The length of one leg of a right triangle is 5 centimeters shorter than the hypotenuse. The hypotenuse is 15 centimeters. What is the length of the unknown leg of the right triangle?

Answer:Roughly Symmetric

Step-by-step explanation:

I'm too lazy

There is about 295.11335 cubic inches of space left in the container, not including the balls.

We must first determine the cylinder's total volume before deducting the volume of the 25 spheres in order to determine the amount of space still inside the container.

The formula for calculating a cylinder's volume is V_cylinder = * r2 * h, where V_cylinder denotes the cylinder's volume, r stands for the cylinder's radius, and h denotes the cylinder's height.

The cylinder's radius (r) in this instance is specified as 3 inches, while its height (h) is specified as 12 inches. We may determine the volume of the cylinder by entering these values into the formula.

V_cylinder equals 3.14159 * 3 2 * 12 V_cylinder is 339.292 in3 in volume.

Next, we must determine the volume of each sphere. The following equation determines a sphere's volume:

Where: V_sphere = (4/3) * * (r3) V_sphere is the sphere's volume, is a mathematical constant roughly equal to 3.14159, and r is the sphere's radius.

The spherical balls' diameter (d) in this instance is 1.5 inches, which means the radius (r) is equal to half of the diameter.

r = 1.5/2d/2 = 0.75 inches.

We may get the volume of each spherical ball using this value as a plug-in in the formula.

V_sphere is equal to 4.33 * 3.14159 * 0.75.

1.7671459 in3 V_sphere

The volume of one sphere is multiplied by the quantity of spheres in order to determine the combined volume of the 25 spherical balls.

V_total_spheres is calculated as V_sphere * 25 V_total_spheres 44.17865 in3.

Finally, we can determine how much room is still in the container by deducting the volume of the 25 spheres from the cylinder's volume.

Space left is equal to V_cylinder - V_total_spheres.

339.292 - 44.17865 space_left

295.11335 in3 of space is remaining.

Without accounting for the balls, there is approximately 295.11335 cubic inches of empty space in the container.

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The value of the original side length is, 6 m

Here, We have to given that;

All the sides of a square have lengthened by,

⇒ 3 m

And, the area of a square becomes,

⇒ 81 m²

Since, We know that;

A square is a two dimension figure with 4 equal sides, 4 corners and 4 right angles. The sides of the square are equal and parallel to each other.

Now, We can assume that,

the original side length is,

⇒ x

Hence, We can formulate by given condition,

⇒ (x + 3)² = 81

Taking square root both side,

⇒ x + 3 = √81

⇒ x + 3 = 9

Subtract 3 both side,

⇒ x = 9 - 3

⇒ x = 6 m

Therefore, We get;

The solution of the original side length is,

⇒ 6 m

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Answer:

-7x=-31+3

-7x=-28

÷ by -7 both sides

x=3

Answer:

Step-by-step explanation:

You want the areas of a kite and a rhombus, given certain segment lengths.

The area of a quadrilateral in which the diagonals cross at right angles can be found from ...

  A = (1/2)(d1·d2) . . . . . where d1 and d2 are the lengths of the diagonals.

The vertical diagonal is 6m +10m = 16m. The horizontal diagonal is 8m +8m = 16m.

The area is ...

  A = (1/2)(16m)(16m) = 128 m²

The area of the kite is 128 square meters.

Each triangle is a right triangle, so the missing half-diagonal length is ...

  d2 = √(13² -5²) = √144 = 12

The area is ...

  A = (1/2)(2·5 cm)(2·12 cm) = 120 cm²

The area of the rhombus is 120 square centimeters.

__

Additional comment

You can save the trouble of using the Pythagorean theorem to find the missing rhombus diagonal if you remember the Pythagorean triple {5, 12, 13}. That triple, along with {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, and (9, 40, 41} are among those commonly seen in algebra, trig, and geometry problems.

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Answer:

The true statements about solving equations are:

-You are using inverse operations to isolate the variable.

-Order of operations is often done in reverse order.

