Answer:
62.12% to 77.88%
Step-by-step explanation:
We proceed as follows mathematically;
From the question
n=130
Estimate for sample proportion=70% = 70/100 = 0.7 = p
Level of significance is =1-0.95=0.05
Z critical value(using Z table)=1.96
Confidence interval formula is ;
p ± Z * √(p(1-p)/n
= 0.70 ± √(0.7(1-0.7)/130
=(0.6212,0.7788)
Lower confidence interval limit =0.6212
Upper confidence interval limit =0.7788
In percentages , we simply multiply by 100 in both cases =
62.12 % to 77.88%
The test statistic of zequalsnegative 3.43 is obtained when testing the claim that pless than0.39. a. Using a significance level of alphaequals0.05, find the critical value(s). b. Should we reject Upper H 0 or should we fail to reject Upper H 0?
Answer:
a
[tex]z_t = -1.645[/tex]
b
We should reject the Upper [tex]H_o[/tex]
Step-by-step explanation:
From the question we are told that
The test statistics is [tex]t_s = -3.43[/tex]
The probability is [tex]p < 0.39[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Now looking at the probability we can deduce that this is a left tailed test
The second step to take is to obtain the critical value of [tex]\alpha[/tex] from the critical value table
The value is
[tex]t_ {\alpha } = 1.645[/tex]
Now since this test is a left tailed test the critical value will be
[tex]z_t = -1.645[/tex]
This because we are considering the left tail of the normal distribution curve
Now since the test statistics falls within the critical values the Null hypothesis is been rejected
The function A(b) relates the area of a trapezoid with a given height of 10 and
one base length of 7 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 10.57?
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. B(a) = -7
B. B(a) = 9, -5
Answer:
[tex]B(a)=\frac{a}{5} -7[/tex]
Step-by-step explanation:
The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.
y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),
y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )
Now switch the positions of y and b -
b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,
[tex]y+7=\frac{a}{5}[/tex],
[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]
Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7
The sum of three consecutive natural numbers is 555, find the numbers.
Answer:
184, 185, 186
Step-by-step explanation:
If the first number is x, the other numbers are x + 1 and x + 2, therefore we can write:
x + x + 1 + x + 2 = 555
3x + 3 = 555
3x = 552
x = 184 so the other numbers are 185 and 186.
A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function (t) - - 161+ 804 + 96 models the ball's height about the ground, A(t), in feet, e
seconds after it was thrown.
a) What is the maximum height of the ball?
Preview
feet
b) How many seconds does it take until the ball hits the ground?
Preview
seconds
Answer:
196 ft
6 seconds
Step-by-step explanation:
Solution:-
We have a quadratic time dependent model of the ball trajectory which is thrown from the top of a 96-foot building as follows:
[tex]y(t) = -16t^2 + 80t + 96[/tex]
The height of the ball is modeled by the distance y ( t ) which changes with time ( t ) following a parabolic trajectory. To determine the maximum height of the ball we will utilize the concepts from " parabolas ".
The vertex of a parabola of the form ( given below ) is defined as:
[tex]f ( t ) = at^2 + bt + c[/tex]
Vertex: [tex]t = \frac{-b}{2a}[/tex]
- The modelling constants are: a = -16 , b = 80.
[tex]t = \frac{-80}{-32} = 2.5 s[/tex]
- Now evaluate the given function " y ( t ) " for the vertex coordinate t = 2.5 s. As follows:
[tex]y ( 2.5 ) = -16 ( 2.5 )^2 + 80*(2.5) + 96\\\\y ( 2.5 ) = 196 ft\\[/tex]
Answer: The maximum height of the ball is 196 ft at t = 2.5 seconds.
- The amount of time taken by the ball to hit the ground can be determined by solving the given quadratic function of ball's height ( y ( t ) ) for the reference ground value "0". We can express the quadratic equation as follows:
[tex]y ( t ) = -16t^2 + 80t + 96 = 0\\\\-16t^2 + 80t + 96 = 0[/tex]
Use the quadratic formula and solve for time ( t ) as follows:
[tex]t = \frac{-b +/- \sqrt{b^2 - 4 ac} }{2a} \\\\t = \frac{-80 +/- \sqrt{80^2 - 4 (-16)(96)} }{-32} \\\\t = \frac{-80 +/- 112 }{-32} = 2.5 +/- (-3.5 )\\\\t = -1, 6[/tex]
Answer: The value of t = -1 is ignored because it lies outside the domain. The ball hits the ground at time t = 6 seconds.
