Answer:
value of k is ± 24√2
Decimal form: -33.94, 33.94
Step-by-step explanation:
⇒ The given equation \(6x^{2} -kx +48=0\)
⇒ To find, The value of k if the roots are equal and real.
⇒ Solution,We can easily solve this problem by following the given steps.
According to the question,
We have the following quadratic equation: \(6x^{2} -kx +48=0\)
Now, we know that if the roots are real and equal then the value of the determinant (D) is zero.
D = \(\sqrt{b^{2} - 4ac}\) = 0
b² = 4ac
b² - 4ac = 0
Here, a = 6, b = -k, c = 48
⇒ (-k)² − 4(6)(48) = 0
⇒ k² − 24(48) = 0
⇒ k² − 1,152 = 0
⇒ k² − 1,152 + 1,152 = 0 + 1,152
⇒ k² = 1,152
⇒ k =√1,152
⇒ k = ±24√2
Hence, the value of k is ± 24√2
Consider the function f(x)= 3x^2-6x/x-2. What is the factored form of the numerator?
in me girl 7735293+3;$7373-$-$-37372+2
can you please help me
Answer:
i would say none of the above can i get brainlest
Step-by-step explanation:
Please help ASAP. The picture is above
Correct Answers only!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest dollar.
Answer:
128,000
Step-by-step explanation:
I=prt
I=80,000 x 15 x 4
I=128,000
Answer:
$128000
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 80000 × 15/100 × 4
I = $48000
He saves = 48000 +80000 = $128000
5x+ 10y =300
what is x and y?
Answer:
5x + 10y + -10y = 300 + -10y
Step-by-step explanation:
what is the slope of 9x -5y = 4
the general equation of a graph is given by
y = mx + c
where m= slope
c=intercept
the equation given is
9x-5y=4
make y subject of formula
9x-4=5y
5y=9x-4
divide through by 5
y=9/5x-4/5
comparing with the general equation
mx=9/5x
m=slope=9/5
The population of an island was 2 million in 1950. The population grew in an exponential trend for 63 years and became 6.5 million in 2013. It is estimated that the carrying capacity of the island is 10 million. Assuming the population growth rate in the future remains the same as in the last 50 years, what will be the population of the island in 2050? (Assume constant carrying capacity and consumption/capita.)
The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.
If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050
The population is given to be increasing exponentially, which means it will follow the equation:
\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.
We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:
\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)
Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.
Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:
\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)
where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)
where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)
Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)
To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):
\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.
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Harry receives a package for his birthday the package weighs 50 Oz what is the weight of the package in pounds and ounces?
Answer:
3 pounds 2 oz
Step-by-step explanation:
1 pound = 16 oz
x pounds = 50 oz
Cross Multiply
16x = 50 oz Divide by 16
x = 50 / 16
x = 3 pounds with 2 oz left over.
Your calculator will give you 3.125
0.125 = 1/ 8
1/8 * 16 = 2
tch and his brother, Terry, went on a hiking expedition. Starting at sea level, the brothers climbed to a scenic cliff located 6.6 kilometers above them. From there, they descended 1.3 kilometers in one hour. Mitch discovered that he had left behind some essential supplies on the cliff. So, the brothers decide to head back up. They climbed 0.8 kilometer within the next hour. At this point, Mitch and Terry were
away from the scenic cliff.
Mitch and Terry were 0.5 km away from the scenic cliff
What is Sea Level ?Sea level is the base for calculating the depth and the elevation of Earth
It is given that
Total Height of the scenic Cliff = 6.6km
After 1 hour the brothers are at = 6.6 - 1.3 km = 5.3 km from the sea level.
They climb back 0.8 km in the next hour so they will be
5.3 +.8 = 6.1 km from the sea level
6.6 - 6.1 = 0.5 km
Therefore the brothers are 0.5 km away from the scenic cliff
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Based on this data, the difference in the dollar value of Assistantship (Stipend) between these two fields is how many standard errors away from the hypothesized difference?
t-Test : Two-sample assuming unequal variances
Assistantship (stipend) Assistantship arts (stipend) science
Mean 24041.62203 25952.36501
variance 621483.0801 615193.5853
observations 521 479
hypothesized mean different 0
df 992
t stat -38.39036076
P(T<=t) one tail 1.1775E-198
t critical one-tail 1.646391129
P(T<=t) two tail 2.3551E-198
t critical two-tail 1.962358258
The difference in the dollar value of Assistantship (Stipend) between art and science fields with standard errors is equal to 1.214.
