Answer:
Lower class Limit: 20,25,30,35,40,45,50
Upper class limit: 24,29,34,39,44,49,54
Class width: 4
Class Midpoints : 22,27,32,37,42,47,52
Class Boundries : 19.5,24.5,29.5,34,5,39.5,44.5,49.5,54.5
Total Individuals: 93
Step-by-step explanation:
Lower class limit is the lowest value of a class e.g in the first class, the lowest value is 20. Similarly find lower class limit of othere classes.
Upper class limit is the highest value of a class e.g in the first class, the highest value is 24. Similarly find upper class limit of othere classes.
Class width is the difference between highest and lowest value of a class e.g 24-20=4
Class Midpoints can be found by adding lowest and highest value of a class and dividing it by 2 e.g (20+24)/2 = 22
Class boundaries are the halfway point which seperates the classes e.g for first classes, clasee boundry is (19.5,24.5)
Total individuals are founf by adding all the frequencies.
Please answer this correctly
Answer:
Board Games: 30%
Karaoke: 50%
Bowling: 20%
Step-by-step explanation:
Board Games: [tex]\frac{3}{3+5+2} =\frac{3}{10} =\frac{30}{100}[/tex] or 30%
Karaoke: [tex]\frac{5}{3+5+2} =\frac{5}{10} =\frac{50}{100}[/tex] or 50%
Bowling: [tex]\frac{2}{3+5+2} =\frac{2}{10} =\frac{20}{100}[/tex] or 20%
Answer:
Board Games: 30%
Karaoke: 50%
Bowling: 20%
Step-by-step explanation:
3 + 5 + 2 = 10 so there are 10 family members.
3 out of 10 equals 30%
5 out of 10 equals 50%
2 out of 10 equals 20%
Please mark Brainliest if correct
Hope this helps!
my last question and im done, please help!
Answer:
2 acute and one right.
Step-by-step explanation:
plz mark brainliest!
Answer:
2 acute 1 right, you asked for ASAP so theres no explanation
You cant mix right and obtuse, and you cant have more than 1 obtuse in a triangle. There has to be at least 2 acute angles.
ASK YOUR TEACHER Two streets meet at an 84° angle. At the corner, a park is being built in the shape of a triangle. Find the area of the park if, along one road, the park measures 190 feet, and along the other road, the park measures 235 feet. (Round your answer to the nearest whole number.)
Answer:
22,203 ft^2
Step-by-step explanation:
The area of a triangle with angle ∅ and two sides a and b is;
Area A = 1/2 × absin∅ ......1
The park is in the shape of a triangle, with two sides and an angle given;
Given;
a = 190 ft
b = 235 ft
∅ = 84°
Substituting the values into equation 1;
Area of the park;
A = 1/2 × 190 × 235 × sin84°
A = 22,202.70131409 ft^2
A = 22,203 ft^2 (to the nearest whole number)
Area of the park is 22,203 ft^2
x⁴+1/x⁴=47,find the value of x³+1/x³
Answer:
The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5
Step-by-step explanation:
x^4 + 1/x^4 = 47
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5
A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a random sample of 800 people is taken and its determined that 478 people have Internet access. The following is the setup for this hypothesis test: H0:p=0.63 Ha:p<0.63 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
Answer:
Step-by-step explanation:
For the null hypothesis,
H0 : p = 0.63
For the alternative hypothesis,
Ha : p < 0.63
This is a left tailed test
Considering the population proportion, probability of success, p = 0.63
q = probability of failure = 1 - p
q = 1 - 0.63 = 0.37
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 478
n = number of samples = 800
P = 478/800 = 0.6
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76
From the normal distribution table, the area below the test z score in the left tail 0.039
Thus
p = 0.039
Answer:
-3.66
Step-by-step explanation:
4x and 16y are like terms.
