The giant kangaroo rat is an endangered species native to California. Each decade, researchers at a nearby university estimate the giant kangaroo rat population in the San Joaquin Desert. The most recent estimate, conducted this year, concluded that there are about 73,000 giant kangaroo rats in the desert. The population is expected to decrease by a factor of 1 3 each decade. Write an exponential equation in the form y=a(b)x that can model the estimated population of giant kangaroo rats in the San Joaquin Desert, y, in x decades.

So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

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The measure of ∠N' after rotating clockwise 90° about the origin of triangle MNP as per given measurements is equal option A . 46°.

In triangle MNP,

Measure of the angles in triangle MNP are:

∠M = 89°

∠N = 46°

∠P = 45°

Rotating triangle MNP clockwise 90° about the origin forms M'N'P'.

Measure of ∠N' = Measure of ∠N

                          = 46°

It change the coordinates of the triangle MNP  but measure of angles remain same.

Therefore, the measure of angle N' after rotation of triangle MNP clockwise 90 degrees about the origin gives option A . 46°

The above question is incomplete , the complete question is:

Triangle MNP has angles of measure ∠M = 89 degrees, ∠N = 46 degrees, and ∠P = 45 degrees . Triangle MNP is rotated 90 degrees clockwise about the origin to form triangle M'N'P'. What is the measure of angle N'?

Α: 46°

B: 45°

C: 44°

D: 89°

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The value of the equation is x = 348

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x ÷ 4 = 87   be equation (1)

On simplifying the equation , we get

x/4 = 87

Multiply by 4 on both sides of the equation , we get

x = 87 ( 4 )

x = 348

Therefore , the value of x is 348

Hence , the equation is x = 348

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Step-by-step explanation:

Finding slope, m, as follows

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

This is where we choose two random (x,y) coordinates

Let's use (8,19) and (6,13). Now we plug these numbers into the equation

[tex]m = \frac{19 - 13}{8 - 6} = \frac{6}{2} = 3[/tex]

Concluding m = 3

Answer: B

Step-by-step explanation:

The container having same volume and greater surface area than Amanda's container is -

Option 3: Container with dimensions 6 ft × 2 ft × 2 ft.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The measurements of the box filled by Amanada is -

Length = 3 feet, Width = 2 feet and height = 4 feet

The formula for volume of a cuboid is -

Volume = l×w×h

Substitute the values in the equation -

Volume = 3 × 2 × 4

Volume = 24 ft³

The formula for surface area of a cuboid is -

Total Surface Area = 2(lw + wh + lh)

Substitute the values in the equation -

Total Surface Area = 2[(3 × 2) + (2 × 4) + (3 × 4)]

Total Surface Area = 2(6 + 8 + 12)

Total Surface Area = 2(26)

Total Surface Area = 52 ft²

Amanada wants a container with greater surface area and same volume.

The first and fourth containers are cubes and not cuboids so they are not considered.

The second container has same measurements as that Amanda filled, so they will have same volume and surface area.

Consider the third container with measurements -

Length = 6 feet, Width = 2 feet and height = 2 feet

The formula for volume of a cuboid is -

Volume = l×w×h

Substitute the values in the equation -

Volume = 6 × 2 × 2

Volume = 24 ft³

The formula for surface area of a cuboid is -

Total Surface Area = 2(lw + wh + lh)

Substitute the values in the equation -

Total Surface Area = 2[(6 × 2) + (2 × 2) + (6 × 2)]

Total Surface Area = 2(12 + 4 + 12)

Total Surface Area = 2(28)

Total Surface Area = 56 ft²

Therefore, the third container is the right choice.

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Answer:

[tex]9*5[/tex]

Step-by-step explanation:

9(5s) are 9*5.

Answer:

256

Step-by-step explanation:

The expression "2 × 2^7" means 2 multiplied by 2 raised to the power of 7. The power of 2 raised to 7 is 128, so 2 × 2^7 = 2 × 128 = 256.

Answer:

There are 44 jackets and 12 coats.

Step-by-step explanation:

hope this helps

a) The weekly factor of growth for the insect population is given as follows: 3.

b) The initial population is given as follows: 300.

An exponential function is defined as follows:

y = ab^x.

In which:

In 2 days, the population increased from 900 to 8100, hence the factor of growth is obtained as follows:

b² = 8100/900

b² = 9

b = 3.

Meaning that the initial population is obtained as follows:

900/3 = 300.

The first problem is incomplete, hence it could not be answered.

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When a point T(- 1, 2) is rotated 180° clockwise about the origin, the coordinates of the new point T' may be obtained using coordinate plane rotation rules would be (1, -2).

The x-coordinate changes its sign with a 180° clockwise rotation, as does the y-coordinate.

