The length and the width of the fencing are 85 feet and 30 feet respectively.
What is a rectangular perimeter?The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.
Given:
Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that encloses his rectangular front yard.
The length is five feet less than three times the width.
Let w be the width.
Then, 3w - 5 is the length.
So, the perimeter of the rectangular fence = 200 + w.
Now, 2(3w - 5 + w) = 200 + w
6w - 10 + 2w = 200 + w
7w = 210
w = 30
Then length = 85
Therefore, length = 85 feet and width = 30 feet.
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Using time value of money tables, calculate the following. Use (Exhibit 1-A, Exhibit 1-B, Exhibit 1-C, Exhibit 1-D).
(a) The future value of $450 six years from now at 7 percent.
(b) The future value of $900 saved each year for 10 years at 8 percent.
(c) The amount a person would have to deposit today (present value) at an interest rate of 6 percent to have $1,000 five years from now.
(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent.
Using time value of money tables the following are -
(a) The future value of $450 six years from now at 7 percent is $675.33.
(b) The future value of $900 saved each year for 10 years at 8 percent is $13037.91.
(c) The amount a person would have to deposit today (present value) at an interest rate of 6 percent to have $1,000 five years from now is $747.26.
(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent is $8691.93.
What in annuity?
An annuity is a contract that you have with an insurance provider that calls for regular payments to be made by the insurer to you, either now or in the future.
(a) The future value of $450 six years from now at 7 percent.
FV= PV × (1 + r)n
FV= $450 × (1 + 7%)6
FV= $450 × (1.07)6
FV= $450 × 1.50073
FV= $675.33
(b) The future value of $900 saved each year for 10 years at 8 percent.
This is annuity as $900 is saved each year
Formula :: FV = PMT * (((1 + r%)n - 1) / r%)
FV = $900 × (((1 + 8%)10 - 1) / 8%)
FV= $900 × 14.4865624
FV= $13037.91
(c) The amount a person would have to deposit today (present value) at a 6 percent interest rate to have $1,000 five years from now.
PV= FV / (1 + r)n
PV= $1000 / (1 + 6%)5
PV= $1000 / 1.3382255
PV=$747.26
(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent.
Annuity value = $600
FV= Annuity value × Annuity factor(10%,8 year)
= $600 × (((1 + 8%)10 - 1) / 8%)
= $600 × 14.4865624
= $8691.93
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A retail fabric store advertises a storewide sale and it lists a certain material for 0.88/yd. A fabric warehouse is selling the same material for $0.92/m.
a) Which store has the better price? Explain your answer.
b) How much money would you save if you purchased 15 ft of the less expensive material.
in 2014, there were about 7 billion cell phone subscribers in the world. during the next 5 years, the number of cell phone subscribers increased by about 3% each year. a. write an exponential model that represents the number of cell phone subscribers y (in billions), t years after 2014.
The exponential model that represents the number of cell phone subscribers y (in billions), t years after 2014 is; F = 233 ( 1.06)^t
What are exponential functions?When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.
The general formula for an exponential growth is:
F = P( 1 + i ) ^t
where F is the future amount in t years
P is the present amount
i is the fraction of increase per time
t is the time
For the increase cellphone subscriber
P = 233
i = 0.06
Therefore,
F = 233 ( 1 + 0.06)^t
F = 233 ( 1.06)^t
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twelve times the square of a positive number is five more than four times the same number. find the number. (please give answer as an integer or simplified proper/improper fraction)
The positive number we're looking for is 5/16.
What is the Equation?
An equation is a mathematical statement that asserts the equality of two expressions.
Let's call the positive number we're looking for x. Then, the problem can be expressed as two equations:
[tex]12x^2 = 4x + 5x^2 = (4/12)x + 5/12\\\x^2 = (1/3)x + 5/12\\\\x^2 - (1/3)x = 5/12\\(4/3)x = 5/12\\x = 5/12 * (3/4)\\x = 5/16[/tex]
Hence, the positive number we're looking for is 5/16.
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The positive number we're looking for is 5/16.
What is the Equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, the equation 6x + 5 = 20 consists of the two equations 6x + 5 and 20, which are separated by the 'equal' sign.
A mathematical statement that claims the equivalence of two expressions is known as an equation.
Let's call the positive number we're looking for x.
