The total cost of the set and the tax is 2653.6 dollars.
How to find the total cost of the set and the tax?The Myer family purchased a bedroom set for $2,480. The sales tax rate is 7 percent.
Therefore, the total cost of the set and the tax can be calculated as follows:
tax = 7% of 2480
tax = 7 / 100 × 2480
tax = 17360 / 100
tax = $173.6
Therefore, let's find the total cost of the set and tax.
total cost = 173.6 + 2480
total cost = 2653.6 dollars
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Find the radius of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 12.
A right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.
What is a right circular cylinder?The right circular cylinder is a cylinder with circular bases that are parallel to one another.
Three dimensions make up its form.
The two bases of the cylinder are joined at their centers by the cylinder's axis.
Sphere:
A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.
The radius of the right circular cylinder will be:
The formula for the volume of a sphere: V = 4/3πr²
Now, substitute r = 12 as shown:
V = 4/3πr²
V = 4/3π12²
V = 4/3π144
V = 7238.22947
Rounding off: 7238 units³
Nw, the formula for the volume of a right circular cylinder:
V = πr²h
Substitute V = 7238 and calculate for r as follows:
V = πr²h
7238 = πr²h
r² = 7238/πh
r = √7238/πh
Therefore, a right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.
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write the general antiderivative. (use c for the constant of integration. remember to use absolute values where appropriate.) 1 8 x 1 8x 1 8 x dx
The integration of the given function is as follows.
What is anti derivative?
In calculus, an antiderivative, inverse derivative, primitive perform, primitive integral or integral of a perform f could be a differentiable perform F whose spinoff is adequate to the initial perform f. this could be explicit symbolically as F' = f
Main body:
f (x) = x/8 +1/8x + (1/8)^x
to find the anti derivative , we need to integrate the function;
apply sum rule:
[tex]\int\ f{(x)} + g (x)\, dx[/tex] = [tex]\int\ f {(x)} \, dx + \int\ g {(x)} \, dx[/tex]
[tex]\int\ {(x/8)} \, dx[/tex] = x² /16
[tex]\int\ f {(1/8x)} \, dx[/tex] = 1/8 ln|x|
[tex]\int\ f {(1/8^x)} \, dx[/tex] = [tex]-\frac{1}{3\ln \left(2\right)\cdot \:8^x}[/tex]
hence
[tex]\int \frac{x}{8}+\frac{1}{8x}+\frac{1}{8^x}dx[/tex]= [tex]\frac{x^2}{16}+\frac{1}{8}\ln \left|x\right|-\frac{1}{3\ln \left(2\right)\cdot \:8^x}+C[/tex]
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what is a simpler form for the equation ^4√2401x^12y^16
Simplified form of fourth root of 2401x¹²y¹⁶ is 7x³y⁴
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
Given,
⁴√2401 x¹² y¹⁶=⁴√7*7*7*7 (x³)⁴(y⁴)⁴
=⁴√(7)⁴ (x³)⁴(y⁴)⁴
=⁴√(7 x³y⁴)⁴
= 7 x³y⁴
Therefore, Simplified form fourth root of 2401x¹²y¹⁶ is 7x³y⁴.
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ways 3 people can divide a 10 segment into a equal amount of shares
The number of ways to divide the shares into 10 equal segments is 120
How to determine the to divide the shares into equal segments?from the question, we have the following parameters that can be used in our computation:
Total number of segments, n = 10
Numbers to people, r = 3
The number of ways of dividing the segment is then calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 10 and r = 3
Substitute the known values in the above equation, so, we have the following representation
Total = ¹⁰C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have the following representation
Total = 10!/7!3!
Evaluate the quotient
Total = 120
Hence, the number of ways is 120
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In a statistical test of hypotheses, we say the data are statistically significant at level α if.
If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
What is hypotheses ?An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts. A hypothesis used to examine the link between two or more variables is known as a research hypothesis.
One dependent variable and one independent variable are shown to be related. For instance, eating more vegetables will help you lose weight more quickly. In this scenario, increasing your vegetable intake is an independent variable, while weight loss is the dependent variable.
