The national history museum has collected 45 dinosaurs. George has collected 3/5 of this amount. How many dinosaurs has george collected?

(g3 math)

Answer:

Here, given

present population = 20000

according to question,

population gets double every 34 years

i.e P = 20000 × 2

= 40000

now,

P = 40000

T = 68-34 = 34

ie, again p is double

so, P = 40000×2

= 80000

Hence, the population after 68 years from now is 80000

Answer:

Roberto will pay a total of $525,654 for the house.

Answer: a. To shift the graph of f(x) downward 5 units, we subtract 5 from the function: f(x) - 5. To shift it left 3 units, we replace x with x + 3: f(x + 3) - 5. To stretch it vertically by a factor of 4, we multiply the entire function by 4: 4[f(x + 3) - 5]. Finally, to reflect it about the x-axis, we take the negative of the function: -4[f(x + 3) - 5]. Therefore, the equation of the new function g(x) is:

g(x) = -4[1/2^(x+3) - 5]

b. To find the y-intercept, we set x = 0 in the equation of g(x):

g(0) = -4[1/2^(0+3) - 5] = -4[1/8 - 5] = -4[-39/8] = 195/2

Therefore, the y-intercept is (0, 195/2).

c. The domain of g(x) is all real numbers, since there are no restrictions on x.

d. To find the range of g(x), we first observe that the function is decreasing and asymptotic to y = -5 as x approaches infinity. This means that the range of g(x) is all real numbers less than or equal to -5.

Step-by-step explanation:

The correct option is (a) ŷ = -1.34x+21.5 , that is the best model to fit the scatter plot.

A scatter plot (or scatter chart, scatter graph) uses dots to represent values for two(2) different numeric variables. The position of each dot on horizontal and vertical axis indicates values for an individual data point.

The model of the equation best for the plot is,

ŷ = -1.34x+21.5

At point (1,20),

ŷ  = -1.34x+21.5

20 = (-1.34 ×  1) + 21.5

20 ≈ 20.15

At point (3,19),

ŷ = -1.34x+21.5

19 = (-1.34 × 3) + 21.5

19 ≈17.45

At point (5,15),

ŷ = -1.34x+21.5

15 = (-1.34 × 5) + 21.5

15 ≈ 14.75

The model ŷ = -1.34x+21.5   is giving the best estimation.

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The terms for the definitions are matched -

National markets - Statement 1

International markets - Statement 2

Interdependence - Statement 3

Goods and services - Statement 4

Globalization - Statement 5

What is interdependence?

Inter- is short for "between," hence interdependence is the dependence of two or more things. Interdependence is a common term used to characterize complicated systems. Couples become interdependent once they are married.

National markets: These are the places where goods and services are bought and sold within a single country.

These markets are the result of the development of transportation and communication technologies such as railroads and advertising.

International markets: These are the places where goods and services are bought and sold between countries.

These markets involve buyers in other countries, including consumers, producers, resellers, and governments.

The development of international markets is a result of globalization and the increasing interdependence of countries.

Interdependence: This refers to the relationship between countries in which they rely on one another for resources, goods, or services.

Interdependence is a result of the development of national and international markets and is a key feature of globalization.

Goods and services: These are the objects and actions that people value and produce to satisfy human wants.

Goods are physical products such as clothing, food, and cars, while services are non-physical products such as education, healthcare, and transportation.

Globalization: This refers to the process by which businesses or other organizations develop international influence or start operating on an international scale.

Globalization is a result of the development of national and international markets and involves the increasing interdependence of countries.

It has led to the growth of international trade, the spread of cultural values and ideas, and the development of global networks and technologies.

Therefore, the keywords are matched using the definition.

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A)
i) the inequality to show the number of ballons that the dance committee can buy is: 0.80b + 65 ≤ 125

ii)  solving the inequality above, we arrive at b ≤ 75
B) The graph is attached accordingly.

C) See the description of the solution below.

Let's start by defining our variables. Let b be the number of balloons that the dance committee could buy.

