By converting to an exponential expression, solve log2 (x + 5) = 4

Answer:

Step-by-step explanation:

If J can paint a room in 3 hours, in 1 hour she gets [tex]\frac{1}{3}[/tex] of the job done.

If A can paint a room in 4 hours, in 1 hour she gets [tex]\frac{1}{4}[/tex] of the job done. We need to find out how long it takes them if they paint together. The equation for this is:

[tex]\frac{1}{3}+\frac{1}{4}=\frac{1}{x}[/tex] where x is the number of hours it takes them to get the job done together. Multiply everything through by 12x to get

4x + 3x = 12 so

7x = 12 and

x = 1.7 hours to get the room painted together.

Answer:

Decison region :

Reject H0 : if χ² > 6.251

12.229

Step-by-step explanation:

Given :

Manufacturer A B C D

Unacceptable 29 17 9 22

Acceptable 171 183 191 178

Total 200 200 200 200

H0: There is no relationship between quality and manufacturer.

H1: There is a relationship.

Testing using the goodness of fit :

Chisquare = (observed - Expected)² / Expected

Expected Values:

19.25 19.25 19.25 19.25

180.75 180.75 180.75 180.75

Chi-Squared Values:

4.93831 0.262987 5.45779 0.392857

0.525934 0.0280083 0.581259 0.0418396

χ² = 4.93831 + 0.262987 + 5.45779 + 0.392857

+ 0.525934 + 0.0280083 + 0.581259 + 0.0418396 = 12.229

Degree of freedom, df = (4-1)(2-1) = 3*1= 3

The critical value,

χ² at 0.10, 3 = 6.251

Decison region :

Reject H0 : if χ² > 6.251

Reject H0 : 12.229 > 6.251

Answer:

hope you find it useful and helpful

Answer:

Yes

Step-by-step explanation:

Yesterday would be Thursday and the day after next would be Sunday

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Answer:

  snow

Step-by-step explanation:

The relationship between temperature and altitude is given as ...

  T = -2 +((13000 -a)/1000)×2.1

We can put a=2000 into this equation to find the temperature at that altitude.

  T = -2 +((13000 -2000)/1000)×2.1 = -2 +11(2.1) = -2 +23.1 = 21.1

The airport temperature of 21.1 °F is below 32 °F, so we expect the precipitation to be snow.

Answer:

d(A,B)=100

Step-by-step explanation:

The distance between two points A([tex]x_A,y_A[/tex]) and B=([tex]x_B,y_B[/tex]) is:

d(A,B)=[tex]\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]

In this case:

[tex]x_B = - 93\\x_A = 3\\y_B = -37\\y_A = -9[/tex]

In this case:

[tex]d(A,B)=\sqrt{( - 93 -3)^2+( - 37 - (-9))^2} =\\=\sqrt{( - 96)^2+(-28)^2} =\\=\sqrt{9.216+784} \\=\sqrt{10000}=\\=\sqrt{10^4} =\\=100[/tex]

Answer:

tow degree of freedom.

this inform I know that from vibration method

Answer:

6x -15

Step-by-step explanation:

plug in gx for x in fx. So you have 2(3x-9) + 3

Answer:

Ok so on a clock there is 12 numbers where 12 is on top so at 12 am and 12 pm noon and midnight you will be at the top of the clock

Hope This Helps!!!

During the ride on the London Eye, you will be at the same height as the top of the Elizabeth Tower at approximately 21 minutes and 43.16 seconds after the start of the ride.

To determine the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower (commonly known as Big Ben), we need to consider the height of the London Eye and its rotational motion.

Given that the Elizabeth Tower is 320 feet tall, we need to find the position of the London Eye when its height aligns with the top of the tower.

The London Eye has a height of 443 feet, and it completes one full rotation in approximately 30 minutes (or 1800 seconds). This means that it moves at a constant angular velocity of 360 degrees per 1800 seconds.

To find the time(s) when the heights align, we can set up a proportion:

(Height of the Elizabeth Tower) / (Height of the London Eye) = (Angle covered by the London Eye) / 360 degrees

Substituting the given values:

320 / 443 = (Time to align) / 1800

Simplifying the equation:

(Time to align) = (320 / 443) * 1800

Calculating the value:

(Time to align) ≈ 1303.16 seconds

Converting the time to minutes and seconds:

(Time to align) ≈ 21 minutes and 43.16 seconds

Therefore, during the ride on the London Eye, you will be at the same height as the top of the Elizabeth Tower at approximately 21 minutes and 43.16 seconds after the start of the ride.

