Answer:
Since the z score for the male is z=-2.1589 and the z score for the female is z=-2.6844, the female has the weight that is more extreme.
Step-by-step explanation:
To find the z score, we use the following equation:
[tex]z=\frac{x-m}{s}[/tex]
Where m is the mean and s is the standard deviation.
So, the z score for a male who weighs 1700 g is:
[tex]z=\frac{1700-3259.6}{722.4}=-2.1589[/tex]
At the same way, the z score for a female who weighs 1700 g is:
[tex]z=\frac{1700-3031.2}{495.9}=-2.6844[/tex]
Finally, -2.6844 is farther from zero than -2.1589, so the female has the weight that is more extreme.
Solve x-6y = 11 for y
Answer:
2
Step-by-step explanation:
Answer: y = 11 - x / -6
Step-by-step explanation:
X - 6y = 11
Since we are solving for y, we need to isolate the variable.
Move x to the other side of the equation.
- 6y = 11 - x
Now divide bith sides by -6 to cancel out -6y and get the variable y
-6y/ -6 = 11 - x/ -6
y = 11 - x / -6
Im not sure if it was solving for y, or if it was solve for x if y = 11
What is the value of the discriminant for the quadratic equation?
6x^2 - 2x + 5 = 0
Answer: -116 is value of discriminant
Help! Please do a,b,c and d with explanation
Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
__
b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
__
c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
__
d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
At the beginning of an experiment, a scientist has 300 grams of radioactive goo. After 150 minutes, her sample has decayed to 37.5 grams.
What is the half-life of the goo in minutes?
________
Find a formula for
G(t),
the amount of goo remaining at time T.
G= _________
How many grams of goo will remain after 32 minutes?
Answer:
Half-life of the goo is 49.5 minutes
[tex]G(t)= 300e^{-0.014t}[/tex]
191.7 grams of goo will remain after 32 minutes
Step-by-step explanation:
Let [tex]M_0\,,\,M_f[/tex] denotes initial and final mass.
[tex]M_0=300\,\,grams\,,\,M_f=37.5\,\,grams[/tex]
According to exponential decay,
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt[/tex]
Here, t denotes time and k denotes decay constant.
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\\\ln \left ( \frac{37.5}{300} \right )=-k(150)\\-2.079=-k(150)\\k=\frac{2.079}{150}=0.014[/tex]
So, half-life of the goo in minutes is calculated as follows:
[tex]\ln \left ( \frac{50}{100} \right )=-kt\\\ln \left ( \frac{50}{100} \right )=-(0.014)t\\t=\frac{-0.693}{-0.014}=49.5\,\,minutes[/tex]
Half-life of the goo is 49.5 minutes
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\Rightarrow M_f=M_0e^{-kt}[/tex]
So,
[tex]G(t)= M_f=M_0e^{-kt}[/tex]
Put [tex]M_0=300\,\,grams\,,\,k=0.014[/tex]
[tex]G(t)= 300e^{-0.014t}[/tex]
Put t = 32 minutes
[tex]G(32)= 300e^{-0.014(32)}=300e^{-0.448}=191.7\,\,grams[/tex]
If P(-2, 1) is rotated 90°, its image is
The image of P(-2,1) after it is rotated 90° is (-1,-2).
In ABC, mA = 46, mB = 105, and c = 19.8. Find a to the nearest tenth.
Answer:
a = 29.3785
Step-by-step explanation:
Given ∠A = 46° and ∠B = 105°
we know that ∠A +∠B+∠C = 180°
46° + 105° +∠C = 180°
∠C = 180 - 46 -105
∠ C = 29°
By using sine rule
[tex]\frac{a}{sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
[tex]\frac{a}{sin A} = \frac{c}{Sin C}[/tex]
Given ∠A = 46° and ∠ C = 29° and c = 19.8
[tex]\frac{a}{sin 46} = \frac{19.8}{Sin 29}[/tex]
on cross multiplication , we get
[tex]a = \frac{19.8 X sin 46}{Sin 29}[/tex]
a = 29.3785
Breakfast Bar’s scrambled egg recipe uses 8 eggs to feed 5 people. How many eggs are they going to need to serve 100 people on Saturday morning?
Explain the steps you would use to solve the problem.
Answer:
800 eggs
Step-by-step explanation:
You would first thing about the starting numbers, Then look at the number 100 and multiply by 8. This would give you 800. This means that you will need 800 eggs to serve 100 people.
