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Answer:

Step-by-step explanation:

The length measure of the second leg of the right-angle triangle is 12 units.

Given the parameter:

Hypotenuse = 15 units

Length of leg1 = 9 units

Length of leg2 = x

To determine the measure of the missing side length of the right triangle, we use the Pythagoras theorem.

It is expressed as:

( hypotenuse )² =  ( leg 1 )² + ( leg 2 )²

Plug in the given values:

( 15 )² =  ( 9 )² + ( leg 2 )²

Simplifying, we get:

225 = 81 + ( leg 2 )²

( leg 2 )² = 225 - 81

( leg 2 )² = 144

Take the square roots:

leg 2 = √144

leg 2 = 12 units

Therefore, the second leg measures 12 units.

The question is not complete, the complete question is:

A right triangle's leg is 9 and the hypotenuse is 15, What is the length of of the other leg of the triangle?

Learn more about trigonometric ratio here: https://brainly.com/question/28038732

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Using the data presented in the problem, you are asked to predict the probability that future customers will cancel their preorders. To find the probability, you have to divide the number of people who cancelled their preorders by the total number of people who preordered.

35 people / 140 people = .25 or 25% probability that the future customers will cancel their preorders.

Answer:

A

Step-by-step explanation:

we are given

m∠3 = 120° and m∠12 = 80°

we will check all

Calculation of m∠1:

we can see that angles 1 and 3 are linear

so, their sum must be 180

m∠1+m∠3 = 180°

now, we can plug values

m∠1+ 120°= 180°

m∠1=60°

Calculation of m∠13:

we know that

angles 12 and 13 are alternate angles

so, they must be equal

m∠13=m∠12 = 80°

m∠13= 80°

Calculation of m∠6:

we know that

angles 3 and 6 are alternate angles

so, they must be equal

m∠3=m∠6 = 120°

m∠6= 120°

Calculation of m∠5:

we know that

angles 1 and 5 are corresponding angles

so, they must be equal

m∠1=m∠5 = 60°

m∠5= 60°

Calculation of m∠10:

we can see that angles 10 and 12 are linear

so, their sum must be 180

m∠10+m∠12 = 180°

now, we can plug values

m∠10+ 80°= 180°

m∠10=100°

Calculation of m∠14:

we know that

angles 10 and 14 are corresponding angles

so, they must be equal

m∠10=m∠14 = 100°

m∠14= 100°

Answer:

A, B, D, F

Step-by-step explanation:

Well to summarize what the previous person mentioned:

1 = 60

13 = 80

6 = 120

5 = 60

10 = 100

14 = 100

So given that information the correct answers are:

A, B, D, F

Answer:

[tex]x_1 = -8[/tex]

[tex]x_2 = -3[/tex]

Step-by-step explanation:

Given the equation:

[tex]x^2+24 = -11x[/tex]

Add 11x to both sides we have;

[tex]x^2+11x+24 = 0[/tex]

Split the middle terms we have;

⇒[tex]x^2+8x+3x+24 = 0[/tex]

⇒[tex]x(x+8)+3(x+8)= 0[/tex]

⇒[tex](x+8)(x+3)= 0[/tex]

By zero product property we have;

x+8 = 0 and x+3= 0

⇒x = -8 and x = -3

Therefore, the roots of the given equations are:

[tex]x_1 = -8[/tex]

[tex]x_2 = -3[/tex]

Answer: {1, 2, 3, 4, 5, 6}

Step-by-step explanation:

Given : A student rolls a number cube whose six faces are numbered 1 through 6.

Then, the possible outcomes of rolling it = 1, 2, 3, 4, 5, 6

Then , the sample space for this experiment = set of all possible outcomes

= {1, 2, 3, 4, 5, 6}

Final answer:

In a normal distribution, the mean, median, and mode are all the same, since it is symmetric around the mean. The standard deviation affects the shape of the distribution, and the empirical rule states that most values lie within two standard deviations of the mean. Differences in symmetry may cause the mean, median, and mode to diverge, with the mean being most affected by skewness.

