P = {4,5,8, 11, 13) and
Q = {11, 12, 13, 15, 17, 19).
a An element is selected at random from P.
What is the probability that it is odd?
​

Answer:

0

Step-by-step explanation:

3 cards

P( odd) = 1 odd/ 3 cards = 1/3

No replacement

2 cards 6,8

No odds

P( odd) = 0/2

P( odd, no replacement, odd) = 1/2 * 0 = 0

Answer:

100%

Step-by-step explanation:

First, let's determine the probability for each of the conditions.

For P(greater than 2), we will have the cards 3, 4, 5, 6, 7, and 8.

For P(less than 3), we will have the cars 2.

In other words, every single card fits the conditions.

Thus, P(greater than 2 or less than 3)=7/7=100%

100%

Answer:

100%

Step-by-step explanation:

Greater than 2 is 3, 4, 5, 6, 7, 8

And less than 3 is 2 so that’s all the numbers which is 100%

Answer:

21564 ÷ 2 = 10782

40565 ÷ 5 = 8113

6365 ÷ 8 = 795.625

1436 ÷ 7 = 205.142857143

Answer:

3

Step-by-step explanation:

Answer:124

Step-by-step explanation:

2x + 8 + x - 2 = 180

Add like terms

3x + 6 = 180

Subtract the 6 from both sides

3x + 6 - 6 = 180 - 6

3x = 174

Divide by 3

x = 58

Now we have to find the measure of angle ACD

2(58) + 8 = 124

Answer:

Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion that support the candidate has significantly changed.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=800 has a proportion of p1=0.58.

[tex]p_1=X_1/n_1=460/800=0.58[/tex]

The sample 2, of size n2=1000 has a proportion of p2=0.52.

[tex]p_2=X_2/n_2=520/1000=0.52[/tex]

The difference between proportions is (p1-p2)=0.05.

[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/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{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]

As the P-value (0.02) 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 the proportion that support the candidate has significantly changed.

Answer:

The height of the hill is 116.9 meters.

Step-by-step explanation:

The diagram depicting this problem is drawn and attached below.

From Triangle ABC

[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]

From Triangle XBC

[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]

Therefore:

[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]

Therefore, the height of the hill

[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]

The height of the hill is 116.9 meters.

Answer:

Pair of compasses.

Step-by-step explanation:

These are used to inscribe circles/arcs.

Compasses are used in maths, navigation,e.t.c.

Hope it helps.

Answer:

to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]

The resulting function can be written as

[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]

Step-by-step explanation:

Hello,

f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0

and [tex]f(x)\geq 0[/tex]

so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]

and then we can write

[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]

hope this helps

Answer: 5182

To get the value of all 100 numbers you would need to multiply.

Step-by-step explanation:

51.82x100= 5182

Answer:

[tex]y = 4x-3[/tex]

Step-by-step explanation:

The coordinates are (-0.5,-5) and (2,5)

Finding the slope, m:

=> Slope = [tex]\frac{rise}{run}[/tex]

=> Slope = [tex]\frac{5+5}{2+0.5}[/tex]

=> Slope = [tex]\frac{10}{2.5}[/tex]

=> Slope = 4

Now, y-intercept, b:

Taking any of the two coordinate and putting it in the slope intercept equation:

=> Point = (x,y) = (2,5)

So, x = 2, y = 5

=> [tex]y = mx+b[/tex]

=> 5 = (4)(2) + b

=> 5 = 8 + b

=> b = 5-8

=> b = -3

Now, Putting in slope intercept equation:

=> [tex]y = mx+b[/tex]

=> [tex]y = 4x-3[/tex]

Gradient (m) = x2-x1

y2-y1

considering

y1 = -5 y2 = 5

x1 = -0.5. x2 = 2

m = 2-(-0.5)

5-(-5)

m = 5.5

10

m = 11. = 0.55

20

equation of a line is given by

y-y1 = m+(x-x1)

y-(-5) =0.55 + {x-(-0.5)}

y+5 = 0.55 + x+0.5

making y the subject

y = 0.55 +0.5 -5 + x

y = -3.95 + x

Answer: (a) The chart is in the first attachment named table frequency.

(b) The histogram is in the second attachment named frequency vs. enrollment

(c) Mode

(d) x = 9071.4

(e) s = 6677.64

(f) It is -0.16 standard deviation away

Step-by-step explanation:

(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.