It makes a claim that conflicts with the premise. There is no connection between the independent and dependent variables, which is a negative assertion. The emblem stands for.
Hence, If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
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What is the solution to square root of 7x - 4 = 2 square root of x
The square root √(7 · x - 4) = 2 has a solution for the variable x is 8 / 7.
How to find the solution to a square root
In this problem, we find a square root whose solution for the variable x has to be found solely by algebra properties. First, write the radical equation:
√(7 · x - 4) = 2
Second, elevate to the square of the expression:
7 · x - 4 = 4
Third, clear the variable x by algebra properties:
7 · x = 8
x = 8 / 7
The solution to the square root is equal to 8 / 7.
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the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound. what is the increase in percent
The increase in the price of the bananas = 8%
We know that the formula for percent change:
percent change = [(new value - old value)/ old value ] * 100
Here, the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound.
old value = 75 cents per pound
new value = 81 cents per pound
So, the percent increase in the price of bananas would be,
percent increase in price = [(81 - 75)/ 75 ] * 100
percent change = (6/75) * 100
percent change = 8%
Therefore, the increase is 8%
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This graph shows the different gang-related activities reported in small and large communities.
A graph titled Report of Gang Related Criminal Activity shows activities on the horizontal axis and percentage of people reporting on the vertical axis. 15% reported aggravated assault. 10% reported burglary. 23% reported drug sales. 47% reported graffiti. 8% reported larceny/theft. 6% reported motor vehicle theft. 5% reported robbery.
According to the graph, which gang-related activity is least reported in a large community?
graffiti
robbery
drug sales
aggravated assault
Mark this and return
Based on the graph showing the different gang-related activities reported in small and large communities, a gang-related activity which is least reported in a large community is: B. robbery.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.
Additionally, a pie chart is generally considered as the best graph to be used in graphically representing percentages and relative proportions.
According to the graph, we can logically deduce the following percentages of people that reported the different gang-related activities in small and large communities;
Aggravated assault = 15%.Burglary = 10%. Drug sales = 23% Graffiti = 47% Larceny/theft = 8% Motor vehicle theft = 6%Robbery = 5%In conclusion, robbery is the least reported gang-related activity in a large community with a percentage of 5 percent (5%).
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A circle with radius of 2 cm sits inside a 7 cm x 11 cm rectangle
I believe the answer you seek would be that the area of the shaded region would be [tex]64.43 cm^2[/tex].
Hope this helps!
Please help me solve this one.
Thank u!
Answer:
20 cm²
Step-by-step explanation:
It is a right triangle.
So, using Pythagorean theorem: OS² = OR² - RS²
OR = r (radius) + 8
OS = r
RS = 16
=> r² = (r+8)² - 16²
r² = r² + 16r + 64 - 256
r² = r² + 16r - 192
16r = 192
r = 192 / 16 = 12cm²
a) 12 cm²
b) 12 + 8 = 20 cm²
how is 27.25 divided by 5 = 5.05. Doesn't it equal 5.45
Answer:
Yes you are right
Step-by-step explanation:
It equals 5.45
Ignoring resistance, a sailboat starting from rest accelerates (dv/dt) at a rate proportional to the difference between the velocities of the wind and the boat. (a) The wind is blowing at 20 knots, and after 1 half-hour, the boat is moving at 10 knots. Write the velocity v as a function of time t. (b) Use the result of part (a) to write the distance traveled by the boat as a function of time.
V=Vw-ce^-kt is the velocity V as a function of time t when wind is blowing 20 knots and after 1 half hour the boat moves at 10 knots
What is acceleration?Acceleration is a vector quantity that is defined as the rate at which an object's velocity varies. When an object's velocity changes, it is said to be accelerating.
On occasion, sports broadcasters will suggest that a person is accelerating if they are traveling quickly. But speed has nothing to do with acceleration. Even while traveling very quickly, a person may not be accelerating. Changing the speed at which an item is travelling is what acceleration is all about. A substance is not accelerating if its velocity is not changing. The information on the right depicts an object that is speeding as it moves northward. Throughout time, the velocity is shifting. Every second, the velocity is changing by a fixed amount of 10 m/s.
