Therefore , the solution of the given problem of triangle comes out to be BZ = (8/9) * BC = 40/9 as a result.
Exactly what is a triangle?Due to its two or more extra sections, a trapezoid is a polygon. Its shape is a simple rectangle. Only the three edges A, B, but instead C distinguish a triangle from a regular triangle. Euclidean geometry produces a singular area rather than a cube when the borders are not perfectly collinear. Triangular shapes are defined as having three sides and three angles. Angles are formed by the meeting of a quadrilateral's 3 sides.
Here,
Let D represent the intersection of the angle bisector BY and the side AC, and let E represent the intersection of the angle bisector CZ and the side AB.
=>BC² = AB² + AC² - 2AB * AC * cos(BAC)
However, since BY and CZ are angle bisectors, we can calculate BAC as follows:
=> BC² = 8² + 9² - 2(8)(9)cos[(180° - (ABC + ACB))/2]
If we simplify, we get:
=> BC² = 145 - 144cos[(ABC + ACB)/2]
Using the angle bisector theory once more, we have the following:
=> AD/DC = 8/BC
=> DC = BC(AD/8)
Simplifying and substituting into the Law of Cosines equation yields:
=> BC² = 145 - 144cos[(ABC + ACB)/2]
=> 145 - 144cos[(180° - BAC)/2]
=> 145 - 144cos(B/2)
in which B Equals ABC.
We can now replace the value of BZ that we discovered earlier with:
=> BZ = (8/9) * BC
and solve for BC:
=> BC² = 145 - 144cos(B/2)
=> (9/8)² * (145 - 144cos(B/2)) + (8/9)² * BZ²
Simplifying and substituting BZ results in:
BC² = 25
Since BC is a length, we obtain: by taking the positive square root.
=> BC = 5
=> BZ = (8/9) * BC = 40/9 as a result.
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Benny purchased $400,000 of Peach Corporation face value bonds for $320,000 on November 13, 2020. The bonds had been issued with $80,000 of original issue discount (OID), because Peach was in financial difficulty in 2020. On December 3, 2021, Benny sold the bonds for $283,000 after amortizing $1,000 of the original issue discount.
What are the nature and amount of Benny's gain or loss?
Benny has a $fill in the blank 1
long-term capital loss
from the sale of the bonds.
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Colin's mom had a long day at work. "I feel like I drank 3 gallons of coffee today!" she joked. If she really drank that much coffee, how many times would she have filled her 12-fluid-ounce mug?
If Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.
What is multiplication ?
Multiplication is a mathematical operation that involves combining groups of equal sizes to find a total quantity. It is represented by the symbol "×" or "⋅" and involves two or more factors. The result of a multiplication operation is called the product.
1 gallon is equal to 128 fluid ounces, so 3 gallons is equal to 3 x 128 = 384 fluid ounces.
To find out how many times Colin's mom would have filled her 12-fluid-ounce mug, we divide the total amount of coffee by the size of the mug:
384 fluid ounces ÷ 12 fluid ounces/mug = 32 mugs
Therefore, if Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.
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Wesley is a member of the
kennel club in his area. His club uses
accordion fencing like the section shown
at the right to block out areas at dog
shows.
a. Identify two pairs of congruent
segments.
b. Identify two pairs of supplementary
angles.
The two pairs of congruent segments are PS = QR and PQ = SR
The two pairs of supplementary angles are P and Q; and S and R.
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:
A + B = 180 degrees
For example, if angle A is 60 degrees, then its supplementary angle would be angle B, which is 120 degrees, because:
A + B = 60 + 120 = 180 degrees
Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and lines. For instance, if two lines intersect, the opposite angles formed are always supplementary.
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I need help with this immediately
The digits in the hundreds place is 2.
The digits in the hundredths place is 9.
The digits in the ten thousandths place is 1.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsTen thousandthsHundred thousandthsMillionths.UnitTensHundredsThousands.Tens of thousands.Based on the numerical data (number) provided above 248.7961, we can reasonably infer and logically deduce that the place value of one (1) is ten thousandths, nine (9) is hundredths, and two (2) represent hundreds.
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The weight of Amara to the weight of toyin is 3:5, if Amara weighs 30 kg , how many more does Toyin weight?
What is the surface area of the rectangular prism formed by the pattern below?
Answers -
56 cm
108
136
162
Answer:
C. 136
Step-by-step explanation:
Add up the surface areas of each individual section. Area is length times width.
