2x + 3y = 12
Complete the missing value in the solution to the equation.
1,8)

Answer:

x=106 degrees

Step-by-step explanation:

The two opposite angles in a parallelogram are always the same and we know 360 degrees in a parallelogram.

x+x+74+74=360.

2x+148=360

2x=212

x=106 degrees

Answer:

x= 60°, y = 80°, z = 40°

Step-by-step explanation:

Look at the line substending 40° and Z°; you would see that both lines are parallel and so their angles are they the same.

Hence z= 40° { corresponding angles of parallel lines}

Similarly;

Look at the line substending 60° and x°; you would see that both lines are parallel and so their angles are they the same.

60° = x° { corresponding angles of parallel lines}

Now looking at the angle between x and y; let's call the angle between them r

And you would observe closely that r = z° = 40°{ vertically opposite angles are equal}

Note that x + r + y = 180°{ angle on a straight line}

y = 180° - ( x + r)

y = 180 - (60+40)

y = 180° - 100°

= 80°

Answer:

The committes can be selected in [tex]1.752507297 \times 10^{19}[/tex] ways

Step-by-step explanation:

The order in which the members are chosen to the committee is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The two committees must be disjoint.

This means that a person cannot be part of both committes.

If there are 385 members of congress, how many ways could the committees be selected?

Since the committes are disjoint, 5(math) + 5(computer science) = 10 people will be chosen from the set of 385. So

[tex]C_{385,10} = \frac{385!}{10!(385-10)!} = 1.752507297 \times 10^{19}[/tex]

The committes can be selected in [tex]1.752507297 \times 10^{19}[/tex] ways

9514 1404 393

Answer:

Step-by-step explanation:

If order doesn't matter, the number is the combinations of 50 things taken 20 at a time:

  50C20 = 47129212243960 ≈ 4.713×10^13

If order does matter, then the number of ways is this value multiplied by 20!:

  50P20 = 114660755112113373922453094400000 ≈ 1.147×10^32

_____

nCk = n!/(k!(n-k)!)

nPk = n!/(n-k)!

Answer:

As x gets smaller, pointing to negative infinity, the value of f decreses, pointing to negative infinity.

As x gets increases, pointing to positve infinity, the value of f decreses, pointing to negative infinity.

Step-by-step explanation:

To find the end behaviour of a function f(x), we calculate these following limits:

[tex]\lim_{x \to +\infty} f(x)[/tex]

And

[tex]\lim_{x \to -\infty} f(x)[/tex]

In this question:

[tex]f(x) = -4x^{6} + 6x^{2} - 52[/tex]

At negative infinity:

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} -4x^{6} + 6x^{2} - 52[/tex]

When the variable points to infinity, we only consider the term with the highest exponent. So

[tex]\lim_{x \to -\infty} -4x^{6} + 6x^{2} - 52 = \lim_{x \to -\infty} -4x^{6} = -4*(-\infty)^{6} = -(\infty) = -\infty[/tex]

So as x gets smaller, pointing to negative infinity, the value of f decreses, pointing to negative infinity.

Positive infinity:

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} -4x^{6} + 6x^{2} - 52 = \lim_{x \to \infty} -4x^{6} = -4*(\infty)^{6} = -(\infty) = -\infty[/tex]

So as x gets increases, pointing to positve infinity, the value of f decreses, pointing to negative infinity.

f(x) = -4x^6 +6x^2-52

The leading coefficient is negative so the left end of the graph goes down.

f(x) is an even function so both ends of the graph go in the same direction.

Answer:

A. 38.3

Step-by-step explanation:

[tex]circumference \\ \: \: \: \: \: = 2 \times radius \times \pi \\ or =diameter \times \pi \\ thus \: the \: answer \: is \\ 12.2 \times 3.14 = 38.3 \\ ( \: a \: ) [/tex]

Answer:

66g of polyethylene ointment base!

Answer: approximately 5148 feet directly north of point A

This is equivalent to 0.975 miles

==============================================================

Explanation:

Check out figure 1 (attached image below) to see how the drawing is set up.

Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.

Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.

The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.

Note that triangle ABC is a right triangle. The 90 degree angle is at point A.

We can use the pythagorean theorem to solve for x

See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.

This means the sound wave takes about 4.68 seconds to go from point C to point A.

With this x value, we can compute the expression 1100x to get

1100*x = 1100*4.68 = 5,148 feet

To convert this to miles, divide by 5280

(5148)/(5280) = 0.975

Therefore,

5148 feet = 0.975 miles

Answer:

Oioj[

Step-by-step explanation:

Step-by-step explanation:

Write the equation to solve it in order to know the exact value of X.

Answer:

The company must sell 60 or 70 items to obtain a weekly profit of 200.

Step-by-step explanation:

The profit is the difference between the revenue and the cost of a given task, therefore:

[tex]\text{profit} = R - C\\\text{profit} = 66*x - 0.2*x^2 - (40*x + 640)\\\text{profit} = 66*x - 0.2*x^2 - 40*x - 640\\\text{profit} = - 0.2*x^2 + 26*x - 640[/tex]

To have a profit of 200, we need to sell:

[tex]-0.2*x^2 + 26*x - 640 = 200\\-0.2*x^2 + 26*x -840 = 0\text{ } *\frac{-1}{0.2}\\x^2 -130 + -4200 = 0\\x_{1,2} = \frac{-(-130) \pm \sqrt{(-130)^2 - 4*1*(-4200)}}{2*1}\\x_{1,2} = \frac{130 \pm \sqrt{16900 + 16800}}{2}\\x_{1,2} = \frac{130 \pm \sqrt{100}}{2}\\x_{1,2} = \frac{130 \pm 10}{2}\\x_{1} = \frac{130 + 10}{2} = \frac{140}{2} = 70\\ x_{2} = \frac{130 - 10}{2} = \frac{120}{2} = 60[/tex]

The company must sell 60 or 70 items to obtain a weekly profit of 200.

Answer: Repeated contrast

Step-by-step explanation:

In the two way ANOVA that was performed above, there were 3 groups of which 30 people (15 men and 15 women) participants who had never learnt to play a musical instrument before were recruited and divided equally.

The ANOVA is of repeated measures. There is within group effect, between group effect and interaction effect. The result also shows significant main effect for the gender and the hours used practicing. Hence, to breakdown the effect of gender, the repeated contrast method will be utilized. The repeated contrast method compares the mean of every level with the succeeding level except the last level.

Answer:

6000

Step-by-step explanation:

6 six

60 sixty

600 six hundred

6000 six thousand

//have a great day//

Answer:

Joanna bought 21 items that come out to a total of $33.33. She bought 9 notebooks and 12 pencils.

Step-by-step explanation:

Notebooks (N) = $1.85 Pencils (P) = $1.39

9N+12P= $33.33

9*1.85=16.65

12*1.39=16.68

16.65+16.68=33.33

Answer:

The truncated cube has 6 more faces than the truncated tetrahedron.

Step-by-step explanation:

==>Given:

truncated cube=>

edges (E) = 36

vertices (V) = 24

faces (F) = ? (unknown)

According to Euler's polyhedron formula, Vertices (V) - Edges (E) + Faces (F) = 2, let's find how many faces the truncated cube has

=> 24 - 36 + F = 2

- 12 + F = 2

F = 2 + 12

F = 14

truncated tetrahedron=>

edges (E) = 18

vertices (V) = 12

faces (F) = ? (unknown)

Using V - E + F = 2, find F

=>12 - 18 + F = 2

- 6 + F = 2

F = 2 + 6

F = 8

Comparing the faces of the truncated cube (14) and the truncated tetrahedron (8), the truncated cube has 6 more faces than the truncated tetrahedron (14 - 8 = 6)

Answer:

Answer A:The truncated cube has 6 more faces than the truncated tetrahedron.

Step-by-step explanation:

Answer:

252

Step-by-step explanation:

Answer:

A, C, D

Step-by-step explanation:

Answer: A , C , D

Step-by-step explanation: edge2022

Answer:

D

Step-by-step explanation:

Find out if they match in all of them

Hope this helps

Answer:

68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 250, \sigma = 8, n = 64, s = \frac{8}{\sqrt{64}} = 1[/tex]

What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean?

This is the pvalue of Z when X = 64 + 1 = 65 subtracted by the pvalue of Z when X = 64 - 1 = 63. So

X = 65

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{65 - 64}{1}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413.

