Answer:
1.4:1
= 14:10
= 7:5
Hence, ans is 7:5
Hope it helps, please mark me as brainliest...
Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.
3x^2−30x=−2
The solutions to this quadratic equation are x = √(73/3) + 5 or x = -√(73/3) + 5.
What is a quadratic equation?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
3x² - 30x = -2
By dividing all through by 3, we have:
x² - 10x = -2/3
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = -2/3 + (-10/2)²
x² - 10x + 25 = -2/3 + 25
x² - 10x + 25 = 73/3
By simplifying, we have;
(x - 5)² = 73/3
x = √(73/3) + 5 or x = -√(73/3) + 5
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Help please
The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 1000 years? -----------
after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
what is approximately ?
Approximately means "about" or "roughly" and is used to indicate an estimated or approximate value or quantity, rather than an exact or precise one. For example, if someone says "the population of the city is approximately 1 million people," it means that the population is around 1 million,
In the given question,
The half-life of Radium-226 is 1590 years, which means that in 1590 years, half of the original sample will have decayed. After another 1590 years (or a total of 2 half-lives), half of the remaining sample will have decayed, leaving 25% of the original sample.
To find how much of the original sample remains after 1000 years, we need to first determine how many half-lives have passed.
Number of half-lives = elapsed time ÷ half-life = 1000 years ÷ 1590 years/half-life = 0.63
So, approximately 0.63 half-lives have passed. Therefore, the fraction of the original sample remaining is:
fraction remaining = (1/2)⁰°⁶³ ≈ 0.518
To find the remaining mass, we can multiply the fraction remaining by the initial mass:
remaining mass = fraction remaining x initial mass
remaining mass = 0.518 x 500 mg ≈ 259 mg
Therefore, after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
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Triangle ABC is being enlarged using a scale factor of and centre (2,9) to
give triangle A'B'C'.
a) What are the coordinates of the vertex C'?
b) What is the length of the side A’B’
a) The coordinates of the vertex C' are C'(x, y) = (5, 5).
b) The length of the side A'B' is equal to 4.
In this problem we find the case of a right triangle, whose image must be found by a kind of rigid transformation known as dilation. The dilation formula for a vertex is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
k - Dilation factor
O(x, y) - Center of dilation
P(x, y) - Original vertex
P'(x, y) - Resulting vertex
And the dilation formula for a formula is:
L' = k · L
Where:
L - Original length.
L' - Resulting length.
Please notice that side lengths can be found by Pythagorean theorem.
we know that O(x, y) = (2, 9), k = 1 / 2, A(x, y) = (6, 7), B(x, y) = (10, 7) and C(x, y) = (6, 1), then the resulting vertices and sides are:
C'(x, y) = (2, 9) + (1 / 2) · [(6, 1) - (0, 9)]
C'(x, y) = (2, 9) + (1 / 2) · (6, - 8)
C'(x, y) = (2, 9) + (3, - 4)
C'(x, y) = (5, 5)
And the length of the side A'B' is:
AB = 8
A'B' = (1 / 2) · AB
A'B' = 4
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Jamar is going to invest $2200 and leave it in an account for 14 years. Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200
Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.
How is the interest rate for continuous compounding determined?Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:
Total P+I (A) = $4,200.00
Principal (P) = $2,200.00
Compound (n) = Compounding Continuously
Time (t in years) = 14 years
R = 4.619% per year
The calculation steps are as follows:
Solving for rate r as a decimal
r = ln(A/P) / t
r = ln(4,200.00/2,200.00) / 14
r = 0.0461877
Then convert r to R as a percentage:
R = r * 100
R = 0.0461877 * 100
R = 4.62%/year
Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
How to solveHeight (in centimeters) Frequency
0 - 3 | 5
4 - 6 | 10
7 - 9 | 15
10 - 12 | 7
13 - 15 | 3
To find the average height, we can follow these steps:
Determine the midpoint of each height range.
Multiply the midpoint of each range by the frequency.
Add up the products from step 2.
Add up the frequencies.
Divide the sum from step 3 by the sum from step 4.
Step 1: Determine the midpoint of each height range.
Height Range Midpoint
0 - 3 | 1.5
4 - 6 | 5
7 - 9 | 8
10 - 12 | 11
13 - 15 | 14
Step 2: Multiply the midpoint of each range by the frequency.
Height Range Frequency Midpoint Midpoint x Frequency
0 - 3 | 5 | 1.5 | 7.5
4 - 6 | 10 | 5 | 50
7 - 9 | 15 | 8 | 120
10 - 12 | 7 | 11 | 77
13 - 15 | 3 | 14 | 42
Step 3: Add up the products from step 2.