Brainliest is greatly appreciated
Answered by: Skylar
6/8/2020
9:59 AM (Eastern Time)
Answer:
the answer is 12.5 i know because i divided 100 by 8 and got 12.5 then multiply then got 100
Step-by-step explanation:
got it right just did the test
A $210 suit is marked down by 10%. Find the sale price.
Answer:
sale prices = $252
Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252
Answer:
$189
Step-by-step explanation:
10% of 210 = 21
210 - 21 = 189
need answers to 30 and 31
Answer:
C ; A
Step-by-step explanation:
Question 30:
Perimeter is the sum of all sides.
Perimeter for a recatngle can be found with the formula:
2(L+W)
Length is 7
Width is 4
Plug our values in.
2(7+4)
2(11)
22
Answer C
Question 31:
Circumference of a circle can be found with the formula:
πd.
Diameter of the given circle is 6.
Plug it in
6π
Round π to 3.14
6(3.14)
18.84
Answer A
Aurora saved $850. Ahe used 35% of her savings on a new TV. How much did the TV cost?
Multiply her savings by the percent spent:
850 x 0.35 = 297.50
The tv cost $297.50
Answer:
the price of TV is = 297.5$
Step-by-step explanation:
all money= 850$
purchased money= 35% of all money ==> 850 ( 35%) = 297.5$
A car rental company charges a daily rate of $35 plus $0.20 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $97. How many miles did you drive?
Answer:
360 miles
Step-by-step explanation:
97= 25+0.2m0.2m= 97-250.2m= 72m= 72/0.2m= 360 milesDan and Camille each have a gift card with a combined balance of $350.00. Dan spent 1/2 of his card balance while Camille spent 1/3 of her card balance. They are both left with an equal amount on their gift cards left. What are they left with.
Really easy math question!
the answer is A: 146 ≤ 9c + 10
How to find a vertical asymptote
Answer:
Step-by-step explanation:
Generally's rational functions that have vertical asymptotes, even trig functions (which, like the tangent function, are often rational).
If the given function is the ratio of two functions, polynomial or otherwise, the graph of the given function has an asymptote at any x value for which the denominator is zero. Example: y = tan x = (sin x) / (cos x) has vertical asysmptotes at π/2, 3π/2, and so on, because the denominator cos x is zero for those angles.
A large car insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period. Single Policyholders Married Policyholders n1 = 450 n2 = 925 # making claim = 67 # making claim = 93 Using alpha = 0.05, determine whether the claim rates are higher for single male policyholders verses married male policyholders. Solve using the p-value approach only.
Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders (P-value = 0.004).
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that rates are higher for single male policyholders verses married male policyholders.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
The significance level is 0.05.
The sample 1 (single group), of size n1=450 has a proportion of p1=0.1489.
[tex]p_1=X_1/n_1=67/450=0.1489[/tex]
The sample 2 (married group), of size n2=925 has a proportion of p2=0.1005.
[tex]p_2=X_2/n_2=93/925=0.1005[/tex]
The difference between proportions is (p1-p2)=0.0483.
[tex]p_d=p_1-p_2=0.1489-0.1005=0.0483[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{67.005+93}{450+925}=\dfrac{160}{1375}=0.1164[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.1164*0.8836}{450}+\dfrac{0.1164*0.8836}{925}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0001}=\sqrt{0.0003}=0.0184[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.0483-0}{0.0184}=\dfrac{0.0483}{0.0184}=2.62[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=P(z>2.62)=0.004[/tex]
As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders.
An urban economist is curious if the distribution in where Oregon residents live is different today than it was in 1990. She observes that today there are approximately 3,109 thousand residents in NW Oregon, 902 thousand residents in SW Oregon, 244 thousand in Central Oregon, and 102 thousand in Eastern Oregon. She knows that in 1990 the breakdown was as follows:
72.7% NW Oregon, 20.7% SW Oregon, 4.8% Central Oregon, and 2.8% Eastern Oregon.
Can she conclude that the distribution in residence is different today at a 0.05 level of significance?
a) Yes, because the p-value = .0009.
b) No, because the p-value = .0009.
c) Yes, because the p-value = .0172.
d) No, because the p-value = .0172.
Answer:
c) Yes, because the p-value = 0.0172
Step-by-step explanation:
The following table is obtained:
Categories Observed(fo) Expected (fe) (fo-fe)²/fe
NW Oregon 3109 4357*0.727=3167.539 1.082
SW Oregon 902 4357*0.207=901.899 0
Central Oregon 244 4357*0.048=209.136 5.812
Eastern Oregon 102 4357*0.028=121.996 3.277
Sum = 4357 4357 10.171
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
H0:p1=0.727,p2=0.207,p3=0.048,p4=0.028
Ha: Some of the population proportions differ from the values stated in the null hypothesis
This corresponds to a Chi-Square test for Goodness of Fit.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df=4−1=3, so then the rejection region for this test is R={χ2:χ2>7.815}.
