simplify 4x/7-x/21 find​

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Given:

Total number of glasses = 16

Number of glasses containing prune juice = 4

Number of glasses containing apple juice = 2

To find:  fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice

Solution:

A fraction refers to the parts of a whole. In a fraction, a top number is the numerator, and a bottom number is the denominator.

Number of glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = 16 - 4 - 2 = 10

Total number of glasses = 16

So,

Fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = [tex]\frac{10}{16}=\frac{5}{8}[/tex]

Answer:

25

Step-by-step explanation:

AB is a tangent to the circle hence the angle ABO is a right angle !!! With that knowledge we can construct a right-angled triangle with sides AB ,BO and OA .

Applying the Pythagorean theorem we get that OA is the hypotenuse and thus

[tex]oa = \sqrt{ab {}^{2} + ob {}^{2} } [/tex]

Answer:

117 units cubed.

Step-by-step explanation:

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

Answer:

117

Step-by-step explanation:

find all the shown surface area

Answer:

D. Parabola; 0°

Step-by-step explanation:

Answer:

relative maximum: x = 1

relative minimum: x = 7

Step-by-step explanation:

Critical points:

Values of x for which f'(x) = 0.

Second derivative test:

For a critical point, if f''(x) > 0, the critical point is a relative minimum.

Otherwise, if f''(x) < 0, the critical point is a relative maximum.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = x^{3} - 12x^{2} + 21x - 8[/tex]

Finding the critical points:

[tex]f'(x) = 3x^{2} - 24x + 21[/tex]

[tex]3x^{2} - 24x + 21 = 0[/tex]

Simplifying by 3

[tex]x^{2} - 8x + 7 = 0[/tex]

So [tex]a = 1, b = -8, c = 7[/tex]

[tex]\bigtriangleup = (-8)^{2} - 4*1*7 = 36[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{36}}{2} = 7[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{36}}{2} = 1[/tex]

Second derivative test:

The critical points are x = 1 and x = 7.

The second derivative is:

[tex]f''(x) = 6x - 24[/tex]

[tex]f''(1) = 6*1 - 24 = -18[/tex]

Since f''(1) < 0, at x = 1 there is a relative maximum.

[tex]f''(7) = 6*7 - 24 = 18[/tex]

Since f''(x) > 0, at x = 7 there is a relative minumum.

Answer:

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

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 = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214[/tex]

Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

This probability is 1 subtracted by the pvalue of Z when X = 66.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{66.5 - 66}{0.214}[/tex]

[tex]Z = 2.336[/tex]

[tex]Z = 2.336[/tex] has a pvalue of 0.99.

1 - 0.99 = 0.01

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Answer:

CO = 15

Step-by-step explanation:

Since it's a right Angled Triangle (because of the tangent) so using Pythagoras theorem

OC² = CW²+OW²

CO²=(9)²+(12)²

CO²=81+144

CO²=225

Taking square root on both sides

CO = 15

Answer:

  3x²

Step-by-step explanation:

The area is the product of the dimensions of the base:

  area = x(3x) = 3x²

Answer: 2 ÷ 17

Step-by-step explanation: When you have something in this form, a/b, it means the same thing as a divided by b.

So 2/17 means the same thing as 2 ÷ 17.

Answer: statistical

Step-by-step explanation: A statistical – is a question that can be answered by collecting data and that anticipates variability in those data • Statistics – the science of collecting, reviewing, and analyzing data

Answer:

GRAPH OF 3X+2 IS 6

Step-by-step explanation:

Answer:

The graph below

Step-by-step explanation:

Answer:

Step-by-st

respond  poorfa

Answer:

180-168=12

12+48=60x

Step-by-step explanation:

Answer: 268 hamburgers

Answer:

She has to pay income tax of  8,570 Euros

Step-by-step explanation:

On the 28,000 Euros,the floor manager would pay taxes at the rate of 20% which is computed thus:

tax at 20%=28,000 Euros*20%=5,600 Euros

The remaining earnings would be charged to tax at higher tax rate of 41% as follows:

tax at 41%=45,000 Euros-28,000 Euros=17,000 Euros*41%=6,970  Euros

Total amount of taxes=5,600+6970 = 12,570 Euros

Taxes payable =total taxes -tax credit

The manager has a tax credit of 4,000 Euros

taxes payable= 12,570-4,000=8,570 Euros

Answer:

