According to a Gallup poll, 60% of American adults prefer saving over spending. In a random sample of 10 American adults, what is the probability that more than 3 adults in the sample prefer saving over spending

Answer:

Notice that for 3 out of the 4 numbers, there is a relationship between the x and the y coordinate of the number; for 3+i, -2i, -2-4i we have that the real part is larger by 2 from the imaginary part. Thus, the points are on the same line in the imaginary plane; they satisfy x=y+2 or Re{z}=Im{z}+2. However, 2-4i does not satisfy this equation since 2 is not equal to -4+2. Hence, this point does not belong to the line that the other 3 points define.

Step-by-step explanation:

Answer:

1) g is the dependent variable.(A)

2) u is the independent variable.(D)

Step-by-step explanation:

Answer:

distance = 11

Step-by-step explanation:

distance = [tex]\sqrt{[3-(-8)]^{2} +(4-4)^{2}}[/tex]

             = [tex]\sqrt{11^{2} }[/tex]

             = 11

Answer:

(-2,-1)

Step-by-step explanation:

let the number=x

its reciprocal=1/x

x+2(1/x)=-3

x+2/x=-3

x²+2=-3x

x²+3x+2=0

(x+2)(x+1)=0

x=-2,-1

Answer:

D. KI

Step-by-step explanation:

KI intersects a minimum of two points meaning it is the definition of a secant.

Answer:

The percentage of people that could be expected to score the same as Matthew or higher on this scale is:

= 93.3%.

Step-by-step explanation:

a) Data and Calculations:

Mean score on the scale, μ = 50

Distribution's standard deviation, σ = 10

Matthew scores, x = 65

Calculating the Z-score:

Z-score = (x – μ) / σ

= (65-50)/10

= 1.5

The probability based on a Z-score of 1.5 is 0.93319

Therefore, the percentage of people that could be expected to score the same as Matthew or higher on this scale is 93.3%.

Answer:

[tex]n = 5\frac{10}{13}[/tex]

Step-by-step explanation:

Given

[tex]Call = 6\frac{1}{2}[/tex] cups

[tex]Recipe = 37\frac{1}{2}[/tex] ounce

Required

Number of ounces per cup (n)

To do this, we simply divide the Recipe by the call

So, we have:

[tex]n = \frac{Recipe}{Call}[/tex]

[tex]n = 37\frac{1}{2} \div 6\frac{1}{2}[/tex]

Express as improper fraction

[tex]n = \frac{75}{2} \div \frac{13}{2}[/tex]

Rewrite as:

[tex]n = \frac{75}{2} * \frac{2}{13}[/tex]

[tex]n = \frac{75}{13}[/tex]

[tex]n = 5\frac{10}{13}[/tex]

Answer:

7% probability that the next 2 cards are hearts.

Step-by-step explanation:

Cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

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]

In this question:

10 cards, which means that [tex]N = 10[/tex]

3 are hearts, which means that [tex]k = 3[/tex]

Probability that the next 2 cards are hearts:

This is P(X = 2) when n = 2. So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,10,2,3) = \frac{C_{3,2}*C_{7,0}}{C_{10,2}} = 0.0667[/tex]

0.0667*100% = 6.67%

Rounded to the nearest whole number, 7% probability that the next 2 cards are hearts.

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this case:

[tex]f(x) = 4x^2 - 8x - 20[/tex]

[tex]g(x) = 2x + a[/tex]

So

[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So

[tex]4a^2 - 8a - 20 = 25[/tex]

[tex]4a^2 - 8a - 45 = 0[/tex]

Solving a quadratic equation, by Bhaskara:

[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]

The possible values are a = -2.5 or a = 4.5.

Answer:

9a²b

Step-by-step explanation:

Hi there!

We need to find the greatest common factor out of 45a²b³ and 18[tex]a^{4}[/tex]b

We can split apart the monomials to make it easier

45a²b³ is 45*a²b³

18[tex]a^{4}[/tex]b is 18*[tex]a^{4}[/tex]b

First, let's find the GCF out of 45 and 18 (the number coefficients)

we can find all of the multiples of the 2 numbers:

45 is made up of 9 and 5

9 is made up of 3 and 3

so 3*3*5 is 45

18 is made up of 2 and 9

9 is made up of 3 and 3

so 2*3*3 is 18

3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18

Now let's find the GCF out of a²b³ and [tex]a^{4}[/tex]b

a²b³ made up of a² and b³

so a²b³ is a*a*b*b*b

[tex]a^{4}[/tex]b is made up of [tex]a^{4}[/tex] and b

so [tex]a^{4}[/tex]b is a*a*a*a*b

a*a*b is in both a²b³ and [tex]a^{4}[/tex]b, so the GCF out of a²b³ and [tex]a^{4}[/tex]b is a²b

Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials

9*a²b=9a²b

there's the greatest common factor of the 2 monomials

Hope this helps!

Answer:

it's third option the one who says 10 units up

Answer:

I think A

Step-by-step explanation:

Answer:

Step-by-step explanation:

A)

The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.

B)

The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.

4x + 1 = 2x + 12                   Subtract 1 from both sides.

   - 1              -1

4x = 2x + 11                         Subtract 2x from both sides

-2x   -2x

2x  =  11                               Divide by 2

x = 11/2

x = 5.5

C)

P = L + L + w + w

P = 4(5.5) + 1  + 2(5.5) + 12 + 5.5 + 5.5

P = 22 + 1 + 11 + 12 + 11

P = 23 + 23 + 11

P = 57

Answer:

x = 16

Step-by-step explanation:

The product of the lengths theorem is a property that can be sued to describe the relationships of the sides between the tangents and secants in a circle. One of these products states the following;

The distance between the point of tangency and its intersection point with the exterior secant squared is equal to the product of the exterior secant times the interior secant.

