Answers
Answer:
#15 (a)
[tex]{ \sf{a + 2b - c + 4d}} \\ \\ \hookrightarrow \: { \sf{ \binom{4}{6} + 2 \binom{4}{ - 2} - \binom{ - 3}{ - 2} + 4 \binom{5}{1} }} \\ \\ \hookrightarrow \: { \sf{ \binom{4}{6} + \binom{8}{ - 4} + \binom{3}{2} + \binom{20}{4} \: \: \: \: \: \: }} \\ \\ { \sf{ \hookrightarrow \: \binom{4 + 8 + 3 + 20}{6 - 4 + 2 + 4} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \sf{ \hookrightarrow \: { \boxed{ \binom{45}{8} }}}}[/tex]
#15 (b)
Step-by-step explanation:
15 (a)
if it is a vector
First, we need to multiply each vector component by its corresponding scalar value and then add them together.
a + 2b - c + 4d = (4)(1) + (4)(2) + (-3)(-1) + (5)(4) = 4 + 8 + 3 + 20 = 35
Therefore, the value of a + 2b - c + 4d is 35.
if it is a matrix
we can form a 1x4 matrix for vector a, b, c, and d respectively. We can also form a 4x4 matrix for the scalar values. Then we can perform matrix multiplication as follows:
(4 4 -3 5) (1 0 0 0) (0 2 0 0) (0 0 -1 0) (0 0 0 4)
= (41 + 40 - 30 + 50) (40 + 42 - 30 + 50) (40 + 40 - 3*(-1) + 50) (40 + 40 - 30 + 5*4)
= (4, 8, 3, 20)
Therefore, the value of a + 2b - c + 4d is (4, 8, 3, 20).
15 (b)
To find the product of the two matrices, we need to multiply each element of the first matrix by its corresponding element in the second matrix and add the products. The resulting matrix will be a 2 x 2 matrix.
| 5 -2 | | 2 6 | |(5)(2) + (-2)(5) (5)(6) + (-2)(3)|
| 4 1 | x | 5 3 | = |(4)(2) + (1)(5) (4)(6) + (1)(3)|
Performing the matrix multiplication, we get:
| 5 -2 | | 2 6 | | 10 -12 |
| 4 1 | x | 5 3 | = | 13 27 |
Therefore, the product of the matrices (5 -2, 4 1) and (2 6, 5 3) is the 2 x 2 matrix:
| 10 -12 |
| 13 27 |
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Related Questions
according to A1 Jazeera approximately what percentage of deaths were civilians as of September 2015
Answers
According to Al-Jaz/eera, approximately, 90% of deaths were civilians as of September 2015 in Syria.
What caused the Civilian death in Syria in 2015?The Syrian conflict, which began in 2011, has resulted in widespread violence and civilian casualties. In 2015, the primary causes of civilian deaths were airstrikes and shelling by the Syrian government and its allies including Russia against rebel-held areas.
These attacks often targeted hospitals, schools, and residential areas, causing significant collateral damage and loss of life. In addition, various rebel groups also carried out attacks on civilians, including sui/cide bombings and shelling of government-controlled areas. The conflict has also led to displacement, with millions of Syrians forced to flee their homes and seek refuge in neighboring countries.
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HELP ASAP ILL GIVE BRAINLIEST!!
Answers
Answer:109-6b degrees + P but we do not know P yet.
Step-by-step explanation:
you have 2 buckets, one which can hold 1 gallon of liquid and the other hold a half of gallon liquid. you must use these two buckets to fill up your gas tank with exactly 5 and 1/2 gallons of gas. what type of problem is this?
Answers
Answer:
The problem is the answer to your equation
Step-by-step explanation:
Im sorry to disappoint but these questions don't really have a name.
As part of a manufacturing process for widgets, an quality controller at ACME Corporation randomly samples 856 widgets during a day of production to test the current rate of defective widgets. The controller finds 34 defective widgets.The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, how many standard deviations is the point estimate from 7%?
Answers
The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, 91.2 is the standard deviations is the point estimate from 7%.
In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values are spread over a wider range.
The standard deviation can be abbreviated SD, and is most commonly used in mathematical texts and equations with the lowercase Greek letter σ (sigma) for the population standard deviation, or the Latin letter s for the standard deviation of the sample.
