Solution for b: The events "all boys," "all girls," "2 boys and 1 girl," and "2 girls and 1 boy" are equally likely because each has probability 1/8. Solution for c: The events "0 tails," "1 tail," "2 tails," "3 tails," and "4 tails" are equally likely because each has probability 1/16. Solution for d: the events are not equally likely.
b) For a family having 3 children, the sample space is {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}, where B represents a boy and G represents a girl. Each outcome in the sample space has probability 1/8. The events "all boys," "all girls," "2 boys and 1 girl," and "2 girls and 1 boy" are equally likely because each has probability 1/8.
c) For tossing four coins, the sample space is {TTTT, TTTH, TTTT, TTHH, TTHH, THHH, THHT, THHH, HHHH, HHTH, HHTT, HHHT, HHTH, HTHH, HTTH, HTTT}, where T represents tails and H represents heads. Each outcome in the sample space has probability 1/16. The events "0 tails," "1 tail," "2 tails," "3 tails," and "4 tails" are equally likely because each has probability 1/16.
d) For tossing a coin 10 times, the sample space is all possible sequences of 10 H's and T's. There are 2^10 = 1024 outcomes in the sample space, each with probability 1/1024. The events "longest run of heads is 1," "longest run of heads is 2," "longest run of heads is 3," "longest run of heads is 4," "longest run of heads is 5," and "longest run of heads is 6 or more" are not equally likely, because the probability of getting a long run of heads is much lower than the probability of getting a short run of heads. For example, the probability of getting a run of 6 heads in a row is (1/2)^6 = 1/64, while the probability of getting a run of 1 head is 1/2. Therefore, the events are not equally likely.
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A laboratory observes an average of five unaclaimed results in a day, what is the probability that it will observe 3 unaclaimed results?
The confidence level is a percentage between 0% and 100% that measures the success rate of the method used to construct the confidence interval. If we were to draw many samples and use each one to construct a confidence interval, then in the long run, the percentage of confidence intervals that cover the true value would be equal to the
The confidence level is the probability that a confidence interval will contain the true population parameter in repeated sampling.
Confidence level is a statistical measure used to indicate the level of certainty or reliability in a statistical inference or estimate. In other words, it represents the success rate of the method used to construct a confidence interval. For example, a 95% confidence level indicates that if we were to repeat the same experiment many times and calculate the confidence interval for each trial, then we would expect 95% of these intervals to contain the true value.
The confidence level is typically chosen by the researcher based on the level of certainty they want to achieve. A higher confidence level corresponds to a wider confidence interval, which increases the likelihood of containing the true value, but reduces the precision of the estimate.
It is important to note that the confidence level does not guarantee that a particular confidence interval contains the true value, but rather it indicates the long-run success rate of the method used to construct the interval. Therefore, it is crucial to understand the underlying assumptions and limitations of the statistical method used to construct the confidence interval.
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The confidence level is a percentage between 0% and 100% that measures the success rate of the method used to construct the confidence interval. If we were to draw many samples and use each one to construct a confidence interval, then in the long run, the percentage of confidence intervals that cover the true value would be equal to the ________?
Calculate the area of the shaded region below. Area of Compound Shapes
The area of the shaded region is 176 m² and area of compound shapes are 208 m² and 16 m².
What is rectangle?
A rectangle is a two-dimensional geometric shape with four straight sides and four right angles (90 degrees). It is a type of quadrilateral, which means it has four sides. The opposite sides of a rectangle are equal in length, and the adjacent sides are perpendicular to each other.
The formula for calculating the area of a rectangle is A = l x w, where "A" is the area, "l" is the length, and "w" is the width. The perimeter of a rectangle can be calculated by adding the lengths of all four sides, which is given by the formula P = 2(l + w).
Rectangles are commonly found in many aspects of everyday life, such as in buildings, furniture, electronic devices, and books. They can be used in architecture and engineering for creating stable and functional structures. In mathematics, rectangles are often used in geometry and algebraic expressions, as well as in statisticalanalysis and graphing.
Here we have a rectangle with length 16m and breadth 13 m.
Now, area of the rectangle is length × breath = 13×16 = 208 m².
