The proof is shown in the solution.
Given is an expression (2k + x)", we need to expand and prove,
Expand the binomials and cancel the 2k's:
n(n−1) / 2 (2k) = n(n−1)(n−2) / 6
Solving,
3(2k) = n−2
n = 6k+2
Hence proved.
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help me Find the base angles of the figure below.
A) 130°
B) 65°
C) 25°
D) 50°
Answer:
C) 25°
Step-by-step explanation:
You want the base angles in an isosceles triangle with vertex angle 130°.
Base anglesThe base angles of an isosceles triangle are congruent. If each is represented by 'b', then the sum of angles in the triangle is ...
2b +130° = 180°
2b = 50° . . . . . . . . subtract 130°
b = 25° . . . . . . . divide by 2
The base angles of the triangle are 25°, choice C.
<95141404393>
need and answer and explanation
Factoring Polynomials Formative
QUESTION 1
Solve the following by factoring:
y³ - 6y² = 0
[tex]y^3 - 6y^2 = 0\\y^2(y-6)=0\\y^2=0 \vee y-6=0\\y=0 \vee y=6[/tex]
Calculator
Pyramid ABCDE is a square pyramid.
What is the lateral area of pyramid ABCDE?
URGENT
The lateral area of the pyramid is 512√3 in.
What is area?Area is the region bounded by plane shape.
To calculate the area of the pyramid, we use the formula below
Formula:
A = 8aL.................................... Equation 1Where:
A = Area of the pyramida = Length of the square baseL = Slight height of the PyramidFrom the question,
Given:
a = 16 inL = 8sin60° = 4√3 inSubstitute these value into equation 1
A = (8×16×4√3)A = 512√3 inHence, the right option is D. 512√3 in.
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Practice A shuttle space suit, including the life support system, weighs about 310 pounds. The break in the y-axis represents the values from 0-300. What does each ordered pair on the line represent? 2. Write an equation to represent the relationship shown in the graph. 3. Is this a proportional relationship? Justify your answer. 4. In this problem situation, do all the points on the line make sense? Explain your reasoning. 5. Determine the weight of an astronaut without the shuttle suit given that the astronaut's weight while wearing the shuttle suit. a. 480 lb b. 467 lb c. 520 lb Weight of Astronaut With Suit (pounds)
Step-by-step explanation:
Each ordered pair on the line represents the weight of an astronaut with the shuttle space suit, given in pounds, and the total weight of the shuttle space suit and life support system, also given in pounds.
Let x represent the weight of the astronaut without the shuttle suit, and let y represent the weight of the astronaut with the shuttle suit and life support system. Then the equation for the relationship shown in the graph is: y = x + 310.
No, this is not a proportional relationship because the slope of the line is not constant. In a proportional relationship, the ratio of y to x would always be the same, but in this case, the ratio changes depending on the value of x.
No, not all the points on the line make sense in the context of the problem situation. For example, the point (0, 310) would represent an astronaut with no weight without the shuttle suit, which is not physically possible. Also, the point (480, 790) would represent an astronaut with a weight of 480 pounds without the suit, which is also not physically possible. Therefore, we need to restrict the domain of the equation to make sense in the context of the problem situation.
To determine the weight of an astronaut without the shuttle suit, we need to solve the equation y = x + 310 for x, given that y = 480. Substituting y = 480 into the equation, we get: 480 = x + 310. Solving for x, we get: x = 170. Therefore, the weight of the astronaut without the shuttle suit is 170 pounds.
You are interested in finding a 95% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 11 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.
13 5 10 11 26 20 18 18 24 23 5
a. To compute the confidence interval use a
t
Correct distribution.
b. With 95% confidence the population mean number of visits per physical therapy patient is between
and
visits.
c. If many groups of 11 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About
percent of these confidence intervals will contain the true population mean number of visits per patient and about
percent will not contain the true population mean number of visits per patient.
For finding a 95% confidence interval:
a. To compute the confidence interval, use a t distribution with 10 degrees of freedom.b. With 95% confidence, the population mean number of visits per physical therapy patient is between 13.011 and 19.249 visits.c. About 95% of these confidence intervals will contain the true population mean number of visits per patient and about 5% will not contain the true population mean number of visits per patient.How to solve confidence interval?a) The sample mean is x = 16.13.