How to solve?
Based on the information from the exercise, we have the equation:
dt/dv=k(Vw−V)
where V is velocity of the boat in knots/hour, tt is time in hours, Vw is velocity of wind.
This equation can be written:
dv/dt = k(Vw -V)
dv/Vw-V =kdt
Now, the variables are separated, tt appears only on the right side, and v only on the left. Integrate the left side in relation to v, and the right side in relation to t:
dv/Vw-V =kdt
∫dv/Vw-V =∫kdt
let Vw -V = u
-dv=du
dv= -du
∫-du/u =k∫dt
-ln|u| =kt +C
-ln|Vw-V| = kt + C
V=Vw-ce^-kt
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mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. a recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. the recruiting office randomly surveys 46 entry level mechanical engineers and 52 entry level electrical engineers. their mean salaries were $46,100 and $46,900, respectively. their standard deviations were $3450 and $4230, respectively. conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary. let the subscript m = mechanical and e = electrical. i. In words, state what your random variable X- Xe represents ii. State the distribution to use for the test. (Enter your answer in the form z or taf where df is the degrees of freedom. Round your answer to two decimal places.) iii. What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) iv. What is the p-value? (Round your answer to four decimal places.) v. Alpha (Enter an exact number as an integer, fraction, or decimal.)
Answer:
i. X represents the difference between the mean entry-level mechanical engineering salary and the mean entry-level electrical engineering salary.
ii. t distribution with df = 96
iii. t = -2.38
iv. p-value = 0.0190
v. Alpha = 0.05
i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).
ii. We used the t-distribution for the test due to unknown population standard deviations and relatively small sample sizes.
iii. The calculated test statistic is -2.1095.
iv. The degrees of freedom for the t-distribution are approximately 113242.
v. The p-value associated with the test statistic and degrees of freedom is approximately 0.0001.
i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).
ii. We will use the t-distribution for the test since the population standard deviations are unknown, and the sample sizes are relatively small (less than 30).
iii. The test statistic for this hypothesis test is calculated as:
[tex]t = (X - Xe) / \sqrt(s_m^2 / n_m) + (s_e^2 / n_e))}[/tex]
Where:
X = sample mean for mechanical engineering
Xe = sample mean for electrical engineering
Sm = standard deviation for mechanical engineering
Se= standard deviation for electrical engineering
nm = sample size for mechanical engineering
ne = sample size for electrical engineering
t = (46100 - 46900) / √(3450² / 46) + (4230² / 52))
= -800 / √(3450² / 46) + (4230² / 52))
= -800 / 379.4303
= -2.1095
iv.
Calculating the degrees of freedom:
df = (3450² / 46 + 4230² / 52)² / ((3450² / 46)² / (46 - 1) + (4230² / 52)² / (52 - 1))
= (119023.913 + 180714.2308)² / ((119023.913)² / 45 + (180714.2308)² / 51)
= 113242.1436
The degrees of freedom are approximately 113242.
Now, we need to find the p-value associated with the test statistic and degrees of freedom.
We can use a t-distribution table to look up the p-value.
Since the test is one-tailed and the test statistic is negative, we will look up the p-value in the left tail of the t-distribution with the given degrees of freedom.
Assuming the p-value is less than 0.0001, we can state that the p-value is approximately 0.0001.
v. To conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.
So, the significance level (alpha) is given as 5%.
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A credit card company charges 10% interest at the end of every month on the outstanding balance of a credit card. Jacqueline’s last credit card bill was $250. For 3 months, she makes the minimum payment of $50 each month, and does not use the credit card. How much does she owe the credit card company at the end of 3 months?
She owe $167.25 of the credit card company at the end of 3 months.
What is simple interest?To compute simple interest, duplicate the chief sum by the loan fee and the time. The recipe worked out is "simple interest = Principal x Interest Rate x Time." This condition is the easiest approach to ascertaining interest.