84%

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

So for 190000 we have:

z = (190000 - 200000) / (10000)

z = -1

and this value represents 0.1587

for 230000 we have:

z = (230000 - 200000) / (10000)

z = 3

and this value represents 0.9987

we subtract:

0.9987 - 0.1587 = 0.84

Which means that it represents 84% of the houses

Answer:

4.4=-4

Step-by-step explanation:

just solving maths

Step-by-step explanation:

Replace x = 3

f(3) = 2(3) - 2

= 6 - 2

= 4

Answer:

f(3) =4

Step-by-step explanation:

f(x) = 2x - 2

Let x=3

f(3) = 2*3 - 2

     = 6-2

     = 4

Answer:

Lauren is wrong

Step-by-step explanation:

1. Lauren is wrong

2. What’s the cost of the shirts before tax

Each shirt cost $15 and the total = $15 x 3 = $45

3. How much is the sales tax for all shirts

Sale tax for all shirts is $45 x 0.08 = $3.6

4. What is the total cost of the shirts, including tax?

Total cost  = $45 + $3.6 = $48.60

Answer:

Step-by-step explanation:

A coin has two faces, a head (H) or tail (T). Tossing a coin twice in succession would give the following sample size;

                                 {HH, HT, TH, TT}

Given that: A = first toss is heads, B = second toss is heads, then:

i. P(A) = {HH, HT} = 2

ii. P(B) = {TH} = 1

iii. P(A∩B) = {HH} = 1

iv. P(B /A) = [tex]\frac{1}{2}[/tex]

Answer:

a) Population of adults who watch local news

b) Population of adults who use cell phones or tablets.

c) They conducted a sample survey

d) I will find the results interesting.

I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.

Step-by-step explanation:

a) This finding is applicable to the population of adults who watch local news.

This is because the sample will be collected from the population of adults who watch local news to see the percentage that actually get those local news from their cell phones or tablet computers.

b) This finding is applicable to the population of adults who use cell phones or tablets.

The sample will be collected from the population of adults who use cell phones or tablets. A survey can now be carried out to find out what they use their phones or tablets for, whether to search for restaurants or get weather reports.

c) The Pew Researchers conducted a sample survey because a census data cannot contain the information about weather reports, local restaurants or news channel. Precise information can only be gotten from a sample survey.

d) Yes, I will. Having an idea of how large the population of those that search for local restaurants on phones and tablets will enable me to channel my publicity towards this media. I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.

Answer:

The Answer is 10, 50, and 54

Step-by-step explanation:

You want to figure this answer out by using the Pythagorean Theorem. If 10 squared plus 50 squared does not equal 54 squared, then those side lengths can not make a triangle.  

Answer:

Step-by-step explanation:

The volume of a cone of height h and a circular base of radius r is given by [tex]V=\frac{\pi r^2 h }{3}[/tex]. Note that [tex]\pi r^2[/tex] is the area of the base, therefore, if we want to find the area of the base we must multiply the equation by 3 and divide by h.  Hence

[tex]\pi r^2 = \frac{3V}{h}[/tex]

In this case, h=12. Given a value of V, we can find the area of the base

Answer:

24% of those surveyed liked neither

Step-by-step explanation:

Set concepts:

We use set concepts to solve this question.

I am going to say that:

P(A) is the percentage of people that liked to swim.

P(B) is the the percentage of people that liked to run.

The percentage of people that liked at least one of these activities is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In which [tex]P(A \cap B)[/tex] is the probability that a person liked both these activities.

The percentage of people that liked neither is:

[tex]P = 1 - P(A \cup B)[/tex]

Of those surveyed, 58% said they liked to swim and 36% said they liked to run.

This means that [tex]P(A) = 0.58, P(B) = 0.36[/tex]

18% said they liked both swimming and running

This means that [tex]P(A \cap B) = 0.18[/tex]

What percent of those surveyed liked neither?