(3) Test Statistics
The Chi-Squared statistic is computed as follows:
[tex]X^2=\sum^n_{i=1}\frac{(O_i-E_i)^2}{y} \\\\= 1.082+0+5.812 +3.277 = 10.171[/tex]
(4) Decision about the null hypothesis
Since it is observed that
[tex]X^2 = 10.171 > X_c^2 = 7.815[/tex]
it is then concluded that the null hypothesis is rejected.
(5) Conclusion
It is concluded that the null hypothesis H_o is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.
please help, limited on time!!
Answer:
D. 5/13
Step-by-step explanation:
Cosin is adjacent/hypotenuse so, the adjacent would be 5 and the hypotenuse is 13 since it is the longest side. This is viewed from angle B.
Answer:
5/13 (answer D)
Step-by-step explanation:
cos beta = adjacent side / hypotenuse = 5 / 13 (answer D)
The temperature in a town is −2.7°C. The temperature decreases 3°C. What is the new temperature? Incorrect
Answer:
-5.7° C
Step-by-step explanation:
-2.7 °C (degrees Celsius) - 3 °C (degrees Celsius) = -5.7° C
3u - 3 = 15
give me a lecture so i can try to do it in the future please
Answer:
u=6
Step-by-step explanation:
One rule in algebra is what you do to one side, you do it to other side. So if you multiply a number in one side, multiply the same number in other side. Here in this question, you are trying to find the value of the variable u. Variable is called so because the value of it varies depending on different question. Here u is going to be a constant number which when multipled by 3 and then subtracted by 3 equals 15.
So first step is we try to get constants on one side. So we add 3 on both sides to get rid of 3 on left.
3u - 3 + 3= 15+3
3u= 18
Now we divide by 3 on both sides to get u by itself.
3u/3 = 18/3
u= 6
Mr. Azu invested an amount at rate of 12% per annum and invested another amount, 580 ghana cedis more than the first at 14% . if Mr. Azu had total accumulated amount of 2,358.60, how much was his total investment?
Answer:
2082.12 was the total invested
Step-by-step explanation:
Let x represent the amount invested at 14%. Then the amount invested at 12% was (x-580). The total accumulated amount was ...
112%(x -580) +114%(x) = 2358.60
2.26x -649.60 = 2358.60
2.26x = 3008.20 . . . add 649.60
x = 1331.06 . . . . . . divide by 2.26
x -580 = 751.06
The total invested was 1331.06 +751.06 = 2082.12 cedis.
__
Check
The investment at 12% was 751.06, so the accumulated amount of that investment was 751.06×1.12 = 841.19.
The investment at 14% was 1331.06, so the accumulated amount of that investment as 1331.06×1.14 = 1517.41.
The accumulated total amount was 841.19 +1517.41 = 2358.60.
Need Help!...anyone!
(a)
[tex] \sqrt[5]{ {x}^{3} } [/tex]
(b)
[tex] \sqrt[8]{x} [/tex]
(c)
[tex] \sqrt[3]{ {x}^{5} } [/tex]
(d)
[tex] \sqrt{ {x}^{3} } [/tex]
Any help would be greatly appreciated.
There are 300 raffle tickets.
The prizes are as follows:
First prize - voucher for meal at local restaurant
Second prize - food hamper
Third prize - chocolate cake
4x homemade jams
3x homemade pickles
A prize is won after the first raffle ticket is drawn.
What is the probability of winning a prize when the next ticket is drawn?
Answer: 0.007
Step-by-step explanation:
Suppose that you have a ticket.
We have 3 prizes, and 300 tickets.
After the first tiket is drawn, someone win a prize, so now we have 299 tikets left and 2 prizes left.
Then, for the next draw, you have p = 1/299 of wining a prize.
If you did not win there, the probability for the third price is p = 1/298 (because there are 2 less tickets now)
Then the probability of winning at least one prize is:
P = 1/299 + 1/298 = 0.007
4. The average annual income of 100 randomly chosen residents of Santa Cruz is $30,755 with a standard deviation of $20,450. a) What is the standard deviation of the annual income? b) Test the hypothesis that the average annual income is $32,000 against the alternative that it is less than $32,000 at the 10% level. c) Test the hypothesis that the average annual income is equal to $33,000 against the alternative that it is not at the 5% level. d) What is the 95% confidence interval of the average annual income?
