The probability values are obtained as -
P(X + Y > 3) = 0.45
P(XY = 2) = 0.10
P(XY > 1) = 0.55
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The joint probability mass function XX and YY is given as -
p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1.
The first operation is -
P(X + Y > 3)
Substitute the values in the equation -
P(X + Y > 3) = P(3,1) + P(2,2) + P(3,2) + P(1,3) + P(2,3) + P(3,3)
P(X + Y > 3) = 0.05 + 0.1 + 0.1 + 0.05 + 0.05 + 0.1
P(X + Y > 3) = 0.45
Therefore, the value is obtained as 0.45.
The second operation is -
P(XY = 2)
Substitute the values in the equation -
P(XY = 2) = P(2,1) + P(1,2)
P(XY = 2) = 0.05 + 0.05
P(XY = 2) = 0.10
Therefore, the value is obtained as 0.10.
The third operation is -
P(XY > 1)
Substitute the values in the equation -
P(XY > 1) = 1 - [P(XY ≤ 1)]
P(XY > 1) = 1 - [P(1,1)]
P(XY > 1) = 1 - 0.45
P(XY > 1) = 0.55
Therefore, the value is obtained as 0.55.
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The joint probability mass function of XX and YY is given by
p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1
Compute the following probabilities:
P(X+Y>3)=
P(XY=2)=
P(XY>1)=
A veterans office recorded one select the correct answer from each drop down menu particular week that they had 50 patients the table shows the record numbers of dogs use the given data to complete the sample proportion and confidence intervals for the situation 
the confidence intervals for the situation is 46%
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
the particular week that they had 50 patients the table shows the record numbers of dogs use the given data to complete the sample proportion.
Let's calculate the percentage or proportion of patients that were dogs:
p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46
Hence the confidence intervals for the situation is 46%
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1513 ÷ 3 Enter your answer by filling in the boxes. I need help.
Required value of (1513÷3) is 504R1.
What is division?
Division is the opposite of multiplication. If 3 groups of four are multiplied by 12, 12 divided into three equal groups gives 4 in each group.
The main purpose of distribution is to see how many equal groups are formed or how many are in each group in a fair distribution.
In the above example, to divide the 12 donuts into 3 similar groups, you need to put 4 donuts in each group. So, 12 divided by 3 is 4.
Here given two digits are 1513 and 3.
We want to find value of 1513 ÷ 3.
Now,
[tex]1513 ÷ 3 = \frac{1513}{3} = 504 R1[/tex]
Therefore, the quotient is 504 and the remainder is 1.
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Joana is meeting her friend at the Fair and the admission to get in is $10. Each ride/food costs $1.25 each Create an equation for Joana to use so she can calculate how much money she will be spending while she’s at the fair.
Answer:
y=1.25x+10
Step-by-step explanation:
you can put this into the formula “y=mx+b”. y is the final amount, x is how many times joana gets food or goes on a ride. You can plug into the equation the two parts we know. We know that no matter what, if she goes into the fair, she is going to spend $10 on the admission, even if she does not go on any rides or gets any food. So we put 10 where the “b” is. Then each time she gets food or goes on a ride, she pays another $1.25. Therefore, you can plug 1.25 into where the m is. That leaves you with “y=1.25x+10”.
A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you walk diagonally across the park than along the two sides of it? Round to the nearest tenth if necessary.
You would need to walk 4 miles less if you walk along the diagonal rather than the two sides.
What is Pythagoras Theorem?A key concept in mathematics is the Pythagorean Theorem, which describes the relationship between the sides of a right-angled triangle. Pythagorean triples are another name for the right triangle's sides. Here, examples are used to explain the theorem's formulation and proof.
The Pythagorean theorem is mostly used to determine a triangle's angle and the length of an ambiguous side. The base, perpendicular, and hypotenuse formulas can all be derived using this theorem.
Given that, park is in the shape of a rectangle 8 miles long and 6 miles wide.
