An underwater robot takes a picture at an elevation of -8 5/12m relative to sea level. What is the robot’s elevation expressed sans decimal?

Answer:

[tex]\textsf{a)} \quad y=3\left(\dfrac{5}{3}\right)^x[/tex]

[tex]\textsf{b)} \quad y=40\left(\dfrac{1}{3}\right)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

From inspection of the diagram, two points on the graph are:

The y-intercept is the y-value when x = 0.

As a is the y-intercept, and the y-intercept is 3:

[tex]\implies y=3 \cdot b^x[/tex]

Substitute point (1, 5) into the equation and solve for b:

[tex]\begin{aligned}(1,5) \implies 5&=3 \cdot b^1\\5&=3b\\b&=\dfrac{5}{3}\end{aligned}[/tex]

Therefore, the equation of the exponential function is:

[tex]y=3\left(\dfrac{5}{3}\right)^x[/tex]

From inspection of the diagram, two points on the graph are:

The y-intercept is the y-value when x = 0.

As a is the y-intercept, and the y-intercept is 40:

[tex]\implies y=40 \cdot b^x[/tex]

Substitute point (-1, 120) into the equation and solve for b:

[tex]\begin{aligned}(-1,120) \implies 120&=40 \cdot b^{-1}\\\dfrac{120}{40}&=\dfrac{1}{b}\\b&=\dfrac{40}{120}\\ b&=\dfrac{1}{3}\end{aligned}[/tex]

Therefore, the equation of the exponential function is:

[tex]y=40\left(\dfrac{1}{3}\right)^x[/tex]

Answer:a

Step-by-step explanation:

Answer:

Step-by-step explanation:

You have a piecewise defined function f(x) and you want the values of f(-5), f(-2), and f(1).

The first step in finding the value of a piecewise defined function is to determine the function definition on the domain containing the x-value of interest.

The value x=-5 is in the interval x < -2, so the first part of the function definition applies: f(x) = 3.

  f(-5) = 3

The value x = -2 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².

  f(-2) = -(-2 -1)² = -(-3)²

  f(-2) = -9

The value x = 1 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².

  f(1) = -(1 -1)² = -(0)²

  f(1) = 0

The required value of f(5) would be 81.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

We have been given the function below as:

f(n) = f(n-1) - 3   ....(i)

f(1) = 3

To determine the value of f(5)

Substitute the value of n = 2 in the equation (i);

f(2) = - 3f(1) = - 3;

n = 3,

f(3) = - 3f(2) = 9;

n = 4,

f(4) = - 3f(3) = - 27,

n = 5,

f(5) = - 3f(4) = 81

Thus, the required value of f(5) would be 81.

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Answer:

y = 31

Step-by-step explanation:

2y-5+123=180

123 - 5 = 118

2y+118=180

subtract 118 from both sides

2y+118 - 118 = 180 - 118

180 - 118  = 62

2y = 62

divide 2 by both sides

2y/2 = 62/2

y = 31

Answer:

Step-by-step explanation:

2y+−5+123=180

Step 1: (Combine Like Terms)

(2y)+(−5+123)=180

Step 2:  (Subtract 118 from both sides)

2y+118−118=180−118

2y=62

Step 3: Divide both sides by 2

2y/2= 62/2

y=31

The value of 3¾ft in yards would be = 1 6/25 yard

A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.

To convert to yards;

1 ft = 0.33 yard

3¾ = X yards

make x yards the subject of formula;

X yards = 3¾ × 0.33

X yards = 3.75×0.33

X yards = 1.24 yards

X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.

Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25

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The maximum width and area of rectangle are 475 feet and 225625 sq. feet respectively.

Any given rectangle  has ONE region - there is no base or most extreme, simply a region. To find the region of a rectangle  shape, increase the length times the width. For instance, a rectangle  shape 4′ long by 5′ wide will have an area of 20 square feet.

We have

l×w = area of rectangle-------------------------(1)

2w + l = 950

l = 950 - 2w

Put the value if l in equation (1)

(950 - 2w) × w = area

This is a quadratic equation for maximum value of w we have of it one zeros is zero

so,

950 - 2w = 0

w = 950/2

W =475 feet

Te

Then length = 950 - 475 =475

Area of rectangle = 475 × 475 = 225625 sq. feet

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The probability that a comfortable chair in the store is blue is 4%

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

Proportion of blue chairs = 20%

Proportion of orange chairs = 50%

Proportion of black chairs = 30%

Comfortable Blue chairs = 20%

Comfortable non-blue chairs = 5%

The required probability is then calculated as

Probability = Proportion of blue chairs x Comfortable Blue chairs

Substitute the known values in the above equation, so, we have the following representation

Probability = 20% * 20%

Evaluate

Probability = 4%

Hence, the probability is 4%

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Answer:

14 base 10

Step-by-step explanation:

Remember what the digits mean in the base 10 system we use.