The standard deviation of a random variable, sample, population, data set, or probability distribution is the square root of its variance. It is algebraically simpler than the mean absolute deviation, although less robust in practice. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.
According to the Question:
Given that:
Defective widgets produced by ACME corporation was 7%
Total sample was 856 widgets.
Therefore, the Standard Deviation estimates from 7% is:
856 of 7% = 91.2
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The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
Answers
the vertex of the quadratic function is (7.5, 3.675).
Company revenue quadratic function.
Angel
The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:
r(x) = a(x - h)^2 + k
where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
We can use the given revenue values to set up a system of three equations:
2.7 = a(0 - h)^2 + k
3.4 = a(1 - h)^2 + k
2.7 = a(6 - h)^2 + k
Subtracting the first equation from the second, and the first equation from the third, we get:
0.7 = a(1 - h)^2
0 = a(6 - h)^2
Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:
6 - h = 10
which gives us h = -4.
Substituting h = -4 into the first equation, we get:
2.7 = a(0 - (-4))^2 + k
2.7 = 16a + k
Substituting the revenue value for 2005, we get:
3.9 = a(3 - (-4))^2 + k
3.9 = 49a + k
Solving for a and k, we get:
a = -0.1
k = 4.3
Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:
r(x) = -0.1(x + 4)^2 + 4.3
The vertex of this function is at (-4, 4.3).
Find the area of each composite figure
Show ur work
Answers
Answer:
285 cm²
Step-by-step explanation:
Area of square = 15² = 225 cm²
Area of triangle = bh/2 = 15*8/2 = 60 cm²
Area of composite figure = 225+60 = 285 cm².
M is the midpoint of line AB and N divides the line BC in the ratio 1:3 ,given that vector AM=a and vector AC=C
(a) express vector AN in terms of a and c
(b) Show that vector NM=¼(2a-3c)
Answers
Vector AN = a + ¾ c and we have shown that vector NM = ¼(2a – 3c) where M is the midpoint of line AB and N divides the line BC in the ratio 1:3 .
(a) To express vector AN in terms of a and c, we need to find the vector from A to N. Since N divides BC in the ratio 1:3, we can write:
BN = 3NC
Since M is the midpoint of AB, we have:
AM = MB
Adding these two equations, we get:
AM + BN = MB + 3NC
Substituting the vectors, we get:
a + BN = ½ (a + b + 2c) + 3c
Simplifying, we get:
BN = ½ (b – a) + 2c
But b = 2a – c (since M is the midpoint of AB)
So, we can write:
BN = ½ (2a – 2a + c) + 2c = ¾ c
Therefore, vector AN = vector AB + vector BN = (b – a) + ¾ c
Substituting b = 2a – c, we get:
Vector AN = a + ¾ c
(b) To show that vector NM = ¼(2a – 3c), we need to find vector NM and simplify it. Since M is the midpoint of AB, we have:
Vector NM = vector NC – vector MC
We know that N divides BC in the ratio 1:3, so we can write:
Vector NC = 3/4 vector BC = 3/4 (vector AB + vector AC)
Since M is the midpoint of AB, we have:
Vector MC = 1/2 vector AB
Substituting these vectors, we get:
Vector NM = 3/4 (vector AB + vector AC) – 1/2 vector AB
Simplifying, we get:
Vector NM = 1/4 vector AB + 3/4 vector AC
But AB = 2a – c (since M is the midpoint of AB)
Substituting, we get:
Vector NM = 1/4 (2a – c) + 3/4 c
Simplifying, we get:
Vector NM = ½ a – 3/4 c
Multiplying by 2, we get:
Vector NM = 2/2 (½ a) – 3/4 c
Simplifying, we get:
Vector NM = ¼ (2a – 3c)
Therefore, we have shown that vector NM = ¼(2a – 3c).
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The perimeter of a right angled triangle is 96cm
The lengths of its sides are in the ratio 6:8:10
Work out the area of the triangle in cm^2
Answers
Answer:
384 cm^2
Step-by-step explanation:
Let the lengths of the sides of the right-angled triangle be 6x, 8x, and 10x, where x is a constant.