(d) To calculate sample mean of a frequency data:

1) Find the midpoint for each interval;

2) Multiply each midpoint for its correspondent frequency;

3) Sum up each multiplication obtained in the previous step;

4) Sum up all the frequencies;

5) Divide the sum in step 3 by the sum in step 4;

For this chart:

x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]

x = 9071.4

(e) To find the standard deviation:

1) With each midpoint, calculate its square;

2) Multiply the midppoint square by its correspondent frequency;

3) Use the following formula to determine the sample standard:

s = √∑f.M²  - n(μ)² / n-1

For this chart:

s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]

s = 6677.64

(f) To find how many standard deviations away is the enrollment:

z = [tex]\frac{8000-9071.4}{6677.64}[/tex]

z = - 0.16

8000 enrollments are -0.16 standard deviations away from the mean.

Answer: NO, class limits and class marks are not meaningful to qualitative data.

Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.

Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.

Answer:

4

Step-by-step explanation:

8×5÷10

PEMDAS says multiply and divide from left to right

40÷10

4

Answer:

4

Step-by-step explanation:

Follow the PEMDAS order of operations

8*5=40

40÷10=4

=4

OR

8x5÷10

8x0.5=4

=4

Have a good day and stay safe!

Answer:

Option (C)

Step-by-step explanation:

Given expression is,

[tex]4+4\times \text{log}_2(x)=14[/tex]

By subtracting 4 from both the sides of the equation.

[tex]4\times \text{log}_2(x)=14-4[/tex]

Now divide the equation by 4

[tex]\text{log}_2(x)=\frac{10}{4}[/tex]

[tex]\text{log}_2(x)=2.5[/tex]

[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]

[tex]x=(2)^{2.5}[/tex]

[tex]x = 5.657[/tex]

x ≈ 5.66

Therefore, Option C will be the correct option.

4+4•log2 x=14

x= 5.66

Answer:

The Empirical Rule

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

So the answer to this question is the Empirical Rule

Answer:

B) 0.894

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

A local animal rescue organization receives an average of 0.55 rescue calls per hour.

This means that [tex]\mu = 0.55[/tex]

Probability that during a randomly selected hour, the organization will receive fewer than two calls.

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.55}*(0.55)^{0}}{(0)!} = 0.577[/tex]

[tex]P(X = 1) = \frac{e^{-0.55}*(0.55)^{1}}{(1)!} = 0.317[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.577 + 0.317 = 0.894[/tex]

Step-by-step explanation:

Q1. 1,075÷12.5 =8

So Therefore 1g of medicine cost 8 naira

Q2.645÷42=15.3

so therefore 1 hour cost 15.3 naira

The cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours  is 27090 naira.

A division is a process of splitting a specific amount into equal parts.

Given that 12.5g of medicine cost 1,075 naira.

We have to find the cost of 1g of medicine.

12.5g=1075 naira

1g=1075/12.5

1g=86 naira.

the total pay for someone who works 42 hours and gets 645 naira per hour

The cost for 42 hours

42×645

27090 naira

Hence,  the cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours  is 27090 naira.

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ2

Answer:

Volume of the sphere= 113.112 cubic inch(Inch ³)

Step-by-step explanation:

First of all the formula for the volume of a sphere Is given as 4πr³

Already the radius r is already given as 3 inches

While π = 3.142

Volume of the sphere = 4/3πr³

Volume of the sphere = 4/3(3.142)(3)³

Volume of the sphere= 4/3(3.142)(27)

Volume of the sphere= 4/3(84.834)

Volume of the sphere= 339.336/3

Volume of the sphere= 113.112 Inch ³

Volume of the sphere= 113.112 cubic inch

Answer:

8

Step-by-step explanation:

don't cheat sike i cheat

Answer: the real answer is c you can go to both places I gave you the answer in both

Step-by-step explanation:

Because I got it right please have a good day or night

Answer:

<

Step-by-step explanation:

750,000,000 times 10^5 can be expressed as 7.5 times [tex]10^{11}[/tex]

7.55 times 10^13 is greater than 7.5 times 10^11.

Answer:

The appropriate sign that makes the statement true is <

Hope this helps you

Answer:

1) We have to multiply both sides by  1/(de)

2) c=ab/(cd)

Step-by-step explanation:

We have to achieve the right side expression be c only.  To do that we have to multiply cde by   1/(de) .  However we have to multiply the left side by

1/(de) as well.

