In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.

Graph of two intersecting lines. The line g of x is solid and goes through the points 0, 2, negative 2, 0 and is shaded in below the line. The other line f of x is dashed, and goes through the points 0, 6, 3, 0 and is shaded in below the line.

The graph represents which system of inequalities?

y < −2x + 6
y ≤ x + 2
y ≤ −2x + 6
y < x + 2
y < 2 over 3x − 2
y ≥ 2x + 2
None of the above

Answer:

[tex]G(t) = 120e^{-0.0257t}[/tex]

Step-by-step explanation:

Amount of substance:

The amount of the substance after t minutes is given by:

[tex]G(t) = G(0)e^{-kt}[/tex]

In which G(0) is the initial amount and k is the decay rate.

At the beginning of an experiment, a scientist has 120 grams of radioactive goo.

This means that [tex]G(0) = 120[/tex], so:

[tex]G(t) = G(0)e^{-kt}[/tex]

[tex]G(t) = 120e^{-kt}[/tex]

After 135 minutes, her sample has decayed to 3.75 grams.

This means that [tex]G(135) = 3.75[/tex].

We use this to find k. So

[tex]G(t) = 120e^{-kt}[/tex]

[tex]3.75 = 120e^{-135k}[/tex]

[tex]e^{-135k} = \frac{3.75}{120}[/tex]

[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]

[tex]-135k = \ln{\frac{3.75}{120}}[/tex]

[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]

[tex]k = 0.0257[/tex]

So

[tex]G(t) = 120e^{-0.0257t}[/tex]

Answer

i think it's C. $2,643.61

Answer:

she can make 12 sandwiches

Step-by-step explanation:

3/.25 is the solution

Answer: B. Right Scalene

Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.

Answer:

b

Step-by-step explanation:

Answer:

The replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.

Step-by-step explanation:

Given that a pyramid art installation has a surface area of 24 m2, and an artist creates replicas with scale factors of 1/8, 1/10, and 1/12, to determine what is the surface area of each replica, the following calculation has to be done:

24 x 1/8 = 3

24 x 1/10 = 2.4

24 x 1/12 = 2

Therefore, the replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.

Answer:

1/8 = 0.38 m^2

1/10= 0.24 m^2

1/12= 0.17 m^2

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

Given that Avi used 11 toothpicks to form a row of 5 attached triangles.

Total number of toothpicks used = 89

Let the total number of triangles formed be represented by x, so that:

11 toothpicks = 5 triangles

It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;

the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]

                                  = 2.2

The number of toothpicks per triangle = 2.0

Thus,

x = [tex]\frac{89}{2.0}[/tex]

  = 44.5

x = 44

The total number of triangles formed is 44.

Step-by-step explanation:

(-2,-1,0,3,4) are the domain

(x,y)=(domain,range)

simply x components are the domain whereas y components are the range

Answer:

the option c is the answer for this question

Answer:

There is no significant difference in somatic symptoms for abused and non-abused women. ( B )

Step-by-step explanation:

Given that OR = 1   simply shows that there is no difference in data for both groups

and 95% of Cl for the variable OR  = ( 0.79 - 1.71 )

given the relationship between Cl and OR we can conclude that Cl is inclusive in the value OR = 1

Finally : we can conclude that There is no significant difference in somatic symptoms for abused and non-abused women

9514 1404 393

Answer:

2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3

Step-by-step explanation:

Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².

The function can be simplified to ...

  f(x) = 5/x² -5

which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.