The diagonal of the park is calculated using the Pythagoras theorem.
The Pythagoras theorem is given as:
c² = a² +b²
c² = 8² + 6²
c² = 64 + 36
c² = 100
c = 10
If you walk along the diagonal you need to walk 10 miles.
If you walk along the two sides the distance is:
d = 8 + 6 = 14 miles
Hence, the difference between the distance is:
14 - 10 = 4 miles.
Hence, you would need to walk 4 miles less if you walk along the diagonal rather than the two sides.
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The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,80 and 5,100 and 6,120 and 7,140. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.
How much more would the value of y be on the graph than its value in the table when x = 12? (1 point)
a
20
b
90
c
150
d
180
At Cookout, 4 burgers and 3 containers of fries cost $16.40. Your finger rubbed off part of your receipt but you could see that each burger was $3.20. Find the cost of a container of fries. Explain your thinking.
The required container of fries costs $1.20, as er the given condition
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Let's call the cost of a container of fries "x".
We know that 4 burgers cost 4 * $3.20 = $12.80.
So the total cost of burgers and fries is $12.80 + 3x = $16.40.
Subtracting the cost of the burgers from both sides:
3x = $16.40 - $12.80 = $3.60
Dividing both sides by 3:
x = $3.60 / 3 = $1.20
So each container of fries costs $1.20.
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1. The Corollary to the Polygon Angle-Sum Theorem finds the measure of each interior angle of a regular n-gon.
*Write a formula to find the measure of each interior angle using n=number of sides.
2. The Polygon Exterior Angle-Sum Theorem states that the exterior angles of any polygon add up to 360 degrees.
*Write a formula that can help you find the measure of each individual exterior angle in any polygon. Use n for the number of sides.
3. What is the most precise name for quadrilateral ABCD with vertices A(-2, -1), B(2, 2), C(1, -2), and D(-3, -3)?
1. The formula to find the measure of each interior angle of a regular n-gon is (180 * (n-2))/n degrees.
2. The formula to find the measure of each individual exterior angle in any polygon is 360/n degrees.
3. The most precise name for the quadrilateral ABCD with the given vertices is a parallelogram.
How did we arrive at these assertions?The formula to find the measure of each interior angle of a regular n-gon is given by:
(180 * (n-2))/n degrees
In a regular n-gon, all interior angles are equal.
The sum of the interior angles of a polygon can be found using the formula:
(n-2) * 180 degrees, where n is the number of sides in the polygon.
Dividing the sum of the interior angles by the number of sides (n) gives us the measure of each interior angle:
(180 * (n-2))/n degrees.
2. The formula to find the measure of each individual exterior angle in any polygon is:
360/n degrees.
In any polygon, the sum of the exterior angles is equal to 360 degrees.
3. To find the measure of each individual exterior angle, we divide the sum of the exterior angles (360 degrees) by the number of sides (n) in the polygon:
360/n degrees.
The precise name for the quadrilateral ABCD is a parallelogram because:
It has opposite sides that are parallel to each other.
It has equal opposite sides.
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graph f(x) = (x+2) (x-4)
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answer:
The vertex of the parabola is at x = 3, and a point on the parabola can be (4, 0). Here is a Brainly link that can provide you with more information about graphing the function f(x) = (x+2) (x-4): https://brainly.com/question/31009433.
Arrange the following measurements from smallest to largest. Show the calculations. A. 1.5 cm B. 2.5 x 10^3 mm C. 3.5 x 10-5 m D. 4.5 km
The measurements arranged from smallest to largest are 0.15 cm, 2.5 mm, 0.000035 m, and 4.5 km.
A. 1.5 cm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m
D. 4.5 km
Convert all units to the same unit type.
A. 1.5 cm = 15 mm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m = 0.000035 m
D. 4.5 km = 4500 m
Arrange the measurements from smallest to largest.
A. 15 mm
B. 2.5 x 10^3 mm
C. 0.000035 m
D. 4500 m
Convert the measurements back to their original units.