Lets start by figuring out the area of the 2 by 6 rectangle on the bottom. 2cm*6cm=12 sq cm. The rectangle on the top right also has an area of 2cm*6cm. So it also has an area of 12 sq cm. lets figure out the area of the smaller rectangle on the right side. 7cm times 2 cm equals 14 cm squared. There is also a 7cm by 2cm box in the middle of the pattern. so 14 + 14 = 28, + 12 + 12= 52. so all of the tiny rectangles added up equal 52. Finally, lets figure out the area of the two 6*7 rectangles. 6*7= 42. 42*2= 84. 84 is the area of the two big rectangles added together. So add the two totals to get 52 sq cm+ 84 sq. cm = 136 sq. cm.
Find the value of p in this proportion show work below answer here P=
The value οf p that satisfies the prοpοrtiοn is 16.
What is a prοpοrtiοn in math?Prοpοrtiοn is explained majοrly based οn ratiο and fractiοns. A fractiοn, represented in the fοrm οf a/b, while ratiο a:b, then a prοpοrtiοn states that twο ratiοs are equal. Here, a and b are any twο integers. The ratiο and prοpοrtiοn are key fοundatiοns tο understand the variοus cοncepts in mathematics as well as in science.
Prοpοrtiοn finds applicatiοn in sοlving many daily life prοblems such as in business while dealing with transactiοns οr while cοοking, etc. It establishes a relatiοn between twο οr mοre quantities and thus helps in their cοmparisοn.
Tο sοlve fοr p in the prοpοrtiοn:
10/p = 5/8
We can crοss-multiply tο οbtain:
5p = 80
Dividing bοth sides by 5, we get:
p = 16
Therefοre, the value οf p that satisfies the prοpοrtiοn is 16.
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A 6-meter roll of fabric costs $15.29. What is the unit price, rounded to the nearest cent?
Answer: $2.55
Step-by-step explanation:
Unit price = Total cost ÷ Length of fabric
$15.29 ÷ 6 = 2.54833333
Rounded to the nearest tenth is 2.55
There is a mound of g
pounds of gravel in a quarry. Throughout the day, 200
pounds of gravel is added to the mound. Two orders of 700
pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,000
pounds of gravel.
Answer:
2400
Step-by-step explanation:
before anything got taken away they added 200 wich means before they added that they had 2200 and if 700 pounds were removed twice that would mean the mound lost 1400 pounds and so if you add 1000 to the 1400 that they took you can find the amount that was there before.l
The weights for newborn babies is approximately normally distributed with a mean of 5.8 pounds and a standard deviation of 2.1 pounds.
Consider a group of 1100 newborn babies:
1. How many would you expect to weigh between 4 and 7 pounds?
2. How many would you expect to weigh less than 6 pounds?
3. How many would you expect to weigh more than 5 pounds?
4. How many would you expect to weigh between 5.8 and 10 pounds
Answer:
Step-by-step explanation:
To find the number of newborn babies weighing between 4 and 7 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.
For 4 pounds: z = (4 - 5.8) / 2.1 = -0.857
For 7 pounds: z = (7 - 5.8) / 2.1 = 0.571
Using the normal distribution table, the area between z = -0.857 and z = 0.571 is 0.5418.
So, the expected number of newborn babies weighing between 4 and 7 pounds is:
0.5418 x 1100 = 596 (rounded to the nearest whole number)
To find the number of newborn babies weighing less than 6 pounds, we need to calculate the z-score for 6 pounds and use the normal distribution table.
z = (6 - 5.8) / 2.1 = 0.095
Using the normal distribution table, the area to the left of z = 0.095 is 0.5375.
So, the expected number of newborn babies weighing less than 6 pounds is:
0.5375 x 1100 = 591 (rounded to the nearest whole number)
To find the number of newborn babies weighing more than 5 pounds, we need to calculate the z-score for 5 pounds and use the normal distribution table.
z = (5 - 5.8) / 2.1 = -0.381
Using the normal distribution table, the area to the right of z = -0.381 is 0.6499.
So, the expected number of newborn babies weighing more than 5 pounds is:
0.6499 x 1100 = 715 (rounded to the nearest whole number)
To find the number of newborn babies weighing between 5.8 and 10 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.
For 5.8 pounds: z = (5.8 - 5.8) / 2.1 = 0
For 10 pounds: z = (10 - 5.8) / 2.1 = 1.905
Using the normal distribution table, the area between z = 0 and z = 1.905 is 0.4713.