Answer: the true statements are. you are inverse operations to isolate the variable. the addition property is usually used first. and Order of operations is often done in reverse order

Step-by-step explanation:

The perimeter of the right triangle ABD is 31 units.

Given is right triangle ADB, we need to find the perimeter of the triangle,

So, according to properties of a triangle we have,

x² = 9 × 4

x = √36

x = 6

Now using Pythagoras theorem,

6² + 4² = AD²

AD = 7.2

Similarly,

BD² = 6² + 9²

BD = 10.8

So, we know that the perimeter of a polygon is the sum of all its sides,

So,

P = AD + BD + AB

= 10.8 + 7.2 + 9 + 4

= 31 units.

Hence the perimeter of the right triangle ABD is 31 units.

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To find the domain of the function f(x, y) = ln(16 − x^2 − 16y^2), we need to determine the values of x and y for which the function is defined.

The natural logarithm function ln(x) is defined only for positive values of x. Therefore, for the given function to be defined, the expression inside the logarithm (16 − x^2 − 16y^2) must be greater than zero.

Setting 16 − x^2 − 16y^2 > 0, we can solve for the values of x and y that satisfy this inequality:

16 − x^2 − 16y^2 > 0

-x^2 − 16y^2 > -16

x^2 + 16y^2 < 16

This is the inequality of an ellipse centered at the origin with semi-major axis length 2 and semi-minor axis length 1. Therefore, the domain of the function f(x, y) is the interior of this ellipse.

To sketch the domain, draw the ellipse centered at the origin and shade the interior of the ellipse. The shaded region represents the domain of the function.

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A common control procedure in a group design is b. random assignment of subjects to groups. Random assignment is a crucial step in experimental research designs to ensure that participants have an equal chance of being assigned to different groups. It helps in minimizing the influence of confounding variables and increasing the internal validity of the study.

Random assignment involves assigning participants to different groups (e.g., experimental group and control group) based on chance alone. This process helps ensure that any observed differences between groups after the intervention can be attributed to the independent variable (the variable being manipulated) rather than pre-existing differences between participants.

By randomly assigning participants to groups, researchers can create groups that are statistically equivalent in terms of their characteristics, which allows for better comparison of the effects of the independent variable. Random assignment helps control for potential biases and ensures that any observed differences in the dependent variable (the outcome being measured) can be attributed to the treatment or intervention.

Random assignment also helps reduce the potential for systematic bias, as it minimizes the chances of experimenter bias or self-selection bias influencing the results. It enhances the reliability and generalizability of the findings by providing a more rigorous and unbiased comparison between groups.

Random assignment of subjects to groups is a common control procedure in group designs because it helps ensure the internal validity of the study by reducing confounding variables and increasing the likelihood that any observed differences between groups are due to the treatment or intervention being studied.

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The best interpretation of a 90% confidence interval is that if we were to take 1000 repeated samples of the same size and compute the confidence interval for each sample, approximately 950 of these intervals would contain the true population mean, while approximately 50 would not.

A confidence interval is a range of values within which we are confident that the population parameter (such as the mean) lies. The confidence level refers to the percentage of intervals, computed from repeated samples, that would include the true population parameter.

A 90% confidence interval means that we are 90% confident that the true population parameter falls within the computed interval. Therefore, if we were to take 1000 repeated samples and compute the confidence interval for each sample, we would expect approximately 900 of these intervals to contain the true population parameter (since 90% of the intervals would be expected to contain the true parameter), while approximately 100 intervals would not contain the true parameter.

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The median annual salary would be more useful to Jaime in making the decision between pursuing graduate studies or applying for a job.

The median annual salary represents the middle value in a salary distribution, which indicates the typical or central salary of college graduates in that profession. It is less affected by extreme values or outliers in the data. Therefore, the median provides a more reliable measure of the average salary that Jaime can expect as a college graduate. On the other hand, the mean annual salary can be influenced by a few individuals with exceptionally high or low salaries, which may not accurately reflect the typical salary range. Hence, the median salary would be a better indicator for Jaime to make an informed decision.

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If those two angles are equal (alt exterior angles)  then lines u and v are parallel.

