If Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48 , what is the principal loan amount?
When Bobby takes out a mortgage for $30 years at 4% interest with $835.48 in monthly payments, the total principal loan amount is $255644.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Here,
The interest paid per month=$835.48
Interest paid in 30 years=835.48*12*30
Rate of interest=4%=0.04
Time=30 years
Principal=I/RT
=(835.48*30*12)/(0.04*30)
=$250644
The principal loan amount is $250644 when Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48.
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a line passes through the point (-9,-8) and has a slope of 2/3
. Write a equation in slope intercept form for this line
Answer:
y=2/3x-2
Step-by-step explanation:
The equation is y = mx + b and m is the slope. You were already given the slope and you were even given a point. All you have to do is graph the point and use the slope until it intercepts the y-axis.
1. Plot the point (9,-8)
2. Go up 2, left 3 spots until the line hits the y-axis (the vertical one)
3. That point is what b will be equal to in y = mx + b
OR you can convert a point-slope equation into slope intercept
1. The formula for point slope is y – y1 = m(x – x1)
2. Plug in the given numbers and it will look like this: y+8=2/3(x+8)
3. Do the math and get a solution of y=2/3x-2
In a class of 30 students, 16 have a cat and 15 have a dog. There are 11 students who have a cat and a dog. what is the probability that a student has a dog given that they do not have a cat?
Find the point of intersection for the pair of linear equations.
x+y= -8.5
y = 2x + 4.4
A. (-4.3, -4.2)
B. (-4.1, 4.4)
C. (1.9, -3.7)
D. (-3.1, 2.4)
What is the answer to this?
A clothing designer is selecting models to walk the runway for her fashion show. The clothes she designed require each model’s height to be no more than y inches from 5 feet 10 inches, or 70 inches. Which graph could be used to determine the possible variance levels that would result in an acceptable height, x?
The graph that could be used to determine the possible variance levels that would result in an acceptable height is the third graph.
How can one depict the graph?Fron the information, the required model height for the designed clothes should be less than or equal to 5 feet 10 inches. In this case, the equation for the variance in height is of the straight line form;
y = m·x + c
Where x is the height in inches
Given that the maximum height allowable is 70 inches, when x = 0 we have;
y = m·0 + c = 70
Therefore, c = 70
Also when the variance = 0 the maximum height should be 70 which gives the x and y-intercepts as 70 and 70 respectively such that m = 1
The equation becomes;
y ≤ x + 70
Also when x > 70, we have y ≤ -x + 70 with a slope of -1
In this case, to graph an inequality, we will need to shade the area of interest which in this case of ≤ is on the lower side of the solid line.
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In this problem, assume that the effect of friction can be discounted. (Remember to include the unit in the answer.)
Referring to the above diagram, how high will the ball rise on the right-hand incline?
The ball will rise 15 cm height on the right-hand incline when friction is discounted.
What is friction?The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction.
Given that,
The height of the ball = 15 cm
Since, the friction force is not counted here, this implies that there will be no friction force to stop the object.
The rise of the height on the right-hand incline will be same to the initial height.
Therefore, the ball will rise 15 cm height on the right-hand incline.
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If n = 19,
¯
x
= 36, and s = 2, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.
<
μ
The three decimal places are :28.288< μ < 43.712
What is meant by normally distributed population?A normal distribution is one in which the values are evenly distributed above and below the mean. A population has a perfectly normal distribution if the mean, mode, and median are all equal. The mean, mode, and median for a population of 3,4,5,5,5,6,7 are all 5. The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, indicating that data near the mean occur more frequently than data far from the mean.degree of freedom = 17-1 = 16
critical t value = 2.1199
lower limit = 36-2.1199*15/sqrt(17) = 28.288
Upper limit = 36+2.1199*15/sqrt(17) = 43.712
Answer:28.288< μ < 43.712
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The formula below models the number of calories consumed daily by a person owning x acres of land in a developing country. Estimate the number of a 2200 calories per day.
C(x)=270 ln (x+1)+1900
For an average intake of 2200 calories per day, the number of acres of land owned is approximately (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)
For an average intake of 2200 calories per day, the number of acres of land owned will be 2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, The function that models the number of calories consumed daily by a person owning x acres of land in a developing country is,
C(x)=270 ln (x+1)+1900
If an average intake of 2200 calories per day,
C(x)= 2200
2200=270 ln (x+1)+1900
2200-1900=270 ln (x+1)
270 ln (x+1)=2200-1900
270 ln (x+1)=300
ln (x+1)=300/270
ln (x+1)=1.11
(x+1)=ln⁻¹(1.11)
x+1=e¹¹¹
x=e¹¹¹-1
x=3.034-1
x=2.034≈2
Thus, for an average intake of 2200 calories per day, the number of acres of land owned will be 2.
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2. For each of the following functions, determine the average rate of change over the specified interval.
