The solution of the equation x²-x -3 = 0 are x = (1±√13) /2.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Here we are given the equation x²-x -3 = 0 ---(i) which is a quadratic equation which we can solve using Sri Dharacharya Method.
Sri Dharacharya Formula: For a quadratic equation ax² + bx + c = 0
The value of x is x= (-b ± [tex]\sqrt{b^{2}-4ac }[/tex]) /2a.
Using this formula in (i), we get
x = (-(-1) ± [tex]\sqrt{(-1)^{2} -4*1*(-3)}[/tex]) /2*1
⇒ x = (1±√13) /2.
The solution of the equation are irrational which are x = (1±√13) /2.
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Malia ue 51 yard of ribbon to make 17 bow. The relationhip between ribbon and bow i proportional. How many yard of ribbon doe Malia need to make 68 bow?
In given proportinal relation , Maila need 204 yards for make 68 bow.
What is proportion?
In mathematics, proportional means that two quantities or variables are linearly related. When one quantity doubles, the other quantity also doubles. When one of the variables decreases to 1/10th of its previous value, the other also decreases. A ratio is a comparison of two numbers, each representing a part of a whole. Essentially, percentages show that two fractions are equal, even if they are of different magnitudes. For example, 1/2 of 10 marbles has the same ratio as 1/2 of 50 marbles.
Here the relationship between ribbon and bow is proportional. Let us take ribbon as r and bow as b.
=> r ∝b
=> r= kb . Where k is constant.
Now put r=51 and b =17 then,
=> 51=k*17
=> k = 3
then the equation is r = 3b.
Now b=68 then ,
=> r = 3*68
=> r = 204 yard.
Therefore Maila need 204 yard ribbon to make 68 bow.
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in a local university 70% of the students live in the dormitories. A random sample of 75 students is selected for a particular study The probability that the sample proportion (the proportion living in the dormitories) is at least 0.60 is
a.0.0294
b.0.9706
c.0.0228
d. 0.9772
The probability that the sample proportion is at least 0.60 is 0.0294.
Given data,
In a local university, 70% of the students live in dormitories. A random sample of 75 students is selected for a particular study The probability that the sample proportion (the proportion living in the dormitories) is at least 0.60 is,
The sample size in this case,
n = 75
The proportion of students living in dormitories p,
⇒ 70% = 0.7
Since we are taking a distribution of 75-sample samples from the given population into consideration, we have:
The mean, p = 0.7
The standard deviation, s = √p * (1 − p)/n
= √0.7 * (1 − 0.7)/75
= 0.0529
Now, by figuring out their respective Z-scores, we can calculate the probability values corresponding to the supplied proportion values.
The Z-score for a proportion value of 0.60;
Z₀.₆₀ = (0.6 - p)/s
= (0.6 - 0.7)/0.0529
= -1.890
The Standard Normal Distribution table can be used to determine the corresponding probability. Consequently, the overall likelihood value for,
Z₀.₆₀ = -1.890
P-value from Z-Table,
P(x < 0.6) = 0.029355 = 0.0294
Hence, there is a 0.0294 percent chance that the sample proportion is at least 0.60.
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a simple random sample of 5 months of sales data provided the following information: month: 1 2 3 4 5 units sold: 94 85 85 94 92 (a) develop a point estimate of the population mean number of units sold per month. x
The point estimate of the population mean number of units sold per month is given by:
90.
How to obtain the point estimate of a parameter?The point estimate of a population parameter is obtained as the value of the parameter in the sample.
The parameter that we want to obtain the estimate in this problem is:
The mean.
The sample in this problem is given by:
94, 85, 85, 94, 92.
(number of units sold each month).
The sample mean is given by the sum of all observations in the sample divided by the number of observations, hence it is obtained as follows:
Mean = (94 + 85 + 85 + 94 + 92)/5 = 90.
