There would be $2203.50 in Stony's account by September 2020 using simple interest formula.
As the bank charges an annual 8% simple interest, we may apply the following formula:
Simple interest is calculated as follows: Principle is the initial investment, Rate is the annual interest rate, and Time is the duration in years.
Here, the principal (P) is $1575, the interest rate (r) is 8%, and the time (t) is 5 since we need to know how much money Stony will have in his account by September 2020, which is five years from now.
We may calculate Stony's interest earnings over a five-year period using the simple interest formula:
Interest is calculated as follows: $1575 x 0.08 x 5 = $628.50
Stony's account will therefore have the following balance by September 2020: Total Amount = Principal + Interest = $1575 + $628.50 = $2203.50
Therefore by September 2020, Stony would have $2203.50 in his account.
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Devon wants to plant 84 tomato plants in his garden.
He wants to put 7 plants in each row. How many rows
will he need?
Given: AM = MC, BN = NC Prove: ΔABC ~ ΔMNC.
The prove to show that ΔABC is similar to ΔMNC is explained below.
How to prove that two triangles are similar?Similar triangles are triangles that have the same shape but are not necessarily the same size. More precisely, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
Considering the given diagram, we can say:
AM = MC (Given)
BN = NC (Given)
BC = BN + NC (addition property of a line segment)
AC = AM + MC (addition property of a line segment)
NC/ BC = MC/ AC = constant
∠ACB = ∠MCN (Reflexive property)
Thus, ΔABC ~ ΔMNC (Side-Angle-Side theorem)
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17. Write an equation of a circle that has
no x-intercepts, no y-intercepts, and a
radius of 5. Draw a sketch of your circle on
the grid provided.
Answer:
(x - 5)^2 + (y - 5)^2 = 25
Step-by-step explanation:
If a circle has no x-intercepts and no y-intercepts, it means that the circle does not intersect either the x-axis or the y-axis. In other words, the center of the circle must lie at some point (h, k) where h and k are not equal to zero.
The general equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Since we know that the circle has a radius of 5, we can substitute r = 5 into the equation:
(x - h)^2 + (y - k)^2 = 25
Now, we need to find values for h and k such that the circle has no x-intercepts and no y-intercepts. Since the x-intercepts occur when y = 0 and the y-intercepts occur when x = 0, we need to make sure that neither of these values satisfies the equation.
Let's first consider the x-intercepts. We want to make sure that the circle does not intersect the x-axis, which means that the y-coordinate of the center must be equal to the radius. In other words, k = 5. Now, the equation becomes:
(x - h)^2 + (y - 5)^2 = 25
Next, we need to make sure that the circle does not intersect the y-axis, which means that the x-coordinate of the center must be equal to the radius. In other words, h = 5. Now, the equation becomes:
(x - 5)^2 + (y - 5)^2 = 25
Therefore, the equation of the circle that has no x-intercepts, no y-intercepts, and a radius of 5 is:
(x - 5)^2 + (y - 5)^2 = 25
What is the area of this trapezoid?
Enter your answer in the box.
Answer:
80
Step-by-step explanation:
HELP ME ASAP I NEED A NUMERICAL ANSWER
Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.
bran muffins 25
blueberry muffins 12
poppy seed muffins 3
chocolate chip muffins 10
Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins?
After answering the given query, we can state that Therefore, we can function anticipate that 8 to 16 of the upcoming pastries will be bran muffins.
what is function?Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.
We must determine the percentage of muffins that were bran muffins in the prior sales in order to determine how many of the subsequent 16 muffins sold would be bran muffins.
In the prior auction, the following amount of muffins were sold in total:
25 + 12 + 3 + 10 = 50
The percentage of muffins that were wheat muffins is as follows:
25/50 = 0.5
This indicates that wheat muffins accounted for 50% of all sales.
This ratio can be used to make a forecast about how many bran muffins will be sold over the course of the following 16 muffins. Therefore, we anticipate that roughly 50% of the subsequent 16 batches of muffins sold will be wheat muffins:
0.5 x 16 = 8
Therefore, we can anticipate that 8 to 16 of the upcoming pastries will be bran muffins.
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Find each angle measure to the nearest degree.
Answer:
5) A = 70°
6) X = 55°
7) Y = 8°
8) A = 51°
Step-by-step explanation:
There really no way to explain. All you ahve to do is inverse function to solve for the angle. Use a calculator.
5) sin(A) = 0.9397
[tex]A=sin^-1(0.9397)\\\\A=69.701...\\\\A = 70\\[/tex]
6) cos(X) = 0.5763
[tex]X=cos^-1(0.5763)\\\\X=54.998...\\\\X=55\\[/tex]
7) tan(Y) = 0.1405
[tex]Y=tan^-1(0.1405)\\\\Y=7.997...\\\\Y = 8\\[/tex]
8) sin(A) = 0.7771
[tex]A=sin^-1(0.7771)\\\\A=50.995...\\\\A = 51\\[/tex]
6.5 practice the measure of the exterior of a triangle is equal to the sum of the remote interior angles?