Then, the problem can be expressed as two equations:
12x² = 4x + 5x² = (4/12) x + (5/12)
x² = (1/3) x + (5/12)
x² - (1/3) x = (5/12)
(4/3) x = (5/12)
x = (5/12) × (3/4)
x = 5/16
Hence, the positive number we're looking for is 5/16.
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Find the value of x:
Answer:
155
Step-by-step explanation:
see attached.
A particular brand of toilet paper is offered at two stores
Note that given the question which is related to Dimensional Analysis, Sam's Club package is more expensive. This means WalMarts prices are a better option.
What is Dimensional Analysis?Dimensional analysis is the examination of the connection between physical quantities using dimensions and measuring units.
To determine the better option, we simply derive the cost per sheet as follows:
For Sam's Club we have:
26.99/ (36 x 248)
= $0.0030230735/ Sheet
For Walmart, we have:
5.99/ (8 * 350)
= $0.0021392857/ Sheet
So based the above, it clear that the Sam's Club package is more expensive because:
$0.0021392857 < $0.0030230735
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Full Question:
A particular brand of toilet paper is offered at two stores in different kinds of packaging. To practice using rates, for each package determine both the number of sheets per dollar and the cost in dollars per sheet. Then determine which package is the better buy.
Sam's Club sells a 36-pack of toilet paper with 248 sheets per roll for $26.99
Walmart sells the toilet paper for $5.99 in an 8-pack with 350 sheets per roll. The Sam's Club package: ?
A triangular prism has the
dimensions as shown below.
Each congruent base is an
equilateral triangle.
24.2 mm
28 mm
40 mm
Which of the following
measurements is closest to the
total surface area of the
triangular prism in square
millimeters?
the vector v has initial point p(1, 0) and terminal point q that is on the y-axis and above the initial point. find the coordinates of terminal point q such that the magnitude of the vector v is 5.
The required terminal point is Q(0,2).
Vector magnitudeBy using the symbol |v|, the magnitude of a vector formula can be utilized to determine the length for a given vector (let's say v). In essence, this measurement represents the separation between the vector's starting and ending points.
For a vector v with endpoints at [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex], its magnitude is
[tex]v=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We are given the following in the question:
Initial point of vector, P(1,0)
The terminal point Q has coordinates in the following format because it is on the y-axis:
Q(0,y)
The magnitude of the vector is [tex]\sqrt{5}[/tex].
Magnitude is given by,
[tex]v=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \sqrt{5} =\sqrt{(0-1)^2+(y-0)^2} \\5=1+y^2\\y^2=4\\y=_-^+2[/tex]
But because the terminal position is higher than the starting point,
y is greater than 0.
Therefore,
y=2
Thus, the terminal point is Q(0,2)
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Prove that if the lengths of two sides of a triangle are a and b, respectively, then
the lengths of the corresponding altitudes to those sides are in the ratio b
Prove of that if the lengths of two sides of a triangle are a and b, respectively, then the lengths of the corresponding altitudes to those sides are in the ratio b.
What is triangle?A triangle is a three by three-sided polygon having three angles and three sides. It is one of the most fundamental and basic shapes in geometry and is used in many other fields of physical science. Triangles are also utilized in architecture and other areas of design and come in a variety of shapes.
Let, a triangle Δ ABC be given, and let its sides be BC = a and AC = b
(figure is given below)
Let, AM and BN are altitudes of corresponding sides of traingle Δ ABC.
We know that the altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.
Notice two right-triangles triangles Δ AMC and Δ BNC
We can conclude that the pairs of congruent angles are:
Δ AMC ≅ Δ BNC ≅ 90°
∠ACM ≅ ∠BCN (common angle)
So, Δ AMC ≈ Δ BNC by the Angle-Angle Similarity Theorem
The triangles are similar and therefore their corresponding angles are congruent:
AM/BN = AC /BC = a/b
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NEED ASAP HELP IS VERY APPRECIATED TY!!!!
what is the rate of change over the interval 15≤x≤18
The rate of change over the interval 15 ≤ x ≤ 18 is equal to 2/3 or 0.67.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function y(x) over the interval [15, 18]:
a = 15; g(a) = 3
b = 18; g(b) = 5
Substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (5 - 3)/(18 - 15)
Average rate of change = 2/3
Average rate of change = 2/3 or 0.67.
