The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
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Please help I will give brainliest
The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).
What is Segment?
In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.
To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:
((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.
So, let's first find the coordinates of the midpoint of segment AB:
Midpoint = ((-3 + 7)/2, (2 - 10)/2)
= (2, -4)
Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:
((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)
= (-1/2, -1)
So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).
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How do you work this out?
Anyone help please .
Answer:
x=5/4 or x=5/9
pls mark me brainliest
Answer:
x=5/4 (for the first x),x=5/9 (for the second x)
Using the given variable, write an inequality to model the scenario.
Bowlers that score at least 228 points will make it to the next round.
Let p = the number of points
Answer:
p ≥ 228
Step-by-step explanation:
p ≥ 228
This inequality means the Bowlers have to score at least 228 points to move on.
Hope this helped!
out of total student 3/5 are girls .On a particular day one third boys and 2/5 girls were absent. If total absentees was 280 find total number of students
Answer:
Step-by-step explanation:
Calculate fraction of boys
If girls =3/5, then boys = 1 - 3/5 = 2/5.
Calculate fraction of students absent
Girls - 2/5 of 3/5 = 6/25
Boys - 1/3 of 2/5 = 2/15
6/25+2/15=28/75
Calculate total number of students
If 28/75 = 280
280/28=10
10x75=750
Total number of students = 750
Geometry Altitudes Questions
The value for the height h of the right triangle is equal to 4.8990.
How to evaluate for the value of h for the triangleThe height h of the right triangle divides the triangle in two triangles with the same proportions as the original triangle, which implies that if the adjacent for the smallest triangle is 4 and the adjacent of the other triangle is h, then:
h/6 = 4/h {considering the tangent ratio}
h² = 4 × 6 {cross multiplication}
h = √24
h = 4.8990
Therefore, value for the height h of the right triangle is equal to 4.8990.
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(a) Factorise 25t²₋ 4
(b) Factorise x²₋6x₋3xy₊18y
Step-by-step explanation:
(a) To factorize 25t² - 4, we can use the difference of squares formula:
a² - b² = (a + b)(a - b)
In this case, a = 5t and b = 2. So we have:
25t² - 4 = (5t + 2)(5t - 2)
Therefore, 25t² - 4 can be factorized as (5t + 2)(5t - 2).
(b) To factorize x² - 6x - 3xy + 18y, we can group the terms:
(x² - 3xy) - (6x - 18y)
We can then factor out the common factors from each group:
x(x - 3y) - 6(x - 3y)
Notice that both terms have a factor of (x - 3y), so we can factor it out:
(x - 3y)(x - 6)
Therefore, x² - 6x - 3xy + 18y can be factorized as (x - 3y)(x - 6).
(a)
.
in this case, a= 25t and b= 4.
.
ans: (5t-4)(5t+4)
On The Standard Normal Curve, The 68th Percentile Corresponds To The Mean Value Of The Data Set Is That True Or False
The 68th percentile on the standard normal curve corresponds to the mean value of the data set. This statement is false.
The 68th percentile on the standard normal curve corresponds to one standard deviation away from the mean. In other words, approximately 68% of the data falls within one standard deviation of the mean on the standard normal distribution. This is a property of the normal distribution, which is a continuous probability distribution commonly used in statistics.
To clarify, the mean value of a data set is the arithmetic average of all the values in the data set. It is not directly related to the 68th percentile on the standard normal curve. The mean is a measure of central tendency and is influenced by all the data values, while the percentile is a measure of relative position in the distribution of data.
Therefore, it is important to understand the difference between percentiles and measures of central tendencies, such as mean, median, and mode, when analyzing data using statistical techniques.
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In the past 5 years company A sold 7.5x10^4 reams of paper. Company B sold 9.5 x10^3 reams. How many total reams did they sell altogether and how many more did company a sell than B?
Giving 20 pts please help!
84500 reams of paper are the total amount the two companies sell in the past five years.
65500 is the amount that Company B performed better than company A.
What is a Company?A company can be defined as the part in which the main aim or goal is to earn a profit. This was to generate the income that they will be having in the firm. There are various employees that are present in the company and work towards a common goal.