O A. True
O B. False
A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of these 25 are selected at random to be checked by a particular technician, what is the probability that exactly 3 of those selected are laser printers (so that the other 3 are inkjets)
Answer:
The probability is 0.31
Step-by-step explanation:
To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.
In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is [tex]\binom{25}{6}[/tex], where [tex]\binom{n}{k} = \frac{n!}{(n-k)!k!}[/tex]. We have that [tex]\binom{25}{6} = 177100[/tex]
Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in [tex]\binom{10}{3}\cdot \binom{15}{3} = 54600[/tex]
So the probability of having 3 laser printers and 3 inkjets is given by
[tex] \frac{54600}{177100} = \frac{78}{253} = 0.31[/tex]
Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives
Answer:
0.2946
Step-by-step explanation:
Number of tosses, n = 200
P(obtaining a 5), p = 1/6
q = 1 - p = 5/6
Normal approximation for binomial distribution
P(X < A) = P(Z < (A - mean)/standard deviation)
Mean = np
= 200 x 1/6
= 33.33
Standard deviation = √npq
= √(200(1/6)(5/6) )
= 5.27
P(at most 30 fives) = P(X ≤ 30)
= P(Z < (30.5 - 33.33)/5.27) (continuity correction of 0.5 is added to 30)
= P(Z < -0.54)
= 0.2946
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.
60
25
Answer:
65
Step-by-step explanation:
C^2= A^2 + B^2
C^2 = (60)^2 + (25)^2
C^2 = 4225
Take the square root of C
C = 65
Answer:
65
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
I'm assuming that '60' and '25' are measures of the legs, since the question asks to find the hypotenuse.
[tex]60^2+25^2=c^2\\\rightarrow 60^2=3600\\\rightarrow 25^2 = 625\\3600+625=c^2\\4225=c^2\\\sqrt{4225}=\sqrt{c^2}\\\boxed{65=c}[/tex]
The hypotenuse should measure 65 units.
What is the value of g-1(7)
Answer:
g-7
Step-by-step explanation:
Multiply the numbers
g-(1*7)
g-7
Answer:
5
Step-by-step explanation:
We know that g is an invertible function and so it must also be a one-to-one function.
This means that each input is paired with exactly one output and that each output is paired with exactly one input.
We know that g(a)=7g and g(5)=7. If the output of 7 is to be paired with exactly one input, then a must be equal to 5.
The top of a lighthouse is 100 m above sea level. The angle of elevation from the
deck of the sailboat to the top of the lighthouse is 28°. Calculate the distance
between the sailboat and the lighthouse.
Answer:
188 m
Step-by-step explanation:
The tangent of the angle is the ratio of the side opposite (height of the lighthouse) to the side adjacent (distance to the lighthouse):
tan(28°) = (100 m)/distance
distance = (100 m)/tan(28°) ≈ 188 m
The distance between the sailboat and the lighthouse is about 188 m.
solve the equation 4x +30 = 2(x-10)
A digital scale measures weight to the nearest 0.2 pound. Which measurements shows an appropriate level for the scale ?
Answer: Answer choices 1, 3, 4
Step-by-step explanation:
As long as it ends in .0, .2, .4, .6, or .8 it's fine. Therefore the first and last 2 work, since 0.2 can end in either of those 5 values.
Hope that helped,
-sirswagger21
Arlinda says there is a linear relationship between the price (p) of 500ml soft drink and the number sold (x). The formula is x = ap + b where a and b are constants. At N$20 she sells 1500 of the 500ml soft drinks but the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. At what price will 600 of the 500ml energy drinks be sold?
Answer: 600 of the 500ml energy drinks be sold be sold at $45
Step-by-step explanation:
The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as
x = ap + b
At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be
1500 = 20a + b - - - - - - - - -1
the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300
The price at which they were sold is
20 + (50/100 × 20) = $30
The second equation would be
1300 = 30a + b - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
200 = - 10a
a = 200/- 10 = - 20
Substituting a = - 20 into equation 2, it becomes
1300 = 10 × - 20 + b
1300 = - 200 + b
b = 1300 + 200 = 1500
The linear relationship becomes
x = - 20p + 1500
If x = 600, then
600 = - 20p + 1500
- 20p = 600 - 1500 = - 900
p = - 900/ - 20
p = $45
A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees.