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Ja In
2. Erin and Lucia both have coffee shops. The graph below represents how
many cups of tea Erin made and the amount of sugar used. The equation
represents how many cups of tea Lucia made and the amount of sugar used.
Who uses sugar at a faster rate?
Number of Cup
30
24
18
12
6
2
Erin
6 8 10
4
Sugar (pounds)
Lucia
y = 10x
*Suger (pounds)
v is no. of cup
Erin uses sugar at a faster rate than Lucia. This can be seen by comparing the equation for Lucia's cups of tea (y = 10x) to Erin's cups of tea (6, 8, 10, 4).
What is equation ?An equation is a statement that expresses the equality of two values. It consists of an expression containing variables, constants, and operators, and is used to solve mathematical problems. Equations are used to describe the relationships between different variables and can be used to solve for the unknown value of one of those variables. As the number of cups increases, the amount of sugar used by Erin increases at a faster rate than the amount of sugar used by Lucia.
For example, for 6 cups of tea, Erin uses 8 pounds of sugar, while Lucia uses 10 pounds of sugar. For 12 cups of tea, Erin uses 10 pounds of sugar, while Lucia uses 20 pounds of sugar.
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What fraction represents x if 63/120 + x = 1 23/120? Show your steps.
Answer:
[tex]\frac{2}{3}[/tex]
Step by Step Explanation:
Convert any mixed numbers to fractions.
Reduce fractions where possible.
Then your initial equation becomes:
[tex]\frac{143}{120}[/tex] - [tex]\frac{21}{40}[/tex]
Applying the fractions formula for subtraction,
= (140 × 40) - (21 × 120)
120 × 40
= [tex]\frac{5720 - 2520}{4800}[/tex]
= [tex]\frac{3200}{4800}[/tex]
Simplifying [tex]\frac{3200}{4800}[/tex], the answer is [tex]\frac{2}{3}[/tex].
The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. The table below shows the ratios of boxed donuts to the cost. Donuts 2 4 5 C Cost A B 38.00 45.60 Determine which table has the correct values for A, B, and C. Donuts 2 4 5 7 Cost 15.80 30.40 38.00 45.60 Donuts 2 4 5 6 Cost 15.20 27.60 38.00 45.60 Donuts 2 4 5 6 Cost 15.20 30.40 38.00 45.60 Donuts 2 4 5 7 Cost 15.80 31.60 38.00 45.60
Using proportional relationships, it is found that:
1. A = 15.8, B = 5, C = 63.2.
2. A table with a rate of 0.82 represents the data.
3. Candidate B received 54 votes.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, also called unit rate, as follows:
y = kx
here, we have,
For item 1, the constant is given as follows:
k = 31.6/4 = 7.9.
Hence the equation is:
y = 7.9x.
Then the value of A is found as follows:
A = 7.9(2)
= 15.8.
The value of B is found as follows:
7.9B = 39.5
B = 39.5/7.9
B = 5.
The value of C is:
C = 7.9(8) = 63.2.
For item 2, the rate is given as follows:
k = 35/42.5 = 0.82.
Hence a table with a rate of 0.82 represents the data.
For item 3, we have that the relation is:
B = kA.
Hence the constant is:
k = 18/15
k = 1.2.
Then the number of votes received by Candidate B is:
B = 1.2 x 45 = 54 votes.
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Construct one table that includes relative frequencies based on the frequency distributions shown below, then
compare the amounts of tar in nonfiltered and filtered cigarettes. Do the cigarette filters appear to be effective? (Hint:
The filters reduce the amount of tar ingested by the smoker.)
Click the icon to view the frequency distributions.
Complete the relative frequency table below.
Relative
Frequency
(Filtered)
%
%
%
%
%
%
%
Relative
Frequency
Tar (mg) (Nonfiltered)
5-9
%
10-14
%
15-19
%
20-24
%
25-29
%
30-34
%
35-39
%
(Simplify your answers.)
Therefore , the solution of the given problem of relative frequency comes out to be nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.
How does frequency work in Example?A class interval's frequency is the amount of observations that take place during a specific predetermined interval. In other words, the frequency for such 5–9 age range is 20 if there are 20 children between the ages of 5 and 9 in the data from our study.
Here,
Tar(mg) Rel. freq.(Non-filtered) Rel. freq.(filtered)
4 to 9 0 0.12
10 to 15 0 0.08
16 to 21 0.04 0.2
22 to 27 0.08 0.6
28 to 33 0.52 0
34 to 39 0.32 0
40 to 45 0.04 0
and
Yes, since nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.