7.5 + 50 + 120 + 77 + 42 = 296.5
Step 4: Add up the frequencies.
5 + 10 + 15 + 7 + 3 = 40
Step 5: Divide the sum from step 3 by the sum from step 4.
296.5 / 40 = 7.4125
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
What is the average height of the bean plants in Mr. Anderson's class after 7 days?
Describe the following function
The transformation in the function y = -1/3f(x + 4) - 5 is described below
Describing the transformation in the functionFrom the question, we have the following parameters that can be used in our computation:
y = f(x)
The transformed function g(x) is given as
y = -1/3f(x + 4) - 5
The sequence of transformation on the transformed function is as follows
Horizontal shift to the left by 4 unitsVertical stretch by a factor of 1/3Reflection across the x-axisLastly, vertical shift down by 5 unitsRead more about transformation at
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Using the GCF, what is the factored form of 75 - 3x?
please i need help!!!
u will get 100 points!!!
The GCF (Greatest Common Factor) is the largest number that divides evenly into two or more numbers. In this case, we can find the GCF of 75 and 3 by listing their factors and finding the largest one they have in common. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 3 are 1 and 3. The largest factor they have in common is 3. Therefore, the GCF of 75 and 3 is 3.
We can use the GCF to factor the expression 75 - 3x by dividing each term by the GCF and writing the expression as a product. In this case, we can divide both terms by 3 to get 75/3 - (3x)/3, which simplifies to 25 - x. We can then write the original expression as a product by multiplying this simplified expression by the GCF: 3(25 - x).
Therefore, the factored form of 75 - 3x using the GCF is 3(25 - x).
Answer:
3(25-x)
Step-by-step explanation:
First we find the GCF of 75 and -3x, which is 3
3 is the highest number we can divide both 75 and -3
Hence, the answer is 3(25-x)
A man earned wages of 38,800 received 1600 in interest from savings account and contributed to 3200 to tax deferred retirement plan he was entitled to personal exemption of 2900 and had had deductions totaling 4950 find his gross income adjust gross income and taxable income
The gross income amount is $35,750
Given data ,
To find the gross income, we add up all of the man's income sources:
Gross Income = Wages + Interest + Retirement Plan Contribution
Gross Income = 38,800 + 1,600 + 3,200
Gross Income = 43,600
To find the Adjusted Gross Income (AGI), we subtract any eligible deductions from the gross income. In this case, the personal exemption and deductions are eligible.
AGI = Gross Income - Personal Exemption - Deductions
AGI = 43,600 - 2,900 - 4,950
AGI = 35,750
Finally, to find the taxable income, we subtract any additional deductions or exemptions from the AGI. We will assume that there are no additional deductions or exemptions in this case.
Taxable Income = AGI
Taxable Income = 35,750
Hence , the gross income is $43,600, the adjusted gross income is $35,750, and the taxable income is $35,750
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Calculate the area of a circle 4ft ,2in,18ft,5.2in,7.3in,14cm,9m,3m,9.2cm,7m,5m,6m
Answer:
Step-by-step explanation:
It seems like you have provided multiple measurements for the radius of the circle. I'm sorry, but a circle can only have one radius, so I am not able to calculate its area with the given information.
Please provide the correct measurement for the radius of the circle, and I will be happy to help you calculate its area.
Triangle GFH has vertices G(2, –3), F(4, –1), and H(1, 1). The triangle is rotated 270° clockwise using the origin as the center of rotation. Which graph shows the rotated image?
On a coordinate plane, triangle G prime H prime F prime has points (negative 3, negative 2), (1, negative 1), (negative 1, negative 4).
On a coordinate plane, triangle G prime H prime F prime has points (3, 2), (negative 1, 1), (1, 4).
On a coordinate plane, triangle G prime H prime F prime has points (2, negative 3), (1, 1), (4, negative 1).
On a coordinate plane, triangle G prime H prime F prime has points (2, 3), (4, 1), (1, negative 1).
Check the picture below.
Answer:
b
Step-by-step explanation:
edge 2023
Find cordinates of point of inter section
7x+4y=23
8x-10y=19
Answer:
To find the coordinates of the point of intersection between the two lines, we can solve the system of equations by elimination or substitution. Here, we will use the elimination method.