The cost of b balloons is $0.80b. We want to make sure that the cost of the balloons plus the amount already spent on decorations ($65) is less than or equal to the budget of $125. So we can write the following inequality:

0.80b + 65 ≤ 125

Now we can solve for b:

0.80b + 65 ≤ 125

0.80b ≤ 125 - 65

0.80b ≤ 60

b ≤ 75

Therefore, the dance committee can buy up to 75 balloons to stay within their budget.

To graph the solution set, we can plot b on the horizontal axis and shade the region to the left of b = 75, since b must be less than or equal to 75.

The solution set represents all possible values of b that satisfy the inequality. In this case, the solution set is b ≤ 75, which means that the dance committee can buy up to 75 balloons and still stay within their budget.

As the number of balloons increases, the cost of the balloons also increases, and the amount of money left in the budget decreases.

Therefore, the more balloons the dance committee buys, the less money they will have left for other decorations or expenses.

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Full Question:


Since the above question is incomplete, it appears you are referring to the question below.


The dance committee has a budget of $125 to decorate the gym for a spring dance. They already spent $65. Some members want to buy helium balloons that cost $0.80 each.

A) Write and solve an inequality to show the number of balloons that the dance committee could buy.

B) Graph the solution set for the inequality.
C) Describe what the solution means and how the number of balloons affects the amount in the budget.

Answer: Let's assume the two original numbers to be x and y.

If one of them is increased by 50%, then the new value will be 1.5x, and if the other one is decreased by 50%, the new value will be 0.5y.

The product of the two new numbers will be:

1.5x * 0.5y = 0.75xy

So, the new product is 0.75 times the original product. This means the product of the two numbers has decreased by 25%.

To summarize:

If one number is increased by 50% and the other number is decreased by 50%, the product of the two numbers will decrease by 25%.

The new product is 0.75 times the original product.

Brainiest is appreciated (:

Answer:

0.48

Step-by-step explanation:

By the law of sines, the ratio of the sides of a triangle to the sine of the angles opposite the side must be the same

Therefore
[tex]\dfrac{EG}{\sin90} =\dfrac{ FG}{\sin E}\\\\\\\dfrac{\sqrt{69}}{\sin 90} = \dfrac{4}{\sin E}}\\\\\\\sin 90 = 1\\\\\dfrac{\sqrt{69}}{1} = \dfrac{4}{\sin E}\\\\\sqrt{69} = \dfrac{4}{\sin E}\\\\\sin E = \dfrac{4}{\sqrt{69}}\\\\\\= 0.481543\\\\= 0.48 \text{ rounded to the nearest hundredth}[/tex]

In response to the question, we may say that  Hence, 2 131/200 is the decimal mixed number in its most basic form.

The decimal number system is frequently used to express both integer and non-integer quantities. Non-integer values have been added to the Hindu-Arabic numeral system. The technique used to represent numbers in the decimal system is known as decimal notation. A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole quantities is expressed using decimal numbers, which are in between integers. The full number and the fractional part of a decimal number are separated by a decimal point. The decimal point is the little dot that appears between whole numbers and fractions. An example of a decimal number is 25.5.

We must separate the whole number and fraction components of 2.655 in order to change it into a mixed number. The integer portion of the decimal, which is 2 in this instance, represents the full number.

We take the total number and divide it by the decimal to determine the fractional portion.

2.655 - 2 = 0.655

The combined number is therefore 2 and 655/1000.

By dividing the numerator and denominator by their largest common factor, we may reduce the fraction to its simplest form and so make it easier to understand. The highest common factor between 655 and 1000 in this instance is 5.

655 ÷ 5 = 131

1000 ÷ 5 = 200

Hence, 2 131/200 is the mixed number in its most basic form.

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Answer: Ax+By=C This is the formula

Answer:

b i think let me know if im right

Step-by-step explanation:

This problem involves finding the probability of an event (a student being absent) given that another event has already occurred (today is Friday). This is an example of conditional probability.

