The staircase would extend 104.3cm farther into the room if the run were made 28cm instead of 23cm.
To find out how much farther into the room the staircase would extend if the run were 28 cm instead of 23 cm, we need to calculate the difference in the run and then multiply it by the number of steps.
The difference in the run is 28cm - 23cm = 5cm
To find the number of steps, we need to divide the total height of the staircase by the height of each step:
4.57m / 0.22m = 20.86 steps.
So the difference in the run multiplied by the number of steps is:
5cm * 20.86 steps = 104.3cm.
Therefore, the staircase would extend 104.3cm farther into the room if the run were made 28cm instead of 23cm.
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work out the area of this shape
Answer:
the answer is 45 cm^2
how many questions are left lol
Will give brainly thanks
The domain of the function is 0≤ x ≤ 30
The range of the function is 0≤ y ≤ 75
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
Here, x represents the input values ( time)
from the graph,
0≤ x ≤ 30
Here, y represents the output values ( amount of water)
from the graph,
0≤ y ≤ 75
Thus, the domain of the function is 0≤ x ≤ 30
The range of the function is 0≤ y ≤ 75
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describe the set of points in space whose coordinates satisfy the given combination of equations and inequalities.
The set of points in space whose coordinates satisfy a given combination of equations and inequalities can be described by a geometric shape or region in 3-dimensional space.
Enumerate the collection of spatial points whose coordinates fulfil the specified set of equations and inequalities.
The equations and inequalities will define the properties of the region, such as its shape, size, and location.
For example, if we have the equation x + y + z = 3 and the inequality x^2 + y^2 <= 1, the set of points that satisfy these conditions would be the points on or inside a sphere of radius 1 centered at the point (0,0,-1) in the x-y plane, and points on the plane x+y+z = 3.
Another example, if we have the equation x + y = 4 and the inequality y >= 2x-5, the set of points that satisfy these conditions would be the points on the line x+y = 4, above or on the line y = 2x-5.
It's important to note that the type of shape or region that is formed by the equations and inequalities will depend on the specific equations and inequalities being used and the number of variables in the problem.
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plssss I really need helpp on thiss, Someone help this is the last question.
The volume of the given solid is 464 cubic inches.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
From the given figure,
We know that, the volume of a cuboid is Length×Width×Height
Volume of two identical cuboid is
2(8×3×7)
= 336 cubic inches
Volume of small cuboid is
8×4×4
= 128 cubic inches
The volume of the solid =336+128
= 464 cubic inches
Therefore, the volume of the given solid is 464 cubic inches.
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Find the area of parallelogram ABJF
Step-by-step explanation:
the area of a parallelogram is
base × height
the graphic shows us that the base (AB) is 3 units long.
and the height (BF) is also 3 units long.
so the area of ABJF is
3 × 3 = 9 units²
What is an example of a absolute value function?
Answer:
f(x) = |x| g(x) = |3x - 7| f(x) = |-x + 9|
a standard deck of cards has $52$ cards divided into $4$ suits, each of which has $13$ cards. two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?a standard deck of cards has $52$ cards divided into $4$ suits, each of which has $13$ cards. two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?
Probability of drawing two red cards = (26/52) * (25/51) = 25/102 = 24.509%
a standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. two of the suits (heart suit and diamond suit, called `hearts' and `diamonds') are red, the other two (spade suit and club suit, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?
A standard deck of 52 cards has 26 red cards ( of Hearts and Diamonds) and 26 black cards ( of Spades and Clubs).
