The difference between the 51st term of a and the 51st term of b is 1000.
the nth term of an arithmetic series is given by [tex]a_{n}= a_{0}+(n-1)*d[/tex]
where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference
Given that,
[tex]a_{0}=b_{0}=30[/tex]
Common difference of both series that have absolute value = 10
common difference of series a is 10 as this series is increasing
similarly, the common difference of series b is -10 as it is decreasing
Putting the values in the above equation we get:
[tex]a_{51}= a_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*10
=> 30 + 500 = 530
Thus, the value of [tex]a_{51}[/tex] is 530.
[tex]b_{51}= b_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*-10
=> 30 -500 = -470
Thus, the value of [tex]b_{51}[/tex] is -470.
so we have to find the value of [tex]a_{51}-b_{51}[/tex] which is 530 - (-470) =530 +470 =1000
Therefore, The difference between the 51st term of a and the 51st term of b is 1000.
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At the neighborhood grocery, 55 pounds of steak cost $36.50. How much would it cost to buy 3.93.9 pounds of steak?
The amount it would cost to buy 3.9 pounds of steak is $2.59
Calculating the cost it would take to buy steakFrom the question, we are to determine how much it would cost to buy 3.9 pounds of steak
Let the cost be $x
From the given information, we have that
55 pounds of steak cost $36.50
If 55 pounds of steak cost $36.50
Then,
3.9 pounds of steak will cost $x
Thus,
55 × x = 3.9 × 36.50
55x = 142.35
x = 142.35/55
x = 2.588
x ≈ 2.59
Hence, the cost is $2.59
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Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Question 10
[tex]\frac{\sin x}{7}=\frac{\sin 85^{\circ}}{8}\\\\\sin x=\frac{7\sin 85^{\circ}}{8}\\\\x \approx 60.7^{\circ}, 119.3^{\circ}[/tex]
However, the second case does not satisfy the angle sum of a triangle, so [tex]x \approx 60.7^{\circ}[/tex].
Question 12
[tex]\frac{\sin x}{19}=\frac{\sin 34^{\circ}}{12}\\\\\sin x=\frac{19\sin 34^{\circ}}{12}\\ \\ x \approx 62.3^{\circ}, 117.7^{\circ}[/tex]
Both of these cases satisfy the angle sum of a triangle.
If 7 girls each own 7 dresses and each
of the 7 dresses has 7 different hats to
go with it, how many hats are there?
7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are 49.
What is multiplication?Calculating the sum of two or more numbers is the process of multiplication. It is stated as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied.
Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number.
What are word problems?A word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation. Most word problems incorporate some type of narrative, hence they are sometimes called "story problems," and the quantity of technical jargon they employ can vary.
Given that 7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are:
Hats = (7)(7) = 49.
Hence, there are a total of 49 hats.
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The dotplots below show an approximation to the sampling distribution for three different estimators of the same population parameter.If the actual value of the population parameter is 5, which dotplot displays the estimator with both low bias and high variability?Choose 1 answer:A. Statistic AB. Statistic BC. Statistic C
Statistic C has the highest variability compared to the other two dotplots, meaning it has a greater range of expected value. This indicates that it has both low bias and high variability, since the actual value of the population parameter is 5.
Statistic C has the highest variability among the three dotplots, indicating that it has the highest range of values. This suggests that it has both low bias and high variability, since the actual value of the population parameter is 5. This means that it is likely to provide the most accurate estimation of the population parameter. On the other hand, Statistic A and B have much lower variability, meaning that their range of values is more restricted. This suggests that they are more likely to be biased, as they are not as likely to accurately represent the actual value of the population parameter. The low variability of these two dotplots also suggests that they are less reliable than Statistic C.
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Answer:
statistic A
Step-by-step explanation:
what are the mean and standard deviation of the sampling distribution of the sample mean for samples of size 4 ?
On solving the provided question, we can say that standard deviation 15.4 is the mean of the sample means' sampling distribution.
What is standard deviation?Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.
