The theoretical probability of an albino Galapagos tortoise being born is 0.001%. If 500,000 Galapagos tortoises hatch, how many would you expect to be albino?

The length of the third side ​of a triangle cannot be 15 cm

The correct answer is an option (b)

We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

For example if a, b, c represents the side of a triangle then by above theorem a + b ≥ c

Here, the two sides of a triangle measure 4 cm and 8 cm.

Let a = 4 cm and b = 8 cm and c represents the third side of a triangle.

Using triangle inequality theorem,

a + b ≥ c

4 + 8 ≥ c

12 ≥ c

This means that the third side of the triangle must be less than or equal to 12 cm.

Thus, the correct answer is an option (b)

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The complete question is:

A triangle has two sides measuring 4 cm and 8 cm. Which lengths cannot be the length of the third side ​

a) 7 cm

b) 15 cm

c) 10 cm

d) 5 cm

The missing measures for the triangle are given as follows:

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is obtained as follows:

m < B + 73 + 42 = 180

m < B = 180 - 115

m < B = 65º.

Then the relation is:

34/sin(73º) = a/sin(42º) = b/sin(65º).

Then the value of a is obtained as follows:

34/sin(73º) = a/sin(42º)

a = 34 x sine of 42 degrees/sine of 73 degrees

a = 23.8.

The value of b is obtained as follows:

34/sin(73º) = b/sin(65º)

b = 34 x sine of 65 degrees/sine of 73 degrees

b = 32.2.

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For a 10,000 linear feet of fencing and wants to enclose a rectangular field, the maximum area of each pasture is equals to the 2,083,333.33 square feet .

A rancher wants to enclose about 10,000 linear feet of fencing in a rectangular field. There are two equal pastures. Let, W the Width and L the Length with 3 pieces. The total length will be equal to 2W + 3L. As we know, the Area of rectangle, A = L×W ---(1)

Perimeter of rectangle = 10,000 feet, so sum of all sides of rectangle, 2W + 3L = 10000

Solve for determining value of L, 3L

= 10000 - 2W

[tex]L = \frac{ 10000 - 2W }{3}[/tex]

Substitutes for L into the first equation, A = L×W

[tex]A = W(\frac{ 10000 - 2W }{3})[/tex]

For maximum area, set the 1st derivative = 0.

differentiating above Area equation w.r.t W,[tex] A = \frac{(10000 \: W - 2W^2)}{3}[/tex]

[tex] \frac{dA}{dW} = \frac{d(\frac{10000 \: W - 2W^2}{3})}{dW}[/tex]

=> [tex]\frac { 1}{3}(10000 - 4W) = 0 [/tex]

=> W = 2500 meters

Now, using above relation, 2W + 3L= 10000

=> 5000 + 3L = 10000

=> 3L = 5000

=> L = 1667 meters

Area = 2500× 5000/3 = 4,166,666.67 sq feet. Now, maximum area of each pasture

= 4,166,666.67/2 = 2,083,333.33333 sq. feet. Hence, required value is 2,083,333.33 sq. feet.

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The value of solution of the expressions are,

⇒ 84.05

We have to given that;

The expression is,

⇒ (8 × 10) + (4 × 1) + (5 × 1/00)

Now, We can simplify as;

⇒ (8 × 10) + (4 × 1) + (5 × 1/100)

⇒ 80 + 4 + (5 × 0.01)

⇒ 84 + 0.05

⇒ 84.05

Thus, the value of solution of the expressions are,

⇒ 84.05

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The man is 23 km west of his home after driving 169 km to the east and 192 km to the west.

To determine how far the man is from his home after driving 169 km to the east and 192 km to the west, we can think of his movements as a displacement vector.

The vector representing the man's movement to the east has a magnitude of 169 km and is directed towards the east. Similarly, the vector representing his movement to the west has a magnitude of 192 km and is directed towards the west.

Since these two vectors are in opposite directions, we can subtract them to find the net displacement vector.

Net displacement = 169 km east - 192 km west

= -23 km west

The negative sign indicates that the net displacement vector is directed towards the west, which means that the man is 23 km west of his home.

