Applications of exponential functions

Answer:

the first blank is 2, the second one is 1

Answer:

Yellow box #1=2

Yellow box #2=1

Step-by-step explanation:

#1) 8-6=2

#2)8-7=1

Answer:

Graph is attached below

Step-by-step explanation:

You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.

The plotted straight line is as shown in below graph.

Given straight line equation is y = x + 2

To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.

After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.

Example, take x = 1 and x = 2 for straight line y = x + 2

Then we get:

For x = 1, y = 1 + 2 = 3

For x = 2, y = 2 + 2 = 4

The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.

Learn more here:

https://brainly.com/question/959487

Answer:

x=7

Step-by-step explanation:

Answer:

the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]

C) 59

Step-by-step explanation:

Recall that;

[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]

Therefore, we can evaluate the series;

[tex]\sum_{k=1}^{6}(25-k^2)[/tex]

by summing the values of the series within that interval.

the values of the series are evaluated by substituting the corresponding values of k into the equation.

[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]

So, the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]

Answer:

45°

Step-by-step explanation:

This is a special 6 - 6 - 6√2 right triangle with angle measures 45° - 45° - 90°

Answer:  m∠R = 45°

Step-by-step explanation:

[tex]6^{2}\ +\ 6^{2} = 72[/tex]

[tex]\frac{\left(6\right)}{\sqrt{72}}=0.7071067812[/tex]

[tex]\sin^{-1}\left(\frac{\left(6\right)}{\sqrt{72}}\right)= 45[/tex]

Answer:

try 3x=30 or 10

Step-by-step explanation:

a) Simply do 0.135(13.5%)*550 to get that his rent increases by $74.25.

b) Simply do 550+74.25 to get that his new rent is $624.25.

c) 624.25/550 = 1.135, or 100%+13.5%, the amount his rent increased.

Hope it helps <3

Answer:

A. $74.25

B. $624.25

C. 1.135, and this is a connection to part a because it's what we multiplied 550 by to get our new rent.

Step-by-step explanation:

If Shawn pays $550 per month for rent, and he has a 13.5% increase, we can multiply 550 by [tex]1+\frac{13.5}{100}[/tex] to get our new number.

[tex]1+0.135=1.135[/tex]

[tex]550\cdot1.135=624.25[/tex]

This is the new monthly rent, part B. To find Part A, let's subtract 550 from thi number.

[tex]624.25-550=74.25[/tex]

Now, for part C, let's divide 624.25 by 550.

[tex]624.25\div550 = 1.135[/tex]

If you notice, 1.135 is the same number we multiplied 550 by to get our new cost, and as a percent, 1.135 is 113.5%.

Hope this helped!

Answer:

1/6

Step-by-step explanation:

As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.

The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2  divided by total number of defective bulbs.

P(defective in box 2)= N(defective in box 2)/N(defective total)

As we know there is only 1 defective lamp in box 2.

So N(defective in box 2)=1

Total number of defective bulbs is Box1- 2 defective  bulbs,  box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.

So N(defective total)=6

So P(defective in box 2)=1/6

Answer:

Step-by-step explanation:

If you take 10 percent of a number and get 35, then what is that number?

In other words, you know that 10 percent of a number is 35 and you want to know what that initial number is.

To solve this problem you multiply 35 by 100 and then divide the total by 10 as follows:

(35 x 100) / 10

When we put that into our calculator, we get the following answer:

350

Therefore, you can derive that 10 percent of 350 equals 35.

Answer:

[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]

Step-by-step explanation:

divide each term by 2y^3

Multiply through by the least common denominator.