6x + 14 =80

6x = 80-14

6x = 66

x = 11

So when x =11, then lines u and v are parallel.

The Surface area of the rectangular prism is 1232 square inches

To find the surface area of a rectangular prism, we need to find the areas of all six faces and add them together.

The two faces that have dimensions of 14 inches by 16 inches have a combined area of 2(14 in)(16 in) = 448 square inches.

The other four faces are all rectangles with dimensions of 14 inches by 14 inches, giving us a total area of 4(14 in)(14 in) = 784 square inches.

Therefore, the surface area of the rectangular prism is:

448 + 784 = 1232 square inches.

So the surface area of the rectangular prism is 1232 square inches.

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There are 70 ways to split 8 people into two teams of 4. There are 1680 ways to split 9 people into 3 teams of 3. There are 945 ways to choose 2 teams of 4 from 10 prospects.

To find the number of ways to split 8 people into two teams of 4, we can first choose the first team in $\binom{8}{4} = 70$ ways, and the second team will be the remaining 4 people.

To split 9 people into 3 teams of 3, we can first choose the first team in $\binom{9}{3} = 84$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{3} = 20$ ways. The final team will be the remaining 3 people.

To choose 2 teams of 4 from 10 prospects, we can first choose the first team in $\binom{10}{4} = 210$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{4} = 15$ ways. However, since the order in which we choose the two teams does not matter, we must divide by 2 to get the final answer of $\frac{210 \cdot 15}{2} = 945$.

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The term that describes an event that increases the likelihood of a response being repeated is known as reinforcement.

Reinforcement can be defined as any consequence that strengthens or increases the probability of a behavior occurring again in the future. This can include positive reinforcement, which involves adding a desirable consequence after a behavior, or negative reinforcement, which involves removing an aversive consequence after a behavior. Both types of reinforcement have been shown to be effective in increasing the likelihood of a behavior being repeated.

Overall, understanding the concept of reinforcement is essential in the field of psychology, particularly in the areas of behaviorism and behavior modification. By providing positive consequences after desired behaviors, individuals can be motivated to continue engaging in those behaviors, which can lead to long-term positive changes. Reinforcement can also be used to shape new behaviors or replace unwanted behaviors with more desirable ones.

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If Bill has 20 apples and Sarah has 15 apples, and they put them in a big pile and eat half, then There are 17.5 apples left.

Bill has 20 apples and Sarah has 15 apples. When they put them together in a pile, the total number of apples is 20 + 15 = 35. They eat half of the apples, which is equivalent to dividing the total number of apples by 2.

35 / 2 = 17.5

Therefore, there are 17.5 apples left after they eat half of the pile. It's important to note that while the concept of "half an apple" may not be physically possible, we can still express the result as a decimal to represent the fractional amount remaining. In this case, 17.5 represents the remaining apples after dividing the original pile in half.

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Calculating this expression, we find that the probability of exactly 4 arrivals in a one-minute period is approximately 0.0902.

The probability of at least 4 arrivals in a one-minute period is approximately 0.8571.

The probability of exactly 4 arrivals in a one-minute period can be calculated using the Poisson distribution formula. With a mean arrival rate of 2 customers per minute, we can substitute λ = 2 into the formula. The probability of exactly 4 arrivals is given by:

P(X = 4) = (e^(-λ) * λ^4) / 4!

Substituting λ = 2:

P(X = 4) = (e^(-2) * 2^4) / 4

The probability of at least 4 arrivals in a one-minute period can be calculated by summing the probabilities of having 4, 5, 6, and so on, arrivals. Using the same Poisson distribution formula, we can calculate the individual probabilities and sum them up.

P(X ≥ 4) = 1 - P(X < 4)

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Substituting λ = 2 into the Poisson formula, we can calculate each individual probability and sum them up.

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Answer:

1.8

Step-by-step explanation:

speed = distance/time

Distance measured in km

Time measures in hours

750m = 0.75

25mins = 0.42 of an hour

0.75/0.42 = 1.8 to 1dp

Answer:

-----------------------

We know that:

Find the speed and convert as below:

The number that Alice is writing is 9,008,352.

