The gcd of 630 and 147 can be expressed as 21 = (-3) x 630 + 13 x 147.
Here are the solutions for each pair of numbers:
(a) To find the gcd of 56 and 42, we can use the Euclidean algorithm:
56 = 42 x 1 + 14
42 = 14 x 3 + 0
So the gcd of 56 and 42 is 14. To express 14 as a linear combination of 56 and 42, we can use the extended Euclidean algorithm:
14 = 56 - 42 x 1
= (-1) x 56 + 1 x 42
So the gcd of 56 and 42 can be expressed as 14 = (-1) x 56 + 1 x 42.
(b) To find the gcd of 81 and 60, we can again use the Euclidean algorithm:
81 = 60 x 1 + 21
60 = 21 x 2 + 18
21 = 18 x 1 + 3
18 = 3 x 6 + 0
So the gcd of 81 and 60 is 3. To express 3 as a linear combination of 81 and 60, we can use the extended Euclidean algorithm:
3 = 21 - 18 x 1
= 21 - (60 - 21 x 2) x 1
= (-1) x 60 + 3 x 21
= (-1) x 60 + 3 x (81 - 60 x 1)
So the gcd of 81 and 60 can be expressed as 3 = (-1) x 60 + 3 x 81.
(c) To find the gcd of 259 and 77, we can use the Euclidean algorithm:
259 = 77 x 3 + 28
77 = 28 x 2 + 21
28 = 21 x 1 + 7
21 = 7 x 3 + 0
So the gcd of 259 and 77 is 7. To express 7 as a linear combination of 259 and 77, we can use the extended Euclidean algorithm:
7 = 28 - 21 x 1
= 28 - (77 - 28 x 2) x 1
= 3 x 28 - 77 x 1
= 3 x (259 - 77 x 3) - 77 x 1
So the gcd of 259 and 77 can be expressed as 7 = 3 x 259 - 10 x 77.
(d) To find the gcd of 72 and 42, we can use the Euclidean algorithm:
72 = 42 x 1 + 30
42 = 30 x 1 + 12
30 = 12 x 2 + 6
12 = 6 x 2 + 0
So the gcd of 72 and 42 is 6. To express 6 as a linear combination of 72 and 42, we can use the extended Euclidean algorithm:
6 = 42 - 30 x 1
= 42 - (72 - 42 x 1) x 1
= (-1) x 72 + 2 x 42
So the gcd of 72 and 42 can be expressed as 6 = (-1) x 72 + 2 x 42.
(e) To find the gcd of 80 and 61, we can use the Euclidean algorithm:
80 = 61 x 1 + 19
61 = 19 x 3 + 4
19 = 4 x 4 + 3
4 = 3 x 1 + 1
3 = 1 x 3 + 0
So the gcd of 80 and 61 is 1. To express 1 as a linear combination of 80 and 61, we can use the extended Euclidean algorithm:
1 = 19 - 4 x 3
= 19 - (61 - 19 x 3) x 3
= 10 x 19 - 3 x 61
= 10 x (80 - 61 x 1) - 3 x 61
So the gcd of 80 and 61 can be expressed as 1 = 10 x 80 - 13 x 61.
(f) To find the gcd of 630 and 147, we can use the Euclidean algorithm:
630 = 147 x 4 + 42
147 = 42 x 3 + 21
42 = 21 x 2 + 0
So the gcd of 630 and 147 is 21. To express 21 as a linear combination of 630 and 147, we can use the extended Euclidean algorithm:
21 = 147 - 42 x 3
= 147 - (630 - 147 x 4) x 3
= (-3) x 630 + 13 x 147
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Suppose two cards are drawn randomly.
What is the probability of
drawing two green cards, if
the first card IS replaced
before the second draw?
Assume the first card
drawn is green.
[?]
Show your answer as a
fraction in lowest terms.
Enter the numerator.
The probability of drawing two green cards is 25/169
Calculating the probability of drawing two green cardsFrom the question, we have the following parameters that can be used in our computation:
Cards = 13
Green = 5
Selecting the first card we have
P(Green) = 5/13
The card is returned
So, we have the probablility of the second to be
P(Green) = 5/13
The probability of drawing two green cards is
P = 5/13 * 5/13
Evaluate
P = 25/169
Hence, the probability is 25/169
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Which of the ages of children taking a hip-hop dance class are 10, 9, 9, 7, 12, 14, 14, 9, and 16 years old. Which of the following box plots accurately represents the data set?