According to question:We ave,
interest = 10%, loaned amount = $250, monthly payment = $50
Then,
interest of first month = $250×1×0.1 = $25
She makes a payment of $50
Then $250 - $50 + $25 = $225
Second month:
interest = $225 ×0.1 = $22.5
Payment of $50
remain loan = $225 - $50 + 22.5 = $197.5
And third month
interest = $197.5×0.1 = $19.75
payment of $50 Then
Net payable loan = $197.5 - $50 + $19.75 = $167.25
Thus, remaining loan amount is $167.25.
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Many cars have keyless entry. To open the lock, you may press a 5-digit code on a set of buttons like that illustrated. The code may include repeated digits like 11433 or 55512. 1-2 3-4 5-67-8 9-0 a) How many different 5-digit codes can be made using the 10 digits if repetition is permitted?
Answer:
You can make up to "9" different 5-digit codes
show intro/instructions chance is skiing on a circular ski trail that has a radius of 0.9 km. chance starts at the 3-o'clock position and travels 2.75 km in the counter-clockwise direction. how many radians does chance sweep out? radians how many degrees does chance sweep out? degrees when chance stops skiing, how many km is chance to the right of the center of the ski trail? km when chance stops skiing, how many km is chance above the center of the ski trail?
The angle sweeped by chances during counterclockwise direction is 175.15° and in radian is 3.05, the distance of chance is from right and the above the centre of the circle is 0.27 km and 0.261km respectively.
Chance is running on a circular track that has a radius 0.9 km and he goes 2.75km into the counter clockwise direction from the 3-o'clock position.
The arc length of the circle is given by,
L = 2πR(A/360)
R is the radius,
L is the length of the arc,
A is the angle made in degrees.
Putting values,
2.75 =2π(0.9)(A/360)
A = 175.15°C.
Now, converting it into radians,
A in radian is 3.05.
Distance D of chance to the right of centre of the ski trail is,
D = R(1-0.7)
D = R(0.3)
D = 0.27 Km.
The distance D' of chance above the centre of the ski trail is,
D' = R(1-0.71)
D' = R(0.29)
D' = 0.261 Km.
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how do you calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity?
The degrees of freedom for goodness-of-fit chi-square tests are calculated with the formula: df=bins(or categories)−1−number of parameters of the distribution and the degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) .
In the given question we have to calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity.
When a categorical variable has more than two levels, a chi-square goodness-of-fit test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.
The degrees of freedom in this case are calculated with the formula:
df=bins(or categories)−1−number of parameters of the distribution.
The degrees of freedom for the chi-square are calculated using the following formula:
df = (r-1)(c-1)
where r is the number of rows and c is the number of columns.
The null hypothesis can be rejected if the observed chi-square test statistic is higher than the crucial value.
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Which represents a side length of a square that has an area of 450 square inches?15 startroot 2 endroot inches in. 16 startroot 3 endroot inches in. 112. 5 in. 115. 5 in.
Using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².
What is the area?A shape's area can be calculated by contrasting it with squares of a known size.
The square meter (abbreviated as m2), which is the area of a square whose sides are one meter long, is the common unit of area in the International System of Units (SI).
Three such squares would be the same size as a form with a three-square-meter area.
The area of any other shape or surface is a dimensionless real number, and the unit square is defined in mathematics to have area one.
So, the area of the square:
A = b²
Where B is the square's long side.
A = 450in²
A = b²
b² = 450
b = √450
b = 15√2 in
Therefore, using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².
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Correct question:
Which represents a side length of a square that has an area of 450 square inches?
a. 15 start root 2 end root inches in.
b. 16 start root 3 end root inches in.
c. 112. 5 in.
d. 115. 5 in.
Which number is a composite number?
A.11
B.21
C.31
D.41
Answer:
B. 21
Step-by-step explanation:
Composite numbers have more than two factors.
Answer: 21
Step-by-step explanation:
which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?
The correct statement to represent the comparison between defective parts produced by machines is option d. Machine A usually, but not always, produced fewer defective parts than machine B.
As given in the question,
Number of machines in a factory = 2
Statement compares the :
Number of defective parts produced by machines during first 4 hours
for 19 days.
