Jake just learned to identify the difference between an oak tree and a
maple tree. He was curious about the concentration of these trees in his
neighborhood, so he went out and identified several trees that were either
by the pond or in the field.
Unfortunately, he smudged his data tables and can't read some of the
values. The absolute and relative frequency tables below show Jake's
salvaged data. Can you help him figure out the rest?
Fill in the missing values from each table.

The equation of the line that passes through the point (4, 2) and is perpendicular to the line y = 43x is y = (-1/43)x + (90/43).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line has a slope of 43.

To find the slope of the line perpendicular to it, we use the fact that the product of the slopes of two perpendicular lines is -1.

So, the slope of the perpendicular line is -1/43.

Using the point-slope form of a line, we can write the equation of the line as:

y - y1 = m(x - x1),

where (x1, y1) = (4, 2) and m = -1/43

Plugging in the values, we get:

y - 2 = (-1/43)(x - 4)

y - 2 = (-1/43)x + (4/43)

y = (-1/43)x + (4/43) + 2

y = (-1/43)x + (90/43)

Therefore, the equation of the line is y = (-1/43)x + (90/43).

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Here are five combinations of nickels and dimes that add up to 80 cents:

4 dimes and 4 nickels

3 dimes and 7 nickels

2 dimes and 12 nickels

1 dime and 16 nickels

8 dimes and 4 nickels

a) The total number of balls in a bag is 9.

b) The probability that the first ball chosen is orange is 1/3.

c) The probability that the 2nd ball is also orange is 1/4.

d) The probability that both balls are orange is 1/12.

Given that:

Balls, White = 6 and Orange = 3

a) The total of ping-pong balls in the bag at the start is calculated as,

Total ball = 6 + 3

Total ball = 9

b) The probability that the first ball chosen is orange is calculated as,

P(Orange) = 3/9

P(Orange) = 1/3

c) There will be 8 balls in the bag, of which 2 are orange if the first ball selected was an orange ball. Then the probability is calculated as,

P(Orange) = 2/8

P(Orange) = 1/4

d) The product rule of probability may be used to determine the likelihood that the first and second balls are both orange:

P(Orange and Orange) = 1/3 x 1/4

P(Orange and Orange) = 1/12

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Answer:

Step-by-step explanation:

y=-2x+2

The equation that best models the data from the table after the data has been linearized is y=294755 * 1.21728^x. This equation follows an exponental model.

Looking at the data, it is very evident that it is not increasing linearly but rather exponentially.

An exponential equation has the general pattern of formula which y = ab^x, where a is the main value and b is the growth factr.

The question below is as seen in the picture, and the above answer is dependent on it.

What is the equation that best models the data from the table after the data has been linearized?

X                                 y

2                                4.4

7                               18.2

13                              120.0

19                              715.4

22                            1,768.3

26                            5,775.9

30                           10.508.5

(1 point)

logy=0.12502x+0.427231

y=1,350 76x+1,350.76

y=294755 * 1.21728^x

y=5,927 281og x-3,880 59

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The two octagonal prisms are similar because their corresponding sides are proportional.

We can find out if two octagonal prisms are similar by checking if they have the same shape but may be different sizes. Two shapes are similar if their corresponding sides are proportional, and their corresponding angles are congruent.

Let's represent the dimensions of octagonal prism1:

Base edge length = a

Height = h

The octagonal prism2 dimensions:

Base edge length = b

Height = k

From the surface area and volume equations of an octagonal prism, we have the following system of equations:

50 = 2a² + 8ah

88 = 2a²h

450 = 2b² + 8bk

792 = 2b²k

We can simplify these equations by dividing the second equation by the first, and the fourth equation by the third, to eliminate h and k:

88/50 = 2a²h / (2a² + 8ah) => 44/25 = h / (a + 2h)

792/450 = 2b²k / (2b² + 8bk) => 44/25 = k / (b + 2k)

Then, we rearrange the equations to obtain expressions for h and k in terms of a and b, respectively:

h = (44/25) * (a + 2h)

k = (44/25) * (b + 2k)

Multiplying both sides of each equation by 25/19, we obtain:

h = (44/19) * a

k = (44/19) * b

We can now check if the corresponding sides are proportional:

Base edge length = a:b = 1:3

Height = h:k = 1:3

Since the corresponding sides are proportional, the two octagonal prisms are similar.

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Answer:

[tex] \sqrt{ {13.5}^{2} - {8.6}^{2} } = \sqrt{108.29} = 7 \sqrt{2.21} = \frac{7}{10} \sqrt{221} [/tex]

V = (1/2)(8.6)(.7√221)(22.4) = 1,002.33 square meters

The closest answer is 1,001.73 square meters.

Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

The value of the measure of each side indicated are,

⇒ x = 12.48

⇒ BC = 16

We have to given that;

In triangle ABC;

AC = x

AB = 10

Hence, We can formulate;

⇒ tan 58° = BC / AB

⇒ 1.60 = BC / 10

⇒ BC = 16

By using Pythagoras theorem;

⇒ x² + 10² = 16²

⇒ x² = 256 - 100

⇒ x² = 156

⇒ x = 12.48

Thus, The value of the measure of each side indicated are,

⇒ x = 12.48

⇒ BC = 16

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Answer:

577

Step-by-Step Explanation:

577 is right between 327 and 827.

327+827=1,154

1,154/2=577

The dimension is gioven as 69.26 feet

xy = 1836

This is the area

The cost of fence = 2x + 2y

cost of interior fencing

2x + 4y

C = 20.40(C1) + 12.00(C2)

We have to put the vakues in the formula above

C = 20.40(2x + 2y) + 12.00(2x + 4y)

= 40.80x + 40.80y + 24.00x + 48.00y

= 64.80x + 88.80y

from xy = 1836

y = 1836 / x

We have to put the value in C

C = 64.80x + 88.80(1836/x)

= 64.80x + 164236.80/x

Take the deriveative with respect to x

64.80 - 164236.80/x^2 = 0

x = √(164236.80/64.80)

=  69.26 feet

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The position function is s(t) = -5t³ + 3t² + 8t + 2.

We have,

To find s(t), we need to integrate the velocity function v(t) since velocity is the rate of change of position with respect to time.

To do this, we need to first find the velocity function v(t) by integrating the acceleration function a(t):

a(t) = -30t + 6

Integrating with respect to t, we get:

v(t) = -15t² + 6t + C1

We are given that v(0) = 8, so we can use this to solve for the constant C1:

v(0) = -15(0)² + 6(0) + C1 = C1

C1 = 8

Now we have the velocity function:

v(t) = -15t² + 6t + 8

To find s(t), we need to integrate v(t) with respect to t:

s(t) = -5t³ + 3t² + 8t + C2

We are given that s(0) = 2, so we can use this to solve for the constant C2:

s(0) = -5(0)³ + 3(0)² + 8(0) + C2 = C2

C2 = 2

Now we have the position function:

s(t) = -5t³ + 3t² + 8t + 2

Therefore,

The position function is s(t) = -5t³ + 3t² + 8t + 2.

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The number of childs plate are 201 and  adult's plate are 203.

Let's use C to represent the number of child plates and A to represent the number of adult plates.

We know that a child's plate costs $2.80 and an adult's plate costs $6.90.

Therefore, we can write two equations based on the information given:

The total number of plates served is 404

C + A = 404 ...(1)

C=404-A

The total amount collected is $1,963.50

2.8C + 6.9A = 1963.5 ..(2)

2.8(404-A)+6.9A= 1963.5

1131.2 - 2.8A +6.9A=1963.5

4.1 A =1963.5 -1131.2

4.1A=832.3

Divide both sides by 4.1

A=832.3/4.1

A=203

Now put A in equation (1)

C+203=404

C=404-203

C=201

Hence, the number of childs plate are 201 and  adult's plate are 203.

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Answer:

  (b)  10; 150°

Step-by-step explanation:

You want the polar coordinate equivalent of (-5√3, -5).

The polar form of (a, b) is ...

  (a, b) = (r; θ)

where ...

  r = √(a² +b²)

  θ = arctan(b/a) . . . . . with attention paid to quadrant

For the given values, the polar form is ...

  r = √((-5√3)² +5²) = √(75 +25) = 10

  θ = arctan(5/(-5√3)) = arctan(-1/√3) = 150°

The angle is a quadrant II angle with a reference angle of 30°.

The polar form is (10; 150°).

__

Additional comment

Some calculators will do the coordinate conversion based on a vector or ordered pair. Others require the coordinates of the point to be expressed as a complex number, as in the attachment. (Note the calculator mode is set to DEGrees.)

For the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively

The given function is h(x) 4x+5

h of x equal to four times of x plus five

We have to find the values of h(x) for different values of x

x=0, h(x) = 5

x=1, h(x)=9

x=2, h(x)=13

x=3, h(x)=17

x=4, h(x)=21

x=5, h(x)=25

Hence, for the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively

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Matching of the statements with their respective linear equations are:

1) The line contains (0, -8) and a slope of 3/2: y = ³/₂x - 8

2) A line that contains the point (0, -2) and (4, 0): 2y - x = -4

3) y-intercept is (0, -2) and slope is -3/4: y = -³/₄x - 2

4) A line that has a slope of 5/3 and a y-intercept of -4: 5x + 3y = -12

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

1) The line contains (0, -8) and a slope of 3/2

The only option that even has a slope of 3/2 is option B with the equation: y = ³/₂x - 8

2) A line that contains the point (0, -2) and (4, 0)

The only one that fits this is option C with the equation:

2y - x = -4

3) y-intercept is (0, -2) and slope is -3/4.

