Which functions show a negative rate of change?

By using the equation of the trend line, the​ hiker's elevation after 145 minutes is equal to 2,077.3 feet.

In order to determine the​ hiker's elevation after 145 minutes, we would have to substitute the value representing the number of minutes (x) into the linear equation that models the​ hiker's elevation in feet and then evaluate as follows;

y = 9.54x + 694

When the value of x = 145 minutes, the hiker's elevation (y) in feet is given by;

Hiker's elevation (y) = 9.54x + 694

Hiker's elevation (y) = 9.54(145) + 694

Hiker's elevation (y) = 1,383.3 + 694

Hiker's elevation (y) = 2,077.3 feet.

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Answer: A) The decay constant (λ) is a measure of the rate at which a radioactive isotope decays. It is defined as the probability per unit time that an atom of the isotope will decay. The decay constant can be calculated using the formula:

λ = -ln(1 - x) / t

Where x is the fraction of the original activity that has decayed (in this case, 0.40), and t is the time over which the decay occurred (in this case, one week).

B) The half-life (T1/2) is the amount of time it takes for half of the original activity of a radioactive isotope to decay. It can be calculated using the formula:

T1/2 = ln(2) / λ

C) The mean lifetime (τ) is the average amount of time an atom of a radioactive isotope will survive before it decays. It can be calculated using the formula:

τ = 1 / λ

It's important to note that the above formulas are based on the exponential decay model, which assumes that the decay process is random and that the decay constant is constant over time. If the isotope does not decay in this way, these formulas may not give accurate results.

Step-by-step explanation:

Answer:

3x - 24

Step-by-step explanation:

24 less is the same as: - 24

3 times itself is: 3x

Answer:

200,000 times

Step-by-step explanation:

80 km × (1000 m)/(1 km) × (100 cm)/(1 m) = 8,000,000 cm

8,000,000 cm / 40 cm = 200,000

Answer: 200,000 times

Answer: DJ appears to be moving at the same speed as the car

Step-by-step explanation:

DJ is inside of the car, so he moves with it. Jabari is outside of the car and is standing still, so both DJ and the car he is in seems to be moving at 40 miles per hour at the same time

The weight lies between the whole numbers 8 and 9.

The length, breadth, and height of a package are multiplied using the longest point on each side to determine the dimensional (DIM) weight.

If each of the 4 boxes has the same weight, the weight of each box can be found by dividing the total weight by the number of boxes. Given that the total weight is 34 kilograms, the weight of each box is:

w = 34 kg / 4 boxes = 8.5 kg

So, each box weighs 8.5 kilograms. The weight lies between the whole numbers 8 and 9.

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Answer: The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers. To solve 66 divided by 7 using the standard algorithm, you can follow these steps:

Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:

66 | 7

--- |

Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.

66 | 7

--- | 0

Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).

66 | 7

--- | 0

0 |

Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.

66 | 7

--- | 0

0 | 6

Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).

66 | 7

--- | 0

0 | 6

| 66

Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.

66 | 7

--- | 09

0 | 6

| 66

Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).

66 | 7

--- | 09

0 | 6

--- | 63

Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

So, 66 divided by 7 = 9 with a remainder of 3

So the answer is 9 R 3

Step-by-step explanation:

The solution is: 66 divided by 7 is  9 with a remainder of 3.

The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers.

To solve 66 divided by 7 using the standard algorithm, you can follow these steps:

Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:

66 | 7

--- |

Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.

66 | 7

--- | 0

Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).

66 | 7

--- | 0

0 |

Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.

66 | 7

--- | 0

0 | 6

Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).

66 | 7

--- | 0

0 | 6

| 66

Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.

66 | 7

--- | 09

0 | 6

| 66

Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).

66 | 7

--- | 09

0 | 6

--- | 63

Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

So, 66 divided by 7 = 9 with a remainder of 3

So the answer is 9 R 3.

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Answer: 6 2/3

Step-by-step explanation: 2 5/12 + 4 1/4  29/12 + 4 1/4 29/12 + 17/4 (3/3) 29/12 + 51/12 80/12/4/4 20/3 6 2/3

The inverse matrix of the given matrix is

[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]

What is meant by inverse matrix?

If A is a non-singular square matrix, then A^-1, often known as the inverse matrix of A, must exist if it is to satisfy the following property:

AA^-1 = A^-1A = I, Where I is the Identity matrix

Now, we will first find the determinant of the given matrix, whichis as follows:

Determinant = 6-4 = 2

Since, the determinant is not zero, this means that the inverse matrix exists.

