60 POINTS Explain the process and solve a logarithmic equation. log x + log 8 – 2log 4 = 7.

Answer:

18

Step-by-step explanation:

Do 72 divided by 4 because it is a square so all sides are equal

Hiya! ✌.ʕʘ‿ʘʔ.✌

Okay, so with a square, ALL sides are EQUAL.

To find the perimeter of a shape, you just need to add the measure of all sides together.

What you can do, is since all sides are equal, and a square has four sides, just get the measure of ONE side and multiply that by 4! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

The perimeter is 72 meters and if we find the value of u, we get the value of all sides.

Let's set this up as an equation:

P = 4u where P = perimeter and u = measure of one side

Let's insert the given value (72) into the equation for perimeter

72 = 4u

Now we have to solve for u, and to do that, we have to get it by itself on that side of the equation. u is being multiplied by 4, so do the opposite by dividing both sides of the equation by 4!

72/4=18

4u/4=u

Now our equation looks like this:

18 = u

So the value of u is 18! (✿◠‿◠)

To prove it, insert it into the formula... P = 4(18)... P = 72.

Boom! :D

Have a lovely day~ ≧◡≦

Answer:

60y

where y is the number of houses each volunteer can build

Step-by-step explanation:

I'll assume this is a complete question and i'll try to solve it the best way i can mathematically.

Let us assume that one volunteer can build a certain number of houses, say y houses.

Also, it is stated that the amount of houses that can be built varies directly as the with the number of volunteers. Therefore, it will be mathematically logical to say that if 1 volunteer can build y number of houses, then 60 volunteers will build 60y houses

Answer:

76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Step-by-step explanation:

Given:  In​ 1990, 28 % of babies in the United States were born to parents who were not married. This increased by approximately 0.6 % per year.

To find: year when 76 % of babies born out of​ wedlock

Solution:

A sequence is said to be in arithmetic progression if the difference between the terms is same.

For a sequence with first term as 'a' and common difference as 'd', the nth term is given by [tex]a_n=a+(n-1)d[/tex]

The given situation also forms an arithmetic progression with  [tex]a=28\,,\,d=0.6[/tex]

Also, put [tex]a_n=76[/tex]

So,

[tex]a_n=a+(n-1)d\\76=28+(n-1)(0.6)\\76-28=0.6(n-1)\\48=0.6(n-1)\\\frac{48}{0.6}=n-1\\\\80=n-1\\n=80+1\\n=81[/tex]

So, 76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Answer:

V=16x^5+8x^4+56x^3.

Step-by-step explanation:

The volume of the rectangular prism is V=16x^5+8x^4+56x^3.

Formula for rectangle prism: V=whl

Formula: L*W*H

Answer: V=16x^5+8x^4+56x^3

Hope this helps.

Answer:

Since Interquartile Range consider the middle values in the data set, i.e. 50%, it is not affected by outliers or extreme values. While other statistics mean, standard deviation and range are all affected by outliers or extreme values.

Step-by-step explanation:

hope this helps you :) can you help me please northc04 :(

Answer:

The answer is Interquartile Range. I know this is the right answer is because I got it right on a quiz.

Answer:

Step-by-step explanation:

Since; the density function diagrams were not included in the question; we will be unable to determine the  best which depicts this problem.

However;

Let use X to represent the time required for the delivery.

Then X~N(3.8 ,0.8)

i.e

E(x) = 3.8

s.d(x) = 0.8

NOW; P(x>4) = P(X-3.8/0.8 > 4-3.8/0.8)

= P(Z > 0.25)

= 1-P(Z < 0.25)

=1 - Φ (0.25)

= 1 - 0.5987  ( from Normal table  Φ (0.25) = 0.5987 )

= 0.4013

Thus;  the probability a single delivery would take more than 4 hours is 0.4013

What is the z value corresponding to the interval boundary?

The z value is calculated as:

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{4- 3.8}{0.8}[/tex]

z = 0.25

Answer:

D = 24 units

Step-by-step explanation:

Using Distance Formula

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(1-25)^2+(-3+3)^2}[/tex]

D = [tex]\sqrt{(-24)^2+(0)^2}[/tex]

D = [tex]\sqrt{576}[/tex]

D = 24 units

Answer:

ED = 8

Step-by-step explanation:

AC = 21 which means AE is 1/3 of the length of AC.

So, ED must also be 1/3 of the length of BC.

1/3 x 24 = 8

Answer: angle A = 72 and angle C = 72

Step-by-step explanation:

Angle A and C are opposites so they have to equal each other so do the equation 3y+27=5y-3. y would come out to be 15 and so to find the angles you would replace y with 15.