Answer:
a) The standard deviation of the annual income σₓ = 2045
b)
The calculated value Z = 0.608 < 1.645 at 10 % level of significance
Null hypothesis is accepted
The average annual income is greater than $32,000
c)
The calculated value Z = 1.0977 < 1.96 at 5 % level of significance
Null hypothesis is accepted
The average annual income is equal to $33,000
d)
95% of confidence intervals of the Average annual income
(26 ,746.8 ,34, 763.2)
Step-by-step explanation:
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation = $20,450
a)
The standard deviation of the annual income σₓ = [tex]\frac{S.D}{\sqrt{n} }[/tex]
= [tex]\frac{20,450}{\sqrt{100} }= 2045[/tex]
b)
Given mean of the Population μ = $32,000
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation ( σ)= $20,450
Null Hypothesis:- H₀: μ > $32,000
Alternative Hypothesis:H₁: μ < $32,000
Level of significance α = 0.10
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{30755-32000 }{\frac{20450}{\sqrt{100} } }[/tex]
Z= |-0.608| = 0.608
The calculated value Z = 0.608 < 1.645 at 10 % level of significance
Null hypothesis is accepted
The average annual income is greater than $32,000
c)
Given mean of the Population μ = $33,000
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation ( σ)= $20,450
Null Hypothesis:- H₀: μ = $33,000
Alternative Hypothesis:H₁: μ ≠ $33,000
Level of significance α = 0.05
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{30755-33000 }{\frac{20450}{\sqrt{100} } }[/tex]
Z = -1.0977
|Z|= |-1.0977| = 1.0977
The 95% of z -value = 1.96
The calculated value Z = 1.0977 < 1.96 at 5 % level of significance
Null hypothesis is accepted
The average annual income is equal to $33,000
d)
95% of confidence intervals is determined by
[tex](x^{-} - 1.96 \frac{S.D}{\sqrt{n} } , x^{-} + 1.96 \frac{S.D}{\sqrt{n} })[/tex]
[tex](30755 - 1.96 \frac{20450}{\sqrt{100} } , 30755 +1.96 \frac{20450}{\sqrt{100} })[/tex]
( 30 755 - 4008.2 , 30 755 +4008.2)
95% of confidence intervals of the Average annual income
(26 ,746.8 ,34, 763.2)
What is 2 1/2 + 1 1/3
Answer:
[tex]=3\frac{5}{6}[/tex]
Step-by-step explanation:
[tex]2\frac{1}{2}+1\frac{1}{3}\\\mathrm{Add\:whole\:numbers}\:2+1:\quad 3\\\mathrm{Combine\:fractions}\:\frac{1}{2}+\frac{1}{3}:\quad \frac{5}{6}\\=3\frac{5}{6}[/tex]
How far from zero would you move on the x-axis to reach the point (10, 8)?
Answer:
You would move 10 units to the right from zero on the x-axis.
The given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
The given coordinate point (10, 8).
The distance of any point from the x-axis is called the x-coordinate.
In the point (10, 8), 10 units from the x-axis
Therefore, the given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).
Learn more about the coordinate plane here:
https://brainly.com/question/24134413.
#SPJ6
4x-y+ 2z=-1
Given the system -x+2y + 5z = 2, which is true?
|-x+y-3z= 1
Answer:
Y = 0
X= 1/2
Z = -1/2
Step-by-step explanation:
4x-y+ 2z=-1
-x+y-3z= 1
-x+2y + 5z = 2
Solving simultenously
Y= 4x + 2z -1
Y =1+ 3z+ x
Y =x/2 -( 5z/2) - 1
Equating y will give two equations
3x-z = 2
3x + 11z = -4
Subtracting the equations
-12z =6
Z= -1/2
Substituting z
3x +1/2 = 2
3x = 3/2
X= 1/2
Substituting x and z to find y in
-x+y-3z= 1
-1/2 + y +3/2 = 1
Y = 1-1
Y = 0
Answer: b) is answer
Step-by-step explanation:
The following data represent the number of flash drives sold per day at a localcomputer shop and their prices.Price Units Sold34 336 432 635 530 938 240 1a. Develop the estimated regression equation that could be used to predict thequantity sold given the price. Interpret the slope.b. Did the estimated regression equation provide a good fit? Explain.c. Compute the sample correlation coefficient between the price and the number offlash drives sold. Use a= 0.01 to test the relationship between price and units sold.d. How many units can be sold per day if the price of flash drive is set to $28.
