 11
Fourth term = 11 + 5 = 16
Fifth term = 16 + 5 = 21
For Pattern B = a - 4
Second term = 28 - 4 = 24
Third term = 24 - 4 = 20
Fourth term = 20 -4 = 16
Fifth term = 16 - 4 = 12
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Select all the correct answers. If the measure of angle is , which statements are true? The measure of the reference angle is . The measure of the reference angle is . The measure of the reference angle is . 0 =9/2
The statement cos(theta) = √3/2 is correct.
Which statement is correct?Angles are the angles formed by 2 bisecting lines or surfaces at or near their intersection.
The following information has been provided:
The angle (theta) = [tex]\frac{2\pi }{3}[/tex] measurement has been given to us.
We must determine which propositions are true by determining the measure of angle (theta) = [tex]\frac{2\pi }{3}[/tex]
cos(theta) = [tex]\frac{\sqrt{3} }{2}[/tex]
= cos30
theta = 30
tan(theta)= [tex]-\sqrt{3} = tan(90 + 30)[/tex]
tan(theta) = tan120
theta = 120
sin(theta) = [tex]-\frac{1}{2}[/tex] = [tex]cos(90 + 30)[/tex]
sin(theta) = sin120
theta = 120
Therefore the correct statement is cos(theta) = √3/2
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Complete question:
The measure of angle(theta) Is 2pi/3, which statements are true?
cos(theta) = √3/2
The measure of the reference angle is 30°.
The measure of the reference angle is 45°.
The measure of the reference angle is 60°.
tan(theta) = -√3
sin(theta)=-1/2
Who knows how to do thisssssss
I Got U Bro! Answer:(x+5)2+(y+3)2=16
:D
A mirror is placed 45 feet from the base of a waterfall by a hiker. The hiker walks backwards until they are 7.5 feet from the mirror. Determine how tall the waterfall is if the hiker is 6 feet tall.
36 ft
39.5 ft
56.25 ft
72 ft
If the hiker is 6 feet tall, then the height of the waterfall will be: 32.57 feet.
How to determine the height of the waterfallWe can solve this problem using similar triangles. Let us call the height of the waterfall "h". Then, the distance from the base of the waterfall to the mirror is also "h" (since the mirror reflects the top of the waterfall down to the hiker's eye).
Using similar triangles, we can set up the following proportion:
(h + 6 feet) / 45 feet = 6 feet / 7.5 feet
Cross-multiplying and simplifying, we get:
h + 6 feet = 270 feet / 7
h + 6 feet = 38.57 feet
h = 32.57 feet
So, the correct height given the variables is 32.57 feet.
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Answer:
36 ft
Step-by-step explanation:
We can use the concept of similar triangles to solve this problem. The ratio of the heights of the hiker and the waterfall is the same as the ratio of their distances to the mirror.
Given:
Distance from mirror to waterfall = 45 feet
Distance from mirror to hiker = 7.5 feet
Hiker's height = 6 feet
Let's set up a proportion:
(Hiker's height) / (Hiker's distance to mirror) = (Waterfall's height) / (Waterfall's distance to mirror)
Substitute the given values:
6 / 7.5 = (Waterfall's height) / 45
Now solve for the height of the waterfall:
Cross-multiply:
6 * 45 = 7.5 * (Waterfall's height)
270 = 7.5 * (Waterfall's height)
Divide by 7.5:
Waterfall's height = 270 / 7.5
Waterfall's height = 36 feet
So, the height of the waterfall is 36 feet.
Among the provided options, the correct answer is:
a) 36 ft
A basketball with a 12 cm radius is placed into a 24 cm x 24 cm x 24 cm box. The
amount of space inside the box but outside the basketball is
cm³
(Use 3.14 for 7).
The amount of space or volume inside the box but outside the basketball is 6589.44 cm³.
We have to find the volume of the box and volume of the basketball to determine the space outside it.
Box is in rectangular shape.
Volume of the box = 24 × 24 × 24
= 13824 cm³
Basketball is spherical in shape.
Volume of the sphere = 4/3 π r³
= 4/3 π (12)³
= 2304π
= 7234.56 cm³
Amount of space inside the box but outside the basketball is,
13824 cm³ - 7234.56 cm³ = 6589.44 cm³
Hence the required space is 6589.44 cm³.
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Use the following scenario. Five surf shops sell the same pair of flip-flops for the following set of prices: {$17.00, $15.50, $15.00, $18.00, $15.00}.