Mean 24041.62203 25952.36501
Sample mean difference between Assistantship (stipend) in arts and science is equal to
= $25952.36501 - $24041.62203
= $1910.74298.
Hypothesized mean difference is 0 (there is no difference in stipend between the two fields).
Variance 621483.0801 615193.5853
Sample size 521 479
Standard error of the difference is,
=√[(variance in arts / sample size in arts) + (variance in science / sample size in science)]
= √[(615193.5853 / 479) + (621483.0801 / 521)]
= $49.77
t-statistic
= (sample mean difference - hypothesized mean difference) / standard error of the difference
Substitute the values into the t-statistic formula,
⇒ t-statistic = ($1910.74298 - 0) / $49.77
⇒ t-statistic = 38.39
t-critical value for a two-tailed test with 992 degrees of freedom at a significance level of 0.05 is 1.9624.
t-statistic (38.39) > t-critical value (1.9624)
⇒Reject the null hypothesis that there is no difference in stipend between the two fields.
standard errors
= t-statistic / √(sample size)
= 38.39 / √(479 + 521)
= 38.39 /31.62
=1.214
Therefore, the difference in the dollar value of Assistantship (Stipend) between these two fields is 1.214 standard errors away from the hypothesized difference.
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small p-values indicate that the observed sample is inconsistent with the null hypothesis. T/F?
True. Small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.
Small p-values indicate that the observed sample data provides strong evidence against the null hypothesis. The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of observing the obtained sample data, or more extreme data, if the null hypothesis is true.
When the p-value is small (typically less than a predetermined significance level, such as 0.05), it suggests that the observed sample data is unlikely to have occurred by chance under the assumption of the null hypothesis. In other words, a small p-value indicates that the observed data is inconsistent with the null hypothesis.
Conversely, when the p-value is large (greater than the significance level), it suggests that the observed sample data is likely to occur by chance even if the null hypothesis is true. In such cases, there is not enough evidence to reject the null hypothesis. Therefore, small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.
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For a particular cleaning product, it is recommended that 4 ounces of product are diluted using 20 ounces of water. Which of the following fractions represents the recommended ratio of cleaning product to water?
A. 1/5
B. 5/1
C. 1/6
D. 6/1
E. 5/6
The ratio of cleaning product to water for the condition is 1/5
What are ratios?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.
Given it is recommended that 4 ounces of the product are diluted using 20 ounces of water.
to find the ratio of cleaning products to water
ratio = cleaning product/water
cleaning product = 4 ounce
water = 20 ounces
ratio = 4/20
4/20 is equivalent to 1/5
ratio = 1/5
Hence option A is correct.
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Check out this cube: The figure presents a cube. The length of one edge is labeled as 3 units The figure presents a cube. The length of one edge is labeled as 3 units Find the surface area of the cube (above) using its net (below). The figure presents a surface net of a cube. The net consists of 4 squares connected in a row. The second square from the left is also connected to a square above it, and a square below it. The length of one side of one square is labeled as 3 units. The figure presents a surface net of a cube. The net consists of 4 squares connected in a row. The second square from the left is also connected to a square above it, and a square below it. The length of one side of one square is labeled as 3 units. units 2 2
Answer: look it up-
Step-by-step explanation:
For an input array of size n, the number of multiplications that are performed when the algorithm is executed equals the number of iterations of the inner loop, namely _____. The number of additions that are performed when the algorithm is executed equals the number of iterations of the outer loop namely ____. Hence, when the total number of multiplications and additions is expressed as a polynomial in n, the result is ____. Thus, by the theorem on polynomial orders, the term-by-term polynomial algorithm has the following order. O Θ(n) O Θ(n2) O Θ(2n) O Θ(n3) OΘ(3n)
For an input array of size n, the number of multiplications performed when the algorithm is executed equals the number of iterations of the inner loop, namely n2.
The number of additions performed when the algorithm is executed equals the number of iterations of the outer loop namely n.
Hence, when the total number of multiplications and additions is expressed as a polynomial in n, the result is Θ(n2).
How to solveThe outer and inner loops of the term-by-term polynomial evaluation process are two nested loops. One term of the polynomial is calculated for each iteration of the outer loop by multiplying each term's coefficient by the corresponding value from the input array.
The number of terms in the polynomial, which is n, equals the number of iterations in the outer loop. One multiplication is carried out during each inner loop iteration. The degree of the term, which is also n, determines how many times the inner loop iterates.
Therefore, the total number of multiplications performed when the algorithm is executed equals the product of the number of iterations of the outer loop and the number of iterations of the inner loop, which is n * \(n = n^2.\)
This is why the number of multiplications that are performed when the algorithm is executed is expressed as \(O(n^2).\)
Hence the answer to the first blank will be n2.