And here we also have two square parts with side 4 m .
So, area of the square is side × side = 4×4 = 16 m².
Now, numbers of square are 2.
So, total area of two square is (2×16) = 32 m².
If we will subtract the total area of two square from area of the rectangle then we will get the area of shaded region .
So, area of the shaded region [tex] = 208 - 32 = 176 \: {m}^{2} [/tex]
Therefore, area of the shaded region is 176 m² .
Here compound shapes are one rectangle and two squares.
So, area of compound shapes are 208 m² and 16 m².
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Suppose the die has been “loaded” so that P(1)=1∕12, P(6)=3∕12, and the remaining four outcomes are equally likely with one another. Now find the probability that the number rolled is both even and greater than two
The "loading" of the die makes P(1)=112, P(6)=312, and the following four outcomes equally likely. A roll with an even number larger than two has a 50% probability of occurring.
The probability of rolling an even number is 1/2 since there are three even numbers (2, 4, 6) and six possible outcomes in total.
The probability of rolling a number greater than two is 5/6 since there are five outcomes (3, 4, 5, 6) greater than two and six possible outcomes in total.
To find the probability that the number rolled is both even and greater than two, we need to find the probability of rolling a 4 or a 6 since these are even numbers that are greater than two.
The probability of rolling a 4 is P(4) = 1/12 + 1/6 = 1/4 since the die is loaded to favour a 6 over the other numbers, but all other outcomes are equally likely.
The probability of rolling a 6 is P(6) = 3/12 = 1/4 since the probability of rolling a 6 is given as 3/12.
Therefore, the probability of rolling an even number that is greater than two is:
P(even and greater than two) = P(4 or 6) = P(4) + P(6) = 1/4 + 1/4 = 1/2.
So the probability of rolling an even number that is greater than two is 1/2.
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A contractor is considering a sale that promises a profit of $26,000 with a probability of 0.7 or a loss (due to bad weather, strikes,
and such) of $8000 with a probability of 0.3. What is the expected profit? On average, should the contractor expect to make
money or lose money from the sale? (Hint: write this information as a probability distribution table first. Another hint: Is a
LOSS a positive or negative number? Is a PROFIT a positive or negative number?)
6×y^2=240in^2
Solve for Y
Answer:
[tex]y=40\sqrt{\frac{6}{x} }[/tex]
[tex]y=-40\sqrt{\frac{6}{x} } ,x > 0[/tex]
Step-by-step explanation:
pls tell me if wrong have a good night/day
HELP ASAP WILL GIVE 100 PTS AND BRAINLYEST AND IF YOU DON'T ANSWER TRYING TO JUST GET POINTS I WILL REPORT YOU!
Using equations,
The quotient of 3 times a number and 7: 3n/7
5 less than a number is x: x = n - 5
The sum of twice a number and 9: 2n + 9
Two times the sum of a number and 9: 2 (n+9)
The product of 3 times a number and 7: (3n) (7)
The difference between 5 and a number is x: 5 - n = x
What are equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15.
Many types of equations exist, including linear, quadratic, cubic, and others.
The quotient of 3 times a number and 7: 3n/7
5 less than a number is x: x = n - 5
The sum of twice a number and 9: 2n + 9
Two times the sum of a number and 9: 2 (n+9)
The product of 3 times a number and 7: (3n) (7)
The difference between 5 and a number is x: 5 - n = x
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Solve the following system by substitution. CHECK the solution.
3y = 2x + 12
y + 3x = -7
We can use substitution to solve this system of equations. We can solve the first equation for y and get:
y = (2x + 12)/3
We can then substitute this expression for y into the second equation:
(2x + 12)/3 + 3x = -7
Multiplying both sides of this equation by 3 to eliminate the denominator, we get:
2x + 12 + 9x = -21
Simplifying this equation gives:
11x = -33
Dividing both sides by 11, we get:
x = -3
We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:
3y = 2(-3) + 12
3y = 6
y = 2
Therefore, the solution to the system of equations is x = -3 and y = 2.