For the fraction, we have that:
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For each 50mm of coloured fabric, I ue 10cm of white fabric. Expre to amount of white fabric to coloured fabric a a ratio of it implet form
amount of white fabric to coloured fabric a a ratio of it implet form is given by 1/2
2cm = 2 * 10 mm
2 cm = 20 mm
for every 50 mm of colored fabric, Gavyn uses 100 mm of white fabric.
The ratio is expressed as white fabric to colored fabric.
Ratio white to colored = 50/100 = 1/2
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a block cipher algorithm operates more slowly if we change the key every time we use it. which of the following concepts is most responsible for this delay?
Key expansion is most responsible for this delay.
A block cipher encrypts and decrypts a block of data with an algorithm and symmetric key. In order to expand the keyspace of a block cipher and make it more difficult to break the key through brute force, an initialization vector (IV) must be added to the plaintext that is being used as input. Key Expansion: In the initial stage, it uses just one key, but in later rounds, it expands to multiple keys. Data bytes: Instead of working with bit data, the AES encryption algorithm performs operations on byte data. Consequently, during the encryption process, it treats the size of the 128-bit block as 16 bytes.
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Can we construct a triangle with the sides 2cm 3cm and 5cm justify?.
Answer:
No
Step-by-step explanation:
The sum of two sides of a triangle should be greater than the size of the third side.
2 + 3 is not greater than 5, so it's impossible to construct a triangle using the given lengths for the sides.
Ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. How many minutes of the ride are spent higher than 17 meters above the ground?
0.769 minutes of the ride is spent higher than 17 meters above the ground.
What is the unit conversion in mathematics?
Unit conversion is a multi-step process that includes multiplying or dividing by a numerical factor, determining the appropriate number of significant digits, and rounding.
The given figure is a Ferris wheel we have to find the time spent on the ride higher than 17 m.
It means we have to find time spent riding from A to C through B (i.e., Arc ABC)
From the figure, in ΔAOD, we have
OA = 12.5 m
OD = 12.5 - 1 = 11.5 m
Now find 'θ'
θ = [tex]cos^{-1}(\frac{11.5}{12.5})[/tex]
= 23.07°
The total angle of arc ABC = 2θ
= 2 * 23.07
= 46.14°
It is given that, 1 full revolution is completed in 6 minutes.
so 46.14° will be completed in = 6/360 * 46.14
= 0.769 minutes.
Hence, 0.769 minutes of the ride is spent higher than 17 meters above the ground.
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Given X (5, -8). What are the coordinates of X" if X" = Rx-axis
(Ry-axis(X))?
A. (5,8)
B. (-5,-8)
C. (-5,8)
D. (5,-8)
(-5, 8)
=========================================================
These are two rules to memorize
[tex]\text{x-axis reflection: } \ \ (\text{x},\text{y})\to (\text{x},-\text{y})\\\\\text{y-axis reflection: } \ \ (\text{x},\text{y})\to (-\text{x},\text{y})\\\\[/tex]
----------
I'll relabel the point X as point A.
We apply a y-axis reflection first.
So we have:
[tex](\text{x},\text{y})\to (-\text{x},\text{y})\\\\(5,-8)\to (-5,-8)\\\\[/tex]
after the y axis reflection is applied.
This is the location of point A'
----------
Then we apply an x-axis reflection.
[tex](\text{x},\text{y})\to (\text{x},-\text{y})\\\\(-5,-8)\to (-5,-(-8))\\\\(-5,-8)\to \boldsymbol{(-5,8)}\\\\[/tex]
This is the location of point A''
which points us to choice C as the final answer.
----------
Side note:
The composition of an x-axis reflection and y-axis reflection, in either order, is the same as a 180 degree rotation around the origin.
The rule for a 180 degree rotation is [tex](\text{x},\text{y})\to (-\text{x},-\text{y})\\\\[/tex]
What is the equation of the line that passes through the point (8,4) and has a slope of 0
The equation of the line that passes through the point (8,4) and has a slope of 0 is y = 4.