Now, let's find the inverse matrix i.e. A^-1

[tex]A^{-1} = \frac{1}{D} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]

[tex]A^{-1} = \frac{1}{2} \left[\begin{array}{ccc}3&-4\\-1&2\end{array}\right][/tex]

[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-4/2\\-1/2&2/2\end{array}\right][/tex]

[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]

Hence, the inverse matrix of the given matrix is as under

[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

6 2/5

Number 5 is denominator, keep it for denominator.

Numerator will be 6x5+2 =32

so, a fraction of 6 2/5 greater than 1 is 32/5

(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division

The synthetic division for the polynomial (x^4+10x^3+10x^2-15x-6) divided by (x+2) would be:

x^3 + 8x^2 - 19x - 12 + (R)

Where R is the remainder.

The quotient is x^3 + 8x^2 - 19x - 12

A synthetic division, also known as long division of polynomials or polynomial synthetic division, is a method of dividing polynomials that is faster and simpler than the traditional polynomial long division method. It is particularly useful for dividing a polynomial by a linear factor of the form (x - a), where a is a real number.

Synthetic division allows you to divide a polynomial by a linear factor without having to perform the traditional long division algorithm, by using the polynomial's coefficients instead of the polynomial itself. Synthetic division is also useful for finding the remainder of a polynomial division. The quotient and the remainder are written in a form of simplified polynomials.

Therefore, the correct answer is as given above

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The first car consumed 35 number of  gallons and the second car consumed 15 gallons.

1. Calculate the total efficiency of both cars: 35 mpg + 15 mpg = 50 mpg

2. Calculate total gallons consumed: 1150 miles/50 mpg = 23 gallons

3. Divide total gallons by each car: 23/2 = 11.5 gallons (round down to 11 for the first car and round up to 12 for the second car)

4. The first car consumed 11 gallons and the second car consumed 12 gallons.

The first car consumed 35 gallons and the second car consumed 15 number of gallons.

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An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.

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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.

If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.

Let cost token be x and golf games be y, i.e.

16x + 3y = 30

22x + 5y = 43

Lets Solve by using Elimination method both the expression in equal terms

 80x + 15y = 150

- 66x + 15y = 129

14x = 21

x = 21/14

x = 1.5

Then, for y

16(1.5) + 3y = 30

y = 2

Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

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The triangle △FUN is congruent to the triangles △CAR.  And the diagram is given below.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles △FUN and △CAR, then we have

∠FUN = ∠CAR = 90°    

∠UFN = ∠ACR    

FN = CR

Then the triangles △FUN and △CAR are congruent triangles. And the diagram is given below.

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Answer:

what's the question? how many days? 4 day is the breakeven mark.

Step-by-step explanation:

80+60x = 100+55x

5x =20

x=4

for a 4-day rental, it'll be the same.  

if longer than 4 days, go with enterprise.  shorter than 4 days go with hertz.

Answer: B. The speed limit changing from 40 mph to 55 mph represents the least percent of change.

In A, a watch selling for $90 from $125 represents a 28% decrease,

In C, the stock market dropping from 250 to 175 points represents a 30% decrease,

In D, Marissa's math grade increasing from 75 to 99 represents a 32% increase.

While in B, the speed limit changing from 40 mph to 55 mph represents a 37.5% increase.

So, B represents the least percent of change.

Step-by-step explanation:

Answer: Annie made a mistake in step 1 by plotting the point (1, -3) instead of (1, 0) which is the x-intercept of the given equation.

Step-by-step explanation:

She should have used the x-intercept of the equation instead of just any point.

To fix her mistake, Annie should find the x-intercept of the equation by setting y to 0, and solve for x. Then she can plot the point (1,0) and proceed with step 2 and 3.

The amounts of liters of gasoline that you need to drive from the first town to the second is given as follows:

1.5 liters.

The amount of gasoline needed is obtained using the proportions in the context of this problem.

The scale is given as follows:

1 inch = 25 km.

Meaning that each inch on the drawing represents an actual distance of 25 km, then the actual distance of the towns separated by 3 inches on the map is given as follows:

3 x 25 = 75 km.

A liter of gasoline lasts for 50 kilometers, hence the amount of liters of gasoline needed for 75 kilometers are given as follows:

75/50 = 1.5 liters.

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The simplest form of √12x⁸/√3x² is 2x³.

What is simplification?

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Here, we have

Given: √12x⁸/√3x²

We have to simplify this function.

We combine both terms in one and we get

= √12x⁸/3x²

= √4x⁶

= 2x³

Hence, the simplest form of √12x⁸/√3x² is 2x³.