Answer:
Step-by-step explanation:
Yes, that is correct. The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles. In other words, if you extend one side of a triangle to form an exterior angle, then the measure of that exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to the exterior angle. This property is known as the Exterior Angle Theorem.
Mathematically, we can express this as:
Exterior angle = Sum of remote interior angles
Or, in symbols:
∠ABC = ∠A + ∠C
where ∠ABC is the exterior angle formed by extending side BC of triangle ABC, and ∠A and ∠C are the two remote interior angles.
Here are two more examples that illustrate the Exterior Angle Theorem:
Example 1:
Consider a triangle ABC with angles A, B, and C as shown below. If we extend side AC to form an exterior angle, then we can label the exterior angle as ∠DCE. The remote interior angles are ∠B and ∠A.
css
Copy code
C
/ \
/ \
/ \
/ \
/ \
/______\
A B
D
According to the Exterior Angle Theorem, we have:
∠DCE = ∠B + ∠A
Find the length of side � x in simplest radical form with a rational denominator. 30° 60° x 2
The length οf side x can be any value, as lοng as it is nοt 0.
We can use the trigοnοmetric ratiοs fοr 30°-60°-90° triangles tο sοlve fοr the value οf x.
In a 30°-60°-90° triangle, the sides are in the ratiο:
1 : √3 : 2
In this case, we have the side οppοsite the 60° angle (which is the lοnger leg) equal tο x√3 and the side οppοsite the 30° angle (which is the shοrter leg) equal tο x.
Sο we can set up the fοllοwing equatiοn:
x√3 = 2x sin 60°
Simplifying the right side:
sin 60° = √3/2
2x sin 60° = 2x(√3/2) = x√3
Substituting back intο the equatiοn:
x√3 = x√3
This is true fοr any value οf x, as lοng as x is nοt equal tο 0. Therefοre, the length οf side x can be any value, as lοng as it is nοt 0.
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The road is 7m wide. The Corner is in the shape of a quarter of a Cude the inside radius of the Corner is 70m. Ali Walks round the Corner on the inside, from A to B, Obi walks round the Corner On Obe Outside from C Go D. How much further does Obi walk than Ali? use the Value 22 for To- 7
Divide 240g in the ratio 5: 3: 4.method
To divide 240g in the ratio 5:3:4, we need to find out the total number of parts of the ratio:
5 + 3 + 4 = 12
Now, we can find the value of one part of the ratio by dividing the total quantity by the total number of parts:
240g ÷ 12 = 20g
So, one part of the ratio is equal to 20g.
To find the quantities of each part of the ratio, we multiply the value of one part by the respective ratio number:
5 parts x 20g = 100g (for the first part)
3 parts x 20g = 60g (for the second part)
4 parts x 20g = 80g (for the third part)
Therefore, the quantities of 240g divided in the ratio 5:3:4 are 100g, 60g, and 80g respectively.
The table below shows the grade and reading level for 5 students. Grade Reading Level Student 1 2 6 Student 2 6 14 Student 3 5 12 Student 4 4 10 Student 5 1 4 For grade, the mean is 3.6 and the standard deviation is 2.1. For reading level, the mean is 9.2 and the standard deviation is 4.1. Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices are rounded to the nearest hundredth. r equals fraction numerator 1 over denominator n minus 1 end fraction sum from blank to blank of open parentheses fraction numerator x minus x with bar on top over denominator s subscript x end fraction close parentheses open parentheses fraction numerator y minus y with bar on top over denominator s subscript y end fraction close parentheses
The cοrrelatiοn cοefficient οf data is 1.
What is cοrrelatiοn cοefficient?A statistical measure knοwn as cοrrelatiοn expresses hοw clοsely twο variables are related linearly (meaning they change tοgether at a cοnstant rate).
The cοnstant cοefficient (οr cοnstant term) is the cοefficient nοt attached tο variables in an expressiοn. Fοr example, the cοnstant cοefficients οf the expressiοns abοve are the number 3 and the parameter c, respectively.
The cοefficient attached tο the highest degree οf the variable in a pοlynοmial is referred tο as the leading cοefficient. Fοr example, in the expressiοns abοve, the leading cοefficients are 2 and a, respectively.