Probability of drawing the first red card = 26/52
Probability of drawing the second red card = 25/51
So, probability of drawing two red cards = (26/52) * (25/51) = 25/102 = 24.509%
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On a coordinate plane, point b(–6, 1) is translated to b prime(–3, –2). indira uses these steps to find a rule to describe the translation. step 1 substitute the original coordinates and the translated coordinates into (x, y) right-arrow (x a, y b): b (negative 6, 1) right-arrow b prime (negative 6 a, 1 b) = b prime (negative 3, negative 2) step 2 write two equations: negative 6 a = negative 2. 1 b = negative 3. step 3 solve each equation: negative 6 a = negative 2. a = negative 2 6. a = 4. 1 b = 3. b = negative 3 minus 1. b = negative 4. step 4 write the translation rule: (x, y) right-arrow (x 4, y minus 4) which corrects indira’s first error? indira should have substituted b (negative 6, 1) right-arrow b prime (negative 3 a, negative 2 b) = b prime (negative 6, 1) in step 1. indira should have written the equations negative 6 a = negative 3 and 1 b = negative 2 in step 2. indira should have solved the equations to find that a = negative 8 and b = negative 2 in step 3. indira should have written the translation rule (x, y) right-arrow (x minus 4, y 4) in step 4.
Indira should have written the equation negative 6 + a = negative 3, and the equation 1 + b = negative 2 in step 2, as according to coordinate geometry.
For translation from point B(-6,1) to point B'(-3,-2);
Step 1 : Substitute the original coordinates and the translated coordinates into (x,y) → (x+a,y+b) ; B (negative 6,1) → B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2)
Step 2 ( Indira's mistake) : Two equations to be written, as in coordinate geometry; first one being negative 6 + a = negative 3 ; and the second one being 1 + b = negative 2
Step 3 : Solving the equations to get the values of a and b;
a = negative 3 + 6
a = 3, and
b = negative 2 minus 1
b = -3
Step 4 : By substitution method, using values of a and b we find B prime;
original coordinates of point B = (-6,1)
Translated coordinates of point B' = (-6 + a, 1 + b)
= ((-6) + 3 , 1 + (-3))
= (-3,-2)
Thus, that is how, step-by-step using basic linear equation method, we solved for translated coordinates.
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On another day, Martin bought 123
5
pounds of grapes for a picnic. His friend bought 3
8
of that amount. Use compatible fractions to estimate how many pounds of grapes Martin’s friend bought.
123
5
→
3
8
→
Martin's friend bought about
pounds of grapes.
The amount of grape that the friend gets will be 4 29/40.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this situation, Martin bought 12 3/5 pounds of grapes for a picnic. His friend bought 3/8 of that amount.
The amount that the friend gets will be:
= 3/8 × 12 3/5
= 3/8 × 63/5
= 189 / 40
= 4 29 / 40
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in a survey of 320 customers, 84 say that service is poor. you select two customers without replacement to get more information on their satisfaction. what is the probability that both say service is poor?
Probability is the branch of mathematics dealing with numerical descriptions of how likely a situation is to occur, or how likely it is that a proposition is true.
An expression for the probability of an event.
Probability of an event = Required number of event / Total number of possible events
Required number of events = 84
Total number of events = 320
Find the probability that both customers selected without replacement say service is poor.
customers say service is poor = 84 / 320
customer selected without saying service is poor= 83 / 319.
The final probability is: 84 ÷ 320 ×83 ÷ 319.
= 6972 ÷ 201080
= 1743 ÷ 25520
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The expession 3p +2f+s isnumber of points earned by a basketball team for p 3 point shots, f 2-point field goals and s 1-foul shots, your oppenent made 8 3-pointers,12 2-point field goals and 11 1-point foul shots you team made 10 3-pointers and 8 2-point field goals what is the mininum number of 1-point foul shots your team must make to win the game?
The minimum number of 1-point foul shots the home team must make to win the game, obtained using inequalities, is 14 shots.
What is an inequality?An inequality is a comparison between expressions that are non equal.
The function for the number of points earned is; 3·p + 2·f + s
Where;
p = 3 point shots
f = 2 point shots
s = 1 point foul shot
The number of 3-point shots by the opponent = 8
Number of 2-point field goals by the opponent = 12
Number of 1-point foul shot by the opponent = 11
The sum of the score of the opponent = 8 × 3 + 12 × 2 + 11 × 1 = 59
Number of 3-pointers by the home team = 10
Number of 2-pointers by the home team = 8
The number of 1-point foul shots, f, the home team must make to win the game can be found using the following inequality;
10 × 3 + 8 × 2 + f × 1 > 59
f > 59 - (10 × 3 + 8 × 2) = 13
f > 13The minimum number of 1-point foul shots the home team must make to win the game is therefore, more than 13 or at least 14
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Scale is 1' =1mm What is the circle's actual diameter
The circle's actual diameter is given as follows:
90 inches.
