In a class of 30 students, 12 have a cat and 19 have a dog. There are 6 students who
do not have a cat or a dog. What is the probability that a student chosen randomly
from the class has a dog?

The measurement that is the same for Charles and Jermod is the median

The dot plots show the distribution of the number of minutes that Charles and Jermod spent on homework per day for three weeks. To determine which measurement is the same for both of them, we need to compare the dot plots.

Looking at the dot plots, we can see that both Charles and Jermod have a dot at 35 minutes, indicating that they both spent 35 minutes on homework on at least one day.

Therefore, the measurement that is the same for Charles and Jermod is the median, since it is the middle value of the data when arranged in order. In this case, the median is not clearly identifiable from the dot plots

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1. The table of at least 4 values of the function is

x 0   -6   6  3

y  36  0  0 27

2. The domain is All set of real values and the range: y ≤ 36

3. The x and y intercepts of the rainbow are x = (-6, 0) and (6, 0) y = (0, 36)

Given that we have

y = -x² + 36

From the graph, we have the following values

x      y

0    36

-6    0

6    0

Set x  = 3

So, we have

y = -3² + 36

Evaluate

y = 27

So, we have

x      y

0    36

-6    0

6    0

3    27

From the graph, we have

These values mean that;

For the x and y intercepts of the rainbow, we have

x = (-6, 0) and (6, 0)

y = (0, 36)

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The Exponential equation is 8x = 64. the correct answer is option A: log8 64 = x.

The exponential equation is 8x = 64.

To rewrite the exponential equation in logarithmic form, we use the following format:

log base a of b = c if and only if ac = b

Here, the base is 8 and the result is 64.

So, we can rewrite the equation as:

log8 64 = x

Therefore, the correct answer is option A: log8 64 = x.

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The probability of obtaining 14 successes in 19 trials with a probability of success of 0.8 is approximately 0.1025.

Using the binomial probability formula:

P(X = 14) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials,

p is the probability of success, and

k is the number of successes.

Plugging in the given values, we have:

P(X = 14) = (19 choose 14) * 0.8^14 * (1-0.8)^(19-14)

P(X = 14) = 0.1025 (rounded to four decimal places)

Therefore, the probability of obtaining 14 successes in 19 trials with a probability of success of 0.8 is approximately 0.1025.

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The corresponding angles of the parallel lines are ∠4 and ∠8

Given data ,

Let the parallel lines be represented as b and c

Let the line a be the transversal line

Now , Corresponding angles are equal

Co-interior angles add up to 180°

When two parallel lines are intersected by a transversal, the corresponding angles formed are congruent. Corresponding angles are pairs of angles that are in the same relative position at each intersection.

So , the angles ∠4 and ∠8 are the corresponding angles from the figure

This property of corresponding angles holds true for any pair of corresponding angles formed by intersecting parallel lines with a transversal.

Hence , the corresponding angles are ∠4 and ∠8

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Answer:

derivative of cosx/sin2x is (1 + secx) / [2sinx cosx].

Step-by-step explanation:

To differentiate cosx/sin2x, we can use the quotient rule of differentiation, which states:

(d/dx) [f(x)/g(x)] = [g(x) * f'(x) - f(x) * g'(x)] / [g(x)]^2

Here, f(x) = cosx and g(x) = sin2x. So we have:

f'(x) = -sinx (differentiation of cosine)

g'(x) = 2cos2x (differentiation of sine2x using chain rule)

Now, using the quotient rule:

(d/dx) [cosx/sin2x] = [sin2x * (-sinx) - cosx * (2cos2x)] / [sin2x]^2

= [-2cos2x cosx + sin2x sinx] / [sin2x]^2

= [-2cosx cos2x + sinx] / [2sinx cosx]^2

= [-2cosx(1-2sin^2(x)) + sinx] / [2sinx cosx]^2

= [-2cosx + 4cosx sin^2(x) + sinx] / [2sinx cosx]^2

= (sinx + 2cosx sin^2(x)) / [2sinx cosx]^2

= sinx / [2sinx cosx]^2 + 2cosx / [2sinx cosx]^2

= 1/[2sinx cosx] + secx/[2sinx cosx]

= (1 + secx) / [2sinx cosx]

Therefore, the derivative of cosx/sin2x is (1 + secx) / [2sinx cosx].

Answer:

216 in. 3

Step-by-step explanation:

math ...