Answer:

The probability that a defective ball bearing was manufactured on a Friday = 0.375

Step-by-step explanation:

Let the event of making a mistake = M

The event of making a precision ball bearing production on Monday = Mo

The event of making a precision ball bearing production on Tuesday = T

The event of making a precision ball bearing production on Wednesday = W

The event of making a precision ball bearing production on Thursday = Th

The event of making a precision ball bearing production on Friday = F

the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04

4% on Wednesday, P(M|W) = 0.04

4% on Thursday, P(M|Th) = 0.04

8% on Monday, P(M|Mo) = 0.08

and 12% on Friday = P(M|F) = 0.12

The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.

P(Mo) = 0.20

P(T) = 0.20

P(W) = 0.20

P(Th) = 0.20

P(F) 0.20

The probability that a defective ball bearing was manufactured on a Friday = P(F|M)

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F)

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

We can obtain each of these probabilities by using the expression for conditional probability.

P(Mo n M) = P(M|Mo) × P(Mo) = 0.08 × 0.20 = 0.016

P(T n M) = P(M|T) × P(T) = 0.04 × 0.20 = 0.008

P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008

P(Th n M) = P(M|Th) × P(Th) = 0.04 × 0.20 = 0.008

P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

P(M) = 0.016 + 0.008 + 0.008 + 0 008 + 0.024 = 0.064

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F) = 0.024

P(M) = 0.064

P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375

Hope this Helps!

Answer:

24

Step-by-step explanation:

Y is 60% of 40

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 60% * 40

Converting percent to decimal:

p = 60%/100 = 0.6

Y = 0.6 * 40

Y = 24

Answer:

The standard error of the proportion is 0.0367.

Step-by-step explanation:

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.

For a proportion p in a sample of size n, the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.16, n = 100[/tex]

So

[tex]s = \sqrt{\frac{0.16*0.84}{100}} = 0.0367[/tex]

The standard error of the proportion is 0.0367.

Answer: 133 m^2

Step-by-step explanation:

The area of the parallelogram is:

[tex]A = b\times h=9.5\times14=133 m^2[/tex]

Answer:

The expression created is: [tex]3x^2+3x+8x-7[/tex]

Simplified, we obtain : [tex]3x^2+11x-7[/tex]

Step-by-step explanation:

We are to create an expression that satisfies the following conditions

Let the two like terms be 3x and 8x

Let the integer term = -7

Let the other term [tex]=3x^2[/tex]

Our written expression is therefore:

[tex]3x^2+3x+8x-7[/tex]

We simplify the expression by solving the like terms for a single term

[tex]3x+8x=11x\\$Therefore\\3x^2+3x+8x-7=3x^2+11x-7[/tex]

Answer:

A.

Step-by-step explanation:

Since VA and BC are equal in length so their central angles would also be equal.

So

<VWA = <BWC

32x-27 = 120

32x = 120+27

32x = 147

Dividing both sides by 32

x ≈ 4.6

Answer:

4.6

Step-by-step explanation:

3x-27=120

32x=147

x=147/32

x=4.59

x≈4.6

Answer:

The axis of symmetry is  -b/2a

The x-intercept shown is 3 units away from the axis of symmetry.

The other x-intercept also must be 3 units away from the axis of symmetry but on the opposite side.

Subtract 3 from the axis of symmetry.

The other x-intercept is  (-b/2a-3,0)

Step-by-step explanation:

Answer:

a.

Network             CBS   NBC   FOX   ABC

f                           9          9         1           6

Relative f          0.36     0.36    0.04     0.24

Percent f            36          36       4          24

b.

CBS and NBC have done best in presenting top-rated television shows.

The most top rated shows are from CBS and NBC while ABC network also has top rated shows but CBS and NBC percentages are higher.

Step-by-step explanation:

a.

Network        f Relative f  Percent f

CBS          9         0.36 36

NBC       9         0.36 36

FOX        1         0.04 4

ABC       6         0.24 24

"f" represents the frequency of network.

"Relative  f" represents relative frequency of Network.

"Percent f" represents percent frequency of Network.

Frequency is computed by counting the number of times value repeated in the data. So, the frequency distribution is

Network  Frequency

CBS         9

NBC         9

FOX         1

ABC         6

Relative frequency is computed by dividing the frequency to the sum of frequencies.

sum of frequencies=9+9+1+6=25.

So, the relative frequency distribution is

Network  Relative frequency

CBS          9/25=0.36

NBC         9/25=0.36

FOX         1/25=0.04

ABC         6/25=0.24

Percent frequency is computed by multiplying relative frequencies to 100.

