There are currently 21 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days. How long will it take (in days) for there to be 130 frogs in the pond?

Answer:

For #5: There are 3 children and 4 adults.

Step-by-step explanation:

Let x= number of children

y= number of adults

y = x + 1

x + y = 7

x + (x+1) = 7

x + x + 1 = 7

2x + 1 = 7

2x = 7 - 1

2x = 6

x = 6/2

x = 3

y = x + 1

y = 3 + 1

y = 4

Therefore, the number of children is 3 and the adults are 4.

Answer:

\(4 \alpha ngles\)

4 angles

hope it help!

have a nice night

Complete question

A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.

What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)

Answer:

\(\frac{dx}{dt}=11.94m/min\)

Step-by-step explanation:

From the question we are told that

Slant height \(z=29m\)

Change in Vertical height  \(\triangle y=7m/s\)

Horizontal length \(x=21\)

Generally in finding the distance form the  top to the bottom of the wall it is mathematically given by

 \(x^2+y^2=z^2\)

 \(21^2+y^2=29^2\)

 \(y^2=29^2+21^2\)

 \(y=35.81\)

Generally solving for the differential equation is mathematically represented as

 \(x^2+y^2=29^2\)

 \(2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0\)

 \(x*\frac{dx}{dt} +y*\frac{dy}{dt} =0\)

 \((21)*\frac{dx}{dt} +(35.81)*(-7) =0\)

 \((21)*\frac{dx}{dt} -250.64 =0\)

 \(\frac{dx}{dt}=\frac{250.64}{21}\)

 \(\frac{dx}{dt}=11.94m/min\)

The rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.

Let us consider that distance between the top of the ladder and the ground is x meter and distance between the bottom of the ladder and the wall is y meter.

So, A right angle triangle is formed.

Since, the bottom of the ladder is 21 meters from the wall.

So,    \(y=21\)

Applying Pythagoras theorem,

                         \(x^{2} +y^{2}=(29)^{2} \\\\x^{2} +(21)^{2}=(29)^{2} \\\\\\x^{2} =841-441=400\\\\x=\sqrt{400} =20\)

Given that,   the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.

                           \(\frac{dx}{dt}=-7meter/min\)

Differentiate below equation with respect to time.

                     \(x^{2} +y^{2}=(29)^{2} \\\\2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 \\\\2(20)(-7)+2(21)\frac{dy}{dt}=0\\\\\frac{dy}{dt}=\frac{280}{42}=6.67meter/min.\)

Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.

Learn more about Differentiation here:

https://brainly.com/question/14023950

30/2 = 15

it could be any positive number that is smaller than 15

Answer:

x = -5

Step-by-step explanation:

0.2x-8=0.4x-7

First, add 8 to both sides.

0.2x-8+8=0.4x-7+8

0.2x=0.4x-1

Next, subtract 0.4x from both sides.

0.2x-0.4x=0.4x-1-0.4x

-0.2x=1

Divide both sides by -0.2:

-0.2x/-0.2=1/-0.2

x=-5

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

Read more:

https://brainly.com/question/11067755

Answer:

the last option

Step-by-step explanation:

slope: 4/1

y-intercept: 12

hopefully this helps :)

Answer:

Divide 52.8 by 9 = 5.866 ounces per bag

Step-by-step explanation:

Divide 52.8 by 9

52.8/9 = 5.866 ounces per bag

Answer: y+7 = 3(x-5) A

Step-by-step explanation: Plug in the points into y-y1= m(x-b)

We can write (15 + 45) as a product of 2 factors using GCF and the distributive property 15(1 + 3).

We are given the following expression-

15 + 45

Now, we can factorize 15 into prime factors as follows -

= 3 × 5 (15 × 1)

Similarly, we can factorize 45 into prime factors as follows -

= 3 × 3 × 5 (15 × 3)

Thus, the greatest common factor of 15 and 45 is 15, so we can

= 15 × 1 = 15 and 15 × 3 is 45

Hence, we can write (15 + 45) as 15(1 + 3).