Answer: The complete question is "A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees. What is the length of the arc?"
The length of the arc is 1.06667 units.
Step-by-step explanation:
According to the question the radius of the circle [tex]R=3 \, units[/tex] and central angle of arc is [tex]\Theta =20^{o}[/tex]
As we know that the length of the arc is given as: [tex]L=R\Theta[/tex]
Where R is radius of the circle, L is the length of the arc and [tex]\Theta[/tex] is central angle in radian.
Now, [tex]\Theta =20^{o}\times \frac{\Pi }{180}=\frac{\Pi }{9} \, rad[/tex]
Therefore, length of the arc is
[tex]L=3\times \frac{\Pi }{9}=\frac{\Pi }{3} =\frac{3.14}{3}=1.0466667 \, units[/tex]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
C. F(x) = 4x² + 1
Step-by-step explanation:
→The function F(x) shifted 1 unit upwards, meaning there needs to be a 1 being added to the function.
→In addition, the function F(x) has grown narrower, compared to the function G(x). This is from the absolute value of a number being greater than 1, which is being multiplied.
This means the correct answer should be "C. F(x) = 4x² + 1."
What’s the correct explanation for this question?
Step-by-step explanation:
=> The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid
=> The volume of a cone can be found by V = 1/3(Ab)(H) where Ab is base area and H is the height of the cone
The difference between both is that is it's base. A cone has a polygonal base while a pyramid has a tetragonal base
Simplify the expression 4x^3 2x^3
Answer:
Step-by-step explanation:
2 3x6
the 3 is an exponet so supost to be smaller
the answer- 2^3 x^6
i think its right
Suppose that the functions p and q are defined as follows.
Answer:
Step-by-step explanation:
Hello,
qop(2)=q(p(2))
p(2) = 4+3=7
[tex]q(7) = \sqrt{7+2}=\sqrt{9}=3[/tex]
so
qop(2)=3
and poq(2)=p(q(2))
[tex]q(2)=\sqrt{2+2} = \sqrt{4}=2[/tex]
p(2) = 7
so poq(2)=7
thanks
The answer is "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]" and the further explanation can be defined as follows;
Given:
[tex]\to \bold{p(x)=x^2+3}\\\\\to \bold{q(x)=\sqrt{x+2}}[/tex]
Find:
[tex]\bold{(q \circ p)(2)=?}\\\\\bold{(p \circ q)(2)=?}[/tex]
Solve the value for [tex]\bold{(q \circ p)(2)}\\\\[/tex]:
[tex]\to \bold{(q \circ p)(2)= q \circ p(2) =q(p(2))}\\\\[/tex]
[tex]\therefore\\\\ \to \bold{p(2)=2^2+3= 4+3=7}\\\\\ \because \\\\ \to \bold{q(p(2))=\sqrt{7+2}=\sqrt{9}=3}[/tex]
Solve the value for [tex]\bold{(p \circ q)(2)}\\\\[/tex]:
[tex]\to \bold{(p \circ q)(2)= p \circ q(2)= p (q(2))}\\\\[/tex]
[tex]\therefore\\\\ \to \bold{q(2)=\sqrt{2+2}=\sqrt{4}=2}\\\\\ \because \\\\ \to \bold{p(q(2))=2^2+3= 4+3=7}[/tex]
Therefore the final answer of "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]"
Learn more:
brainly.com/question/14270968
Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?
Answer:
[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]
[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a gender selection method used to increase the likelihood of a baby being born a girl, 1936 users of the method gave birth to 950 boys and 986 girls. There is about a 21% chance of getting that many girls if the method had no effect.