For example, the number 539 (base 10) means:

The 5 in the hundreds place means 5 × 100 = 500.

The 3 in the tens place means 3 × 10 = 30.

The 9 in the ones place means 9 × 1 = 9.

The number 539 means

5 × 100 + 3 × 10 + 9 × 1 = 500 + 30 + 9 = 539

Also keep in mind one more thing. The ones digit means the number of ones. 1 = 10^0. The number in the ones digit means the number if 10^0 you have.

The ten digits is the digit of 10^1.

The hundreds digit is the digit of 10^2 since 10^2 = 100.

In other words, the ones digit is the number of 10^0 you have.

The tens digit is the number of 10^1 you have.

The hundreds digit is the number of 10^2 you have.

Now let's look at base 5.

Here, each place to the left is a successively higher power of 5 instead of a power of 10.

Think of the number 432 base 5.

The 2 is in the units place. it represents the number of 5^0 or ones you have. In this case, it is 2 × 5^0 = 2 × 1 = 2

The 3 is in the 5^1 place. It represents the number of fives you have.

3 × 5 = 15

The 4 is in the 5^2 place. It represents the number of 25's you have.

4 × 25 = 100

The number 432 base 5 means:

4 × 5^2 + 3 × 5^1 + 2 × 5^0

= 4 × 25 + 3 × 5 + 2 × 1

= 100 + 15 + 2

= 117 base 10

In other words, 432 base 5 = 117 base 10.

Now we do the same with your number, 24 base 5.

24 base 5 =

= 2 × 5^1 + 4 × 5^0

= 2 × 5 + 4 × 1

= 10 + 4

= 14

Answer: x =4

Step-by-step explanation: The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4 thus option (A) will be correct.

What is the equation?

There are many different ways to define an equation.

More than one variable may be present inside a linear equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

24 + 0.44x = 19 + 1.69x

24 - 19 = 1.69x - 0.44x

5 = 1.25x

x = 4

Hence "The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4".

Answer: It is B

Step-by-step explanation:

If you put leg a (3) and leg b (4) into a Pythagorean equation it will turn out like this

3^2+4^2=x^2

9+16=x^2

25=x^2

√25=√x

5=x

5 is the missing side length, which corresponds to option b

Answer:

The man's monthly rental rate is $1600.

Step-by-step explanation:

To figure out the answer to your question, it says to find how much is monthly rental is. So, we can do this by simply dividing the two numbers:

4800 ÷ 3 = $1600

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[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ c = \sqrt{100^2+60^2~-~2(100)(60)\cos(60^o)} \implies c = \sqrt{ 13600 - 12000 \cos(60^o) } \\\\\\ c = \sqrt{ 13600 - 12000 \cdot \frac{1}{2} }\implies c=\sqrt{7600}\implies c=20\sqrt{19}\implies c\approx 87.18[/tex]

Answer: the percent decrease is 9%

Step-by-step explanation:

Formula :12500/14000x100% and this formula can use in any of question likes this

The minimum volume of the box =  11220 cubic centimeters

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

One notebook:

length, l= 29 cm

width = 21.5 cm

height = 1.5 cm

Volume of 1 notebook =  l*w*h

                                     =  29*21.5*1.5

                                     =  935.25

                                     ≈  935 cubic centimeters ( nearest whole number )

Volume of 12 notebooks = 935 * 12 = 11220 cubic centimeters

So, the minimum volume of the box =  11220 cubic centimeters

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Answer:

11,223

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) =-2 (x+4)

f(x)=2

x+4

Answer: d -3

Step-by-step explanation:

The answer I got was 11 = 21, which does not make sense

–2x + 11 = x + 21 + (-3)x

+3x                         +3x

x + 11 = x + 21

-x        -x

11 = 21

Answer:

-3

Step-by-step explanation:

The value of b in x²+ bx + 16/49 is 8/7 and the squared binomial is (x + 4/7)²

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

X^2+bx+16/49

Rewrite properly

So, we have the following representation

x²+ bx + 16/49

When represented as a square, we have

x²+ bx + 16/49 = (x + a)²

Expand the bracket

So, we have the following representation

x²+ bx + 16/49 = x² + 2ax + a²

By comparison, we have

bx = 2ax

a² = 16/49

Take the square root of both sides

a = 4/7

Substitute a = 4/7 in bx = 2ax

bx = 2 * 4/7x

So, we have

b = 2 * 4/7

Evaluate

b = 8/7

In (a), we have

x²+ bx + 16/49 = (x + a)²

Where

a = 4/7

So, we have

x²+ bx + 16/49 = (x + 4/7)²

Hence, the binomial is (x + 4/7)²

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Answer:

[tex]\textsf{1)} \quad b = \dfrac{8}{7}[/tex]

[tex]\textsf{2)} \quad \left(x+\dfrac{4}{7}\right)^2[/tex]

Step-by-step explanation:

Perfect Square Trinomial

A trinomial that can be written as the square of a binomial.