Since the perimeter of the triangle is 96 cm, we have:
6x + 8x + 10x = 96
24x = 96
x = 4
Therefore, the lengths of the sides of the triangle are 24 cm, 32 cm, and 40 cm.
The area of a right-angled triangle is given by the formula:
Area = (1/2) * base * height
where the base and height are the two shorter sides of the triangle.
Using the Pythagorean theorem, we can determine that the base and height of the triangle are 24 cm and 32 cm, respectively.
Therefore, the area of the triangle is:
Area = (1/2) * base * height
Area = (1/2) * 24 cm * 32 cm
Area = 384 cm^2
Therefore, the area of the right-angled triangle is 384 cm^2.
0.81 x 9.4 work sown
Answers
If anyone could help that would help so much!
Answers
1. The center of circle is (5, -10)
2. The new center of circle is (4, -12)
3. Equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]
Define the term Circle identities?The Circle identities defines a set of fundamental identities in trigonometry that depends on the six trigonometric functions of an angle in a right-angled triangle.
Given circle equation is [tex](x-5)^2+(y+10)^2 = 64[/tex]
after translated 1 left and 2 down, by simply add 1 in x and add 2 in y axis, So, the new circle equation will be,
[tex](x-4)^2+(y+12)^2 = 64[/tex]
1. The center of the given circle [tex](x-5)^2+(y+10)^2 = 64[/tex]
Generally the equation of circle is [tex](x-h)^2 +(y-k)^2 =r^2[/tex]
where, (h, k)is center of circle and r is radius.
by comparing the given equation, we get, h = 5, k = -10
So, the center of circle is (5, -10)
2. New center after translation
equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]
comparing the given equation, we get, h = 4, k = -12
So, the new center of circle is (4, -12)
3. Equation of the resulting circle is [tex](x-4)^2+(y+12)^2 = 64[/tex]
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kathy needs money for her trip to europe. if she has us dollars in the bank but wants to withdraw half of it in british pounds and half of it in euros, how many more euros than pounds will she have? assume pound is equal to usd and euro is equal to usd, and round to the nearest whole number.
Answers
The difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero.
Kathy needs to exchange half of her US dollars into British pounds and half of her US dollars into euros. Since it is given that pound is equal to USD and euro is also equal to USD, when she withdraws half of her US dollars as British pounds and half of it as euros, she will have the same amount of pounds and euros. Thus, the difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero. Therefore, she will have the same amount of money in both currencies, and the answer to the question is 0 (rounded to the nearest whole number).
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Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 J Q K
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
one over 26
four over 25
one fourth
8 over 13
Answers
The experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.
What is the prοbability?The study οf prοbability examines the likelihοοds οf results οccurring and is based οn the ratiο οf likely and imprοbable scenariοs.
Tο find the experimental prοbability οf drawing a K οr 6, we need tο add the frequencies οf card K and card 6 and divide by the tοtal number οf draws:
Frequency οf K οr 6 = 7 + 6 = 13
Tοtal number οf draws = 4 + 7 + 5 + 6 + 7 + 6 + 8 + 10 + 7 + 10 + 8 + 12 + 10 = 100
Experimental prοbability οf drawing a K οr 6 = Frequency οf K οr 6 / Tοtal number οf draws = 13 / 100
Hence, the experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.
Answer: 8 οver 13 is the clοsest οptiοn tο 13/100, sο the answer is 8 οver 13.
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factor completely 3x^2+9x-3
Answers
Answer:
3(x^2+3x-1)
Step-by-step explanation:
3x^2+9x-3
3(x^2+3x-1)
Find the 8th term of the geometric sequence 2, -10, 50, ...
Answers
The 8th term of the given geometric sequence is -156250.
What is geometric sequence?A sequence of numbers is called a geometric sequence if each term, except for the first term, is obtained by multiplying the previous term by a constant factor, which is called the common ratio.
According to given information:The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by -5.
So, the common ratio (r) between any two consecutive terms is -5.
To find the 8th term, we can use the formula for the nth term of a geometric sequence:
[tex]an = a1 * r^{(n-1)[/tex]
where,
an = 8th term
a1 = first term = 2
r = common ratio = -5
n = 8 (since we want to find the 8th term)
Therefore, substituting the values in the formula, we get:
[tex]a8 = 2 * (-5)^{(8-1)}\\\\a8 = 2 * (-5)^7\\\\a8 = 2 * (-78125)\\\\a8 = -156250[/tex]
Hence, the 8th term of the given geometric sequence is -156250.
