O
14) Determine which of the following functions is
an example of exponential decay.
A) f(x) = 6.7e*
C) f(x)=3.2*
2
4·(9)
(³)
D) f(x) = -7 8 -x
3
B) f(x) = 1

The slope of the line shown is -2.

Option D is the correct answer.

We have,

Take two coordinates from the graph.

(0, 7) and (2, 3)

Now,

Slope.

= (3 - 7) / (2 - 0)

= -4/2

= -2

Thus,

The slope of the line shown is -4/2.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = \((1-p)^{k-1}\)×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

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Answer:

6

Step-by-step explanation:

e = number of elephants

9 times as many monkeys as elephants

m = 9e

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

60 animals all together

e + m = 60

e + 9e = 60

Combine like terms

10e = 60

Divide both sides by 10

e = 6

Answer: There’s technically no answer to this question, unless you specify that the zoo only has monkeys and elephants. If the zoo has more than two types of animal then the ratio doesn’t help because there are unknown variables.

However, if we knew that the zoo only has monkeys and elephants, then:

E = number of elephants

M = number of monkeys

M=9E

M + E = 60

9E+E= 60

10E = 60

E = 6

There are 6 elephants (and 54 monkeys).

It can be noted that the true statements about the relations include:

A. The equality relation on the real numbers is an equivalence relation.

C. A relation from a set with n elements to itself can have up to elements.

E. A function is a special relation.

G. The equality relation on the real numbers is anti-symmetric.

H. If is a reflexive relation on a set S, then any two - related elements of S must also be related.

I. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric.

It should be noted that a relation simply means the relationship between the set of values.

The information given about the relations above are true in these cases.

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Greetings from Brasil...

Solving this equation, we obtain:

X/5 + 7 = 16       multiplying everything by 5

X + 35 = 80

refer to attached

Answer:

45

Step-by-step explanation:

\(\frac{x}{5} = \frac{1}{5} x\)

First, we subtract 7 from each side

\(\frac{1}{5} x = 9\)

Next, we find the reciprocal of "1/5" and multiply that number on both sides

\(\frac{5}{1} * \frac{1}{5} x = \frac{9}{1} *\frac{5}{1}\)

Now, we multiply.

\(x = 45\)

Answer:

rawr :)

Step-by-step explanation:

Answer:

17/18 because

17/18=0.944444444

The value of angle a is approximately 36.87°.

We are given that;

Height = 6 and hypotenuse = 10

Now,

To find the angle a in a right triangle, we can use the trigonometric ratios12:

sin(a) = opposite/hypotenuse cos(a) = adjacent/hypotenuse tan(a) = opposite/adjacent

where opposite is the side opposite to the angle a, adjacent is the side next to the angle a, and hypotenuse is the longest side of the right triangle.

we can use the sine ratio to find the angle a:

sin(a) = 6/10 a = sin^-1(6/10) a ≈ 36.87°

Therefore, by Pythagoras theorem the answer will be 36.87°.

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Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

Answer:

$1000

Step-by-step explanation:

Check answers

1000x .03= 30

1000 - 30 = 970

Step-by-step explanation:

\( - 36 \times 72 + 64 \times ( - 72)\)

first carry out the multiplication operation:

\( = ( - 36 \times 72) + (64 \times - 72) \\ = - 2592 + ( - 4608)\)

then addition operation:

\( = - 7200\)

Answer:

\( - 36 \times 72 + 64 \times ( - 72) \\ - 2592 + ( - 4608) \\( - 7200)\)

Answer:

\(L(t) = 170 - 10t\)

Step-by-step explanation:

The amount that Alexa owes after t weeks is given by a linear equation in the following format:

\(L(t) = L(0) - bt\)

In which L(0) is the initial amount borrowed and b is how much is paid per week.

Alexa agreed to pay back her friend $10 per week and originally borrowed $170.

This means that, respectivelly, \(b = 10, L(0) = 170\). So

\(L(t) = L(0) - bt\)

\(L(t) = 170 - 10t\)

The function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

The given parameters are:

Perimeter = 210 meters

Let the length parallel to the wall be represented as z and the width be x

So, the perimeter of the fence is

P = 2x + z

This gives

210 = 2x + z

Make x the subject

x = 1/2(210 - z)

The area of the wall is calculated as

A = xz

So, we have

A = 1/2(210 - z) * z

This gives

A = z/2(210 - z)

Rewrite as

A(z) = z/2(210 - z)

Hence, the function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

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Answer:

1, -5

Step-by-step explanation:

first mark the point (2, -5) then go 2 right which brings you to (4, -5) and then 3 left to (1,-5)

The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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Answer:

It just is see explanation

Step-by-step explanation:

75% is equal to 0.75, or 3/4. If you multiply the full 60 minutes to 3/4, then your product is 45 minutes. That's how 75% of 60 minutes is 45 minutes.

Answer: 75% of a number is the same thing as 3/4 of the number.

so for example, divide 100 by 4. you get 25 right?

right, so multiply 25 by 3 and you get 75. That's what 3/4 of something is.

now divide 60 by 4. you get 15 right?

right, so multiply 15 by 3, and you get 45 :)))

that's why 75% of 60 is 45.

i hope this helps!!

BTW when you get a question with percentages, you can flip them! In this case it doesn't really help to do so, but for example if you had a question asking:

what is 16% of 50?