At least one:

[tex]P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76[/tex]

Neither:

[tex]P = 1 - P(A \cup B) = 1 - 0.76 = 0.24[/tex]

24% of those surveyed liked neither

Let the amount that Sky receives be S, and the amount that Natalia recieves be N.

[tex] \dfrac{s}{n} = \dfrac{6}{5} [/tex]

[tex]s = n + 3 \\ \\ \dfrac{n + 3}{n} = \frac{6}{5} \\ \\ 5n + 15 = 6n \\ \\ n = 15[/tex]

15 euros

Answer:

Yes. Some examples are √2, √3, √5.

You better believe it !  In fact, if you don't count an infinite number of examples, you'll find that MOST of their square roots are irrational.

Let's examine the smallest 1,000 integers . . .

-- They're all rational numbers, but ...

-- only 31 of them have rational square roots !

Answer:

a) 0.0668

b) 0.3085

c) 0.6247

Question:

A population is normally distributed with μ = 100 and σ= 20.

a. Find the probability that a value randomly selected from this population will have a value greater than

130.

b. Find the probability that a value randomly selected from this population will have a value less than 90.

c. Find the probability that a value randomly selected from this population will have a value between 90

and 130.

Step-by-step explanation:

a) The probability that a value randomly selected from this population will have a value greater than 130 = P(X >130)

A z-score also referred to as a standard normal table shows the number of standard deviations a raw score lays either above or below the mean.

Let's determine the z-score using:

z = (x - µ)/σ

µ = 100

σ = 20

z = (130-100)/20

z = 30/20 = 1.5

The probability from the standard normal table associated with z = 1.50 is 0.4332. This is the area between z = 1.50 and the mean.

The total area under any normal curve is 1. Due to the fact that the normal curve is symmetric about the mean, the area on either sides of the mean is 0.5.

The desired probability = 0.5000 - 0.4332

= 0.0668

Find attached the diagram.

b) The probability that a value randomly selected from this population will have a value less than 90 = P(X<90)

Using the z-score formula:

z = (x - µ)/σ

z = (90-100)/20

z = (-10)/20 = -0.5

The probability from the standard normal table associated with

z = -0.50 is 0.1915. This is the area between z = -0.50 and the mean.

The desired probability = 0.5000 - 0.1915

= 0.3085

Find attached the diagram.

c) The probability that a value randomly selected from this population will have a value between 90 and 130 = P(90≤X≤130)

We earlier found the z score when P(X<90) = -0.5

And the probability associated with

z = -0.50 is 0.1915.

The z score when P(X>130) = 1.5

And the probability associated with z = 1.50 is 0.4332.

The desired probability is the addition of the two probabilities:

P(90≤X≤130) = 0.1915+0.4332

P(90≤X≤130) = 0.6247

Answer:

[tex] y = -\frac{1}{3}x-2[/tex]

Step-by-step explanation:

From the table it is clear that the line is passing through the points [tex] (0,\: -2)= (x_1, \:y_1) \: \&\: (-6, \:0)=(x_2,\:y_2) [/tex]

(There are many other points in the table and any two of them can chosen as per our convenience)

Equation of line in two point form is given as:

[tex] \frac{y-y_1}{y_1 - y_2} = \frac {x-x_1}{x_1 - x_2} \\\\

\therefore \frac{y-(-2)}{-2 - 0} = \frac {x-0}{0 - (-6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{0+6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{6)} \\\\

\therefore 6(y + 2) = - 2(x)\\

\therefore 6y + 12 = - 2x \\

\therefore 6y = - 2x - 12\\\\

\therefore y = -\frac{2}{6}x-\frac{12}{6}\\\\

\huge \red {\boxed {y = -\frac{1}{3}x-2}} \\\\[/tex]

Step-by-step explanation:

We have,

If a quadratic equation with real coefficients has a discriminant of -36.

The general form of quadratic equation is :

[tex]ax^2+bx+c=0[/tex]

The discriminant of this equation is : [tex]D=b^2-4ac[/tex]

If D=0, it will have 1 real roots

If D>0, it will have 2 real roots

If D<0, it will have no real roots

We have,

D = -36 < 0, so, the quadratic equation will have no real roots.