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!! URGENT !! The following data points represent the number of points the Hawaii Eagles football team scored each game.
17
,
33
,
28
,
23
,
10
,
42
,
3
17,33,28,23,10,42,317, comma, 33, comma, 28, comma, 23, comma, 10, comma, 42, comma, 3
Using the data, create a histogram.
Answers
Answer:
See image.
Step-by-step explanation:
Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.
3 and 10 fall in 0-15, so thats 2 values
17, 23, and 28 fall in 15-30, so thats 3 values,
33 and 42 fall in 30-45, so thats 2 values.
circumference
Calculate the
of a pie that has a 12 inch
diameter.
Answers
Answer:
12pi
Step-by-step explanation:
circumfrence : 2*pi*r
the radius is found by dividing the diameter in half so, 12/2 or 6
now multiply 6 with 2 and pi and you get 12pi
~lmk if you got Qs
What is the value of f?
Answers
Answer:
f = 120
Step-by-step explanation:
1. The Entire line in which the angles rest on = 180 degrees.
2. 180-60 = 120
3. 120 Degrees is your answer
Suppose there is a 70% chance that Reagan will make a field goal at any given time. A computer was used to generate 10 sets of random numbers from 1 to 10, 1-7 represent a successful field goal and numbers 8-10 represent a missed field goal. The results are shown. Trial 1 2 3 4 5 6 7 8 9 10 Numbers Generated 1, 9, 1, 2, 10, 6, 5, 2, 7,2 8, 10, 4, 10, 2, 2, 3, 6, 7, 10 6, 9, 9, 10, 4, 10, 10, 2, 6, 6 8 & 2, 3, 4, 6, 5, 6, 5, 3 1, 10, 1, 2, 5, 6, 9, 4, 10, 3 7, 1, 9, 1, 6, 3, 3, 7, 5, 6 2, 5, 2, 7, 5, 5, 10, 5, 6, 3 9, 6, 10, 4, 9, 6, 8, 9, 9,9 5, 1, 4, 5, 2, 8, 5, 7, 5, 6 7, 6, 5, 5, 1, 10, 9, 3, 9, 2 Find the experimental probability that Reagan will miss the first two field goals and make the third one.
Answers
The experimental probability that Reagan will miss the first two field goals and make the third one is 20%
What is experimental probability?Experimental is the probability is the probability of an event occurring based on the performance of actual experiment.
The probability of making or missing a field goal is 0.7 and 0.3 respectively. The probability that Reagan will miss the first two field goals and make the third one, can be obtained from the result by counting the number of times the specific sequence of results occurs in the 10 sets of random numbers and divide by the total number of trials.
The analysis of the sets of numbers indicates that the specific sequence of missing the first two field goals and making the third one occurs twice in 2nd and 4th trials
2; 8, 10, 4, 10, 2, 2, 3, 6, 7, 10
4; 8, 8, 2, 3, 4, 6, 5, 6, 5, 3
Therefore, the experimental probability of the specific sequence occurring is 2/10 = 1/5 (since there are 10 sets of numbers in total)
Theoretically, the probability of making and missing field goals for the three kicks in the sequence are;
0.3 × 0.3 × 0.7 = 0.063
Therefore, the experimental probability of Reagan missing the first two field goals and making the third one is approximately 0.2 (or 20%), while the theoretical probability is 0.063 (or 6.3%)
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what is the measurement of the unknown angle?
Answers
The measure of the unknown angle is 93°
What is the measurement of the unknown angle?First we should get the interior angles of the triangle in the right side.
The angle in the left side is given by:
x + 127° = 180°
x = 180° - 127°
x = 53°
While the angle in the right side is:
y + 146° = 180°
y = 180° - 146°
y = 34°
Now remember that the sum of the interior angles of a triangle must be 180°, then if the angle at the top is z we can write:
z + 34° + 53° = 180°
z = 180° - 34° - 53°
z = 93°
And this angle is a vertical angle of the one we want to find, so the measure of the unknown angle is also 93°.