From x=4 to x=10
Average rate of change for given function from x=4 to x=10 is -0.66
What is average rate of change?Average rate of change can be defined as slope of function between two fixed values of x. It can also be defined as change in function per unit or we can say as an average.
At x = 4 we have y = 8
At x = 10 we have y = 4
As y is nothing but value of function f(x) at x.
So, we can write them as f(4) = 8 and f(10) = 4
Average rate of change (from x = a to x=b) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using above formula of average rate of change and substituting for x=4 to x=10, we get
Average rate of change = [tex]\frac{4-8}{10-4} = \frac{-2}{3}[/tex]
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Determine whether each ordered pair is a solution of the given linear equation.
2x + 7y = 16;
a. (9,1)
b. (8,0)
c. (0,0)
Answer:
A. No
B. Yes
C. No
Step-by-step explanation: To determine if each pair is a solution to the equation, substitute the x and y variables in the pairs for the corresponding variables in the equation. If the left and right sides are equal once you solve, you will know that the pair is a solution,
(9,1) 2(9)+7(1)=16 18+7=16 25=16 No
(8,0) 2(8)+7(0)=16 16+0=16 16=16 Yes
(0,0) 2(0)+7(0)=16 0+0=16 0=16 No
The strongest recorded earthquake was in Chile in 1960 and had an intensity of 316227.77 cm. What was its magnitude? (Round your answer to one decimal place.)
Answer:
5.5
Step-by-step explanation:
earthquake is measured with the Ritcher Scale:
R (Magnitude) = ㏒base 10 (I)
where I = Intensity
thus,
R = ㏒ base 10 (316227.77)
R ≅ 5.5
I need help please ??? ASAP???! And what can I write ?? thank you so much!
Answer:
You need to multiple
Step-by-step explanation:
Calculate the distance between the points P=(0, 1) and J=(4, -2) in the coordinate plane. Give an exact answer (not a decimal approximation).
Using the distance formula, [tex]JP=\sqrt{(0-4)^2+(1-(-2))^2}=\boxed{5}[/tex]
let be the amount of coffee (in ounces) that an undergraduate student at uiuc drinks per day. suppose we know that has a mean of 10 oz and a standard deviation of 5.2 oz. suppose there are 120 students in stat 107. assuming stat 107 students are a random sample, calculate the standard error of the average amount of coffee a stat 107 student drinks per day . is greater than 12.7 oz.
0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.
Given that,
Standard deviation (σ) = 5.2 oz
mean (μ) = 10 oz
Number of students (n) = 120
As we know,
P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ[tex]\sqrt{n}[/tex]}/σ])
= P (z > [{12.7 - 10[tex]\sqrt{120}[/tex]}/5.2])
= P (z > 1.86)
= 1 - P ( z < 1.86)
= 1 - 0.862394
= 0.137606
Thus, P( z > 12.7 oz.) = 0.137606
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The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following.
S = 10(1-ekx)
When $675 is spent on advertising 2900 units are sold.
(a) Complete the model by solving for k. (Round your answer to 4 decimal places.)
k =
(b) Estimate the number of units that will be sold if advertising expenditures are raised to $925.
units
Answer:
as a result you get approximately 2.8949 which in thousands of units is 2894 (rounded down since you can't have a fraction of a unit).
which expressions are equivalent to 5x + 6y - 3x
Step-by-step explanation:
The expression 5x + 6y - 3x is equivalent to:
2x + 6y
This is because 5x and -3x can be combined by adding them together, which gives 2x.
The expression 5x + 6y - 3x is also equivalent to:
x + 6y - 3x
This is because 5x and -3x can be combined by adding them together, which gives x.
However, the expression 5x + 6y - 3x is not equivalent to:
2x - 3y
This is because the coefficient of the y term is 6, not -3.
The expression 5x + 6y - 3x is also not equivalent to:
x + y
This is because the coefficient of the y term is 6, not 1.
Evaluate the function graphically.
Find f(-1)
The required value of the given function f(-1) is 2.
What is a function?
Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.
For the given graph,
For x = -1, the exact y value will be 2.
So, f(-1) = 2
Hence, the required value of the given function f(-1) is 2.
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John earned $45.90 during the summer break. He used of the money to buy trading cards. Then, he used of the remaining amount to buy a sketchbook, and also spends $4.50 on comic books.
How much money does John have left after these purchases?
Answer:
Not possible with given
Step-by-step explanation:
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining.
Which equations could you use to find the price of one tire patch? Select all that apply.
4x – 1.9 = 22.2
4x – 22.2 = 1.9
4x + 1.9 = 22.2
4x + 22.2 = –1.9
22.2 – 4x = 1.9
Answer:
he paid 20.20 for the patch
Answer:
The equation could you use to find the price of one tire patch select all that apply 4x + 1.9 = 22.2 and 22.2-4x= 1.9
Kira wants to attend a college that will cost her $14,800 for the first year. To pay for it, her aunt gave her a special gift of $10,000 . Kira is also going to start saving $100 per month. How many years will it take Kira to save enough for the first-year cost?
