The quadratic equation we use to find the dimensions of the rectangle is w^2 + 6w - 16 = 0
What is Quadratic equation?
The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax^2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients.
What is Rectangle?
A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.
Let W be the width of rectangle.
then, length of the rectangle is W + 6 .
and the Area, A = 16 inches^2
And the area of recatngle is A = L x W
Hence, A = (W+6)W
So, 16 = W^2 + 6W
Hence the quadratic equation whichuse to find the dimensions of the rectangle is ;
W^2 + 6W - 16 = 0
By the quadratic formula we have
[tex]w = \frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]w = \frac{-6 \pm \sqrt{6^{2}-4*1*(-16) } }{2*1}[/tex]
[tex]w = \frac{-6 \pm \sqrt{36 + 64} }{2}[/tex]
[tex]w = \frac{-6 \pm 10 }{2}[/tex]'
Hence, we take width as a positive because width never be negative .
so,the value of width is ;
w = 2
and length o rectangle is ;
l = w + 6 = 2 + 6 = 8
l = 8
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3.
Which is cheaper: 115 plums for $276.00 at Shop ZYX or 198 plums for $633.60 at Shop PWR?
3a What is the cost of a single plum at Shop ZYX?
3b
3c
Enter your next step here
() ba
dollars
The cheaper plan is given as follows:
Shop ZYX.
The cost of a single plum at Shop ZYX is given as follows:
$2.4.
How to obtain the cheaper plan?To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.
The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.
Hence the cost per plum in each shop is given as follows:
Shop ZYX: 276/115 = $2.4.Shop PWR: 633.6/198 = $3.2.More can be learned about proportions at https://brainly.com/question/24372153
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Please help with the question below
The area of the given image design is; 15 in²
How to find the area of a triangle?The formula to find the area of a triangle is;
Area = ¹/₂(base * height)
Let us divide the image into two triangles and as such;
Area of biggest triangle = ¹/₂(14 * 15)
= 85 in²
We will now deduct the rectangle that was removed by finding its' area to get;
Area of rectangle = length * width
= 10 * 7 = 70 in²
Thus;
Area of image = 85 - 70
Area of image = 15 in²
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Of the 6 vacant positions to be filled at a company, 3 must be given to men, 2 to woren and can be ether gender. In how many ways can these different positions be filled given that 5 men and o women have applied for these positions?
There are a total of 6 vacant positions to be filled at a company, with 3 of those positions being given to men, 2 to women and 1 being either gender.
How many ways can these different positions be filled given that 5 men and o women have applied for these positions?Given that there are 5 men and 0 women who have applied for these positions, there are a total of 150 ways to fill the 6 positions.Firstly, the 3 positions that must be given to men can be filled in a total of 5 ways, as there are 5 men applying for those positions.Secondly, the 2 positions that must be given to women cannot be filled in this instance, as there are no women applicants for these roles.Finally, the position that must be given to either gender can be filled by any of the 5 men who have applied. This can be done in a total of 5 ways.Combining these three scenarios, the total number of ways to fill the 6 positions is 5 x 5 x 1, or 5 x 5, which is equal to 150.In conclusion, there are a total of 150 different ways to fill the 6 vacant positions at the company, given that 5 men and 0 women have applied for the positions.To learn more about the gender-neutral position refer to:
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Work out the value of g in the following equation:
g sin 34° =3.5
The value of g in the following equation is 6.25. The solution has been obtained using trigonometry formula.
What is trigonometry?
The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. Therefore, applying the trigonometric formulas, functions, or trigonometric identities aids in locating the unknown or missing angles or sides of a right triangle. In trigonometry, angles can be stated in either degrees or radians. For calculations, the most common trigonometric angles are 0, 30, 45, 60, and 90 degrees.
We are given g sin 34° =3.5
⇒ g = 3.5/sin34° (Dividing both sides by sin34°)
Now, value of sin34° = sin(30+4)° = 0.5592
So, we get
⇒ g = 3.5/0.5592
⇒ g = 6.25
Hence, the value of g in the following equation is 6.25.