To know more about  London Eye. here

https://brainly.com/question/16401602

#SPJ2

Answer:

Step-by-step explanation:

we are given  the angles ∠5 , ∠4 , ∠3 , but with one variable,  "X"  :)

also we are told ∠AOC is bisected by OB , meaning that ∠1 = ∠2

and the EC is perpendicular to OD ,  so ∠4+∠5=90°

since we are given ∠4 & ∠5,  lets use that to solve for "X"

:)

90= x-6 + 2x+4

90= 3x -2

92 =3x

30[tex]\frac{2}{3}[/tex] ° = x

30.6666666666666666 ° = x

Answer:

24

Step-by-step explanation:

18 times 5 is 90 so that means that the given numbers have to add up to 90 (including x)

so,

6+10+20+30=66

90-66=24

I hope this helps!

Answer:

[tex]x = 24[/tex]

Step-by-step explanation:

[tex]6 + 10 + x + 20 + 30 = 18[/tex]

There are 5 numbers that we must add to average out to get 18 so let set this equation up

[tex] \frac{6 + 10 + x + 20 + 30}{5} = 18[/tex]

[tex]6 + 10 + x + 20 + 30 = 90[/tex]

[tex]x = 24[/tex]

Answer: Simply the expression = 5

Step-by-step explanation:

Simplify = 5

Step-by-step explanation:

-5-(-10) = -5+10 = 5

Therefore the answer of your question is 5.

Mark me as the brainliest answer.

Answer:

Point C represents the unit rate

Step-by-step explanation:

Answer:

[tex]z + 4 = 15 \\ z + 4 - 4 = 15 \\ z = 15 - 4 \\ z = 11[/tex]

z>11

*see attachment for missing diagram

Answer:

AC = 5 and BC = 5√3

Step-by-step explanation:

Given:

m<A = 60°

m<B = 30°

AB = 10

Required:

AC and BC

Solution:

Recall, SOH CAH TOA

✔️Find AC:

Reference angle (θ) = 30°

Hypotenuse = 10

Opposite = AC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 30° = AC/10

10*Sin 30° = AC

10*½ = AC (sin 30° = ½)

5 = AC

AC = 5

✔️Find BC:

Reference angle (θ) = 60°

Hypotenuse = 10

Opposite = BC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 60° = BC/10

10*Sin 60° = BC

10*√3/2 = BC (sin 60° = √3/2)

5*√3 = BC

BC = 5√3

Answer:

I guess the question is incomplete

Answer:

0.3209

in case you dont know  A z-score tells you if the distribution it comes from is normal.

Step-by-step explanation:

Answer:

To divide a decimal by another decimal:

Move the decimal point in the divisor to the right until it is a whole number.

Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.

Then divide the new dividend by the new divisor

Step-by-step explanation:

see in the example

Answer:

-3

Step-by-step explanation:

12x + 1 - 2(y + 2)

=> 12x + 1 - 2y - 4

=> 12x - 3 - 2y

Answer:

-3

Step-by-step explanation:

12x+1-2y-4

12x+1-2y-4

12x-2y-3

Answer:

504 arrangements are possible

Step-by-step explanation:

Arrangements of n elements:

The number of arrangements of n elements is given by:

[tex]A_{n} = n![/tex]

Arrangements of n elements, divided into groups:

The number of arrangements of n elements, divided into groups of [tex]n_1, n_2,...,n_n[/tex] elements is given by:

[tex]A_{n}^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n!}[/tex]

In this case:

9 pens, into groups of 5, 3 and 1. So

[tex]A_{9}^{5,3,1} = \frac{9!}{5!3!1!} = 504[/tex]

504 arrangements are possible

Step-by-step explanation:

solved in the diagram above

I hope it helps you

Answer:

Step-by-step explanation:

Arrival rate = ∧ = 2.2 customers per hour  

Service rate = u = 5 customers per hour  

1. Probability that one customer is receiving a haircut and one customer is waiting  

P(2 customers)=(∧/u)^2 * (1-∧/u)=(2.2/5)^2 * (1-2.2/5)=0.1936*0.56= 0.108416

2. Probability that one customer is receiving a haircut and two customers are waiting  

P(3 customers)= (∧/u)^3 * (1-∧/u)=(2.2/5)^3 * (1-2.2/5)= 0.085184  

* 0.56= 0.04770304

3. Probability that more than two customers are waiting  

P(more than 3 customers)=1- P(less than 3 customers) =  

1- [P(0)+P(1)+P(2)+P(3)]=  

= 1- [(1-2.2/5) +2.2/5*(1- 2.2/5) + 0.108416+0.04770304]=1-0.9625=0.0375

Answer:

The z-score for this data is Z = -0.26.

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 normal distributions can be solved using the z-score formula.

In a set 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]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

This is based on knowledge that in the U.S., the mean PAL is 1.65 and the standard deviation is 0.55.

This means that [tex]\mu = 1.65, \sigma = 0.55[/tex]

A study took a random sample of 51 people who lived in low income neighborhoods and found their mean PAL to be 1.63.

This means that [tex]n = 51, X = 1.63[/tex]

Using a one-sample z test, what is the z-score for this data

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

By the Central Limit Theorem

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

[tex]Z = \frac{1.63 - 1.65}{\frac{0.55}{\sqrt{51}}}[/tex]

[tex]Z = -0.26[/tex]

The z-score for this data is Z = -0.26.

Answer:

:D

Step-by-step explanation:

Cost of sales. Administrative expenses. Distribution costs. Property costs. Depreciation. [13]. Page 6. 6. © UCLES 2019. 9706/23/M/J/19.

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Answer:

  1,222,200

Step-by-step explanation:

A search using a computer program found ...

  5432 × 225 = 1,222,200

__

1000 mod 225 = 100

4 × 225 = 900

This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.

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Answer:

  C, E

Step-by-step explanation:

The solutions are found by setting each of the factors to zero:

  3x -4 = 0 . . . . . matches C

  x +2 = 0 . . . . . matches E

Answer:

1.5/2

Step-by-step explanation:

slope formula = y2-y1/ x2 - x1

point one (2,0)

point 2 (0, 1.5)

you dont really need to subtract anything because the intercepts, so the slope is 1.5/2

(slope or m = 1.5 - 0 / 2 - 0 )

x intercept = value of x when y is 0

y intercept = value of y when x is 0

Answer:

x = 5 and y = 1.5

Step-by-step explanation:

hope this helps please like and mark as brainliest

Answer:

Length of first cut = 140

Length of second cut = 60

Step-by-step explanation:

Given:

Length of wire = 200

Find:

Length of each cut

Computation:

Assume;

Side of first square = x/4

Side of second square = [200 - x] / 4 = 50 - x/4

So,

[x/4]² - [50 - x/4]²

x²/16 - x²/16 - 2500 + 25x = 1000

- 2500 + 25x = 1000

25x = 3500

x = 140

Side of first square = 140/4

Side of first square = 35

Side of second square = 50 - 140/4

Side of second square = 15

Length of first cut = 4 x 35

Length of first cut = 140

Length of second cut = 200 - 140

Length of second cut = 60

Answer:

60 ft and 140 ft

Step-by-step explanation:

Total length = 200 ft

Let the length of one piece is L and other is 200 - L.

[tex]1000 + \left (\frac{L}{4} \right )^2 = \left ( \frac{200 - L}{4} \right )^2\\\\16000 +L^2 = 40000 + L^2 - 400 L\\\\L= 60 ft[/tex]

So, the length of the other piece is 140 ft.

Given:

[tex]\phi=1.618[/tex]

22nd number in Fibonacci sequence = 17,711

To find:

The 23rd number in the Fibonacci sequence.

Solution:

The nth term of a Fibonacci sequence is:

[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]

Substituting [tex]\phi=1.618, n=21[/tex], we get

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=10941.1724024[/tex]

[tex]f_{21}\approx 10941[/tex]

Now,

[tex]f_{23}=f_{21}+f_{22}[/tex]

[tex]f_{23}=10941+17711[/tex]

[tex]f_{23}=28652[/tex]

It is about 28,656. Therefore, the correct option is D.