The value of the building would be $699,400 in 4 years.
What will be the value of the building?Depreciation is the when the value of an asset reduces as a result of wear and tear. Straight line depreciation is a method used in depreciating the value of an asset linearly with the passage of time.
The equation that can be used to determine the value of the building with a straight line depreciation is:
Value of the asset = initial value of the asset - (number of months x deprecation rate)
y = 829,000 - 2700x
The first step is to determine the number of months it would take for the building to have a value of $699,400.
$699,400 = 829,000 - 2700x
829,000 - 699,400 = 2,700x
129,600 = 2,700x
x = 129,600 / 2,700
x = 48 months
Now convert, months to years
1 year = 12 months
48 / 12 = 4 years
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Let v be the vector from initial point P1=(−4,−9) to terminal point P2=(6,2). Write v in terms of i and j.
Step 1;
P1 = ( - 4 , -9 )
P2 = ( 6 , 2 )
Step 2:
[tex]\begin{gathered} \text{Let P}_1=(x_1,y_1)_{} \\ P_2=(x_2,y_2\text{ ) } \end{gathered}[/tex]Step 3:
[tex]\text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j}[/tex]Step 4:
[tex]\begin{gathered} \text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j} \\ \text{v = (6}-(-4))i+_{}(2-(-9)\text{) j} \\ v\text{ = (6+4)i + (2 + 9)j} \\ v\text{ = 10i + 11 j} \end{gathered}[/tex]Jo borrowed $3800 for 8 months from a bank at 5.5% a. how much interest did jo pay the bank for the us of it's money?b. how much did he pay total?
Let's begin by listing out the given information:
Loan (p) = $3,800
Time (t) = 8 months = 8/12 year
Interest rate (r) = 5.5%
a)
We calculate it thus:
[tex]\begin{gathered} I=\frac{p\times r\times t}{100} \\ I=\frac{3800\times5.5\times\frac{8}{12}}{100}=139.33 \\ I=\text{\$}139.33 \end{gathered}[/tex]b)
The amount paid in total is:
[tex]\begin{gathered} A=p+I \\ A=3800+139.33=3939.33 \\ A=\text{\$}3939.33 \end{gathered}[/tex]Rectangle CARD has a length of 2x-5 and a width of 6x+10. Triangle BEST has a length of 10x+3 and a width of 4x-7. Find the difference between triangle CARD and triangle BEST. *
Given:
Rectangle CARD: {length = 2x-5 and width = 6x+10}
Triangle BEST: {length = 10x+3 and width = 4x-7}
To find the differnce, let's first the perimeter of both.
Perimeter of rectangle CARD: 2(length + width)
= 2(2x - 5 + 6x + 10)
= 2(2x + 6x - 5 + 10)
= 2(8x + 5)
= 16x + 10
Perimeter of triangle BEST: 2(length + width)
2(10x + 3 + 4x - 7)
= 2(10x + 4x + 3 - 7)
= 2(14x - 4)
= 28x - 8
Therfore, the difference between both of them is calculated below:
(28x - 8) - (16x + 10)
= 28x - 8 - 16x + 10
= 28x - 16x - 8 10
= 12x - 18
ANSWER:
12x -
what is 2^-3 as a fraction
Answer:
Solution below.
Step-by-step explanation:
The question tests on the concept of indices.
We know the following indices rule:
[tex] {x}^{ - y} \\ = \frac{1}{ {x}^{y} } [/tex]
Which means by inversing the power, we will multiply the power by -1.
So in the case of this question, we can:
[tex] {2}^{ - 3} = \frac{1}{ {2}^{3} } \\ = \frac{1}{8} [/tex]
What is the probability that a data value in a normal distribution is between a Z score of -1.52 and Z score of -.34
We are asked to find the probability that a data value in a normal distribution is between a Z score of -1.52 and -0.34
[tex]P(-1.52First, we need to find out the probability corresponding to the given two Z-scoresFrom the Z-table, the probability corresponding to the Z-score -1.52 is 0.0643
From the Z-table, the probability corresponding to the Z-score -0.34 is 0.3669
So, the probability is
[tex]\begin{gathered} P(-1.52Therefore, the probability that a data value in a normal distribution is between a Z score of -1.52 and a Z score of -0.34 is 30.3%Option A is the correct answer.
The linear regressionequation andcorrelation coefficientfrom the above datawas calculated to be:Predicted y = 16.2+2.45(x) with r = 0.98What is the coefficientof determination?Answer Choices:A. Coefficient of determination = 0.98B. Coefficient of determination = 0.96C. Coefficient of determination = 0.99D. Coefficient of determination cannot be determined with only the given information.
Given:
[tex]\text{ coefficient of correlation \lparen r\rparen = 0.98}[/tex]To find:
Coefficient of determination
Explanation:
The coefficient of determination is also known as the R squared value, which is the output of the regression analysis method.