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In the equation below, g has a value of 6.25. The trigonometric formula has been used to arrive at the solution.
What is a triangle?The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulae, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in computations are 0, 30, 45, 60, and 90 degrees.
Given is g sin 34° = 3.5.
g = 3.5/sin34° (both sides divided by sin34°)
The cost of sin today
34° = sin(30+4)° = 0.5592
So, we obtain
⇒ g = 3.5/0.5592
⇒ g = 6.26
Thus, the importance of g in the following equation is 6.26.
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A new car is purchased for $23,000 and over time its value depreciates by one half every 3 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $7,800 (25 PTS)
It take for the value of the car is 4.7 years.
Now, According to the question:
A new car is purchased for $23,000
and, over time its value depreciates by one half every 3 years.
It take for the value of the car to be $7,800.
According to the statement :
The equation will be :
y = 23,000 × [tex](\frac{1}{2} )^n[/tex]
7,800 = 23,000 × [tex](\frac{1}{2} )^n[/tex]
By simplification, we get:
n = 1.56
Over time its value depreciates by one half every 3 years.
So, 1.56 × 3 = 4.68 ≈ 4.7 years.
Hence, It take for the value of the car is 4.7 years.
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Choose all the multiplication sentences that have 5/6 as the missing part
PLEASE ANSWER ASP
If the value be 5/6 then the equation be [tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex].
What is meant by fraction?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
A fraction is a piece of a whole number and a means to divide a number into pieces that are each equal. The numerator, also known as the number of equal parts being counted, is expressed as being greater than the denominator, also known as the number of parts in the entire.
Let the value be 5/6 then
simplifying the equation as
[tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex]
Multiply both sides by 3
[tex]$3 x \frac{2}{3}=\frac{5 \cdot 3}{9}$$[/tex]
Simplifying the above equation, we get
2x = 5/3
Divide both sides by 2, we get
[tex]$\frac{2 x}{2}=\frac{\frac{5}{3}}{2}$$[/tex]
x = 5/6
Therefore, the correct answer is option a.
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evaluate (8+t power of 3)-6
Answer:
t³+2Step-by-step explanation:
(8+t³)-68+ t³-6t³ +(8 - 6)t³+2- Hope this helps!
A ring is now reduced to 840 this is saving 40%of the original price .work out the original price of the ring
Answer: 1400
Step-by-step explanation: If it is saving 40% of the original price than it is 60% of the original price. 840=60/100*x, and so we divide both sides by 60/100. 840*100/60=1400. Therefore, 1400 is the original price.
Here are ingredients from recipes for two different banana cakes.
First recipe is in the table shown.
Second recipe is shown in the relationship cups of flour y and cups of sugar x in the second recipe is y=7/4x.
1.if you used 4 cups of sugar, how much flour does each recipe need? Type your answer in the boxes below.
2. What is the constant of proportionality for each situation and what does it mean?
1. The amounts of flour, considering 4 cups of sugar for each recipe, are given as follows:
First recipe: 6 cups.Second recipe: 7 cups.2. The constant for each recipe is given as follows:
First recipe: 3/2, meaning that for each cup of sugar, 3/2 cups of flour are needed.Second recipe: 7/4, meaning that for each cup of sugar, 7/4 cups of flour are needed.How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input x: amount of sugar.Input y: amount of flour.From the table, the constant is given as follows:
k = (3/4)/(1/2)
k = 3/2.
Meaning that for each cup of sugar, 3/2 cups of flour are needed.
Hence the relation is:
y = 3x/2.
The amounts of flour, considering 4 cups of sugar for each recipe, are obtained as follows:
First recipe: 3 x 4/2 = 6 cups.Second recipe: 7 x 4 / 4 = 7 cups.More can be learned about proportional relationships at brainly.com/question/10424180
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Figure 2 is a scale image of Figure 1, as shown below.
What is the scale factor applied to Figure 1 to produce Figure 2?
A.
The scale factor is equivalent to {k} = 4/3.
What is scale factor?Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically - {K} = y/x = constantScale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities.Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.In case of length scaling, we can write -{K} = L{final}/L{initial}
Given is that figure 2 is a scale image of figure 1.
We can write the scale factor as -
K = {y}/{x} = 8/6 = 4/3
Therefore, the scale factor that is applied to figure {1} to get figure {2} is equivalent to {k} = 4/3.
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The veterinarian orders 15 mg of Vitamin K. The vial is labeled 10mg/mL how many mL is needed?
please explain how to do it
Each ml of the vial contains 10 mg of Vitamin K. So to obtain 15 mg of Vitamin K, we needs a volume 1.5 ml of the solution.
We can calculate the required amount in two ways. We can use either proportions, or we can use the unit value determination.
By using proportions.In 1 ml we have 10mg , to get 15 mg we can use x ml
[tex]\frac{1}{10} = \frac{x}{15}[/tex]
[tex]x = \frac{15* 1}{10}[/tex]
x = 1.5
So, to get 15 mg of Vitamin K, we need 1.5 ml of solution.
By finding the unit valueVolume required to get 10 mg of vitamin K = 1 ml
Volume required to get 1 mg of vitamin K = [tex]\frac{1}{10}[/tex] ml = 0.1 ml
Volume required to get 15 mg of Vitamin K = 15 × 0.1 = 1.5 ml
So volume required to get 15mg = 1.5 ml
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people with type o-negative blood are universal donors. that is, any patient can receive a transfusion of o-negative blood. only 7.2% of the american population have o-negative blood. if we choose 10 americans at random who pg 327 pg 329 gave blood, what is the probability that at least 1 of them is a universal donor?
The probability that at least one of 10 randomly chosen Americans has O-negative blood is 0.722.
The probability that at least one of 10 randomly chosen Americans has O-negative blood can be calculated by first determining the probability that none of them have O-negative type blood. Since 7.2% of the population has O-negative blood, the probability that one of 10 randomly chosen Americans has O-negative blood is (1 - 0.072)^10. To determine the probability that at least one of 10 randomly chosen Americans has O-negative blood, we subtract this value from 1. Therefore, the probability that at least one of 10 randomly chosen Americans has O-negative blood is 1 - (1 - 0.072)^10, which is equal to 0.722.
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A kettle holds
4
44 liters of magic potion. There are
11
1111 liters of potion.
About how many kettles can we fill with magic potion?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Between
0
00 and
1
11 kettles
(Choice B)
B
Between
1
11 and
2
22 kettles
(Choice C, Checked)
C
Between
2
22 and
3
33 kettles
Which equation tells us exactly how many kettles we can fill?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
11
÷
4
=
4
11
11÷4=
11
4
11, divided by, 4, equals, start fraction, 4, divided by, 11, end fraction
(Choice B)
B
4
÷
11
=
4
11
4÷11=
11
4
4, divided by, 11, equals, start fraction, 4, divided by, 11, end fraction
(Choice C)
C
11
÷
4
=
11
4
11÷4=
4
11
The correct option regarding the number of kettles that can be filled with the potion is given as follows:
C. Between 2 and 3.
How to obtain the number of kettles?The number of kettles is obtained applying the proportions in this problem, dividing the total number of litters by the number of liters of each kettle.
The parameters for this problem are given as follows:
Total of 11 liters.Capacity of 4 liters per kettle.Hence the number of kettles is obtained as follows:
11/4 = 2.75.
Meaning that the correct option is given by option C.
Missing InformationA kettle holds 4 liters of magic potion. There are 11 liters of potion.
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what is the distance from y to wx
Step-by-step explanation:
this distance YZ is the height of the triangle WXY.
it splits the main triangle into 2 right-angled triangles WYZ and XYZ.
we can use Pythagoras
c² = a² + b²
with any of the 2 smaller right-angled triangles to get YZ.
remember, "c" is the Hypotenuse (the side opposite to the 90° angle). a and b are the legs.
so, when picking the larger one :
26² = 24² + YZ²
676 = 576 + YZ²
100 = YZ²
YZ = sqrt(100) = 10 = distance of Y to WX.
1) b^2 -4=0
2)2x^2 =21+11x
3)5x^2 =3x+92
Answer:
1. b1=-2, b2=2
2. x1= -3/2, x2=7
3. x1=-4, x2= 23/5
Follow formula
b = -b [+][-] sq| b^2-4ac/ 2a
what is the shift
y = log(x+4) -3
The shift of the function y = log(x+4) -3 is 4 units left and 3 units down
How to determine the shiftFrom the question, we have the following parameters that can be used in our computation:
y = log(x + 4)
The above equation is a logarithmic equation
So, the parent function is
y = log(x)
When the parent function is compared to the given function, we have
3 units down and 4 units left
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If the trend continued, about how many cds were sold in 2019?
If the trend continued, the number of CDs that were sold in 2019 is approximately equal to: D. 2,000.
How to determine the line of best fit?In order to write a linear function that models the data point contained in the table and determine the slope, we would have to use the point-slope form to determine the line of best fit based on the data points provided on the scatter plot (see attachment).
Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
y represents the number of CDs.x represents the number of years.m represents the slope.y - 800 = (700 - 800)/(2005 - 2002)(x - 2002)
y = 33.33(x - 2002) + 800
y = 33.33x - 65,266
When x = 2019, the number of CDs sold is given by:
y = 33.33(2019) - 65,266
y = 2,027 ≈ 2,000 million CDs.
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Complete Question:
The scatter plot shows a number of CD's (in millions) that were sold from 1999 to 2005. If the trend continued, about how many CDs were sold in 2019?
A. 3000
B. 8500
C.3500
D. 2,000
Deshaun must choose a number between 49 and 95 that is a multiple of 4, 7 , and 14 . Write all the numbers that he could choose. If there is more than one number, separate them with commas.
Answer: To find the numbers that Deshaun could choose, we need to find the least common multiple (LCM) of 4, 7, and 14. The LCM is the smallest number that is a multiple of all the given numbers.
We can find the LCM using the prime factorization method:
4 = 2^2
7 = 7
14 = 2 * 7
The least common multiple of 4, 7, and 14 is 2^2 * 7 = 28
So, the numbers Deshaun could choose are multiples of 28, which means they must be in the form of 28n, where n is a positive integer.
The numbers between 49 and 95 that are multiples of 28 are: 56, 84
So the numbers that Deshaun could choose are 56, 84.
Step-by-step explanation:
Colton puts geapes in plastic bags to sell at the farmer's market. He weighs each bag and records the weights in a line plot. What is the difference between the lightest bag of grapes?
The difference between the lightest bag of grapes that has been recorded by Colton will be 3/2 or 1 - 1/2.
[tex]2 - \frac{1}{2} [/tex]
[tex] = \frac{4}{2} - \frac{1}{2} [/tex]
[tex] = \frac{3}{2} or \: 1 - \frac{1}{2} [/tex]
Data gathering, analysis, interpretation, presentation, and organization are all topics covered in the study of statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics can be considered a subfield of applied mathematics.
Uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can be used to determine the uncertainty and variation in various fields. Probability, which has a significant impact on statistics, essentially determines these uncertainties.
Note that the graph for the following question is: (check the attached image).
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Find P(blue and odd).
The probability of getting blue and an odd number will be 1/10.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The probability of getting blue is 2/10 and the probability of getting odd number is 5/10.
Therefore, the probability of getting blue and an odd number will be:
= 2/10 × 5/10
= 1/10.