Answer: { 0.5995, 0.8025 }

Step-by-step explanation:

Given that

                   Estimates          Std. Error         t value            Pr(>/t/)

Intercept:         -90.020          16.702           -5.390             0.000

length    :           0.701             0.044            15.798              0.000

Now using the given information to compute a 95% confidence interval for the slope:

We use the formula

β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁

So we know that number of values (n) = 10

therefore error of degree of freedom df = n -2 = (10-2) = 8

Level of significance α ( 1 - 0.95 ) = 0.05

so tₐ/₂, ₙ₋₂ = t ₍₀.₀₅/₂, ₁₀₋₂

t ₀.₀₂₅, ₈ = 2.306 (critical value)

From the given table ( regression analysis output)

slope regression β₁ = 0.701

The standard error of the slope is Sβ₁  = 0.044

Let “the maximum size of salmonids consumed by a northern squaw fish” be the response variable and “squawfish length” be the explanatory variable.

The 95% confidence interval for the slope of the regression is:

β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁ = 0.701 ± 2.306 (0.044)

= 0.701 ± 0.101464

= { 0.701 - 0.101464, 0.701 + 0.101464 }

= { 0.599536, 0.802464 } ≈  {0.5995, 0.8025 }

The confidence interval of the slope is (0.599, 0.803)

The sample size is given as:

[tex]\mathbf{n = 10}[/tex]

The confidence interval is given as:

[tex]\mathbf{CI = 95\%}[/tex]

Start by calculating the degrees of freedom

[tex]\mathbf{df = n - 2}[/tex]

So, we have:

[tex]\mathbf{df = 10 - 2}[/tex]

[tex]\mathbf{df = 8}[/tex]

The level of significance is calculated as:

[tex]\mathbf{\alpha = 1 - CI}[/tex]

So, we have:

[tex]\mathbf{\alpha = 1 - 95\%}[/tex]

[tex]\mathbf{\alpha = 0.05}[/tex]

The critical value at 0.05 level of significance and 8 degrees of freedom is:

[tex]\mathbf{t_{\alpha} =2.306}[/tex]

The confidence interval of the slope is then calculated as:

[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]

From the question, we have:

[tex]\mathbf{S\beta_1 = 0.044}[/tex] --- standard error of the slope

[tex]\mathbf{\beta_1 = 0.701}[/tex] -- the slope

So, the equation becomes

[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]

[tex]\mathbf{CI = 0.701 \pm 2.306 \times 0.044}[/tex]

[tex]\mathbf{CI = 0.701 \pm 0.102}[/tex]

Split

[tex]\mathbf{CI = (0.701 - 0.102,0.701 + 0.102)}[/tex]

[tex]\mathbf{CI = (0.599,0.803)}[/tex]

Hence, the confidence interval of the slope is (0.599, 0.803)

Read more about confidence intervals at:

https://brainly.com/question/24131141

Step-by-step explanation:

8.x×8-12=50

8x-12=50

9.1/2x>or=100

10.2 whole number5/9-x=31

Answer:

( A -c) /B =t

Step-by-step explanation:

A=Bt+c

Subtract c from each side

A-c=Bt+c-c

A -c = Bt

Divide each side by B

( A -c) /B = Bt/B

( A -c) /B =t

Answer:

Hey there!

A=Bt+c

A-c=Bt

t=(a-c)/B

Hope this helps :)

Answer:

10

Step-by-step ex1planation:

Here is the correct format for the question

At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h².Let v(f) be the velocity of the car t hours after 2:00 PM.Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex]. By the Mean Value Theorem, there is a number c such that 0 < c < [tex]\Box[/tex]  with v'(c) = [tex]\Box[/tex]. Since v'(t)  is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 80 mi/h^2.

Answer:

Step-by-step explanation:

From the information given :

At  2:00 PM ;

a car's speedometer v(0) = 30 mi/h

At 2:15 PM;

a car's speedometer v(1/4) = 50 mi/h

Given that:

v(f) should be the velocity of the car t hours after 2:00 PM

Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex] will be:

[tex]= \dfrac{50-30}{1/4 -0}[/tex]

[tex]= \dfrac{20}{1/4 }[/tex]

= 20 × 4/1

= 80 mi/h²

By the Mean value theorem; there is a number c such that :

[tex]\mathbf{0 < c< \dfrac{1}{4}}[/tex]     with [tex]\mathbf{v'(c) = \dfrac{v(1/4)-v(0)}{1/4 -0}} \mathbf{ = 80 \ mi/h^2}[/tex]

By the mean value, theorem a number [tex]C[/tex] is [tex]0 < C < \frac{1}{4}[/tex].