This essentially means the following equation can be formed;

[tex](AB)^2=(DC)(CB)[/tex]

Substitute,

[tex]12^2=x*9[/tex]

Simplify,

[tex]144=9x[/tex]

Inverse operations,

[tex]\frac{144}{9}=x\\\\16=x[/tex]

Answer:

[tex]\boxed{\sf x=7}[/tex]

Step-by-step explanation:

By Targent-secant theorem...

[tex]\sf 9(x + 9) = {12}^{2} [/tex]

Use the distributive property to multiply 9 by x+9.

[tex]\sf 9x+81= {12}^{2} [/tex]

Now, let calculate 12 to the power of 2 and get 144.

[tex]\sf 9x+81=144[/tex]

Subtract 81 from both sides.

[tex]\sf 9x=63[/tex]

Divide both sides by 9.

[tex] \sf \cfrac{ 9x}{9} = \cfrac{63}{9} [/tex]

[tex]\sf x=7[/tex]

Answer:

Step-by-step explanation:

I'm sure he was making a joke at the expense of people who rely on mathematics rather than common sense. It is funny, but then Twain was a remarkably funny author..

The problem is that the comparison is apt using some sort of proportion, but it is absurd to think that the land holding the river would also shrink a proportional amount.  

The river reached a minimum (presumably) in 1875 by cutting out all the loops that were there in 1700. The Mississippi was then a straight line from it's beginning to its delta on the gulf of Mexico. It could not get any shorter. Still, Twain managed to get laughs with his whimsical humor.

Thanks for posting. This made my evening.

Answer:

4.24 inches

Step-by-step explanation:

1 inch / 50 miles = x / 212 miles      Cross multiply

1 inch * 212 miles = 50 miles * x      Divide by 50 miles

1 inch * 212 miles / 50 miles = x

x = 4.24 inches.

How much is 0.24 of an inch?

0.24 * 50 = 12

So 0.24 inches represents 12 miles.

Answer:

Im sorry but why is this a question? Like what school gives this out

Answer:

1024

Step-by-step explanation:

Given :-

Value of -2x²y³

Answer:

254

Step-by-step explanation:

^ <- this is the square sign

-2x^y^3

x=2

y=4

put x values in to x place and y value in to y place.

-2(2)^2(4)^3

Find the squares and - it with 2

-2(4)(64)

2-256=254

:. the value of -2x^2y^3 =254

That the answer.

Hope this is what you asked.

Answer:

[tex]x=-1\text{ or }x=11[/tex]

Step-by-step explanation:

For [tex]a=|b|[/tex], we have two cases:

[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]

Therefore, for [tex]18=|15-3x|[/tex], we have the following cases:

[tex]\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}[/tex]

Solving, we have:

[tex]\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}[/tex].

Therefore,

[tex]\implies \boxed{x=-1\text{ or }x=11}[/tex]

Let the number = X

4x + 8x = 36

Simplify:

12x = 36

Divide both sides by 12:

x = 3

The number is 3

Answer:

a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].

b) There are 2975 bacteria after 3 hours.

c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.

d) A population of 10,000 will be reached after 4.072 hours.

Step-by-step explanation:

a) The population growth of the bacteria culture is described by this ordinary differential equation:

[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)

Where:

[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].

[tex]P[/tex] - Population of the bacteria culture, no unit.

[tex]t[/tex] - Time, in hours.

The solution of this differential equation is:

[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)

Where:

[tex]P_{o}[/tex] - Initial population, no unit.

[tex]P(t)[/tex] - Current population, no unit.

If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:

[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]

[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]

[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]

[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]

[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]

[tex]k\approx 1.131\,\frac{1}{h}[/tex]

Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].

b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:

[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]

[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]

[tex]P(3) \approx 2975.508[/tex]

There are 2975 bacteria after 3 hours.

c) The rate of growth of the population is represented by (1):

[tex]\frac{dP}{dt} = k\cdot P[/tex]

If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:

[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]

[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]

The rate of growth after 3 hours is about 3365.3 bacteria per hour.

d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:

[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]

[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]

[tex]100 = e^{1.131\cdot t}[/tex]

[tex]\ln 100 = 1.131\cdot t[/tex]

[tex]t = \frac{\ln 100}{1.131}[/tex]

[tex]t \approx 4.072\,h[/tex]

A population of 10,000 will be reached after 4.072 hours.

Answer:

i think you need to attach a fine for us to do so?

Step-by-step explanation:

Answer:

I can't tell you without the problem

Answer:

9.2

Step-by-step explanation:

You can do this calculation with a calculator by taking the square root of 85.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

9.2

»»————-　★　————-««  

Here’s why:

Assuming that you mean "the square root of 85 rounded to the nearest tenth..."  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\\rightarrow \sqrt{85} = 9.21954445729....[/tex]

⸻⸻⸻⸻

Since the digit to the right of the tenth (the 1) is less than or equal to four, we round down.

⸻⸻⸻⸻

[tex]9.21954445729...\approx\boxed{9.2}[/tex]

⸻⸻⸻⸻  

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.

Answer:

Step-by-step explanation:

[tex]\frac{34-40}{8}= -.75[/tex]

Answer:

6.

Step-by-step explanation:

.

Answer:

[tex]C)\:8[/tex]

8 units tiles must be added

--------------------------------------

~HOPE IT HELPS~

~HAVE A GREAT DAY!!~

Answer:

D = [4, 10]

Step-by-step explanation:

Since the line starts when x = 4, the domain begins there. And since the line ends when x=10, the domain ends there.

Answer:

I don't really understand the question

Step-by-step explanation:

c