Eight horses run a race. In how many ways can the first three finishers turn out?

Answer:

Perimeter of ΔABC: \(\frac{27}{2}\) + \(\frac{9}{2} * \sqrt6\) units

Area of ΔABC: \(\frac{81}{8}*\sqrt3 + \frac{243}{8}\) units

Skills required: HS Geo, Special Triangles

Step-by-step explanation:

1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.

2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.

AB is 9 units, and it is opposite the 90 degree angle. This means that \(2x=9, x = \frac{9}{2}\) ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is \(\frac{9}{2}\) units. Segment BD (the height) is \(\frac{9}{2} * \sqrt3\).

3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.

BD is \(\frac{9}{2} * \sqrt3\), which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is \(\frac{9}{2} * \sqrt6\).

4) Area is \(\frac{1}{2}*b*h\), the base (b) is AC (which is \(\frac{9}{2}+\frac{9}{2}*\sqrt3\)), the height is BD (\(\frac{9}{2}*\sqrt3\)). When multiple you will get \(\frac{81}{4}*\sqrt3 + \frac{243}{4}\), then this multiplied by 1/2 is

\(\frac{81}{8}*\sqrt3 + \frac{243}{8}\) <--> this is the area!

5) Perimeter is just the sum of all side: 9 + \(\frac{9}{2}\) + \(\frac{9}{2} * \sqrt6\) = \(\frac{27}{2}\) + \(\frac{9}{2} * \sqrt6\) unit

Step-by-step explanation:

By the secant tangent theorem,

21(21+25)=x^2

x^2 = 966

x = sqrt(996)

Step-by-step explanation:

the area of a rectangle is

length × width.

so, in our case

30 × 6 = 180 cm²

be careful to use the right unit for the result. an area is measured in square units based on the units of the given lengths. hence cm² as the given lengths are in cm.

Answer:

The answer is 64 customers

Step-by-step explanation:

We are told that 40% of the customers who bought groceries also bought a bag of ice.

The total customers is 160 customers

Required.

the number of customers that bought a bag of ice?

Step two:

Let us compute what 40% will amount to

40/100*160

=0.4*160

=64

Hence 64 customers bought rice

10 procent

Step-by-step explanation:

150 / 150 = 10

Answer:10%

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

.75-.25 is .5

1/2 is equal to .5 so .5 +.5 is 1

Answer:

0.75 - 0.25 + 1/2

convert the decimals to fractions

that's

0.75 = 3/4

0.25 = 1/4

We get

3/4 - 1/4 + 1/2

Find the common denominator which is 4

3/4 - 1/4 + 1/2 = 3 - 1 + 2 / 4

=4/4

= 1

The final answer is 1

Hope this helps

Answer:

4.63636363636

Step-by-step explanation:

Answer:

1 -2 5 /11 - -7 1 / 11

2 5/11

= 2.27

7 1 / 11

6.45

= -4 . 18

Answer:

Here Is Your Answer Less Than 0 But Greater Than 10

correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children is a. child-adoptive: 0.20; child-biological: 0.40

Children for adoption

Adoption is the social, emotional, and legal process in which children who will not be raised by their birth parents become full and permanent legal members of another family while maintaining genetic and psychological connections to their birth family.

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Answer:

YES!!! It really cool, you should create an Instagram account and post you art there!!

Step-by-step explanation:

The probability that the married couple will have adjacent desks is 0.22.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible arrangements where the married coupe has adjacent desks is 80640.

= 8 x 7! x 2

= 80640

Ans the total number of possible arrangements is 362880.

= 9!

= 362880

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

probability = 80640/362880

probability = 0.22

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Answer:

49π

Step-by-step explanation:

The formula for the area of a circle is \(\pi r^{2}\).

When you insert the numbers, you get \(a=\pi *7^{2}\)

\(7^{2} =49\)

Hope this helped :)

Answer: 120 ways

Step-by-step explanation:

Let's label the routes a, b, c, d, and e. The goal is to come up with as many unique permutations as possible.

1 route: a=1.               one factorial (1!) =1*1=1

2 routes: ab, ba=2.      2!=1*2=2

3 routes: abc, acb, bac, bca, cab, cba=6.      3!=1*2*3=6

4 routes: 4!=1*2*3*4=24

5 routes: 5!=1*2*3*4*5=120 ways

(C) "serpentine"

Serpentine is a winding word. The phrase would read "The mountain road was distinctly serpentine: it twisted back and forth along the contours of the hillside" if this term were added to the text.

The comma denotes that the meaning of the omitted phrase will be clarified in the second clause of the sentence. Because a winding road does actually curve "back and forth," the word "serpentine" matches the text. The answer is not (A).

A panoramic view is one that encompasses the entire surrounding region. (B) is the wrong answer. Precipitous refers to a steep slope. The answer is not (D). The term "circumscribed" describes something that is restrained or encircled by a line. The answer is not (E). Moving backward is referred to as retrograding.