Select all the correct measures of center and variation for the data set.
a. Range = 4
b. IQR = 2.50
c. Median = 15.50
d. Third quartile = 17.50
e. Mean = 15.80
Answer: b, c, d,
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A group of scientists is conducting an experiment on the effects of media on children. They randomly select 100 children and randomly assign each child to one of four treatment groups. Each treatment group has a specific amount of screen time during a one-week time frame. The first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. After the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. Which statements about this study are true?
1. This study uses blocking.
2. This study uses blinding.
3. This study uses a control group.
4. This study uses a repeated measures design.
5. This study uses random sampling.
This study uses blocking: True. The study randomly assigns each child to one of the four treatment groups, which helps to control for individual differences that could affect the results.
This study uses blinding: It is not mentioned in the scenario whether the study uses blinding or not in individual.
This study uses a control group: True. The first group, with no screen time, serves as the control group. By comparing the results of the other groups to the control group, the scientists can see the effects of different amounts of screen time.
This study uses a repeated measures design: True. Each subject experiences each of the four treatments, so the study design is repeated measures.
This study uses random sampling: True. The study randomly selects group of 100 children for the experiment.
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i-Ready
Classify and Compare Quadrilaterals-Instruction - Level C
How are these rectangles alike? Choose true or false for each statement.
Both have 4 sides.
Both have 4 right angles.
Both have all sides the same
length.
True False
O
O O
X
According to Classification of Quadrilaterals,
i. Both rectangles have 4 sides - True
ii. Both rectangles have 4 right angle - True
iii. Both rectangles have all sides the same length - False
The classification of Quadrilaterals
Quadrilaterals are a type of geometric shape that have four sides. There are different types of quadrilaterals, and they can be classified based on the characteristics of their sides and angles. The main classifications of quadrilaterals are:
Trapezoid or Trapezium: a quadrilateral with only one pair of parallel sides.
Kite: a quadrilateral whose two adjacent pairs of sides are of equal length.
Parallelogram: a quadrilateral with opposite sides that are parallel to each other.
Rhombus: a quadrilateral with all sides equal in length.
Rectangle: a quadrilateral with opposite sides that are parallel and all four angles are right angles (90 degrees).
Square: a quadrilateral with all sides equal in length and all four angles are right angles (90 degrees).
These are the main classifications of quadrilaterals, and each type has its own specific properties and characteristics that distinguish it from the others.
According to the given information:
i. Both have 4 sides - True
A rectangle has four sides because it is defined as a quadrilateral with two pairs of parallel sides and four right angles. This means that opposite sides of a rectangle are parallel to each other and have the same length, while adjacent sides are perpendicular to each other and form right angles.
So, by definition, a rectangle must have four sides in order to meet these criteria and be classified as a rectangle.
ii. Both have 4 right angle - True
In a rectangle, by definition, opposite sides are parallel to each other and adjacent sides are perpendicular to each other. This means that each of the four corners of a rectangle must form a right angle, where two sides meet at a 90-degree angle.
iii. Both have all sides the same length - False
Not all rectangles have all sides the same length. While a square is a type of rectangle where all sides are equal, rectangles can have different lengths for their adjacent sides.
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eading Tools
Two students began a proof of the law of sines.
C
A
Student I
sin(A)=
Sin(B) =
bsin(A) =h
asin(B) = h
bsin(A)= asin(B)
sin(A)=sin(B)
b
Student 2
sin(A)=
sin(B) ==
asin(A) = h
bsin(B) = h
B
asin(A)=bsin(B)
sin(A)=sin(B)
a
Which student correctly started the proof, and what should that student do next to complete the proof?
Answer: no answer
Step-by-step explanation:
Casey is going to deposit $500 in an account that earns 6% interest for 10 years. How much more interest will
he earn if the account earns an accual compound interest rather than annual simple interest?
The interest he earns in 10 years = $395.42.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.
Here the Principal P = $500
Rate of interest= 6% = 6/100 = 0.06
Number of years t= 10 years.
Now using compound interest formula then,
=> Amount = [tex]P(1+r)^t[/tex]
=> Amount = 500[tex](1+0.06)^{10[/tex] = [tex]500\times1.06^{10[/tex]
=> Amount = $895.42.
Now interest = $895.42 - $500 = $395.42
Hence the interest he earns in 10 years = $395.42.
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The group thought there was enough food for all 5 group members to complete the trip, with each person getting the required 5600 calories per day. However, they discover that they are missing 28,000 calories. Using the map, create a plan for the rest of the trip that includes taking as many group members as possible to the South Pole, while sending the rest of the group members directly back to base camp. Remember that each person must have 5,600 calories of food per day until he or she gets back to base camp.