To determine the distance between the man and his home, we can use the Pythagorean theorem. Since the man moved only in the east-west direction, the distance between him and his home is the absolute value of the net displacement, which is 23 km.

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The technique being described is random sampling without replacement, which is option a.

This technique is called "sampling without replacement."

However, you've also mentioned convenience sampling, which is a different method.

Let me briefly explain both concepts.

Sampling without replacement is a method in which each item, score, event, or participant is chosen from the population and is not returned to the pool for further selections.

This ensures that each element can only be selected once, eliminating the chance of duplication in the sample.

This method is often used in surveys, experiments, and research to maintain the independence of observations and provide a more accurate representation of the population.
Select an item, score, event, or participant from the population.
Record the selected item and remove it from the population.

Repeat steps 1-2 until the desired sample size is obtained.
Convenience sampling, on the other hand, is a non-probability sampling method where researchers select participants based on their accessibility and ease of recruitment.

This approach may introduce bias and limit the generalizability of the study results, as it does not ensure that the sample is representative of the population.
Identify the target population.
Recruit participants who are easily accessible and willing to participate.
Collect data from the selected participants.
In summary, sampling without replacement is a technique that prevents the same item from being selected more than once, while convenience sampling is an approach that focuses on selecting participants based on their accessibility. Both methods serve different purposes in research and should be chosen based on the study's objectives and available resources.

Option a is correct.

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The scatter plot that shows a negative nonlinear association is option C.

A scatter plot is a type of graph that displays the relationship between two variables. It is used to show how much one variable is affected by another variable. One variable is plotted on the horizontal axis (x-axis) and the other variable is plotted on the vertical axis (y-axis).

Here,

In this scatter plot, as the x-axis values increase, the y-axis values initially increase and then decrease. This type of association is referred to as a negative nonlinear association, where the direction of the association is negative (decreasing) and the shape of the association is nonlinear (not a straight line). The other options either show a positive association (increasing values of x and y) or a linear association (a straight line).

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation [tex]x_1-x_2[/tex], we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

[tex]1(x_1=22.8)[/tex] and deducting it from the mean of Sample [tex]2(x_2=20.1)[/tex].

With the use of the equation [tex]df=n_1+n_2-2[/tex], it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because [tex]n_1[/tex] = 20 and [tex]n_2[/tex] = 30.

We must apply the formula to determine the margin of error at 95% confidence [tex]ME=t*\sqrt[s]{n}[/tex].

The sample standard deviation (s) is equal to the average of [tex]s_1[/tex] and [tex]s_2[/tex] (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of [tex]n_1[/tex] and [tex]n_2[/tex] (25). When these values are entered into the formula, we get [tex]ME=1.67*\sqrt[3.4]{25}=1.7[/tex].

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means [tex]CI=x_1-x_2+/-ME[/tex].

The confidence interval's bottom limit in this instance is [tex]x_1-x_2-ME2.7-1.7=0.0[/tex] and the upper limit is [tex]x_1+x_2+ME=2.7+1.7=5.4[/tex].

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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The total 460 cards are sold on Mothers day.

Given that, Bob's gift shop sold a record number of cards for Mother's Day.

One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day.

Let the number of cards sold on mothers day be x.

Here, 10% of x =46

10/100 ×x= 46

10x=4600

x=460

Therefore, total 460 cards are sold on Mothers day.

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y=-1/2x-1 is equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3.

The slope of given line is 2

The slope of perpendicular line is -1/2

Now let us find the y intercept

1=-1/2(-4)+b

1=2+b

b=-1

Now the equation is y=-1/2x-1

Hence,  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3 is y=-1/2x-1.