Answer:
Step-by-step explanation:
The answer is B because it goes 7,9,9,9,10,12,14,14,16 The number in the middle is the median(10) 4 on each side so second number from the front is your Q1 (9) second number from the back is your Q2 (14) smallest number is 7 and biggest nimber is 14 so that is your min. and max. so your answer is D
find a basis for the given subspace by deleting linearly dependent vectors. very little computation should be required. s
To find a basis for a given subspace by deleting linearly dependent vectors, we start with a set of vectors that spans the subspace and then remove any vectors that can be expressed as a linear combination of the other vectors in the set. The remaining vectors form a basis for the subspace.
The term "subspace" refers to a subset of a vector space that is closed under addition and scalar multiplication. In other words, if we take any two vectors in the subspace and add them together or multiply them by a scalar, the result is also in the subspace.
The term "linearly" refers to the idea that vectors in a set are independent if none of them can be expressed as a linear combination of the others. A linear combination is simply a sum of scalar multiples of vectors. If we can find a non-trivial (i.e. not all zero) linear combination of vectors in a set that equals zero, then the vectors are linearly dependent.
Therefore, to find a basis for a given subspace by deleting linearly dependent vectors, we must start with a set of vectors that spans the subspace and then remove any vectors that can be expressed as a linear combination of the others. The remaining vectors form a linearly independent set that spans the subspace, and thus they form a basis for the subspace.
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Giving the mid-point as( -4,7 ) and end point 3,8 calculate the other end point justify your answer
The other end point of the line segment is (-11, 6)
Calculating the other end pointFrom the question, we have the following parameters that can be used in our computation:
Midpoint = (-4, 7)
Endpoint 1 = (3, 8)
Represent the other point with (x, y)
using the above as a guide, we have the following:
Midpoint = 1/2(x1 + x2, y1 + y2)
So, we have
1/2(x + 3, y + 8) = (-4, 7)
This gives
(x + 3, y + 8) = (-8, 14)
Evaluate
(x, y) = (-11, 6)
Hence, the other point is (-11, 6)
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Which equation represents the graph? a graph of a line that passes through the points 0 comma negative 2 and 3 comma negative 1 y = −3x + 6 y equals negative one third times x plus 6 y equals one third times x minus 2 y = 3x − 2
The correct equation which represents the graph is,
⇒ y = 1/3x - 2
We know that;
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (3, -1) and (0, -2).
Now,
Since, The equation of line passes through the points (3, -1) and (0, -2).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 2 - (-1)) / (0 - 3)
m = - 1 / -3
m = 1/3
Thus, The equation of line with slope 1/3 is,
⇒ y - (-1)= 1/3 (x - 3)
⇒ y + 1 = 1/3x - 1
⇒ y = 1/3x - 2
Therefore, The equation of line passes through the points ((3, -1) and
(0, -2).will be;
⇒ y = 1/3x - 2
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if there are 10 family practice physicians at center clinic and 2 pediatricians, what is the ratio of family practice physicians to pediatricians? how might this ratio be used by the clinic administrator?
The ratio of family practice physicians to pediatricians is 5:1.
The ratio of family practice physicians to pediatricians can be found by dividing the number of family practice physicians by the number of pediatricians:
Ratio = Number of family practice physicians / Number of pediatricians
Ratio = 10 / 2
Ratio = 5
Therefore, the ratio of family practice physicians to pediatricians is 5:1.
The clinic administrator can use this ratio to assess the balance of the clinic's medical staff. If the ratio is not ideal, the administrator may need to take steps to hire more pediatricians or family practice physicians to better meet the needs of the clinic's patients.
Additionally, the ratio can be used to allocate resources, such as staff time and medical equipment, more effectively based on the patient population the clinic serves.
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One angle of an isosceles triangle measures 76°. What measures are possible for the other two angles? Choose all that apply.
Answer:
Step-by-step explanation:
0.6 divided by 1.80 please i need help
Answer: 0.333333333->
Step-by-step explanation:
It goes on forever
y = . y = ___? (5 points) Group of answer choices 2
Answer:
The equation 2 has a graph which is a straight line.
Step-by-step explanation:
Why?
We can know which of the given equations has a graph which is a straight line just checking the exponents of the variables.
We must remember that every variable that has an exponent equal or higher than 2 (quadratic) will not have a straight line as a graphic.