As a result, the coordinates of T' following a 180° clockwise revolution around the origin are:

T'(x', y') = ( -(-1), -(2)) = (1, -2)

So, point T' is located at (1, -2).

It's worth noting that rotations about the origin keep the distance between the source and the point being rotated constantly.

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If  (12, -33) is solution of Equation then LHS= RHS.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have the points (12, -33).

As, we know that the points are said to be the solution of equation if the LHS part of Equation becomes equal to RHS part of Equation.

For instance we have Equation x+ 2y= 3.

Then we have solution of the Equation then by solving x+2 y we get the value 3.

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Reason:

Focus on Q(0, 5) and Q′(9, 5)

More specifically, focus on the x coordinates. We go from x = 0 to x = 9, which means "shift 9 units to the right" since we added 9 to the old x coordinate to get the new x coordinate. The y coordinates stay the same.

The translation rule is [tex](\text{x},\text{y}) \to (\text{x}+9, \text{y})[/tex]

It is given that, for the three-digit numbers (abb) and (baa), and the two-digit number (aa), (abb) + (aa)+ 1 = (baa).

Therefore, a + b = 5 + 4 = 9

Digit Number :

A number is an individual number used to represent a value in mathematics. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in various combinations and repetitions to represent all values ​​in mathematics. Ten digits from 0 to 9 can be represented by symbols called digits.

In mathematics, each digit of a number has a numeric value. A place value can be defined as a value represented by a number of digits depending on the position of the digit.

For example, 7th place in 3743 is 700 or 700. But 7432's 7th place is 7000 or 7000. Here, the number 7 is the same in both digits, but the place value changes depending on the position.

Now,

A + 8 = 3, then A has to be 5 because unit digit of the sum has to be 3.

There is a carry-over of 1.

So, 4+ 9+ 1 = 14

A = 5, B = 4 and C=1

Therefore, a + b

                 = 5 + 4 = 9

Complete Question :

Find the values of the letters in the following and give reasons for the steps involved.

     4  A

+   9  8  

_________

​  C  B  3

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Answer:

C.) 105°

Step-by-step explanation:

We can see that angles 2 and 6 are corresponding angles, which means they are congruent and equal.  We also know that a is straight line, which means angles 5 and 6 are supplementary and must equal 180°.

Thus, since <6 = 75°, we simply subtract this from 180 to find the measure of <5:

180 - 75 = 105° = m <2

Answer:

The damaged area of rubber will touch the ground 834 times. This can be determined by using the formula for circumference, which is 2πr where r is the radius. In this case, the radius is 0.67 meters, so the circumference of the wheel is 4.24 meters. Since the farmer drives 1.5 km, this would be equal to 1500 meters. Therefore, the damaged piece of rubber will touch the ground 1500 meters/4.24 meters = 834 times.

Answer:

x° = 89+ 34 °

= 133is the answer

Answer: (1) -17 And (2) 17

Step-by-step explanation:

1)

-√8^2+15^2

Calculate the numbers under the square first

-√(64)+(225)

Add them (keeping them under the square)

-√289

now take the square of the calculated number

- (√289)

remember to multiply with the -

-(17)

2.1) Long Version

√5^2 + √12^2

Calculate the numbers under the square first

√25 + √144

Take the individual squares

5 + 12

Add

17

2.2) Short Version

Rule - A square root will always cancel out a power of 2

√5^2  = 5  And √12^2 = 12

5 + 12 = 17

Therefore , the solution of the given problem of equation comes out to be (2/3)x + 7 = 2x .

In arithmetic equations, the identical figure (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12. Calculations can be made to determine how many protagonists are also present at either end of a particular character. Conflicting sign interpretations are frequent.

Here,

Let's call the number we're looking for "x".

According to the problem, "two-thirds of a number" can be expressed as (2/3)x, and "is added 7" can be expressed as +7. Finally, "the result is twice the same number" can be expressed as 2x.

Putting it all together, we can write the equation:

(2/3)x + 7 = 2x

This equation represents the information given in the problem.

Therefore , the solution of the given problem of equation comes out to be (2/3)x + 7 = 2x .

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The probability that the first card is a 4, the second card is a club, and the third card is a 2 is equals to 6/5,525.

We have a standard deck has 52 cards. Three cards are dealt randomly from a standard deck. It is assumed that the cards are not changed after the transaction. Since there are four 4s in the deck of cards, the probability of rolling a 4 = 4/52. Now, the second dealt card is "club". The probability that the second card will be a club is = 13/52.

However, we have already drawn 1 card, which was a 4. This means that out of 51 cards, only 12 club cards remain. Thus the probability of club cards = 12/51. The third card can now be a 2. Therefore, the probability of falling third card will be a 2 = 3/50 (since two cards already dealt so total = 50 and one drawn card is a 4 then remaining= 3).