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a) The exact solutions on [0, 2π) are t = π/3, π, and 5π/3. b) The exact solution on the interval [0, π) is t = 2π/3. c) The solutions are θ = π/3 and θ = 5π/3. d) The exact solutions on the interval [0, 2π) are: t = arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4] and t = 2π - arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4] using trigonometric identities.

a) We can rewrite the equation as:

2[tex]cos^{2}t[/tex] + cos(t) - 1 = 0

Using the quadratic formula, we get:

cos(t) = [-1 ± [tex]\sqrt{1-4(2)(-1)}[/tex] ] / (4)

cos(t) = [-1 ± [tex]\sqrt{9}[/tex]]/4

cos(t) = [-1 ± 3]/4

Thus, we have two solutions:

cos(t) = 1/2, which gives us t = π/3 and t = 5π/3

cos(t) = -1, which gives us t = π

Therefore, the exact solutions on [0, 2π) are t = π/3, π, and 5π/3.

b) We can use the identity [tex]tan^{2}t[/tex] + 1 = [tex]sec^{2}t[/tex] to rewrite the equation as:

[tex]tan^{2}t[/tex] = - [tex](3/2)^{2}[/tex]

Taking the square root of both sides and remembering that tan(t) is negative in the third quadrant, we get:

tan(t) = -3/2

Using the identity tan(t) = sin(t)/cos(t), we can rewrite this as:

sin(t)/cos(t) = -3/2

Multiplying both sides by cos(t) and rearranging, we get:

sin(t) = -3cos(t)/2

Squaring both sides and using the identity [tex]sin^{2}t[/tex] + [tex]cos^{2}t[/tex] = 1, we get:

9[tex]cos^{2}t[/tex]/4 + [tex]cos^{2}t[/tex] = 1

Expanding and simplifying, we get:

13 [tex]cos^{2}t[/tex] /4 = 1

[tex]cos^{2}t[/tex]  = 4/13

Taking the square root of both sides and remembering that cos(t) is negative in the third quadrant, we get:

cos(t) = -2[tex]\sqrt{13}[/tex] /13

Using the identity  [tex]sin^{2}t[/tex] +  [tex]cos^{2}t[/tex]  = 1, we can solve for sin(t) as:

sin(t) = -3/2 cos(t) = 3[tex]\sqrt{13}[/tex] /13

Therefore, the exact solution on the interval [0, π) is t = 2π/3.

c) We can use the identity sin(2θ) = 2sin(θ)cos(θ) to rewrite the equation as:

sin(θ) = 2sin(θ)cos(θ)

Dividing both sides by sin(θ) (assuming sin(θ) is non-zero), we get:

1 = 2cos(θ)

cos(θ) = 1/2

Therefore, the solutions are θ = π/3 and θ = 5π/3.

d) We can use the identity cos(2t) = 1 - 2 [tex]sin^{2}t[/tex]  and rearrange the equation as:

2 [tex]sin^{2}t[/tex]  + sin(t) - 5 = 0

Solving this quadratic equation using the quadratic formula, we get:

sin(t) = [-1 ± [tex]\sqrt{41}[/tex]]/4

Since the sine function has a range of [-1, 1], only the positive solution is possible, so we have:

sin(t) = (-1 + [tex]\sqrt{41}[/tex])/4

Using the identity [tex]cos^{2}t[/tex] = 1 -  [tex]sin^{2}t[/tex] , we can solve for cos(t) as:

cos(t) =[tex]\sqrt{1-sin^{2}t}[/tex] = [tex]\sqrt{17-\sqrt{41} }/4[/tex]

Therefore, the exact solutions on the interval [0, 2π) are:

t = arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4] and t = 2π - arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4]

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As a result, the account will be worth $398,634.52 in 25 years as by estimating the future worth of the yearly deposits.

Interest is the fee incurred when paying interest or the compensation given when lending money. The principal, which is the obtain desired or lent, is typically stated as a percentage. The period, and or duration for which the principal is lent or invested, as well as the interest rate determine how much interest is charged or generated. There are two types of interest: simple and compound. Compound interest is calculated based on the original and the total interest.

given

Let's begin by estimating the future worth of the yearly deposits:

[tex]$3000 * ((1 + 0.0925)25 - 1) / 0.0925[/tex] = $263,361.05 FV annuity

Then, let's determine the initial deposit's future value:

FV initial is $19,675.13 multiplied by (1 + 0.0925)25 to get $135,273.47.

Let's finally combine the two future numbers to determine the account's total future value:

$135,273.47 + $263,361.05 = $398,634.52

where FV total = FV initial + FV annuity

As a result, the account will be worth $398,634.52 in 25 years as by estimating the future worth of the yearly deposits.