If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size:
u = 15.4;
⊕ = 5.6
now
μ = 5.6[tex]\sqrt{5}[/tex] =
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solve for w
-5/2 + 1/4w = -5/8
Answer: 15/2
Step-by-step explanation: -5/2 + 1/4W = -5/8
- 1/4W = -5/8 + 5/2
- 1/4W = 15/8
- W = 15/8 × 4
- W = 15/2
if i had 8.3% female viewers, 91.2% male viewers, and 0.5% user-specified viewers how many female viewers would i have in numbers (without percent)
Answer:
there is no way to answer that
Step-by-step explanation:
if anyone gives you a number answer they are lying to you. we need to know how. many people in total viewed it to know the specific number. like if a total of a hundered people viewed it then 8 of them where female and 91 of them were male and 1 was user spevified. get what i am saying?
→
Round 21245 to the nearest thousand
Answer:
21245 rounded to the nearest thousand is 21000.
Rounding to the nearest thousand means finding the number that is closest to the original number, but ends in three zeroes. In this case 21000 is the nearest number ending in three zeroes to 21245.
Answer:
21000
Step-by-step explanation:
If the hundreds place is 500 or bigger, round to 22000, if the number is 499 or under it will be 21000.
Erin needs 4 5 of a cup of chocolate chips to make a cake and 1 2 of a cup of chocolate chips for the frosting. She's trying to decide if a one cup bag of chocolate chips will be enough for the cake and the frosting. Determine whether Erin needs to buy more chocolate chips.
Answer:
Yes, she needs to buy more
Step-by-step explanation:
4/5 + 1/2 = 8/10 + 5/10 = 13/10 cups of chocolate needed
13/10 > 10/10
13/10-10/10 = 3/10
she needs 3/10 cup of chocolate more
Calculate the range, variance, and standard deviation for the following samples a. 43, 41, 48, 47, 49 b. 100, 1, 3, 95, 70, 4, 6, 10, 5 c. 100, 1, 3, 30, 70, 30, 43, 5 a. The range is 8 Type an integer or a decimal. Do not round.) The variance is 11.80 (Round to two decimal places as needed.) The standard deviation is 3.4 (Round to one decimal place as needed.) b. The range is 99 (Type an integer or a decimal. Do not round.) The variance is 1813.50 (Round to two decimal places as needed.) The standard deviation is 42.6 (Round to one decimal place as needed.) c. The range is 99 (Type an integer or a decimal. Do not round.) The variance is 1234.79 (Round to two decimal places as needed.) he standard deviation is (Round to one decimal place as needed.)
The range, variance, and standard deviation are 8, 21.10, 445.21.
The range, variance, and standard deviation are 99, 40.14,1612
What is data?
Data is a collection of measurements or observations used as a source of information. There are numerous types of data and numerous ways to represent data.
Given data is
43, 41, 48, 47, 49
Arrange them in ascending order:
41, 43, 47, 48,49
The range is (49 - 41) =8
The mean is (41+43+47+48+49)/5 =45.6
Data deviation from mean square deviation
41 4.6 21.16
43 2.6 6.76
47 -1.4 1.96
48 -2.4 5.76
49 -3.4 11.56
Total 47.2
The standard deviation is s = √[(x-μ)²/N] = 21.10
The variance is s² = 445.21
Given data is
100, 1, 3, 95, 70, 4, 6, 10, 5
Arrange them in ascending order:
1, 3, 4, 5, 6, 10, 70, 95, 100
The range is (100 - 1) = 99
The mean is (1+3+4+6+5+10+70+95+100)/9 =32.67
Data deviation from mean square deviation
1 31.67 1002.99
3 29.67 880.31
4 28.67 821.97
5 27.67 756.63
6 26.67 711.29
10 22.67 513.93
70 -37.33 1393.52
95 -62.33 3885.03
100 -3.33 4533.33
Total 14508.0001
The standard deviation is s = √[(x-μ)²/N] = 40.14
The variance is s² = 1612
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How many roots does a degree 3 polynomial have?
A degree 3 polynomial has either 1 real root, 2 real roots, or 3 real roots. It is possible for the polynomial to have imaginary roots as well, but these are not counted.
A polynomial of degree 3 is a equation in the form of ax3 + bx2 + cx + d = 0. For a polynomial of degree 3, the number of roots it has depends on the value of the discriminant, which is calculated using the formula b2 - 4ac. If the discriminant is positive, the polynomial has three real roots. If the discriminant is equal to zero, the polynomial has two real roots. If the discriminant is negative, the equation has one real root and two imaginary roots. In the case of one real root, the polynomial can be factored into (x - r) (ax2 + bx + c). In the case of two real roots, the polynomial can be factored into (x - r1) (x - r2). In the case of three real roots, the polynomial can be factored into (x - r1) (x - r2) (x - r3).