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Annual sales for a fast food restaurant are $649,995 and increasing at a rate of 3.5% per year. Use an exponential function to find the annual sales after 8 years.
Answers
After seven years, the yearly sales are 855,355.65.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
the following parameters
a = 650000
r = 4% = 0.04
t = 7
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Number of large boxes:
Number of small boxes:
a system of linear...
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 25 pounds each. There
are 135 boxes in all. If the truck is carrying a total of 5475 pounds in boxes, how many of each type of box is it carrying?
Answers
If a delivery truck is transporting boxes of two sizes: large and small. there are 70 large boxes and 65 small boxes in the truck.
How many of each type of box is it carrying?Let's assume that x represents the number of large boxes, and y represents the number of small boxes.
We know that there are 135 boxes in total, so:
x + y = 135
We also know that the total weight of the boxes is 5475 pounds, so:
55x + 25y = 5475
Now we have a system of linear equations with two variables. We can use substitution or elimination to solve for x and y. Let's use substitution:
From the first equation, we can solve for x in terms of y:
x = 135 - y
Substitute this expression for x into the second equation:
55x + 25y = 5475
55(135 - y) + 25y = 5475
Simplify and solve for y:
7425 - 55y + 25y = 5475
30y = 1950
y = 65
Now we can use the first equation to solve for x:
x + y = 135
x + 65 = 135
x = 70
Therefore, there are 70 large boxes and 65 small boxes in the truck.
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PLEASE HELP!!
ABCD is a kite, so AC ⊥ DB and DE = EB. Calculate the length of AC, to the nearest tenth of a centimeter.
Answers
Answer:
12.7 cm----------------------------
Since diagonals of a kite are perpendicular to each other, the triangles AED and CED are right triangles.
Find the length of ED:
ED = BE = BD/2 = 8 / 2 = 4 cmFind the length of legs AE and CE using Pythagorean theorem:
[tex]AE=\sqrt{AD^2-ED^2}=\sqrt{7^2-4^2}=\sqrt{49-16}=\sqrt{33}=5.74[/tex][tex]CE=\sqrt{CD^2-ED^2}=\sqrt{8^2-4^2}=\sqrt{64-16}=\sqrt{48}=6.93[/tex]Find the length of AC:
AC = AE + CE = 5.74 + 6.93 = 12.67 ≈ 12.7 cmAnswer:
AC = 12.7 cm
Step-by-step explanation:
To find:-
The length of AC.Answer :-
We are here given a kite in which AC ⊥ DB and DE = EB = 4cm . We are interested in finding out the length of AC .
[tex]\rule{200}2[/tex]
D I A G R A M : -
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\sf A$}\put(0.5,-0.3){$\sf B $}\put(5.2,-0.3){$\sf D $}\put(1,0){\line(1,-2){2}}\put(5,0){\line(-1, - 2){2}}\put(2.9,-4.4){$\sf C $}\put(3,3){\line(0, - 1){7}}\put(4,2){$\sf 7cm $}\put(4.5,- 2){$\sf 8cm $}\put(3.4,0.2){$\sf 4cm $}\put(2,.2){$\sf 4cm $}\put(3.2, - .5){$\sf E $}\multiput(2,0.2)(2.2,0){2}{\line(0,-1){0.4}}\multiput(1.9,0.2)(2.2,0){2}{\line(0,-1){0.4}}\put(5,-4){$\boxed{\bf \textcopyright Tony Stark}$}\put(3.01,0.01){\framebox(0.25,0.25)}\end{picture}[/tex]
[tex]\rule{200}2[/tex]
We can see that,
[tex]\sf:\implies AC = AE+EC\\[/tex]
We can seperately find AE and EC and then add them up to find AC . We can see that due to the diagonals intersecting each other at right angles , there is formation of 4 right angled triangle, the triangles which we will be using are ∆AED and ∆CED .
We can use Pythagoras theorem here according to which
The square of hypotenuse (longest side) is equal to the sum of squares of other two sides.[tex]\sf:\implies h^2 = a^2 + b^2 \\[/tex]
In two triangles AED and CED hypotenuse are 7cm and cm respectively.