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The English sentences that are translated from single letters, such as P, Q, R, etc., can either be true or false depending on the context in which they are used.

For example, if P is translated as "the sky is blue," then this sentence is true. However, if P is translated as "the sky is orange," then this sentence is false. In order to determine the truth value of the translated sentence, we must first identify the context in which the letter is being used. Then, we can decide whether the translation is true or false by using logic and reasoning. For example, if we know that the sky is not orange, then the translation of P can be determined to be false.

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A right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides.

The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

So, the parameters listed are:

69-degree angle.

Ladder length (l) equals 26 feet.

The following cosine ratio is used to compute the horizontal distance (h).

cos(θ) = h/l

Replace known values:

cos(69) = h/26

Make the topic "h":

h = 26 * cos(69)

Consider the product:

h = 9.3

Therefore, a right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.

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Answer:

45%

Step-by-step explanation:

Answer:

45%

Step-by-step explanation:

[tex]\frac{9*5}{20*5}[/tex] = [tex]\frac{45}{100}[/tex]

The solution for given linear inequalities is (-0.5,4.25) from the given graph.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

As we know the solution for the lines which intersect at a certain point is that point or the coordinates of that point i.e. (-0.5,4.25).

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The circumference of a circle with diameter 8 units is equal to 25.14 units.

Circumference is the perimeter of a circle, circles are featured solely by diameter. The formula for circumference is described below:

s = π · D

Where D is the diameter, in units.

If we know that D = 8 units, then the circumference of the circle is:

s = π · 8

s = 8π

s = 25.14

The circle (diameter: 8 units) has a circumference of 25.14 units.

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The sum of the two consecutive numbers is 31.

Let the two consecutive number are n and n+1.

Given the difference between square of two consecutive Numbers is 31.

Then, two consecutive number = n, n+1 = 15, 16

Therefore

( A ): the sum of two consecutive number = 15 + 16 = 31

( B ): Their difference = 16 – 15 = 1

( C ): Subtract their sum by 8 = 31 – 8 = 23

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The probability that ben and tom will pass is 0. 87 and 0. 7 respectively will be 0.38

The answers to the questions are as follows:

Please refer to the attached file for point a.

Since both of them pass their driving tests at the same time, we double the odds of each one passing, which results in a probability of "56%".

Tom passes but Ben fails, or Tom passes but Ben succeeds. Therefore, the likelihood and the response is "38%."

(a)The tree diagram is attached.

P(Ben Fails)=1-0.8=0.2

P(Tom Fails)=1-0.7=0.3

(b)Probability that both will pass their driving test.

P(both will pass)=0.8 X 0.7 =0.56

(c)Probability that only one of them will pass their driving test.

P(Tom Bass, Ben Fails OR Ben Pass, Tom Fails)

=(0.7 X 0.2)+(0.8 X 0.3)

=0.14+0.24

=0.38

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Nelson hourly wage is $11.8

Nelson earned $379.25 in net pay for working 40 hours

He paid $56.64 in federal and state taxes

He also paid $36.11 in FICA tax

Therefore Nelson hourly wage can be calculated as follows

The first step is to calculate the total earnings

= 379.25 + 56.64 + 36.11

= 472

The next step is to calculate the hourly wage

472/40

= 11.8

Hence Nelson hourly wage is $11.8

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The real world scenario that would represent a causal relationship in causation:

Example 1: Shark attacks and sales of ice cream

Example 2: Box Office Income and Master's Degrees

Example 3: Nuclear Energy Production vs. Pool Drownings

Example 4: Marriage Rate versus. Measles Cases

The concept of causation states that one occurrence results in another event. Just a test with a correct engineering can demonstrate correlation. Similar groups are given various treatments in these trials, and the results of each group are examined. Only when there is a discernible difference between the groups' results can we say that a treatment had an impact.

People frequently misunderstand and misuse the concept of causality in statistics because they believe that just because data reveals a correlation, there must definitely be an underlying causal relationship.

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The surface area of the rectangular prism is 100m²

The formula for calculating the surface area of a rectangular prism is expressed as;

Surface area = 2(wl + hw + lh)

Given that;

From the diagram shown, let's substitute the values, we have;

Surface area = 2(2× 7 + 4× 2 + 7 × 4)

multiply the values, we get;

Surface area = 2(14 + 8 + 28)

Add the values

Surface area = 2(50)

Expand the bracket

Surface area = 100m²

Hence, the value is  100m²

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