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Answer:

hence the value of w is 12

Step-by-step explanation:

[tex]area = 2 {w}^{2} - 16w \\ by \: the \: question \: if \: area \: is \: equal \: to \: 8w \\ 8w = 2w {}^{2} - 16w \\ 8w + 16w = 2 {w}^{2} \\ 24w = 2 w {}^{2} \\ w = 12[/tex]

He needs to make 15 throws if the ratio is the same as the first game

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

Player was successful on 18 out of his 24 last free throws attempts

Using the above as a guide, we have the following:

Proportion = 18/24

For the number of games, we have

Throws made = Proportion  * Number of throws

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

Throws made = 18/24 * 20

Evaluate

Throws made = 15

Hence, the number of throws made is 15

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The interval for which the ball's height is increasing on the graph, would be 0 seconds to 1.5 seconds.

The interval for which the ball's height is increasing is when the slope of the graph is positive, or when the height is increasing with respect to time.

Looking at the graph, we can see that the ball starts at a height of 0 meters and reaches a peak of 11.025 meters at 1.5 seconds. After 1.5 seconds, the ball begins to fall back to the ground.

Therefore, the interval for which the ball's height is increasing is from 0 seconds to 1.5 seconds. During this interval, the height of the ball is increasing as it travels upwards, reaching its peak at 1.5 seconds. After 1.5 seconds, the height of the ball starts decreasing as it falls back down to the ground.

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For a normally distribution of daily demand of fresh boston lettuce produce by skinner. the probability that skinner will have at least 20 units left over by the end of the day is equals the one.

Skinner produce buys fresh boston lettuce daily. There is daily demand is normally distributed,

Mean = 100 units

Standard deviations = 15 units

At beginning of the day skinner orders 140 units of lettuce. We have to determine the probability that skinner will have at least 20 units left over by the end of the day, P( X ≥ 20). Using the Z-Score for normal distribution is written as

[tex]z = \frac{ X - \mu}{\sigma} [/tex]

where, z --> z-score

X --> excepted value

--> standard deviations

--> population mean

Subsritute the known values in above formula, [tex]z = \frac{ 20 - 100}{15} [/tex]

= - 5.33

Now, probability value, P ( X < 20)

[tex]= P( \frac{X - \mu}{\sigma} < \frac{ 20 - 100}{15} )[/tex] = P( z < - 5.33 )

= 0.000

So, P( X < 20) = P( z< -5.33) = 0 . Also, required probability is P( X≥ 20) = 1 - 0

= 1

Hence, required value is one.

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Answer:

16

Step-by-step explanation:

To round 15.98 to the nearest tenth, we look at the digit in the hundredths place which is 8. Since 8 is greater than or equal to 5, we round up the digit in the tenths place which is 9. Therefore, rounding 15.98 to the nearest tenth gives us 16.

Answer:

16

Step-by-step explanation:

15 . 98

8 round up is 10

0.10 + 0.9 = 1

15 + 1 = 16

The volume of the solid is (256π/15) - (128π/3) cubic units, which is formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8.

To find the volume of the solid formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8, we can use the disk method.

First, we need to find the bounds of integration. Since x = 2 is the right boundary, we can integrate from 0 to 2.

The distance between the line y=8 and the curve y=2x² is 8 - 2x². Therefore, the radius of the disk at a given x-value is 8 - 2x².

The area of each disk is given by π(radius)². Therefore, the volume of the solid is given by the integral of π(radius)² dx from 0 to 2;

V = ∫₀² π(8 - 2x²)² dx

This integral can be evaluated by expanding the square and using the power rule of integration. After simplification, we get;

V = (256π/15) - (128π/3)

Therefore, the volume of the solid is (256π/15) - (128π/3) cubic units.

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The predicted length for a catfish with weight of 48 pounds is given as follows:

45 inches.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Two points on the graph of the linear function are given as follows:

(20, 3) and (30, 21).

When x increases by 10, y increases by 18, hence the slope m is given as follows:

m = 18/10

m = 1.8.

Hence:

y = 1.8x + b.

When x = 20, y = 3, hence the intercept b is given as follows:

3 = 1.8(20) + b

b = 3 - 36

b = -33.

Hence the equation is:

y = 1.8x - 33.