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Answer:

This expression equals 22

Step-by-step explanation:

2(a-5)+2 a=15

2(15-5)+2

2(10)+2

20+2

=22

Answer:

42cm

Step-by-step explanation:

so if for every 11 feet you get 2 inches then for every 5.5 feet you get 1 cm. so if you break up the total number of feet into 220+16 it will be easier to solve. because 11*20=220ft so then you know you can do 2*20=40cm. now you can simplify 16 into 11+5 and get 11*1=11ft and 2*1=2cm. now youre left with 5ft and 5.5ft is 1 cm so you know that you have just under 1 cm. now add them all up 220ft+11ft+5ft=236ft and 40cm+2cm=42 cm

Answer:

8b-5=6b+23

8b-6b=23+5

2b=28

b=14

Step-by-step explanation:

Answer:

274

Step-by-step explanation:

187, 199, 211, 250, 298, 331, 347, 362 <<< First order least to greatest

187, 199, 211, 250, 298, 331, 347, 362 <<< Since there are an even amount of terms, take the middle TWO numbers

(250+298)/2 = 548/2 = 274 <<< Take the mean of the two numbers

Your final answer is 274!

Hope this helps!

Answer:

274

Step-by-step explanation:

1.Arrange your numbers in numerical order.

2.Count how many numbers you have.

3.If you have an odd number, divide by 2 and round up to get the position of the median number.

4.If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Answer:

Kate is 13years and 4 months old,I suggest.

Answer: I believe it's 5 I am not sure

Step-by-step explanation:

Answer:

_

6.1

Step-by-step explanation:

_

11/3 * 5/3 = 11·5/3·3 = 55/9 = 6.1

The graph of line a and line b is shown in the image attached below. The lines do not intersect each other.

To check if both lines intersect, we need to graph the system of equations. First, use the points given to write out the equations.

Line a:

Slope (m) = change in y / change in x = 6 - 4 / 8 - 0 = 2/8

m = 1/4

Find the y-intercept (b) by substituting m = 1/4, x = 0 and y = 4 into y = mx + b:

4 = 1/4(0) + b

b = 4

The equation of line a is: y = 1/4x + 4.

Line b:

Slope (m) = change in y / change in x = 1 - (-2) / 8 - 0

m = 3/8

Find the y-intercept (b) by substituting m = 3/8, x = 0 and y = -2 into y = mx + b:

-2 = 3/8(0) + b

b = -2

The equation of line b is: y = 3/8x - 2.

Both lines are graphed in the image attached below. Line a is the red line and line b is the red line. They do not intersect at any point.

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Answer:

Besides the givens:

12.

AC = EC, BC = DC; Definition of Midpoint

<ACB = <ECD; Vertical Angles Theorem

Triangle ABC = Triangle EDC; SAS Congruence Postulate

13.

AD = CD; Definition of Median

BD = BD; Reflexive Property

Triangle ABD = Triangle CBD; SSS Postulate

Step-by-step explanation:

None necessary.

Answer:

(4, 0)

Step-by-step explanation:

D is clearly (1, 2).

so, for D' we have (1+3, 2-2) = (4, 0).

that's it. there is nothing more to it.

Answer:

The 99% confidence interval estimate for the difference between the percentage of women and men who prefer the beach over the mountains is -18.72% < (p₁ - p₂) < 4.72%

Step-by-step explanation:

The given parameters are;

Sample size of the women sample, n₁ = 200

Percentage of the women that prefer beach, p₁ = 45%, \(\hat p_1\) = 0.45

Sample size of the men sample n₂ = 300

Percentage of the men that prefer beach, p₂ = 52%, \(\hat p_2\) = 0.52

Confidence level of the confidence interval = 99%

α = 1 - 0.99 = 0.01, therefore, α/2 = 0.005

The equation for the confidence interval for the difference between two proportions is given as follows;

\(\left (\hat{p}_{1} - \hat{p}_{2} \right )\pm z_{\alpha /2}\sqrt{\dfrac{\hat{p}_{1}(1-\hat{p}_{1})}{n_{1}}+\dfrac{\hat{p}_{2}(1-\hat{p}_{2})}{n_{2}}}\)

\(z_{\alpha /2}\) = ±2.57 from the z score tables

Plugging in the vales, we have;

\(\left (0.45 - 0.52 \right )\pm 2.57\sqrt{\dfrac{0.45(1-0.45)}{200}+\dfrac{0.52(1-0.52)}{300}}\)

Which gives;

-0.1872 < \((\hat p_1 - \hat p_2)\) < 0.0472

The 99% confidence interval estimate for the difference between the percentage of women and men who prefer the beach over the mountains = -18.72% < (p₁ - p₂) < 4.72%.

Answer:

The paper is not clear :(

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

9x3 is 27. Coefficient is the number in the term.

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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