The sum of a number and 9 is subtracted from 60. The result is 10. Find the number.
Answer:
Number : 41
Step-by-step explanation:
Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,
60 - (x + 9) = 10,
60 - x - 9 = 10,
51 - x = 10,
- x = 10 - 51 = - 41,
x = 41
This number will be 41
If y ∝ 1∕x and y = –2 when x = 14, find the equation that connects x and y.
Question 11 options:
A)
y = –28x
B)
y = –7∕x
C)
y = –28∕x
D)
y = –7x
C. y= -28/x
y=k/x
cross multiply
k= y×x
k = -2×14
k = -28
y = -28/x [ equation connecting x and y]
The equation that connects x and y si y = –28∕x.
The correct option is (C)
What is proportionality constant?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant. The proportionality constant's value is determined by the proportion between the two specified quantities.
For example, The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
We have given that
y ∝ 1∕x
To remove proportional sign we use proportionality constant
y=k/x
Now, cross multiply
k= y×x
k = -2×14
k = -28
y = -28/x
Hence, the equation is y = -28/x .
Learn more about proportionality here:
https://brainly.com/question/8598338
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A pyramid shaped building is 311 feet tall and has a square base with sides of 619 ft. The sides of the building are made from reflective glass. what is the surface area of the reflective glass
Answer:
Surface area of the reflective glass is 543234.4 square feet.
Step-by-step explanation:
Given that: height = 311 feet, sides of square base = 619 feet.
To determine the slant height, we have;
[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]
= 96721 + 95790.25
= 192511.25
⇒ l = [tex]\sqrt{192511.25}[/tex]
= 438.761
The slant height, l is 438.8 feet.
Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height
area = [tex]\frac{1}{2}[/tex] × 619 × 438.8
= 135808.6
= 135808.6 square feet
Since the pyramid has four reflective surfaces,
surface area of the reflective glass = 4 × 135808.6
= 543234.4 square feet
Out of 600 people sampled, 66 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.
Required:
Use a 90% confidence level, and give your answers as decimals, to three places.
Answer:
11% of the Total the entire voting population
Step-by-step explanation:
Let's bear in mind that the total number of sample candidates is equal to 600.
But out of 600 only 66 preffered candidate A.
The proportion of sampled people to that prefer candidate A to the total number of people is 66/600
= 11/100
In percentage
=11/100 *100/1 =1100/100
=11% of the entire voting population
Shawn has 25 coins, all nickels and dimes. The total value is $2.00. How many of each coin does he have ?
Answer:
[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]
Step-by-step explanation:
1 dime = 10 cents
1 nickel = 5 cents
So,
If there are 15 dimes
=> 15 dimes = 15*10 cents
=> 15 dimes = 150 cents
=> 15 dimes = $1.5
Rest is $0.5
So, for $0.5 we have 10 nickels coins
=> 10 nickels = 10*5
=> 10 nickels = 50 cents
=> 10 nickel coins = $0.5
Together it makes $2.00
Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
Answer:
D.
m = 2 = figures/month
b = 20 = # of action figures
The population of a city can be modeled with a linear equation Y equals -80 X +3450 where X is the number of years after 2000 and why is the cities population by the description of the cities population based on equation
Answer:
retype that im not understanding .
Step-by-step explanation:
please help all i need is the slope in case the points are hard to see here they are problem 1. (-2,2) (3,-3) problem 2. (-5,1) (4,-2) problem 3. (-1,5) (2,-4)
Answer: 1. [tex]-\dfrac{5}{6}[/tex] 2. [tex]-\dfrac{1}{3}[/tex] . 3. [tex]-3[/tex]
Step-by-step explanation:
Formula: Slope[tex]=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
1. (-2,2) (3,-3)
Slope [tex]=\dfrac{-3-2}{3-(-2)}[/tex]
[tex]=\dfrac{-5}{3+2}\\\\=\dfrac{-5}{6}[/tex]
Hence, slope of line passing through (-2,2) (3,-3) is [tex]-\dfrac{5}{6}[/tex] .