How to obtain the actual diameter of the circle?The radius of a circle represents the distance between the circle of the center to any point on the circumference of the circle.
The diameter of a circle represents the distance between two points on the circumference of the circle, passing through the center.
Hence the diameter length is twice the radius length.
From the image given at the end of the answer, the radius of the circle is given as follows:
r = 45 mm.
Hence the diameter is given as follows:
d = 2r
d = 90 mm.
The scale is that each mm on the drawing represents one inch of actual distance, hence the actual diameter is given as follows:
90 inches.
Missing Information
The circle is given by the image presented at the end of the answer.
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The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x - 1)
b. y = f(²)
c.
d.
y - 1 = f(x)
²/₁ = f(x)
Answer:
c
Step-by-step explanation:
given f(x) then f(x) + c is a vertical translation of f(x)
• if c > 0 then a shift up of c units
• if c < 0 then a shift down of c units
here the red graph is i unit above the black graph , then c = + 1
and equation is
y = f(x) + 1 ( subtract 1 from both sides )
y - 1 = f(x)
Which graphs represents a function?
Answer:
1 i think 2 if not
Step-by-step explanation:
In the video game Digging Up Dinos, players gain and lose points while digging for dinosaur bones. In Level 1, Emmet earned 14 points for finding the foot bone of a dinosaur. Then, he lost 17 points for accidentally stepping on and breaking the bone.
What was Emmet's score at the end of Level 1?
Based on mathematical operations, Emmet's score at the end of Level 1 of the Digging Up Dinos video game was -3.
What are mathematical operations?The basic mathematical operations include addition, subtraction, division, and multiplication.
These mathematical operations manipulate variables, values, numbers, and constants, including mathematical operands and the equal symbol, to solve mathematical problems.
In this situation, the 17 points Emmet lost are subtracted from the 14 points that he gained to arrive at the final score at Level 1.
The number of points earned in Level 1 = 14
The number of points lost in Level 1 = 17
The net points at the end of Level 1 = -3 (14 - 17)
Thus, the subtraction operation shows that Emmet lost 3 more scores than he gained during Level 1.
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How are 2 graphs related?
A line graph is marked by a correlation in the form of a line. The dependent variable is placed on the y-axis and the independent variable is on the x-axis.
You can see their relationship in terms of the slope. By explanation, the slope is the ratio of the change of the y-coordinates to the change of the x-coordinates (Δy/Δx). Visually, you determine the relationship of the variables by the orientation of the line as shown in the graph. If the slope is increasing, means that the two variables are increasing together.
If the slope is decreasing, it means that when x increases, y decreases. In other words, they are inversely proportional.
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The complete question is:
How are line graphs used to show how two variables are related?
what is the area, in square units, of a regular hexagon inscribed in a circle whose area is $324\pi$ square units? express your answer in simplest radical form.
The area of a regular hexagon inscribed in a circle is equal to two-thirds of the area of the circle. [tex]$324\pi\div 2\div 3[/tex]= [tex]108\pi$ $108\pi \approx 339.292$[/tex] square units The answer in simplest radical form is[tex]$\sqrt{339.292}$[/tex] square units.
it is important to first understand the concept of a regular hexagon inscribed in a circle. A regular hexagon inscribed in a circle is a six-sided polygon whose interior angles are all equal and whose sides are all of equal lengths. This means that the hexagon will have six equal-length sides and six equal-sized angles.
The area of such a hexagon is equal to two-thirds of the area of the circle in which it is inscribed. In this problem, the area of the circle is given as [tex]$324\pi$[/tex] square units. To determine the area of the regular hexagon inscribed in the circle, the area of the circle needs to be divided by two and then by three.