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Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?
Answer:
Taylor is 15 and Spencer is 3.
Step-by-step explanation:
3×5=15
15+3=18
Answer:
Taylor is 15 years old.
Spencer is 3 years old.
Step-by-step explanation:
Let Taylor's age be x
Let Spencer age be y
x = 5y ......…...........(1)
x + y = 18...................(2)
Make y the subject of the formula in equation (1)
y = x/5
Substitute x/5 for y in equation 2
x + y = 18...................(2)
\(x+\frac{x}{5} =18\\\frac{6x}{5} = 18\\Cross multiply .\\6x = 90\\Divide both sides of the equation by 6\\x = 15\\Substitute 15 for x in equation 1\\\)\(x = 5y (1)\\15 = 5y\\Divide both sides of the equation by 5\\y = 3\)
Select the correct answer.
If f(x) = 3x+2 and g(x) = 2x - 2. what is (f- g)(x)?
OA. X+4
OB. X-2
OC. X
OD. 5x-2
O E.
X-4
Answer:
A
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1
= 3x + 2 - 2x + 2 ← collect like terms
= x + 4
a restaurant offers a choice of 4 salads, 10 main courses, and 4 desserts. how many possible meals are there?
Answer:
160
Step-by-step explanation:
4 × 10 × 4 = 160
(Random words to hit the character limit please ignore)
a30 arithmetic sequence of 1,-4,-9,-14
The 30th term a30 of the sequence is -1445
How to determine the value of a30?The definition of the function is given as
arithmetic sequence of 1,-4,-9,-14
The above definitions imply that we simply subtract 5 from the previous term to get the current term
Using the above as a guide,
so, we have the following representation
First term, a = 1
Common difference, d = 5
An arithmetic sequence is represented as
a(n) = a + (n - 1)d
For the 30th term, we have
a(30) = a + 29d
So, we have
a(30) = 1 + 29 * -5
Evaluate
a(30) = -144
Hence, the value of a30 is -144
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This is compliacted. 3 answers. Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ.
Prove: ΔWXY ~ ΔWVZ
100 points
4. \(WX=WY, WV=WZ\)
6. Substitution property of equality
9. SAS similarity
Two cars are traveling along a straight road. Car A maintains a constant speed of 77.0 km/h. Car B maintains a constant speed of 114 km/h. At t=0, car B is 45.0 km behind car A. How long does it take before car A is overtaken by car B?
Answer: 72.97 Minutes
Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.
To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.
Relative speed = Speed of car B - Speed of car A
Relative speed = 114 km/h - 77.0 km/h
Relative speed = 37.0 km/h
So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.
To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.
Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours
Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).
Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes
Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.
Hope this helps!
plzzzzzz help due in 20 mins
the answer is lines 3 and 5
Peter was thinking of a number. peter adds 6 to it, then doubles it and gets an answer of 48.5. what was the original numbe
Answer: The original number was 18.25 or 18 1/4
18.25 plus 6 is 24.25
24.25 times 2 is 48.5
Step-by-step explanation:
mark as brilliant answer
Answer:
18.25
Step-by-step explanation:
x = number
add 6: (x+6)
double it : 2(x+6)
result = 48.5
2 (x+6) = 48.5
x+6 = 24.25
x = 18.25
A baseball pitcher won
80% of the games he
pitched. If he pitched 48
winning ballgames, how
many total games did he
pitch?
Answer:
If 80% of the games he pitched were winning ballgames, then 100% - 80% = 20% of the games he pitched were not winning ballgames.
Since 48 games represent 80% of the total number of games he pitched, then 48 / 0.8 = <<48/0.8=60>>60 games represent 100% of the games he pitched.
Thus, he pitched a total of 60 games. Answer: {60}.
Step-by-step explanation:
what is 8+9 pllllllllllllssssssssssssssssssssssssss
Answer:
17
Step-by-step explanation:
8+9 is 17
Answer:
89
it's helpful ya lol :)
I think it's 17 :(
What is the slope of a line that is perpendicular to the graph of y = 4/5x+9?
Answer:
m = -5/4
General Formulas and Concepts:
Algebra I
The slope of the perpendicular line is the negative reciprocal of the original slope.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope-Intercept Form (Original): y = 4/5x + 9
Step 2: Break Original Function
Slope m = 4/5
y-intercept b = 9
Step 3: Find slope of perpendicular line
Take the negative reciprocal.