If the value of R square is zero, the dependent variable cannot be predicted from the independent variable.
So, here the required coefficient of determination is:
[tex]r^2=(0.98)^2=0.9604\approx0.96[/tex]Final answer:
Hence, the required coefficient of determination is (B) 0.96.
do you know the north Zone at the football stadium has 95 Rose there are 48 seats in a row how many people will the North end zone seat
The North zone at the football stadium has 95 rows.
There are 48 seats in a row.
How many people will the North end zone seat?
Since there are 95 rows and each row has 48 seats, multiply them to get the total number of seats.
[tex]\begin{gathered} total\: seats=rows\times seats \\ total\: seats=95\times48 \\ total\: seats=4560 \end{gathered}[/tex]Therefore, there are 4560 people sitting in the North zone.
Triangle CHE Is drawn below. What is the measure of y in the diagram?* I 2 meters 3 meters O 12 meters 6 meters None of the above
The given triangles are similar to each other, this means that we can get the length of the sides of the larger triangle by multiplying the corresponding lengths of the smaller one by a scale factor.
We can get the scale factor by dividing the length of one of the sides of the larger triangle by the length of the corresponding side in the smaller triangle, like this:
By taking the left sides
[tex]s=\frac{8}{4}[/tex]Then, in order to get the length of the base of the larger triangle (6), we just have to multiply the length of the base of the smaller triangle (y) by the scale factor (2), like this:
6 = 2×y
From this equation, we can solve for y to get:
2y = 6
2y/2 = 6/2
y = 3
Then, y equals 3 meters
Solve the following compound inequality:0< x+7< 9
you need to subtract 7 in each section of the inequality is
-7< x<2
-7< x and x<2
In a recent year, 26.3% of all registered doctors were female. If there were 47,400 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
From the problem statement we can write:
47,400 is 26.3% of total registered doctors
We need to convert this word equation to algebraic equation noting that,
• "is" means "="
,• "of" means "x"
Also, remember to convert the percentage to decimal by dividing by 100,
[tex]\frac{26.3}{100}=0.263[/tex]The algebraic equation, thus, is:
[tex]47,400=0.263\times\text{total}[/tex]We let total be "t" and solve :
[tex]\begin{gathered} 47,400=0.263t \\ t=\frac{47,400}{0.263} \\ t=180228.14 \end{gathered}[/tex]Rounding to the nearest whole number,
Total Registered Doctors = 180,228
Answer:
180,228Can you please help me solve this question. Thank you
Answer:
0.4384 < p < 0.5049
Explanation:
The confidence interval for the population proportion can be calculated as:
[tex]p^{\prime}-z_{\frac{\alpha}{2}}\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}}Where p' is the sample proportion, z is the z-score related to the 95% level of confidence, n is the size of the sample and p is the population proportion.
Now, we can calculate p' as the division of the number of voters of favor approval by the total number of voters.
[tex]p^{\prime}=\frac{408}{865}=0.4717[/tex]Additionally, n = 865 and z = 1.96 for a 95% level of confidence. So, replacing the values, we get:
[tex]\begin{gathered} 0.4717-1.96\sqrt[]{\frac{0.4717(1-0.4717)_{}}{865}}Therefore, the confidence interval for the true proportion is:
0.4384 < p < 0.5049
find the value of the expression 4d ÷ c when c=3and d=6 simplify your answer
Which sample size will produce the widest 95% confidence interval, given asample proportion of 0.5?A. 40B. 70C. 60D. 50
The confidence interval depends on the margin of error. When finding the margin of error, the z score corresponding to the 95% confidence level would be multiplied by the square root of the product of the estimated proportion of success and failure divided by the sample size. The greater the sample size, the smaller thie value that would be gotten from this operation. The smaller the sample size, the greater the value that would be gotten from this operation. A greater value would give a bigger margin of error. Thus, the confidence interval would be wider. Hence, the correct option for the sampe size is
A. 40
which is an incorrect rounding for 53.864a) 50b) 54c) 53.9d) 53.87
The incorrect rounding is 53.87
Explanations:The given number is 53.864
If the number is approximated to 2 decimal places
53.864 = 53.86
If the number is approximated to 1 decimal place
53.864 = 53.9
If the number is approximated to the nearest unit
53.864 = 54
If the number is approximated to the nearest tens:
53.864 = 50
Note: 53.864 cannot be approximated to 53.87 because the third decimal place (4) is not up to 5
Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x,y). 3x-2y=55x+10y=35
System of equations
• Equation 1
[tex]3x-2y=5[/tex]• Equation 2
[tex]5x+10y=35[/tex]Procedure
Solving the system by substitution.