Observations from the given scatterplot are:
a. Machine A always produced the same number of defective parts as machine B.
False. Variation in producing number of defective parts.
b. Machine A always produced fewer defective parts than machine B.
False.
c. Machine A always produced more defective parts than machine B.
False.
d. Machine A usually, but not always, produced fewer defective parts than machine B.
True. Sometimes like when Machine A produce 7 defective parts machine B produce 5.
e. Machine A usually, but not always, produced more defective parts than machine B.
False.
Therefore, option d) Machine A usually, but not always, produced fewer defective parts than machine B is the correct answer.
The complete question is:
A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days.
Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?
a. Machine A always produced the same number of defective parts as machine B.
b. Machine A always produced fewer defective parts than machine B.
c. Machine A always produced more defective parts than machine B.
d. Machine A usually, but not always, produced fewer defective parts than machine B.
e. Machine A usually, but not always, produced more defective parts than machine B.
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During a certain period of time, 2,000 penguins had an annual growth rate of 19%. What will the population of penguins be after 5 years?
Plot the points (-4, 6) and (5,3) and find the slope.
Answer:
-1/3
Step-by-step explanation:
3-6/5-(-4) = -3/9
simplify -3/9
-1/3
Calculate the expected value, the variance, and the standard deviation of the given random variable x. (round all answers to two decimal places. ) x is the number of red marbles that suzan has in her hand after she selects five marbles from a bag containing five red marbles and two green ones.
The expected value of the mean, variance and standard deviation are-
μ ≈ 4 (mean)σ = 0.61 (variance)δ = 0.78 (standard deviation)Explain the term mean of the data?The sum of all the numerical values in a series is divided by entire number to determine the mean of that number. The mean can also be used to assess the standard deviation or variable of a given set of data.For the given data in the question-
Random variable = x.Total marbles N = 7.Selected marble n = 5The formula for the mean;
μ = n×n /N
Put the values,
μ = 5×5/7
μ = 3.57
μ ≈ 4 (mean)
The formula for the variance is;
σ = nμ/N × (N - μ)(N - n)/N(N - 1) ....eq 1
σ = 5×4/7 × (7 - 4)(7 - 5)/7(7 - 1)
σ = 0.61 (variance)
For the calculation of the standard deviation-
δ = √σ ...eq 2
δ = √0.61
δ = 0.78 (standard deviation).
Thus, the expected value of the mean, variance and standard deviation are calculated.
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• we have two concentric circles. a chord of the larger circle is tangent to the smaller circle and has length 8. what’s the area of the annulus–the region between the two circles?
The Area of annulus - the region between the two circle is 50.26cm²
According to the question,
The length of chord of the large circle which is tangent to the small circle : AB = 8cm
Le the radius of large circle "R" and radius of smaller circle "r"
AB is a tangent to the smaller circle
AM = 8/2
=> AM = 4cm
In ΔOAM,
Using Pythagoras theorem ,
OA² = OM² + AM²
=> R² = r² + (4)²
=> R² - r² = 16
So, the area of annulus = π(R² - r²)
=> 16π (putting π = 3.14)
=> 50.26cm² is required area
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juliet rented a car for one day from a company that charges $80 per day plus $0.15 per mile driven. if she was charged a total of $98 for the rental and mileage, for how many miles of driving w
Juliet was charged $18 for driving 120 miles.
Given,
The rent of car per day = $80
The charge for per miles driven = $0.15
Juliet was charged a total of $98 for the rental and mileage.
We have to find the total miles of driving;
Here,
Charge for miles driven = Total charge - Rent of car for a day
Charge for miles driven = 98 - 80
Charge for miles driven = $18
Now,
Total miles driven = Charge for miles driven / Charge for one mile
Total miles driven = 18/0.15
Total miles driven = 120
That is,
Juliet was charged $18 for 120 miles of driving.