Therefore, the correct answer is A) conditional probability.

Answer:

A.

Step-by-step explanation:

This is a conditional probability. None of the other choices make sense, but the most distinct word is "given". This is a sure sign of a conditional probability, or Bayes Theorem. The condition A is that it is Friday. Event B is that a student is absent. P (A|B)

To find the equation of the drone's path, we can first find the coordinates of the center of the circle that the drone is flying around. We can do this by finding the midpoint between the two points the drone passes over:

Midpoint in the x-direction: (220 ft - 180 ft)/2 = 20 ft to the right of the origin.

Midpoint in the y-direction: (230 ft - 180 ft)/2 = 25 ft above the origin.

Therefore, the center of the circle is located at (20, 25) ft.

The radius of the circle can be found by calculating the distance between the center of the circle and either of the two points the drone passes over:

Radius: sqrt((20-(-180))^2 + (25-180)^2) = sqrt(40000 + 15625) = 205 ft (rounded to the nearest whole number)

So the equation for the drone's path is:

(x - 20)^2 + (y - 25)^2 = 205^2

To find how far north of Megan's position the drone is when it passes due north, we can substitute x = 0 into the equation:

(0 - 20)^2 + (y - 25)^2 = 205^2

400 + (y - 25)^2 = 42025

(y - 25)^2 = 41625

y - 25 = +/-sqrt(41625)

y = 25 +/- 204.06

So the drone is either 229.06 ft north or 22.94 ft south of Megan's position when it passes due north. Rounded to three decimal places, the answer is 229.06 ft north.

Solution is in da attachment mate!! :D

Step-by-step explanation:

that is a college question ?

x = cost of a ham sandwich

y = cost of a turkey sandwich

2x + 3y = 29

3x + 2y = 31

let's multiply the first equation by 3, abd the second equating by -2, and then we add them :

6x + 9y = 87

-6x - 4y = -62

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

0 5y = 25

y = 25/5 = $5

let's use the original first equation to get x (but we could use also the second equation, it does not matter).

2x + 3×5 = 29

2x + 15 = 29

2x = 14

x = $7

each ham sandwich costs $7.

each turkey sandwich costs $5.

The value of the functions are;

f(3) = - 3

g(5) = -77

A function can be defined as an equation or expression hat shows the relationship between two variables.

These variables are termed;

From the information given, we have that;

f(x) = -5x + 2

g(x) = -3x²- 2

To determine the function, f(3), and g(5), we have to substitute the value of x as 3 in the function f(x) and the value of x as 5 in the function g(x).

We have;

f(3) = -5(3) + 2

expand the bracket

f(3) = - 13

For the second function;

g(5) =  - 3(5)² -2

g(5) = -77

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Answers:

[tex]\text{Derivative: } \ \ \frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\ \text{Tangent line at (1,1) is: } \ y = -32x + 33\\\\[/tex]

==========================================================

Work Shown:

Let's determine the derivative dy/dx.

Part 1

[tex]26x^{10} + 6x^{26}y+y^7 = 33\\\\ \frac{d}{dx}(26x^{10} + 6x^{26}y+y^7) = \frac{d}{dx}(33)\\\\ \frac{d}{dx}(26x^{10}) + \frac{d}{dx}(6x^{26}y)+\frac{d}{dx}(y^7) = 0\\\\ 10*26x^{10-1} + \frac{d}{dx}(6x^{26})y+(6x^{26})*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\[/tex]

Part 2

[tex]260x^{9} + 26*6x^{26-1}y+6x^{26}*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\ 260x^{9} + 156x^{25}y+6x^{26}*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\ 260x^{9} + 156x^{25}y+(6x^{26}+7y^6)\frac{dy}{dx} = 0\\\\ (6x^{26}+7y^6)\frac{dy}{dx} = -260x^{9} - 156x^{25}y\\\\ \frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\[/tex]

There are many other possible ways to express the dy/dx expression.