So, checking the exponents from the given equations, we have:
Hence, we can see that the only equation that has a linear term (straight line graph), is the second equation.
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
the average residential electrical power use (in hundreds of watts) per hour is given in the following table.
The average residential electrical power use refers to the amount of electrical energy consumed by households. It is typically measured in hundreds of watts per hour. By examining the provided table, you can identify the specific values for average power consumption in a residential setting.
According to the given table, the average residential electrical power use is measured in kilowatt-hours (kWh) per month, not hundreds of watts per hour. However, to convert it to the requested unit, we can divide the monthly average by the number of hours in a month (720 hours) and then multiply by 100 to get the average residential electrical power use in hundreds of watts per hour.
So, for example, if the monthly average is 600 kWh, the hourly average would be (600 kWh / 720 hours) x 100 = 83.33hundreds of watts per hour.
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help math is my week point help pls
A. m∠1 = 45° because m∠1 and the angle measuring 135° are supplementary angles
B. m∠2 = 95° because m∠2 and the angle measuring 95° are vertical angles
C. m∠3 = 40° because m∠1, m∠2, and m∠3 form a triangle.
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
m∠1 + 135° = 180° {supplementary angles}
m∠1 = 180° - 135°
m∠1 = 45°
m∠2 and 95° are vertical angles thus they are equal so;
m∠2 = 95°
m∠1 + m∠2 + m∠3 = 180° {sum of interior angles of a triangle}
45° + 95° + m∠3 = 180°
140° + m∠3 = 180°
m∠3 = 180° - 140°
m∠3 = 40°
In conclusion:
A. m∠1 = 45° because m∠1 and the angle measuring 135° are supplementary angles.
B. m∠2 = 95° because m∠2 and the angle measuring 95° are vertical angles
C. m∠3 = 40° because m∠1, m∠2, and m∠3 form a triangle.
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Theorem 9.6.4: when is the function V(x, y) = ax² + bxy + cy² positive definite? When is it negative definite?
The function V(x, y) = ax² + bxy + cy² is positive definite if and only if a > 0 and ac - b²/4 > 0.
The function V(x, y) is negative definite if and only if a < 0 and ac - b²/4 > 0.
The function V(x, y) is indefinite if and only if ac - b²/4 < 0.
In other words, the sign of a determines whether V(x, y) is positive or negative definite, and the discriminant ac - b²/4 determines whether it is definite or indefinite.
The proof of this theorem is based on the properties of the eigenvalues of the symmetric matrix A = [[a, b/2], [b/2, c]], which corresponds to the Hessian matrix of V(x, y) at the critical point (0, 0). The eigenvalues of A are λ1 = a + c + √(ac - b²/4) and λ2 = a + c - √(ac - b²/4), and their signs determine the definiteness of V(x, y).
If both eigenvalues are positive, V(x, y) is positive definite. If both eigenvalues are negative, V(x, y) is negative definite. If the eigenvalues have opposite signs, V(x, y) is indefinite. If one of the eigenvalues is zero, the test is inconclusive and higher-order derivatives must be considered.
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What is A number h
is at least −12
.
Answer:
Step-by-step explanation:
The statement "A number h is at least -12" means that h is greater than or equal to -12. In other words, any value of h that is -12 or greater would satisfy this statement. For example, h could be -10, -5, 0, 5, or any other number that is greater than or equal to -12.
A dairy farmer is looking at methods for transporting milk from her farm to a dairy plant. Three different methods are trialed over fourteen working days, and the daily costs of the methods (in $ 100) were as follows: Method 1 5.51 6.47 7.08 5.22Method 2 6.32 4.96 6.70 7.55 9.08Method 3 10.11 9.17 8.17 7.22 8.33Part a) TRUE or FALSE: If applying the analysis of variance (ANOVA) to these data, we must assume... i) The sample mean costs for the three methods are equal A. True B. Falseii) The daily costs from each method are from a Normal distribution A. True B. Falseiii) The daily costs for each method are independent. A. True B. Falseiv) The sample standard deviations of the costs for each method are equal. A. True B. Falsev) The daily costs for the different methods are independent. A. True B. False
ANOVA assumes that the observations from different groups (methods) are independent of each other.
i) The sample mean costs for the three methods are equal
A. False
Explanation: ANOVA tests the hypothesis that the population means of the three methods are equal, not the sample means.
ii) The daily costs from each method are from a Normal distribution
A. True
Explanation: ANOVA assumes that the data within each group (method) are normally distributed.
iii) The daily costs for each method are independent.