So that , in ∆AED ,
[tex]\sf:\implies 7^2 = AE^2 + DE^2 \\[/tex]
[tex]\sf:\implies AE^2 = 7^2 - DE^2 = 7^2 - 4^2 \\[/tex]
[tex]\sf:\implies AE^2 = 49 - 16 \\[/tex]
[tex]\sf:\implies AE = \sqrt{ 33} \\[/tex]
[tex]\sf:\implies\red{ AE = 5.74} \\[/tex]
Similarly, in ∆CED ,
[tex]\sf:\implies 8^2 = CE^2 + DE^2 \\[/tex]
[tex]\sf:\implies CE^2 = 8^2 - DE^2 = 8^2 - 4^2 \\[/tex]
[tex]\sf:\implies CE^2 = 64- 16 \\[/tex]
[tex]\sf:\implies CE = \sqrt{ 33} \\[/tex]
[tex]\sf:\implies\red{ CE = 6.93} \\[/tex]
Now add them up to find AC , as ;
[tex]\sf:\implies AC = AE + CE\\[/tex]
[tex]\sf:\implies AC = 5.74 + 6.93 \\[/tex]
[tex]\sf:\implies AC = 12.67 \\[/tex]
Rounding off to nearest tenth, will give us,
[tex]\sf:\implies \red{ AC = 12.7 \ cm } \\[/tex]
Hence the length of AC is 12.7 cm.
10. advantages and disadvantages of the related-samples design advantages of using a related sample (either one sample of participants with repeated measures or two matched samples) versus using two independent samples include which of the following? check all that apply. a related-samples design reduces or eliminates problems caused by individual differences such as age, iq, gender, or personality. related samples (specifically, one sample of participants with repeated measures) can have an order effect such that a change observed between one measurement and the next might be attributable to the order in which the measurements were taken rather than to a treatment effect. related samples have less sample variance, increasing the likelihood of rejecting the null hypothesis if it is false (that is, increasing power). related samples (specifically, one sample of participants with repeated measures) require fewer participants for the same degree of power.
Answers
All the given options applies to the statement. A related-samples design reduces problems due to individual differences; can have an order effect; have less sample variance, increases the likelihood of rejecting the null hypothesis; needs few participants for same degree of power.
1. A related-samples design decreases or eliminates problems that is caused by individual differences such as age, IQ, gender, or personality.
2. Related samples (specifically, one sample of participants with repeated measures) can have an order effect such that a change observed between one measurement and the next might be attributable to the order in which the measurements were taken rather than to a treatment effect.
3. Related samples have less sample variance, which increases the likelihood of dismissing the null hypothesis if it is false (that is, increasing power).
4. Related samples (specifically, one sample of participants with repeated measures) needs very less participants for the same degree of power.
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Classify each number below as an integer or not.
12
55.3
18
2
Integer?
12
17
Yes
O
O
O
No
O
O
-260.43 O O
O
X
Answers
Answers:
12 is an integer55.3 is NOT an integer18 is an integer2 is an integer17 is an integer-260.43 is NOT an integerExplanation:
An integer is any positive or negative whole number. Zero is also an integer. Examples include 12, 15, and -27.
Non-integer values are anything with a fractional or decimal part. An example is 2.47; another example is 2/3 (since it turns into roughly 0.667).
SOMEONE PLEASE HELP:
A gift shop uses a commercial minivan for deliveries. The fuel expenses are defined by
the function C = 0.005 V^2, where V mph is the speed of the minivan and C = cost of fuel
per hour. If the driver's rate is $20 per hour, find what speed the driver should use to
minimize the cost of a 80 mile delivery for the gift shop. Consider only cost of fuel and
wages. Find exact value and then round your answer to the nearest whole number.
Answers
The optimal speed for the delivery minivan to minimize the cost of an 80 mile delivery for the gift shop considering only the cost of fuel and wages is approximately 126 mph.