The sample standard deviation is s = 6.948.
The degrees of freedom are df = 10.
The critical value of t for a 95% confidence interval is t = 2.228.
The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.
The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).
b) The 95% confidence interval is (11.867, 20.393).
This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.
c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.
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Type the correct answer in each box. If necessary, use / for the fraction bar(s).
A shaded right triangle uppercase C uppercase A uppercase B with side uppercase C uppercase A equals lowercase b, side uppercase A uppercase B equals lowercase c, and side uppercase C uppercase B equals lowercase a. Right angle is at uppercase A.
In this triangle, the product of sin B and tan C is , and the product of sin C and tan B is .
The product of sin B and tan C is c/a.
The product of sin C and tan B is b/a.
Given is a right triangle, ABC, we need to find the product of sin B and tan C and the product of sin C and tan B,
So, we know,
Sine = Opposite ÷ Hypotenuse.
Cosine = Adjacent ÷ Hypotenuse.
Tangent = Opposite ÷ Adjacent.
Therefore,
Sin B = b/a
Tan C = c/b
Sin B x Tan C = b/a x c/b = c/a
And,
Sin C = c/a
Tan B = b/c
Sin C x Tan B = c/a x b/c = b/a
Hence the products are c/a and b/a.
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The complete is attached.
HELP ASAPPP
the checks might not be correct on picture
Answer:
Step-by-step explanation:
yea the checks are not correct
Answer:
1,2
4,-1
5,-3
6,-5
Step-by-step explanation:
the question is unclear but if you put it in desmos this is what you get
Find the new balance in each problem.
19. Your balance on May 20 was $189.75,
and you made a $112.45 deposit on
May 22. On May 29, you wrote a $75.68
check, and on June 1, you made an
ATM withdrawal of $50.00.
Answer:
To find the new balance, we'll start with the initial balance on May 20 and then perform the transactions in chronological order.
Step-by-step explanation:
Initial balance on May 20: $189.75
Deposit on May 22: +$112.45
To calculate the balance after the deposit, we add the deposit amount to the initial balance:
New balance after deposit = $189.75 + $112.45 = $302.20
Check written on May 29: -$75.68
To calculate the balance after writing the check, we subtract the check amount from the previous balance:
New balance after check = $302.20 - $75.68 = $226.52
ATM withdrawal on June 1: -$50.00
To calculate the final balance after the ATM withdrawal, we subtract the withdrawal amount from the previous balance:
Final balance after ATM withdrawal = $226.52 - $50.00 = $176.52
Therefore, the new balance after all the transactions is $176.52.
Mr brainiac has found the Treasure Chest help him to get the code to open the chest the last digit is the half of 18 the sum of the two middle digit is 10 the third of and the fourth digit is the same the first digit is double the second digit what's the answer
A contradiction in the given clues and it is not possible to find a valid code with the given information.
The code to open the treasure chest can be determined using a few simple steps.
Firstly, we know that the last digit is half of 18, which is 9.
This means that the code ends with the number 9.
Next, we are given the information that the sum of the two middle digits is 10.
This tells us that the two middle digits must be 4 and 6, as they add up to 10.
Thirdly, we know that the third and fourth digits are the same.
Since we already know that the last digit is 9, this means that the third digit must also be 9.
Finally, we are told that the first digit is double the second digit.
Since we know that the second digit is 4, we can determine that the first digit must be 8.
Therefore, the code to open the treasure chest is 8469.
Mr Brainiac can now use this code to unlock the chest and discover the treasures inside.
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Prior to June 30, a company has never had any treasury stock transactions. The company repurchased 185 shares of its $1 par common stock on June 30 for $42 per share. On July 20, it reissued 90 of these shares at $46 per share. On August 1, it reissued 70 of the shares at $40 per share. What is the journal entry necessary to record the reissuance of treasury stock on July 20?
On July 20, the company recorded a journal entry debiting cash for $4,140, crediting treasury stock for $3,780, and crediting paid-in capital from treasury stock for $360.