Be sure to explain how you came up with your plan. Include all work necessary to support your answer.
Please answer as soon as possible due in an hour. Thank you.
The word problem shows that we only have enough food for 5 days, which means we need to make some tough decisions about who gets to continue to the South Pole and who needs to turn back.
How to calculate the valueThe plan for the rest of the trip involves splitting the group into two parts: 3 members continuing to the South Pole with 2.5 days of food, and 2 members returning to base camp with 2.5 days of food.
28,000 calories / 5,600 calories per day = 5 days of food
So we only have enough food for 5 days, which means we need to make some tough decisions about who gets to continue to the South Pole and who needs to turn back.
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Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
(b) How much does Jack receive the following Christmas?
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
a) Jill receives £45
b) Jack receives £20 the following Christmas
c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.
Explain the term years
Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.
According to the given information
(a) Let's first find the total ratio of their ages:
1 + 3 = 4
So Jack's share will be:
1/4 x £60 = £15
And Jill's share will be:
3/4 x £60 = £45
Therefore, Jill receives £45.
(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:
2/6 x £60 = £20
So Jack receives £20.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:
1/4 x £60 = £25
Multiplying both sides by 4/60, we get:
x = 5/4
So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.
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The rectangular coordinates of a point are (17,0). Find the polar coordinates.
The polar coordinates of the point (17,0) are (r,θ) = (17,0). This means that the point is located on the positive x-axis, at a distance of 17 units from the origin.
To find the polar coordinates of a point given in rectangular coordinates, we need to use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point.
In this case, the point is (17,0), so x = 17 and y = 0. Using the formulas above, we get:
r = √(17² + 0²) = 17θ = tan⁻¹(0/17) = 0
In polar coordinates, a point is represented by an ordered pair (r,θ), where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point, measured in radians.
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7. Which statement is NOT part of a debt-reduction plan? a. Lower debts with the highest interest rates. b. Slow or eliminate credit card spending c. Only pay the minimum amount when possible. d. Use an online debt management calculator.
need help on this question from edmentum
The correct location of each of the expressions obtained the properties of exponents are;
2; (3²·4³·2⁻¹)/(3·4)², ((3·2)⁴·3⁻³)/(2³·3)
1; (3⁻³·2⁻³·6³)/((4⁰)²)
1/2; (2⁴·3⁵/(2·3)⁵)
What are exponential operations?Exponential operations are operations involving two numbers, which includes the base number and the exponent.
The exponential expressions can be simplified using laws of indices or the properties of exponents as follows;
(2⁴·3⁵)/((2·3)⁵) = (2⁴·3⁵)/(2⁵·3⁵) = (2⁴/2⁵) × (3⁵/3⁵)
(2⁴/2⁵) × (3⁵/3⁵) = (2⁴/2⁵) × 1 = 1/2
Therefore; (2⁴·3⁵)/((2·3)⁵) = 1/2
(3²·4³·2⁻¹)/((3·4)²) = (3²/3²)·(4³/4²)·(2⁻¹)
(3²/3²)·(4³/4²)·(2⁻¹) = 1 × 4 × (1/2) = 2
Therefore; (3²·4³·2⁻¹)/((3·4)²) = 2
((3·2)⁴·3⁻³)/(2³·3) = ((3⁴·2⁴)·3⁻³)/(2³·3)
((3⁴·2⁴)·3⁻³)/(2³·3) = (3⁴/3)·(2⁴/2³)·3⁻³ = (3³·3⁻³)·2 = 2
Therefore; ((3·2)⁴·3⁻³)/(2³·3) = 2
(3⁻³·2⁻³·6³)/((4⁰)²) = (3⁻³·2⁻³·6³)/1
(3⁻³·2⁻³·6³)/1 = (6³/3³)/2³
6³/3³ = 2³
Therefore; (6³/3³)/2³ = 2³/2³ = 1
(3⁻³·2⁻³·6³)/((4⁰)²) = 1
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32 is what percent of 50?
Answer:
To find the percentage, you need to divide the first number by the second number and then multiply by 100. In this case:
32 ÷ 50 = 0.64
Multiplying by 100 gives:
0.64 × 100 = 64
Therefore, 32 is 64% of 50.
Step-by-step explanation:
Answer:
64%
Step-by-step explanation:
32/50 x 2 (you need to make it over 100)
= 64/100
= 64%