GeoGebra and WolframAlpha are two useful tools to help verify the answer. Make sure you use the CAS mode in GeoGebra.

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

Part 3

Now that we know dy/dx, we can determine the slope of the tangent at any point (x,y) on the implicit function curve.

Plug in x = 1 and y = 1.

[tex]\frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\ \frac{dy}{dx} = \frac{-260(1)^{9} - 156(1)^{25}(1)}{6(1)^{26}+7(1)^6}\\\\ \frac{dy}{dx} = \frac{-260(1) - 156(1)(1)}{6(1)+7(1)}\\\\ \frac{dy}{dx} = \frac{-260 - 156}{6+7}\\\\ \frac{dy}{dx} = \frac{-416}{13}\\\\ \frac{dy}{dx} = -32\\\\[/tex]

The slope of the tangent line at (1,1) is m = -32.

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

Part 4

Apply the point-slope formula to determine the tangent line.

[tex]m = -32 = \text{ slope}\\(x_1,y_1) = (1,1) = \text{the point the tangent line goes through}[/tex]

So,

[tex]y - y_1 = m(x - x_1)\\\\y - 1 = -32(x - 1)\\\\y - 1 = -32x + 32\\\\y = -32x + 32 + 1\\\\y = -32x + 33\\\\[/tex]

Answer:

A maybe

Step-by-step explanation: sorry if wrong

a. There are three N's in PENNSYLVANIA. The probability of choosing an N can be calculated as follows:

Probability of choosing an N = (Number of N's in the word) / (Total number of letters in the word)

Probability of choosing an N = 3 / 12

Probability of choosing an N = 1 / 4

Therefore, the probability of choosing an N is 1/4.

b. There are two A's in PENNSYLVANIA. The probability of choosing an A can be calculated as follows:

Probability of choosing an A = (Number of A's in the word) / (Total number of letters in the word)

Probability of choosing an A = 2 / 12

Probability of choosing an A = 1 / 6

Therefore, the probability of choosing an A is 1/6.

c. There is only one E in PENNSYLVANIA. The probability of choosing an E can be calculated as follows:

Probability of choosing an E = (Number of E's in the word) / (Total number of letters in the word)

Probability of choosing an E = 1 / 12

Therefore, the probability of choosing an E is 1/12.

The correct option is (D) i.e. It took 15 gallons of water to fill the swimming pool.

What is Measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, volume, and many others. It is used to quantify and describe the properties of objects and phenomena in the natural world, as well as in many fields of science, engineering, commerce, and everyday life.

Measurements are typically made using standard units, such as meters for length, kilograms for mass, seconds for time, and so on.

We are given that, there are 3.8 liters in 1 gallon.

So, we can say that,

 1 gallon = 3.8 liters

Now, It took 57 liters of water to fill a small swimming pool

we can convert it into gallons as follows:

1 gallon = 3.8 liters

1 / 3.8 gallon = 1 liter

57 / 3.8 gallon = 57 liters

So, 57 liters = 15 gallons of water.

Hence, (d) is the correct option.

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Answer:

120km/h

Step-by-step explanation:

Distance=14km

Time       =7m

A driver was fined for speeding in 100km/h

∴ we convert time into hours

Time =(7/60)h

Average speed of the car = total distance ÷total time

                                           =14km×60/7h=120km/h which is greater than                          

                                                                                                        100km/h

Answer:

2^7 or 128

Step-by-step explanation:

When we multiply two powers with the same base, we add their exponents. In this case, the base is 2 and the exponents are 3 and 4.

So, 2^3 • 2^4 can be simplified as:

2^3 • 2^4 = 2^(3+4) = 2^7

Therefore, 2^3 • 2^4 is equal to 128.

Answer:128

Step-by-step explanation:

i assume that by ^ you meant power,

2^3=2*2*2=8

2^4=2*2*2*2=16

8*16=128

Answer: The answer to this equation is In (252) + 5.