Therefore , the solution of the given problem of relative frequency comes out to be nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.
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If a represents the number of books that sam has, and g represents the number of books that Gerard has, which inequality models the situation “Sam has more than twice the number of books as Gerard?”
A van moves for two hours with a constant speed of 36 km/h and then for another 1 hour 30 minutes with a constant speed of 84 km/h.
What distance did it go ?
What was the average speed over the whole journey ?
Answer:
56.57 km/h.
Step-by-step explanation:
Distance traveled:
First, we need to convert the time into hours to have the same unit. 1 hour 30 minutes is equivalent to 1.5 hours.
The total time the van traveled is 2 hours + 1.5 hours = 3.5 hours.
The distance traveled during the first 2 hours is 36 km/h * 2 hours = 72 km.
The distance traveled during the next 1.5 hours is 84 km/h * 1.5 hours = 126 km.
The total distance traveled is 72 km + 126 km = 198 km.
Average speed over the whole journey:
The average speed is the total distance traveled divided by the total time traveled.
Average speed = Total distance traveled / Total time traveled = 198 km / 3.5 hours = 56.57 km/h.
Answer:
56.6km/hr
Step-by-step explanation:
2 hours with a speed of 36km/hr is with a distance of (36×2) = 72km
1.5 hours with a speed of 84km/hr = 126km
Total distance = 72+126 = 198km
Average speed = 198/ total time taken = 198/3.5 = 56.6km/hr
In witch equation does x=7
Answer:First, use the positive value of the
±
to find the first solution.
x
=
7
Next, use the negative value of the
±
to find the second solution.
x
=
−
7
The complete solution is the result of both the positive and negative portions of the solution.
x
=
7
,
−
7
Step-by-step explanation: First, use the positive value of the
±
to find the first solution.
x
=
7
Next, use the negative value of the
±
to find the second solution.
x
=
−
7
The complete solution is the result of both the positive and negative portions of the solution.
x
=
7
,
−
7
I need help knowing if this is a function or not
Answer:
yes
Step-by-step explanation:
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
So if you plug in the following values for x & y, you'll get a curve crossing the Y axis at 0,0
-1,-1
-2,-2
-3,-3
0,0
1,1
2,2
3,3
Select ALL of the expressions that represent the verbal phrase. The difference of 12 and 20% of a number
A. 2.4x
B. -0.2x + 12
C. 12-20x
D. 12-0.2x
E. -20x+12
Answer:
e and b!
Step-by-step explanation:
the difference is basically a "-minus"
- meaning it's getting smaller
meaning that it's subtracting from this number so basically 12 - 20% is basically what it means but if you take those altogether it takes out the b and e
basically in your head C&D will also be an answer
is definitely out of your track with the difference between those
could you please crouwn me brainliest?
please help asap i will award brainliest
Answer:
I think the coefficient is 1/3.
Because (x, y) to (1/3x, 1/3y)
Solve for x.
√x+12= √x+2
Answer:
No solution.
Step-by-step explanation:
First, we can simplify both sides of the equation by squaring them. This gives:
(√x+12)² = (√x + 2)²
Expanding both sides, we get:
x + 24√x + 144 = x + 4√x + 4
Moving all the terms to one side, we get:
20√x + 140 = 0
Subtracting 140 from both sides, we get:
20√x = -140
Dividing both sides by 20, we get:
√x = -7
However, this is not a valid solution for x, since the square root of a number cannot be negative. Therefore, there is no solution for x that satisfies the given equation.
If $3000 is invested for 5 years with an interest rate of 10%
per annum, calculate the final balance, rounded to the
nearest cent, if:
Simple interest was used.
Answer:
Step-by-step explanation:
The simple interest can be calculated as follows:
I = P * r * t
Where:
I = interest
P = principal amount (3000)
r = interest rate (0.10)
t = time in years (5)
So,
I = 3000 * 0.10 * 5
I = 1500
The final balance would be:
P + I = 3000 + 1500
P + I = 4500
The final balance, rounded to the nearest cent, is $4500.
how to solve a division problem vertically? For example, 2/3/8/4?