A. 15 mm = 0.15 cm
B. 2.5 x 10^3 mm
C. 0.000035 m = 3.5 x 10-5 m
D. 4500 m = 4.5 km
Rearrange the measurements from smallest to largest.
A. 0.15 cm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m
D. 4.5 km
Simplify the units to the same unit type.
A. 0.15 cm
B. 2.5 mm
C. 0.000035 m
D. 4.5 km
Rearrange the measurements from smallest to largest.
A. 0.15 cm
B. 2.5 mm
C. 0.000035 m
D. 4.5 km
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The measurements arranged from smallest to largest are:
C. 3.5 x 10^-5 m
A. 1.5 cm
B. 2.5 x 10^3 mm
D. 4.5 km
To arrange the measurements from smallest to largest, it is necessary to convert all the units to the same type. The units in the measurements A, C, and D are different, so they need to be converted.
Measurement A is 1.5 cm, which can be converted to millimeters by multiplying by 10: 1.5 cm x 10 mm/cm = 15 mm.
Measurement C is 3.5 x 10^-5 m, which can be converted to millimeters by multiplying by 1000: 3.5 x 10^-5 m x 1000 mm/m = 3.5 mm.
Measurement D is 4.5 km, which can be converted to millimeters by multiplying by 10^6: 4.5 km x 10^6 mm/km = 4.5 x 10^6 mm.
Now that all the units are in millimeters, the measurements can be arranged from smallest to largest:
Measurement C (3.5 mm) is smallest, followed by Measurement A (15 mm), Measurement B (2.5 x 10^3 mm), and finally Measurement D (4.5 x 10^6 mm) is largest.
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Really stuck on this problem can someone help
The triangles are not similar because the dimensions of GDM are larger than those of PQR.
What are congruent shapes ?Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
Even though triangles GDM and PQR have the same angle measure, the triangles are not congruent / similar because they are not the same size. Triangle GDM is larger than PQR and so is not congruent to it.
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38. PROBLEM SOLVING The paths of water from three
different garden waterfalls are given below. Each
function gives the height h (in feet) and the horizontal
distance d (in feet) of the water,
Waterfall 1h
-3.1d² + 4.8
Waterfall 2h-3.5d² + 1.9
Waterfall 3 h = -1.1d2 + 1.6
a. Which waterfall drops water
from the highest point?
b. Which waterfall follows the
narrowest path?
c. Which waterfall sends water the farthest?
Answer:
a. 1; b. 2; c. 1.
Step-by-step explanation:
1] if the given functions are:
[tex]1: \ h=-3.1d^2+4.8;\\2: \ h=-3.5d^2+1.9;\\3: \ h=-1.1d^2+1.6, \ then[/tex]
2] a. d=0, ⇒ max[h] is no.1 (h=-3.1d²+4.8);
b. h=0, ⇒ min[d] is no.2 (h=-3.5d²+1.9);
c. h=0, ⇒ max[d] is no.1 (h=-3.1d²+4.8).
Choose a new vehicle sold in the United States in December at random. The probability distribution for the type of vehicle chosen is given here. (a) What is the probability that the vehicle is a crossover? Round your answer to decimal places. Leave your answer in decimal form. (
b) Given that the vehicle is not a passenger car, what is the probability that it is a pickup truck? Round your answer to decimal places. Leave your answer in decimal form. (c) What is the probability that the vehicle is a pickup truck, SUV, or minivan? Round your answer to decimal places. Leave your answer in decimal form.
(a) The probability that the vehicle is a crossover is 0.30.
(b) Given that the vehicle is not a passenger car, the probability that it is a pickup truck is 0.50.
(c) The probability that the vehicle is a pickup truck, SUV, or minivan is 0.90.