Answer:
Due to the fact that there is 21% chance of getting that many girls by chance and also In conjunction to that; there is no test involved as well , we can conclude that the method does not have statistical significance.
The result does not appear to have a practical significance.
Step-by-step explanation:
Given that:
In a random selection 1936 users, we observed that the method gave birth to 950 boys and 986 girls
There is about a 21% chance of getting that many girls if the method had no effect.
Due to the fact that there is 21% chance of getting that many girls by chance and also In conjunction to that; there is no test involved as well , we can conclude that the method does not have statistical significance.
Given that:
The number of girls = 986
Number of boys = 950
Number of babies born = 1936
The percentage of girls = number of girls born/ number of babies born
The percentage of girls = 986 /1936
The percentage of girls = 0.5093
The percentage of girls = 50.93%
We can infer that this method does not have a practical significance because most couples would not prefer to use a method that raise the likelihood of a girl from the approximately 50% rate expected by chance to the 50.93% .
Halle is enteros cuyo producto sea 253 y uno de los enteros debe ser uno más que el doble del otro.
Answer:
11 y 23
Step-by-step explanation:
Nombrando los números como [tex]x[/tex] y [tex]y[/tex],
Planteamos las siguientes ecuaciones:
[tex]xy=253[/tex] (el producto de los numeros es 253)
[tex]x=2y+1[/tex] (uno de los enteros debe ser uno más que el doble del otro).
Sustituimos la segunda ecuación en la primera:
[tex](2y+1)(y)=253[/tex]
resolvemos para encontrar y:
[tex]2y^2+y=253\\2y^2+y-253=0[/tex]
usando la formula general para resolver la ecuación cuadrática:
[tex]y=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
donde
[tex]a=2,b=1,c=-253[/tex]
Sustituyendo los valores:
[tex]y=\frac{-1+-\sqrt{1-4(2)(-253)} }{2(2)} \\\\y=\frac{-1+-\sqrt{2025} }{4}\\ \\y=\frac{-1+-45}{4} \\[/tex]
usando el signo mas obtenemos que y es:
[tex]y=\frac{-1+45}{4} \\y=\frac{44}{4}\\ y=11[/tex]
(no usamos el signo menos, debido a que obtendriamos fracciones y buscamos numeros enteros)
con este valor de y, podemos encontrar x usando:
[tex]x=2y+1[/tex]
sustituimos [tex]y=11[/tex]
[tex]x=2(11)+1\\x=22+1\\x=23[/tex]
y comprobamos que el producto sea 253:
[tex]xy=253[/tex]
[tex](23)(11)=253[/tex]
We wish to see if the dial indicating the oven temperature for a certain model of oven is properly calibrated. Four ovens of this model are selected at random. The dial on each is set to 300 °F, and, after one hour, the actual temperature of each is measured. The temperatures measured are 305 °F, 310 °F, 300 °F, and 305 °F. Assuming that the actual temperatures for this model when the dial is set for 300° are Normally distributed with mean μ, we test whether the dial is properly calibrated at 5% of significance level.
Actual Temp: 305, 310, 300, 305
Required:
a. Based on the data, calculate the sample standard deviation and standard error of X bar (round them into two decimal places) Standard Deviation: Standard Error:
b. What is a 95% confidence interval for μ? (upper and lower bound)
c. Provide your test statistic and P-value
d. State your conclusion clearly (statistical conclusion and its interpretation).
e. Even if 5% of significance level looks like default of test, we can use different significance levels as well. If we change the significance level into 10% (= 0.1), how does it affect your conclusion?
Answer:
a. Standard deviation: 4.082
Standard error: 2.041
b. The 95% confidence interval for the actual temperature is (298.5, 311.5).