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2. ALGEBRA On April 14, Mikos Souvakis borrowed $100,000 to remodel
his restaurant kitchen with a single-payment loan at 10. 5% ordinary
interest. If his loan's maturity value was $104,375, when does Mikos
have to pay it back?
and
We may apply the simple interest formula to find the due date for repayment from Mikos is 5 months.
I = P*r*t, where I represents interest, P the principal (initial sum), r the interest rate, and t the period of time in years.
The maturity value formula can be used to calculate interest given that the loan's principal is $100,000 and its maturity value is $104,375:
Where MV is the maturity value, P is the principal, and I is the interest, the formula is: MV = P + I.
With the above data, we obtain: 104,375 = 100,000 + I
I = 4,375.
Now we can use this value of I to find the time t in years:
I = P*r*t
4,375 = 100,000 (0.105) t
t = 4.375 / (100,000 x 0.105)
t = 4.375 / 10,500
t = 0.417 years or approximately 5 months
So, it takes approximately 5 months to repay the pay back amount .
Therefore, Mike must repay the amount by April 14, which is around five months after the day he took out the loan.
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if 1,000,000 people are exposed to 10 msv, then what is the expected number of radiation induced cancers according to the linear no threshold model of cancer induction
The expected number of radiation induced cancers according to the linear no threshold model of cancer induction is 500
Radiation is defined as the energy that comes from a source and travels through space at the speed of light.
Here we have given that 1,000,000 people are exposed to 10 msv and here we need to find the the expected number of radiation induced cancers according to the linear no threshold model of cancer induction.
As we all know that the amount of dose depends on the type of x-ray examination. A CT examination with an effective dose of 10 milli Sieverts
And it may be associated with an increase in the possibility of fatal cancer of approximately 1 chance in 2000.
therefore, here we have the total number as 1,000,000
Then the expected number if calculated as,
=> 1,000,000/2000
=> 500
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find thee dimensiions of aa 12 oz can of soda thaat can be cconstruccted wiith the least amount of metal
The can is a cylinder with the smallest height and a radius that is the square root of the volume divided by 2[tex]\pi[/tex].
What is the volume of a cylinder?The formula to calculate the volume of a cylinder is given by the product of the base area and its height. The volume of a cylinder = πr2h cubic units.
To find the dimensions of a 12-oz can that can be constructed with the least amount of metal, we need to minimize the surface area of the can while maintaining a volume of [tex]355 cm^3[/tex]. The surface area of a cylindrical can is given by [tex]2\pi r(r+h)[/tex] where r is the radius of the base of the can and h is the height of the can.
Minimizing the surface area of the can is equivalent to minimizing the total material used in constructing the can. This can be achieved by making the height of the can as small as possible while maintaining a volume of 355 cm^3. The volume of a cylindrical can is given by πr^2h,
So the equation is:
[tex]\pi r^2h= 355cm^3[/tex]
We can get the value of h in terms of r by dividing both sides by πr^2
[tex]h= 355cm^3 / (\pi r^2)[/tex]
Now we can substitute this value of h in the equation for the surface area:
[tex]2\pi r(r+h) = 2\pi r(r + 355cm^3 / (\pi r^2))[/tex]
Now we can differentiate the above equation with respect to r and set it equal to zero to find the minimum value of the surface area.
[tex]d(2\pi r(r+h))/dr = 2\pi r + 2\pi (355cm^3 / (\pi r^2)) = 0\\r = sqrt(355cm^3 / (2\pi ))[/tex]
Now we can substitute this value of r back into the equation for the volume of the can to find the corresponding value of h:
[tex]\pi r^2h = 355cm^3[/tex]
h = [tex]355cm^3 / (\pi r^2) = 355cm^3 / (\pi (355cm^3 / (2\pi ))^2)[/tex]
The dimensions of the 12-oz can that can be constructed with the least amount of metal are a radius of sqrt(355cm^3 / (2π)) and a height of 355cm^3 / (π (355cm^3 / (2π))^2).
Hence, the can is a cylinder with the smallest height and a radius that is the square root of the volume divided by 2π.
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Complete question: A soda can is to hold 12 fluid ounces. Find the dimensions that will minimize the amount of material used in its construction, assuming the thickness of the material is uniform?