To record the reissuance of treasury stock on July 20, the following journal entry should be made:
Date: July 20
Debit: Cash ($46 * 90) $4,140
Credit: Treasury Stock ($42 * 90) $3,780
Credit: Paid-In Capital from Treasury Stock $360
Explanation:
The debit to Cash represents the amount received from the reissuance of 90 shares at $46 per share, totaling $4,140.
The credit to Treasury Stock reduces the balance of the treasury stock account by the cost of the 90 shares, which is $42 per share, totaling $3,780.
The credit to Paid-In Capital from Treasury Stock accounts for the difference between the cost of the treasury stock and the amount received from its reissuance, which is $46 - $42 = $4 per share, totaling $360.
This journal entry properly reflects the increase in cash from the reissuance of the shares, reduces the treasury stock account balance, and recognizes the gain in paid-in capital resulting from the reissuance at a higher price than the repurchase cost.
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Which equation has infinitely many solutions?
O 2(3x - 10) = 6x + 20 Jhry
O 16 + 3x
-
3x + 16
O 4x10-2(-2x + 5)
O-7x +9 = 9x - 7
Answer:
it's is D
This is because equation 1 to 3 results in only a constant but D x will be 1
Answer: 4x - 10 = -2(-2x + 5)
Step-by-step explanation:
An equation has an infinitely many solutions when both sides are equal to each other.
-2(-2x+5) expands to become (-2*-2)*x + 5*(-2) = 4x - 10
Since the other side of the equation is also 4x - 10, both sides of the equation are identical and thus the equation has infinitely many solutions.
The rule is y = |x| sketch the graphs for y+x and y = -x
Where the rules is is y = |x| the graph for y+x and y = -x will become the graph for y+x and y = x. Because x has to become an absolute (positive) value.
What is a graph?In discrete mathematics, and more particularly in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way.
Distances between locations are often measured using the absolute value function. The absolute value function can also be used to address applied issues such as ranges of feasible values.
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Which shows the equation of the line containing the point (3, -2) and having a slope of 2 in slope-intercept form
The equation of the line is y = 2x - 8.
The equation of a line in slope-intercept form (y = mx + b) is determined by the slope (m) and the y-intercept (b).
Given that the point (3, -2) lies on the line and the slope is 2, we can substitute these values into the slope-intercept form to find the y-intercept.
Using the point-slope formula:
y - y1 = m(x - x1)
Substituting (3, -2) and m = 2:
y - (-2) = 2(x - 3)
Simplifying:
y + 2 = 2x - 6
Rearranging to slope-intercept form:
y = 2x - 8
The equation of the line containing the point (3, -2) with a slope of 2 in slope-intercept form is y = 2x - 8.
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Will give brainliest to whoever solves this properly, Please help me
The positions will be filled in 56,280 ways
How to find the number of waysThere are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows
For the position of president
11 combination 1 = 11
For the position of secretary
10 combination 1 = 10
For the position of treasurer
10 combination 1 = 10
For the position of three directors
8 combination 3 = 56 ways
the total number of ways to fill these positions is
11 x 10 x 9 x 56 = 56,280.
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pls also calculate this problem: (ty)
x=1/3
33x-1=10
add 1 on both sides
33x=11
divide 33 on both sides
and it should equal 1/3
NO LINKS!! URGENT HELP PLEASE!!!
Write a rule for the nth term of this arithmetic sequence. Then find a_20.
3. 8, 21, 34, 47, 60, . . .
4. 6, 2, -2, -6, -10, . . .
Answer:
3) an = 8 +13(n -1); a20 = 255
4) an = 6 -4(n -1); a20 = -70
Step-by-step explanation:
You want the rule and the 20th term for the arithmetic sequences ...
3) 8, 21, 34, ...
4) 6, 2, -2, ...
RuleThe n-th term of an arithmetic sequence is given in terms of the first term (a1) and the common difference (d) as ...
an = a1 +d(n -1)
3.The first term is 8. The common difference is 21 -8 = 13. The rule is ...
an = 8 +13(n -1)
The 20th term is ...
a20 = 8 +13(20 -1) = 255
4.The first term is 6. The common difference is 2 -6 = -4. The rule is ...
an = 6 -4(n -1)
The 20th term is ...
a20 = 6 -4(20 -1) = -70
#95141404393
Answer:
3. 255
4. -70
Step-by-step explanation:
3.