The Amount that is made by company A is
[tex]7.5 \times 10000[/tex]
[tex]=75000[/tex]
The amount of paper manufactured by company B is
[tex]= 9.5 \times 1000[/tex]
[tex]= 9500[/tex]
A) The total that is made by both companies in 5 years will be
[tex]= \text{Company A + Company B}[/tex]
[tex]= 75000 + 95000[/tex]
[tex]= 84500[/tex]
B) Company B made better products as compared to Company A
[tex]= \text{Company B - Company A}[/tex]
[tex]=75000 - 9500[/tex]
[tex]=65500[/tex]
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Answer:
total: 84,500 or 8.45×10⁴difference: 65,500 or 6.55×10⁴Step-by-step explanation:
You want the sum and difference of 7.5×10^4 and 9.5×10^3.
Scientific notationNumbers are most conveniently added or subtracted in scientific notation when the multipliers have the same exponent. For this we can rewrite Company B's volume as ...
9.5×10^3 = 0.95×10^4
total sales = 7.5×10^4 + 0.95×10^4 = 8.45×10^4 = 84,500
difference in sales = A -B = 7.5×10^4 -0.95×10^4 = 6.55×10^4 = 65,500
__
Additional comment
You can enter the numbers "as is" in a calculator or spreadsheet and format the output in whatever form you need.
If θ = 1 π 6 , then find exact values for the following: sec ( θ ) equals csc ( θ ) equals tan ( θ ) equals cot ( θ ) equals Add Work
If θ = 1π/6 then six trigonometric functions of θ are: sec(θ), cos(θ), tan(θ), cot(θ), is [tex]((2 \sqrt{(3)})[/tex], [tex]\sqrt(3)/2[/tex], [tex]\sqrt{(3)}/3[/tex], and [tex]\sqrt{(3)[/tex], respectively.
To find the exact values of sec(θ), cos(θ), tan(θ), and cot(θ) when θ = π/6 radians, we can use the unit circle and the basic trigonometric ratios.
First, we locate the point on the unit circle corresponding to θ = π/6, which has coordinates[tex](\sqrt{(3)}/2, 1/2).[/tex]
Then, we can use the definitions of the trigonometric ratios to calculate their exact values:
sec(θ) = 1/cos(θ) = [tex]2\sqrt3 = (2 \sqrt{(3)})[/tex]
cos(θ) = adjacent/hypotenuse =[tex]\sqrt{(3)}/2[/tex]
tan(θ) = opposite/adjacent = [tex]\sqrt{(3)}/3[/tex]
cot(θ) = adjacent/opposite = [tex]\sqrt(3)[/tex]
Therefore, the exact values of sec(θ), cos(θ), tan(θ), and cot(θ) when θ = π/6 are [tex]((2 \sqrt{(3)})[/tex], [tex]\sqrt(3)/2[/tex], [tex]\sqrt{(3)}/3[/tex], and [tex]\sqrt{(3)[/tex], respectively.
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A student thinks of a number. They square it and then subtract 9. Their answer is 315. What number is the student thinking of?
The number that the student is thinking of is 18.
What is number?
A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers.
Let x be the number that the student is thinking of.
According to the problem, the student squares the number and subtracts 9:
x² - 9 = 315
To solve for x, we can add 9 to both sides of the equation:
x² = 324
Then, we can take the square root of both sides:
x = ±18
Since x must be a positive number (according to the problem statement), we can discard the negative solution. Therefore, the number that the student is thinking of is 18.
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Solve for x in the triangle.
Answer:
D. 87
Step-by-step explanation:
You want to know the measure of the angle opposite the longest side in a triangle with side lengths 13, 16, and 20 inches.
Angle relationsThe angle x is opposite the side of length 20 inches in this triangle, which is the longest side. That tells you x is the largest angle.
The largest angle in any triangle is never less than 60°. This eliminates all answer choices except the last one:
x = 87
Law of CosinesIf you want to go to the trouble to solve the triangle, the law of cosines is helpful. For sides a, b, c and angle C, it tells you ...
c² = a² +b² -2ab·cos(C)
Solving for the angle, we have ...
C = arccos((a² +b² -c²)/(2ab))
C = arccos((13² +16² -20²)/(2·13·16)) = arccos(25/416) ≈ 86.55°
x ≈ 87
a random variable x has the following probability distribution. values of x -1 0 1 probability 0.3 0.4 0.3 (a) calculate the mean of x.
The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.
The mean of x is calculated by the following formula:
mean of x = ∑(x * P(x))
Where, ∑ = Summation operator
x = Value of random variable
P(x) = Probability of the corresponding value of x.
Let's calculate the mean of x using the formula provided above.
mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)
= -0.3 + 0 + 0.3
= 0
Therefore, the mean of x is 0.