In what ratio is the line segment joining the points (- 3 2 and 6'1 is divided by Y axis?
Y-axis divides the line segment formed by the points ( -3 ,2) and ( 6,1) in the ratio equals to 1 :2.
As given in the question,
Coordinates of the line segment is given by :
( x₁ , y₁ ) = (-3, 2)
(x₂ , y₂ ) = ( 6,1)
Let the ratio of the given line segment divided by the y -axis that is ( x, y) = ( 0, y ) be m : n given by the formula:
( x, y ) = [ ( mx₂ + nx₁) /(m +n) , (my₂ + ny₁ ) / ( m + n ) ]
Substitute the values we get,
( 0 ,y ) = [ ( 6m -3n) /(m +n) , (1m + 2n ) / ( m + n ) ]
⇒ ( 6m -3n) /(m +n) = 0
⇒ 6m -3n = 0
⇒ 6m = 3n
⇒m : n = 1 : 2
Therefore, y-axis divides the given line segment into the ratio 1 : 2.
The above question is incomplete, the complete question is :
In what ratio is the line segment joining the points (- 3 2) and (6,1) is divided by Y-axis?
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helphelphelphelphelphelp
As y varies directly with x, The value of y when x = -4 is 8/5.
What is the value of y when x = -4?Proportional relationships are relationships between two variables where their ratios are equivalent.
Direct variation is expressed as;
y ∝ x
Then, y = k(x)
Where k is the proportionality constant.
Given that y = -8 and x = 20.
First determine the constant of proportionality k.
y = k(x)
-8 = k( 20 )
-8/20 = k
k = -8/20
k = -2/5
Next, we determine the value of y when x = -4.
y = k(x)
Plug in k = -2/5 and x = -4
y = -2/5( -4 )
y = -2/5 × -4
y = 8/5
Therefore, the numerical value of y is 8/5.
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Complete the system of equations with a linear equation so that the graphs of the equations intersect at their x- and y-intercepts.
y=x^3+4x+3x+12
y=?
The required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Given equation,
y=x³+4x²+3x+12
To determine the x-intercept put equation y = 0
0 = x³+4x²+3x+12
Factorize the above equation
0=(x²+3)(x+4)
One of the factors from above is given as
x+4=0
x = -4
The x-intercept is (-4,0)
For the y-intercepts, x=0 and solve.
y = 12
y = 12
The y-intercept is (0,12)
Now equation of the line passing these points is given as.
m = (y₂ - y₁) / (x₂ - x₁)
m = 12/3
m = 3
C, we already have C=12
So the equation of the line is
y = mx + c
y=3x+12
Thus, the required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.
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what is the approzimate surface area (including both side and base) of a 4m high right circular cone
The surface area is approximately 100.5m².
Surface Area = πrl + πr²
Where r is the radius of the base and l is the slant height.
Surface Area = π(2m)(4m) + π(4m)²
Surface Area = 100.5m²
The surface area of a right circular cone can be calculated by using the formula surface area = πrl + πr². In this particular case, the height of the cone is 4m and the radius of the base is 2m. Therefore the surface area of the cone is calculated as follows: π(2m)(4m) + π(4m)² = 100.5m². This surface area includes both the base and sides of the cone.
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If the temperature outside is 36 °C, what is the temperature in °F?
Answer: I believe 96.8 degrees F
Step-by-step explanation:
36°C x 9 ÷ 5 + 32= 96.8
Which congruence theorem can be used to prove △WXZ ≅ △YZX?
Triangles W X Z and Y Z X share side X Z. Angles W X Z and X Z Y are right angles. Angles X W Z and X Y Z are congruent.
AAS ASA SAS HL
Therefore, the congruence theorem that may be employed to demonstrate that △WXZ and △YZX are equivalent is: AAS
Define congruence.Angles are considered congruent if the ratios of two shapes are equal. Similar to this, if the sides with one form are the same length and match the sides of yet another figure, the sides are congruent.
Here,
We are informed that ΔWXZ and ΔYZX share the same side.
The right angles ∠WXZ and ∠XZY are.
It is consistent for ∠XWZ and ∠XYZ.
Now that the parameters have been provided, we may infer that XZ is equal to itself according to the reflexive property for congruence, and as a result, we have a congruent side in each triangle.
Second, because ∠WXZ and ∠XZY were right angles, they are comparable and hence congruent to one another.