The predicted length for a catfish with weight of 48 pounds is obtained as x when y = 48, hence:

48 = 1.8x - 33

x = 81/1.8

x = 45 inches.

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Supplementary angles are angles that add up to 180°. Angle 6 is a right angle, so it's worth 90°. This means that the other angle(s) have to be 90° as well.

As you can see, the other angle with 90° is angle 3, thus, making it the correct answer.

The values of a that make (x - a) a factor of x^4 - 5x³ - 21x² - 23x - 8 are given as follows:

a = 8 and a = -1.

The polynomial is given as follows:

f(x) = x^4 - 5x³ - 21x² - 23x - 8

By the factor theorem, x - a is a factor of a polynomial f(x) if f(a) = 0.

The numeric value at x = a is given as follows:

f(a) = a^4 - 5a³ - 21a² - 23a - 8.

Hence the values of a are obtained solving the equation presented as follows:

a^4 - 5a³ - 21a² - 23a - 8 = 0.

Using a calculator, the values of a are given as follows:

a = 8 and a = -1.

(the root of -1 has a multiplicity of 3).

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The coordinates of the point which is an outlier would be ( 14, 13).

The correlation between the 13 British towns is Linear.

The number of hours of sunshine for the British town with the maximum of 17.4 degrees Celsius is 13 hours of sunshine.

The coordinates of the outlier would be ( 14, 13). This is because, that point on the graph is far from the other points and does not follow their correlation.

The rest of the towns seem to be increasing in the same direction so they are linear.

The number of hours of sunshine in the British town with the maximum temperature of 17.4 degrees Celsius, based on the line of best fit drawn, would be 13 hours of sunshine.

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Full question is:

The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.

A line of best fit has also been drawn.

One of the points in an outliner.

a) Write down the coordinates of this point. (1)

b) For all the other points write down the type of correlation in just one word. (1)

On the same day, in another British town, the maximum temperature was 17.4C.

c) Estimate the number of hours of sunshine in this town on this day. (2)

Answer: True

Step-by-step explanation:

Answer:

Step-by-step explanation:

330/2 = 165

330/3 = 110

330/5 = 66

330/6 = 55

330/10 = 33

330/11 = 30

the answer is true

The given figure is a hexagonal pyramid and it has 7 faces, 7 vertices, and 12 edges. The correct option is c)

A hexagonal pyramid is a three-dimensional geometric figure that has a hexagonal base and triangular faces that meet at a common vertex. It is also known as a hexagonal pyramid or a hexagonal pyramid.

According to the given information:

The given shape is a Hexagonal pyramid

Here are the characteristics of a hexagonal pyramid:

Faces: 7 (1 hexagonal base and 6 triangular faces)

Vertices: 7 (1 common vertex where all the triangular faces meet and 6 vertices on the hexagonal base)

Edges: 12 (6 edges on the hexagonal base and 6 edges connecting the base to the common vertex)

So, a hexagonal pyramid has 7 faces, 7 vertices, and 12 edges.

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We will use the "Either of the rules" to calculate the probability that either the top card is the ace of spades or the bottom card is the ace of spades.

The either of the rules states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. In this case, the events are the top card being the ace of spades and the bottom card being the ace of spades. Since the two events are mutually exclusive (the ace of spades cannot be both at the top and at the bottom of the deck), we can add their probabilities to get the total probability.

The probability of the top card being the ace of spades is 1/52 (since there is only one ace of spades in the deck of 52 cards), and the probability of the bottom card being the ace of spades is also 1/52 (assuming that the deck has been sufficiently shuffled). Therefore, the probability of either the top card or the bottom card being the ace of spades is:

P(top or bottom is ace of spades) = P(top is ace of spades) + P(bottom is ace of spades)

= 1/52 + 1/52

= 2/52

= 1/26

So the chance that either the top card is the ace of spades or the bottom card is the ace of spades is 1/26 or approximately 0.038 or 3.8%.

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The probability is 2/52 or 1/26.

To find the chance that the top card is the ace of spades or the bottom card is the ace of spades, you will use the

Addition rule.

Calculate the probability of the top card being the ace of spades:

There are 52 cards in a deck, and 1 ace of spades, so the probability is 1/52.