In excel, use fοllοwing cοmmand tο find r
=>cοrrel(select data οf grade, select data οf Reading level)
press enter
=> 1
i.e. 1.00
The required cοrrelatiοn cοefficient r is 1.00
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3x(x-3)=12 How do you solve this
Step-by-step explanation:
3x squared -9 = 12
3x squared = 12 + 9
3x squared = 21
am i doing the wrong maths?
is it find what 3x squared is or....
please helpppp asap thank you !!:)
[tex]f(-11) = 3(-11)^{2} - 5 = 3(11)^{2} - 5 = 3(121) - 5 = 363-5= \bf 358[/tex]
Answer:D
Step-by-step explanation:
if x==-11
then,
f(-11) means you should write -11 in every x you see.
[tex]f(-11)=3*(-11)^{2} -5=3*121-5=363-5=358[/tex]
NEED HELP ASSIGNMENT DUE IN AN HOUR WOULD BE MUCH APPRECIATED!
The suspension cable that supports a footbridge hangs in the shape of a parabola. The height h, in feet, of the cable above the bridge is given by the function
h(x) = 0.25x ^ 2 - 0.8x + 30, 0 < x < 3.2
where x is the distance in feet measured from the left tower toward the right tower. What is the minimum height of the cable above the bridge? (Round your answer to two decimal places.)
Step-by-step explanation:
The height of the cable above the bridge is given by the function:
h(x) = 0.25x^2 - 0.8x + 30
To find the minimum height of the cable above the bridge, we need to find the vertex of the parabola, which is the lowest point.
The x-coordinate of the vertex is given by:
x = -b / 2a
where a = 0.25 and b = -0.8. Substituting these values, we get:
x = -(-0.8) / 2(0.25) = 1.6
So the vertex is at x = 1.6.
To find the height of the cable at the vertex, we substitute x = 1.6 into the equation for h(x):
h(1.6) = 0.25(1.6)^2 - 0.8(1.6) + 30 = 29.48
Therefore, the minimum height of the cable above the bridge is approximately 29.48 feet (rounded to two decimal places).
work out the question
23 - 81 =
The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically
How to evaluate the expressionGiven the following expression
23 - √81
The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.
We know that the square root of 81 is 9, so we can simplify the expression to:
23 - √81 = 23 - 9
Evaluate the difference
23 - √81 = 14
Therefore, the value of the expression is 14.
In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.
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PLEASE ITS MY DCP While Amy and Sherry are talking, Amy discovers her earring fell off somewhere in the room. Amy goes 11 feet in one direction to look for it and Sherry goes 15 feet in a different direction. What are all the possible values, d, of the distance between Sherry and Amy? (Drawing is not to scale) Amy Starting point 11 15 Sherry A 4 < d < 26 B4 < d < 15 C11 < d < 15 D11 < d < 26
This means that option A, "4 < d < 26," is the correct answer.
The triangle inequality can be used to calculate various distances between Sherry and Amy. The lengths of any two sides of a triangle must add up to more than the length of the third side in order for the triangle inequality to hold.
If we assume that d is the separation between Amy and Sherry in this instance, we can then create a triangle with sides that are 11, 15, and d in length. The inequality of the triangle indicates that:
11 + 15 > d
or
d < 26
and
15 + d > 11
or
d > 4
So, d might have any of the following values:
4 < d < 26
This indicates that "4 d 26" in option A is the right response.
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Which of the loans should you try to pay off first?
A. a loan for $3,400 at 16%
B. a loan for $3,500 at 15%
C. a loan for $3,600 at 14%
D. a loan for $3,700 at 13%
A loan for $3,400 at 16% should be paid first as it has the highest interest rate.
What is loan?A loan is a financial agreement in which one party (the lender) agrees to give money, property, or other assets to another party (the borrower) in exchange for the promise of repayment with interest or other charges. Loans are typically used by individuals, businesses, or governments to finance specific projects, make purchases, or cover expenses.
Assuming that all other factors such as minimum payments and penalties are the same, the loan that you should try to pay off first is the one with the highest interest rate, as it will be accruing interest at a faster rate than the others.
Based on this reasoning, the loan that you should try to pay off first is option A, which has a higher interest rate of 16%.
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A) 3
B) 6
C) 9
D) 12
The value of x, considering the similar triangles, is given as follows:
B) 6.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Considering that the triangles for this problem are similar, the proportional relationship for the side lengths is given as follows:
9/3 = 12/4 = x/2.
Since the constant is of 3, the value of x is obtained with cross multiplication as follows:
x/2 = 3
x = 6.
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) Using matrix method solve the following simultaneous equations 1x + 4y = 9 2x – 3y = 7
Answer: To solve the system of equations using the matrix method, we first need to set up the corresponding coefficient matrix and augmented matrix:
Coefficient matrix:
[1 4]
[2 -3]
Augmented matrix:
[1 4 | 9]
[2 -3 | 7]
To solve the system using matrix method, we perform row operations on the augmented matrix to get it into row echelon form, and then back substitute to obtain the solutions.