Given:
point (8,4) and has a slope of 0
slope m = 0
Standard line equation is y = mx + c
substitute (8,4) and m values in y = mx + c
4 = 0*8 + c
4 = 0 + c
c = 4
c , m values in y = mx + c
y = 0*x + 4
y = 0 +4
y = 4.
Therefore The equation of the line that passes through the point (8,4) and has a slope of 0 is y = 4.
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Trekkers footwear bought a piece of machinery on january 1, 2006 at a cost of $2. 3 million, and the machinery is being depreciated annually at an amount of $230,000 for 10 years. Its market value on december 31, 2008 is $1. 75 million. The firm's accountant is preparing its financial statement for the fiscal year end on december 31, 2008. The asset's value should be recognized on the balance sheet at.
The asset's value should be recognized on the balance sheet at $1.61 million.
Given,
On January 1st, 2006, Trekkers Footwear paid $2.3 million for a piece of equipment that will be depreciated at a rate of $230,000 per year for ten years. As of December 31, 2008, IT was worth $1.75 million in the market. The company's accountant is putting the finishing touches on the financial statement for the fiscal year that ends on December 31, 2008.
The balance sheet should reflect the asset's value at,
Cost of Asset = $2.3 million
Annual depreciation = $230000
Total no. of years depreciated till December 31, 2008, = 3 years
Hence, total depreciation = $230000 x 3 = 690000 = 0.69 million
Hence, book value as on 31 December 2008 = $2.3 million - $0.69 million = 1.61 million
Given Market Value on Dec 31, 2008, = $1.75 million.
But as per accounting conventions, Assets are recorded at Book value.
Hence $1.61 million is the right answer.
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For the triangles to be congruent by hl, what must be the value of x? 8 9 17 34
Using equations we know that the value of x needs to be (E) 4 to make HL congruent to AC.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, HL is a hypotenuse that will be congruent to the hypotenuse AC.
We know that HL is 3x + 3.
Ac is 15.
Then the equation will be:
3x + 3 = 15
Now, solve the equation to get x as follows:
3x + 3 = 15
3x = 15 - 3
3x = 12
x = 12/3
x = 4
Therefore, the value of x needs to be (E) 4 to make HL congruent to AC.
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Correct question:
For the triangles to be congruent by hl, what must be the value of x?
a. 8
b. 9
c. 17
d. 3
e. 4
Yearly expenses at a state university have increased from $14,000 to $18,500 in the last 4 years. What has been the average annual growth rate in expenses? If this growth rate continues, what will the expenses be 4 years from now?
The annual growth rate in the expenses is 0.08035 or 8.03 % and with the same rate the expenses after 4 years will be equal to $24,642.
How annual growth rate is calculated?
Annual growth rates are calculated by taking the average revenue for a particular time period into account. The yearly growth rate formula divides the final value of an investment or asset by its original value. When you subtract one from this amount, you are left with a decimal point that can be translated into a percentage. You may determine the percentage by simply moving the decimal point two spaces to the right.
The growth in the 4 years is = 18,500 – 14,000 = 4,500
Growth = initial amount (rate) (time)
4500 = x(4)(14,000) = 0.08035
It means the annual growth rate is 8.03 %
To know the expenses after 4 years, lets take initial value = 18,500, rate = 8.03% = 0.083, time = 4 years,
Increase = 18500(0.083)(4) = 6,142
So, the expenses after 4 years,
Expenses = 18,500 + 6,142 = 24,642
Therefore, the expenses after 4 years are $24,642
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HELP MEEEE PLEASEEEEEEE
Answer:
91.1 cm
Step-by-step explanation:
the formula to find circumferences is pi times diameter
29pi
91.1
Hopes this helps please mark brainliest
BBQ Corp. had a 3:1 stock split ratio. Pre-split the company had 1.35 Million outstanding shares at a price of $72.45 per share.
How many outstanding shares does BBQ Corp. have post-split?
The number of outstanding shares that BBQ Corp. will have post-split, given the number of outstanding shares is, 4, 050, 000 shares
What is a stock split?A stock split refers to when the number of outstanding shares that a company has, are divided into a certain number of shares which is based on the split ratio.