So, the Percent frequency distribution is

Network    Percent frequency

CBS             0.36*100=36

NBC             0.36*100=36

FOX             0.04*100=4

ABC             0.24*100=24

b.

From frequencies, relative frequencies and percent frequencies we can see the CBS and NBC have equally higher cont of top rated shows comparative to ABC and  FOX. ABC has second highest top rated shows while Fox has least top rated shows among other networks.

Answer:

Step-by-step explanation:

The probability that the forester does not get the seedlings is 1/2 if the mean density of seedlings is 5 per square metre.

Density means the area within which a substance is collected or taken.

We have been given the mean density =5 square metre.

And we  have to calculate the probability that the forester will not get any seedlings.

So the probability that he will get the seedlings will be=5/10

which is 1/2

So the probability that he will not get the seedlings will be 1-1/2

that is 1/2.

Hence the probability that he will not get seedlings will be 1/2.

Learn more about probability at https://brainly.com/question/24756209

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Answer:

I got 35

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

5-8

-3

Answer:

=-3

Step-by-step explanation:

we have to find the difference when 8 is subtracted from 5

difference=5-8

the digit after from will come first

=-3

i hope it will help you

Answer:

X=0 and Y= 4(2i-1)/5

Step-by-step explanation:

Here is my solution, assuming that the equation equals 0. For y, just remember the definition of complex numbers and multiply by its conjugate.

The value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number:

(x + yi) + 2(3x - y) + 4i = 0

After arranging:

x + yi + 6x - 2y + 4i = 0

7x - 2y + yi + 4i = 0

7x - 2y + (y + 4)i = 0

7x - 2y = 0

y + 4 = 0

This is the linear equation in two variables:

Plug y = -4 in the other equation:

7x - 2(-4) = 0

7x = -8

x = -8/7

y = -4

Thus, the value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.

Learn more about the complex number here:

brainly.com/question/10251853

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Answer:

Step-by-step explanation:i really am lost,

The work rate for the associate is 5.3 hours.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given; Jane can paint the office by herself in 7 hours.

with an associate, she can paint the office in 3 hours.

The combined work rate is 3 hours per office.

WE need to find the work rate for the associate

Let the expression for the work rate be;

1/A+1/B= 1/T

1/7+1/B=1/3

1/B=1/3-1/7

1/B= 8-4/21

1/B= 4/21

B= 21/4

B=5.3 hours

Therefore, the work rate for the associate is 5.3 hours.

Learn more about equations here;

https://brainly.com/question/10413253

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Answer:

m = 3

Step-by-step explanation:

Assuming these shapes are similar, you can set up a proportion:

[tex]\frac{8}{12} =\frac{2}{m}[/tex]

→Cross multiply:

[tex]\frac{8m}{24}[/tex]

→Divide 24 by 8:

m = 3

Answer:

35

Step-by-step explanation:

Given

Sample of rat

Population = 36

Required

Find the degree of freedom.

Given that the sample is a single-sample t test;

A single-sample t test has just one parameter has its estimate;

And its degree of freedom is calculated as thus;

[tex]df = n - 1[/tex]

Where df represents the degree of freedom and n represents the sample size;

By substituting n = 36;

[tex]df = 36 - 1[/tex]

[tex]df = 35[/tex]

Hence, the degree of freedom of the sample of 36 rats for a single-sample t test is 35

Answer:

The degrees of freedom if we are conducting a test about the true mean are given by:

[tex] df =n-1[/tex]

And replacing the info given we got:

[tex] df = 36-1=35[/tex]

And the best option would be:

35

Step-by-step explanation:

For this case we know that the sample size is n=36.

The degrees of freedom if we are conducting a test about the true mean are given by:

[tex] df =n-1[/tex]

And replacing the info given we got:

[tex] df = 36-1=35[/tex]

And the best option would be:

35

Answer:

8.62% probability that all have the same color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected 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]

What is the probability that all have the same color?

Desired outcomes:

Either all red(from a set of 9), all white(from a set of 9) or all blue(from a set of 8). So

[tex]D = C_{9,3} + C_{9,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{9!}{3!6!} + \frac{8!}{3!5!} = 224[/tex]

Total outcomes:

3 marbles, from a set of 9 + 9 + 8 = 26. So

[tex]T = C_{26,3} = \frac{26!}{3!23!} = 2600[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{224}{2600} = 0.0862[/tex]

8.62% probability that all have the same color

Answer:

The three numbers are 1, 2, and 4.

Step-by-step explanation:

[tex]x+y+z=7\\3x+1=z\\z+x=5[/tex]

From these equations, we get:

[tex]x=1\\y=2\\z=4[/tex]

Which fits all the equations we have written.