Perpendicular Slope m = -5/4
Factor completely
125x-27x^4
Step by step explanation
Answer:
125x - 33x⁴
Pull out like factors :
125x - 27x⁴ = -x • (27x3 - 125)
Factoring: 27x³- 125
Theory : A difference of two perfect cubes, a³ - b³ can be factored into
(a-b) • (a² +ab +b²)
(a-b)•(a²+ab+b²) =
a³+a²b+ab²-ba²-b²a-b³ =
a³+(a2b-ba²)+(ab²-b²a)-b³ =
a³+0+0+b³ =
a³+b³
Check : 27 is the cube of 3
Check : 125 is the cube of 5
Check : x³ is the cube of x¹
Factorization is :
(3x - 5) • (9x² + 15x + 25)
\( \)
A triangle has two angles that measure 73 degrees and 38 degrees.
What is the measurement of the third angle? ( please help)
Answer:
The third is sixty-nine degrees
Step-by-step explanation:
73°+38°+69°=180°
Zippy's Zip Line Land plans to install a new zip line between two trees. One tree is 45 feet east (x coordinate) of the storage hut and the other is 25 feet north ( y coordinate) of the storage hut. The end of the zip line on the tree cast of the hut will be at a height (z coordinate) of 46 feet and the other end will be at a height of 39 feet on the tree north of the hut. If the zip line is stretched taut, how many feet of zip line is needed. Round your answer to the hundredths place.
We can set the first point of our zip line as follows:
(x₁ , y₁ , z₁) = (0, 0, 46)
So the end of the zip line would be:
(x₂ , y₂ , z₂) = (45, 25, 39)
Now let's use the given distance formula to solve this problem:
Evaluate the expression for A=3
32-4a
Hi ! Dude
Answer:
20 is the correct answer
Step-by-step explanation:
Given :a = 3 and ,An expression = 32 - 4aWhat we have to do :After reading question we can understand that we have to find the value of expression by plugin the value of a .
Solution Starts :\( \qquad \: \rightarrow 32 - 4a \)
Plugin value of a ,
\( \qquad \:\rightarrow \: 32 - 4(3)\)
\(\qquad \: \rightarrow \: 32 - 12\)
\(\qquad \: \rightarrow \: \underline{ \underline{20}}\)
Hence , 20 is the answer .
- - - -- - -- - - -- - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - --
\(\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\)
Evaluate the expression for a=3
32-4a
\(\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\)
Provided Information:-
a=3The expression \(\bold{32-4a}\)
To Find:-
Simplify the expression 32-4a
In order to do that, we should
Substitute 3 in lieu of a:-\(\tt{32-4(3)}\)
Multiply:-
\(\tt{32-12}\)
Subtract:-
\(\dashrightarrow\bigstar\boxed{\boxed{\underline{\bold{20}}}}\dashleftarrow\)
So our final solution is 20.
Good luck.- - -- - - - - - - - - - - - - - - - - -- - - - - - - - - - -- -- - - - - -- - - - - - - - - - - - -
6. A lighting fixture manufacturer has daily production costs of c=0.25n²-10n+800, where C is the total
daily cost in dollars and n is the number of light fixtures produced.
a) Is the manufacturer's cost increasing or decreasing when they produce between 10 and 15 light fixtures?
Prove your claim with math. (2 pts)
b) Is the manufacturer's cost increasing or decreasing when they produce between 20 and 25 light fixtures?
Prove your claim with math. (2 pts)
By finding the average rate of change, we can see that:
a) The cost decreases.
b) The cost increases.
How to know when the cost is increasing or decreasing?
To check that, we need to find the average rate of change on the interval.
Remember that for function f(x) on an interval (a, b), the average rate of change is:
R = (f(b) - f(a))/(b - a)
Here the cost function is:
c(n) = 0.25*n² - 10n + 800
a) In the interval [10, 15] the average rate of change is given by:
R = (c(15) - c(10)/(15 - 10)
Where:
c(15) = 0.25*15^2 - 10*15 + 800 = 706.25
c(10) = 0.25*10^2 - 10*10 + 800 = 725
Then the average rate of change is:
R = (706.25 - 725)/(15 - 10) = -3.75
This means that between 10 and 15 light fixtures, the cost is decreasing.
b) Now we have the interval [20, 25], so let's do the same ting:
c(20) = 0.25*20^2 - 10*20 + 800 = 700
c(25) = 0.25*25^2 - 10*25 + 800 = 706.25
Here the average rate of change is:
R = (706.25 - 700)/(25 - 20) = 1.25
It is positive, which means that the cost is increasing.
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