A. True
Explanation: ANOVA assumes that the observations within each group (method) are independent of each other.
iv) The sample standard deviations of the costs for each method are equal.
A. False
Explanation: ANOVA tests the hypothesis that the population variances of the three methods are equal, not the sample standard deviations.
v) The daily costs for the different methods are independent.
A. True
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You have a square pyramid sitting on top of a cube. The slant height of the pyramid is 5 and the sides of the cube are 3. What is the volume of both of the shapes?
The total volume of figure which has cube and pyramid is 33 cubic units.
The volume of a square pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
Let's call the side length of the square base of the pyramid s.
(1/2)s² + h² = 5²
s² + 4h² = 25
Since the sides of the cube are 3, the side length of the square base of the pyramid is also 3.
9 + 4h² = 25
h = 2
So the height of the pyramid is 2.
Volume of pyramid = (1/3)(3^2)(2) = 6
The volume of a cube is given by the formula V = s³, where s is the length of a side.
Since the sides of the cube are 3, the volume of the cube is:
Volume of the cube = 3³ = 27
Therefore, the total volume of the pyramid and the cube is:
Total = 6 + 27
= 33
Hence, the total volume of figure which has cube and pyramid is 33 cubic units.
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3.3g of metal A of density 2.7g/cm3 is mixed with 2.4g of metal B of density 4.8g/cm3 Determine the density of the mixture.
Answer:
To determine the density of the mixture, we need to first find the total volume of the mixture, which can be calculated by adding the volumes of metal A and metal B.
The volume of metal A can be calculated using the formula:
Volume = Mass / Density
So, the volume of metal A is:
Volume of A = 3.3g / 2.7g/cm³ = 1.2222... cm³ (rounded to four decimal places)
Similarly, the volume of metal B is:
Volume of B = 2.4g / 4.8g/cm³ = 0.5 cm³
The total volume of the mixture is therefore:
Total Volume = Volume of A + Volume of B
= 1.2222... cm³ + 0.5 cm³
= 1.7222... cm³ (rounded to four decimal places)
To find the density of the mixture, we can use the formula:
Density = Mass / Volume
The total mass of the mixture is:
Total Mass = Mass of A + Mass of B
= 3.3g + 2.4g
= 5.7g
So, the density of the mixture is:
Density = Total Mass / Total Volume
= 5.7g / 1.7222... cm³
= 3.3103... g/cm³ (rounded to four decimal places)
Therefore, the density of the mixture is approximately 3.3103 g/cm³
Step-by-step explanation:
At a university, 10% of students smoke. Calculate the expected number of smokers in a random sample of 150 students from this university.
The expected number of smokers in a random sample of 150 students from this university is 15.
To calculate the expected number of smokers in a random sample of 150 students at a university where 10% of students smoke, you simply multiply the total number of students in the sample by the percentage of students who smoke:
Expected number of smokers = Total number of students x Percentage of smokers
= 150 students x 10%
= 150 x 0.10
= 15
So, if we know that 10% of students smoke at this university, and we have a random sample of 150 students, we can calculate the expected number of smokers as follows:
Expected number of smokers = 150 x 0.10 = 15
Therefore, we can expect that there will be approximately 15 smokers in a random sample of 150 students from this university.
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Help me ASAPPPPPPPPPPP!!
Liam said that the following graph shows a positive correlation between ice cream sales and temperature.
A: Is he correct? Why or why not?
B: Liam’s friend Armonte said he believes this represents causation instead of a correlation. Is Liam or Armonte correct? Give at least two reasons to help support your claim.
A: Liam is correct. The graph shows a positive correlation between ice cream sales and temperature. As the temperature increases, ice cream sales also increase.
B: Armonte is not correct. There are a few reasons why the graph represents a correlation and not causation:
Correlation does not imply causation. Just because two variables are correlated, it does not mean that one variable causes the other.
There could be other variables that are affecting both ice cream sales and temperature. For example, if the graph was plotted over a long period of time, there may be seasonal factors that affect both variables, such as summer months having higher temperatures and more ice cream sales.
The graph only shows a relationship between ice cream sales and temperature, but it does not prove causation. To establish causation, a controlled experiment would need to be conducted to show that changes in temperature cause changes in ice cream sales.
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A: Plot point C so that its distance from the origin is 1. B: Plot point E 4/5 closer to the origin than C. What is its coordinate? DUE IN 10 MINUTES. HELP
A) A point C such that the distance from the origin can be plotted at (1, 0).