Vehicle Type Probability CalculationI determined the probabilities based on the information provided in the problem. The problem states that the probability distribution for the type of vehicle chosen is given and lists the probabilities for each type of vehicle (crossover, pickup truck, SUV, minivan, and passenger car). To find the requested probabilities, I simply used basic probability formulas and the given probabilities for each type of vehicle.
For example, for part (a), the probability that the vehicle is a crossover is simply the given probability of 0.30.For part (b), given that the vehicle is not a passenger car, the probability that it is a pickup truck is found by using Bayes' Theorem:P(pickup truck | not passenger car) = P(not passenger car | pickup truck) * P(pickup truck) / P(not passenger car).
0.40 / (1 - 0.20) = 0.50.
The denominator P(not passenger car) is found by subtracting the probability of a passenger car (0.20) from 1, and the numerator P(not passenger car | pickup truck) is 1, since a vehicle can either be a pickup truck or not a pickup truck but not both. The requested probability is then equal to 0.50.
For part (c), the probability that the vehicle is a pickup truck, SUV, or minivan is found by adding the individual probabilities for each type of vehicle: 0.40 + 0.30 + 0.20 = 0.90.Learn more about Vehicle Type Probability Calculation here:
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For what value of c is p(x) = 2x^4 - 5x^2 + cx - 1 divisible by x - 1? Show work.
Answer:
c = 4
Step-by-step explanation:
if (x - a) is a factor , that is divisible by, of f(x) then f(a) = 0
then for p(x) to be divisible by (x - 1) , p(1) = 0
then
2[tex](1)^{4}[/tex] - 5(1)² + c(1) - 1 = 0
2 - 5 + c - 1 = 0
- 4 + c = 0 ( add 4 to both sides )
c = 4
5 times of the age of a son is the age of his father. If the sum of their ages is 42 years, determine the age
Answer:
The son is 7 years old.
The father is 35 years old.
Step by step explantation:
Father's age-[tex]5x[/tex]
Son's age-[tex]x[/tex]
[tex]5x+x=42[/tex]
[tex]6x=42[/tex]
[tex]42[/tex]÷[tex]6=7[/tex]
[tex]7[/tex]×[tex]5[/tex][tex]=35[/tex]
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A 17-foot-long ladder leans on a wall, as shown in the accompanying figure. The bottom of the ladder is 8 feet from the wall. If the bottom is pulled out 3 feet farther from the wall, how far does the top of the ladder move down the wall?
(Round to the nearest thousandth as needed.)
The 17-foot-long ladder pulled out 3 feet farther from the wall from a distance of 8 feet, indicates, using Pythagorean Theorem that the top of the ladder moves about 2.039 feet down the wall.
What is the Pythagorean Theorem?Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the length of the legs of the right trianglde.
Length of the ladder = 17 foot ladder
Distance of the bottom of the ladder from the wall = 8 feet
The extra distance to which the bottom of the ladder is pulled = 3 feet
The ladder resting on the wall forms a right triangle, with the length of the ladder being the hypotenuse side.
The initial vertical distance reached by the ladder on the wall, h, can be found using Pythagorean Theorem as follows;
h² = 17² - 8² = 225 = 15²
h² = 15²
The initial vertical distance up the wall the ladder reaches, h, is therefore;
h = √(15²) = 15
The ladder initially reaches 15 feet high on the wall
The ladder is then pulled 3 feet farther, from which we get;
New horizontal distance of the ladder from the wall = 8 feet + 3 feet = 11 feet
The square of the new height the ladder reaches up to on the wall, h'², can therefore be found as follows;
h'² = 17² - 11² = 168
√h'² = h' = √(168) = 2·√(42)
The new height the ladder reaches up to on the wall, h' ≈ 2·√(42) feet
The distance the ladder moves down the wall, Δh = h - h', therefore;
Δh = 15 - 2·√(42) ≈ 2.039
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Sally saved $182 in March. Her father gave her $20 for every
$50 she saved. How much did Sally's father give her?