To check the solution, we substitute these values back into both equations:
3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6
This equation is true, so the solution (x = -3, y = 2) checks out.
pick a region of your choice. write out the integrals needed to find the volume of the region using a triple integral with rectangular, cylindrical and spherical coordinates. (you must use all three types coordinates on the same region - choose wisely!). setup but do not evaluate the integrals.
The volume integral for f(x,y,z) = 1 over the region E : x² + y² + z² ≤ 4,
1) In spherical coordinates system is
[tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
2) In cylinderical coordinates system is
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
3) In rectangular coordinates syatm is
[tex]V = \int_{0}^{2}\int_{-\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
We pick a region E : x² + y² + z² ≤ 4 and determine volume over the region E for function, f(x,y,z ) = 1 .
Use of Spherical coordinates (ρ,θ, φ), Volume can be written as[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
In spherical coordinates system we plug,
[tex]x = \rho sin \phi cos \theta[/tex]
[tex]y = \rho sin \phi sin \theta[/tex]
[tex]z = \rho cos \phi [/tex]
[tex]dV = dx dy dz = |J| d\rho d\phi d\theta [/tex]
where, [tex]|J| = \rho² sin \phi[/tex]
=> [tex]dx dy dz = \rho² sin \rho d\rho d\phi d\theta[/tex]
So, [tex]V = {\int \int \int}_{x² + y² + z² ≤ 4} 1 \: dxdy dz[/tex]
Now, [tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
Using Cylindrical coordinates (r,θ,z)Region , E : x² + y² + z² ≤ 4
=> z² ≤ 4 - x² - y²
=> z ≤ ± √4 - x² - y²
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
here, r∈[0, 2], θ∈[0,2π]
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
Using rectangular coordinates (x,y,z), Volume integral can be written as :[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
Here, y² ≤ 4 - x²
=> y = ± √4 - x² and x∈ [0,2], So,
[tex]V = \int_{0}^{2}\int_{ -\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
Hence, in above we determined the volume integral for region, E in all three coordinates systems.
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since 1961 there has been a total of 6688 peace corp volunteers from the university of California Berkeley and the university of Wisconsin. the number of volunteers from the university of California is 464 more than the number of volunteers from the university Wisconsin. find the number of peace Corp volunteers from each university.
show work
Please help step by step :)
Answer: √698 or 26.42 (2 d.p.)
Step-by-step explanation:
Pythagoras' Threorem is a² + b² = c²
Substitute 13 for a and 23 for b
13² + 23² = x²
169 + 529 = x²
698 = x²
x = √698 = 26.42 (2 d.p.)
Solve the inequality of 2(x-6)<-3(x-1)
Answer: 2(x-6) < -3(x-1) is x < 3.
Step-by-step explanation:
2(x-6) < -3(x-1)
Expanding the brackets, we get:
2x - 12 < -3x + 3
Adding 3x to both sides, we get:
5x - 12 < 3
Adding 12 to both sides, we get:
5x < 15
Dividing both sides by 5, we get:
x < 3
Answer:
x>12
Step-by-step explanation:
1/3(x-6)>2
distribute 1/3
1/3x-2>2
add 2 to both sides
1/3x>4
multiply both sides by 3
x>12
The Richardson family is out to dinner at
their favorite restaurant. The bill comes to
$32.00. How much money should they leave
for the bill and a 20% tip?
Answer:
$38.40
Step-by-step explanation:
20% = 0.2
32 x 0.2 = $6.40
20% tip = $6.40
How much money should they leave for the bill and a 20% tip?
We take
32 + 6.40 = $38.40
So, they should leave $38.40 for the bill and a 20% tip.
Can’t find the answer help!!
The value of the angle m<C is 27 degrees. Option B
How to determine the angle
First, we need to know the different trigonometric identities and their ratios.
We have;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given in the diagram, we have;
Opposite side of angle C = 5
Adjacent side of angle C = 7.5
Hypotenuse side of angle C = 11
Using the sine identity
sin C = 5/11
sin C = 0. 4545
Take sine inverse
C = 27 degrees
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Olive flipped a coin and rolled a number cube with the numbers 1-6 on it. What is the probability that she flipped heads and rolled an even number?