So, the expected number of newborn babies weighing between 5.8 and 10 pounds is:
0.4713 x 1100 = 518 (rounded to the nearest whole number)
Describe a situation that could be represented by the expression `4-2.27`.
Answer:
I had 4 dollars, but I spent 2.27 on my new pencil.
Step-by-step explanation:
You need to create a situation where you have 4 of 'blank' and you take away 2.27 of 'blank' to answer this question.
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Graph the line that passes through the points (-6, -8) and (3,-2) and determine
the equation of the line.
In a high-quality coaxial cable, the power drops by a factor of 10 approximately every 2.75 km. If the original signal power is 0.375 W (= 3.75 × 10-1 W), how far will a signal be transmitted before the power is attenuated to 37.5 μW?
Every [tex]2.75[/tex] kilometres in an elevated coaxial cable, the energy decreases by a factor of 10. This indicates that the transmit strength drops with one (0.1) of its original value after every [tex]2.75[/tex] kilometres.
Let's write "d" to represent the signal's maximum range before it loses strength and dips to [tex]37.5 W[/tex]. The following formula can be used to determine the distance [tex]d: P(d) = P(0) / 10^(d / L)[/tex]
[tex]P(d)[/tex] is the signal's power after travelling a distance of d,[tex]P(0)[/tex] is the signal's initial strength,[tex]L[/tex] is indeed the attenuation length in this instance ([tex]2.75 km[/tex]), and "([tex]37.5 W[/tex])" stands for "to the power of d/L".
Inputting the values provided yields: [tex]37.5 μW = 0.375 W / 10^(d / 2.75 km)[/tex]0 The result of dividing both sides with [tex]0.375 W is: .0 /001 = 1 10^(d / 2.75 km)[/tex]The result is: when we take the logarithmic (based 10) of both sides. [tex]-4 = -(d / 2.75 km)[/tex]By dividing all sides by [tex]2.75[/tex] kilometres, we arrive at:[tex]11 km = d[/tex]
As a result, the signal may travel 11 kilometres before losing power and becoming weaker [tex](37.5W) .[/tex]
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(x² + 3x + 2) ÷ (x + 2)
Answer:
x+1
Step-by-step explanation:
For the first part of the expression, factor into (x+2)(x+1).
(x+2)(x+1)/(x+2)
The x+2 cancels out, so the answer is x+1
If h(x) = √6 +5f(x), where f(2)= 6 and f'(2) = 5, find h'(2).
Tip: 6 + 5f(x) is all under the square root.
By using the chain rule, we will see that the derivative is:
h'(2) = 5/12
How to find the value of h'(2)?Remember the chain rule, for the derivative of a composition of two functions f(x) and g(x), if we define:
k(x) = g(f(x))
Then:
k'(x) =g'(f(x))*f'(x)
In this case we know that:
h(x) = √(6 + 5*f(x))
We can define then:
g(x) = √(6 + 5x)
and write h(x) = g(f(x))
Now the differentiation will give:
h'(x) = (1/2)*(√(6 + 5f(x))⁻¹*f'(x)
Evaluating this in x = 2 we will get:
h'(2) = (1/2)*(√(6 + 5f(2))⁻¹*f'(2)
And we know that f(2) = 6 and f'(2) = 5
Then:
h'(2) = (1/2)*(√(6 + 5*6))⁻¹*5
h'(2) = (1/2)*(6)⁻¹*5 = 5/12
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Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is
x = 61 − p1
thousand units and the demand for brand 2 is
y = 71 − p2
thousand units, where
p1 and p2
are prices in dollars. If the joint cost function is
C = xy,
in thousands of dollars, how many of each brand should be produced to maximize profit?
brand 1=
Brand 2=
What is max profit?
To maximize profit, the manufacturer should produce 22 thousand units of each brand, and the maximum profit is:
Profit = (39 × 22) + (49 × 22) - (61 - 39)×(71 - 49) = $256 thousand.
What is profit?Profit is a term used in business and economics to refer to the amount of money or value that is gained after deducting the cost of production or acquisition from the revenue earned.