0. Isolating ,x ,from equation 2:
[tex]5x=35-10y[/tex][tex]x=\frac{35}{5}-\frac{10y}{5}[/tex][tex]x=7-2y[/tex]2. Replacing the expression of x obtained in equation 1:
[tex]3\cdot(7-2y)-2y=5[/tex]3. Simplifying:
[tex]21-6y-2y=5[/tex][tex]-8y=5-21[/tex][tex]y=\frac{-16}{-8}[/tex][tex]y=2[/tex]4. Finally, we replace this value in the isolated expression of x and solve it:
[tex]x=7-2\cdot(2)[/tex][tex]x=7-4[/tex][tex]x=3[/tex]Answer: (3, 2)
Question 5 of 10 Solve the proportion below. 23 A 6 B. 8 C. 9 D.
solve for x
[tex]\begin{gathered} 12.6\times\frac{x}{12.6}=\frac{5}{7}\times12.6 \\ x=\frac{63}{7}=9 \end{gathered}[/tex]answer: C. 9
I need an quadratic equation with -3 and 6 for this assignment
If a quadratic equation has solutions
[tex]x=a,x=b[/tex]Then
[tex]x-a=0\text{ and x-b=0}[/tex]Furthermore, the quadratic can be written as
[tex]\begin{gathered} y=(x-a)(x-b) \\ where,y=0 \end{gathered}[/tex]Therefore,
[tex](x-a)(x-b)=0[/tex]Given:
[tex]a=-3,b=6[/tex]Hence,
[tex]\begin{gathered} (x--3)(x-6)=0 \\ (x+3)(x-6)=0 \end{gathered}[/tex]Simplify
[tex]\begin{gathered} x(x-6)+3(x-6)=0 \\ x^2-6x+3x-18=0 \\ x^2-3x-18=0 \end{gathered}[/tex]Hence, the quadratic equation is
[tex]x^{2}-3x-18=0[/tex]Alec wants to purchase a new phone that costs $219.00. His current average net pay is $212.34 each week. What percent of his weekdy net pay does Alec need to save each week, for the next seven weeks, to reach
his goal? Round to the nearest hundredth (1 point)
9.69%
14.73%
O 21.76%
31.28%
Answer:
14.73%
Step-by-step explanation:
firstly let's divide the phone price into 7 equal parts. by this equation 219.00/7=31.28
So Alec needs to save $31.28 but we want the percentage.
by equation x%*212.34=31.28
x=(31.28*100)/212.34=3128/212.34=14.73
so Alec needs to save 14.73% of 212.34 each week.
26÷2.40=10.833333 round to the nearest cent
26÷ 2.40= 10.833333
Nearest cent means ,2 numbers after decimal point
Then it is 10.83
count 2 numbers to right ,and discard rest of 3333
Then answer is = 10.83
what is 3 x 10 to the 4 in standard notation
i need help with this. for 2nd option, select only one sub-option
A matrix being in row echelon form means that Gaussian elimination has operated on the rows.
A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions:
- It is in row echelon form.
-The leading entry in each nonzero row is a 1 (called a leading 1).
-Each column containing a leading 1 has zeros in all its other entries.
The matrix presented on the problem satisfies all conditions, therefore, the matrix is indeed in reduced row-echelon form.
the figure shows a net for a three-dimensional figure. the net includes three squares.a) what is the three dimension figure. b) what is the surface area of the digure.
(b).
The area of the figure is equal to the sum of the area of the three squares and 2 triangles.
The area of the square is
[tex]2\operatorname{cm}\times2\operatorname{cm}=4\operatorname{cm}^2[/tex]The area of the triangle is
[tex]\frac{1}{2}\times1.7\operatorname{cm}\times2\operatorname{cm}=1.7\operatorname{cm}^2[/tex]Hence, two triangles and three squares have a total area of
[tex](4\operatorname{cm}\times3)+(2\times1.7cm)=15.4\operatorname{cm}^2[/tex]3. There are two city buses in Saratoga. Bus A completes its route in 25 minutes. Bus B completes its route in 40 minutes. Both of their routes end at the bus station. If both buses leave the bus station at the same time in the morning, how many minutes will pass before the two buses meet at the train station?
To find the answer, we have to find the LCM of 25 and 40.
To get LCM, we
Write each number as prime factors
take the prime factor that occurs greatest number of time
take the product of those
Thus,
25 = 5 * 5
40 = 2 * 2 * 2 * 5
2 occurs 3 times and 5 occurs 2 times (greatest).
hence,
LCM(25, 40) = 2 * 2 * 2 * 5 * 5 = 200
So,
200 mins will pass before the two buses meet
I need help with this statistics question please!
The margin of error of a z-confidence interval is given by: [tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
The margin of error of a z-confidence interval is 142.945936.