B) A point E which is at 4/5 closer to the origin than C can be plotted at (4/5, 0) = (0.8, 0)
A) Given a point O(0, 0).
A distance of 1 from the origin can be marked at 4 points :
(1, 0), (-1, 0), (0, 1) and (0, -1).
Using the distance formula, all the points from O is 1.
Let's take C as (1, 0).
B) Point E is at 4/5 closer to O than C.
Ratio of the distance between OE and EC is 4/5 : 1/5 = 4 : 1.
The section formula states that If a line with end points (x, y) and (x', y') is divided in the ratio m : n, then the divided point is,
P = [(mx' + nx)/(m + n) , (my' + ny)/ (m + n)]
Here (x, y) = (0, 0) and (x', y') = (1, 0)
m : n = 4 : 1
Using the section formula,
Coordinates of E = ((4 + 0)/ 5 , (0 + 0)/5) = (4/5, 0) = (0.8, 0).
If the distance between (0, 0) and (1, 0) is divided in to 5 segments, then the point E will be at 4th segment.
Hence the required coordinates are C(1, 0) and E(0.8, 0).
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true/false.students count the number of oscillations that occur until the amplitude has decreased to 62.5% of its initial value. from this, it is determined that the damping coefficient is b
True. In this scenario, the students are counting the number of oscillations and monitoring the amplitude to determine the damping coefficient, which is a measure of the rate at which the amplitude decreases over time.
True. Students can count the number of oscillations that occur until the amplitude has decreased to 62.5% of its initial value. By analyzing this information and using the appropriate equations, they can determine the damping coefficient (b) for the system.
Damping is an intervention to an oscillating system or system that has the effect of reducing or preventing oscillations. In the physical system, damping results from the process of dissipating the energy stored in an oscillation. Examples are viscous friction in mechanical systems (the viscosity of a fluid can affect an oscillating system, slowing it down; see Damping that is not based on energy loss can be important in other oscillating systems, as occurs in biological systems and bicycles (such as suspension (mechanical)).
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A grain silo has a cylindrical shape. Its diameter is 14 ft, and its height is 29 ft. What is the volume of the silo?
Answer:
Step-by-step explanation:
Which is a function? {(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)} {(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)} {(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)} {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
Answer:
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
Step-by-step explanation:
In a function, all x-coordinates must be different.
{(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}
7 appears twice as an x-coordinate. Not a function.
{(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}
1000 appears 3 times as an x-coordinate. Not a function.
{(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}
4 appears twice as an x-coordinate. Not a function.
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
All x-coordinates are different. Function.
Factor of (2x-3) and (x -5)
Answer:
(2x-3) and (x-5)
Step-by-step explanation:
To factor the expression (2x-3)(x-5), we can use the distributive property of multiplication over addition or subtraction:
(2x-3)(x-5) = 2x(x-5) - 3(x-5)
Now we can use the distributive property again to factor out the common factor of (x-5):
2x(x-5) - 3(x-5) = (2x - 3)(x - 5)
So the factors of (2x-3)(x-5) are (2x-3) and (x-5).
Find the zeros and describe the behavior of the graph at each zero. x^4 - 16x^3 + 63x^2
The zeros of the function are x = 0, x = 7, and x = 9.
The graph of f(x) is concave down near x = 7 and concave up near x = 9.
We have,
To find the zeros of the function f(x) = x^4 - 16x^3 + 63x^2,
We need to set f(x) equal to zero and solve for x:
x^4 - 16x^3 + 63x^2 = 0
Factor out x^2:
x^2(x^2 - 16x + 63) = 0
Factor the quadratic term:
x^2(x - 7)(x - 9) = 0
So the zeros of the function are x = 0, x = 7, and x = 9.
To describe the behavior of the graph at each zero, we can use the first and second derivative tests.
The first derivative of f(x) is:
f'(x) = 4x^3 - 48x^2 + 126x
The second derivative of f(x) is:
f''(x) = 12x^2 - 96x + 126
At x = 0, we have a double root, since x = 0 is a zero of multiplicity 2.
From the first derivative test, we see that f'(x) changes sign from negative to positive at x = 0, indicating that f(x) has a local minimum at x = 0.
From the second derivative test, we see that f''(0) = 126, which is positive. This means that the local minimum at x = 0 is a relative minimum, and the graph of f(x) is concave up near x = 0.