Mathematically, profit can be calculated as follows:
Profit = Revenue - Cost
To maximize profit, we need to determine the optimal values of P1 and P2. We can do this by setting up the profit function as follows:
Profit = Total Revenue - Total Cost
Profit = (P1 × x) + (P2 × y) - C
Profit = (P1 × (61 - P1)) + (P2 × (71 - P2)) - (61 - P1)×(71 - P2)
Taking the derivative of the profit function with respect to P1 and P2 and setting it equal to zero will give us the optimal values of P1 and P2 that maximize profit:
∂Profit/∂P1 = 61 - 2P1 + P2 = 0
∂Profit/∂P2 = 71 - 2P2 + P1 = 0
Solving these equations simultaneously, we get P1 = 39 and P2 = 49.
To find the quantities of each brand that should be produced, we can substitute P1 and P2 into the demand functions for x and y:
x = 61 - P1 = 22 thousand units of brand 1
y = 71 - P2 = 22 thousand units of brand 2
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What are the key features of the equation y = (x + 12)(x + 6)? Question 5 options: The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute maximum, (–9, –9). The x-intercepts are (12, 0) and (6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 6). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9).
Answer:
y= -x+3
Step-by-step explanation:
We can see that our given equation is in slope-intercept form
, where m represents slope of line and b represents the y-intercept.
Upon looking at our given equation, we can see that the slope of our given line is 1
and the y-intercept is at point
.0,3
Upon graphing our given equation, we will get our required graph as shown below:
2064 0 No. 10 Old if the compound interest on Rs 500 for years is Rs 398 find the compound interest on Rs. 625 15) Ans: Rs. 450 la 15 years at the same rate 5
Proportionately, if the compound interest on Rs 500 for years is Rs 398, the compound interest on Rs. 625 is Rs. 497.50.
What is proportion?Proportion is a part or portion of the whole.
Proportion indicates the ratio that one quantity or value possess in relation to or when compared or equated to another.
We determine proportion as the quotient of one value divided by another. Proportion can also be expressed as a percentage by multiplying the resultant quotient by 100.
The compound interest on Rs. 500 = Rs. 398
Thus, proportionately, the compound interest on Rs. 625 will be Rs. 497.50 (Rs 398/Rs. 500 x 625).
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Find the equation of the line that passes through the given points. (Use x as your variable.) (0,5),(6,0)
Answer:
y = - [tex]\frac{5}{6}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5 ) and (x₂, y₂ ) = (6, 0 )
m = [tex]\frac{0-5}{6-0}[/tex] = [tex]\frac{-5}{6}[/tex] = - [tex]\frac{5}{6}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = - [tex]\frac{5}{6}[/tex] x + 5 ← equation of line
What is the explicit formula for the sequence: .25,5,1,2
The explicit formula for the geometric sequence is [tex]a_n=25(\frac{1}{5})^{n-1}[/tex].
What is explicit formula for geometric series?
The explicit formula for geometric sequence is [tex]a_n=a_1(r)^{n-1}[/tex] where r is common ratio.
Here the given sequence is 25,5,[tex]\frac{1}{2}[/tex]...
Here first term [tex]a_1=25[/tex]
Common ratio = [tex]$ \frac{a_2}{a_1}=\frac{5}{25}=\frac{1}{5}[/tex]
Now, Explicit formula [tex]$ a_n=a_1(r)^{n-1}[/tex]
=> [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex]
Hence the explicit formula of geometric series is [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex].
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Write 4 to the 3ed power using repeated multiplication. Then find the value of 4 to the 3ed power
Answer:
4x4x4 and the value of 4^3=64
Step-by-step explanation:
4x4x4 is equivalent to 4^3. This is because using exponents mean multiplying the base number by itself by 2 if the exponent is 2, if it was 3 then you would multiply 4 by itself three times.
Respass Corporation has provided the following data concerning an investment project that it is considering: Initial investment $ 160,000 Annual cash flow $ 54,000 per year Salvage value at the end of the project $ 11,000 Expected life of the project 4 years Discount rate 15% Click here to view Exhibit 14B-1 and Exhibit 14B-2, to determine the appropriate discount factor(s) using the tables provided. The net present value of the project is closest to:
NOTE : I got an overview of the answer BELOW BUT I want to clarify HOW THE ´´1.12´´ value is obtained please?
For me I would have had ´´1.15´´ (1+0.15 where 0.15 is the 15% discount rate).
Kindly help me to clarify this please.
EXPECTED ANSWER IS CORRECT: $516
The net present value οf the prοject is $516.
What is the net present value?A set οf cash flοws that happen at variοus dates are cοnsidered tο have a net present value οr net present wοrth. The amοunt οf time between nοw and a cash flοw determines the present value οf that cash flοw. The discοunt rate is anοther factοr. NPV takes the time value οf mοney intο the accοunt.