Answer:
a)3145 x 0.01 = 31.45 3145- 31.45 = 3113.55
Compute the sample correlation 3113.55 -? we find the least square pressing at least 15x on the calculator then minus this from 3113.55 to find a better fit and minimum regression.
We add the differences of units then divide by distribution as seen below.
b) unsure.
c) = (see below) just test each number shown unit sold per day / price then x can show the differences in each number from day 1 to day 2.
d) = 16 sold.
Step-by-step explanation:
a) We count the units up and deduct from it from the equation p is recognized as units sold. R1 is cost R2 is total days.
b) The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0).
c) r 2= decimal ; the regression equation has accounted for percentage of the total sum of squares. You cna do this one.
d) = 16 sold at $28 each. - Why ? We using 7 day data and prove a how many units can be sold p/d if the price of flash drive is set to $28 each per unit.
Day 1 = 34 / 28 = 1 = 1.21428571429 = 1 no difference day prior.
Day 2 = 336 / 28 = 12 = 12 = difference day prior is 11
Day 3 = 432 / 28 = 15 = 15.4285714286 = 15 difference day prior is 3
Day 4 = 635 / 28 = 23 = 22.6785714286 = 23 difference day prior is 8
Day 5 = 530 / 28 = 19 = 18.9285714286 = 19 difference day prior is minus - 4
Day 6 = 938 / 28 = 34 = 33.5 = 34 difference day prior is 15
Day 7 = 240 / 28 = 9 = 8.57142857143 = 9 difference day prior is minus -25
Total days 7 = Total revenue / price = average units sold
Average units sold total = 1+ 12+15 +23 +19+34+9 = 113 rounded.
Average units sold total = 1.21428571429 + 12 + 15.4285714286
+ 22.6785714286
+18.9285714286
+ 33.5
+ 8.57142857143 = 112.321428572 units sold weekly when priced at $28
To answer D we divide this by 7 to show;
112.321428572/ 7 = 16.0459183674
Daily units sold = 16
If P(-2, 1) is rotated 90°, its image is
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why?
1. No. The events cannot occur together. 2. Yes. The events can occur together. 3. No. The probability of drawing a specific second card depends on the identity of the first card. 4. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.
(b) Find P(ace on 1st card and jack on 2nd). (Enter your answer as a fraction.)
(c) Find P(jack on 1st card and ace on 2nd). (Enter your answer as a fraction.)
(d) Find the probability of drawing an ace and a jack in either order. (Enter your answer as a fraction.)
Answer:
(a)No. The probability of drawing a specific second card depends on the identity of the first card.
(b)4/663
(c) 4/663
(d) 8/663
Step-by-step explanation:
(a)The events are not independent because we are drawing cards without replacement and the probability of drawing a specific second card depends on the identity of the first card.
(b) P(ace on 1st card and jack on 2nd).
[tex]P$(Ace on 1st card) =\dfrac{4}{52}\\ P$(Jack on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(ace on 1st card and jack on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(c)P(jack on 1st card and ace on 2nd)
[tex]P$(Jack on 1st card) =\dfrac{4}{52}\\ P$(Ace on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(jack on 1st card and ace on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(d)Probability of drawing an ace and a jack in either order.
We can either draw an ace first, jack second or jack first, ace second.
Therefore:
P(drawing an ace and a jack in either order) =P(AJ)+(JA)
From parts (b) and (c) above:
[tex]P$(jack on 1st card and ace on 2nd) =\dfrac{4}{663}\\P$(ace on 1st card and jack on 2nd) =\dfrac{4}{663}\\$Therefore:\\P(drawing an ace and a jack in either order)=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}[/tex]
If (x + k) is a factor of f(x), which of the following must be true?
f(K) = 0
fl-k)=0
A root of f(x) is x = k.
A y intercept of f(x) is x = -k.
Answer:
f(-k)=0Step-by-step explanation:
(x + k) is a factor of f(x)
x+k=0 => x= -k; -k is a root of f(x)
=> f(-k)=0
[tex](x + k) is a factor of f(x)x+k=0 = > x= -k; -k is a root of f(x)= > f(-k)=0[/tex]
So the correct option is B.fl-k)=0.
What is a root function example?
The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression. The following are examples of rational functions: f(x)=√2x4−5 f ( x ) = 2 x 4 − 5 ; g(x)=3√4x−7 g ( x ) = 4 x − 7 3 ; h(x)=7√−8x2+4 h ( x ) = − 8 x 2 + 4 7 .
What is the root function?
The root function is used to find a single solution to a single function with a single unknown. In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns. For now, we will focus on using the root function.
Learn more about root function here: https://brainly.com/question/13136492
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