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Baseball hats are on sale for 12% off the original price of the sale price is $12.50 what was the original price? round the answer to the nearest cent
The original price of the baseball hat before 12% off in the sale was $14.20.
What is a percentage?A number can be expressed as a fraction of 100 using a percentage. It frequently serves to indicate a portion of a total and is represented by the sign %. We may state that 25% of the class is made up of guys, for instance, if there are 100 pupils in the class and 25 of them are male.
The Roman term per centum, which meaning "by the hundred," is where the word "percent" originates.
Let us suppose the original price of the baseball hat = x.
Given that, baseball hats are on sale for 12% off the original price.
That is,
12.50 = x(1 - 12/100)
12.50 = x(100 - 12)/100
12.50 = x(0.88)
x = 14.2
Hence, the original price of the baseball hat was $14.20.
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F= (y + 2x, 2x + 5z, 7y + 8x), C is the circle with radius 5, cen- ter at (2,0,0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0,0,0).
The set of points that represent the intersection of the curve of vector function F and circle C is
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t ranges from 0 to 2π}.
We have,
Vector function F = (y + 2x, 2x + 5z, 7y + 8x)
C is the circle with radius 5, center at (2,0,0), in the plane x = 2
C is oriented counterclockwise as viewed from the origin (0,0,0)
The vector function F represents a three-dimensional curve in space.
The circle C is a two-dimensional object in space, lying in the plane x = 2 and centered at (2,0,0) with a radius of 5. It is also oriented counterclockwise as viewed from the origin (0,0,0).
To find the intersection of vector function curve F and circle C, we can substitute the equation of the circle into the equation of the curve and solve for the parameter(s) that satisfy the equation. However, since the equation of the circle is given in terms of x only, we can simplify the equation of the curve by substituting y = 0 and z = 0:
F = (2x, 2x, 8x)
Now, we can substitute x = 2 + 5cos(t) and y = 5sin(t) (the parameterization of the circle C in the plane x = 2) into the equation of the curve F:
F = (2(2+5cos(t)), 2(2+5cos(t)), 8(2+5cos(t)))
= (4+10cos(t), 4+10cos(t), 16+40cos(t))
Thus, the intersection of vector function curve F and circle C is given by the set of points:
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t in [0, 2π)}
Note- that the parameter t represents the angle of rotation around circle C, and ranges from 0 to 2π to cover the entire circle.
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Find the expected value of the winnings
from a game that has the following
payout probability distribution:
The expected probability distribution is $4.35
We must multiply each supplied chance by the respective payout value in order to determine the expected value.
As a result, we have the payout probability distribution shown below:
0.35(1) + 2(0.2) + 5(0.1) + 8(0.2) + 10(0.15) (0.15)
= 0.35 + 0.4 + 0.5 + 1.6 + 1.5
= $4.35
When the set of possible outcomes is discrete in nature, the distribution is referred to as a discrete probability distribution. When a dice is rolled, all conceivable results, for instance, are discrete and result in a large number of outcomes. A different name for it is the probability mass function.
statistical distributions that can be used
Uniform discrete distribution The chances of each outcome are equal.
Single-trial distribution with two potential results.
A series of Bernoulli events are called the binomial distribution.
Poisson Distribution: The likelihood that a particular occurrence may or may not occur.
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4x 2 +6x−13=3x 2 to the nearest tenth.
The solutions to the equation are x = -4 and x = 1.
What is quadratic formula?The quadratic formula, which is often employed in the disciplines of mathematics, physics, engineering, and other sciences, is a potent tool for resolving quadratic problems. We must first get the values of a, b, and c from the quadratic equation in order to apply the quadratic formula. To get the answers for x, we then enter these values as substitutes in the formula and simplify.
The given equation is 4x² + 6x - 13 = 3x².
Rearranging the equation we have:
x² + 6x - 13 = 0
The quadratic formula is given as:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a = 1, b = 6, and c = -13.
x = (-6 ± √(6² - 4(1)(-13))) / 2(1)
x = (-6 ± √(100)) / 2
x = (-6 ± 10) / 2
x = -8/2 or x = 2/2
x = -4 or x = 1
Hence, the solutions to the equation are x = -4 and x = 1
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4. Find the solution of the following equations:
a) x + 5 = 15
b) 12 – y = 12
c) 3a = 27
d) y/4 = 20
e) 2 + y = 0
dr carl is a mathematics and statistics lecturer. he is interested in studying a new approach at teaching mathematics and statistics in high school. recently this new approach has been adopted. it was previously the case that the mean score for all high school students doing their end of year exam was 71, however, the population standard deviation is unknown. the scores of all students are approximately normally distributed. he thinks that, with this new teaching approach, the mean score may have increased. a random sample of 39 scores is gathered and the sample mean and standard deviation calculated. dr carl will conduct a hypothesis test using a level of significance of 0.01. select the correct null and alternative hypotheses for this test:
The test is one-tailed to the right due to the Alternate hypothesis.
