If f(x) is an exponential function where f(-1.5) 26 and
f(5.5) = 7, then find the value of f(10), to the nearest hundredth.

9514 1404 393

Answer:

  (x, y, z) = (1/3, 2/3, 1)

Step-by-step explanation:

We can use the first equation to write an expression for x that can be substituted into the other equations.

  x = 1 -y

  2(1 -y) -y +z = 1   ⇒   -3y +z = -1

  (1 -y) +2y +z = 8/3   ⇒   y +z = 5/3

Subtracting the first of these equations from the second gives ...

  (y +z) -(-3y +z) = (5/3) -(-1)

  4y = 8/3

  y = 2/3

  z = 5/3 -y = 1

  x = 1 -y = 1/3

The solution is (x, y, z) = (1/3, 2/3, 1).

9514 1404 393

Answer:

  a) (x³ -x² +x +2) +2/(x+1)

  b) (x² +2x -5) +6/(x+3)

Step-by-step explanation:

Polynomial long division is virtually identical to numerical long division, except that the quotient term does not require any guessing. It is simply the ratio of the leading terms of the dividend and divisor. As with numerical long division, the product of the quotient term and the divisor is subtracted from the dividend to form the new dividend for the next step.

The process stops when the dividend is of lower degree than the divisor.

In part (a), you need to make sure the dividend expression has all of the powers of x present. This means terms 0x³ and 0x² must be added as placeholders in the given dividend. They will become important as the work progresses.

Answer:

C. (2,16)

Step-by-step explanation:

[tex]y=12x-8\\y=8x\\\\\\8x=12x-8\\-4x=-8\\x=2\\\\y=8(2)=16[/tex]

Answer:

It might be B

Step-by-step explanation:

12(5)-8

8(11)

52

88

Answer:

18 ft* (1 piece/ 1 1/3 ft)= 13.5 pieces.

Step-by-step explanation:

20. (2) 14

A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.

21. (4) 2, -12

x^2 + 10x + 25 = 24 + 25

(x + 5)^2 = 49

x + 5 = +/- 7

x = 2, -12

22. (3) 3 + sqrt(17)

x^2 - 6x = 8

Complete the Square

x^2 - 6x + 9 = 8 + 9

(x - 3)^2 = 17

x - 3 = +/- sqrt(17)

x = 3 + sqrt(17), 3 - sqrt(17)

23. (1) 1, -5

x^2 + 4x - 5 = 0

x^2 + 4x = 5

x^2 + 4x + 4 = 5 + 4

(x + 2)^2 = 9

x + 2 = +/- 3

x = 1, -5

Hope this helps!

Answer:b

Step-by-step explanation:

Answer:

y = -2|x| + 1.

Step-by-step explanation:

We start with y = 2x which is a straight line passing through the origin with a slope of 2.

Taking the absolute value of x ( |x| ) gives  a graph shaped like a letter V with the point  at the origin.

Making that negative ( y = -2|x| ) inverts it vertically and then the  + 1 translates it up 1 unit.

Answer:

A = 800( 1.075)^(t)

Step-by-step explanation:

The equation for interest is

A = p (1+r/n) ^ nt   where p is the principle, r is the interest rate, n is the number of times per year  and t is the years

A = 800( 1+ .075/1)^(1*t)

A = 800( 1.075)^(t)

Let's see

[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]

[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]

[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]

[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]

Option C

Answer:

542.74 m

Step-by-step explanation:

Tan(48.3) = 250/a Multiply by a

a*tan(48.3) = 250 Divide by tan(48.3)

a = 250/Tan(48.3)

a =222.74

By a similar method b = 250/tan(38)

b = 319.99'

The total length =542.73 meters

Answer:

Step-by-step explanation:

If the √y³ term is in the denominator, then the expression needs to be written with parentheses:  7√x²/(5√y³)

Answer:

21 kilometers

Step-by-step explanation:

Let the height be [tex]x[/tex]. Then, the length of the base is [tex]2x[/tex]. The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to [tex]\frac{x \cdot 2x}{2} = x^2[/tex], which is in turn equal to 441. Since [tex]x[/tex] must be positive, then [tex]21^2=441[/tex], meaning that the height is [tex]21[/tex] kilometers.

Answer:

Amount of sales

Step-by-step explanation:

The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.

Answer:

false

Step-by-step explanation:

f can never have x next to it

False because $1 =$1 not $3

True. The expected value of the bet is positive ($0.2),

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Let's calculate the expected value of the bet for both outcomes:

If your team wins: You get paid $1, so the expected value is 0.8 × $1 = $0.8

If your friend's team wins: You pay $3, so the expected value is 0.2 × -$3 = -$0.6

The overall expected value of the bet is the sum of these two outcomes: $0.8 + (-$0.6) = $0.2

Since the expected value of the bet is positive ($0.2), this means that on average, you can expect to win money if you take this bet. Therefore, the bet is in your favor.

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

Answer:

a) 0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.

b) 0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.

c) 0% probability that the student completes the quiz in exactly 37.23 minutes.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniformly distributed between 30 and 60 minutes.

This means that [tex]a = 30, b = 60[/tex]

a. The student requires more than 55 minutes to complete the quiz.

[tex]P(X > 55) = \frac{60 - 55}{60 - 30} = 0.1667[/tex]

0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.

b. The student completes the quiz in a time between 30 and 40 minutes.

[tex]P(30 \leq X \leq 40) = \frac{40 - 30}{60 - 30} = 0.3333[/tex]

0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.

c. The student completes the quiz in exactly 37.23 minutes.

Probability of an exact value in a continuous distribution, such as the uniform distribution, is 0%, so:

0% probability that the student completes the quiz in exactly 37.23 minutes.