Calculate the probability of the bottom card being the ace of spades:

This is also 1/52 since there's still 1 ace of spades among the 52 cards.

Apply the Addition rule:

Add the probabilities together, then subtract the probability of both events happening at the same time (which is 0, as

the ace of spades can't be in both positions).

So, the probability is (1/52) + (1/52) - 0 = 2/52 or 1/26.

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An equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 20)/(0 + 3)

Slope (m) = -15/3

Slope (m) = -5.

At data point (0, 5) and a slope of -5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -5(x - 0)

y - 5 = -5x

y = -5x + 5

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2 ¼ hours + 1 ½ hours = 3 ¾ hours

Jordan studied for his science test for 3 ¾ hours this weekend.

Science is a systematic process that produces knowledge in the form of testable predictions and universe-related explanations that can be organized and placed into order.

In general, science entails an effort to learn about universal truths or how fundamental laws work. Learning about the components of the universe and how they operate right now, in the past, and perhaps in the future is done through science.

Although science is intricate and multifaceted, its most significant traits are simple: Learning understanding what is in the natural world, how it functions, and how it came to be the way it is through science.

2 ¼ hours + 1 ½ hours = 3 ¾ hours

Jordan studied for his science exam for 3 ¾ hours this weekend.

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Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.

what is arithmetic sequence.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Jordan studied for 2 ¼ hours on Saturday and 1 ½ hours on Sunday for his science test. To find the total number of hours he studied, we can add these two amounts.

2 ¼ hours is the same as 2 + ¼ hours, or 2 hours and 15 minutes.

So, we have:

2 hours and 15 minutes (Saturday) + 1 hour and 30 minutes (Sunday)

To add these two amounts, we can first add the hours and then add the minutes separately.

2 hours + 1 hour = 3 hours

15 minutes + 30 minutes = 45 minutes

Therefore, Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.

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A Reflect triangle over the line x = -1 will take ABC to A"B"C".

What is triangle reflection theorem?

The outcome is the same as rotating the initial triangle 180 degrees around the origin, just as the theorem predicts, when we reflect the triangle over the y-axis and then cross the x and y axes while reflecting the outcome across the x axis.

The single transformation that takes ABC to A"B"C" is a reflection over the line x = -1.

The new triangle A'B'C' is formed by reflecting ABC across the line x = -2, where each point in A', B', and C' is the reflection of the corresponding point in ABC. As a result, A', B', and C''s x-coordinates are all 4 units to the left of A', B', and C''s x-coordinates.

The final triangle A"B"C is formed by reflecting A'B'C' over the line x = 0, where each point in A", B", and C" is a reflection of the corresponding point in A'B'C' over the line x = 0. Accordingly, the x-coordinates of A, B, and C" are all located two units to the right of the x-coordinates of A', B', and C'.

If we combine these two reflections into a single transformation, we can think of it as reflecting ABC over a line that is 2 units to the right of x = -2, which means it has an equation of x = -2 + 2 = -1. This line is the perpendicular bisector of the segment connecting the points (-2, 0) and (0, 0), which is the line that connects the two reflection lines x = -2 and x = 0.

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The approximate value of P(adult ∣ rode a ferris wheel) is 0.6364, which is approximately 63.64%.

To find the approximate value of P(adult|rode a ferris wheel), we can use the conditional probability formula:

[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) = \frac{P(adult \ and \ rode \ a \ ferris \ wheel)}{P(rode \ a \ ferris \ wheel)} }[/tex]

From the data given in the table, you can see that:

Total number of people who rode the ferris wheel: 198 (children + adults)

Number of adults who rode the ferris wheel: 126.

So, P(rode a ferris wheel) = 198/264

And, P(adult and rode a ferris wheel) = 126/264

Now plug these values into the conditional probability formula:

​[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) = \frac{P(adult \ and \ rode \ a \ ferris \ wheel)}{P(rode \ a \ ferris \ wheel)} } \\\\= \frac{126/264}{198/264}[/tex]

[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) } = \frac{126}{198} \\\\ \approx 0.6364[/tex]

Rounded to four decimal places, the approximate value of P(adult ∣ rode a ferris wheel) is 0.6364, which is approximately 63.64%.

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