So the resulting left side expression is:

ab *1/(de)=ab/(de)

So c= ab/(de)

Given equation in the question is,

ab = cde

To solve the given equation for the value of c, follow the algebraic rules,

1). Multiply both the sides of the equation with [tex]\frac{1}{de}[/tex],

   [tex]ab\times \frac{1}{de} = \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}= \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}=c[/tex]

Therefore, resulting equation for c will be,

[tex]c=\frac{ab}{de}[/tex]

Learn more,

https://brainly.com/question/11496615

Answer:

m∠A = 17 degrees       m∠B = 73 degrees     m∠C = 90 (given)    a =   12 (given)    b =  40           c = 42 (given)

Step-by-step explanation:

Use sin to solve m∠A

sin x = 12/42     Simplify

sin x = 0.2857   Use the negative sin to solve for x

sin^-1 x =  17 degrees

Add together all of the angle measures to solve for m∠B

17 + 90 + x = 180    Add

107 + x = 180

-107        -107

x = 73 degrees

Use Pythagorean Theorem to solve for b

12^2 + x^2 = 42^2     Simplify

144 + x^2 = 1764

-144            -144

x^2 = 1620               Take the square root of both sides

x = 40

Answer:

d. 0.459 < p < 0.603

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.531.

[tex]p=X/n=69/130=0.531[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]

The 90% confidence interval for the population proportion is (0.459, 0.603).

Answer:

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

Step-by-step explanation:

[tex]\frac{5x-11}{2x^2+x-6}[/tex]

Factor the denominator.

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

The fraction cannot be simplified further.

Answer:

solution,

[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]

Hope this helps..

Answer:

a) Check Explanation

b) Probability that 11 out of the 17 randomly selected flights are on time = P(X = 11) = 0.0680

c) Probability that fewer than 11 out of the 17 randomly selected flights are on time

= P(X < 11) = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

= P(X ≥ 11) = 0.9623

e) Probability that between 9 and 11 flights, inclusive, out of the randomly selected 17 are on time = P(9 ≤ X ≤ 11) = 0.1031

Step-by-step explanation:

a) How to know a binomial experiment

1) A binomial experiment is one in which the probability of success doesn't change with every run or number of trials. (Probability of each flight being on time is 80%)

2) It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (It's either the flights are on time or not).

3) The outcome of each trial/run of a binomial experiment is independent of one another.

All true for this experiment.

b) Probability that exactly 11 flights are on time.

Let X be the random variable that represents the number of flights that are on time out of the randomly selected 17.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 17 randomly selected flights

x = Number of successes required = number of flights required to be on time

p = probability of success = Probability of a flight being on time = 80% = 0.80

q = probability of failure = Probability of a flight NOT being on time = 1 - p = 1 - 0.80 = 0.20

P(X = 11) = ¹⁷C₁₁ (0.80)¹¹ (0.20)¹⁷⁻¹¹ = 0.06803777953 = 0.0680

c) Probability that fewer than 11 flights are on time

This is also computed using binomial formula

It is the probability that the number of flights on time are less than 11

P(X < 11) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0376634429 = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

This is the probability of the number of flights on time being 11 or more.

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17)

= 1 - P(X < 11)

= 1 - 0.0376634429

= 0.9623365571 = 0.9623

e) Probability that between 9 and 11 flights, inclusive, are on time = P(9 ≤ X ≤ 11)

This is the probability that exactly 9, 10 or 11 flights are on time.

P(9 ≤ X ≤ 11) = P(X = 9) + P(X = 10) + P(X = 11)

= 0.0083528524 + 0.02672912767 + 0.06803777953

= 0.1031197592 = 0.1031

Hope this Helps!!!

Hey there! :)

Answer:

x = 18 minutes.

Step-by-step explanation:

To solve this equation, set up a ratio.

# of towels over time taken:

[tex]\frac{6}{3} = \frac{36}{x}[/tex]

Cross multiply:

6x = 108

Divide both sides by 6:

6x/6 = 108/6

x = 18 minutes.

Answer:

In eighteen minutes she will have folded all 36

Answer:

  41°, 56°, 83°

Step-by-step explanation:

We can find the largest angle from the law of cosines:

  c² = a² +b² -2ab·cos(C)

  C = arccos((a² +b² -c²)/(2ab))

  C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°

Then the second-largest angle can be found the same way:

  B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°

Of course the third angle is the difference between the sum of these and 180°:

  A = 180° -82.8192° -55.7711° = 41.4096°

Rounded to the nearest degree, ...

  the angles of the triangle are 41°, 56°, 83°.

Answer:

50 miles

Step-by-step explanation:

hello,

let's note x the number of miles travelled heading west,

it takes 1 hour to travel 25 miles

so it takes x/25 hours to travel x miles

we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles

so in 7-x/25 hours it travels 19(7-x/25) miles

we can write, as the total distance is 145 miles

[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]

we can verify

50 miles heading West takes 2 hours

in 5 hours it travels 19*5 = 95 miles

the total is 145 miles

so this is correct

hope this helps

Answer:

For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:

2x + 10 + 4x + 80 = 180

6x + 90 = 180

6x = 90

x = 15°