Upper bound: 311.5
Lower bound: 298.5
c. Test statistic t=2.45
P-value = 0.092
d. There is no enough evidence to claim that the dial of the oven is not properly calibrated. The actual temperature does not significantly differ from 300 °F.
e. If we use a significance level of 10% (a less rigorous test, in which the null hypothesis is rejected with with less requirements), the conclusion changes and now there is enough evidence to claim that the dial is not properly calibrated.
This happens because now the P-value (0.092) is smaller than the significance level (0.10), given statististical evidence for the claim.
Step-by-step explanation:
The mean and standard deviation of the sample are:
[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(305+310+300+305)\\\\\\ M=\dfrac{1220}{4}=305[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(305-(305))^2+(310-(305))^2+(300-(305))^2+(305-(305))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(25)+(25)+(0)]}\\\\\\ s=\sqrt{\dfrac{50}{3}}=\sqrt{16.667}\\\\\\s=4.082[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=305.
The sample size is N=4.
When σ is not known, s divided by the square root of N is used as an estimate of σM (standard error):
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{4.082}{\sqrt{4}}=\dfrac{4.082}{2}=2.041[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=4-1=3[/tex]
The t-value for a 95% confidence interval and 3 degrees of freedom is t=3.18.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=3.18 \cdot 2.041=6.5[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 305-6.5=298.5\\\\UL=M+t \cdot s_M = 305+6.5=311.5[/tex]
The 95% confidence interval for the actual temperature is (298.5, 311.5).
This is a hypothesis test for the population mean.
The claim is that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=300\\\\H_a:\mu\neq 300[/tex]
The significance level is 0.05.
The sample has a size n=4.
The sample mean is M=305.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.028.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.082}{\sqrt{4}}=2.041[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{305-300}{2.041}=\dfrac{5}{2.041}=2.45[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=4-1=3[/tex]
This test is a two-tailed test, with 3 degrees of freedom and t=2.45, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>2.45)=0.092[/tex]
As the P-value (0.092) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.
If the significance level is 10%, the P-value (0.092) is smaller than the significance level (0.1) and the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °C does not significantly differ from 300 °C.
please help you will get 10 points and brainliest. and explain your answer.
Answer:
Top prism = 262 in.² Bottom prism = 478 in.²
Step-by-step explanation:
top prism:
front + back: 5 x 3 = 15
sides: 19 x 4 x 2 = 152
bottom: 19 x 5 = 95
15 + 152 + 95 = 262
bottom prism:
front + back: 5 x 6 x 2 = 60
sides: 19 x 6 x 2 = 228
top + bottom: 19 x 5 x 2 = 190
60 + 228 + 190 = 478
What statement best explains The relationshipBetween numbersDivisible by 5 and 10
Answer:
a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Step-by-step explanation:
Given : Statement 'The relationship between numbers divisible by 5 and 10'.
To find : What statement BEST explains the statement?
Solution :
First we study the divisibility rules,
Rule for the number divisible by 5 is that number must end in 5 or 0.
Rule for the number divisible by 10 is that number need to be even and divisible by 5, as the prime factors of 10 are 5 and 2 and the number to be divisible by 10, the last digit must be a 0.
According to the divisibility rules Option D is correct.