Hannah wants to have $ 6500 to help pay for a new deck in 16 years. If she wants to put her money into an account earning 4.75% interest compounded continuously, how much should she invest now, so that she will have $ 6500 in 16 years?
Payment amount =
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6500\\ P=\textit{original amount deposited}\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ t=years\dotfill &16 \end{cases} \\\\\\ 6500=Pe^{0.0475\cdot 16} \implies \cfrac{6500}{e^{0.0475\cdot 16}}=P\implies 3039.83\approx P[/tex]
To the nearest hundredth, 11.6÷0.95
is about
on dividing the given term we get
12.2105.
A. BD bisects AC
B. Triangle ABC is isosceles
C. BD is the perpendicular bisector of AC
D. AD=12
Choices B, C and D are required answer choices.
What is an isosceles triangle?
Any triangle with two equal sides and angles with equal measures on opposite sides is said to be an isosceles.
Based on the given diagram,
BD is perpendicular to AC because the given angle D is 90 degrees.
And, AD = DC (Given)
or, 4x = x + 9
or, 4x -x = 9
or, 3x = 9
or, x = 3
Then, AD = 4x = 4*3 = 12
And, AB = BC
So, the two sides of a given triangle are equal to each other.
Then, triangle ABC is an isosceles triangle.
Based on the above calculation and data, we can conclude that
Hence, Choices B, C and D are required answer choices.
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Complete Question,
Given h of x equals 2 times the square root x minus 5 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 5).
The function h(x) is increasing on the interval (5, ∞).
The function h(x) is decreasing on the interval (–5, ∞).
The function h(x) is decreasing on the interval (–∞, –5).
Answer:
B
Step-by-step explanation:
x -5 ≥ 0
x ≥ 5
the function exists only in the interval [5, +oo) and it keeps growing
12
A culture of bacteria triples every hour. If there are 5 bacteria after the first hour,
how many bacteria will there be after one day?(One day= 24 hours)
5 x 3²⁴ bacteria will there be after one day.
What is exponents?
Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".
Consider what is actually happening in the question.
You begin with 5 bacteria, and after 1 hour it has tripled so you now have
5x 3=15.
Next hour, it triples again so you now have 5 x 3 x 3=45
You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴ means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).
Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:
n x 324 where n is the number of bacteria you begin with.
Since you begin with 1 bacteria, the solution is 5 x 3²⁴.
Hence 5 x 3²⁴ bacteria will there be after one day.
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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 12-x^2. What are the dimensions of such a rectangle with the greatest possible area?
Answer:
if the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2
the area of a rectangle = length * width
thus, area = x*(7-x^2)= 7x-x^3
in order to maximize the area, you would need to take the derivative of the area and set it equal to 0
Area = 7x-x^3Area' = 7 - 3x^2
7-3x^2 = 0thus, x = 1.5275
this x represents the x needed to create the largest possible area with the given parameters.
Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667
PLEASE HELP ME!!! I WILL GIVE BRAINLIST!!!PLEASE
Answer: D. A'(-5,10) B'(-1,10) C'(-1,7) D'(-5,6)
Step-by-step explanation:
A(-5,5) B(-1,5) C(-1,2) D(-5,1)
A'(-5,5+5) B'(-1,5+5) C'(-1,2+5) D'(-5,1+5)
A'(-5,10) B'(-1,10) C'(-1,7) D'(-5,6)
Select all of the verbal phrases which can be represented by the expression 25.75x + 10.
25.75 plus 10
25.75 times a number x, plus 10
25.75 times a number x, plus 10 times a number x
the product of 25.75 and x, plus 10
the product of 25.75 and 10
The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.
What is mathematical verbal expression?An algebraic expression that may contain various operations, quantities, and variables is translated into words as a mathematical verbal expression.This can be demonstrated by verbally expressing the mathematical statement "90 - 4(a + 8)" as "90 reduced by 4 times the sum of a number "a" plus 8."Students may also need to convert verbal expressions into algebraic expressions or equations when studying math. In word problems, where students must search for precise terms that identify the procedure required to answer the problem, this is frequently utilized. Decreased by, increased by, less than, more than, sum of a number and "x," and the total of two numbers are a few examples of these expressions.Hence, The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.
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Y varies directly as x and inversely as the square of z.y=8 when x=25 and z=5. Find y when x=2 and z=6
The value of y when x = 2 is 16/25 and when z = 6 is 200/36
What is proportionality constant?The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
Given that, Y varies directly as x and inversely as the square of z and y=8 when x=25
That means, y ∝ x and y ∝ 1/z²
Let constant of proportionality be k, then,
y = kx and y = k/z²
Now, finding k, when x = 25
8 = k25
k = 8/25
For x = 2,
y = 8/25X2
y = 16/25
Finding k when y = 5
8 = y/25
y = 200
Now, when z = 6
y = 200/36
Hence, The value of y when x = 2 is 16/25 and when z = 6 is 200/36
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