Explanation:

In a normal distribution, the mean is equal to the median and mode, by definition. This is because the normal distribution, which is also known as the Gaussian distribution, is symmetrically shaped like a bell curve around the mean (μ). The mean indicates the center of the distribution and the point of symmetry, while the median divides the data such that half of the values are above it and half are below. The mode is the most frequently occurring value in the data set, and in a perfect normal distribution, it coincides with the mean and median.

The standard deviation (σ) is a measure of the spread of the distribution. If the standard deviation is increased, the curve becomes wider and flatter, while a decrease in σ makes the distribution steeper and narrower. Additionally, the location of μ on the X-axis can shift the entire graph to the left or right, but the shape of the graph remains the same. The empirical rule helps us understand that approximately 95% of values lie within two standard deviations from the mean.

Drawing from the collaborative exercise provided, by recording the heights and creating histograms with smooth bell-shaped curves, one can calculate the mean and identify how characteristics such as skewness affect the mean, median, and mode, especially in non-symmetric distributions. In these cases, the mean can be influenced by the direction of the skew more than the median, pulling it towards the tail of the distribution.

the piano lesson ends at 5:15

Answer: 5 units

Step-by-step explanation:

We know that the general equation of a circle having center at (h,k) and radius r is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given : The equation of a circle : [tex]3x^2 + 3y^2 = 75[/tex]

Taking 3 as common from the left side of the given equation , we get

[tex]3(x^2 + y^2) = 75[/tex]

Divide 3 on both the sides , we get

[tex]x^2 + y^2 = 25[/tex]

Comparing to the general equation of circle , we get

[tex]r^2 = 25\\\\\Rightarrow\ r=5[/tex]

Hence, the radius of the circle = 5 units

Final answer:

Cecil should pay $14.29 for his golf hats.

Explanation:

To determine what Cecil should pay for his golf hats, we need to calculate the cost price and apply the 40% markup. Let's assume the cost price is 'x'. Since Cecil needs a 40% markup on cost, the selling price will be 140% of the cost.

To find the selling price, we can use the equation: 140% of 'x' = $20. Solving this equation, we get: x = $20 / 1.4 = $14.29.

Therefore, Cecil should pay $14.29 for his golf hats.

Answer:

Option C is a cubic function

Step-by-step explanation:

Given the options we have to choose the cubic function

Cubic function is the function with degree 3 i.e the highest power of variable is 3.

Option a: [tex]f(x)=3x+1[/tex]

The above polynomial has highest power 1 i.e of degree 1

∴ not a cubic function

Option b: [tex]f(x)=3x^2+x+2[/tex]

The above polynomial has highest power 2 i.e of degree 2

∴ not a cubic function

Option c: [tex]f(x)=5x^3+2x+1[/tex]

The above polynomial has highest power 3 i.e of degree 3

∴ above is a cubic function

Option d: [tex]f(x)=x^3+x^4+5[/tex]

The above polynomial has highest power 4 i.e of degree 4

∴ not a cubic function

Answer:

[tex](1+0.3)^{6}=(1)^6+6(1)^{5}(0.3)+15(1)^{4}(0.3)^{2}+20(1)^{3}(0.3)^{3}+15(1)^{2}(0.3)^{4}+6(1)^{1}(0.3)^{5}+(0.3)^{6}[/tex]

Step-by-step explanation:

This is an expansion of the expression [tex](a+b)^{6}[/tex]. In general you can expand expressions of this form by a formula known as the binomial theorem. This formula establishes that

[tex](a+b)^{n}=\sum_{k=0}^{n} {n\choose k} a^{n-k}b^{k}[/tex]

Where the coeficients [tex]n\choose k[/tex] are called binomial coeficients, and can be computed by the formula

[tex]{n\choose k} =\frac{n!}{(n-k)! k!}[/tex]

where [tex]n!=1\times 2\times 3\times \cdots\times n[/tex].