Finally, it is stated that ∠XWZ and ∠XYZ are congruent.
In conclusion, the triangles are identical according to the AAS Congruency since there are two corresponding angles one and corresponding sides that are both equal, but the comparable side wasn't with the included angles.
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HELP PLEASE^^ (10 points)
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $5, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 5 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A. A package that weighs 15 pounds will cost $35 for both options.
B. A package that weighs 15 pounds will cost $25 for both options.
C. A package that weighs 10 pounds will cost $15 for both options.
D. A package that weighs 5 pounds will cost $15 for both options.
The solution is, D: A package that weighs 5 pounds will cost $15 for both options.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
The customer can send a package for $5, plus an additional $2 per pound.
The cost, y, can be represented by the equation y = 5 + 2x,
where x represents the amount of pounds of the package.
Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.
so, we get,
2x + 5 = 15
x = 5
Hence, The solution is, D: A package that weighs 5 pounds will cost $15 for both options.
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Answer:
D: A package that weighs 5 pounds will cost $15 for both options.
Step-by-step explanation:
2x + 5 = 15
x = 5
Thus, the person above me is correct :)
Which point is located at 4, -2?
Answer:
B
Step-by-step explanation:
the 4 is how far along you go on the x-axis (horizontal line).
the -2 is saying it needs to be 2 boxes below 0 on the y-axis (vertical line).
therefore the answer is b
The smallest division on main scale of a vernier caplliers is vernier divisions coincide with main scale divisions. While measuring the length of a line, the zero mark of the vernier scale lies between and the third division of vernier scale coincides with a main scale division. (a) Determine the least count of the callopers. (b) Find the length of the line.
The least count of Vernier calipers is 0.01cm and The length of the line is 10.23cm
Mean scale division:
The main scale is graduated with one division value equal to 1 mm. The length of the Vernier scale is the same as the n- scale of the Vernier scale and the (n-1) scale of the main scale.
Vernier Scale Division:
The minimum Vernier caliper number is also called the Vernier constant. Defined as the difference between the major and Vernier scales is represented mathematically as:
VC = 1 MSD – 1 VSD
If the Vernier scale has n divisions, it matches the (n-1) divisions of the main scale. Vernier Caliper :
LC = ( 1 - [tex]\frac{n-1}{n}[/tex]) MSD
According to the problem
1MSD= 1mm
MSR = 10.2cm
Here, 10VSD = 9MSD
1VSD = (9/10)MSD
=(9/10)×1mm
= (9/10)mm
Least count of Vernier calipers L.C = 1MSD - 1VSD
=1mm - (9/10)mm
=0.01mm
Therefore, Least Count (LC) = 0.01cm
Therefore,
Length of the line = MSR + (VSD × L.C)
= 10.2 + (3 × 0.01)
= 10.2+(0.03)p
= 10.23 cm
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rearrange to make x the subject
The value of x given the equation 2x - 5y = p is x = (p + 5y) / 2.
What does it mean when something is made the subject?Making x the subject of an equation or formula entails rearranging the equation or formula so that the x variable is equal to the other variables.
The necessary steps include:
Isolate the variableRearrange the equation so each term containing x is on the same side of the =.Factorization may be needed if there are multiple terms containing x.Perform an operation to ensure only a single x variable is left as the subject2x - 5y = p
2x = p + 5y
Divide through by 2
x = (p + 5y) / 2
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Complete question
rearrange to make x the subject in 2x - 5y = p
Solve each equation.
2y^2+11y+10=0
The solution of the given quadratic equation are,
[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].
What is quadratic equation?
Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a ≠ 0 is true is known as a quadratic equation.
Consider, the given equation:
2y^2 + 11y + 10 = 0
Compare this equation with [tex]ay^2 + by + c = 0[/tex]
⇒ a = 2, b = 11, c = 10
Consider, the quadratic formula
[tex]y = \frac{-b+-\sqrt{xb^2-4ac} }{2a}[/tex]
Plug the values of a, b, c in the quadratic formula.
⇒
[tex]y = \frac{-11+-\sqrt{11^2-4(2)(10)} }{2(2)} \\y = \frac{-11+-\sqrt{121-80} }{4}\\ y = \frac{-11+-\sqrt{41} }{4} \\y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex]
Hence, the solution of the given quadratic equation are,
[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].