FLIP IT. it's the same thing as 50% of 16!!!  This works with like any percentage!!!

The statement that the Property damage liability pays for injuries to a driver or their passengers caused by an uninsured or underinsured driver is false.

Auto insurance policy is a contract between the insurance company and the person being insured which protects the person under any financial loss caused by accident or theft.

There are mainly six types of auto insurance coverage that the company basically provide.

They are Property damage liability, Bodily injury liability, PIP, Uninsured and underinsured motorist coverage, collision and comprehensive.

Property damage liability pays for the damage that the person insured causes to someone else's property, which include someone else's car, buildings or so.

The given coverage in the statement is the Uninsured and underinsured motorist coverage.

Hence the given statement is false.

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The solution of the absolute function is  

t < -4

 t > 22/5

In interval notation it will be    (-∞,-4) ;(22/5,+∞).

What is absolute function?

An absolute value function is a function in algebra which consists of the variable in the absolute value bars. In general form of the absolute value function is f(x) = a |x - h| + k  where h, k are constants and the most commonly used form of this function is f(x) = |x|. Here a = 1 and h = k = 0.

The Absolute Value term is |5t-1|

For the Negative case it will be -(5t-1)

For the Positive case it will be  (5t-1)

at first we will solve for negative case:

-(5t-1) > 21

    Multiplying by the minus sign we get,

     -5t+1 > 21

    Rearranging and Adding up we get,

     -5t > 20

    Dividing both sides by 5

     -t > 4

    Multiplying both sides by (-1) we get,

     t < -4

 Now we will solve for positive case:

(5t-1) > 21

    Rearranging and Adding  up we get,

     5t > 22

    Dividing both sides by 5 we get,

     t > (22/5)

Hence the solution of the absolute function is  

t < -4

 t > 22/5

In interval notation it will be    (-∞,-4) ;(22/5,+∞).

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To set up an integral for the area of the shaded region, we need to consider the shape of the region and decide on an appropriate coordinate system.

Let's assume that the shaded region is bounded by the curve y=f(x) and the x-axis, and that it lies between the vertical lines x=a and x=b.

Then the area of the shaded region can be expressed as the following definite integral:

Area = ∫[a,b] f(x) dx

To evaluate this integral, we can use the Fundamental Theorem of Calculus:

Area = F(b) - F(a)

where F(x) is an antiderivative of f(x).

To find the area of the shaded region, we would need to find an antiderivative of f(x) and then evaluate the integral by substituting the appropriate values for a, b, and F(x)

For example, if f(x) = x^2 and a = 0 and b = 2, then the area of the shaded region would be:

Area = ∫[0,2] x² dx

    = F(2) - F(0)

\(=\frac {(2^3)}3 - \frac{(0^3)}3\\ =\frac{8}{3}\)

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The reasonable domain for the function is (b) x > 0

From the question, we have the following parameters that can be used in our computation:

The function f(x) = 75x + 100

Where x is the number of hours

f(x) is the total cost.

In this case, the number of hours cannot be negative or 0

This means that the values of x in the function would be x > 0

These values of x are the domain

So, the reasonable domain for the function os (b) x > 0

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Answer:

3.14

Step-by-step explanation:

pi

The given two triangles are congruent by  Side Side Side congruency.

As from the question we get to know that ΔRST and Δ UTS  

and

RS = UT

RT = US

The proof for the above claim

RS = UT    {given}

RT = US    {given}

ST = TS     {Common}

Therefore, we can say that by SSS theorem ΔRST and Δ UTS  is congruent to each other.

ΔRST  ≅ Δ UTS    by SSS Theorem

If two geometric figures are identical in every way, they are said to be congruent.

For example, two squares having the same side-length are congruent.

Similarly, two circles with the same radius are congruent.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. ’ ≅’ is the congruence symbol.

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Answer:

11

Step-by-step explanation:

2x + 3

2(4) + 3 .......................replace x with 4

8 + 3

11

Answer:

11

Step-by-step explanation:

2*4+3=8+3=11

this is really simple:)

Answer:

g[1] = -7

Step-by-step explanation:

For the future just substitute x for the number

1.  g[1]= -3(1)-4

2.  g[1] = -3-4

3. g[1] = -7

The value of g [ 1 ] is -7.

Here the function is given as,

g[x] = -3x - 4

What is substitution method?

The algebraic method to solve simultaneous linear equations is called substitution method.

Now,

The function is given as,

g[x] = -3x - 4

The value of  g[1],

g[1] = -3x1 -4

g[1] = -7

Hence, The value of g [ 1 ] is -7.

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Answer:

4*5*7=140 ways

Step-by-step explanation:

First he has to decide on a pair of pants and he has 4 different choices.

For each of those choices he has a choice of 7 different shirts, so that gives him 4 times 7 = 28 different pant/shirt combinations. (I hope none of the pants are striped and none of the shirts have polka-dots).

For each those 28 possibilities, he has 5 different ties he could select, so altogether he has 28 times 5 = 140 different outfits, and some of them may be acceptable to wear in public.

It is simply , 4*5*7=140 ways.

Answer:

The answer is 853

Step-by-step explanation:

22392 - 1920 after you do the minus you should divide the answer Answer ÷ 24

Based on the information provided, the missing number would be number 6.

When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.

In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.

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