Performing row operations:
Multiply the first row by 2 and subtract the result from the second row:
[1 4 | 9]
[0 -11| -11]
Divide the second row by -11:
[1 4 | 9]
[0 1 | 1]
Subtract 4 times the second row from the first row:
[1 0 | 5]
[0 1 | 1]
The row echelon form of the augmented matrix is:
[1 0 | 5]
[0 1 | 1]
Therefore, the solution is x = 5 and y = 1.
So the solution of the system of equations is x = 5 and y = 1.
Step-by-step explanation:
a teachers age is 6 years greater that 2 times a students age. a principles age is 10 years greater than 3 time times the students age. If x represents the students age in years, which expression represents how many years older the principal is than the teacher?
On solving the provided question we cans ay that As a result, x + 4 function denotes the number of years the principal is older than the instructor, where x is the student's age in years.
what is function?Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.
Let's start by writing down the phrases from the problem:
• The teacher's age is six years older than the student's age: T = 2x + 6, where T is the age of the instructor.
• The principal's age is ten years older than the student's age: P = 3x + 10, where P is the age of the principal.
To determine how many years the principal is older than the instructor, subtract the teacher's age from the principal's age:
P - T = (3x + 10) - (2x + 6)
When we simplify the equation, we get:
P - T = x + 4
As a result, x + 4 denotes the number of years the principal is older than the instructor, where x is the student's age in years.
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Find a quadratic function that includes the set of values below.
(0,7), (2,17), (3,16)
The equation of the parabola is Y
x + 5 < 2
the solution is ??
Answer:
x < -3
Step-by-step explanation:
x + 5 < 2
x < -3
So, the answer is x < -3
if i had 1000 apples and gave 39 away
how many wouldd i have left
Answer:
1000-39=961
so 961 apples are left.
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If an exterior angle of a regular polygon is 21.2º, how many sides does the polygon have?
A) 11
B) 13
C) 15
D) 17
Answer:
for any regular polygon, the sum of the exterior angles is always 360 degrees. In a regular polygon, all exterior angles have the same measure, which is equal to 360 degrees divided by the number of sides.
Let n be the number of sides of the polygon. Then we have:
360/n = 21.2
To solve for n, we can cross-multiply and simplify:
360 = 21.2n
n = 360/21.2
n ≈ 16.98
Since n must be a whole number (the number of sides in a polygon must be a whole number), the closest option is D) 17. Therefore, the polygon has 17 sides.
Given the function I need to evaluate question a)
Answer:
a) p(-6) = 30
b) c = -2 ,1
Step-by-step explanation:
[tex]p(c)=c^2+c[/tex]
a) Evaluate p(-6)
This mean input -6 into the equation to solve for p(-6) =
[tex]p(-6)=(-6)^2+(-6)\\\\p(-6)=36-6\\\\p(-6)=30\\[/tex]
(b) Solve for p(c) = 2.
[tex]p(c)=c^2+c\\\\2=c^2+c\\\\c^2+c=2\\\\c^2+c-2=0\\\\Factoring\\(c+2)(c-1)=0\\(c+2)=0,(c-1)=0\\c = -2 , 1[/tex]
Your firm purchases large shipments of a component, subject to the requirement that not more than 4% of a shipment may be defective. If a random sample of 200 parts from a new shipment reveals 12 defectives, can you reject this shipment as not meeting requirements, at the 5% level of significance?
Answer:
see the attachment
Step-by-step explanation:
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the shipment does not meet requirements.
What is the perimeter and area of a piece of land in the shape of a regular octagon with a side of 2 km, and an apothem of 2.4 km?
a) 16km and 21.9 km²
b) 16km and 19.2 km²
c) 16km and 29.1 km²
d) 61km and 19.2 km²
e) 16km and 12.9 km²
Answer:
the answer is b because 16km is resolved by 19.2
Marilou,a buyer of lot,pays Php10,000 every month for ten years.If money is 8%compoundef annually,how much is the cash value of the lot?
Answer:1,200,000
Step-by-step explanation:
Replace the by >, < 0o = to make the sentence -4/9* -5/9
The inequality to replace the symbol is > and the expression is -4/9 > -5/9.
How to determine the inequality to replace the symbolWe can utilize the following parameters in our calculation based on the question:
-4/9* -5/9
Represent the symbol * as a blank
This gives
-4/9 [ ] -5/9
Evaluate the quotients
-0.44444444444 [ ] -0.55555555555
By comparison, 0.44444444444 is greater than -0.55555555555
Using the above as a guide, we have the following:
-0.44444444444 [ > ] -0.55555555555
So, we have
-4/9 > -5/9
Hence, the inequality is >
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