The velocity of the car is [tex]80 \ mi/h^{2}[/tex].

Speed is defined as The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Given that,

at 2:00 pm [tex]v(0)=30 \ mi/h[/tex]

at 2:15 pm [tex]v(1/4)=50 \ mi/h[/tex]

Then,

[tex]=\frac{v(1/4)-v(0)}{1/4-0} \\=\frac{50-30}{1/4} \\=20\times4\\=80 \ mi/h^{2}[/tex]

By the mean value theorem a number [tex]C[/tex] such that express as,

[tex]0 < C < \frac{1}{4}[/tex].

Now with,

[tex]{v}'(c)=\frac{v\left ( \frac{1}{4} \right )-v\left ( 0 \right )}{\frac{1}{4}-0} \\ =80 \ mi/h^{2}[/tex]

Learn more about the topic Speed: https://brainly.com/question/26417650

Notice that C has a clockwise orientation. By Green's theorem, we have

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

where D is the triangule region with C as its boundary, given by the set

[tex]D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}[/tex]

So we have

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx[/tex]

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}[/tex]

I believe the value is negative 4. If not, well, try any negative below that, such as -5,6,7,8, etc.

Answer:

y is less than -3

Step-by-step explanation:

To do this you would just subtract 9 from both sides so you get -y is greater than 3. Since you cannot have y as a negative number you will divide -1 from both sides but when you do that you will have to flip the sign so you get y is less than -3.

Answer:  103 adult tickets

Step-by-step explanation:

Adult tickets (a) = a

Student tickets (s) = 2a

Total = 309

a + 2a = 309

     3a = 309

      a = 103

Answer:

Step-by-step explanation:

Total tickets sold = 309

Let the number of adult tickets sold be x

Let the number of student tickets sold be 2x

Adult tickets + student tickets = 309

[tex]x + 2x = 309[/tex]

Collect like terms

[tex] 3x = 309[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{309}{3} [/tex]

Calculate

[tex]x = 103[/tex]

Hence, 103 adult tickets were sold.

Hope this helps..

Good luck on your assignment...

Answer:

The beryllium atom; 1.99 times larger.

Step-by-step explanation:

The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.

(1.12 * 10^-10) / (5.6 * 10^-11)

= (1.112 / 5.6) * (10^-10 + 11)

= 0.1985714286 * 10

= 1.985714286 * 10^0

So, the beryllium atom is about 1.99 times larger than the other.

Hope this helps!

Greetings from Brasil...

X = 2 liter container

Y = 3 liter container

the total of containers are:

X + Y = 400

the capacity of the containers is

2X + 3Y = 1100

Assembling the equation system

2X + 3Y = 1100

X + Y = 400       x(-2)

2X + 3Y = 1100

-2X  -2Y = - 800    

X + Y = 400    so

X + 300 = 400

X = 400 - 300

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

BR:

Observe que:

1 vasilha de 2L = 1 × 2 = 2L

2 vasilhas de 2L = 2 × 2 = 4L

3 vasilhas de 2L = 3 × 2 = 6L

X vasilhas de 2L = X × 2 = 2X litros

.....

1 vasilha de 3L = 1 × 3 = 2L

2 vasilhas de 3L = 2 × 3 = 4L

3 vasilhas de 3L = 3 × 3 = 6L

X vasilhas de 3L = X × 3 = 3X litros

Logo 2X + 3Y = 1100

Existem X e Y vasilhas que num total sao 400, logo

X + Y = 400

Answer:

Event B is mutually exclusive

Step-by-step explanation:

The mutually exclusive events are one which cannot happen together. The observation is made regarding male biology age. It is not possible that all male biology are 20 years old. There can male biology who are less than or greater than 20 years of age. The can not be all together 20 years old. The event is then considered as mutually exclusive.

