Sara's mom takes the parkway to work. It takes her 30 minutes to travel from mile marker 88 where she enters to her exit at mile marker 121. What is her average speed

The function increases on [0,∞] and decreases on [-∞,0]. The absolute minimum value of f is 0, and its relative minimum value is the same (0,0).

When x<  0, you can see on the graph that there is a "open circle" at (0, 0).

Thus, due to the graph's indefinitely high y values, there is likewise no absolute maximum value for f.

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The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Given:

f(x)=√x - 2 + 3.

The inverse function can be found as shown below,

f⁻(x) = √(y - 2) + 3  (Replace x by y)

x = √(y - 2) + 3

solve the equation as shown below,

x - 3 = √(y - 2)

Squaring both sides,

(x - 3)² = [√(y - 2)]²

x² + 9 - 6x = y - 2

x² + 9 - 6x + 2 = y

y = x² - 6x + 11 or y = (x - 3)² + 2

Thus, the inverse of the function is  (x - 3)² + 2.

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To find the area of a triangle, you can use the formula:

area = (base * height) / 2

In this case, the base of the triangle is 24 inches and the height is 20 inches, so plugging these values into the formula gives:

area = (24 * 20) / 2

area = 240 / 2

area = 120 square inches

So the area of the top of the cheese board is 120 square inches.

Using factorization method to solve the quadratic equation, the number of seed Martha and Miguel donated are 5 and 10 respectively

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants, and x is an unknown variable. The solution to such an equation is a value of x that will make the equation true.

To determine the number of seeds they donated, we have to write two equations and solve.

data;

The product of the seeds is (2x - 3)(4x - 6) = 8x² - 24x + 18

This can be written as

8x² - 24x + 18 = 50

Solving the quadratic equation;

8x² - 24x + 18 - 50 = 0

8x² - 24x - 32 = 0

Using factorization method;

8(x - 4)(x + 1) = 0

x - 4 = 0, x = 4

x + 1 = 0, x = -1

x = 4, x = -1

The number of packs Martha donated is

Martha = 2x - 3 = 2(4) - 3 = 5

The number of packs Miguel donated is

Miguel = 2 * 5 = 10

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A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.

Part B:

The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.

Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

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x = 5

AB = 6

BC = 13

A line can be defined as a straight set of points that extend in opposite directions, It has no ends in both directions(infinite). It has no thickness. It is one-dimensional.

Given,

AB = 2x - 4

BC = 3x - 2

AC = 19

By the figure

AB + BC = AC

2x - 4 + 3x - 2 = 19

5x - 6 = 19

5x = 25

x = 5

AB = 2 × 5 - 4 = 10 - 4 = 6

BC = 3 × 5 - 2 = 15 - 2 = 13

Hence the value of x, AB and BC is 5, 6, 13 respectively.

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The of the function a remainderre 3, 2,1,0

You should understand that substitution means replacing figures in a variable to get a value

the given function is

y=-x/3 +2

The given parameter or table to be completed is

x  -6    -3    0    3    6    

y   4      3    2    1     0  

The table above was completed in the following ways

1)  y= 6/3 +2 = 2+2 4

2) y = 3/3 + 2 = 1+2 = 3

3) 0/2 + 2 = 2

4)  -3/3 +2 = -1+2 = 1

5) y = -6/3+2 = -2+2 = 0

Therefore the table has values descending from 4 to 0

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Answer:

-25, -19, -15, -4, 5, 7, 22

Step-by-step explanation:

-25, -19, -15, -4, 5, 7, 22 is the order from least to greatest

The bigger the negative number, the smaller it is; that is why the order is

-25, -19, -15, -4, 5, 7, 22

Answer:

24

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

the one equation has variables and numbers go in for the variable and the other equation just equals 11

Answer:

x = 40° , y = 140° z = 10°

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , then

x + 60° + 80° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle , then

y = 60° + 80° = 140°

x is also an exterior angle , then

30° + z = x

30° + z = 40° ( subtract 30° from both sides )

z = 10°

Rongopai's age is equal to the total number of candles on the cake, thus I need to determine what that is.