First, we will multiply the first equation by 10 and the second equation by 4, in order to eliminate the y term:
- 70x + 40y = 230
- 32x - 40y = 76
Adding these two equations, we get:
- 102x = 306
Dividing both sides by 102, we get:
- x = 3
Now we can substitute this value of x into either equation to find the value of y. Using the first equation:
- 7(3) + 4y = 23
- 21 + 4y = 23
- 4y = 2
- y = 1/2
Therefore, the point of intersection is (3, 1/2).
Answer:
Step-by-step explanation:
A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 9. Compute the raw, x-value associated with a Z-score of 0.21. Round to two decimal places, as needed.
The raw x-value associated with a Z-score of 0.21 for the given distribution is 145.89.
To compute the raw x-value associated with a Z-score of 0.21 for a distribution with a population mean, μ, of 144 and a population standard deviation, σ, of 9, we can use the formula for standardizing a variable:
Z = (x - μ) / σ
Rearranging the formula to solve for x, we get:
x = Zσ + μ
Substituting the given values, we get:
x = 0.21(9) + 144
Simplifying the expression, we get:
x = 145.89
A Z-score represents the number of standard deviations a value is from the mean, and it can be used to standardize values from different distributions. By standardizing values, we can compare them on a common scale and make more meaningful statistical inferences.
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1.) The average student takes 5 classes a semester. The table represents the probability distribution of the number of classes an average student passes in a given semester.
x P(X=x)
0 0.001
1 0.098
2
3 0.175
4 0.419
5 0.195
a. Find the missing probability
b. Find the expected number of classes passed.
c. Is it unusual for an average student to pass at most 2 class in a given semester?
a. The missing probability is 0.112
b. The expected number of classes passed is 3.38.
c. Is it unusual for an average student to pass at most 2 classes in a given semester is 0.211
a. Since the whole of all probabilities must rise to 1, we are able to discover the lost likelihood by subtracting the whole of the given probabilities from 1:
1 - 0.001 - 0.098 - 0.175 - 0.419 - 0.195 = 0.112
Subsequently, P(X=2) = 0.112.
b. The anticipated number of classes passed can be found by increasing each possible value of X by its particular likelihood, and after that summing the items:
E(X) = 0(0.001) + 1(0.098) + 2(0.112) + 3(0.175) + 4(0.419) + 5(0.195)
= 3.38
Hence, the anticipated number of classes passed is 3.38.
c. To decide in case it is bizarre for an average student to pass at most 2 classes in a given semester, we have to calculate the likelihood of passing at most 2 classes:
P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)
= 0.001 + 0.098 + 0.112
= 0.211
Since this likelihood is more noteworthy than 0.05 (i.e., the commonly utilized threshold for determining whether an occasion is unordinary), it isn't abnormal for a normal understudy to pass at most 2 classes in a given semester.
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What is the correct answer for 17? Plsss help
If lines m and n are parallel, then the value of x must be 4.
How to find the value of x?
If lines m and n are parallel, then the measures of the angles in the correspondent quadrants must be the same ones.
Here we can see that the two angles are in the third quadrant, thus, these angles have the same measure. Then we can write this as:
6x² = 96
Now we can solve this for x, we will get:
x² = 96/6
x² = 16
x = √16
x = 4
That is the value of 4.
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Solve the inequality and graph the solution on the line provided.
> ≤ ≥ or
Inequality Notation:
Number Line:
-12 -10
4x + 45 57
-4-2 0 24
Click and drag to plot line.
6
10 12
The solution of the given inequality is x ≤ 13/4
Since Inequality can be defined as the relation which makes a non-equal comparison between two given functions.
We are given the Inequality as;
4x + 45 ≤ 57
Solving;
4x + 45 ≤ 57
4x ≤ 57 - 45
4x ≤ 13
x ≤ 13/4
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Leslie invests in a bank account that earns interest compounded quarterly. The expression 500(1.026)4t can be used to find the account balance in t years.
Part A
What was Leslie’s initial investment?
$
Part B
What is the quarterly interest rate the account earns?
Leslie's initial investment was $500 and the quarterly interest rate the account earns is 10.4%.