9514 1404 393

Answer:

Step-by-step explanation:

The graph shows the relevant vertex of the feasible region is ...

  (x, y) = (8/3, 8/3).

The value of z there is ...

  z = 11(8/3) +4(8/3) = (88 +32)/3

  z = 40

Answer:

A' (- 1, - 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ), then

A (- 5, 1 ) → A' (- 1, - 5 )

Hi there!  

»»————-　★　————-««

I believe your answer is:  

D. infinite number of solutions

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\\left \{ {{8x + 4y = 20} \atop {-10x - 5y = -25}} \right.\\-----------\\5(8x + 4y = 20)\\4(-10x - 5y = -25)\\\\40x+ 20y = 100\\\-40x-20y=-100\\\\\boxed{0 = 0}[/tex]

⸻⸻⸻⸻

There are an infinite number of solutions.

»»————-　★　————-««  

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

Answer:

9t

Step-by-step explanation:

That's 9 multiplied by t

Explanation:

There are A = 2 westerns out of B = 8+15+2 = 25 movies total

The probability of selecting a western is A/B = 2/25

In decimal form, this is 2/25 = 0.08 which converts to 8%

Answer:

2/25

Step-by-step explanation:

so first u have to add them all up to get 25 because 8 +15+2=25. then, since there are 2 westerns, the probability that he will select a western is 2 out of 25

Answer:

x = -9

Step-by-step explanation:

25^x = 125 ^(x+3)

Rewriting

5^2^x = 5^3^(x+3)

We know a^b^c = a^(b*c)

5^(2x) = 5^(3(x+3))

5^(2x) = 5^(3x+9)

The bases are the same so the exponents are the same

2x = 3x+9

Subtract 3x from each side

2x-3x = 3x+9-3x

-x =9

x = -9

Answer:

x is -9

Step-by-step explanation:

Answer:

inverse it and do fx and gx inverse its value

Answer:

15 - 8x

Step-by-step explanation:

Remark

This all depends on how you read the question. In other words, which comes first 5 - 3x or 5x - 10. It's not clear.

If you do the first one first, you get

5 - 3x - (5x - 10)         Remove the brackets.

5 - 3x - 5x + 10          Collect like terms

15 - 8x                       So that makes the middle one correct.

Now do it the other way.

5x - 10 - (5 - 3x)

5x - 10 - 5 + 3x

8x - 15

That answer isn't available here. So ..

The answer is 15 - 8x

Answer:

Hence the number of plans that cost between $42.72 and $ 85.72 is

95.44 %.

Step-by-step explanation:

Now the given are

μ = $64.22.

σ = $10.75.

Here,

[tex]P\left ( 42.72 < x< 85.72 \right )=P\left ( \frac{42..72-64.22}{10.75}< \frac{x-\mu }{\sigma } < \frac{85.72-64.22}{10.75}\right )\\P\left ( 42.72 < x< 85.72 \right )= P\left ( -2.00< Z <2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (Z<2.00\right )-P\left ( Z<-2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (0.9772\right )-P\left (0.0228\right )\\Probability = 0.9544[/tex]

Probability = 95.44%.

Answer:

1 3/4 or 7/4

Step-by-step explanation:

- 1 1/4 = -5/4

1/2 = 2/4

difference = 5/4+2/4 =7/4

Answer:

first step find LCM method

Answer:

14cm²

Step-by-step explanation:

3x2=6,

3x2=6,

2x1=2,

6+6+2=14 cm^2

Answer:

When t=10, the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

Step-by-step explanation:

Given

[tex]f(t) = 740 * (0.95)^t[/tex]

Required

The true statements

[tex](a)\ f(10) = 443[/tex]

We have:

[tex]f(t) = 740 * (0.95)^t[/tex]

Substitute 10 for t

[tex]f(10) = 740 * (0.95)^{10[/tex]

[tex]f(10) = 443[/tex]

Hence, (a) is true

[tex](b)\ f(t) = 740[/tex]

We have:

[tex]f(t) = 740 * (0.95)^t[/tex]

Substitute 740 for f(t)

[tex]740 = 740 * (0.95)^t[/tex]

Divide through by 740

[tex]1 = 0.95^t[/tex]

Express 1 as 0.95^0

[tex]0.95^0 = 0.95^t[/tex]

Cancel out the bases

[tex]0 = t[/tex]

[tex]t = 0[/tex]

Hence, the area had 740 acres initially;

(b) is true

[tex](c)\ r = 5\%[/tex]

We have:

[tex]f(t) = 740 * (0.95)^t[/tex]

Using the general formula

[tex]f(t) = a * b^t[/tex]

By comparison:

[tex]b = 0.95[/tex]

0.95 < 1 means that:

[tex]b = 1 - r[/tex] --- where r = rates

[tex]0.95 = 1 - r[/tex]

Collect like terms

[tex]r = 1 - 0.95[/tex]

[tex]r = 0.05[/tex]

Express as percentage

[tex]r = 5\%[/tex]

Hence, (c) is true

[tex](d)\ f(10) = 492[/tex]

In (a)

[tex]f(10) = 443[/tex]

Hence, (d) is false

[tex](e)\ r = 95\%[/tex]

In (c)

[tex]r = 5\%[/tex] ---- decrement

Hence, (e) is incorrect

Answer: When the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

Step-by-step explanation:

Answer:

Domain: all reals

Range: 4 ≤y <∞

Step-by-step explanation:

The domain is the possible input values(x)

From the arrows at the left and right ends on the graph, the inputs can be all reals

The range is the possible output values (y)

Y goes from 4 to infinity

4 ≤y <∞