For the arithmetic sequence 8, 21, 34, 47, 60, ...
The common difference between consecutive terms is d =(21-8)= 13. Therefore, the nth term of the sequence can be expressed as:
[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]
where [tex]\bold{a_1}[/tex] is the first term of the sequence,
n is the term number, and d is the common difference.
Substituting [tex]a_1 = 8[/tex] and d = 13, we get:
[tex]a_n = 8 + (n - 1) * 13\\a_n = 13n - 5[/tex]
To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:
[tex]a_{20} = 13(20) - 5\\a_{20}= 255[/tex]
4.
For the arithmetic sequence 6, 2, -2, -6, -10, ...
The common difference between consecutive terms is d =(2-6)= -4. Therefore, the nth term of the sequence can be expressed as:
[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]
where [tex]a_1[/tex] is the first term of the sequence,
n is the term number, and
d is a common difference.
Substituting [tex]a_1[/tex]= 6 and d = -4, we get:
[tex]a_n = 6 + (n - 1) * (-4)\\a_n = 10 - 4n[/tex]
To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:
[tex]a_{20} = 10 - 4(20)\\a_{20}= -70[/tex]
A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A pair of parallel lines
B. A point
OC. A pair of intersecting lines
OD. A single line
When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.
How to know what is formed from a line intersecting a cone?
The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.
This means the intersecting line forms a right angle with the base of the right circular cone.
Therefore, from this interaction is a pair of intersecting lines.
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What conclusion can be determined from the dot plot below?
The conclusion that can be gotten from the dot plot is that the median is 10
what is a dot plot?A dot plot, also known as a dot chart or dot graph, is a simple type of data visualization that displays individual data points on a number line. It is a way to visually represent the distribution and frequency of a dataset.
In a dot plot, each data point is represented by a dot or a marker placed above the corresponding value on the number line. If there are multiple data points with the same value, the dots are stacked vertically above that value.
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please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
The length of the arcs are calculated to the nearest hundredth as:
12. 14.03 meters 13. 6.91 meters
How to Find the Length of an Arc?The formula used to find the length of a an arc is: length of arc = ∅/360 * 2πr, where ∅ is the central angle measure and r is the radius of the circle.
Length of arc XW:
∅ = m<XZW = 180 - 113
∅ = 67 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc XW = 67/360 * 2 * π * 12 ≈ 14.03 meters
Length of arc XW:
∅ = m<YVU = 180 - 67 - 80
∅ = 33 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc YVU = 33/360 * 2 * π * 12 ≈ 6.91 meters
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a) (i) 830 + 50 gives the same answer as x + 100
Work out the value of x.
X =
(ii) What is the value of 830 + 50?
A coach can take 50 people.
(iii) How many coaches would be needed to transport 830 people?
b) Jayne needs to hire 13 coaches.
Each coach costs £450 to hire.
Work out the total cost of hiring 13 coaches. £
Total marks: 6
The value of x is 780 and 830 + 50 equals 880
The number of coaches is 17 and the total cost is £5850
Calculating the value of x.From the question, we have the following parameters that can be used in our computation:
830 + 50 gives the same answer as x + 100
This means that
830 + 50 = x + 100
So, we have
x = 830 + 50 - 100
Evaluate
x = 780
Also, we have
830 + 50 = 880
So, the value of x is 780 and 830 + 50 equals 880
Calculating the number of coachesHere, we have
People = 830
People per coach = 50
So, we have
Coaches = 830/50
Evaluate
Coaches = 16.6
Approximate
Coaches = 17
The total cost of hiring 13 coaches is
Cost = 450 * 13
Evaluate
Cost = 5850
Hence, the number of coaches is 17 and the total cost is £5850
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Help DUE TOMORROW !determine the amount of cardboard needed to make a box for a single slice of pizza. The box is in the shape of a triangular, prism as shown. Giving 88 points if correct answer
Answer:
148 in²
Step-by-step explanation:
The box is made up of two triangles and three rectangles. The formula for the rectangles is length times width. The formula for the triangles is one-half base times height.