Here, we have
Respass Cοrpοratiοn has prοvided the fοllοwing data cοncerning an investment prοject that it is cοnsidering: Initial investment $ 160,000 Annual cash flοw $ 54,000 per year Salvage value at the end οf the prοject $ 11,000.
The prοject has annual inflοws οf $54,000 except in 4th year when it will have inflοws οf $65,000 because the salvage value will be added tο the inflοws.
Present value οf inflοws = 54,000/1.12 + 54,000/1.12² + 54,000/1.12³ + 65,000/1.12⁴
= $160,516
Net Present Value = 160,516 - 160,000
= $516
Hence, the net present value is $516.
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The points C(-8, -9), D(-2,-2), E(0, 7), and F(-6, 0) form rhombus CDEF.
Plot the points then click the "Graph Quadrilateral" button. Then find the area of the
rhombus.
Answer:
The area of the rhombus CDEF is 32 units squared.
Step-by-step explanation:
The area of the rhombus CDEF is 24 square units. This can be determined by using the formula for finding the area of a rhombus which is A = 1/2 × d1 × d2 where d1 and d2 are the lengths of the diagonals of the rhombus. In this case, d1 is the distance from C to E and d2 is the distance from D to F. Calculating the lengths of the diagonals gives d1 = 8.9 and d2 = 8. Therefore, the area of the rhombus is 24 square units.
What is the average rate of change of sales between 2008 and 2010?
f(x)
495
513
410
402
520
580
631
719
624
582
X
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
HELP
Answer:
2008 and 2010 is 52 units per year.
Step-by-step explanation:
To find the average rate of change of sales between 2008 and 2010, we need to calculate the change in sales over that period, and divide by the time interval.
The sales in 2008 is f(2008) = 520, and the sales in 2010 is f(2010) = 624. The time interval is 2 years.
Therefore, the change in sales over that period is:
f(2010) - f(2008) = 624 - 520 = 104
The average rate of change of sales between 2008 and 2010 is:
(104) / (2) = 52
So the average rate of change of sales between 2008 and 2010 is 52 units per year.
NEED AWNSER ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPIdentify the formula used to find total surface area, then calculate total surface area. Select the appropriate choices.
Formula:
Total Surface Area:
The total surface area of the triangular prism is 556 unit²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
The total surface area is the sum of each face area of the triangular prism. Hence:
Total surface area = [(1/2) * 8 * 17] + [(1/2) * 8 * 17] + (10 * 17) + (10 * 14) + (10 * 11) = 556 unit²
The total surface area is 556 unit²
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Consider the following function.
p(x)=1−12x
Plot two points on the line to graph the function.
We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
What is functiοn?A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.
A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.
Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).
Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).
Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.
If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.
Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
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If she makes her goal pace 80% of the time and plans to run for the next 10 days how likely will she make her goal pace
every day
If she makes her goal pace 80% of the time and plans to run for the next 10 days, the probability or likelihood that she will make her goal pace every day is 80%.
What is probability?Probability describes the chance, odds, or likelihood of an expected outcome, event, or success occurring when there are many possible outcomes.
Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.
Thus, it is 80% likely that she will make her goal pace every day if she runs for the next 10 days.
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I neeedddd helppppp???
Answer:
(-2,-4)
Step-by-step explanation:
The solution to a system of equations is the point at which the lines (that are defined by the equations) intersect, or touch each other.
In the graph, we can see that the lines intersect when x = -2 and y = -4.
In the format (x,y), this is expressed as: (-2,-4)
STATISTICS MATH. SOMEONE PLEASE HELP WITH THIS!! ILL GIVE YOU BRAINLIST ANSWER. IMAGE ABOVE
Answer:
u rock tgu hjgr yyihh yihgg
The Ministry of Transport and Mining hired a firm to conduct a traffic study before expanding the city streets. Two companies submitted bids for the job. The ministry hired the second company (company B) because they had more experience and offered a better rate. They studied the movement of the traffic on a specific roadway. The first day of the study was the second Monday in September. They found that 12,665 cars, 23,709 small commercial vehicles, 1,024 medium trucks, 7,096 lange macks, and 660 other vehicles used the roadway during the evaluation period.
0f the vehicles classified as "other vehicles," 213 of them are morcycles How many of the other vehicles were not motorcycles?
Answer: i got 213
Step-by-step explanation: