Divide: ((p^2-q^2)/(p+q)) ÷ ((p-q)/(p+q))

Answer:  nice and funnyyyyy y=4

Step-by-step explanation:

Answer:

The null and alternative hypothesis for this problem are:

[tex]H_0:\mu=380\\\\H_a: \mu>380[/tex]

Step-by-step explanation:

The alternative hypothesis shows the claim of the researchers. In this case, that the new type of fertilizer significantly increase the actual yield with the old fertilizer:

[tex]H_a: \mu>380[/tex]

The null hypothesis is the hypothesis to be nullified, so it states that the claim is not true and the yield is the same (or, at least, not significantly higher) as with the old fertilizer:

[tex]H_0: \mu=380[/tex]

Answer:

3 Pages

Step-by-step explanation:

In the first instance, the student has time to read 50 pages of psychology and 10 pages of economics.

The student could read 30 pages of psychology and 70 pages of economics.

Since the two situations take the same amount of time, we have:

50p+10e=30p+70e

Collect like terms

50p-30p=70e-10e

20p=60e

Divide both sides by 20

p=3e

Therefore, in the time it will take the student to read 1 page of psychology, the student can read 3 pages of economics.

Answer:

idk dont ask me

Step-byi-step explanation:

Answer:

a+b+c=2003

a+b=814

2003-819=189

Step-by-step explanation:

Answer:

56%

Step-by-step explanation:

Percent means out of 100

56/100

56 out of 100

56%

Answer:

56%

Step-by-step explanation:

How much is 56 out of 100 written as a percentage? Convert fraction (ratio) 56 / 100 Answer: 56%

Answer:

A. The probability that a randomly selected sports car from this manufacturer will be white with gray upholstery is P=0.12.

B. Assuming that we know the car has tan upholstery, the probability that the car is either silver or white is P=0.50.

Step-by-step explanation:

We first start by stating that the events "exterior color" and "leather color" are independent, so the probability of the outcomes of each event is not affected by the outcomes of the other event.

A. The probability of having a car that is white (W) with gray upholstery (G) is equal to the probability of having a car that is white multiplied by the probability of having a car with gray leather upholstery. Mathematically, this is:

[tex]P(\text{W\&G})=P(W)\cdot P(G)=0.3\cdot 0.4=0.12[/tex]

B. As the events are independent, the probability of having a silver or white car, given that the car has tan upholstery, is the same as the probabiltiy of having a silver or white car:

[tex]P(S\,or\,W | T)=P(S\,or\,W)=P(S)+P(W)=0.20+0.30=0.50[/tex]

Answer:

∠E≅∠P || Given

∠EKG≅∠PKM || Vertical angles

EK≅KP || Midpoint Theorem

EKG≅PKM || AAS(Angle Angle Side)

EG≅MP || CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Step-by-step explanation:

Properties of the logarithm: for any base of logarithm,

log(a*b) = log(a) + log(b)

If we replace b with 1/b, or b^-1, we have

log(a/b) = log(a) + log(1/b) = log(a) - log(b)

since

log(1/b) = log(b^-1) = - log(b)

using the power property of logarithms,

log(b^n) = n log(b)

Now,

ln35 = ln(5*7) = ln5 + ln7

ln(1/7) = - ln7

ln25 = ln(5^2) = 2 ln5

Putting everything together, we have

(ln35 + ln(1/7))/ln25 = (ln5 + ln7 - ln7)/(2 ln5) = ln5/(2 ln5) = 1/2

Answer:

It is multiplied by a factor of 8

Step-by-step explanation:

Every month, the number of people who receive the email is multiplied by a factor of 8.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

Venera sent a chain letter to her friends, asking them to forward the letter to more friends.

The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:

[tex]\rm P(t) = 2^{3t+7}[/tex]

Every month, the number of people who receive the email is multiplied by a factor will be

For t = 2, we have

P(2) = 2³⁽²⁾⁺⁷

P(2) = 2¹³

For t = 3, we have

P(3) = 2³⁽³⁾⁺⁷

P(3) = 2¹⁶

Then the factor will be

⇒ P(3) / P(2)

⇒ 2¹⁶ / 2¹³

⇒ 2³

⇒ 8

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Answer:

807,205

Step-by-step explanation:

Take the eight hundred and seven thousand and express that has 807,000. Then, add the two hundred and five at the end to get 807,205

The given statement is written in figures 807,205.

The given statement is eight hundred and seven thousand, two hundred and five in figures.

We need to write the given statement as the number.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

Now, eight hundred and seven thousand, two hundred and five=807,205.

Therefore, the given statement is written in figures 807,205.

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Answer:

Step-by-step explanation:

Hello!

The table shows the daily sales (in $1000) of shopping mall for some randomly selected  days

Sales 1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5

Days 18 27 31 40 56 55 23

Use it to answer questions 13 and 14.

13. What is the approximate value for the modal daily sales?

To determine the Mode of a data set arranged in a frequency table you have to identify the modal interval first, this is, the class interval in which the Mode is included. Remember, the Mode is the value with most observed frequency, so logically, the modal interval will be the one that has more absolute frequency. (in this example it will be the sales values that were observed for most days)

The modal interval is [3.1-3.5]

Now using the following formula you can calculate the Mode:

[tex]Md= Li + c[\frac{(f_{max}-f_{prev})}{(f_{max}-f_{prev})(f_{max}-f_{post})} ][/tex]

Li= Lower limit of the modal interval.

c= amplitude of modal interval.

fmax: absolute frequency of modal interval.

fprev: absolute frequency of the previous interval to the modal interval.

fpost: absolute frequency of the posterior interval to the modal interval.

[tex]Md= 3,100 + 400[\frac{(56-40)}{(56-40)+(56-55)} ]= 3,476.47[/tex]

A. $3,129.41 B. $2,629.41 C. $3,079.41 D. $3,123.53

Of all options the closest one to the estimated mode is A.

14. The approximate median daily sales is …

To calculate the median you have to identify its position first:

For even samples: PosMe= n/2= 250/2= 125

Now, by looking at the cumulative absolute frequencies of the intervals you identify which one contains the observation 125.

F(1)= 18

F(2)= 18+27= 45

F(3)= 45 + 31= 76

F(4)= 76 + 40= 116

F(5)= 116 + 56= 172 ⇒ The 125th observation is in the fifth interval [3.1-3.5]

[tex]Me= Li + c[\frac{PosMe-F_{i-1}}{f_i} ][/tex]

Li: Lower limit of the median interval.

c: Amplitude of the interval

PosMe: position of the median

F(i-1)= accumulated absolute frequency until the previous interval

fi= simple absolute frequency of the median interval.

[tex]Me= 3,100+400[\frac{125-116}{56} ]= 3164.29[/tex]

A. $3,130.36 B. $2,680.36 C. $3,180.36 D. $2,664

Of all options the closest one to the estimated mode is C.

Answer:

14.69% probability that defect length is at most 20 mm

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

[tex]\mu = 28, \sigma = 7.6[/tex]

What is the probability that defect length is at most 20 mm

This is the pvalue of Z when X = 20. So

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

[tex]Z = \frac{20 - 28}{7.6}[/tex]

[tex]Z = -1.05[/tex]

[tex]Z = -1.05[/tex] has a pvalue of 0.1469

14.69% probability that defect length is at most 20 mm

Answer:

1. 100[tex]\pi[/tex]

2. 27 [tex]cm^{3}[/tex]

3. 30

Step-by-step explanation:

Area = [tex]\pi[/tex][tex]r^{2}[/tex]

       = [tex]\pi[/tex] x [tex]10x^{2}[/tex]

       = 100[tex]\pi[/tex]

Volume = l x w x h

             = 3 x 3 x 3

             = 27

Answer:

48

Step-by-step explanation:

Esinam shere a common ratio hence,

the lcm of 3 and 5 is 15

Kissi:Esinam= 9:15 and Esinam:Lariba=15:25

Combining; 9:15:25

Let x be the ages such that,

Kissi=9x and Esinam=15x and Lariba=25x

9x+15x+25x=147

49x=147

x=3

Youngest; Kissi=9x=9(3)=27

Oldest; Lariba=25x=25(3)=75

Difference 75-27=48

Answer:  B) Scott sold 1 van

Step-by-step explanation:

A₂,₃ represents:  matrix A - 2nd row - 3rd column

The second row is Scott and and the 3rd row is Vans

If you look at Scott - Vans, you will see that Scott sold 1 van.

Answer:

32 cm²

Step-by-step explanation:

6*4+ 1/2*4*4= 32 cm²

Answer: -8

Step-by-step explanation:

Answer:

Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]

The statistic is given by:

[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]

And replacing we got:

[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]

And the best option would be:

2.19

Step-by-step explanation:

We have the following info given:

n1 = 150 n2 = 275

[tex]\bar x_1 = 72.86, \bar x_2 = 67.34[/tex]

s1 = 15.98 s2 = 35.67

We want to test the following hypothesis:

Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]

The statistic is given by:

[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]

And replacing we got:

[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]

And the best option would be:

2.19

Answer:

2.75 or 2 3/4

Step-by-step explanation:

so here you use the recipricle of 1/3. so you would do 11/12 X 3/1 =33/12= 2 3/4

Answer: 11/4

Step-by-step explanation:

to divide a fraction by another, you multiply by the reciprocal(the opposite of a certain fraction). the reciprocal of 1/3 is 3/1. so:

[tex]\frac{11}{12} / \frac{1}{3} = \frac{11}{12} * \frac{3}{1} = \frac{33}{12} = \frac{11}{4}[/tex]       (divide both sides by 3 to simplify for the last one)

Answer:

300/60=5 more words per minute

80+5 = 85 words per minute

or

80 x 60 = 4800 + 300 = 5100

5100 / 60 = 85 words per minute

Hope this helps

Step-by-step explanation:

Answer:

11.51% probability that the mean annual salary of the sample is between $71000 and $73500

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 = 74000, \sigma = 2500, n = 36, s = \frac{2500}{\sqrt{36}} = 416.67[/tex]

What is the probability that the mean annual salary of the sample is between $71000 and $73500?

This is the pvalue of Z when X = 73500 subtracted by the pvalue of Z when X = 71000. So

X = 73500

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

By the Central Limit Theorem

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

[tex]Z = \frac{73500 - 74000}{416.67}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151

X = 71000

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

[tex]Z = \frac{71000 - 74000}{416.67}[/tex]

[tex]Z = -7.2[/tex]

[tex]Z = -7.2[/tex] has a pvalue of 0.

0.1151 - 0 = 0.1151

11.51% probability that the mean annual salary of the sample is between $71000 and $73500

Answer:

-16x^5

Step-by-step explanation:

f(x)=x^3+10x^2-25x-250

f(x) = x^3-15x+x^2-250

f(x) = x^5-15x-250

f(x) = x^5 -x + 16

f(x) = -x^5+16

f(x) = -16x^5

// have a great day //

Answer:

a) -8/9

b) The series is a convergent series

c) 1/17

Step-by-step explanation:

The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.

If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r

a is the first tern of the series.

a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;

∑(-8)^(n−1)/9^n

= ∑(-8)^(n−1)/9•(9)^n-1

= ∑1/9 • (-8/9)^(n−1)

From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9

The common ratio r = -8/9

b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.

c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.

S∞ = a/1-r

Given a = 1/9 and r = -8/9

S∞ = (1/9)/1-(-8/9)

S∞ = (1/9)/1+8/9

S∞ = (1/9)/17/9

S∞ = 1/9×9/17

S∞ = 1/17

The sum of the geometric series is 1/17

Answer:

The number of the possible outcomes are:

12,13,14,15,16,17

21,23,24,25,26,27

31,32,34,35,36,37

41,42,43,45,46,47

51,52,53,54,56,57

61,62,63,64,65,67

71,72,73,74,75,76

The total number of possible outcomes = 42

Step-by-step explanation:

Given that :

the numbers 1 through 7 are written on different pieces of paper; &

Two of these numbered pieces of paper are selected without replacement;

Also,

a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.

Then:

if the first number drawn is 1 , then the possible outcomes will be :

12,13,14,15,16,17

If the  first number drawn is 2; then the possible outcomes will be:

21,23,24,25,26,27

If the  first number drawn is 3; then the possible outcomes will be:

31,32,34,35,36,37

If the  first number drawn is 4; then the possible outcomes will be:

41,42,43,45,46,47

If the  first number drawn is 5; then the possible outcomes will be:

51,52,53,54,56,57

If the  first number drawn is 6; then the possible outcomes will be:

61,62,63,64,65,67

If the  first number drawn is 7; then the possible outcomes will be:

71,72,73,74,75,76

The number of the possible outcomes are:

12,13,14,15,16,17

21,23,24,25,26,27

31,32,34,35,36,37

41,42,43,45,46,47

51,52,53,54,56,57

61,62,63,64,65,67

71,72,73,74,75,76

The total number of possible outcomes = 7 × 6 = 42

Answer:

Base of the Pennant = 330 pixels

Scale Factor =0.6

Step-by-step explanation:

The base measure of the pennant on screen is 550 pixels.

The height  is 275 pixels.

[tex]A$spect Ratio=\dfrac{Base}{Height}=\dfrac{550}{275} =2:1[/tex]

If Charlotte resizes the pennant, keeping the aspect ratio  constant.

Height = 165 pixels

Therefore:

[tex]\dfrac{Base}{165}=\dfrac{2}{1} \\\\$Base= 2 *165 =330[/tex]

Therefore, the scale factor of the dilation  [tex]=\dfrac{330}{550}= \dfrac{165}{275}=0.6[/tex]

Base of the Pennant = 330 pixels

Scale Factor =0.6

Answer:

C

Step-by-step explanation:

It closely resembles to a sphere.

Answer:

[tex]y^2+88y+484[/tex]

Step-by-step explanation:

[tex]4(y+11)^2-3y^2= \\\\4(y^2+22y+121)-3y^2= \\\\4y^2-3y^2+88y+484= \\\\y^2+88y+484[/tex]

Hope this helps!

Answer:

  698 cm²

Step-by-step explanation:

The volume is given by ...

  V = LWH

Filling in the given values, we have ...

  1020 = (17)(5)y . . . . . . . using L=17, W=5, H=y

  y = 1020/(17·5) = 12

The surface area is given by ...

  A = 2(LW +H(L+W))

  A = 2(17·5 +12(17+5)) = 2(85 +264) . . . . . . . using L=17, W=5, H=y=12

  A = 698 . . . . square centimeters

Answer:

answer c.

y <= x - 2 and y >= x + 1

Step-by-step explanation:

You wrote the given answers wrong. Here are the right choices that are given as possible solutions:

O y >= x - 2 and y <= x + 1

O y < x - 2 and y > x + 1

O y <= x - 2 and y >= x + 1

O y > x - 2 and y < x + 1

The graph clearly shows two lines and the intended area is shaded and it is clearly including the lines.

Because the lines are included in the solution, by that alone, you can exclude two answers b and d.

Now you still need to decide between the in equalities in answer a and c. Both lines have a gradient of 1, so that does not help to distinguish...

The y intercept of the top line is at y= +1 and the shaded area is bigger then that....

By now it is absolutely clear that answer c must be the right answer and you are done!

EXTRA

Although you have deduced beyond any doubt, that answer c must be the right answer, you still can check your findings 'to be sure' by looking and checking for the bottom line...

BE CAREFUL, ONLY DO THIS IF YOU HAVE ENOUGH TIME. Again, you already know the right answer, and this is "just to confirm", so what is the harm in that?

By double checking yourself, it will sort of "undermine" your appproach. Basically you are doing something which is strictly spoken not nessasary any more. So I urge you to basically step over the urge to check yourself, and stick to your answer.

However, if you can not resit the temptation of checking to see if you actually found the right answer, you could test the y intercept of the bottom line, which is at y= -2 and the shaded area is smalller then that....

So again, it is now confirmed that answer c is indeed the right answer.

The correct system of linear inequalities is represented by the graph are,

⇒ y > x - 2

⇒ y < x + 1

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The system of linear inequalities is shown in graph.

Hence, By graph;

The value of y - intercepts are,

⇒ - 2 and - 1

Hence, The correct system of linear inequalities is represented by the graph are,

⇒ y > x - 2

⇒ y < x + 1

Thus, The correct system of linear inequalities is represented by the graph are,

⇒ y > x - 2

⇒ y < x + 1

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