The probability of flipping heads is 1/2, and the probability of rolling an even number is 1/2 (since there are three even numbers and three odd numbers on the cube). To find the probability of both events happening (flipping heads and rolling an even number), we multiply the probabilities together:
1/2 x 1/2 = 1/4
So the probability that Olive flipped heads and rolled an even number is 1/4 or 25%.
Answer: 1/4
Step-by-step explanation:
A bag of the same size balls contains six blue balls firebrand balls five yellow balls and four green balls what is the probability of selecting a blue or green ball on the first draw
The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur. If an event has a probability of 0.5, it means that the event is equally likely to occur or not occur. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability is an important concept in mathematics, statistics, and many other fields, as it allows us to make predictions and decisions based on the likelihood of certain outcomes.
According to the question:
The total number of balls in the bag is:
6 blue balls + 5 yellow balls + 4 green balls = 15 balls
The probability of selecting a blue or green ball on the first draw can be found by dividing the number of blue and green balls by the total number of balls:
P(blue or green) = (number of blue balls + number of green balls) / (total number of balls)
P(blue or green) = (6 + 4) / 15
P(blue or green) = 10 / 15
P(blue or green) = 2/3
Therefore, the probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.
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i need help with finding y and x
Answer: x= 24 and y= 73
Step-by-step explanation:
we know
The opposite interior angles are equal and
The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.
the sum of the interior angles of a parallelogram is 360 degrees.
So 107 + y = 180
180 - 107 = 73
Y = 73
y is equal to its opposite angle so
X can be found by 73 = 3x + 1
Subtract 1 from both sides
73 - 1 = 3x +1 -1
Simplify
72 = 3x
Divide both sides by 3 to solve for x
72/3 = 3/3x
x=24
Check your work by adding the 4 angles together to equal 360
107 + 107 + 73 + 73 = 360
360 = 360
They equal so your solution is correct
Find the missing length. Then find the area and perimeter of the composite figure.
10: Missing length, x = 16 cm
area of the composite figure = 240 cm²
perimeter = 72 cm
11: Missing length, x = 37 mm
area of the composite figure = 240 mm²
perimeter = 90 mm
How to find the missing length, area and perimeter of the composite figure?To find the area and perimeter of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.
No. 10
You will notice that the triangle is sharing one side with the square. And the length of the side is 12 cm. Thus:
x = √(20² - 12²) (Pythagoras)
x = 16 cm
area of the figure = area of square + area of triangle
area of the figure = L² + (1/2 * base * height)
area of the figure = 12² + (1/2 * 16 * 12)
area of the figure = 240 cm²
perimeter = 12 + 12 + 12 + 20 + 16 = 72 cm
No. 11
You will notice that the small triangle is sharing one side with the big triangle. And the length of the side is unknown. Let's call it y. Thus:
y = √(13² - 5²) (Pythagoras)
y = 12 mm
x = √(35² + 12²) (Pythagoras)
x = 37 mm
area of the figure = area of small triangle + area of big triangle
area of the figure = (1/2 * base * height) + (1/2 * base * height)
area of the figure = (1/2 * 5 * 12) + (1/2 * 35 * 12)
area of the figure = 240 mm²
perimeter = 5 + 13 + 37 + 35 = 90 mm
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True or false. When you use multiple adjectives in a sentence, you do not have to put them in a certain order. True False
Answer:
False.
Step-by-step explanation:
When using multiple adjectives in a sentence, there is a general order that native English speakers tend to follow: opinion, size, age, shape, color, origin, material, purpose. This is known as the "OSASCOMP" order. However, this order is not always strictly followed, and there can be exceptions depending on the specific context or style of writing.
Answer:
It is False
Step-by-step explanation:
What is the answer to this question?
The number is 300, as stated in the sentence. A histogram:
What is it and why is this used?One common plotting instrument is the histogram. It is employed to present interval-scaled summaries of discontinuous or continuous data. It is commonly applied to easily represent the key features of the information's distribution.
To create a histogram of the weights of the miniature poodles, we would first divide the weight range into a series of intervals, or bins. The bin width should be chosen so that each bin has a similar number of observations.