2. (-5,1) (4,-2)
Slope [tex]=\dfrac{-2-1}{4-(-5)}[/tex]
[tex]=\dfrac{-3}{4+5}\\\\=\dfrac{-3}{9}\\\\=-\dfrac{1}{3}[/tex]
Hence, slope of line passing through (-2,2) and (3,-3) is [tex]-\dfrac{1}{3}[/tex] .
3. (-1,5) (2,-4)
Slope [tex]=\dfrac{-4-5}{2-(-1)}[/tex]
[tex]=\dfrac{-9}{2+1}\\\\=\dfrac{-9}{3}\\\\=-3[/tex]
Hence, slope of line passing through (-1,5) and (2,-4) is -3.
The mean rate for cable with Internet from a sample of households was $106.50 per month with a standard deviation of $3.85 per month. Assuming the data set has a normal distribution, estimate the percent of households with rates from $100 to $115.
Answer:
The percent of households with rates from $100 to $115. is [tex]P(100 < x < 115) =[/tex]94.1%
Step-by-step explanation:
From the question we are told that
The mean rate is [tex]\mu =[/tex]$ 106.50 per month
The standard deviation is [tex]\sigma =[/tex]$3.85
Let the lower rate be [tex]a =[/tex]$100
Let the higher rate be [tex]b =[/tex]$ 115
Assumed from the question that the data set is normally
The estimate of the percent of households with rates from $100 to $115. is mathematically represented as
[tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]
here x is a random value rate which lies between the higher rate and the lower rate so
[tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]
[tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]
Where
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where z is the standardized value of x
So
[tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]
[tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]
Now from the z table we obtain that
[tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]
[tex]P(100 < x < 115) = 0.941[/tex]
[tex]P(100 < x < 115) =[/tex]94.1%
A fisherman uses a spring scale to weigh a tilapia fish. He records the fish weight as a kilograms and notices that the spring stretches b centimeters. Which expression represents the spring constant (1 =9.8 )? A). 980ab B). 9.8ab C). 9.8ab D). 980ab
Answer:
k = [tex]\frac{980a}{b}[/tex]
Step-by-step explanation:
Fisherman noticed a stretch in the spring = 'b' centimetres
Weight of the fish = a kilograms
If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,
F = kΔx
Where k = spring constant
Δx = stretch in the spring
F = weight applied
F = mg
Here 'm' = mass of the fish
g = gravitational constant
F = a(9.8)
= 9.8a
Δx = b centimetres = 0.01b meters
Therefore, 9.8a = k(0.01b)
k = [tex]\frac{9.8a}{0.01b}[/tex]
k = [tex]\frac{980a}{b}[/tex]
Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]
A person stands 15 ft from an elephant. Determine how tall the elephant is in feet, the given diagram.
Answer:
The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
Step-by-step explanation:
It is given that,
Distance between a person and an elephant is 15 ft
The angle of elevation of the elephant is 30 degrees.
We need to find the height of the elephant. For this let us consider that height is h. So,
[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]
So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
A survey of the average amount of cents off that coupons give was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20cents; 70cents; 50cents; 65cents; 30cents; 55cents; 40cents; 40cents; 30cents; 55cents; $1.50; 40cents; 65cents; 40cents. Assume the underlying distribution is approximately normal.
Construct a 95% confidence interval for the population mean worth of coupons .
What is the lower bound? ( Round to 3 decimal places )
What is the upper bound? ( Round to 3 decimal places )
What is the error bound? (Round to 3 decimal places)
Answer:
The lower bound = 35.443
The upper bound = 71.697
The error bound = 18.127
Step-by-step explanation:
We are given that a survey of the average amount of cents off that coupons gives was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News.
The following data were collected (X): 20cents; 70cents; 50cents; 65cents; 30cents; 55cents; 40cents; 40cents; 30cents; 55cents; 150 cents; 40cents; 65cents; 40cents.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean worth of coupons = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{750}{14}[/tex] = 53.57 cents
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 31.40 cents
n = sample size = 14
[tex]\mu[/tex] = population mean worth of coupons
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.16 < [tex]t_1_3[/tex] < 2.16) = 0.95 {As the critical value of t at 13 degrees of
freedom are -2.16 & 2.16 with P = 2.5%}
P(-2.16 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.16) = 0.95
P( [tex]-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}{[/tex] < [tex]2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]53.57-2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] , [tex]53.57+2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] ]
= [35.443, 71.697]
Therefore, a 95% confidence interval for the population mean worth of coupons is [35.443, 71.697].
a rectangle is three times as long as it is widen. if it perimeter is 56cm, find the width of the rectangle
Hi there! :)
Answer:
w = 7 cm.