For a 3:1 stock split ratio, the number of outstanding shares will be split into three shares each.
BBQ Corp. has 1. 35 million shares so post - split, they will have:
= Outstanding shares x 3
= 1, 350, 000 x 3
= 4, 050, 000 shares
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From standard 52-card deck how many 9-card hands consist of 3 spades and diamonds? There are possible 9-card hands consisting of 3 spades and diamonds
Answer:
6
Step-by-step explanation:
for this I simply divided that numbers and I got my answer as 5.77 and I turned as 6
Consider the following time series data. week 1 2 3 4 5 6 value 16 11 13 10 14 12 (a) construct a time series plot. what type of pattern exists in the data? the data appear to follow a seasonal pattern. the data appear to follow a horizontal pattern. the data appear to follow a trend pattern. the data appear to follow a cyclical pattern. (b) develop the three-week moving average for this time series. (round your answers to two decimal places.) week time series value forecast 1 16 2 11 3 13 4 10 5 14 6 12 compute mse. (round your answer to two decimal places.) mse
The overall MSE for the time series would be (0 + 0 + 0.0289 + 0.0144 + 0.0044 + 0.0144)/6 = 0.0119. This value indicates that the forecasted values are close to the actual time series values, with a small error.
What is MSE?Mean squared error (MSE) is a standard measure of the average squared difference between predicted and actual value. Regression analysis frequently use it to assess a model's performance pattern. The sum of squared discrepancies between the predicted and actual values is multiplied by the number of observations in the dataset to derive the MSE. A lower MSE signifies a better match between the model and the data. In regression analysis, MSE is generally compared to the variance of the response variable, which is a measure of data dispersion. The MSE reveals how well the model fits the data when it is less than the variance.
How to solve?
To construct a time series plot for the given data, we can plot the values of the data against the weeks on the x-axis.
Week 1 | |
Week 2 | |
Week 3 | |
Week 4 | |
Week 5 | |
Week 6 | |
The three-week moving average for each week would be as follows:
Week 1: 16
Week 2: 11
Week 3: 12.67
Week 4: 11.33
Week 5: 12
Week 6: 11.33
The MSE for each week would be as follows:
Week 1: 0
Week 2: 0
Week 3: 0.0289
Week 4: 0.0144
Week 5: 0.0044
Week 6: 0.0144
The overall MSE for the time series would be (0 + 0 + 0.0289 + 0.0144 + 0.0044 + 0.0144)/6 = 0.0119. This value indicates that the forecasted values are close to the actual time series values, with a small error.
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it said her baby weighed 1/2 stone if one pound equals 1/14 of a stone how many pounds did the newborn baby weigh
The weight of the newborn baby in pounds is 7pounds
What is proportion?Proportion is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
The relationship between a pound and stone is
1 pound = 1/14stone
therefore 1stone = 14pounds
The weight of the newborn baby is 1/2 stone
in pounds ,the weight of the baby is 14/2= 7pounds
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michael jordan was said to have a hang-time of 3.0 seconds (at least according to a popular nike commercial). use kinematic equations to determine the height to which mj could leap if he was wearing nike shoes and had a hang-time of 3.0 seconds.
5 t-hirt and a hat cot 17£
2 t-hirt and a hat cot 8£
how much doe a t hirt cot
how much doe a hat cot
The cost of the t-shirt is 3 and the cost of a hat is 2
Let the price of a t-shirt be x
and the price of a hat be y
cost of 5 t-shirt and a hat is 17
5x + y = 17 equation 1
cost of 2 t-shirt and a hat is 8
2x + y = 8 equation 2
subtracting equation 2 from equation 1
5x + y - (2x + y) = 17 - 8
5x + y - 2x - y = 9
3x = 9
x = 3
2x + y = 8
2 (3) + y = 8
y = 8 - 6
y = 2
Therefore, the cost of the t-shirt is 3 and the cost of a hat is 2
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mrs. ibanez has come to the ed with painless jaundice (with an obstructive profile on liver tests), a 30-pound weight loss over three months, and profound dehydration, for which she was admitted to the hospital.