For example the perfect trinomial  x²+2dx+d² can be written  as (x+d)².

Given trinomial:

[tex]x^2+bx+\dfrac{16}{49}[/tex]

To express the given trinomial as a perfect square trinomial, determine the value of b.

As the coefficient of the x² term is one, b equals twice the square root of the constant of the trinomial:

[tex]\implies b = 2 \sqrt{\dfrac{16}{49}}[/tex]

[tex]\implies b = 2 \cdot \dfrac{4}{7}[/tex]

[tex]\implies b = \dfrac{8}{7}[/tex]

Therefore, the perfect square trinomial is:

[tex]x^2+\dfrac{8}{7}x+\dfrac{16}{49}[/tex]

To factor in the form of a squared binomial (x + d)², d is half the value of b:

[tex]\implies d = \dfrac{1}{2}b[/tex]

[tex]\implies d = \dfrac{1}{2} \cdot \dfrac{8}{7}[/tex]

[tex]\implies d=\dfrac{8}{14}[/tex]

[tex]\implies d=\dfrac{4}{7}[/tex]

Therefore, the perfect square trinomial as a squared binomial is:[tex]\implies \left(x+\dfrac{4}{7}\right)^2[/tex]

The amount you will have $6,500 with 5% in six years using continuous compounding is of:

$8,774.

The amount you will need to have the entire $32000 in the 6 years is of:

$18,890.46.

The balance of an account after t years, using continuous compounding, is given as follows:

[tex]B(t) = Pe^{kt}[/tex]

In which the parameters are given as follows:

Putting the $6,500 into the account, the values of the parameters are given as follows:

P = 6500, k = 0.05, t = 6.

Hence the balance will be of:

B(6) = 6500 x e^(0.05 x 6) = $8,774.

The balance to have the entire $32,000, considering what you already have, will be of:

32000 - 6500 = 25500

Hence the principal is obtained as follows:

Pe^(0.05 x 6) = 25500

P = 25500/e^(0.3)

P = $18,890.46.

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Answer:

[tex]C. \; \dfrac{x+2}{x+1}[/tex]

Step-by-step explanation:

Since the vertical asymptotes are at x = -1

This means the denominator must have x + 1 in it

The only expression is the one in choice C

Eva takes 51 errands (mins) to return home.

What do you mean by errands and give example ?

A short trip either to take a message or to take or collect something.

For example , I'll meet you at six, I have some errands to do/run first.

Given that :

Eva left the house at 11.28 am

Returned house at 12.19 pm

From the given information, we can conclude that how long was

she running errands

 11.28 am - 12.00 pm = 32 mins

 12.00 pm - 12.19 pm = 19 mins

                       Totally = 51 mins

Therefore, Eva takes 51 errands to return home.

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Answer:

y = 3.8x

Step-by-step explanation:

Let y = the cost of the cherries

Let x = pounds of cherries

We can find the unit rate by either:

[tex]\frac{7.98}{2.1}[/tex] =  $3.80 per pound

or

[tex]\frac{10.64}{2.8}[/tex] = $3.80 per pound

Now we can write the equation

hy = 3.8x

Answer:

D)The space heater, because it has the greater unit rate for electricity cost.

Step-by-step explanation:

I DID IT AND GOT IT RIGHT!

Decrease in the price is $1887, the price of the next model car is $35,113.

Percentage is a measurement to find value of the given number out of hundred.

Given that,

Price of current model = $37,000

The price of next model car is 5.1% less than the current model.

The price of the next model car = 94.9% of price of current model car

                                                     = 94.9 x 37,000/100

                                                      = 35,113

The decrease in the price = 37,000 - 35,113 = 1887

The price of the next model car is $35,113 and decrease in the price is $1887.

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The linear functions in this problem are given as follows:

First we define the horizontal line l, given as follows:

l: y = 4.

(as no matter the value of x, the output variable assumes a value of 4).

Then the vertical line p is defined as follows:

p: x = -4.

(as no matter the value of the output y, the input variable x assumes a value of -4).

For the remaining two lines, they are defined in the slope-intercept format, as follows:

y = mx + b.

In which the coefficients are given as follows:

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The percent error of the estimate is -2.14%

In this question, the figures are given as

Estimate = 5.5 cm

Actual = 5.62 cm

The percentage of the error is then calculated using the following equation

Error percentage = (Estimate - Actual)/Actual * 100%

Substitute the known values in the above equation, so, we have the following representation

Error percentage = (5.5 - 5.62)/5.62 * 100%

Evaluate

Error percentage = -2.14%

Hence, the error percentage is -2.14%

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Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

(6/9) × (3/8)

Cross simplify:

(3/3) × (1/4)

3/12

1/4