Step-by-step explanation:
Given:
P = 56
Use the formula P = 2l + 2w to solve for the perimeter of the rectangle.
Let w = width, and
3w = length
Plug these into the equation:
56 = 2(3w) + 2(w)
56 = 6w + 2w
Combine like terms:
56 = 8w
Divide both sides by 8:
w = 7 cm.
The width of rectangle is 7 cm.
At a factory that produces pistons for cars, Machine 1 produced 459 satisfactory pistons and 51 unsatisfactory pistons today. Machine 2 produced 360
satisfactory pistons and 40 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from
today's batch. What is the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory?
Hey there! I'm happy to help!
If we add Machine 1's 459 satisfactory pistons and 51 unsatisfactory pistons, we get 510 total pistons.
If we add Machine 2's 360 satisfactory pistons and 40 unsatisfactory pistons, we get 400 total pistons.
First, we want to find the probability of choosing an unsatisfactory piston from Machine 1.
We see that 51/510 (unsatisfactory pistons out of total pistons) simplifies to equal 1/10, so there is a 1/10 chance of getting an unsatisfactory piston from Machine 1.
For Machine 2, there are 360 satisfactory and 400 total. This gives us 360/400, which simplifies to 9/10.
Now, we multiply our two probabilities together to find the probability that they both happen.
1/10×9/10=9/100
Therefore, the probability that a piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 9/100 or 9%.
Have a wonderful day! :D
An aquarium is to be built to hold 60 m3of volume. The base is to be made of slate and the sides aremade of glass, and it has no top. If stone costs $120/m2and glass costs $30/m2, find the dimensions which willminimize the cost of building the aquarium, and find the minimum cost.
Answer:
Aquarium dimensions:
x = 3,106 m
h = 6,22 m
C(min) = 1277,62 $
Step-by-step explanation: (INCOMPLETE QUESTION)
We have to assume:
The shape of the aquarium (square base)
Let´s call "x" the side of the base, then h ( the heigh)
V(a) = x²*h h = V(a)/x²
Cost of Aquarium C(a) = cost of the base (in stones) + 4* cost of one side (in glass)
C(a) = Area of the base *120 + 4*Area of one side*30
Area of the base is x²
Area of one side is x*h or x*V(a)/x²
Area of one side is V(a)/x
C(x) = 120*x² + 4*30*60/x
C(x) = 120*x² + 7200/x
Taking derivatives on both sides of the equation we get
C´(x) = 2*120*x - 7200/x²
C´(x) = 0 means 240 *x - 7200/x² = 0
240*x³ - 7200 = 0
x³ = 7200/240
x = 3,106 m and h = 60 /x² h = 6,22 m
and C (min) = 120*(3,106)³ - 7200 / 3,106
C(min) = 3595,72 - 2318,1
C(min) = 1277,62
WILL MAKE BRAINLIST. - - - If a golden rectangle has a width of 9 cm, what is its length?
Step-by-step explanation:
a = 14.56231 cm
b(width) = 9 cm
a+b = 23.56231 cm
A(area) = 343.1215 cm
Sorry if this doesnt help
Answer:
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
Step-by-step explanation:
In a golden rectangle, the width is a and the length is a + b.
The proportion of the lengths of the sides is:
(a + b)/a = a/b
Here, the width is 9 cm, so we have a = 9 cm.
(9 + b)/9 = 9/b
(9 + b)b = 81
b^2 + 9b - 81 = 0
b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)
b = (-9 +/- sqrt(81 + 324)/2
b = (-9 +/- sqrt(405)/2
b = -9/2 +/- 9sqrt(5)/2
Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2
Length = a + b = 9/2 +/- 9sqrt(5)/2
Since the length of a side of a rectangle cannot be negative, we discard the negative answer.
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.