In a hypothesis test, a Null hypothesis (H0) is a statement of "no effect" or "no difference," whereas the Alternate hypothesis (HA) is a statement of "some effect" or "some difference." Here are the correct null and alternative hypotheses for the given scenario: Null hypothesis: H0: μ = 71, Alternative hypothesis: HA: μ > 71 (One-tailed test) we have a one-tailed hypothesis test since the research hypothesis is directed. In a one-tailed test, we're looking for a difference in one direction only. In this case, Dr Carl thinks that there has been an improvement, so the alternative hypothesis reflects this. Therefore, the test is one-tailed to the right.
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HW7.4. Find the frequency with the largest amplitude Find the frequency w for which the particular solution to the differential equation dạy dy 2- + dt2 + 2y = eiwt dt has the largest amplitude. You can assume a positive frequency w > 0. Probably the easiest way to do this is to find the particular solution in the form Aeiwt and then minimize the modulus of the denominator of A over all frequencies w. W= number (rtol=0.01, atol=1e-08) ?
Answer:
the frequency with the largest amplitude Find the frequency w for which the particular solution to the differential equation dạy dy 2- + dt2 + 2y = eiwt dt ...
Step-by-step explanation: basically bigger is better
Suppose that the speed at which cars go on the freeway is normally distributed with a mean of 66 miles per hour (mph) and standard deviation 10 mph. Letxxbe the speed for a randomly selected car. Round all answers to 4 decimal places where possible.What is the z-score for a car that is caught going 60 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going below 60 mph?P(x≤60)=P(x≤60)=What is the z-score for a car that is caught going 86 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going above 86 mph?P(x≥86)=P(x≥86)=If a highway patrol woman only wants to catch the top 1% of all cars on the freeway , then what speed does the car on the freeway need to be going in order for her want to catch the speeder? mph
To catch the top 1% of all cars on the freeway, the speed of the car needs to be greater than 99 mph. This is because 99 mph is three standard deviations above the mean, which would put it in the top 1% of speeds.
The question asks for the z-scores and probabilities of cars going 60 mph and 86 mph on the freeway. It also asks for the speed at which the highway patrol woman needs to catch the top 1% of cars.
Let xx be the speed for a randomly selected car on the freeway, with a mean of 66 mph and standard deviation of 10 mph.
The z-score for a car that is caught going 60 mph is -2.0000. This means that the car is two standard deviations below the mean. The probability of randomly choosing a car on the freeway and it going below 60 mph is 0.0228.
The z-score for a car that is caught going 86 mph is 2.0000. This means that the car is two standard deviations above the mean. The probability of randomly choosing a car on the freeway and it going above 86 mph is 0.0228.
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A rectangle measures 3 2/3 inches by 1/2 inches. What is its area?
the rectangle has a surface area of 11/6 square inches and perimeter is 23/3 inches.
How is area and perimeter determined?We must multiply the length by the width of the rectangle to determine its area. Applying the provided metrics, we have:
Area is equal to the product of length and width.
Area is equal to (11/3) x (1/2) inches.
11/6 square inches is the area.
As a result, the rectangle has a surface area of 11/6 square inches.
The lengths of all four sides must be added up in order to determine the rectangle's perimeter. Applying the provided metrics, we have:
Perimeter equals 2 (length plus width).
Perimeter equals 2 (3 2/3 inches plus 1 inch).
perimeter equals two (11/33 inch plus 1/2 inch).
P = 2 (or 23/6 inches)
Diameter is 23 3/8 inches.
As a result, the rectangle's perimeter is 23/3 inches.
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when performing regression, why would you want to have a quadratic term? group of answer choices you never want to add a quadratic term when performing regression to better fit a scatterplot with too many outliers to better fit a scatterplot that shows a curve in the data to better fit linear data
So, the right response is that, in order to more accurately fit the scatterplot that depicts a curve in the data, you need add a quadratic component while performing regression.