This yields a result of [tex]$108\pi$[/tex] square units, which is approximately equal to 339.292 square units. This result can be written in the simplest radical form as [tex]$\sqrt{339.292}$[/tex] square units, which is the answer to the problem.
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Two positive numbers are in the ratio 3:7. Their difference is 52. What is the sum of the two numbers?
The two positive numbers are 39 and 91 in the ratio 3:7
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Let x and y represent the two positive numbers. x represent the smaller while y is the larger
Two positive numbers are in the ratio 3:7, hence:
(3/10)(x + y) = x
3x + 3y = 10x
7x - 3y = 0 (1)
Their difference is 52, hence:
y - x = 52 (2)
From both equations:
x = 39, y = 91
The two numbers are 39 and 91
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PLEASE HELP ME......
D. No; a rectangle may have diagonals that are not perpendicular.
What are the 7 basic units?
The seven basic SI units are second, meter, kilogram, candela, ampere, mole, kelvin.
The 11th General Conference on Weights and Measures created the International System of Units, or "Système International d'Unités," in 1960. Older systems, like the Imperial system used in the UK and many other countries, were not all that simple to manage or operate, and none were globally standardized. The seven base quantities of what is now known as the International System of Quantities are defined by the International System of Units (SI) as having standard units of measurement. In particular, they comprise a fundamental set from which all other SI units can be formed.
Second (s) – Unit of Time Meter (m) – Unit of LengthKilogram (kg) – Unit of MassAmpere (A) – Unit of Electric CurrentKelvin (K) – Unit of Thermodynamic TemperatureMole (mole) – Unit of Amount of SubstanceCandela (cd) – Unit of Luminous IntensityLearn more about SI units here:
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A hair product company sells three types of hair products for $30, $20, and $10 per unit. In one year, the total revenue for the three products was $1,100,000, which corresponded to the sale of 54,000 units. The company sold half as many units of the $30 product as units of the $20 product. Use RREF to solve a system of linear equations to find how many units of each product were sold. (Let x correspond to the $30 product, y correspond to the $20 product, and z correspond to the $10 product and use RREF to solve.)
x = 14000
y = 28000
z = 12000 units of each product were sold.
Solving this with the help of equation.
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
Let, x, y and z are the three types of products.
In one year, the total revenue for the three products was $1,100,000, which corresponded to the sale of 54,000 units.
Thus, 30x + 20y + 10z = 1,100,000 ............ (i)
x + y + z = 54000 ............... (ii)
The company sold half as many units of the $30 product as units of the $20 product, so, x = y/2
putting this in equation (i)
thus, 30x + 20 (2x) + 10z = 1,100,000
70x + 10z = 1100000 ......... (iii)
next putting the value of y = 2x in equation (ii) we get -
3x + z = 54000......... (iv)
Solve this two equation we get -
40x = 560000
or, x = 14000
now, y = 2x = 28000
z = 54000 - 3(14000)
z = 12000
Now, x = 14000
y = 28000
z = 12000 units of each product were sold.
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The units of each three types of product sold are 14000, 28000, and 12000 using equations.
What is an equation?Algebraic equations simply state the equivalence of two mathematical terms in a mathematical statement. For instance, the equation 6x + 5 = 11 has the two expressions 6x + 5 and 11 separated by the 'equal' sign.
The two forms of equations are identity equations and conditional equations. For just any value of both variables, equality remains true.
Let, x, y and z are the three types of products.
The three items generated a combined $1,100,000 in revenue in a calendar year, which is equal to the sale of 54,000 units.
30x + 20y + 10z = 1,100,000 ............ (i)
x + y + z = 54000 ............... (ii)
The company sold half as many units of the $30 product as units of the $20 product, so, x = y/2
Putting this in equation (i)
Thus, 30x + 20 (2x) + 10z = 1,100,000
70x + 10z = 1100000 ......... (iii)
Next putting the value of y = 2x in equation (ii) we get -
3x + z = 54000......... (iv)
Solve these two equation we get -
40x = 560000
Or, x = 14000
Now, y = 2x
= 28000
z = 54000 - 3(14000)
z = 12000
Now, x = 14000
y = 28000
z = 12000
These units of each product were sold.