Learn more about the distributive property:

brainly.com/question/28490348

#SPJ4

Answer:

D, 35

Step-by-step explanation:

7b, if b=5, is the same as 7(5), or 7*5, which equals 35.

Answer:

35

Step-by-step explanation:

7B = 5+5+5+5+5+5+5 which equals 35

Remember to press Thanks!

Answer:

$207

Step-by-step explanation:

We do 1242 / 6 = 207

It costs $207 for each family member.

Answer:

207 each

Step-by-step explanation:

Take the total cost and divide by the number of family members

1242 / 6

207 each

Answer:

ive done the math, and im not sure if i have the correct answer or not, but i have arrived at choice B

Step-by-step explanation:

i apologize sincerely if this is incorrect

The residue from $0 to $82 is 44 ≡ x(mod83)

17−1≡x(mod83)

17∗17−1≡17x(mod83)      

5∗1≡5∗17=85(mod83)

5≡2x(mod83)

42∗5=210≡2∗42x=84x≡x(mod83)

44 ≡ x(mod83).

A mathematical operations that performs a calculation on two numbers is known as an arithmetic provider. They are used in everyday arithmetic, and most computer languages include a set of such operators that can be used within equations to perform a variety of sequential calculations. The following are examples of basic arithmetic operations are:

(+) Addition

Subtraction (-) (-)

() Multiplication            

() division

In programming, computers use different symbols to represent multiplication (*) and division (/). More complex operators, such as

Let's look at an ice cream multiplication example.              

There are two  groups, each has its own ice cream.

The total number of ice creams is 2x3=6    

To learn more about  residue
https://brainly.com/question/28690172
#SPJ4
               

The null hypothesis and conclude that high school students carry more textbooks on average than college students.

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen

To compare the number of books carried by high school students versus college students, we can start by calculating some descriptive statistics for each group.

For the high school group, we have the following data:

(5, 3, 2, 5, 6, 4, 7, 6, 5, 4, 3, 2, 1, 4, 3, 0, 2)  

The sample size is n = 17.

The sample mean is:

\($\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i\) =\(\frac{5+3+2+\cdots+0+2}{17} = 3.35$\)

The sample standard deviation is:

\($s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}\) =\(\sqrt{\frac{(5-3.35)^2 + (3-3.35)^2 + \cdots + (2-3.35)^2}{16}} \approx 1.97$\)

For the college group, we have the following data:

(5, 3, 2, 4, 1, 0, 0, 3, 6, 2, 1, 3, 1, 2, 4, 4, 2)

The sample size is n = 17.

The sample mean is:

\($\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i\)= \(\frac{5+3+2+\cdots+4+2}{17} = 2.29$\)

The sample standard deviation is:

$s =\(\sqrt{\frac{1}{n-1} \sum_{i=1}^{n}\) \((x_i - \bar{x})^2} = \sqrt{\{(5-2.29)^2 + (3-2.29)^2\)+ \(\cdots + (2-2.29)^2}{16}} \approx 1.50$\)

Based on these descriptive statistics, it appears that the high school students carried more books on average than the college students.

Learn more about  Probability here

https://brainly.com/question/30034780

#SPJ1

Answer:

a

Step-by-step explanation:

2^2x+1

2^(2x)+2¹

2^(2x)+2

Answer:

Step-by-step explanation:

No, this is not correct.

Step 1: Find the directional distance from every vertex on the blue image to  the center, Point C.

Point A is 1 unit left and 4 units upwards to Point C.

Point B is 4 units right and 5 units upwards to Point C.

Point C is the center of the dilation, so that point will not change.

Step 2: Apply the scale factor to the directional distances to know the distances of the new images.

The scale factor is 2 so

Point A' should be 2 units left and 8 units upwards to Point C.

Point B' should 8 units right and 10 units upwards to Point C.

Step 3:  Move the point in respect to Point C.

The new image should have the these points.

One point that is 2 units left and 8 units upwards to Point C.