What is the quadratic term count?As ax² +bx + c, a quadratic equation can be expressed. In a quadratic equation, the largest exponent is 2, which limits the number of terms to a maximum of 3. These terms are exponent 2 (ax²) and exponent 1 (bx) fixed term.
Regression can be improved by including a quadratic component to better match scatterplots of data that display curves. This is so that the independent and dependent variables can have a nonlinear connection, which is made possible by a quadratic term. A quadratic component can assist capture inherent curvature of a data and enhance the fit of a regression model in cases where the connection between both the variables isn't really strictly linear.
A quadratic term may not be appropriate or required, though. A quadratic factor would not increase the model's fit if the variables' relationships are strictly linear and might even result in overfitting. In addition, if the scatterplot contains too many anomalies or the data is not consistent, adding a quadratic factor might not be beneficial.
In order to properly fit a scatter plot graph that depicts a curve in the data, the correct response is you would like to add a quadratic term while performing regression.
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Use a ruler and pair of compasses to make an accurate drawing of line
AB and its perpendicular bisector, as shown. You must show all of your
construction lines.
Mark point C on your drawing.
Measure the length of AC in your drawing to 1 d.p.
Step-by-step explanation:
1. Draw a line of 8cm.
2. Take a compass and keep it in the length of more than 8 cm.
3. Draw an arc from point A and B which will intersect at point between A and B.
4. Draw a straight line from the arc.
5. You will find out that the line will be drawn exactly between A and B at 4cm.
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 8 times out of 10 attempts. Tasha has hit the ball 9 times out of 12 attempts. Which player has a ratio that means they have a better batting average?
Tasha, because she has the lowest ratio since 0.75 < 0.8
Tasha, because she has the highest ratio since 48 over 60 is greater than 45 over 60
Jana, because she has the lowest ratio since 0.75 < 0.8
Jana, because she has the highest ratio since 48 over 60 is greater than 45 over 60
Jana, because she has the highest ratio since 8/10 is greater than 9/12.
What is ratio?A ratio is a comparison of two numbers or quantities expressed in relation to each other. It represents the relative size or magnitude of one quantity with respect to another. Ratios are typically written as a fraction, with the first number being the numerator and the second number being the denominator, and can also be expressed as a decimal or percentage.
What is batting average?Batting average is a statistical measure used in baseball to evaluate a player's performance at the plate. It is calculated as the ratio of a player's total number of hits to their total number of at-bats (the number of times they attempt to hit the ball).
In the given question,
A higher batting average indicates a better performance, since it means the player is successfully hitting the ball more often.
In this case, we are given the number of hits and attempts for two players, Jana and Tasha. To compare their batting averages, we need to calculate the ratio of their hits to their attempts.
Jana has hit the ball 8 times out of 10 attempts, so her batting average is 8/10 = 0.8.
Tasha has hit the ball 9 times out of 12 attempts, so her batting average is 9/12 = 0.75.
To determine which player has the better batting average, we compare their ratios. Since 0.8 is greater than 0.75, Jana has the higher ratio and therefore the better batting average.
So, the answer is Jana, because she has the highest ratio (8/10 = 0.8), which means she has the better batting average compared to Tasha (9/12 = 0.75).
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Please help me with my math!
Answer:
-3
Step-by-step explanation:
Please hit brainliest if this helped!
To rewrite the quadratic equation 9 = -3x^2 -18x - 25 in the form y = a(x - p)^2 + q, we need to complete the square. First, we factor out the leading coefficient of -3:
-[tex]3(x^2 + 6x + 25/3) = -3(x^2 + 6x + 9 + 16/3)[/tex]
Next, we add and subtract 9 inside the parentheses to complete the square:
[tex]-3(x^2 + 6x + 9 - 9 + 16/3) = -3((x + 3)^2 - 1/3)[/tex]
Simplifying the expression further, we get:
[tex]-3(x + 3)^2 + 3 = y[/tex]
Comparing this to the standard form y = a(x - p)^2 + q, we can see that a = -3, p = -3, and q = 3. Therefore, the value of p is -3.
Please hit brainliest if this helped!
Answer:
[tex]p = - 3[/tex]Step-by-step explanation:
To find:-
The value of p .Answer:-
We are here given that a quadratic equation is written in the form of y = a(x-p)² + q and we are interested in finding out the value of "p" .
So , the given quadratic equation to us is ,
[tex]\longrightarrow y = -3x^2-18x-25\\[/tex]
Now complete the square on the RHS side of the equation as ,
Firstly make the coefficient of x² as 1 . This can be done by taking out -3 as common.