Answer:
$40
Step-by-step explanation:
We know
Her father gave her $20 for every $50 she saved
$50 + $20 = $70
$50 + 20 + 50 + 20 = $140
$182 - $140 = $42
It is not $50 yet, so her father only give her 2 times
So, her father gives her $40
Answer:
182÷50 = 3.64, 3.64x20=72.8$
her dad gave her 72.8$
A crate is 3/4 yard long and 2/4 yard wide. The crate is also 2 feet tall. What is the area of the top of the crate?
(please explain the answer step by step if possible.)
Answer:
The area of the top of the crate can be found by multiplying the length by the width.
First, we need to convert all units to the same unit, either yards or feet. We will convert the length and width to yards:
3/4 yard = 9/12 yards
2/4 yard = 6/12 yards
2. Now we can find the area by multiplying the length by the width:
Area = 9/12 yards * 6/12 yards = (9/12) * (6/12) = 3/4 * 1/2 = 3/8 yards^2
So, the area of the top of the crate is 3/8 yards^2.
You pick a card at random. Without putting the first card back, you pick a second card at
random.
678
What is the probability of picking an 8 and then picking a number greater than 7?
Write your answer as a decimal.
The value of the probability is 0.167
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
6 7 8
The probability of picking a 8 on the first draw and then picking a number above 7 on the second draw is:
P(6 and then >7) = P(6) x P(>7 | 6)
Given that the cards are not replaced, we have
P(6 and then >7) = 1/3 * 1/2
Evaluate
P(6 and then >7) = 0.167
Hence, the probability is 1/6
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Please answer my question. Find the SA (surface area) of the composite shape. Round to the nearest tenth. Please help.
The total surface area of the composite shape is 488.7 in².
What is a composite shape?
A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently. Every day, composite shapes are around us.
The given composite shape can be divided into multiple shapes, to find the area easily.
For the given question, we can see that the lower portion of the shape is a cuboid and the upper portion is half of the cylinder cut vertically.
We find the areas of the figures separately.
Area of cuboid
Length l = 6 in.
Breadth b = 10 in.
Height h = 8 in.
Area = Area of each faces = 2(lb) + 2(bh) +2(lh)
= 2(6*10) + 2(10*8) + 2(6*8)
= 2*60 +2* 80 + 2* 48
= 376 in²
Area of cylinder
Radius of semicircles r = 5 in.
Height of cylinder h = 6 in.
Area = Area of semicircles + Area of half of the curved surface
= 2 *1/2 * πr² + 1/2 * 2πrh = πr² + πrh = 3.14 * 5² + 3.14 * 5 * 6
= 172.7 in²
The total surface area of the composite shape = Area of cylinder + Area of cuboid - Area of the common surface(rectangle)
= 172.7 + 376 - (l *b) = 548.7 - ( 10*6) = 488.7 in²
Hence the total surface area of the composite shape is 488.7 in².
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Find the zeros and give the multiplicity.
f(x) = x2(5x + 6)9(x − 8)2
Answer:
Zeroes & Multiplicity:
x = 0 : Multiplicity = 2
x = -6/5 : Multiplicity = 9
x = 8 : Multiplicity = 2
Step-by-step explanation:
The equation provided is: [tex]f(x)=x^2(5x+6)^9(x-8)^2[/tex]
Factored Form:We're given the polynomial in factored form, which just means the polynomial is broken down into each of its factors. This is a really convenient form to have a polynomial in as we can easily find the zeroes of the polynomial.
This is due to the Zero Property of Multiplication, which essentially states zero times any number results in zero. So we just have to set each factor equal to zero, and solve, since if one of the factors is zero, then the entire thing becomes zero.
So this gives us the following equations:
[tex]x^2=0\implies x = 0\\\\(5x+6)^9=0\implies x = -\frac{6}{5}\\\\(x-8)^2=0\implies x = 8[/tex]
Now for the multiplicity, we just look at the exponent of the factor we set equal to zero. So x^2 gives us a zero of x = 0, and the exponent is 2, which is also the multiplicity of this zero.
The (5x + 6)^9 gives us a zero of x = -6/5, and the exponent is 9, which is also the multiplicity of the zero. Same thing applies for the zero at x = 8, which has a multiplicity of 2.
How would you discover a mathematical relationship between corresponding terms that occur in two separate number sequences, and what can you say about those terms?
Method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.
What is a function?A relation is a function if it has only One y-value for each x-value.
One method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.
To do this, you can start by selecting a set of corresponding terms from each sequence and attempt to express the relationship between them using mathematical operations.
It's important to note that finding a mathematical relationship between two sequences can sometimes be difficult, and in some cases may not be possible.
In such cases, it may be helpful to analyze the sequences using other methods, such as graphical representation or statistical analysis, to gain insight into their behavior.
Hence, method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.
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What is the percent change from 82 to 67
First find the actual difference:
82 - 67 = 15
Now divide that difference by the starting value (82 in this case):
15 / 82 ≈ 0.182927
Convert that to a percent:
0.182927 = 18.2927%
That's the percent change, a decrease of about 18.2927%
Consider the following probability distribution. Complete parts a through e p(x) a. Find u 2.25 (Round to the nearest thousandth as needed.) Find o 3.188 (Round to the nearest thousandth as needed.) b. Find the sampling distribution of the sample mean x for a random sample of n -2 measurements from this distribution. Put the answers in ascending order for x. 0.5 2.5 0.0625 0.25 0.25 0.25 p(x) 0.0625 0.125 (Do not round.) c. Is x an unbiased estimator of H? Yes, x is an unbiased estimator for u
The mean of the probability distribution is 3.188, the sampling distribution is 2.25 and x is an unbiased estimator.
What is the probability distributiona. To find the mean (u) of a probability distribution, we calculate the expected value as follows:
u = ∑x * p(x) = (0.5 * 0.0625) + (2.5 * 0.125) + (0.25 * 0.25) + (0.25 * 0.25) + (0.25 * 0.25) = 2.25
To find the variance (o^2) of the distribution, we calculate it as follows:
o^2 = ∑(x - u)^2 * p(x) = (0.5 - 2.25)^2 * 0.0625 + (2.5 - 2.25)^2 * 0.125 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 = 0.5625
So, o = √0.5625 = 3.188
b. The sampling distribution of the sample mean x for a random sample of n=2 measurements from this distribution is given by:
x = (x1 + x2) / n = (2.25 + 2.25) / 2 = 2.25
As n approaches infinity, the sample mean x approaches the population mean u, and the distribution of x becomes more and more concentrated around u.
c. Yes, x is an unbiased estimator of u because its expected value is equal to the population mean: E(x) = u.
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Angle pQR is a right angle. The measure of angle SQR is 25 degrees. The measure of PQS is x degrees. What is the value of x
The value of x is 65°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
Angle PQR is a right angle.
The measure of angle SQR is 25 degrees.
The measure of PQS is x degrees.
The angle addition postulates:
∠PQR = ∠SQR + ∠PQS
90° = 25° + x
x = 90° - 25°
x = 65°
Hence, ∠PQS = 65°.
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Let f:[0,2]→R be a twice differentiable function such that f"(x)>0, for all x∈(0,2) If ϕ(x)=f(x)+f(2−x), then ϕis:
A. decreasing on (0,2)
B. decreasing on (0,2) and increasing on (1,2)
C. increasing on (0,2)
D. increasing on (0,1) and decreasing on (1,2)
The answer is C. increasing on (0,2).
What is Strictly convex function?
A real-valued function is said to be convex if the line segment connecting any two points on its graph falls above the graph connecting the two points. A function is convex if and only if its epigraph is a convex set.
Since f"(x) > 0 for all x in (0,2), it follows that f is a strictly convex function on that interval, meaning that its second derivative is positive and its first derivative is increasing.
If f is a strictly convex function on [0,2], then f(2-x) is a strictly concave function on [0,2]. The sum of a strictly convex and a strictly concave function is also a strictly convex function.
Therefore, since f''(x) = f(x) + f(2-x), it follows that f''(x) is a strictly convex function on [0,2], which means that its first derivative is increasing.
Thus, The answer is C. increasing on (0,2).
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NO LINKS!!! NEED URGENT HELP!!!
1. Describe the shape of the graph and any special features you see.
2. What is the greatest area possible for a rectangle with this perimeter? What are the dimensions of this rectangle?
3. What is the area of the rectangle whose length is 10 meters? What is the area of the rectangle whose length is 30 meters> How are these rectangles related?
Answers:
1. The graph is in the shape of a parabola, there is a vertex point at (20, 400), and the zeros (x-intercepts) of the graph are at the origin of the coordinate plane (0, 0) and (40, 0).
2. The greatest area possible for a rectangle with a perimeter of 80 meters is 400 [tex]m^2[/tex], and the dimensions of this rectangle will be 20 meters in length and 20 meters in width.
3. The area of the rectangle whose length is 10 meters and the area of the rectangle whose length is 30 meters are the same, both being 300 [tex]m^2[/tex]. This is because the perimeter is set as 80 meters total, and as they are both rectangles, the opposite sides must be the same length.
For the rectangle with a length of 10 meters, 2 of the 4 sides will use 20 meters of material, so there will be 60 meters of material left for the remaining 2 sides, or 30 meters per side. So the dimensions of that rectangle would be 10 meters in length and 30 meters in width.
For the rectangle with a length of 30 meters, it's the same thing, except the length is 30 meters, and the width is 10 meters. And for both rectangles, their areas are 30 meters multiplied by 10 meters, which equals 300 [tex]m^{2}[/tex], so the way these two rectangles are related is that they have the same area.
Have a great day! Feel free to let me know if you have any more questions :)
Answer:
1. See below.
2. 400 m²
20 m x 20 m
3. 300 m²
Step-by-step explanation:
Question 1The graph is a parabola that opens downwards.
Its vertex is (20, 400) and its axis of symmetry is x = 20.
Question 2From inspection of the given graph, the greatest possible area (y-value) is 400 m². This is when the length of the rectangle is 20 m.
The largest possible area of a rectangle is when the length equals the width. Therefore, the dimensions of the rectangle with the greatest area possible are:
width = 20 mlength = 20 mQuestion 3From inspection of the graph, when the length of the rectangle is 10 m, its area is 300 m².
Similarly, when the length of the rectangle is 30 m, its area is also 300 m².
A rectangle has two pairs of parallel sides of equal length.
Therefore, as both rectangles have the same area, this means that the one pair of parallel sides is 10 m in length and the other pair of parallel sides is 30 m in length. The dimensions of both rectangles are the same: 10 m x 30 m, where the width and length are interchangeable.
It’s math please help
Answer:
D because angle U is equal to angle W because it is diverting angle
Charlie buys 3 computer tables for $390. How much did he pay for each table?
Answer:
Step-by-step explanation:
If Charlie buys 3 computer tables for $390, then he paid $390 / 3 = $130 for each table.
Answer: 130 dollars for each table
Step-by-step explanation: Because 3 tables is 390 dollars, we have to divide 390 and 3 to see how much 1 table costs.
390 / 3 = 130
A rectangular
farm has an area of 1/5 square miles. If
its length is 2/3 miles, what is its width?
Input your answer as a fraction.
Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?
Answer:
He would be 15 years old.
Step-by-step explanation:
If the difference is 15, and sarah is double the age, whatever age the youngest brother is, that number if multiplied by 2 or added to 15 needs to be the same answer. You could make a equation by writing those two on either side of the equation and making the unknown sum “x”. This would look like “2x=x+15”. Then to get the final product you would subtract the x on the right side from both side, ending up to be “x=15” in this scenario, that would be the final answer.