Another point that is Point B' should 8 units right and 10 units upwards to Point C.

One point that coincides  with  Point C.

The correct inequality according to the given situation of the teacher would be (A) $385.41 ≤ m ≤ $539.58.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

When resolving an inequality, you can do one of the following: • Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount.

We must flip the inequality sign if you multiply or divide each side by a negative number.

So, we know that teacher earns:

$1,541.65

25% of $1,541.65:

1,541.65/100 * 25

$385.4125

35% of $1,541.65:

1,541.65/100 * 35

$539.5775

Inequality: $385.4125 < x < $539.5775

Rounding off: $385.41 ≤ m ≤ $539.58

Therefore, the correct inequality according to the given situation of the teacher would be (A) $385.41 ≤ m ≤ $539.58.

Know more about inequality here:

https://brainly.com/question/28964520

#SPJ1

Correct question:
A high school teacher earns an average bi-weekly net pay of $1,541.65. which compound inequality correctly shows the amount of money, m, the teacher can spend if the monthly budget for housing is between 25% and 35%.

a. $385.41 ≤ m ≤ $539.58

b. $668.05 ≤ m ≤ $1,002.07

c. $770.83 ≤ m ≤ $1,079.16

d. $835.06 ≤ m ≤ $1,169.08

Answer:

b

Step-by-step explanation:

Answer:

5 rational no.can exist between 0and -1

Answer:

It's 8.93 x 103

As per the concept of z - score, the percentile would this client's score is 0.4772

Z - score:

In statistics, z - score is also termed the standard score, is used to determine how much each data point position is away from its mean. Where as in other words, it measures the deviation of x (data point) in terms of the standard deviations. Here the percentage of the population above or below the score can be obtained using z tables.

Given,

A test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test.

Here we need to find at what percentile (rounded off) would this client's score place her.

As per the formula of z score, here we have the values,

mean = 100

standard deviation = 15

Score = 130

Therefore, the z score is calculated as,

=> z score = (130 - 100) / 15

=> z score = 30 / 15

=> z score = 2

According to the z score table the resulting value is 0.4772.

To know more about Z score here.

https://brainly.com/question/15016913

#SPJ4

Step-by-step explanation:

Since ∠E is right angle, its opposite side is DF and the legs are DE and EF.

Pythagorean applied:

As per we know according to Pythagorean theorem

Here

\(\\ \tt\hookrightarrow DF^2=DE^2+EF^2\)

There are 2000 pounds in a ton. Therefore, there would be 2000 one-pound units in a ton.

The pound (lb) is a unit of mass or weight commonly used in the United States and other countries. A ton is a unit of weight that is equal to 2000 pounds in the US customary system. So, 1 ton is equal to 2000 pounds.

To convert from pounds to tons, you need to divide the weight in pounds by 2000. For example, if you have 4000 pounds of weight, to convert it to tons, you would do:

4000 lb ÷ 2000 lb/ton = 2 tons

Similarly, if you have 1 pound of weight and want to know how many of them are in a ton, you would divide the weight of a ton (2000 pounds) by 1 pound:

2000 lb/ton ÷ 1 lb = 2000 units of 1 pound in a ton

Therefore, there are 2000 one-pound units in a ton.

To learn more about ton please click on below link.

https://brainly.com/question/14761940

#SPJ4

★» -30, 10

★» Yes, I use ★» at the beginning of each sentence, it's my style.

Answer:Its c

Step-by-step explanation:

Answer: Part 1: DC=2 units

BC=13 units

Part  2: AB=40 units

DE=26

Step-by-step explanation:

Answer:

Step-by-step explanation:

X axis intercept (y=0)

3x+2(0)=5

3x=5

x=5/3

Y axis intercept (x=0)

3(0)+2y=5

2y=5

y=5/2

so, the interception points are: (5/3,0) and (5/2,0)

Answer:

3.75+3.75=7.5

or

3×2.5=7.5

Step-by-step explanation:

Your welcome :)