To find the initial investment and quarterly interest rate we can use the following compound formula of
A = P [tex](1 + \frac{r}{n} )^{nt}[/tex]
Given expression =[tex]500(1.026)^{4t}[/tex]
principal P = $500
rate of interest r = 1.026
A) Leslie's initial investement A = [tex]500 (1.026) ^{0}[/tex] = 500 [ initially time t = 0]
B) for finding quarterly interest,
given expression =[tex]500(1.026)^{4t}[/tex]
=[tex]500(1 + 0.026)^{4t}[/tex]
= [tex]500(1 + 0.026 * 4/4)^{4t}[/tex]
= [tex]500(1 + \frac{0.104}{4} )^{4t}[/tex]
From the above expression, we can conclude that the quarterly interest is 0.104 which is 10.4%
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Kelly purchased a toaster for $115. She made a down payment of 10% and financed the rest for 9 months with payments of $16.78. Find (a) the down payment and (b) the total installment price of the toaster.
(A) The down payment of the toaster = $ 11.5
(B) The total installment price of the toaster = $151.02
(A) The down payment of the toaster made by Kelly is 10 % of $ 115
Down payment = 115 × 10/100
Down payment = 1150/100
Down payment = 11.5
The down payment of the toaster = $ 11.5
(B) Total installment price of the toaster for 9 months with payment of $ 16.78
Total installment price of toaster = 9 × 16.78
Total installment price of toaster = $ 151.02
The total installment price of the toaster = is $ 151.02
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Which explanation correctly analyzes the difference between an irrational number and a rational number?
The statement that analyzes difference between an irrational number and a rational number is: the expression √25 - √21 can be rewritten as 5 - √21. since the exact value of √21 cannot be found, the difference is irrational, The Option D is correct.
What is difference between irrational number & rational number?A rational number refers to number that can be expressed as the ratio of two integers where the denominator is not zero. For example 1/2, 3/4, and -5/7 all rational numbers.
Irrational number refers to one that cannot be expressed as a ratio of two integers. Examples include pi (π) and the square root of 2 (√2).
The difference is that one is expressed as a ratio of two integers or a decimal that either terminates or repeats other cannot be expressed as a ratio of two integers and have a decimal representation that does not terminate or repeat.
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crack the code
09, 15. 18. 20, 22, 25, 03
The next number in the sequence would be 25 + 4 = 29.
How to break the sequence?
First off, we rearrange these numbers in ascending order and this gives us:
3 9 15 18 20 22 25
Next, we try and find the pattern:
The pattern seems to be adding consecutive odd numbers starting from 3.
3 + 6 = 9
9 + 6 = 15
15 + 3 = 18
18 + 2 = 20
20 + 2 = 22
22 + 3 = 25
Therefore, the next number in the sequence would be 25 + 4 = 29.
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crack the code
09, 15. 18. 20, 22, 25, 03
Find the next number
The acts in a talent competition consist of 10 instrumentalists, 12 singers, and 8 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first?
Answer:
P=4/15
Step-by-step explanation:
P(dancer first) = 8/30=4/15
The Ferris Wheel can carry 4 passengers in each of its 15 cars in one ride. How many passengers can it carry on a total of 35 rides?
The Ferris Wheel can carry 2100 passengers on a total of 35 rides.
According to the question,
Number of cars in the Ferry Wheel = 15
Number of passengers in each car = 4
∴ Number of passengers in 15 cars = 15×4 = 60
So, the number of passengers on the Ferry Wheel = 60
Now,
The number of passengers the Ferry Wheel carries in one ride = 60
∴ The number of passengers in 35 rides = 60×35 = 2100.
Hence the Ferris Wheel can carry 2100 passengers on a total of 35 rides.
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Correct answer gets brainliest!!!!
Answer:is b
A line segment has both of its end-points fixed and so it has a definite length.
Step-by-step explanation:
pl z give me brianlieyst and have a good day
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HELP ME PLEASE!
Whoever answers right gets brainliest!
Therefore, the range of the relation shown is (1, 3, 4, 6, 7). Option C is the correct answer.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are used to model relationships between variables in many areas of mathematics and other fields such as physics, engineering, economics, and computer science. They are used to describe various phenomena, such as the growth of populations, the trajectory of a projectile, or the behavior of financial markets. Functions are also important tools in calculus, where they are used to study rates of change and continuity, among other things.
Here,
The range of a relation refers to the set of all possible output values or y-values of the relation. Looking at the image reference, we can see that the y-values or the outputs are 1, 3, 4, 6, and 7.
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campaign. Evaluate how community respond to women and children in (3x4)(12) light of the following aspects: Bill of Rights Discrimination Human Rights Violations ■ . B
The community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms.
Now, The evaluation of community response to women and children in the context of Bill of Rights, Discrimination, and Human Rights Violations can be done as follows:
Bill of Rights:
The Bill of Rights guarantees certain rights and freedoms to all individuals regardless of their gender or age. Therefore, any discrimination or violation of women and children's rights would be a direct violation of the Bill of Rights. The community must ensure that women and children are not denied their right to life, dignity, equality, and freedom from all forms of violence and exploitation.