A. yp(x)=Ax2+Bx+C,
B. yp(x)=Ae2x,
C.yp(x)=Acos2x+Bsin2x,
D. yp(x)=(Ax+B)cos2x+(Cx+D)sin2x
E. yp(x)=Axe2x,
F.yp(x)=e3x(Acos2x+Bsin2x)
1. d2ydx2+4y=x−x220
2. d2ydx2+6dydx+8y=e2x
3. y′′+4y′+20y=−3sin2x
4. y′′−2y′−15y=3xcos2x
Answer and Step-by-step explanation:
1. Data provided
[tex]\frac{d^2y}{dx^2} + 4y = x - x^2 + 20\\\\ \frac{d^2y}{dx^2} + 4y = - x^2 + x + 20[/tex]
Now as a non homogeneous part which is
[tex]- x^2 + x + 20[/tex] let us assume the computation is
[tex]y_p(x) = Ax^2 + Bx + C[/tex]
2. Data provided
[tex]\frac{ d^2y}{dx^2} + \frac{6dy}{dx} + 8y = e^{2x}[/tex]
As a non homogeneous part is [tex]e^2x[/tex] , let us assume the computation is
[tex]y_p(x) = Ae^{2x}[/tex]
3. Data provided
[tex]y'' + 4y' + 20y = -3sin2x[/tex]
As a non homogeneous part −3sin(2x), let us assume the computation is
[tex]y_p(x) = Acos(2x) + Bsin(2x)[/tex]
4. Data provided
[tex]y'' - 2y' - 15y = 3xcos(2x)[/tex]
As a non homogeneous part 3xcos(2x), let us assume the computation is
[tex]y_p(x) = (Ax+B)cos2x+(Cx+D)sin2x[/tex]
what's the solution for 9ײ/81×⁵
Answer:
answer 1 /9x^3
Step-by-step explanation:
9ײ/81×⁵
change the expression to indices form
3^2 x^2 /3^4 x^5
1 /3^2 x^3
1 /9x^3
20 points! Brainliest will be given!
Answer:
I always factor out the -1 so my leading coefficient is 1
Step-by-step explanation:
-x^2 + 10x -24
I always factor out the -1 so my leading coefficient is 1
-1 ( x^2 -10x +24)
Then what 2 terms multiply to 24 and add to -10
-6*-4 = 24
-6+-4 = -10
-1( x-6)(x-4)
Need help with trig questions
Answer:
-8 i + 19 j , 105.07°
Step-by-step explanation:
Solution:
- Define two unit vectors ( i and j ) along x-axis and y-axis respectively.
- To draw vectors ( v and w ). We will move along x and y axes corresponding to the magnitudes of unit vectors ( i and j ) relative to the origin.
Vector: v = 2i + 5j
Mark a dot or cross at the originMove along x-axis by 2 units to the right ( 2i )Move along y-axis by 5 units up ( 5j )Mark the point.Connect the origin with the marked point determined aboveMake an arrow-head at the determined pointLies in first quadrant
Vector: w = 4i - 3j
Mark a dot or cross at the originMove along x-axis by 4 units to the right ( 4i )Move along y-axis by 3 units down ( -3j )Mark the point.Connect the origin with the marked point determined aboveMake an arrow-head at the determined pointLies in 4th quadrant- The algebraic manipulation of complex numbers is done by performing operations on the like unit vectors.
[tex]2*v - 3*w = 2* ( 2i + 5j ) - 3*(4i - 3j )\\\\2*v - 3*w = ( 4i + 10j ) + ( -12i + 9j )\\\\2*v - 3*w = ( 4 - 12 ) i + ( 10 + 9 ) j\\\\2*v - 3*w = ( -8 ) i + ( 19 ) j\\[/tex]
- To determine the angle ( θ ) between two vectors ( v and w ). We will use the " dot product" formulation as follows:
v . w = | v | * | w | * cos ( θ )
v . w = < 2 , 5 > . < 4 , -3 > = 8 - 15 = -7
[tex]| v | = \sqrt{2^2 + 5^2} = \sqrt{29} \\\\| w | = \sqrt{4^2 + 3^2} = 5\\\\[/tex]
- Plug the respective values into the dot-product formulation:
cos ( θ ) = [tex]\frac{-7}{5\sqrt{29} }[/tex]
θ = 105.07°
Find the equation of a line parallel to −x+5y=1 that contains the point (−1,2)
Answer:
y=1/5x+11/5
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula y-y^1=m(x-x^1) to find line parallel to -x+5y=1
Hope this helps
Answer: y = 1/5x+ 2.2
Step-by-step explanation:
First, change the expression into y-intercept form
-x+5y=1
5y=x+1
y=1/5x+1/5
For a line to be parallel to another line, it must have the same slope. Thus, the slope must be 1/5x. Then, to find the y-intercept simply do:
y = 1/5x+b, where x = -1 and y = 2
2=1/5(-1)+b
2 = -1/5+b
b = 2 1/5.