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Triangle ABC has AB = 13, BC = 14, and AC = 15. The points D, E, and F are the midpoints of AB, BC, and AC respectively. Let X ≠E be the intersection of the circumcircles of Δ BDE and Δ CEF. What is XA + XB + XC?a. 24b. 14√3c. 195/8d. 129√7/14e. 69√2/4
The answer is C) 195/8
First, we can use the fact that A, B, C, D, E, and F are concyclic and that D, E, and F are the midpoints of AB, BC, and AC respectively.
Let r be the radius of the circumcircle of triangle ABC. Then using the Pythagorean theorem, we can find that r = (151413) / (4*K) where K is the area of the triangle.
Now we can use the property that the perpendicular bisectors of any triangle pass through the circumcenter of the triangle. We know that the midpoint of a line segment is the foot of the perpendicular from that point to the other endpoint. Then we can use the property that the radius from the circumcenter of the triangle to the midpoint of a side is half the length of that side.
Therefore, the circumcenter of triangle BDE is located at X = (BD/2, DE/2) = (13/2, 7/2) and the circumcenter of triangle CEF is located at X = (CE/2, EF/2) = (15/2, 7/2).
So the coordinates of X are (13/2, 7/2) and since the circumcenter of a triangle is equidistant from each vertex of the triangle, we can find that XA = XB = XC = r = r = (151413) / (4*K)
Therefore, XA + XB + XC = 3r = 3(151413) / (4*K) = (195/8)
So the answer is c. 195/8.
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Triangle J K L is cut by line M N. Line segment M N is drawn from side J K to side L K. Sides J L and M N are parallel. Based on the side-splitter theorem, which side length would complete the proportion
The required proportion of side lengths is JK/LK= JM/LN.
The Side-Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it splits those sides proportionally. In the case of triangle J K L, with line segment M N drawn parallel to side J L and intersecting sides J K and L K, the proportion of the lengths of the sides that are split can be determined by the ratio of the corresponding segments on each side.
Let's call the length of side J K as x, the length of side J L as y, and the length of side L K as z. Let the length of segment J M be a and the length of segment L N be b.
According to the side-splitter theorem, the proportion of the length of side J K to side L K is equal to the proportion of the length of segment J M to segment L N. This means that:
x/z = a/b
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Containers of gochujang, a Korean chili sauce, are sold at a market. The scatter plot shows the relationship between the cost of different containers and the amount of sauce in each container. A line of best fit is drawn through the data. Based on the line of best fit, what is the approximate cost per ounce of a container of gochujang at the market?
The approximate cost per ounce of a container of gochujang at the market is given as follows:
$0.5.
How to obtain the cost per ounce?As we have the graph of the linear function, the best way to define it is in slope-intercept form, as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x = 0.The cost per ounce is represented by the slope.
From the graph, we have that the graph starts at the origin, and when the number of ounces increases by 4, the cost increases by 2, hence the slope representing the cost per ounce is given as follows:
m = 2/4
m = $0.5.
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Answer the following:-
[tex]\sf 4\div 2+33-2+5[/tex]
Answer:
38
Step-by-step explanation:
4/2+33-2+5=2+33-2+5=35-2+5=33+5=38
on an old-fashioned bicycle the front wheel has a radius of 2.5 feet and the back wheel has a radius of 4 inches. if there is no slippage, how many revolutions will the back wheel make while the front wheel makes 100 revolutions?
Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.
What does a circle represent?Each point in the plane whose distance from that other point is a certain value forms a circle (center). It is therefore a curve composed of vertices that are spaced apart from one another in the plane by a specific amount. Furthermore, it is symmetrical about the center at all angles in terms of rotation. The closed, two-dimensional plane of a circle has all pairs of endpoints equally separated from the "center." When a line is drawn through the circle, a circle symmetry line is created. Furthermore, it rotates equally from all angles about the center.
Here,
The circle of the rear wheel is equal to circle = diameter x π, or 2.5 feet by 12 inches, or 30 inches.
The length of the front axle is 30 x 2 = 60 inches.
The diameter of the front wheel, C, is equal to 60 x Pi, or 60π, in inches.
The diameter of a back wheel is 4 x 2 = 8 inches.
The circumference of back wheel is C = 8 x Pi = 8π in inches.
750 revolutions are equal to
100 × [60Pi/8π] = 6,000π/8π.
100 rotations of the front tire will be made by the back wheel.
Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.
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