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MARKING BRAINLIEST! please help asap, and show your work
Answer:
Line AC is 8
Since the lines are parallel, the angles are the same, and the triangles are equally proportional. The ratio of 12 and 24 is 2, so you multiply 4 by 2 to get 8.
Forgotten how to do this
Explanation to please.
Answer:
2√(13)= 7.21
Step-by-step explanation:
The formula for Pythagoras' theorem is a² + b² = c². In this equation, c is the longest side of a right-angled triangle. This line is also known as the hypotenuse. A and b represent the other two sides of the triangle.
so h = √(6²+4²) = 2√(13)= 7.21 (approximately)
How many 3 1/4 inch pieces of yarn can be
cut from a roll that has 52 inches of yarn?
Answer:
16 peices
Step-by-step explanation:
52/3.25 = 16
Look at picture for question!
Allocating the congressional seats among the states in a fair manner would mean that the seats per state would be:
State A - 13 seats State B - 18 seats State C - 22 seats State D - 37 seats How to allocate the seats ?The fairest way to allocate the seats in a fair manner would be by proportional representation where the population of a state determines the seats it gets in Congress.
State A seats :
= Population / Total population x Number of seats available
= 258 / 1, 858 x 90
= 13 seats
State B seats :
= 377 / 1, 858 x 90
= 18 seats
State C seats :
= 456 / 1, 858 x 90
= 22 seats
State D seats :
= 767 / 1, 858 x 90
= 37 seats
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Que es un transportador?
Answer: it is a transporter or conveyer in english. Used for transporting goods
Step-by-step explanation:
In quadrilateral ABCD, the diagonals intersect at point T. Jasmine has used the Alternate Interior Angles Theorem to show that angle DAC is congruent to angle BCA and that angle ADB is congruent to angle CBD. Which of the following can Jasmine use to prove that triangle ATD is congruent to triangle CTB
This question is based on the concept of congruent. Therefore, the correct option is C, i.e. DA ≅ BC.
What is quadrilateral?A quadrilateral is a closed form that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The total of quadrilateral inner angles is always 360 degrees. A quadrilateral is a closed shape with four sides. These are quadrilateral figures: Raphael was used to create this. A quadrilateral form. The form contains only one pair of parallel sides and no right angles. A quadrilateral has four straight sides and is a two-dimensional form. Examples of quadrilaterals include parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
Here,
Given:
In quadrilateral ABCD, the diagonals intersect at point T.
By the alternate interior angles theorem :
Angle DAC is congruent to angle BCA and
angle ADB is congruent to angle CBD
Definition of alternate interior angles theorem:
The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , then resulting alternate interior angles are congruent .
In given quadrilateral ABCD,
DAC ≅ BCA
ADB ≅ CBD
And to prove that ATD ≅ CTB,
Then,
DA ≅ BC
Therefore, the correct option is C, i.e. DA ≅ BC.
The idea of congruence lies at the heart of this question. As a result, the right answer is C, which is DA ≅ BC.
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This question is based on the concept of congruent. Therefore, the correct option is C, i.e. DA ≅ BC.
What is quadrilateral?A quadrilateral is a closed form that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The total of quadrilateral inner angles is always 360 degrees. A quadrilateral is a closed shape with four sides. These are quadrilateral figures: Raphael was used to create this. A quadrilateral form. The form contains only one pair of parallel sides and no right angles. A quadrilateral has four straight sides and is a two-dimensional form. Examples of quadrilaterals include parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
Here,
Given:
In quadrilateral ABCD, the diagonals intersect at point T.
By the alternate interior angles theorem :
Angle DAC is congruent to angle BCA and
angle ADB is congruent to angle CBD
Definition of alternate interior angles theorem:
The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , then resulting alternate interior angles are congruent .