[tex]\longrightarrow y = -3\bigg(x^2+6x +\dfrac{25}{3}\bigg)\\[/tex]
we can rewrite it as ,
[tex]\longrightarrow y = -3\bigg( x^2+2(3)(x) +\dfrac{25}{3}\bigg) \\[/tex]
Add and subtract 3² , as ;
[tex]\longrightarrow y = -3\bigg( x^2+2(3)(x) + 3^2-3^2+\dfrac{25}{3}\bigg) \\[/tex]
Rearrange the terms as ,
[tex]\longrightarrow y = -3 \left\{ (x^2+2(3)(x) + 3^2) - 9 +\dfrac{25}{3}\right\} \\[/tex]
Notice the terms inside the small brackets are in the form of [tex]a^2+b^2+2ab[/tex] which is the whole square of [tex] (a+b)[/tex] . Hence , we can write it as ,
[tex]\longrightarrow y =-3\bigg\{ (x+3)^2 + \dfrac{-27+25}{3}\bigg\} \\[/tex]
Simplify,
[tex]\longrightarrow y = -3\bigg\{ (x+3)^2 -\dfrac{2}{3}\bigg\} \\[/tex]
Open the curly brackets by multiplying the terms inside the brackets by -3 as ,
[tex]\longrightarrow y = -3(x+3)^2 - 2 \\[/tex]
Now compare it with [tex] y = a(x-p)^2+q [/tex] . On comparing we get ,
[tex]\longrightarrow \boxed{\boldsymbol{ p =-3}}\\[/tex]
Hence the value of p is -3 .
(Find the Smallest Value) Write an application that finds the smallest of several integers. Assume that the first value read specifies the number of values to input from the user.
To find the smallest of several integers, you will need to write a program that takes in a number of values specified by the user as input, and then outputs the smallest value. First, you will need to create a loop that reads in the number of values specified by the user. To do this, you can use a 'for' loop that reads in the values until it reaches the user-specified number of values. Inside the loop, you can create a variable to store the smallest value and compare each value to the smallest value to determine if it is smaller. If the value is smaller, then the smallest value should be updated.
Finally, once the loop has gone through all of the values, the smallest value should be outputted. In summary, to find the smallest value of several integers, you will need to use a 'for' loop to read in the specified number of values from the user, compare each value to the smallest value, and update the smallest value if it is smaller. Then, you can output the smallest value once the loop is complete.
To learn more about loops : https://brainly.com/question/15410285
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Which statement is correct? A -5 < 0 because -5 is to the left of 0 on a number line B -5 < 0 because -5 is to the right of 0 on a number line C -5 > 0 because -5 is to the left of 0 on a number line D -5 > 0 because -5 is to the right of 0 on a number line
The correct statement is A -5 < 0 because -5 is to the left of 0 on a number line. Here's a step-by-step explanation:
On a number line, the smaller numbers are to the left and the larger numbers are to the right. Since -5 is to the left of 0, -5 is a smaller number and 0 is a larger number. Therefore, -5 is less than (or <) 0.
So the statement A -5 < 0 because -5 is to the left of 0 on a number line is correct.
A parking garage has 230 cars in it when it opens at 8???????? (???? = 0). On the interval 0 ≤ ???? ≤ 10, cars enter the parking garage at the rate ???? ′ (????) = 58 cos(0.1635???? − 0.642) cars per hour and cars leave the parking garage at the rate ???? ′ (????) = 65 sin(0.281????) + 7.1 cars per hour (a) How many cars enter the parking garage over the interval ???? = 0 to ???? = 10 hours? (b) Find ????′′(5). Using correct units, explaining the meaning of this value in context of the problem. (c) Find the number of cars in the parking garage at time ???? = 10. Show the work that leads to your answer. (d) Find the time ???? on 0 ≤ ???? ≤ 10, when the number of cars in the parking garage is a maximum. To the nearest whole number, what is the maximum number of cars in the parking garage? Justify your answer
maria makes a quilting pattern with two similar isosceles triangles. in one triangle, the base is 1.4 in. and the other side lengths are each 3.2 in. find the length of each side, r, of the other triangle if its base is 4.48 in.
Answer:10.24
Step-by-step explanation: Since the triangles are similar, then
r/3x2= 4x48/1x4,
r=3.2x4.48=10.24
help with number 2 question
Step-by-step explanation:
To make it simple, since the radius is 15, two points on the circle could be (15,0) and (0,-15). Two more straightforward options are (-15,0) or (0,15)