So, the overall probability = 4/52 x 12/51 x 3/50 =144/132,600 = 6/5,525.

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Complete question:

Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a 4, the second card is a club, and the third card is a 2?

The solution of the operation is -0.814 approximately.

Therefore the answer is E. None of the above.

The expression being evaluated in this problem is the result of performing several mathematical operations in a specific order. First, the expression inside the parentheses is evaluated:

(-2.6 + 56 - 16)

= 56 - 2.6 - 16

= 37.4

(-87 × 0.35) = -30.45

Next, the expression outside the parentheses is evaluated:

(−87 × 0.35) ÷ (−2.6 + 56 - 16)

= -30.45 ÷ 37.4

≈ -0.814

So, the solution to the expression is -0.814.

--The question is not in English, the question in English is--

"What is the solution of the operation, (−87 × 0.35) ÷ (−2.6 + 56 - 16)?

A. -629

B. -196

C. 629

D. 296

E. None of the above"

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The formula h = 63.2 + 2.31f ,relates the length of someone's femur (f) to their expected height (h) within a certain population. When f = 39, height(h) is 153.29 cm.

The constant term, 63.2, is the y-intercept of the line that represents the relationship between femur length and height. It represents the expected height of someone with a femur length of 0 cm.

The constant 2.31 represents the slope of the line. It represents the expected change in height for a 1 cm change in femur length. So, for every additional centimeter of femur length, the expected height increases by 2.31 cm.

When f = 39, we can substitute this value into the formula to find the expected height:

h = 63.2 + 2.31 * 39

h = 63.2 + 90.09

h = 153.29 cm

So, when the length of someone's femur is 39 cm, their expected height is 153.29 cm.

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The cylinder container has a radius of 1.63 centimeters.

The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder.

V = πr²h

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

Given that cylinder container has a height of 15 centimeters and a volume of 125.6 cubic centimeters.

Substitute the known values in the formula, and solve for radius:

125.6  = π(r)² × 15

(r)² = 125.6/π × 15

(r)² = 2.66

r = √2.66

r = 1.63 cm

Thus, the radius of the cylinder is 1.63 centimeters.

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The type of probability situation being used depends on the type of situation being analyzed.

Single event: A single event refers to a single outcome of a random process. For example, the outcome of a coin flip (heads or tails) is a single event.

Two mutually exclusive events: Two events are said to be mutually exclusive if they cannot occur at the same time. For example, the events "rolling a 4 on a die" and "rolling a 6 on a die" are mutually exclusive, because a die cannot show both 4 and 6 at the same time.

Multiple independent events: Multiple independent events are events that do not influence each other. For example, the outcome of rolling two dice is made up of two independent events (the outcome of each individual die roll).

Multiple dependent events: Multiple dependent events are events that are influenced by each other. For example, if you draw two cards from a deck, the outcome of the second draw depends on the outcome of the first draw (since there are fewer cards left in the deck).

Conditional: A conditional probability is the probability of an event occurring given that another event has already occurred. For example, the probability of getting heads on a coin flip given that the first flip was tails is still 50%, because the outcome of the first flip does not change the probability of the second flip.

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During the times the Sun is facing the equator, the length of day and night is nearly equal (12 hours each) at the equator because the sun's rays are hitting the earth at a 90-degree angle.

The Equator is an imaginary line that circles the Earth, equidistant from the North and South Poles and dividing the Earth into the Northern and Southern Hemispheres.

It is important because it serves as a reference for determining the latitude of a location, as well as its climatic and ecological zones. The Equator also plays a crucial role in the distribution of sunlight, affecting weather patterns and ocean currents, and is a key factor in the Earth's climate and ecosystems.

The Equator, as should be noted is used as a reference for navigation, mapping, and astronomical observations.

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Full Question:

Short answer questions:

The Sun faces the Equator twice in a year. How is the length of the day and night during that time and why?

Answer:

56 is the right answer

Step-by-step explanation:

7*8=56

Grace read 5/15 of the book during the day, so she read 10/15 of the book at night can use the following equation: 1/3 + x = 10/15

Grace read 1/3 of the book in the morning, and by the end of the day she still had 2/5 of the book left. To calculate how much she read at night, we can use the following equation: 1/3 + x = 10/15, where x represents the amount of the book she read at night. Solving for x, we get x = 5/15. This means that Grace read 5/15 of the book during the day and 10/15 of the book at night. To put this into context, if the book was 300 pages long, she would have read 100 pages in the morning and 200 pages at night. This equation shows that it is important to use fractions when solving these types of problems. Fractions allow us to easily calculate the amount of something that has been used or read. Without fractions, it would be much more difficult to solve these types of problems.

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