2. Solve the following:
a. When six is added to four times a number the result is 50. Find the number.
b. The sum of a number and nine is multiplied by -2 and the answer is -8. Find the
number.
c. The length of a rectangular map is 37,5 cm and the perimeter is 125 cm. Find the
width.​

Answer:

Graph (a)

Step-by-step explanation:

Given

[tex]y = \sqrt[3]{x+ 6} -3[/tex]

Required

The graph

First, calculate y, when x = 0

[tex]y = \sqrt[3]{0+ 6} -3[/tex]

[tex]y = \sqrt[3]{6} -3[/tex]

[tex]y = -1.183[/tex]

The above value of y implies that the graph is below the origin when x = 0. Hence, (c) and (d) are incorrect because they are above the origin

Also, only the first graph passes through point (0,-1.183). Hence, graph (a) is correct

Answer:

the answer is A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the function for this graph is:

[tex]y = {(x - 1)}^{2} [/tex]

so the domain (the input AKA THE x values) is all the real numbers.

Answer:

12

Step-by-step explanation:

Answer:

2ab(3b^2+2a+4)

Step-by-step explanation:

6ab^3 + 4a^2b + 8ab

2*3*a*b*b^2 +2*2*a*a*b +2*2*2*a*b

Factor out the common terms

2ab( 3*b^2 +2*a +2*2)

2ab(3b^2+2a+4)

Answer:

(w^3)^8 * (w^5)^5 = w^49

Step-by-step explanation:

(w^24) * (w^25)

using exponent rule

w^24 • w^25 = w^24+25

w^49

Answer:

Step-by-step explanation:

(W^24)*(W^25)

W^24+25

=W^49

Answer:

is the second answer 2x+1/x-1

Answer:

-36/7

Step-by-step explanation:

-22-14=6x+x

-36=7x

-36/7=7x/7

x=-36/7

Answer:

4(a).

Expression of dy/dx :

[tex]{ \tt{ \frac{dy}{dx} = - 2(3 - 2x) {}^{2} + 24}}[/tex]

5(a).

[tex]{ \tt{ \frac{dy}{dx} = 54 - 2(2x - 7) {}^{2} }}[/tex]

Answer:

Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.

Step-by-step explanation:

Take a number, x.

Now increase it by 5%.

1.05x

Now increase it by 20%.

1.2 * 1.05x = 1.26x

1.26x = 126% of x = 100% of x + 26% of x

100% of x is the same as x, so it is the same as the original x.

The increase is 26% of the original number.

Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.

Answer:

0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

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]

Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population.

This means that [tex]p = 0.34, n = 124[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.34[/tex]

[tex]s = \sqrt{\frac{0.34*0.66}{124}} = 0.0425[/tex]

What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?

This is the p-value of Z when X = 0.31, so:

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

[tex]Z = \frac{0.31 - 0.34}{0.0425}[/tex]

[tex]Z = -0.705[/tex]

[tex]Z = -0.705[/tex] has a p-value of 0.2405.

0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

Answer:

46,000 yards

Step-by-step explanation:

if in the hundreds place the number is 0-499 round down

if it's 500-999 round up

Answer:

faster and smarter Homes its b

Step-by-step explanation:

I did this one

Answer:

b

Step-by-step explanation:

Work Shown:

1 pound = 16 ounces

4*(1 pound) = 4*(16 ounces)

4 pounds = 64 ounces

Answer:

B. 28, 32, 36 millions

Step-by-step explanation:

Given:

P(t) = 24 + 0.4t

Where,

P(t) = population in millions

t = number of years

✔️Value of the population when t = 10:

Plug in t = 10 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(10)

P(t) = 24 + 4

P(t) = 28 million

✔️Value of the population when t = 20:

Plug in t = 20 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(20)

P(t) = 24 + 8

P(t) = 32 million

✔️Value of the population when t = 30:

Plug in t = 30 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(30)

P(t) = 24 + 12

P(t) = 36 million

let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. Note that there can be the possible outcomes  

h-h, h-t, t-h, t-t.  

How this affects the possibility of two dogs & two cats. Note that there are 1/2 a chance of getting those two (with the others being one of each), which means that out of 4 chances, 2 are allowed.  

2/4 = 1/2  

50% is your answer

Heads represents cats and tails represents dogs. There is two coins because we are checking the probability of two pets. You have to do the experiment to get your set of data, once you get your set of data, you will be able to divide it into the probability for cats or dogs. To change the simulation to generate data for 3 pets, simply add a new coin and category for the new pet.

Hope this helps you out!

Answer:

25288

Step-by-step explanation:

shown in the picture

9514 1404 393

Answer:

  (b)  x = 1

Step-by-step explanation:

A graph shows the solution to f(x) = g(x) is x = 1.