At x = 7 and x = 9, we have simple zeros.
From the first derivative test, we see that f'(x) changes sign from positive to negative at x = 7 and from negative to positive at x = 9, indicating that f(x) has local maximums at x = 7 and x = 9.
From the second derivative test, we see that f''(7) = -42 and f''(9) = 54, so the local maximum at x = 7 is a relative maximum, and the local maximum at x = 9 is a relative minimum.
Thus,
The zeros of the function are x = 0, x = 7, and x = 9.
The graph of f(x) is concave down near x = 7 and concave up near x = 9.
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The zeros of the graph are 0, 7, and 9.
To find the zeros of the function, we can set it equal to zero and factor:
[tex]x^4 - 16x^3 + 63x^2 \\= x^2(x^2 - 16x + 63) \\= x^2(x - 7)(x - 9)[/tex]
So the zeros are x = 0, x = 7, and x = 9.
We may look at the function's sign on either side of each zero to understand how the graph behaves there. The function's factored form may be used to our advantage here:
At x = 0, the function changes sign from negative to positive, indicating a local minimum.At x = 7, the function changes sign from positive to negative, indicating a local maximum.At x = 9, the function changes sign from negative to positive, indicating another local minimum.Examining the leading coefficient (which is positive) and the degree of the polynomial will also reveal the graph's general behavior (which is even). This indicates that if x increases or decreases, the graph will be upward-facing and will go closer to infinity in both directions.
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Find the value of x.
The value of x is √93.
The correct option is A.
We have,
Hypotenuse= 17
Base= 14
Using Pythagoras theorem
H² = P² + B²
P² = H² - B²
P² = 17² - 14²
P² = 289 - 196
P²=93
P= 9.64
Thus, the value of x is √93.
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2-72. Steve and Cathy are playing a card game with a standard deck of 52 playing cards.Cathy is dealt an ace and a four. Steve is dealt a jack.a. How many cards are left in the deck? [ 49 ]b. How many of the remaining cards are aces? [ 3 ]c. If Steve gets an ace, he will win. What is the probability that he will get an ace on the next card he is dealt? [ 3/49 ]d. Next Steve gets a two and Cathy gets a five. What is the probability that Stevewill get a nine on the next card he is dealt? [ 4/47 ]
The probability that Steve will get a nine on the next card he is dealt is 4/47. Steve and Cathy are playing a card game with a standard deck of 52 playing cards. After Cathy is dealt an ace and a four and Steve is dealt a jack, there are 49 cards left in the deck. Out of the remaining cards, there are three aces.
If Steve gets an ace on the next card he is dealt, he will win. The probability of this happening is 3/49, as there are three aces left in the deck out of a total of 49 cards remaining.
After Steve gets a two and Cathy gets a five, there are now 47 cards left in the deck. The probability of Steve getting a nine on the next card he is dealt is 4/47, as there are four nines left in the deck out of a total of 47 cards remaining.
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The measures of the exterior angles of a hexagon are x°, 2x°, 6x°, 8x°, 9x°, and 10x°. Find the measure of the smallest exterior angle.
the measure of the smallest exterior angle is 13. 846 degrees
How to determine the value
It is important to note that the sum of the exterior angles of a polygon is expressed with the formula;
Sum of exterior angles = 360
Note that are hexagon is defined as a polygon with 6 sides and six vertices.
Now, substitute the measure of the angles
x + 2x + 6x + 8x + 9x = 360
collect the like terms, we have;
26x = 360
Divide both sides by the coefficient of x, we have;
26x/26 = 360/x
x = 13. 846 degrees
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Kendall had $5 in her wallet and after doing her chores for the week her parents gave her $7 more. Cambrie had $7 in her wallet and earned $5 for doing her chores. How much money do each of them have and what property is this an example of
1. What is the area of the trapezoid? The diagram is not drawn to scale. (1 point)
6 cm
4 cm
8 cm
048 cm²
064 cm²
072 cm²
O104 cm²
The area of the trapezoid is 72 cm².
We have,
AB = EF = 8 cm
and CE = FD = 4 cm
So, CD = CE + EF + FD
CD = 4 + 8 + 4
CD = 16 cm
Now, the Area of trapezoid
= 1/2 x (sum of parallel sides) x height
= 1/2 x (16+ 8) x 6
= 1/2 x 24 x 6
= 72 cm²
Thus, The area of trapezoid is 72 cm²
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