In given quadrilateral ABCD,
DAC ≅ BCA
ADB ≅ CBD
And to prove that ATD ≅ CTB,
Then,
DA ≅ BC
Therefore, the correct option is C, i.e. DA ≅ BC.
The idea of congruence lies at the heart of this question. As a result, the right answer is C, which is DA ≅ BC.
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Bianca took out a $2,600 unsubsidized stafford loan. she will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. the loan has an interest rate of 6.2%, compounded monthly. how much will she have to pay monthly to avoid interest capitalization? a. $12.40 b. $19.29 c. $13.43 d. $17.36 please select the best answer from the choices provided a b c d
The total monthly payment would be $17.36.
Option (d) is correct.
What is the annuity payment?
An annuity payment is a fixed, regular payment made to an individual or organization over a specific period of time. It is typically used in the context of financial transactions, such as loans, investments, and insurance.
To calculate the monthly payment Bianca will have to make to avoid interest capitalization, we can use the formula for the annuity payment:
PMT = (Loan Amount * Interest Rate / (1 - (1 + Interest Rate)^(-n))) / (Interest Rate / 12)
Where:
PMT is the monthly payment
Loan Amount is the amount of the loan, in this case, $2,600
Interest Rate is the annual interest rate, in this case, 6.2%
n is the total number of payments, in this case, 5 years * 12 months/year = 60 months
Plugging in the values, we get:
PMT = (2600 * 0.062 / (1 - (1 + 0.062)^(-60))) / (0.062 / 12)
PMT = $17.36
Hence, the total monthly payment would be $17.36
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Answer: C
Step-by-step explanation:Bianca took out a $2,600 unsubsidized Stafford loan. She will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. The loan has an interest rate of 6.2%, compounded monthly. How much will she have to pay monthly to avoid interest capitalization?
a.
$12.40
b.
$19.29
c.
$13.43
d.
$17.36
Please select the best answer from the choices provided
All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration. Data from the FHWA inspections are compiled into the National Bridge Inventory (NBI). Several of the nearly 100 variables maintained by the NBI are listed below. Classify each variable as quantitative or qualitative.'
Therefore, the supplied variable problem's solution is found to be quantitative.
Variable : What is it ?A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.
Here,
Quantitative variables are numerical variables, whereas categorical/qualitative variables assign the people into a category.
Because the length is quantified by numbers, it is (a) quantitative (such as 200 ft).
So , by observing the following information we can conclude that it is quantitative.
As a result, it is quantitative.
Therefore, the supplied variable problem's solution is found to be quantitative.
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The complete question is " All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration (FHWA). Data from the FHWA inspections are compiled into the National Bridge Inventory (NBI). Several of the nearly 100 variables maintained by the NBI are listed below. Classify and explain each variable as a) quantitative or qualitative; b) discrete or continuous; and c) by level of measurement. (10 points)
Route type (interstate, U.S., state, county, or city)
Length of maximum span (feet)
Number of vehicle lanes
Bypass or detour length (miles)
Condition of deck (good, fair, or poor)
Average daily traffic
Toll bridge (yes or no)"
a system of 5 identical components are connected in a series. if even one of the components fails, the entire system will fail. what is the probability that the system fails if the probability that each component fails is 0.1 and different components fail independently of one another.
So the probability that the system fails is 41% if the probability that each component fails is 0.1 and different components fail independently of one another.
The probability that the system fails is the probability that even one of the 5 components fails. Since the components fail independently of one another, we can use the probability of failure for each component and multiply it by the number of components to find the probability that the system fails.
The probability that the system fails is:
1 - (1 - probability of failure of one component)^(number of components)
Given that the probability of failure of each component is 0.1, the probability that the system fails would be:
1 - (1 - 0.1)^5 = 1 - 0.59 = 0.41 or 41%
So the probability that the system fails is 41% if the probability that each component fails is 0.1 and different components fail independently of one another.
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