Answer:

The level of significance to be used is α = 0.0025

Step-by-step explanation:

Here, we are interested in calculating the the level of significance which at most must be used for each of the hypothesis test

We proceed as follows;

P(type 1 error) = α

From the question, n = number of hypotheses = 20

P( of one or more type one error) ≤ 0.05

1- P(no type one error) ≤ 0.05

Hence;

1- (1-α)^20 ≤ 0.05

(1-α)^20 ≥ 0.95

1- α ≥ 0.997438621223

α ≤ 0.00256

Thus α = 0.0025

Answer:

15 people

Step-by-step explanation:

since Raul and his friends each weigh 1/20 ton,

and the total weight reads 3/4 ton

The total number pf people on the scale will be:

The total weight of Raul and his friends divided by their individual weight

==> (3/4 ton) ÷ (1/20 ton)

= 3/4 X 20/1 = 15 people

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

This is the plato answer, I hope this is the answer youre looking for! :))

Answer:

Step-by-step explanation:

An equilateral triangle is a triangle that has all of its sides equal. Let a, b and c be the sides of the equilateral triangle. Since all the sides are equal, then

a = b = c.

The perimeter of the triangle is the sum of all the sides of the triangle.

P  = a + b+ c

GIVEN THE PERIMETER OF THE EQUILATERAL TRIANGLE AS P = 15 x + 30 units and a = b = c, then;

15 x + 30 = a + b + c

15 x + 30 = a + a + a (since all sides are equal)

15 x + 30 = 3a

3a = 15 x + 30

3a = 3(5x+10)

Dividing both sides by 3 will give;

3a/3 =   3(5x+10)/3

a = 5x+10

Hence, the length of one side of the equilateral triangle is 5x + 10 units.

Answer:

D.

Step-by-step explanation:

Edge 2020

Answer:

7

Step-by-step explanation:

Take the amount of money and divide by the cost per fish

46/6 =7 with 4 dollars remaining

She can buy 7 goldfish

Answer:

7

Step-by-step explanation:

7 x 6 = 42

Answer:

a. 0.06

b. 0.2

Step-by-step explanation:

a. P(B given A) = P(A and B) / P(A)

0.1 = P(A and B) / 0.6

P(A and B) = 0.06

b. P(A given B) = P(A and B) / P(B)

P(A given B) = 0.06 / 0.3

P(A given B) = 0.2

Answer:

Hello There!

~~~~~~~~~~~~~~~~~~~`

3 − x = 2 =

X = 1

Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you. Brainliest would be nice!

Answer: x = 1 / 1 = x.

Step-by-step explanation:

3 - x = 2

First, since you can't subtract x from 3, we find ways to subtract 2 from 3.

So, we write the 3 and attach (-) minus/negative sign to the 3 with 2. Because when a number crosses the equal sign and it is negative, it becomes positive and when it is positive, it becomes negative.

And 2 will cross the equal sign so,it will be (-) just like: -2. And -x will cross the equal sign so it will be x. Let's solve it with the steps above:

3 - x = 2

3 - 2 = x

1. = x

OR

3 - x = 2

-x = 2 - 3

-x/- = -1/-

So, negative will cancel negative.

x =1.

Please mark me as the brainliest!!

Thanks!!

Answer:

A: (–0.3, 2.1)

Answer:a

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

In a linear equation, y = mx + b, m is represented as gradient (slope) and b is the y-intercept.

So for this question, m is 2/3 and b is 1.

Answer:

7.7cm

Step-by-step explanation:

Area of a rectangle is expressed as

A = Length × Width

A = LW

Let dL and dW be the errors in the measurements.

If there is an error of at most 0.1cm each in the measurement, then dL = dW = 0.1cm.

The area of the rectangle with error will be expressed as A = LdW + WdL

Given L = 27cm and W = 50cm

A = 27(0.1)+50(0.1)

A = 2.7+5.0

A = 7.7cm

Hence, the maximum error in the calculated area of the rectangle is 7.7cm