What I need to figure out because I am aware that Rongopai's age is equal to the total number of candles on the cake.

The number of pieces the cake was sliced into must first be determined. A quarter has a specific appearance to me. This is how it would seem (the teacher traces a quarter shape on the circle). There must have been more than four pieces since this one seems a little smaller.

Each cut's location may be identified using my finger. Given that all the pieces must be the same size, I'm predicting the locations of each line using the first piece as a reference.

Here would be the approximate location of the first line, followed by here and here (the teacher draws a line with her finger) (tracing two more lines). the third line. In my mind, the lines and parts are somewhat "visible." Four "invisible" pieces plus the one drawn in are present when I count backward.

The complete question is:

A teacher wants a student to see how visualising the size of a share (in this case, a piece of cake) can be used to work out how many shares are needed to make a whole:

“Here is a piece of Rongopai’s birthday cake. Each piece of cake has the same number of candles. How old is Rongopai?”

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Age of Rongopai is 20 years.

One fifth of a circle means if a circle can be divided into five equal parts, then one fifth is one of them.

As per the figure given, there is shown a 1 fifth of a circular birthday cake.

As all the piece of cake is equal in size so the total number of cake piece is five.

the number of candles in each piece is four.

the total number of candles present in the whole cake is = 5 × 4

the total number of candles = 20

Therefore, Rongopai is 20 years old.

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Answer:

There are 47 dimes and 2 pennies.

Step-by-step explanation:

10¢ = 1 dime

$4.70 = 470 ¢

470 dimes = 47 dimes

and 2 pennies

Answer:

203412

Step-by-step explanation:

253

*804

___

16

  40

    32

      20

         12

______

 203412

This is a Vedic Math trick you can use to multiply fast, called the criss-cross method.

The population of Cuba in 10 years will be 1.9243 million.

A process called exponential growth sees a rise in quantity over time. It happens when a quantity changes at an instantaneous rate that is proportionate to the quantity itself with respect to time.

Data patterns that exhibit exponential growth exhibit quicker rate of expansion over time. Compounding produces exponential returns in the financial world. Savings accounts with a compound interest rate have the potential to expand exponentially.

The population growth will be modeled using exponential growth:

f(x) = a(b[tex])^t[/tex]

where:

a be the initial value

b be the growth rate

Substitute the values in the above equation, we get

f(x) = 1.3(1.04[tex])^t[/tex]

The population after 10 years will be:

f(x) = 1.3(1.04[tex])^{10[/tex]

simplifying the equation, we get

f(x) = 1.9243

Therefore, the population in 10 years will be 1.9243 million.

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The population of Cuba in 10 years will be 1.9243 million, if the population is expected to grow at a rate of 4% each year.

Quantities increase over time through a process known as exponential growth. It occurs when a quantity shifts at a pace that is proportional to the quantity's own rate of change with regard to time.

Data patterns that show exponential growth expand more quickly over time. In the world of finance, compounding generates exponential profits. Compound interest savings accounts have the potential to grow tremendously.

The population growth will be modeled using exponential growth:

f(x) = a(b)[tex]^{t}[/tex]

where:

a be the initial value

b be the growth rate

Substitute the values in the above equation, we get

f(x) = 1.3(1.04

The population after 10 years will be:

f(x) = 1.3(1.04

simplifying the equation, we get

f(x) = 1.9243

Therefore, the population in 10 years will be 1.9243 million.

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The Pythagorean triplet of 16 is (8, 15, 17).

This can be calculated using the Pythagorean theorem, which states that in any right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Therefore, given a number, we can find a Pythagorean triplet by calculating the squares of the two legs and then finding the hypotenuse.

Formula:

a² + b² = c²

Find the square of the number.

16² = 256

Subtract the square from the number to get one leg of the triangle.

16 - 256 = -240

Take the square root of the result.

√(-240) = 8

Add the square to the number to get the other leg of the triangle.