Mrs. Ibanez is experiencing symptoms of a potentially serious condition and should be evaluated by a medical professional as soon as possible.
What is a potentially serious condition?Any medical disease that has the potential to get worse or be life-threatening if it is not treated quickly and effectively qualifies as potentially serious. Infections, wounds, and long-term medical issues like diabetes or heart disease or profound dehydration are a few examples of potentially catastrophic illnesses. These illnesses can range in severity from moderate to severe, and they might need to be treated right once to avoid long-term harm or other consequences. If you think you may have a dangerous issue, it's crucial to speak with a doctor right away so you can get the proper care and stop the problem from becoming worse.
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A pile of brick weight 22kg. 18759gram of brick are removed. What weight i left?
Answer: Answer is 3241 gm or 3.2 kg approx.
Step-by-step explanation:
Weight of the brick( in kg) =22 kg
Weight of the brick in gm= 22*1000 gm (1 kg = 1000gm)
= 22000 gm
Weight of bricks removed = 18759 gm
Weight of bricks left in the pile= 22000-18759gm
=3241 gm or 3.2 kg approx
Hence, the weight of the bricks left is 3.2 kg approx.
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Simplify the following please
[tex] log_{3}27 + 2 log_{3}9 - log_{3}54[/tex]
Answer:
4 - log3 (2)
Step-by-step explanation:
2log3 (9) = log3 (9^2)
log3 (27 * 9^2 / 54)
log3 ( 3^3 * 3^4 / 9 * 6)
log3 (3^7 / 3^2 * 3 * 2)
log3 (3^7 / 3^3 * 2)
log3 ( 3^4 /2)
log3 (3^4) - log3 (2)
4 - log3 (2)
What is the prime factorization of 54 exponential form?.
The Prime Factorization of 54 in exponential form is 2¹ × 3³ .
The Exponential Form is a way of writing repeated multiplication that involves base and exponents . For Example : 5×5×5 = 5³ .
In the question ,
it is given that ,
the number is 54 ,
we have to find the prime factorization , and write it in the exponential form .
the number 54 can be expressed in factors as 2 × 3 × 3 × 3 .
which means 54 = 2 × 3 × 3 × 3 .
which can be written as 2 × 3³ .
So , the exponential form is 2¹ × 3³ .
Therefore , The Prime Factorization of 54 in exponential form is 2¹ × 3³ .
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find the minimum value of the function f(x)= x2+2.6x-2 to the nearest hundredth.
Answer:
[tex](-1.3,-3.69)[/tex]
Step-by-step explanation:
Take the derivative of the function and set it equal to 0.
[tex]f(x)=x^2+2.6x-2[/tex]
[tex]f'(x)=2x+2.6 = 0[/tex]
Solve for x.
[tex]2x+2.6=0\\2x=-2.6\\x=-1.3[/tex]
Find [tex]f(-1.3)[/tex]
[tex]f(-1.3)=(-1.3)^2+2.6(-1.3)-2[/tex]
[tex]f(-1.3)=-3.69[/tex]
Percy rides his bike 11.2 miles in 1.4 hours at a constant rate. Write an equation to represent the proportional relationship between the number of hours Percy rides,x, and the distance in miles, y, that he travels.
An equation to represent the proportional relationship between the number of hours and the distance in miles is k=y/x.
Given that, Percy rides his bike 11.2 miles in 1.4 hours at a constant rate.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
The number of hours Percy rides x, and the distance in miles, y, that he travels
So, the proportional relationship is speed = y/x
Thus, 11.2/1.4
= 8 miles per hour
Therefore, an equation to represent the proportional relationship between the number of hours and the distance in miles is k=y/x.
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Simplify cos (arcsin1/4)
Simplify completely
√40x^7
Simplified value of given expression is 2x³√10x.
What is simplification?