__

We want to solve ...

  g(x) -f(x) = 0

  x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0

  x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping

  (x^2 -1)(x +2) +11/3(x -1) = 0 . . . . .  . the difference of squares can be factored

  (x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor

  (x -1)(x^2 +3x +2 +11/3) = 0

The zero product rule tells us this will be true when x-1 = 0, or x = 1.

__

The discriminant of the quadratic factor is ...

  b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3

This is less than zero, so any other solutions are complex.

Answer:

5/4

Step-by-step explanation:

Use the slope formula which is y2-y1/x2-x1.

1. Plug the given values into the equation: 3-(-7)/4-(-4)=5/4

9514 1404 393

Answer:

  15

Step-by-step explanation:

For numbers to be divisible by 3, the sum of their digits must be divisible by 3.

This means we require ...

  (7 + 1 + 2 + 3 + A + 3 + 2) mod 3 = 0   ⇒   A mod 3 = 0

  (2 + B + 2 + 5 + 6 + 8 + 9) mod 3 = 0   ⇒   (2+B) mod 3 = 0   ⇒   B mod 3 = -2

  (4 + 5 + 0 + A + B + C + 6) mod 3 = 0   ⇒   (C -2) mod 3 = 0

Possible values of C are 2, 5, 8. Their sum is 15.

_____

For example, let A=0, B=1, C=2. Then we have ...

  7123032 = 2374344×3

  2125689 = 708563×3

  4500126 = 1500042×3

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]2^{60} =2^{2 \times 30} =(2^{2} )^{30}=4^{30}[/tex]

Answer:

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

Step-by-step explanation:

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.

Mean of 10 minutes and a standard deviation of 3 minutes

This means that [tex]\mu = 10, \sigma = 3[/tex]

Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.

This is 1 subtracted by the p-value of Z when X = 15, so:

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

[tex]Z = \frac{15 - 10}{3}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a p-value of 0.9525.

1 - 0.9525 = 0.0475.

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

Answer:

[tex]P(S&G) =0.7941[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=16+18=>34[/tex]

N0 of  Large [tex]L=16[/tex]

N0 of Small [tex]S=18[/tex]

N0 large Green [tex]L_g=9[/tex]

N0 of small White [tex]S_w=3[/tex]

Therefore

Number of green marbles [tex]N0(G)=9+(18-3)[/tex]

Number of green marbles [tex]N0(G)=24[/tex]

Generally the Number of both small and green Marble is

[tex]N0 of (S&G)= 18 - 3 = 15[/tex]

Generally the  probability that it is small or green P(S&G) is mathematically given by

[tex]P(S&G) = \frac{(18 + 24 - 15)}{(18 + 16)}[/tex]

[tex]P(S&G) =0.7941[/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

Rounding each number to 4 significant figures and expressing in standard notation :

(a) 102.53070,

Since the number starts with a non-zero, the 4 digits are counted from the left ;

102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2

(b) 656.980,

Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.

656.980 = 657.0 (4 significant figures) = 6.57 * 10^2

(c) 0.008543210,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3

(d) 0.000257870,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4

(e) -0.0357202,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2

Step-by-step explanation:

50-20=30 rate of markup

Answer:

p - 2q and p - 3q

Step-by-step explanation:

A Series is given to us and we need to find the next two terms of the series . The given series to us is ,

[tex]\rm\implies Series = p+q , p , p - q [/tex]

Note that when we subtract the consecutive terms we get the common difference as "-q" .

[tex]\rm\implies Common\ Difference = p - (p + q )= p - p - q =\boxed{\rm q}[/tex]

Therefore the series is Arithmetic Series .

Arithmetic Series:- The series in which a common number is added to obtain the next term of series .

And here the Common difference is -q .

Fourth term :-

[tex]\rm\implies 4th \ term = p - q - q = \boxed{\blue{\rm p - 2q}}[/tex]

Fifth term :-

[tex]\rm\implies 4th \ term = p - 2q - q = \boxed{\blue{\rm p - 3q}}[/tex]

Therefore the next two terms are ( p - 2q) and ( p - 3q ) .

Answer:

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Step-by-step explanation:

We have the mean during the interval, which means that the Poisson distribution is used.

Poisson distribution:

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.

Lost-time accidents occur in a company at a mean rate of 0.8 per day.

This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.

10 days:

This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]

What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?

This is:

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

In which

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

[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]

[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]

[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]

So

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Answer:

mean=21.17

mode=20,22

median=3.5

range=15

Step-by-step explanation: MEAN=sum of all observations/ no. of observations

mean=22+20+14+22+29+20/6

mean=127/6

mean=21.17

MODE= most frequent observations

mode=22,20

MEDIAN=1/2(n/2+n+2/2)

=1/2(6/2+6+2/2)

=1/2(3+4)

=1/2(7)

=7/2

=3.5

RANGE=X max -X min

=29-14

=15

Answer:

Orthocenter would be in the middle of the shape.

Step-by-step explanation:

B.