Step-by-step explanation:

To solve this equation, you will need to first apply the logarithm power identity.

Now evaluate the exponent.

5 + In (7) + In (6^2)

5 + In (7) + In (36)

Apply the logarithm power identity again to the rest of this equation.

5 + In (7) + In (36)

5 + In (7 x 36)

After that, simplify the expression.

-Multiply the numbers & rearrange the terms

5 + In(7 x 36)

In(252) + 5

Therefore, your answer for this equation would be In(252) + 5.

Alyssa Wagner

Middle School Srudent

The magnitude of the equilibrant force is 938.893 lb

We can use the concept of vector addition to solve this problem. The equilibrant force is the force that is needed to balance out the two given forces, so that the net force on the broken-down ship is zero.

Let's represent the two given forces as vectors A and B, with magnitudes of 750 lb and 630 lb, respectively. The angle between them is 34.5 degrees.

|C|^2 = |A|^2 + |B|^2 - 2|A||B|cosθ

where

θ is the angle between the two forces.

Substituting the given values, we get:

|C|^2 = (750 lb)^2 + (630 lb)^2 - 2(750 lb)(630 lb)cos(34.5°)

Simplifying this expression, we get:

|C|^2 = 562500 + 396900 - 945000 * cos(34.5°)

|C|^2 = 881520.0752

Taking the square root of both sides, we get:

|C| ≈ 938.893 lb

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Answer:

11 11/12

Step-by-step explanation:

You can change these "mixed numbers" (a big whole numbers and also a fraction) to "improper fractions" (a single fraction with a bigger number on top and a smaller number on the bottom)

4 1/3 × 2 3/4

see image

13/3 × 11/4

Multiply straight across, top×top and bottom×bottom.

see image.

Change back to a mixed number by dividing.

The multiplication of 4 1/3 x 2 3/4 is 11 11/12.

The correct option is C.

A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.

To multiply 4 1/3 and 2 3/4, we can first convert them to improper fractions:

4 1/3 = 13/3

2 3/4 = 11/4

Then we can multiply the fractions by multiplying the numerators and denominators separately:

(13/3) x (11/4) = (143/12)

Finally, we can convert the improper fraction back to a mixed number if desired:

143/12 = 11 11/12

Therefore, the answer is 11 11/12.

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Answer:

g(f(-3)) = 6.

Step-by-step explanation:

To obtain the value of f(-3), we must first determine g(f(-3)), which requires changing x in the expression for f(x) to -3:

f(x) = 2x^2 + 9x - 1

f(-3) = 2(-3)^2 + 9(-3) (-3) - 1\s= 2(9) (9) - 27 - 1\s= 18 - 27 - 1\s= -10

Knowing that f(-3) = -10 allows us to replace it in the expression for g(x):

g(x) = -x - 4

g(f(-3)) = g(-10) (-10)

Now, if we replace x in g(x) with -10, we obtain:

g(f(-3)) = g(-10) = -(-10) (-10) - 4 = 10 - 4 = 6

Hence, g(f(-3)) = 6.

Answer:

g(f(-3))=6

Step-by-step explanation:

To calculate g(f(-3)), we must first determine the value of f(-3), and then we must insert that value into g(x) to obtain the result.

By adding x = -3 to the formula for f(x), we may obtain f(-3).

f(-3) = 2(-3)

² + 9(-3) - 1

f(-3) = 2(9) - 27 - 1

f(-3) = 18 - 28

f(-3) = -10

Knowing that f(-3) = -10 allows us to replace it in the formula for g(x):

g(f(-3)) = g(-10) = -(-10) (-10) - 4 = 10 - 4 = 6

Hence, g(f(-3)) = 6.

the value of 0.45 × 0.91 ÷ 0.0117 is 35.

Why it is and what is PEMDAS?

To find the value of 0.45 * 0.91 ÷ 0.0117, we can use the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

First, we need to perform the multiplication of 0.45 and 0.91:

0.45 ×0.91 = 0.4095

Then, we need to divide the result by 0.0117:

0.4095 ÷ 0.0117 = 35

Therefore, the value of 0.45 * 0.91 ÷ 0.0117 is 35.

PEMDAS is a mnemonic used to remember the order of operations in arithmetic and algebraic expressions. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

The order of operations is as follows:

Parentheses: Perform operations within parentheses first, working from the innermost set of parentheses to the outermost.

Exponents: Perform any calculations involving exponents, such as raising a number to a power or taking the square root.

Multiplication and Division: Perform multiplication and division in the order that they appear from left to right.

Addition and Subtraction: Perform addition and subtraction in the order that they appear from left to right.

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Answer:

±6

Step-by-step explanation:

To find the possible values of x for a point on the circle with equation x² + y² = 64, we can substitute the given y-coordinate of √28 into the equation and solve for x:

x² + (√28)² = 64

x² + 28 = 64

x² = 64 - 28

x² = 36

Taking the square root of both sides, we get:

x = ±6

Therefore, the possible values of x for a point on the circle with coordinates (x, √28) are x = 6 and x = -6.

Answer:

the result of subtracting 1 and 1/2 from the sum of 4 and 2/3 and 5 and 2/5 is 257/30 = 8 and 39/40.

Step-by-step explanation:

To find the result of subtracting 1 and 1/2 from the sum of 4 and 2/3 and 5 and 2/5, we need to first add the two summands:

4 and 2/3 + 5 and 2/5

To add these mixed numbers, we first need to find a common denominator. The least common multiple of 3 and 5 is 15.

4 and 2/3 can be written as an improper fraction with denominator 3:

4 and 2/3 = 4 x 3/3 + 2/3 = 12/3 + 2/3 = 14/3

5 and 2/5 can be written as an improper fraction with denominator 5:

5 and 2/5 = 5 x 5/5 + 2/5 = 25/5 + 2/5 = 27/5

Now we can add the two fractions with a common denominator of 15:

14/3 + 27/5 = (14 x 5)/(3 x 5) + (27 x 3)/(5 x 3) = 70/15 + 81/15 = 151/15

So, the sum of 4 and 2/3 and 5 and 2/5 is 151/15.

Now we can subtract 1 and 1/2 from this sum:

151/15 - 1 1/2

To subtract mixed numbers, we first need to convert 1 and 1/2 to an improper fraction:

1 and 1/2 = 1 x 2/2 + 1/2 = 2/2 + 1/2 = 3/2

Now we can subtract the fractions with a common denominator of 15:

151/15 - 3/2 = (151 x 2)/(15 x 2) - (3 x 15)/(2 x 15) = 302/30 - 45/30 = 257/30

Therefore, the result of subtracting 1 and 1/2 from the sum of 4 and 2/3 and 5 and 2/5 is 257/30.

If the temperature is read every 12 hours, then the eighth temperature reading will be taken at 11.15 pm three days after the first reading.

Temperature is a measure of the degree of hotness or coldness of a substance or object, typically measured using a thermometer in degrees Celsius or Fahrenheit.

If the temperature is read every 12 hours, then the time interval between two consecutive temperature readings is 12 hours.

To find the time of the eighth temperature reading, we need to add 12 hours for each of the previous seven temperature readings:

First reading: 11.15 am

Second reading: 11.15 am + 12 hours = 11.15 pm

Third reading: 11.15 pm + 12 hours = 11.15 am (next day)

Fourth reading: 11.15 am (next day) + 12 hours = 11.15 pm (next day)

Fifth reading: 11.15 pm (next day) + 12 hours = 11.15 am (two days after the first reading)

Sixth reading: 11.15 am (two days after the first reading) + 12 hours = 11.15 pm (two days after the first reading)

Seventh reading: 11.15 pm (two days after the first reading) + 12 hours = 11.15 am (three days after the first reading)

Eighth reading: 11.15 am (three days after the first reading) + 12 hours =

11.15 pm (three days after the first reading)

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