In arithmetic, simplification is reducing the expression / fraction problem during a less complicated type.
Main body:
Factor 40 into its prime factors
40 = 2³ • 5
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
4 = 2²
Factors which will remain inside the root are :
10 = 2 • 5
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
2 = 2
At the end of this step the partly simplified SQRT looks like this:
2 • sqrt (10x7)
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x⁸)=x4
(3.2) sqrt(x-⁶)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x²•sqrt(x)
(4.2) sqrt(x-7)=x³•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(x7) = x³ • SQRT(x)
sqrt (40x7) =
2² x³• sqrt(10x)
Hence the simplification to the value is as 2² x³ • sqrt(10x)
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Which equation represents a line that passes through 5 1 and has a slope of StartFraction one half EndFraction?.
The equation of line which passes through point (5,1) and having slope ½ is (y-1) = ½ (x-5).
What is the equation of a line?
The equation of a line is given as:
y = mx + c
The equation for the point on slope line is given as:
y - y1 = m ( x - x1 )
Substituting the above given values and the slope:
y - 1 = [tex]\frac{1}{2}[/tex] ( x - 5)
Hence, the equation of line which passes through point (5,1) and slope ½ is (y-1) = ½ (x-5).
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Karina travel 70 mile at an average peed of 50 mph. She then travel a further 60 mile. The average peed for the entire journey i 44 mph. Auming Karina didn't top, what wa her average peed for the final 60 mile to 2 dp?
The speed at 60 miles to 2 dp if Karina didn't stop, will be 38.5 mph.
Speed is defined as the rate of change of position of a subject in any direction. We have the basic formula to find the speed given by:
Speed = [tex]\frac{Distance}{Time}[/tex]
s = [tex]\frac{d}{t}[/tex]
To find the average speed for the last 60 miles, we need to know the time spent by Karina during the final 60 miles.
For the initial time during 70 miles, we follow the below calculations:
Initial Speed = [tex]s_{i}[/tex] = 50mph
Initial Distance = [tex]d_{i}[/tex] = 70 miles
Initial time for 70 miles = [tex]t_{i}[/tex]
[tex]s_{i}[/tex] = [tex]\frac{d_{i} }{t_{i} }[/tex]
[tex]t_{i}[/tex] = [tex]\frac{d_{i} }{s_{i}}[/tex]
[tex]t_{i}[/tex] = [tex]\frac{70}{50}[/tex] = 1.4 hr
For the Total time = t,
Total Speed = s = 44 mph.
Total Distance = d = [tex]d_{i} + d_{f}[/tex] = 70 + 60 = 130 miles
Total time = [tex]\frac{d}{t}[/tex] = [tex]\frac{130}{44}[/tex] = 2.96 hr
For the Final time during 70 miles = [tex]t_{f}[/tex]
t = [tex]t_{i} + t_{f}[/tex]
[tex]t_{f}[/tex] = t - [tex]t_{i}[/tex]
[tex]t_{f}[/tex] = 2.96 - 1.4 = 1.56 hr
Hence, the average speed for the final 60 miles can be calculated as:
Final Speed = [tex]s_{f}[/tex] = ?
Final Distance = [tex]d_{f}[/tex] = 60
Final Time = [tex]t_{f}[/tex] = 1.56 hr.
Average Speed = [tex]s_{a}[/tex] = [tex]\frac{d_{f}}{t_{f}}[/tex] = [tex]\frac{70}{1.56}[/tex] = 38.50 mph.
So, the Final average speed for the last 60 miles Karina traveled is 38.50 mph
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Find all solutions of x in degrees for (sinx- 1)(sinx+ 1) = 0.
Answer:
x = 90° + 180° × n, for all integers, n
Step-by-step explanation:
(sin x - 1)(sin x + 1) = 0
sin x = 1 or sin x = -1
The sine function has value 1 at 90° and all coterminal angles.
The sine function has value -1 at 270° and all coterminal angles.
Answer: x = 90° + 180° × n, for all integers, n