Therefore, The correct statement explains the relationship between numbers divisible by 5 and 10 is a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
So, the question is below, please help me find the answer. :)
Answer:
£2.70 fig rolls and £5.72 crisps
Step-by-step explanation:
£1.08+0.54+£1.08= £2.70 fig rolls
£1.43+£1.43+£1.43-£1.43= £2.86 x 2= £5.72 for 6 packets of crisps
£2.70+ £5.72= £8.42
1. Find the equation of the line passing through the point (2,−4) that is parallel to the line y=3x+2 y= 2. Find the equation of the line passing through the point (1,−5) and perpendicular to y=18x+2 y=
Answer:
Step-by-step explanation:
1) Parallel lines have same slope
y = 3x + 2
m = 3
(2, -4) ; m = 3
equation: y - y1 = m (x - x1)
y - [-4] = 3(x - 2)
y + 4 = 3x - 6
y = 3x - 6 - 4
y = 3x - 10
2) y = 18x + 2
m1 = 18
Slope the line perpendicular to y = 18x + 2, m2 = -1/m1 = -1/18
m2 = -1/18
(1 , -5)
[tex]y-[-5]=\frac{-1/18}(x-1)\\\\y+5=\frac{-1}{18}x + \frac{1}{18}\\\\y=\frac{-1}{18}x+\frac{1}{18}-5\\\\y=\frac{-1}{18}x+\frac{1}{18}-\frac{5*18}{1*18}\\\\y=\frac{-1}{18}x+\frac{1}{18}-\frac{90}{18}\\\\y=\frac{-1}{18}x-\frac{89}{18}\\\\[/tex]
In a random sample of six cell phones, the mean full retail price was $538.00 and the standard deviation was $184.00. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean mu. Interpret the results. Identify the margin of error. Construct a 90% confidence interval for the population mean. Interpret the results. Select the correct choice below and fill in the answer box to complete your choice.
Answer:
The margin of error is 370.8.
The 90% confidence interval for the population mean is between $167.2 and $908.8
The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0150
The margin of error is:
M = T*s = 2.0150*184 = 370.8.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 538 - 370.8 = $167.2
The upper end of the interval is the sample mean added to M. So it is 538 + 370.8 = $908.8
The 90% confidence interval for the population mean is between $167.2 and $908.8
The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.
What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?
Oy=-5/2x-1
O y=-5/2x+5
Oy=2/5x-1
Oy=2/5x+5
Answer:
y=-5/2x-1
Step-by-step explanation:
first find the gradient whereas since the two lines are parallel they hav the same gradient. y=mx+c whereas m is the gradient. 5x+2y=12
2y=-5x+12
y=-5/2x+12(so the gradient is -5/2x..... gradient=-5/2
y-4=-5/2
x+2
y-4=-5/2(x+2)
y-4=-5/2x-5
y=-5/2x-5+4
y=-5/2x-1
The equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4) is y = -5/2 x - 1.
What is the Equation of line in Slope Intercept form?Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.
Given that the equation of the line is,
5x + 2y = 12
2y = -5x + 12
y = -5/2 x + 6
This is in the slope intercept form, where the slope = -5/2.
Slopes of two parallel lines are equal.
So any line parallel to the given line will be of the form y = -5/2 x + c
Given line passes through (-2, 4).
Substituting (-2, 4) in y = -5/2 x + c, we get,
(-5/2) (-2) + c = 4
c = -1
So the equation is, y = -5/2 x - 1
Hence the required equation is y = -5/2 x - 1.
Learn more about Slope Intercept form here :
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Professional basketball coaches may coach at one of three levels: Assistant, Associate, or Head. It is possible to transition from any of these levels (states) to another. Each of these three states is transient because once someone leaves coaching at any level they never return (at least according to our model). On average, annual salary for head coaches is $104,485, for associates is $62,993, and for assistants is $41,389. Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix): Assist Assoc Head Assist 6 4 2 Assoc 2 6 6 Head 1 2 10 For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?
Answer:
For someone who is a head coach - their expected income for the remainder of their professional coaching career will be
Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485
Expected income = $1,212,225
Step-by-step explanation:
Professional basketball coaches may coach at one of three levels:
AssistantAssociateHeadOn average, the annual salary is given by
Assistant = $41,389Associate = $62,993Head = $104,485Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix):
Assistant Associate Head
Assistant 6 4 2
Associate 2 6 6
Head 1 2 10
For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?
As per the given P matrix, for someone who is a head coach will be:
Assistant = 1 time
Associate = 2 times
Head = 10 times
Therefore, the expected income will be,
Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485
Expected income = $1,212,225