Discrimination:
Discrimination against women and children is a prevalent issue in many societies. Women and children are often subjected to discrimination on the basis of their gender, age, race, religion, or socio-economic status. The community should work towards eliminating all forms of discrimination against women and children and provide them with equal opportunities in all spheres of life.
Human Rights Violations:
The community must also ensure that the human rights of women and children are protected. Human rights violations against women and children can include physical and emotional abuse, sexual harassment and assault, child labor, child marriage, and human trafficking, among others. The community must take a strong stance against such violations and work towards preventing and punishing the perpetrators.
In conclusion, the community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms. Any form of discrimination or violation of their rights should be condemned and punished to ensure that women and children are safe and empowered members of society.
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For the graph of a function y=f(x) shown to the right, find the absolute maximum and the absolute minimum, if they exist. Identify any local maxima or local minima.
Answer:
B) There is no absolute max for y=f(x)
Step-by-step explanation:
There is no absolute max as the function increases infinitely
However there is an absolute minimum at x=0
Help me please How would you informally prove that you are taking courses online?
A) You could show a registrar’s receipt with the current date.
B) You could show your course notes with the current date.
C) You could repeat all the material you learned.
D) You could ask for an enrollment verification notice from the school.
Answer: b is correct
Step-by-step explanation:
How much would you need to deposit in an account now in order to have $2000 in the account in 15years? Assume the account earns 7% interest compounded monthly.
Answer:
To calculate the amount you would need to deposit in the account now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount you will have after 15 years, P is the principal amount (the amount you need to deposit now), r is the annual interest rate (7%), n is the number of times the interest is compounded per year (12 for monthly compounding), and t is the time in years (15).
Plugging in the values, we get:
2000 = P(1 + 0.07/12)^(12*15)
Simplifying the right side, we get:
2000 = P(1.00583)^180
Dividing both sides by (1.00583)^180, we get:
P = 2000 / (1.00583)^180
P = $775.80 (rounded to the nearest cent)
Therefore, to have $2000 in the account in 15 years with an annual interest rate of 7% compounded monthly, you would need to deposit $775.80 now.
12 A quality control inspector at a plant has found the probability of randomly selecting a defective
battery from a batch of batteries being produced is 0.02. The probability of rain that day has been
projected to be 0.75. If these two events are independent, what is the probability that on that particular
day, it rains, and the inspector chooses a defective battery from the batch being produced?
(1) 0.77
(3) 0.015
(2) 0.5
(4) 0.95
Answer:
The answer is (3) 0.015.
Step-by-step explanation:
This is because to find the probability of finding both independent events happening at the same time, we must multiply them.
The independent events are:
- Randomly selecting a defective battery: 0.02
- Raining tomorrow: 0.75
0.02 x 0.75 = 0.015
Therefore, the answer is (3) 0.015.
Hi can someone please help me out and explain the question in the picture? Thanks I appreciate it. I’ll give brainly :)
Answer:
$52.50
Step-by-step explanation:
1500 * 3.5% = 52.50
Answer:
$52.5 for the first year
Step-by-step explanation:
You can derive a decimal from a percentage by dividing by 100.
For example, 1% is 0.01
3.5% is 0.035
You can also move the decimal point back 2 places, but that's cringy.
So the problem says how much interest she will have to pay after one year, when the interest rate is 3.5%.
Therfore, we must multiply:
1500 by 3.5%
We stated that 3.5% is 0.035, so we can replace that
1500 * 0.035
Plug that into a caluclator and we get.....
$52.5 for the first year
ANSWER CHOICE 1
Phew! That was a long problem! May I please have Brainliest?
Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
we should expect 4 white horses among the next 20 horses that come to board. we can solve by equation .
what is equation ?
An equation is a mathematical statement that uses symbols and variables to show that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables, constants, and mathematical operations such as addition
In the given question,
Out of the 15 horses currently boarded, 3 are white. This means that the proportion of white horses among the currently boarded horses is:
3 / 15 = 0.2 or 20%
Therefore, if we assume that the next 20 horses that come to board will have a similar distribution of coat colors, we can expect approximately 20% of them to be white.
So, the expected number of white horses among the next 20 horses that come to board is:
20 x 0.2 = 4
Therefore, we should expect 4 white horses among the next 20 horses that come to board.
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