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alfred and bonnie play a game in which they take turns tossing a fair coin. the winner of a game is the first person to obtain a head. alfred and bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. suppose that alfred goes first in the first game, and that the probability that he wins the sixth game is m n , where m and n are relatively prime positive integers. what are the last three digits of m n ? (1993,
So, the last three digits of m*n is 001.
Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.
Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:
p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2
Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.
Therefore, the last three digits of m*n is 001.
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4 of 54 of 5 Items
13:00
Skip to resources
Question
The two lines graphed on the coordinate grid each represent an equation.
Which ordered pair represents a solution to both equations?
Responses
A (2, 2)(2, 2)
B no solution solution
C (2, 1)(2, 1)
D (1, 2)
Answer:
Step-by-step explanation:
in every there w234e
Triangle BCD has vertices B(-8,3), C(-4, 6), and D(2, 0). If the triangle is reflected across the x-axis and dilated by a scale factor of 0. 5 with respect to the origin, what are the coordinates of the vertices of triangle B"C"D"?
If the vertices of the triangle BCD with vertices B(-8,3), C(-4, 6), and D(2, 0) , and if they are reflected across x axis and dilated by a scale factor of 0.5 then the coordinates of B"C"D" are B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) .
If the point (x,y) is reflected across the x axis , then the reflected points are (x,-y) .
the vertices of the triangle BCD are : B(-8,3), C(-4, 6), and D(2, 0) ;
So , the reflected vertices are : B'(-8,-3) , C'(-4,-6) and D'(2,0) ;
if the point (x,y) is dilated by a scale factor of "k" , then the dilated vertices are written as : (kx , ky) .
the dilation factors is = 0.5 ;
So , the vertices B'(-8,-3) , C'(-4,-6) and D'(2,0) after dilation will be written as :
⇒ B''(-8×0.5 , -3×0.5) , C"(-4×0.5 , 6×0.5) and D"(2×0.5 , 0) ;
After simplifying further ,
we have ;
⇒ B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) ;
Therefore , the coordinates of the triangle B"C"D" are B''(-4,-1.5) , C"(-2,3) and D"(1,0) .
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(n^3+3n^2-15n+19)/(n-2) Synthetic Division
The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.
What is synthetic division?
Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."
We are given the expression as (n^3+3n^2-15n+19)
The expression is to be divided by (n-2)
So, by using the synthetic division, we get
2 | 1 3 -15 19
- 2 10 -10
1 5 -5 9
Quotient = n^2+5n-5
Remainder = 9
Hence, the quotient is n^2+5n-5 and the remainder is 9.
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angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
solve an equation to determine the measure of angle x.
Applying the sum of angles on a straight line, we have:
Equation = x + 70 + 60 = 180
Measure of x = 50°.
What is angle ?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.
A straight line angle equals 180 degrees.
Therefore, the sum of all the angles on a straight line = 180 degrees.
Thus, the equation to solve for x would be:
x + 70 + 60 = 180
Solving for x
x + 130 = 180
x = 180 - 130
x = 50°
Hence, 50° is the measure of angle x.
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Ben is considering purchasing a new home. His banker has presented a 10-year mortgage at a fixed rate of 7.6%. The cost of the home is $196000 and Ben will be required to provide a 25% down
payment. If we use Sheets to determine his monthly payment, which of the following Sheets commands could be used to determine his payment? (Choose all that apply!)
-PMT(0.076/12,120,-147000)
PMT(0.076/12,10 12,-$147000)
PMT(7.6,10,-196000)
PMT (7.6% / 12,12 10,-147000)
PMT(7.6/12,12 10,-147000)
-PMT(0.076/12,120,-196000+49000)
Answer: The PMT function in Sheets is used to calculate the monthly payment for a loan. The syntax of the function is PMT(rate, nper, pv, [fv], [type]).