Let's first determine the total cost of the delivery as a function of the speed of the minivan. The cost consists of two parts: the cost of fuel and the cost of the driver's wages. Since the driver's rate is $20 per hour and the delivery is 80 miles, the cost of the driver's wages is:
W = $20 × (80/V) = $1600/V
The cost of fuel is given by the formula C = [tex]0.005V^2[/tex], where V is the speed of the minivan in mph. The total cost of the delivery is therefore:
C(V) = [tex]0.005V^2 + 1600/V[/tex]
To find the speed that minimizes the cost of the delivery, we need to find the value of V that makes the derivative of C(V) equal to zero:
C'(V) = [tex]0.01V - 1600/V^2[/tex]
0 = [tex]0.01V - 1600/V^2[/tex]
0 = [tex]V^3 - 160000[/tex]
[tex]V^3[/tex] = 160000
V = cuberoot(160000) = 40√10
The exact speed that minimizes the cost of the delivery is V = 40√10 mph. Rounded to the nearest whole number, the answer is 126 mph (since 40√10 ≈ 126.49).
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Is the formula recursive, explicit, or neither?
NEXT = NOW - 8, starting at 50
Answers
The formula NEXT = NOW - 8 is neither recursive or explicit.
What is recursive and explicit formula?In a recursive fοrmula, we can find the value οf a term in the sequence using the value οf the previοus term. Hοwever, in an explicit fοrmula, we can find the value οf a term in the sequence using its pοsitiοn. Hence, this is anοther difference between recursive and explicit.
Recursive formula = [tex]\rm a_{n}=a_{n-1}+ d[/tex]
Explicit formula = [tex]\rm a_n= a_1 + (n - 1) d[/tex]
Here, NEXT = NOW - 8 resembles Recursive formula, but the value of Next isn't given. Even if it starts at 50, The value of n isn't specified.
Therefore, The formula NEXT = NOW - 8 is neither recursive or explicit.
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Complete question:
Is the formula recursive, explicit, or neither?
NEXT = NOW - 8, starting at 50.
recursiveexplicitneitherCan someone please help me with this question
Answers
The line of best fits that predicts the maximum temperature at this resort is the line that cuts across 2, 3, 5, 6, and 8 hours at 22°C.
The reliability of this estimate is the fact that the line of best fit goes through five data points.
What describes a line of best fits?A line of best fit is a straight line that is used to represent the general trend of a scatter plot of data points. It is also called a regression line. The line of best fit is usually determined using a mathematical method called linear regression, which minimizes the distance between the line and the data points.
The line of best fit can be used to make predictions about data that is not yet collected or to make estimates about the relationship between the variables represented in the scatter plot.
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Image transcribed:
This scatter graph shows the daily hours of sunshine and the daily maximum temperature at 10 seaside resorts in England one day last summer.
(a) Another resort had 10 hours of sunshine each day. Use a line of best fit to predict the maximum temperature at this resort.
(2 marks)
(b) Comment on the reliability of your estimate.
(1 mark)
i need help pls!!!!! question is attached
Answers
Therefore, the value of the investment after 3.5 years is $2325.28.
What is percent?Percent is a unit of measurement that represents a fraction of 100. It is often used to express a proportion or rate in relation to a total of 100. For example, if a sales tax is 7%, that means that for every $100 spent, $7 goes towards the tax. The symbol used to represent percent is %.
Here,
The formula for the value of the investment after t years is:
[tex]A = P(1+r/n)^{nt}[/tex]
where:
A is the amount of money after t years
P is the principal investment (initial amount invested)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time in years
Using this formula, we can plug in the values given in the problem:
P = 2000
r = 0.04
n = 12 (monthly compounding)
t = 3.5
A = [tex]2000(1 + 0.04/12)^{12*3.5}[/tex]
A = [tex]2000*(1.003333)^{42}[/tex]
A = 2000(1.162641)
A = $2325.28
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NEED BY MONDAY PLEASE!!! Select all the true equations:
Answers
#3 is correct, because tangent is equal to opposite over adjacent, which in this case is y/x
#4 is correct because sign is opposite over hypotenuse which in that case is X over 15
#5 is correct because the tangent of 63 degrees is equal to opposite over adjacent which is X over Y
I need this soon its due today
Answers
The amount of filter paper that you need to line the funnel is given as follows:
125.6 cm³.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
The parameters for the cone in this problem are given as follows:
Radius of r = 4 cm -> as the diameter is of 8 cm.Height of h = 7.5 cm.Hence the amount of filter paper that you need to line the funnel is given as follows:
V = 3.14 x 4² x 7.5/3
V = 125.6 cm³.
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