This means the only equation that matches it is:

y = -³/₄x - 2

4) A line that has a slope of 5/3 and a y-intercept of -4.

This means the only equation that matches it is:

5x + 3y = -12

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A graph of f(x) is shown in the image below.

A graph of f(x) is shown in the image below.

The vertex form equation for g(x) is g(x) = -x²

In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Since the parent function is f(x)= (x + 3)² - 2, g(x) would be created by translating f(x) three units to the right, two units up, and reflected vertically over the x-axis as follows;

f(x) = (x + 3)² - 2

g(x) = -[(x + 3 - 3)² - 2 + 2]

g(x) = -x²

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The percentage of cars traveling slower than 62 mph during rush hour is 0.5 or 50%.

Since the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 62 mph and a standard deviation of 5 mph, we can use the cumulative distribution function (CDF) of the normal distribution to find the percentage of cars traveling slower than 62 mph.

Let X be the speed of an automobile on the expressway during rush hour. Then, X follows a normal distribution with mean (µ) = 62 mph and standard deviation (σ) = 5 mph.

We want to find P(X < 62), which represents the probability that a car is traveling slower than 62 mph.

Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find the z-score corresponding to the value X = 62, using the formula;

z = (X - µ) / σ

Plugging in the given values;

z = (62 - 62) / 5 = 0

Now, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 0, denoted as Φ(0), which represents the probability that a standard normal random variable is less than or equal to 0.

Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find Φ(0) to be approximately 0.5.

So, P(X < 62) = Φ(0)

= 0.5

Therefore, the percentage of car is 0.5 or 50%

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Answer:

3 × 2 × 1 + 3 + 8 + 6 + 7 - 9 - 9 ÷ 7 × 0 × 1

= 6 + 3 + 8 + 6 + 7 - 9 - 0

= 31 - 9

= 22

Therefore, the value of the expression is 22

Answer:

what?

Step-by-step explanation:

Answer:  the answer is 13 and one-half

Step-by-step explanation:

C

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

use the table, when it asks f(2) that says what is the output *y) when the input is 2. Find when x=2 your answer is the y value, f(2)=5

Answer:0.5.

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

The probability that a randomly selected person in the region is a woman in the 18-24 age range living alone is approximately 0.14 or 14%.

To find the probability that a randomly selected person in the region is a woman in the 18-24 age range living alone, we need to look at the intersection of the "Female" row and the "0-24" age column in the table.

The probability of selecting a woman in the 18-24 age range living alone is:

P(woman, 18-24, living alone) = (Number of women in the 18-24 age range living alone) / (Total number of people living alone)

From the table, we can see that the number of women in the 18-24 age range living alone is 20.9. The total number of people living alone is 153.6.

P(woman, 18-24, living alone) = 20.9 / 153.6

P(woman, 18-24, living alone) = 0.1362 or approximately 0.14

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The complete question:

The table shows the​ distribution, by age and​ gender, of the million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person in the region is a woman in the 1824 age range living alone. Age |0-24|25-49|50+ |Total

Male|21.9|25.3 |28.6|75.8

Fem |20.9|26.1 |30.8|77.8

Tot |42.8|51.4 |59.4|153.6

The function that can be used to determine the amount of money is f(x) = 40 * (1.05)^x

From the question, we have the following parameters that can be used in our computation:

Principal = 40

Rate = 5% annually

Time = x

The function that can be used to determine the amount of money is represented as

f(x) = P * (1 + r)^x

Substitute the known values in the above equation, so, we have the following representation

f(x) = 40 * (1 + 5%)^x

Evaluate

f(x) = 40 * (1.05)^x

Hence, the function is f(x) = 40 * (1.05)^x

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Answer:

x = 3

Step-by-step explanation:

4x + 2x - 3 = 15 ← collect like terms on left side

6x - 3 = 15 ( add 3 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

Answer:

x=3

Step-by-step explanation:

You can start of by adding 4x and 2x because they both share the same variable "x". Now you have 6x-3=15. Using the addition property of equality, you can add 3 on both sides of the equation to cancel it out. You are left with 6x=18. Divide both sides by 6 and that leaves you with x=3

Based on these factors, the polynomial that graph crosses the x-axis at only one point is A. f ⁡ ( x ) = x ³ − 7 ⁢x² + 3 ⁢x − 21

A polynomial in mathematics is a mathematical statement made up of variables (also known as indeterminates) and coefficients that only include the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Polynomials are a fundamental algebra topic that is used in many areas of mathematics. A polynomial's degree is the largest exponent of the variable x in the expression. The correct option is A.

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