Rate: the interest rate per period
Nper: the total number of payments
Pv: the present value (the total amount of the loan)
Fv: the future value of the loan (optional)
Type: the number 0 or 1 indicating when payments are due (0 = end of period, 1 = beginning of period)
Given the information in the problem, Ben's mortgage is for 10 years, so the total number of payments is 10*12 = 120. The present value of the loan is $196000 and the down payment is 25% of the home's cost so 25%*196000 = $49000. Therefore, the present value of the loan is $196000 - $49000 = $147000
Based on this information, the following commands would be used to determine the monthly payment:
PMT(0.076/12,120,-$147000)
PMT(0.076/12,120,-196000+$49000)
The first command uses the annual interest rate divided by 12 to convert it to a monthly rate, and the total number of payments is 120 (10 years * 12 months/year). The second command also uses the same monthly rate and total payments and the present value which is $147000
The other commands
Step-by-step explanation:
The surface area of a cylinder is 28π m². The distance around the base of the cylinder is 7π meters and the diameter of a base of the cylinder is 4 meters.
What is the height of the cylinder?
Enter your answer, as a simplified fraction, in the box.
m
Answer:
5
Step-by-step explanation:
diameter = 4 so radius =2
open up the cylinder so its top & bottom circle's circumference = 2πr =4π
top & bottom circle's area = πr² = 4π each, 8π for both
total surface = 28π
so lateral surface = 28π - 8π = 20π
so 20π = 4π* height
so height is 5
The table shows the number of laps jogged by Cameron last weekend. Day Number of Laps Saturday 21 Sunday 16.5 What was the percent of decrease in the number of laps jogged from Saturday to Sunday? Round the percent to the nearest tenth if necessary.
Answer: To find the percent of the decrease in the number of laps jogged from Saturday to Sunday, we can use the following formula:
percent decrease = (change in value / original value) x 100
In this case, the original value is the number of laps jogged on Saturday, which is 21 laps. The change in value is the difference in the number of laps jogged from Saturday to Sunday, which is 21 - 16.5 = 4.5 laps.
So, substituting these values into the formula:
percent decrease = (4.5 / 21) x 100
percent decrease = 0.214 x 100
percent decrease = 21.4%
Rounded to the nearest tenth, the percent of decrease in the number of laps jogged from Saturday to Sunday is 21.4%.
Step-by-step explanation:
Arthur is purchasing ingredients to prepare hotdogs for his school's food fair.
Hotdog buns come in packs of 6 while the sausages come in packs of 10.
What is the least number of packs of each item he should buy to get an equal number of buns
and sausages?
Step-by-step explanation:
To have an equal number of buns and sausages, Arthur needs to find the least common multiple (LCM) of 6 and 10.
The LCM of 6 and 10 is 30.
Therefore, he should buy at least 30 packs of buns and 30 packs of sausages to get an equal number of buns and sausages.
That way, he would have 30/6 = 5 packs of buns and 30/10 = 3 packs of sausages.
Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply
The quadratic equation 4 · x² - 7 · x = 3 · x + 24 has the following roots: x₁ = 19 / 4 and x₂ = - 9 / 4.
How to solve a quadratic equation
In this question we find the case of a quadratic equation, whose form is defined below:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficientsx - Independent variabley - Dependent variableThe procedure find the solutions to the quadratic equations:
Modify the polynomial into standard form.Complete the square.Simplify part of the expression into a perfect binomial.Clear the variable x by algebra properties.Now we proceed to determine the solutions to the quadratic equation:
4 · x² - 7 · x = 3 · x + 24
4 · x² - 10 · x - 24 = 0
4 · [x² - (5 / 2) · x - 6] = 0
4 · [x² - (5 / 2) · x + 25 / 4] = 4 · 6 + 4 · (25 / 4)
4 · (x - 5 / 4)² = 49
(x - 5 / 4)² = 49 / 4
x - 5 / 4 = ± 7 / 2
x = 5 / 4 ± 7 / 2
The solutions to the quadratic equation 4 · x² - 7 · x = 3 · x + 24 are x₁ = 19 / 4 and x₂ = - 9 / 4.
To learn more on quadratic equations: https://brainly.com/question/29269455
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