The values of all the solutions are,

16) m QT = 142 deg

17) m ∠STR = 23 deg

18) m ∠RSQ = 19 deg

Given that;

A circle is shown.

Now, We can formulate;

16|) The value of m QT is,

m QT = 2 ∠QST

         = 2 × 71

         = 142 degree

17) The value of m ∠STR is,

m ∠STR = 1/2 m ∠SXR

             = 1/2 × 46

             = 23 deg

17) Since,  ∠ RST = 90°

Then, We get;

m ∠RSQ = 90 - ∠QST

              = 90 - 71

              = 19 degree

Thus, The values of all the solutions are,

16) m QT = 142 deg

17) m ∠STR = 23 deg

18) m ∠RSQ = 19 deg

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Answer: To find the exponential growth of the coin's value over the given period, we can use the formula for exponential growth:

V(t) = V0 × e^(kt)

where V(t) is the value of the coin at time t, V0 is the initial value of the coin, e is the mathematical constant e (approximately equal to 2.71828), k is the growth rate, and t is the time period.

We can use the information given to find the value of k. Let's use 1977 as the initial time period and 1990 as the final time period. The value of the coin in 1977 is V0 = $279, and the value of the coin in 1990 is V(13) = $434 (since 1990 - 1977 = 13 years).

Substituting these values into the formula, we get:

$434 = $279 × e^(k × 13)

Dividing both sides by $279, we get:

e^(k × 13) = $434 / $279

Taking the natural logarithm of both sides, we get:

k × 13 = ln($434 / $279)

Simplifying, we get:

k = ln($434 / $279) / 13

Using a calculator, we find that k is approximately 0.0556.

Now that we have found the growth rate, we can use the formula to find the value of the coin at any time t. For example, to find the value of the coin in 1985 (8 years after 1977), we can use the formula:

V(8) = $279 × e^(0.0556 × 8)

Using a calculator, we find that V(8) is approximately $425.46.

Therefore, we can conclude that the value of the coin grew exponentially at a rate of approximately 5.56% per year, and was worth about $425.46 in 1985.

Answer:

x = 20°

Step-by-step explanation:

m∠CBA = 360 - 90 - 160 - 30 = 80

It's an isosceles Δ, therefore the base angles are congruent.

m∠CBA = m∠ACB = 80

Sum of interior angles of a Δ = 180

x = 180 - 80 - 80 = 20

The domain of the piecewise function is the set of all real numbers.

(-∞, ∞)

For a function y = f(x), we define the domain as the set of the possible inputs of the function (this is the possible values that x can take)

Here we can see the graph of a piecewise function. To find the domain, we need to look at the horizontal axis of the graph.

We can see that the function covers the whole horizontal axis, then the domain is the set of all real numbers, which means that we can write this as:

D = (-∞, ∞)

Then the correct option is the last one.

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Answer:

B: 1/3 log (2-x) - log 3x

Step-by-step explanation:

some log laws:

1) log xy = log x + log y

2) log (x/y) = log x - log y

3) log x^k = k log x

log ((∛2-x) / 3x)

= log ∛2-x  -  log 3x  (just like the 2nd law above)

log ∛2-x = log (2-x)^(1/3)  =  (1/3) log (2-x)   (just like the 3rd law above).

so we now have (1/3) log (2 - x)  - log 3x

This is option B in the question.

[tex]x^2-12x+36=0\\(x-6)^2=0\\x-6=0\\x=6[/tex]

Answer: The angle is 105 degrees

Step-by-step explanation:

In a triangle, there is 180 degrees total. To find x, we can do....

x = 180 - 41 - 34

x = 105

The temperature difference between Rome and Munich is [tex]2[/tex]°C in the first case.

a) To find the difference in temperature between Rome and Munich, we compare their respective temperatures on the bar chart. Let's assume the temperatures on the chart are represented by the heights of the bars. From the chart, the temperature in Rome is [tex]10[/tex]°C, and the temperature in Munich is [tex]8[/tex]°C.

The difference in temperature between Rome and Munich can be calculated as the absolute difference between their values:

[tex]\[ \text{Difference in temperature} = |10 - 8| = 2°C \][/tex]

Therefore, the temperature difference between Rome and Munich is [tex]2[/tex]°C.

b) If the temperature in Oslo rises by [tex]5[/tex]°C over the next [tex]6[/tex] hours, we can add this increase to the current temperature in Oslo to determine the temperature at [tex]6[/tex] pm. However, the initial temperature in Oslo is not provided in the information given.