256 + 16 = 272

Take the square root of the result.

√(272) = 15

Add the two legs together to get the hypotenuse.

8 + 15 = 23

Take the square of the result.

23² = 529

Subtract the sum of the two legs from the hypotenuse.

529 - 23 = 506

Take the square root of the result.

√(506) = 17

Therefore, the Pythagorean triplet of 16 is (8, 15, 17).

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More than one applies to the slope.

The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|. Specifically, display style |x|=x and |x|=-x for positive and negative numbers, respectively, and display style |0|=0 for zero.

The slope of the parent function from any point to the vertex is either 1 or -1. The points in the issue are (-2, 3), and (–1, 0)

The slope is m = 0 - 3 / (-1 - (-2)) between the two sites.

m = 3

It is steeper than one.

As a result, a scale factor other than 1 has been used to dilate the graph.

The complete question is : The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.

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a) The minimum number of dogs that could have a mass of more than 27 kg is 4.

b) The maximum number of dogs that could have a mass of more than 27 kg is 17.

What is interval?

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number one may imagine is a real number.

The given table shows information about the masses of some dogs.

a) As, the minimum number of dogs is needed to be found, then -

Assume all dogs present in the interval 20 to 40 have a mass of more than 27 kg so the minimum value out of 13 and 4 is 4.

b) As, the maximum number of dogs is needed to be found, then -

Assume all dogs present in the interval 20 to 40 have a mass of more than 27 kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17.

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The age group that falls between two standard deviations is 20 to 28.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.

Given, The average age of a university student was found to be 24 with a standard deviation of 2.

Therefore, age group is within 2 standard deviations of the mean is,

24 + 2×2 = 24 + 4 = 28,

And 24 - 2×2 = 24 - 4 = 20.

So, The age group between 20 to 28 falls within 2 standard deviations of the mean.

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The length of the fencing that the city needs to surround the park will be 380.50 yards.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards. Then the length of the rectangular park is calculated as,

8925 = L × 84

L = 106.25 years

Then the length of the fencing that the city needs to surround the park will be given as,

P = 2(106.25 + 84)

P = 2 × 190.25

P = 380.5 yards

The length of the fencing that the city needs to surround the park will be 380.50 yards.

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The needed two values of x are: 59 and -12.

The difference between a sequence's maximum value and minimum value is referred to as the sequence's range.

A sequence's range is just a set that identifies the sequence. The set x1, x2, x3, and so forth is typically used to describe the range; it is also written as xn; n = 1, 2, 3,...

Given sequence of 8 numbers as: 28, 39, 21, x , 33, 38, 2, 45

Given range of above sequence: 57

Since the value x can assume any value, it have option to be minimum value in the sequence or maximum value in the sequence such that  the range remains at 57.

Case 1: x as minimum value of given sequence:

If so, then the maximum value is 45. Then-

range = maximum value - minimum value

57 = 45 - x

x = -12

Case 2: x as maximum value of the given sequence:

If so, then the minimum value of the sequence is 2. Then-

range = maximum value - minimum value

57 = x - 2

x = 59

Thus, the needed two values of x are: 59 and -12.

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The coordinate of N' is (2, -3)

Now, According to the question:

We have the point n (-2, -3) and we need to rotate it 270 degrees clockwise about the origin.

When rotating 270 clockwise about the origin you switch the x and y coordinate and use the opposite sign of the original y coordinate.

A(x, y) becomes A' (-y, x)

This means that point N becomes:

N (-2, -3) => N'(-(-2), (-3))

              => N'(2,- 3)

Hence, The coordinate of N' is (2, -3)

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Answer:

  B.  (see attached)

Step-by-step explanation:

You want the solution and graph of the inequality |x+3| > 2.

The inequality resolves to two inequalities with different domain definitions:

  |x +3| > 2

When the argument is negative, (x+3) < 0, this is ...

  -(x +3) > 2

  -x -3 > 2 . . . . . . eliminate parentheses

  x +3 < -2 . . . . . . multiply by -1

  x < -5 . . . . . . . . . subtract 3; consistent with the domain definition

When the argument is positive, (x+3) > 0, this is ...

  x +3 > 2

  x > -1 . . . . . . . . subtract 3

  -1 < x . . . . . . . . same thing using the < symbol

These differing solution sets do not overlap, but elements of either set are solutions to the inequality. The appropriate conjunction is "OR":

  solution: x < -5 or -1 < x

The graph is attached.

__

Additional comment

We like to use the < or ≤ symbols when expressing the solution to an inequality. That way, the relation of the variable to the boundary value is the same as its relation on a number line. Solution values are left of -5 or right of -1:

  x < -5  or  -1 < x

It helps provide a check that the graph is properly drawn.

The inequality can be rewritten as ...

  |x -(-3)| > 2

which can be interpreted as saying the positive distance from x to -3 is more than 2. This tells you the graph will have two disjoint branches, and the appropriate conjunction is OR.

If the problem were different, and the inequality were ...

  |x -(-3)| < 2

it would be telling you the solution values have a distance less than 2 from -3. They will be in one continuous band from -5 to -1, so the appropriate conjunction is AND. The solution in this case is usually written as a compound inequality with no conjunction: -5 < x < -1. (Note the use of < symbols puts the variable value in the middle, between the boundary values, as in graph D.)

Answer:

Step-by-step explanation:

SQR-PRQ-SRP

SP/RP=RP/PQ

QP/QR=RQ/SQ

Answer:

It will take approximately 14.2 years for April’s money to double.

Step-by-step explanation:

Answer:-14°F

Step-by-step explanation:

-2°F -12°F is basically the same as 12°F+2°F which is 14°F and then you inverse it

Jamal’s test scores are 84, 88, 92, and 94. Natalia’s test scores are 86, 88, 90, 92. Jamal has a greater test average than Natalia. Natalia has more consistent test scores than Jamal.

To find the test average, you add up all the test scores and divide by the number of test scores.

Jamal's average: (84+88+92+94) / 4 = 89.50

Natalia's average: (86+88+90+92) / 4 = 89

Jamal has a greater test average.

To find the consistency of test scores, you can use the range, which is the difference between the highest and lowest scores.

Jamal's range: 94-84=10

Natalia's range: 92-86 = 6

Natalia has the most consistent test scores, as the range of her scores is smaller than Jamal's.

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Explanation:

The equation y = 5x^2+3x^6-10x-8 is not in standard form.

Why not? Because the term with the largest exponent (6) isn't listed first.

The standard form would be y = 3x^6+5x^2-10x-8; note the exponents decrease (6, 2, 1, then 0).

After the polynomial is in standard form, we can read off the leading coefficient to be 3. This is the coefficient of the first term 3x^6.

Side note: The degree is 6 as it's the largest exponent.

The correct option is option (d).

To solve this problem, we need to find the probability that two randomly selected packages are both more than 4.5 pounds. Since the distribution is normal, we can use the standard normal distribution table to find the probability.

The first step is to standardize the weight of the packages by subtracting the mean from the weight and dividing it by the standard deviation. The weight of 4.5 pounds is the mean, so the standardized weight is (4.5 - 4.5) / 1.8 = 0.

The probability that a package weighs more than 4.5 pounds is the same as the probability that a standardized package weighs more than 0. This probability is equal to 1 - P(Z < 0) , where Z is the standardized weight.

Using a standard normal distribution table, we find that P(Z < 0) = 0.5. Therefore, the probability that a package weighs more than 4.5 pounds is 1 - 0.5 = 0.5.

Since the two packages are independent, we can find the probability that both packages are more than 4.5 pounds by multiplying the probability of one package being more than 4.5 pounds by itself. So, the probability that two randomly selected packages are both more than 4.5 pounds is 0.5 * 0.5 = 0.25.

In conclusion, the probability that two randomly selected packages are both more than 4.5 pounds is 0.25

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