X = 63

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{63 - 64}{1}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.

Area = 0.785

Area=0.79

I hope it helps

Answer: There can be 2 gold 1 silver, 2 silver one gold, 3 silver, or 3 gold.

I'm not really sure if this is correct but I hope this helps:)

For A: V = B · h  V = 8 · 14  V = 784 units^3.

For B: V = B · h  V = 9 · 9  V = 729 units^3.

For C: V = B · h  V = 5 · 11  V = 220 units^3.

Answer:

(a)                             n :      20           50          100         500

P (-200 < X - μ < 200) : 0.2886    0.4444    0.5954    0.9376

(b) The correct option is (b).

Step-by-step explanation:

Let the random variable X represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.

The mean amount of deductions is, μ = $16,642 and standard deviation is, σ = $2,400.

Assuming that the random variable X follows a normal distribution.

(a)

Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{20}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{20}})[/tex]

                                           [tex]=P(-0.37<Z<0.37)\\\\=P(Z<0.37)-P(Z<-0.37)\\\\=0.6443-0.3557\\\\=0.2886[/tex]

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{50}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{50}})[/tex]

                                           [tex]=P(-0.59<Z<0.59)\\\\=P(Z<0.59)-P(Z<-0.59)\\\\=0.7222-0.2778\\\\=0.4444[/tex]

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{100}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{100}})[/tex]

                                           [tex]=P(-0.83<Z<0.83)\\\\=P(Z<0.83)-P(Z<-0.83)\\\\=0.7977-0.2023\\\\=0.5954[/tex]

[tex]P(\mu-200<X<\mu+200)=P(\frac{(16642-200)-16642}{2400/\sqrt{500}}<\frac{X-\mu}{\sigma/\sqrt{n}}<\frac{(16642+200)-16642}{2400/\sqrt{500}})[/tex]

                                           [tex]=P(-1.86<Z<1.86)\\\\=P(Z<1.86)-P(Z<-1.86)\\\\=0.9688-0.0312\\\\=0.9376[/tex]

                                 n :      20           50          100         500

P (-200 < X - μ < 200) : 0.2886    0.4444    0.5954    0.9376

(b)

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ([tex]\bar x[/tex]) approaches the whole population mean ([tex]\mu_{x}[/tex]).

Consider the probabilities computed in part (a).

As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.

So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

Thus, the correct option is (b).

Using the normal distribution and the central limit theorem, it is found that:

a)

0.2886 = 28.86% probability that a sample size of 20 has a sample mean within $200 of the population mean.

0.4448 = 44.48% probability that a sample size of 50 has a sample mean within $200 of the population mean.

0.5934 = 59.34% probability that a sample size of 100 has a sample mean within $200 of the population mean.

0.9372 = 93.72% probability that a sample size of 500 has a sample mean within $200 of the population mean.

b)

b. A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence, the probability of sample of size n having a sample mean within 200 is the p-value of [tex]Z = \frac{200}{s}[/tex] subtracted by the p-value of [tex]Z = -\frac{200}{s}[/tex]

In this problem:

Item a:

For samples of 20, [tex]n = 20[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{20}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{20}}} = 0.37[/tex]

0.6443 - 0.3557 = 0.2886.

0.2886 = 28.86% probability that a sample size of 20 has a sample mean within $200 of the population mean.

For samples of 50, [tex]n = 50[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{50}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{50}}} = 0.59[/tex]

0.7224 - 0.2776 = 0.4448.

0.4448 = 44.48% probability that a sample size of 50 has a sample mean within $200 of the population mean.

For samples of 100, [tex]n = 100[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{100}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{100}}} = 0.83[/tex]

0.7967 - 0.2033 = 0.5934

0.5934 = 59.34% probability that a sample size of 100 has a sample mean within $200 of the population mean.

For samples of 500, [tex]n = 500[/tex], and thus:

[tex]s = \frac{2400}{\sqrt{500}}[/tex]

Then

[tex]Z = \frac{200}{s} = \frac{200}{\frac{2400}{\sqrt{500}}} = 1.86[/tex]

0.9686 - 0.0314 = 0.9372

0.9372 = 93.72% probability that a sample size of 500 has a sample mean within $200 of the population mean.

Item b:

A larger sample size reduces the standard error, as [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], that is, the standard error is inversely proportional to the square root of the sample size n, meaning that values are closer to the mean. Thus, the correct option is:

b. A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

A similar problem is given at https://brainly.com/question/24663213

Answer:

Option (B).

Step-by-step explanation:

Percentage change between two numbers a and b can be calculated by the formula,

% change = [tex]\frac{|b-a|}{a}\times 100[/tex]

Where, (b - a) = Change in values

a = Initial value

If a = 16 and b = 20

Percentage change between 16 and 20 will be,

= [tex](\frac{20-16}{16})\times 100[/tex]

= [tex]\frac{4}{16}\times 100[/tex]

= 25%

If a = 20 and b = 16,

Percentage change = [tex]\frac{|16-20|}{20}\times 100[/tex]

                                 = 20%

Therefore, %change between 16 and 24 may be 16% or 20%.

Option (A),

[tex]\frac{20-16}{16}\times 100[/tex] = 25%

Option (B),

[tex]\frac{20}{16}-1\times 100[/tex] = 1.25 - 1 × 100

                   = 1.25 - 100

                   = -98.75%

Option (C),

[tex]100\times \frac{1}{4}[/tex] = 25%

Option (D),

[tex]\frac{(20-16)}{20}\times 100[/tex] = 20%

Therefore, we can not use the calculation used in Option (B).

Answer:

53.33mph

Step-by-step explanation:

Let's calculated the total time spent on the journey first;

For the first 300miles the time spent is ;

From Distance = speed× time

time = Distance/ speed

= 300/60 = 5 hours

Similarly for the last 100mile the time taken is ;

100/40 = 2.5 hours

Total time spent = 5 +2.5 = 7.5 hours

Total distance covered 400miles

Therefore average speed = 400/7.5 =53.33mph

Answer:

53.33 mph

Step-by-step explanation:

I just wanted to say that the other guy's answer is correct, I checked :)

Answer:

P( red, red, red no replacement ) =  2/17

P( 3 cards with same rank, no replacement) =  1/425

Step-by-step explanation:

There are 52 cards, 26 are red

P( red) =  red/total =26/ 52 = 1/2

Now draw the second card without replacement

There are 51 cards, 25 are red

P( red) =  red/total =25/51

Now draw the third card without replacement

There are 50 cards, 24 are red

P( red) =  red/total =24/50 = 12/25

P( red, red, red no replacement ) = 1/2 * 25/51 * 12/25 = 2/17

P ( all have the same rank)

There are 52 cards,  4 of each rank

We don't care what the first rank is, now the second and third draw have to have the same rank as the first

P( rank) = 1/1

Now draw the second card without replacement

There are 51 cards, 3 are left with the same rank

P( same rank) = cards with same rank/total = 3/51

Now draw the third card without replacement

There are 50 cards, 2 are left with the same rank

P( same rank) = cards with same rank/total = 2/50 = 1/25

P( 3 cards with same rank, no replacement) = 1 * 3/51*1/25 = 1/425

Answer:

3 and 8 are the extremes of the given proportion (first listed answer option)

Step-by-step explanation:

In a proportion of the type:

[tex]\frac{A}{B} =\frac{C}{D}[/tex]

the values "A" and "D" are called "extremes of the proportion, while "B" and "C" are called the "means" of the proportion.

This comes from writing it as:   A : B = C : D

where we observe that A and D are the more "extreme" values being further away from the equal sign than the quantities B and C which are more towards the middle (center of the proportion).

So in your case, the numbers 3 and 8 are the extremes

Answer:

3 and 8

Step-by-step explanation:

Answer:

2.52

Step-by-step explanation:

4.2 × 0.6

Multiply the terms.

= 2.52

Answer:

2.52

hope it helps

Step-by-step explanation:

4.2 x 0.6

To solve this first, you simply multiply 42*06

(Exclude the decimal point)

42 x 6

= 252

Now since there are two numbers after the point (one is 4.2 and one is 0.6)

Move 252 two decimal places to left

= 2.52

Answer:

Step-by-step explanation:

Please use " ^ " for exponentiation:  50 - x^2 = 0.

Solving for x^2, we get:                      x^2 = 50

Taking the square root of both sides:    x = ±√(50), or x = ±7.07

None of the three possible answers here is correct.