Thus, the equation y = 1/5x+ 2.2
Hope it helps <3
F(n)=6.5n+4.5 find the 5th term of the sequence defined by the given rule
Answer:
37
Step-by-step explanation:
To find the fifth term , we have to take the value of n as 5
So, F(5)= 6.5 (5) +4.5
= 32.5 + 4.5
= 37
A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours. To test this claim, the Internet provider randomly samples 30 households and finds that these families' mean number of hours spent on the Internet on a Saturday was 6 hours with a standard deviation of 1.5 hours. At a level of significance of 0.05, can the Internet provider's claim be supported?
A) Fail to Reject the Null Hypothesis
B) Reject the Null Hypothesis
C) Reject The Alternative Hypothesis
D) Fail to Reject the Alternative Hypothesis
E) Accept the Null Hypothesis
F) Accept the Alternative Hypothesis
Answer:
A) Fail to Reject the Null Hypothesis
Step-by-step explanation:
Given that:
A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours.
sample size = 30
sample mean [tex]\bar x[/tex] = 6
standard deviation [tex]\sigma[/tex] = 1.5
level of significance ∝ = 0.05
The null hypothesis and the alternative hypothesis can be computed as:
[tex]\mathbf{ H_o: \mu \leq 7}[/tex]
[tex]\mathbf{ H_i: \mu \geq 7}[/tex]
The test statistic can be computed as:
[tex]z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{6 -7} {\dfrac{1.5}{\sqrt {30}}}[/tex]
[tex]z = \dfrac{-1} {\dfrac{1.5}{5.477}}}[/tex]
[tex]z = \dfrac{-5.477} {1.5}[/tex]
z = -3.65
Given that ;
level of significance of 0.05;
z = -3.65
degree of freedom = 30 - 1 = 29
The p-value = P([tex]t_{29}[/tex] > - 3.65)
= 0.9998
Decision Rule: Reject [tex]H_o[/tex] if p-value is less than the level of significance
But since the p -value is greater than the level of significance, we conclude that There is no enough evidence to support the Internet provider claim, Therefore;
Fail to Reject the Null Hypothesis
A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or an 8? Round to nearest thousandth
Answer: 0.476
Step-by-step explanation:
Let A = Event of choosing an even number ball.
B = Event of choosing an 8 .
Given, A lottery game has balls numbered 1 through 21.
Sample space: S= {1,2,3,4,5,6,7,8,...., 21}
n(S) = 21
Then, A= {2,4,6,8, 10,...(20)}
i.e. n(A)= 10
B= {8}
n(B) = 1
A∪B = {2,4,6,8, 10,...(20)} = A
n(A∪B)=10
Now, the probability of selecting an even numbered ball or an 8 is
[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]
[tex]=\dfrac{10}{21}\approx0.476[/tex]
Hence, the required probability =0.476
Savita was given a set of 250 cherries and Gail was given a set
of 350 cherries. Both were also given a set of small plastic bags.
Savita had to pack 8 cherries in a bag and Gail had to pack 12
cherries in a bag. Explain how you know who will have more
bags of cherries at the end.
Answer:
Savita will have more bags
Step-by-step explanation:
Savita: 250 cherries, 8 cherries per bag
Gail: 350 cherries, 12 cherries per bag
Savita: 250/8 = 31.25 bags
Gail: 350/12 = 29.17 bags
Savita will have more bags since 31.25 > 29.17
Answer:
Savita will have more bags
Step-by-step explanation:
Savita has 250 cherries and 8 cherries per bag
Gail has 350 cherries and 12 cherries per bag
Savita
=250/8 = 31.25 bags
Gail
=350/12 = 29.17 bags
therefore Savita will have more bags since 31.25 is more than Gail with 29.17 bags
For each of the following determine a unit rate using the information given. Show the division that leads to your answer. Use appropriate units. All rates will be whole numbers. At a theatre, Mia paid $35 for five tickets
Answer:
Step-by-step explanation:
cool