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When testing the differences between means, the _____ hypothesis suggests that population means are not equal. A. null B. research C. practical D. significant
When testing the differences between means, the research hypothesis suggests that population means are not equal. (Option B)
Hypothesis refers to a concept or explanation for a trend that is based on known facts but has not yet been proved. A research hypothesis, also known as scientific hypothesis, is a statement about the expected result of a study. It is the proposed answer to the research question and generally includes an explanation (e.g., x affect y because …). It introduces a research question and proposes an expected result. It illustrates the relationship between two variables - an independent and dependent variable. Hence, when testing the difference between means, the hypothesis that suggests that population means are not equal is a research hypothesis.
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determine the equation of the hyperbola with foci (13,-1)(13,−1) and (-13,-1)(−13,−1), and co-vertices (0,11)(0,11) and (0,-13)(0,−13).
The equation of the hyperbola is
[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 3650 = 0[/tex]
What is a hyperbola?
In mathematics, a hyperbola is a conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the centre. It is a type of smooth curve lying in a plane and has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The standard form of writing an equation of the hyperbola is,
[tex]\frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]
Where (h, k) is the centre; a is the distance from the centre to vertices; b is the distance from co-vertices to the centre.
Given,
Foci of the hyperbola are (13, -1); (-13, -1)
Co-vertices are (0,11); (0,-13)
As we know that the centre of the hyperbola is the midpoint of the foci, then it will be (h,k) = (0,-1)
Distance from centre to foci is, c = 13 [2c = 26; c = 26 / 2 = 13]
Distance from co vertices to foci is, b = 12 [ 2b = 24; c = 24 / 2 = 12]
let us assume a is the distance from the centre to the vertices.
we know that,
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
then,
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]
[tex]a = \sqrt{ {13}^{2} - {12}^{2} } [/tex]
[tex]a = \sqrt{169 - 144} [/tex]
[tex]a = \sqrt{25} [/tex]
[tex]a = 5[/tex]
Now, the equation of the hyperbola is,
[tex] \frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]
[tex] \frac{ {(x - 0)}^{2} }{ {5}^{2} } - \frac{ {(y + 1})^{2} }{ {12}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{25} - \frac{ {y}^{2} + 2y + 1 }{144} = 1[/tex]
[tex] \frac{144 {x}^{2} - 25 {y}^{2} - 50y - 50 }{25 \times 144} = 1[/tex]
[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 50 = 25 \times 144[/tex]
Hence the required equation is,
[tex]144 {x}^{2} - 25 {y}^{2} - 3650 = 0[/tex]
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What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di).
The correct option D)c = –3, d = –2; for which the expression becomes real number.
Explain the term real number?In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In opposed to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilized in evaluations of continuously altering quantities including size and time.For the given question,
The expression is-
= i(2 + 3i)(c + di)
Simplifying,
= i(2c + 2di + 3ci + 3d²)
= 2ci + 2di² + 3ci² + 3di³
= 2ci - 2d -3c - 3di
= (2c - 3di)i - 2d - 3c
Now, again for expression to produce a real number, the coefficient of must be zero.
Let's evaluate each choice.
A: 2c - 3d = 2x2 -3x3 = -5
B: 2x(-2) - 3x3 = -13
C: 2x3 - 3x(-2) = -12
D: 2x(-3) - 3x(-2) = 0
As option D only has the positive number, thus define the expression.
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The complete question is-
What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di)
choices: A)c = 2, d = 3 B)c = –2, d = 3 C)c = 3, d = –2 D)c = –3, d = –2
Answer: D) c = –3, d = –2
Step-by-step explanation:
Correct on Edge
which of the following would be a correct interpretation of a 99% confidence interval such as 4.15.6? question content area bottom part 1 choose the correct answer below. a. it means that 99% of sample means fall between 4.1 and 5.6. b. we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of . c. there is a 99% chance that will fall between 4.1 and 5.6. d. it means that 99% of a
We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
The correct interpretation of a 99% confidence interval is that we are 99% confident that the true population mean falls in it.
The probability that it contains the true population mean is 99%.
Given 99% confidence interval : 4.1 < μ < 5.6
Then, the correct interpretation is we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
Hence the answer is We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
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Factoring trinomials 8x^2 + 2x -3
Answer:
(2x - 1) (4x + 3)
Step-by-step explanation: