Question:
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $20.70? How much was the tip?
Answer:
Price of meal = $18
Tip price = $2.70
Step-by-step explanation:
Let the price of the meal be y;
Let the tip be t
From the question;
15% of y is the tip charge (t). i.e
t = 15%y
=> t = 0.15y --------(i)
The total amount charged is $20.70 (This means that the sum of the price of the meal and the tip is $20.70)
=> y + t = 20.70 [substitute the value of t=0.15y from equation (i)]
=> y + 0.15y = 20.70
=> 1.15y = 20.70
=> y = [tex]\frac{20.70}{1.15}[/tex]
=> y = $18
Therefore the price of the meal, y, is $18.
From equation (i),
t = 0.15y [substitute the value of y = $18]
t = 0.15(18)
t = $2.70
Therefore the tip was $2.70
Compute the values of dy and Δy for the function y=e^(2x)+6x given x=0 and Δx=dx=0.03.
Answer:
dy = 8·dxΔy = 0.24Step-by-step explanation:
The derivative of your function is ...
y' = dy/dx = 2e^(2x) +6
At x=0, the value is ...
y'(0) = 2e^0 +6 = 8
dy = 8·dx
__
Δy = y'(0)·Δx
Δy = 8(.03)
Δy = 0.24
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
Please help! Find the perimeter and total area of the composite shape below!
Answer:
Perimeter = 19.42 in and area = 26.13 in^2.
Step-by-step explanation:
The perimeter = 2 * 5 + length of the semicircle
= 10 * 3.14 * 3
= 19.42 in.
Total area = area of the semicircle + area of the triangle
= 1/2 * 3.14 * 3^2 + 3 * 4
= 26.13 in^2.
helppppppppppppp pleaseeeeeeeeeeeeee
Answer:
work is shown and pictured
A city council consists of eight Democrats and eight Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans.
(Type answer a fraction Simplify your answer.)
Answer:
The probability is [tex]P[ D n R] = 0.196[/tex]
Step-by-step explanation:
From the question we are told that
The number of Democrats is [tex]D = 8[/tex]
The number of republicans is [tex]R = 8[/tex]
The number of ways of selecting selecting two Democrats and four Republicans.
[tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]
Where C represents combination
substituting values
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]
=> [tex]N = 1568[/tex]
The total number of ways of selecting the committee of six people is
[tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]
The probability of selecting two Democrats and four Republicans is mathematically represented as
[tex]P[ D n R] = \frac{N}{Z}[/tex]
substituting values
[tex]P[ D n R] = \frac{1568}{8008}[/tex]
[tex]P[ D n R] = 0.196[/tex]
Values for relation g are given in the table. Which ordered pair would be found in the inverse of g? X Y 2 2 3 5 4 9 5 13 A: (4,9) B:(-3.-5) C:(13,5) D:(-2,-2)
Answer:
D (13,5)
Step-by-step explanation:
X 2 3 4 5
Y 2 5 9 13
So the ordered pairs are (2,2),(3,5), (4,9), (5,13)
and the ordered pairs for the inverse are
(2,2),(5,3), (9,4), (13,5)
from which D (13,5) is found among the options.
Answer:
b
Step-by-step explanation:
Over the last three evenings, Melissa received a total of 126 phone calls at the call center. The first evening, she received 6 more calls than the third evening. The second evening, she received 4 times as many calls as the third evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening:
Answer:
calls first evening = 26
calls second evening = 80
calls third evening = 20
Step-by-step explanation:
Let x = calls third evening
x+6 = calls first evening
4x = calls second evening
x+6 + 4x + x = total calls = 126
Combine like terms
6x+6 = 126
Subtract 6 from each side
6x =120
Divide by 6
6x/6 =120/6
x = 20
x+6 = calls first evening = 20+6 = 26
4x = calls second evening = 4*20 = 80
Let x = calls third evening = 20
FIRST ANSWER GETS BRAINLIEST!!!
How do you write 0.00696 in scientific notation?
Answer:
6.96x10^-3
Step-by-step explanation:
0.00696
We move the decimal point to between 6 and 9
since the number with the decimal point should be between 0 and 9.
Then we count the numbers.
6.96x10^-3.
Hope this helps. ❤❤❤
Answer: 6.96 * 10^(-3)
Step-by-step explanation:
In scientific notation, you multiply a number that has a value in the ones place and no value in the tens place by 10 raised to an exponent.
Hope it helps <3
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].
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
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
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.
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
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
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
Which equations represent the asymptotes of the hyperbola?
Answer:
see below
Step-by-step explanation:
The equation of the hyperbola can be written as ...
((x -h)/a)² -((y -k)/b)² = 1
This has asymptotes ...
(x -h)/a ± (y -k)/b = 0
Solving for y, we have ...
y = ±(b/a)(x -h) +k
Filling in the given values a=6, b=8, h=1, k=2, we have ...
y = ±8/6(x -1) +2
[tex]y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}[/tex]
Answer:
A. y = 4x+2/3 and y = 10-4x/3
Step-by-step explanation:
this is the correct answer for the question on edmentum and Plato
a.Find the L.C.M of 18, 40, and 75.
Answer:
1800
Step-by-step explanation:
Hello,
First of all we need to find the prime factorisation of the numbers.
18 = 2 * 3 * 3
40 = 2 * 2 * 2 * 5
75 = 3 * 5 * 5
It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3
Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
1800
Step-by-step explanation:
→ First of all we need to find the prime factorisation of the numbers.
18 = 2 × 3 × 3 or 2 × 3²
40 = 2 × 2 × 2 × 5 or 2³ × 5
75 = 3 × 5 × 5 or 5² × 3
→ Now find the number that appear twice or more and write them down
3 and 3 from 18
2, 2 and 2 from 40
5 and 5 from 75
→ Now multiply all of these numbers together
3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800
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
if ade has 23hand bag and he sells one for 409$ and he sells 22 for toby what will be the amount
Step-by-step explanation:
Hello there!
Its simple,
Given that, Ade had 23 hand bags.
selling price of each bag=$409
total sold bags= 22.
now, total amount he got was = no.of sold bag×sp of each bag.
so, total amount = 22×$409
=$8998.
Therefore, he has $ 8998 now.
Hope it helps...
Solve for y: 3(2y + 4) = 4(2y – 1/2).
The solution is y =
Answer:
Answer y=7
Step-by-step explanation:
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
What is the measure of o?
Answer:
2π radians
Step-by-step explanation:
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°
If the 2nd and 5th terms of a
G.P are 6 and 48 respectively,
find the sum of the first four
terms
Answer:
45
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given a₂ = 6 and a₅ = 48, then
ar = 6 → (1)
a[tex]r^{4}[/tex] = 48 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is
r³ = 8 ( take the cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2
Substitute r = 2 into (1)
2a = 6 ( divide both sides by 2 )
a = 3
Thus
3, 6, 12, 24 ← are the first 4 terms
3 + 6 + 12 + 24 = 45 ← sum of first 4 terms
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]
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.
Let x and y be real numbers satisfying 2/x=y/3=x/y Determine the value of x^3
Answer:
64/27Step-by-step explanation:
If x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;
2/x = y/3 ... 1 and;
y/3 = x/y... 2
From equation 1, 2y = 3x ... 3
and from equation 2; y² = 3x ... 4
Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;
2y = y²
2 = y
y = 2
Substituting y = 2 into equation 3 to get the value of x;
2y = 3x
2(2) = 3x
4 = 3x
x = 4/3
The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2
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
A study reports the mean change in HDL (high-density lipoprotein, or "good" cholesterol) of adults eating raw garlic six days a week for six months. The margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl). This means tha:_________a) There is a 95% probability that the true population mean is within 7 mg/dl. b) The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples. c) 95% percent of the population has changed their HDL after eating raw garlic six days a week for six months. d) We can be certain that the study results is within 7 mg/dl of the truth about the population. e) We could be certain that the study result is within 7 mg/dl of the truth about the population if the conditions for inferences were satisfied.
Answer:
Option B
Step-by-step explanation:
The margin of error describes how many percentage points the results will differ from the real population value, thus 'the margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl)' can be interpreted as 'The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples.'