According to the histogram and table: the height of a cell represents 10 15 ≤ x < 20: 120 ÷ 12=10
28 ≤ x <30 has 30 cells, so the frequency is 30 × 10=300
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The wheels on a car have a diameter of 2 ft. How many full revolutions will the wheels need to make to travel 220 feet? Round to the nearest whole number.
Using the circumference formula the number of full revolutions the wheels need to make to travel 220 feet is obtained as 35.
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.
The distance traveled by the car in one full revolution of the wheel is equal to the circumference of the wheel.
The circumference of a circle is given by the formula -
C = 2πr
where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Since the diameter of the wheel is 2 feet, the radius is half of that, or 1 foot.
Therefore, the circumference of the wheel is -
C = 2π(1 foot) = 2π feet
To find how many full revolutions the wheel needs to make to travel 220 feet, we can divide the distance traveled by the circumference of the wheel -
Number of revolutions = distance traveled / circumference of the wheel
Number of revolutions = 220 feet / (2π feet) ≈ 35.03
Therefore, the wheels need to make 35 full revolutions to travel 220 feet.
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Question 4 options:
Quadrilateral WXYZ is inscribed in a circle with m∠W=55° and m∠X=117°. What is the measurement of angle Y?
What is the measurement of angle Z?
Angle Y measures 125 degrees and angle Z measures 63 degrees.
what is a circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.
Since quadrilateral WXYZ is inscribed in a circle, we know that opposite angles add up to 180 degrees. Therefore:
m∠Y + m∠W = 180 degrees ...(1)
m∠Z + m∠X = 180 degrees ...(2)
We are given that m∠W = 55 degrees and m∠X = 117 degrees, so we can substitute those values into equations (1) and (2):
m∠Y + 55 = 180 ...(1)
m∠Z + 117 = 180 ...(2)
Solving for m∠Y and m∠Z, we get:
m∠Y = 125 degrees
m∠Z = 63 degrees
Therefore, angle Y measures 125 degrees and angle Z measures 63 degrees.
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7. The ride length of a roller coaster is 314
minutes. Every ride starts as soon as the
previous ride ends. How many rides take place
in 28 minutes?
Answer: To find out how many rides take place in 28 minutes, we need to divide the total ride length by the length of one side, and then round down to the nearest whole number.
The length of one ride can be calculated by dividing the total ride length by the number of rides. Since we don't know the number of rides, let's call it "n":
length of one ride = total ride length / n
314 minutes / n
Now we can set up an equation to solve for "n":
28 minutes = length of one ride * number of rides
28 minutes = (314 minutes / n) * number of rides
We can simplify this equation by multiplying both sides by "n":
28 minutes * n = 314 minutes * number of rides
Dividing both sides by 314 minutes, we get:
n = (28 minutes * number of rides) / 314 minutes
Multiplying both sides by 314 minutes and dividing by 28 minutes, we get:
number of rides = (n * 314 minutes) / 28 minutes
number of rides = 11.21
Rounding down to the nearest whole number, we get:
number of rides = 11
Therefore, in 28 minutes, 11 rides take place.
Step-by-step explanation:
Select the correct answer. Ron's mother bakes a pizza and divides it into 14 pieces. After serving 6 pieces to Ron and his friends, she has p pieces left. What is the equation for p? A. p × 6 = 14 B. p + 6 = 14 C. p × 14 = 6 D. p + 14 = 6
The equation for p is p + 6 = 14, which means that the number of pieces left is equal to the difference between the total number of pieces (14) and the number of pieces served (6).
Ron's mother bakes a pizza and divides it into 14 pieces. After serving 6 pieces to Ron and his friends, she has a certain number of pieces left. To determine this number, we can use the equation p + 6 = 14. This equation states that the number of pieces left (p) is equal to the difference between the total number of pieces (14) and the number of pieces served (6). Therefore, the equation for p is p + 6 = 14. By solving this equation, we can determine that the number of pieces left is 8. This means that Ron's mother has 8 pieces left after serving 6 pieces to Ron and his friends.
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A submarine is passing by a solar station, located al (0,0), that can detect objects that
are as far away as 5km in any direction. A swiss submarine is traveling along a trajectory defined by y= -2/3x +26/3 where x and y represent distances measured in kilometers. Determine algebraically whether the sonar station will detect the submitline.