Answer:

D:20

sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20

Step-by-step explanation:

Step-by-step explanation:

4. b 612 (72/100) x 850)

5. c. 275 (33/100) x 835

6. b. 39% (3.24 - 2.85) x100%)

Answer:

Y =-4X +12

Y =-0.625X  -0.75

Step-by-step explanation:

(3,0) and (2,4)....

x1 y1  x2 y2

3 0  2 4

(Y2-Y1) (4)-(0)=   4  ΔY 4

(X2-X1) (2)-(3)=    -1  ΔX -1

slope= -4          

B= 12          

Y =-4X +12    

~~~~~~~~~~~~~~~~~

(-6,3) and (2,-2)​

x1 y1  x2 y2

-6 3  2 -2

(Y2-Y1) (-2)-(3)=   -5  ΔY -5

(X2-X1) (2)-(-6)=    8  ΔX 8

slope= -  5/8    

B= -  3/4    

Y =-0.625X  -0.75    

Answer:

Step-by-step explanation:

j/-2 =-12-7

j=(-19)*(-2)

j=38

Answer:

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

Step-by-step explanation:

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.

Mean of 41, standard deviation of 28:

This means that [tex]\mu = 41, \sigma = 28[/tex]

Sample of 92:

This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]

Distribution of the sample means:

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

Answer:

[tex]9[/tex]

Step-by-step explanation:

Step 1:  Find the square root of 81

[tex]\sqrt{81}[/tex]

[tex]\sqrt{9*9}[/tex]

[tex]\sqrt{9^{2}}[/tex]

[tex]9[/tex]

Answer:  [tex]9[/tex]

Answer:

the square root of 81 is 9

Answer:

E &F

Step-by-step explanation:

The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).

Answer:

The correct answer is C)

Answer:

5000 ;

11125

Step-by-step explanation:

Given :

Total principal = 16125

Rates = 8.5% and 4%

Period, t = 2 years

Total interest = 1740

Let :

Principal amount invested at 8.5% = x

Principal amount invested at 4% = 16125 - x

Interest formula :

Interest = principal * rate * time

Hence, mathematically ;

(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740

(0.17x + 1290 - 0.08x ) = 1740

0.09x + 1290 = 1740

0.09x = 1740 - 1290

0.09x = 450

x = 450 / 0.09

x = 5000

Amount invested at 4% :

16125 - 5000 = 11125

Answer:

A) True

Hope this helps!

Answer:

ok

Step-by-step explanation:

.1 - .01 = .99

.1 - .99 = .1

.4 -.03 =37

Answer:

assuming that the equation was [tex]f(x) = e^{x}[/tex]

then the base is "e"

Step-by-step explanation:

Answer:

Surface area = 21 in.²

Step-by-step explanation:

Surface area of the pyramid = sum of all areas of the faces or parts of the net = 4(area of triangle) + area of square base

✔️Area of the four triangles:

A = 4(½*b*h)

Where,

b = 3 in.

h = 2 in.

A = 4(½*3*2)

A = 2*3*2

A = 12 in.²

✔️Area of the square base = s²

s = 3 in.

Area = 3² = 9 in.²

✅Surface area of the pyramid = 12 + 9 = 21 in.²

Answer:

2.334453751

Step-by-step explanation:

Press log on your Casio calculator (if you have one) and plug in 216, then close the parentheses!

Answer:

D is your answer

Step-by-step explanation:

Answer:

Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx

Step-by-step explanation:

Answer:

840 ways.

Step-by-step explanation:

The order is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

4 items from a set of 7, so:

[tex]P_{(7,4)} = \frac{7!}{(7-4)!} = 7*6*5*4 = 840[/tex]

840 ways.

Answer:

a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.

b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Step-by-step explanation:

For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

One out of four cars needs to have oil added.

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

a. One out of the next four cars needs oil.

This is P(X = 1) when n = 4. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]

0.4219 = 42.19% probability that one out of the next four cars needs oil.

b. Two out of the next eight cars needs oil.

This is P(X = 2) when n = 8. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]

0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c.Three out of the next 12 cars need oil.

This is P(X = 3) when n = 12. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]

0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Answer:

100

Step-by-step explanation:

f(5) means find the output value when x=5

When x =5 f(x) = 100

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Explanation:-

we have to find the value of f(5)

But in the questions attachment it tells that

f(5)=100