RECTANGLES: (lxw)
7x2=14
12.5x2=25
12.5x2=25
TRIANGLES: (1/2bh)
1/2x12x7=42
1/2x12x7=42
Add together to get the sum of the surface area:
14+25+25+42+42=148 inches squared
The following figure is made of 1 rectangle and 2 triangles find the area of each part of the figure and the whole figure
The area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the Total area is 44 square units.
1. The rectangle, which has a length of 8 units and a width of 4 units.
2. The two triangles, which are identical and have a base of 4 units and a height of 3 units.
To find the area of the rectangle, we can use the formula:
Area = Length x Width
Area = 8 x 4 = 32 square units
To find the area of each triangle, we can use the formula:
Area = 1/2 x Base x Height
Area = 1/2 x 4 x 3 = 6 square units
So, the total area of both triangles is:
Total area = 6 + 6 = 12 square units
Now, to find the total area of the figure, we can add the areas of the rectangle and the two triangles:
Total area = Area of rectangle + Total area of triangles
Total area = 32 + 12 = 44 square units
Therefore, the area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the total area is 44 square units.
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What is the probability either event will occur?
The probability that either event will occur is given as follows:
P(A or B) = 0.82 = 82%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of events in this problem is given as follows:
23 + 18 + 9 = 50.
The events are given as follows:
A = 23.B = 18.Hence the number of desired outcomes is given as follows:
23 + 18 = 41.
And the probability is of:
p = 41/50 = 0.82 = 82%.
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Question 11 of 30
Suppose that a regression line for some data transformed with logarithms
predicts that when x equals 3, log(y) will equal 2.725. What does the
regression line predict y will equal when x equals 3? Round your answer to the
nearest whole number.
A. 22,577
OB. 531
OC. 20
OD. 27
SUBMIT
The regression line predict y will equal 531 when x equals 3
How to solve the regression linelog(y) = 2.725
To undo the logarithm, we can use the exponential function:
y = 10^(2.725)
Using a calculator, we find:
y ≈ 530.8
We have to approximate this to 531
Rounding to the nearest whole number, the regression line predicts that y will equal 531 when x equals 3.
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Need this ASAP please
Answer:
8 months
Step-by-step explanation:
[tex]4000=400(\frac{(1+.045)^{n}-1 }{.045})[/tex]
Do what's in parentheses.
[tex]4000=400(\frac{(1.045^{n}-1) }{.045})[/tex]
Multiply 400 by the numerator.
[tex]4000=(\frac{400(1.045^{n})-400 }{.045})[/tex]
Divide both sides by .045.
[tex]180=400(1.045)^{n}-400[/tex]
Add 400 to both sides.
[tex]580=400(1.045)^{n}[/tex]
Divide both sides by 400.
[tex]\frac{29}{20} =1.045^{n}[/tex]
Convert to logarithmic equation.
[tex]log_{1.045}\frac{29}{20}=n[/tex]
8.441=8 months
Hope this helps!!
receiving a direct hit will take 15% of your health score if your health score is 24 and you receive a direct hit what will be your health score after the hit
Answer: 20.4
Step-by-step explanation:
(6,7), (-3,7), (-3,2), (6,2) perimeter and area
Answer:
perimeter = 28 units. area = 45 square units.
Step-by-step explanation:
perimeter = (6 - -3) + (7 -2) + (6 - -3) + (7 - 2)
= 9 + 5 + 9 +5
= 28 units.
area = (6 - -3) X (7 -2)
= (6 + 3) X 5
= 9 X 5
= 45 square units
Check the picture below.
At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. What is the probability that the light is red? Using the binomial distribution, what is the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light?
The Probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
The probability that the light is red is given by the ratio of the time the light is red to the total cycle time:
P(red) = 15 / (15 + 5 + 30) = 0.375
Using the binomial distribution, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light is:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
where (8 choose 3) is the binomial coefficient, which represents the number of ways to choose 3 cars out of 8. Evaluating this expression gives:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
= (8! / (3! * 5!)) * (0.375)^3 * (0.625)^5
= 56 * 0.052734375 * 0.1787109375
≈ 0.268
Therefore, the probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
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give the sum of 10+7_5+3
Answer:
17 and 8
Not sure what the underscore is for
Step-by-step explanation:
Answer:
17 and 8
Step-by-step explanation:
10+7 = 17 and 5+3 =8