We are given that;

Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones

Now,

To find the number that Alice is writing, you need to identify the place value of each digit based on the clues given. You can use a place value chart to help you. You can write your solution as:

Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones

3  

5

8  

2

9    

Therefore, by algebra the answer will be 9,008,352.

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The length of AB is 6 units.

Given that two congruent circles, we need to find the distance AB,

Let the point where AB and CD intersects be O,

According to the property of circle, AB⊥CD, and CO = OD.

Therefore, using the Pythagorean theorem,

AC² = OC² + AO²

AO = √5²-4²

AO = 3

Since the circles are congruent then AO = OB = 3

AB = OA + OB

AB = 6 units.

Hence the length of AB is 6 units.

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The value of x which is the radius of the circle in the image above, is calculated to the nearest tenth as: x = 14.3.

The circle that is shown above has a radius whose length is represented as x. Since the segment that is drawn from the center of the circle intercepts the chord and is perpendicular to the chord, therefore, it bisects the chord into equal segments.

Thus, the perpendicular segment and half of the segment of  the chord will form a right triangle with the radius of the circle.

Therefore, using the Pythagorean Theorem, we have:

x = √(13² + 6²)

x = 14.3 [to the nearest tenth].

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0 5/3 21 On the number line, we need to position three numbers: 0, 5/3, and 21.

The number 0 is the starting point and should be placed on the leftmost box. Next, we have the number 5/3. To determine its placement, we can convert it to a decimal. Dividing 5 by 3 yields 1.666..., which is approximately 1.67.

Since 5/3 is greater than 1 but less than 2, it falls between 1 and 2 on the number line. Finally, we have the number 21, which is significantly larger than 5/3. It should be placed on the rightmost box, well past the midpoint between 0 and 5/3. Therefore, the correct placement along the number line would be: 0, 5/3, 21.

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[tex]f(x)=3x^2+5\\g(x)=4x-2\\h(x)=x^2-3x+1\\\\f(x)+g(x)-h(x)=3x^2+5+4x-2-(x^2-3x+1)\\f(x)+g(x)-h(x)=3x^2+4x+3-x^2+3x-1\\f(x)+g(x)-h(x)=2x^2+7x+2[/tex]

Answer:

Since each of the four sides of a rhombus has an equal length, the perimeter of a rhombus may be calculated using the formula, Perimeter = 4a, where 'a' denotes the length of the side of a rhombus.

Step-by-step explanation:

The perimeter of a rhombus is calculated by multiplying one of its four equal sides by four 4. Four times the length of one the sides is applied to determine the perimeter of a rhombus.

The three statements that are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   .......equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

Based on the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

By comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x - 0)² + (y - 0)² = 3²

x² + y² = 9.

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option "The population is the number of people in the town of Westingbrook, and the sample is the number of people who go to the mall" is correct

The coordinates of the midpoint of AB is (2, 4)

If the line y = x+2 meets the curve y² = 4(2x+1) at A and B. Then we can say:

(x + 2)² = 4(2x+1)

Let's solve for x:

(x + 2)² = 4(2x+1)

x² + 4x + 4 = 8x + 4

x² + 4x -8x + 4 - 4 = 0

x² - 4x = 0

x (x - 4) = 0

x = 0, x - 4 = 0

x = 0, x = 4

when x = 0, y = 2

When x = 4, y = 6

Thus, the coordinates of the two points are:

A(0, 2) and B(4, 6)

midpoint of AB = ((0+4)/2 , (2+6)/2)

                          = (2, 4)

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Given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ).

Given the expression:
sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ))
Let's simplify this expression step by step:
1. First, recognize that cos(θ) * cos(θ) can be written as cos²(θ). So, the expression becomes:
sin(θ) + cos²(θ) * (1 - cos(θ))
2. Next, we'll distribute cos²(θ) to both terms inside the parentheses:
sin(θ) + cos²(θ) - cos³(θ)
At this point, we have simplified the expression as much as possible. The final expression is:
sin(θ) + cos²(θ) - cos³(θ)
In summary, given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ). Remember that this is a general expression and its specific value depends on the angle θ.

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