Answer:
The sonar station will not detect the submarine.
Step-by-step explanation:
The area that the sonar station can detect can be modelled as a circle with center (0, 0) and radius 5 km.
The equation of a circle formula is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Therefore, the equation of the circle modelling the perimeter of the sonar station detection area is:
[tex]\implies (x-0)^2+(y-0)^2=5^2[/tex]
[tex]\implies x^2+y^2=25[/tex]
To determine whether the sonar station will detect a swiss submarine traveling along a trajectory defined by y = -2/3x + 26/3, substitute the equation of the trajectory into the found equation of the circle.
[tex]\implies x^2+\left(-\dfrac{2}{3}x+\dfrac{26}{3}\right)^2=25[/tex]
Simplify:
[tex]\implies x^2+\dfrac{4}{9}x^2-\dfrac{104}{9}x+\dfrac{676}{9}=25[/tex]
[tex]\implies 9x^2+4x^2-104x+676=225[/tex]
[tex]\implies 13x^2-104x+451=0[/tex]
Solve the equation for x using the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies x=\dfrac{-(-104) \pm \sqrt{(-104)^2-4(13)(451)}}{2(13)}[/tex]
[tex]\implies x=\dfrac{104 \pm \sqrt{-12636}}{26}[/tex]
[tex]\implies x=\dfrac{104 \pm 18\sqrt{39}\:i}{26}[/tex]
[tex]\implies x=4 \pm \dfrac{9\sqrt{39}}{13}\:i[/tex]
As the solutions are complex numbers, this means that the linear trajectory of the submarine will not intersect the detection area of the sonar station. Therefore, the sonar station will not detect the submarine.
What is the unit rate of 3 1/2 1 1/4
let's firstly convert the mixed fractions to improper fractions.
[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}} \implies \cfrac{1\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{ 7}{ 2} ~~}{\frac{5}{4}}\implies \cfrac{7}{2}\cdot \cfrac{4}{5}\implies \cfrac{7}{5}\cdot \cfrac{4}{2}\implies \cfrac{7}{5}\cdot 2\implies \cfrac{14}{5}\implies 2\frac{4}{5}\implies 2.8[/tex]
Erin wants to buy a new car. To do this, she takes out a loan of $24,000. The loan is to be repaired in seven years with an interest of 12% per annum. What is the total amount of interest she pays?
find the length of the diagonal of the box below. Round to the nearest hundredth (you have to do pythagorean theorem twice)
Answer:
12.5
Step-by-step explanation:
9.6² + 2.8² = 10²
10² + 7.5² = 12.5²
gcd (119,378)=119x+378y using Euclidean alogorithm
GCD (119, 378) = 7 and x = 25 and y = -6 is the value by using Euclidean alogorithm.
What does Euclidean algorithm mean?
By dividing the larger by the smaller, the smaller by the remainder, the first remainder by the second remainder, and so on, until an exact division is achieved, the greatest common divisor is the exact divisor. Euclid's algorithm is also known as.
by Euclidean division algorithm,
378 = 3 × 119 +21
119 = 5 × 21 + 14
21 = 1 × 14 + 7
14 = 2 × 7 + 0
Therefore 7 is GCD of 119 and 378.
so, GCD(119 , 378) = 119x + 378y = 7
now 7 = 119x + 378y
⇒7 = 7 × 13x + 7 × 54y
⇒1 = 13x + 54y
⇒13 × 25 + 54 × (-6) = 13x + 54y
on comparing we get, x = 25 and y = -6
Therefore GCD (119, 378) = 7 and x = 25 and y = -6
Learn more about Euclidean alogorithm
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What value of x will make the triangles similar by the SSS similarity theorem? Show your work.
Answer:
x = 24
Step-by-step explanation:
by the similarity theorem
the ratios of corresponding sides are in proportion , that is
[tex]\frac{x}{9}[/tex] = [tex]\frac{16}{6}[/tex] ( cross- multiply )
6x = 9 × 16 = 144 ( divide both sides by 6 )
x = 24