Answer:
Step-by-step explanation:
2:3 / 8/4
firt step you need factorize
2/3 /2
because 8/4 =2;
2/3:2/1
we have formula
2/3*1/2
answer is :2/6 => 2:2/6:2 => 1/3
Ayuda porfa urjenteee de todas las respuestas
The expressions are solved and answered below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the expressions as shown in the image.
{ 1 } -
2[tex]$\frac{5}{6}[/tex] - 2[tex]$\frac{1}{5}[/tex]
17/6 - 11/5
17/6 - (11 x 1.2/5 x 1.2)
17/6 - 13.2/6
3.8/6
38/60
19/30
{ 2 } -
3[tex]$\frac{5}{8}[/tex] + 7/3
29/8 + 7/3
(29 x 3)/(8 x 3) + (7 x 8)/(3 x 8)
87/24 + 56/24
143/24
Similarly the remaining expressions can be evaluated.
Therefore, the expressions are solved and answered above.
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{Question in english -
Please help urgently with all the answers}
can someone help me please
Answer:
9800
Step-by-step explanation:
The median number is the middle term (or the average of the two middle terms, if there are an even number of terms) when sorted in an ascending order.
Sorting in ascending order:
8900, 9600, 9800, 12000, 15500
Hence, 9800 is the mean.
What do I do her help please
Hello :3
Answer:
C. what is m<ACB
Explanation:
Because you found the angles of ABC and BAC which is 35 and 115, it would only be appropriate to find ACB as well! :)
Hope this helps! ;)
Whats the correct answer answer asap for brainlist
Answer:
A) The verb "waddled" most accurately and vividly describes the action in this situation, as "waddle" is a verb used to describe a slow and awkward gait often associated with a heavily pregnant woman. This verb conveys the idea of the woman's awkward and unsteady movement, making it the most accurate and vivid description of her actions.
if (k+2)x+3k=ax+18 if the equation above is true for all real values of x where k and a are constant what is the value of a
The value of a must be equal to (k + 2), and then the equation is only true if k = 6, then a = 8.
What must be the value of a?We want the equation:
(k + 2)x + 3k = ax + 18
To be true for all values of x, then we must have the same thing in both sides of our equation.
Now we wod want the dependence on x to dissapear, then:
(k + 2)x = ax
(k + 2) = a
That must be value of a, and then the equation becomes:
k*x + 2x + 3k = (k+ 2)x + 18
3k = 18
This is only true if k = 6, then:
k + 2 = a
6 + 2 = a
a = 8
That must the value of a.
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1. What are the four key assumptions which are required for multiple linear regression analysis?
2. For each of the four assumptions, please state:
a) the problem they would cause if relaxed/not achieved;
b) the test(s) to identify them;
c) the potential fixes.
the four key assumptions which are required for multiple linear regression analysis are.
What is multiple linear regression?A regression model known as multiple linear regression uses a straight line to calculate the association between two or more independent variables and a quantitative dependent variable.
1.
the four key assumptions which are required for multiple linear regression analysis are:
First, linearity in the connection between the independent and dependent variables is a prerequisite for multiple linear regression. Scatterplots are the finest tool for testing the linearity assumption. The next two examples show a linear relationship (right) and a curved relationship (left) (right).The residuals of the regression, or the errors between observed and projected values, must be regularly distributed in order to perform a multiple linear regression analysis. You may verify this assumption by examining a histogram or a Q-Q-Plot. A goodness of fit tests, such as the Kolmogorov-Smirnov test, can also be used to determine if a distribution is normal, but it must be applied to the residuals themselves.Third, multiple linear regression makes the assumption that the data are not multicollinear. When the correlation between the independent and dependent variables is excessively strong, multicollinearity arises.Homoscedasticity is the final premise of multivariate linear regression. A useful tool for determining homoscedasticity is a scatterplot of the residuals and projected values. The distribution shouldn't reveal any obvious patterns; if it does, the data is heteroscedastic, as seen below by a cone-shaped pattern.A non-linear data transformation or the inclusion of a quadratic factor may be able to solve the issue if the data are heteroscedastic.
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A fully loaded and fueled spacecraft can weigh close to 3.9 million pounds. What is this weight converted to tons?
Answer:
To convert the weight from pounds to tons, we can divide the weight by 2,000, since there are 2,000 pounds in a ton.
3.9 million pounds / 2,000 = 1,950 tons
So, a fully loaded and fueled spacecraft that weighs close to 3.9 million pounds can be said to weigh 1,950 tons.