Without the initial temperature, we cannot calculate the specific temperature at [tex]6[/tex] pm.

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Answer:

50%

Step-by-step explanation:

if x is the numerator and y is the denominator, we have x/y.

reduce x by 60% so it becomes 0.4x.

reduce y by 20% so it becomes 0.8y.

we now have 0.4x/0.8y = (1/2) (x/y).

so it changes by 50%

The measure of the height of an equilateral triangle with a side length of 6 is 3√3.

We have,

In an equilateral triangle, all three sides are equal, and all three angles are also equal.

To calculate the height of an equilateral triangle, we can use the formula:

Height = (√3 / 2) x side

Given that the side length of the equilateral triangle is 6, we can substitute this value into the formula to find the height:

Height = (√3 / 2) x 6

Height = (√3) x 3

Simplifying, we have:

Height = 3√3

Therefore,

The measure of the height of an equilateral triangle with a side length of 6 is 3√3.

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The complete question.

Calculate the measure of the height of an equilateral triangle of side 6

The inverse function of f(n) is:

g(n) = -(4/7)*n - 8/7

Two functions are inverses if the composition is equal to the identity, so if g(n) is the inverse of f(n), we must have that:

f( g(n) ) = n

Replacing the actual function we will get:

-2 - (7/3)*g(n) = n

Now we can solve this for the inverse function g(n), then we will get:

-2 - (7/3)*g(n) = n

(-7/4)*g(n) = n + 2

g(n)  = (-4/7)*(n + 2)

g(n) = -(4/7)*n - 8/7.

That is the inverse function.

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The volume of right rectangular prism = 42 1/2 cm³.

We have,

height of prism = 2 cm

width of prism = 5 cm

length of prism = 4 1/4 cm  

Now, The volume of right rectangular prism = Length × Width × Height

Substitute all the values, we get;

= 2 × 5 × 4 1/4

= 10 × 17/4

= 170/4 cm³

= 42 1/2 cm³

Thus, The volume of right rectangular prism = 42 1/2 cm³

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To solve this problem, we need to first convert the distance on the map to actual distance using the map scale.

1 cm on the map represents 50,000 cm (or 500m) in actual distance.

So, 8.5 cm on the map represents 8.5 x 500m = 4,250m in actual distance.

Now, we can use the formula: time = distance ÷ speed

Here, distance = 4,250m and speed = 10km/h = 10,000m/h

So, time = 4,250m ÷ 10,000m/h = 0.425 hours

To convert hours to minutes, we can multiply by 60:

time = 0.425 x 60 = 25.5 minutes

Therefore, it will take Myra 25.5 minutes to run from the park entrance to the beach.

Answer: The ratio is 4:1

Answer:

To find the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7), we first need to find the center and radius of the circle.

The center of the circle is the midpoint of the diameter, which can be found using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the diameter.

Using (4,-7) and (-12,-7) as the endpoint coordinates, we get:

Midpoint = ((4 + (-12))/2, (-7 + (-7))/2) = (-4, -7)

So the center of the circle is (-4, -7).

The radius of the circle is half the length of the diameter, which is:

Radius = 1/2 × distance between (4,-7) and (-12,-7)

Radius = 1/2 × (4 - (-12)) = 8

So the radius of the circle is 8.

Now we can write the equation of the circle in standard form:

(x - h)² + (y - k)² = r²

Where (h,k) is the center of the circle and r is the radius.

Substituting the values we found, we get:

(x - (-4))² + (y - (-7))² = 8²

Simplifying this equation, we get:

(x + 4)² + (y + 7)² = 64

Therefore, the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7) is (x + 4)² + (y + 7)² = 64.

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The value of x is equal to 4/3.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

4/x = 6/2

By cross-multiplying, we have the following:

2(4) = 6x

8 = 6x

x = 8/6

x = 4/3

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The area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side. It states that for any triangle ABC, the ratio of the length of a side to the sine of the angle opposite that side is constant, that is;

a/sinA = b/sinB = c/sinC

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

angle m∠O = 180 - (83 + 88) {sum of interior angles of a triangle}

angle m∠O = 9°

Using the sine rule;

6.5/sin9 = ON/sin88

ON = (6.5 × sin88°)/sin9 {cross multiplication}

ON = 41.5

Area of the triangle = 1/2 × 6.5cm × 41.5cm × sin83

Area of the triangle = 133.9

Therefore, the area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.

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