How to estimate the margin of error?The margin of error of a z-confidence interval exists given by:
[tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
Where, z is the critical value.
[tex]$\sigma$[/tex] be the population standard deviation.
n is the sample size.
The first step is finding the critical value, which exists z with a p-value of [tex]$\frac{1+\alpha}{2}$[/tex] in which [tex]$\alpha$[/tex] is the confidence level.
In this problem, [tex]$\alpha[/tex] = 0.95, therefore, z with a p-value of 1 + 0.95 / 2 = 0.975, which means that it is z = 1.96.
The population standard deviation exists of 12.2 meters, thus [tex]$\sigma[/tex] = 12.2.
We want a width of 5 , thus a margin of error of M = 2. Therefore, we have to simplify the equation for the margin of error for n.
Let the equation be [tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
substitute the values in the above equation, we get
[tex]$2=1.96 \frac{12.2}{\sqrt{n}}$[/tex]
[tex]$2 \sqrt{n}=1.96(12.2)$[/tex]
simplifying the above equation, we get
[tex]$\sqrt{n}=\frac{1.96(12.2)}{2}$[/tex]
[tex]$(\sqrt{n})^2=\left(\frac{1.96(12.2)}{2}\right)^2$[/tex]
n = 142.945936
Therefore, the value of n = 142.945936.
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Let w be defined as 2 more than the number of digits in the integer w. For example, 15* = 4 (2 digits in 15 + 2). If whas 7000 digits, then what is the value of (w)*?
The number of digits in 7000 is 4
The number of digits in w=7000
[tex](w)^{\cdot}=\text{ the number of digits in w+2}[/tex][tex](w)^{\cdot}=\text{7000+2}[/tex][tex](w)^{\cdot}=7002[/tex]Hence the required value is 7002.
The graph of y=(x + 2)^2 – 1 is reflected across the x axis and then translated up 3 units and right 4 units. What is the equation for the transformed graph?
ANSWER
[tex]y=-(x-2)^2\text{ + 4}[/tex]EXPLANATION
We have that the graph of y is:
[tex]y=(x+2)^2\text{ - 1}[/tex]It is first reflected about the x axis.
A reflection about the x axis is represented as:
y = -f(x)
which means that we find the negative of the function:
[tex]\begin{gathered} \Rightarrow y=-\lbrack(x+2)^2\text{ - 1\rbrack} \\ y=-(x+2)^2\text{ + 1} \end{gathered}[/tex]Then, it is translated 3 units up (vertical shift) and 4 units right (horizontal shift).
A translation is represented as:
y = f(x - a) + b
where a = horizontal shift; b = vertical shift
So, we have to find:
y = f(x - 4) + 3
That is:
[tex]\begin{gathered} y\text{ = }-\lbrack(x-4)+2\rbrack^2\text{ + 1 + 3} \\ y=-(x-4+2)^2\text{ + 4} \\ y=-(x-2)^2\text{ + 4} \end{gathered}[/tex]Therefore, that is the equation of the transformed graph.
What is the coordinate point location of the y-intercept of the graph below?
The y-intercept is located at the coordinate (0, 4) as shown below. Y-intercept is the point where a line or a graph crosses the y-axis.
What is the most precise name for quadrilateral ABCD with vertices A(−5,7), B(6,−3), C(10,2), and D(−1,12)?A. rectangleB. parallelogramC. squareD. rhombus
Answer:
A. Rectangle
Step-by-step explanation:
12. Jimmy is paid $14.50 per hour for a regular forty-hour work week and 5 point time and a half for any hour worked over 40. This pas week, Jimmy earned $754.00 in total pay. How many hours of overtime did Jimmy work?
Jimmy is paid $14.50 per hour for a regular forty-hour work week and 5 point time and a half for any hour worked over 40. This pas week, Jimmy earned $754.00 in total pay. How many hours of overtime did Jimmy work?
Let
x -----> the total hours worked
we have that
$14.50 --------> 40 hours
5.5($14.50) -------> > 40 hours
so
754=14.50*40+5.5(14.50)x
solve for x
754=580+79.75x
79.75x=754-580
79.75x=174
x=2.2 hours
Solve this system of equations by elimination. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer. If your answer is no solution, type "no solution". If your answer is infinitely many solutions, type "infinitely many solutions".
5x + 2y = -12 (a)
3y + 5x =-8 (b)
First, write (b) in the ax+by=c form:
5x + 3y = -8 (b)
Now, subtract (b) to (a) to eliminate x
5x + 2y = -12
-
5x + 3y = -8
__________
-y = -4
solve for y:
Multiply both sides by -1
y=4
Replace y=4 on (a) and solve for x:
5x + 2 (4) = -12
5x + 8 = -12
5x = -12-8
5x = -20
x = -20/5
x = -4
Solution: (-4,4)
