A, b & c form the vertices of a triangle.
∠cab = 90°,
∠abc = 65° and ac = 8.9.
calculate the length of bc rounded to 3 sf.

Answer:

y = (1/7)(x + 8)³

Step-by-step explanation:

We are given the function; y = x³

There is a vertical compression by a factor of 1/7 which means that we now have the function as;

y = (1/7)x³

We are told that it shifts by 8 units to the left. This means we will have;

f(x + 8)

This gives;

y = (1/7)(x + 8)³

The transformed equation of \(y=x^{3}\) is \(y=-\frac{1}{7} (x+8)^{3}\).

Given equation:- \(y=x^{3}\)

Applying the given transformations, we have:

To have a vertical compression by a factor of \(\frac{1}{7}\), we need to multiply the function by \(\frac{1}{7}\). So, we have:

\(y=\frac{1}{7} x^{3}\)

To have a horizontal shift by 8 units to the left, we need to add 8 to x. So, we have:

\(y=\frac{1}{7} (x+8)^{3}\)

Lastly, to have a reflection over the x-axis, we need to multiply the function by −1. So, we have:

\(y=-\frac{1}{7} (x+8)^{3}\)

Therefore, the transformed equation is \(y=-\frac{1}{7} (x+8)^{3}\)

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The population means may be the same

So, option D is correct.

What is meant by confidence interval?

In statistics, the probability that a population parameter will fall between a set of values a predefined percentage of the time is known as the confidence interval. Analysts typically use confidence intervals that cover 95% or 99% of the expected observations while assessing data. In frequentist statistics, an estimation range for an unknown parameter is referred to as a confidence interval. The most common confidence level for computing confidence intervals is 95%, however other levels, such 90% or 99%, are also occasionally employed. The conclusion is reached that the result is statistically significant if the confidence interval eliminates the value of zero effect.

If (μ₁- μ₂=0) is included in the confidence interval, that means this two means have the same difference that is zero.

Therefore, they may be nearly same,

So, The population means may be the same

Hence, option D is correct.

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Answer:

200.96 ft^2

Step-by-step explanation:

A= πr^2. So the radius is 8, because it's half the diameter. That means A=64π. Then you multiply that to get 200.96, given that pi is estimated to 3.14.

Answer:

28meters and 112meters

Step-by-step explanation:

one piece is x

the other is 4x

therefore; 4x+x=140

5x= 140

divide both sides by 5

x=28

4x=4(28)

=112

The angle D in ADC  of the trapezium ABCD is 61.93 degrees.

Since ABCD is a trapezium with right angles at B and C, we can draw perpendiculars from A and D to BC:

Let h be the height of the trapezium and let E and F be the feet of the perpendiculars from A and D to BC, respectively.

The area of the trapezium is given by the formula:

A = 1/2 × (AB + DC) × h

Substituting the given values, we get:

34 = 1/2 × (5 + 12) × h

= 8.5h

h = 4

Now, we can use the Pythagorean theorem in the right triangles ABE and DCF to find the lengths of AE and DF, respectively:

AE² = AB² - BE² = 5² - h² = 25 - 16 = 9

AE = 3

DF² = DC² - CF² = 12² - h² = 144 - 16 = 128

DF = √128 = 8√2

Finally, we can use the sine rule in the triangle ADC to find angle D:

sin(D) = DF/AC

AC = AE + EC = 5 + CF

CF = DC - BC = 12 - 5 = 7

AC = 5 + 7 = 12

sin(D) = 8√2/12

D = sin⁻¹(8√2/12) = 61.93° (rounded to two decimal places)

Therefore, angle D in ADC is 61.93 degrees.

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Answer:

Step-by-step explanation:

\(Volume = 392.5\\r = 5\\h =?\\\\V= \frac{1}{3} \pi r^2 h\\\\392.5 = \frac{1}{3} \times 3.14 \times 5^2 \times h\\\\392.5 = \frac{78.5h}{3} \\\\392.5 = 26.16h\\\\\frac{392.5}{26.16} =\frac{26.16h}{26.16} \\\\h = 15.00\)

Answer:

h=15 in

Step-by-step explanation:

V=πr²(h/3)

h=3v/πr²

h=[3(392.5)]/[3.14(5)²]

h= 15 in

Answer:

12 boys

Step-by-step explanation:

I believe the answer is 12 boys. I hope this helps!

The probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The probability of being able to form a triangle with three sticks of random length can be found using geometric probability.

First, we can assume that the length of the first stick is x, where 0 ≤ x ≤ 1. The second stick can be any length y such that 0 ≤ y ≤ 1. The third stick can be any length z such that 0 ≤ z ≤ 1.

For the three sticks to form a triangle, they must satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have three cases to consider:

x + y > z

x + z > y

y + z > x

We can graph these three inequalities on a coordinate plane, where x and y are the lengths of two sides of the triangle, and the third side is represented by the area below the line.

The area of the triangle formed by the inequalities is 1/2, and the total area of the square representing the possible lengths of the sticks is 1.

Therefore, the probability of the three sticks forming a triangle is the ratio of the area of the triangle to the area of the square:

P(triangle) = area of triangle / area of square = (1/2) / 1 = 1/2

Hence, the probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.

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Answer:

36

Step-by-step explanation:

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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Answer:

the answer is x^2+8x+ c

Step-by-step explanation:

If  x 2 + b x + c  is a perfect square, then there is always the same relation ship between  b and c "Find half of  b  and square it" , so  c = ( b /2 ) ^2

 x^ 2 + 8 x + ( 8/ 2 )^2  =

x^ 2 + 8 x + 4^ 2 =

x^ 2 + 8 x + 16  =

( x + 4 ) ^2

I hope that helps you

Answer:

=3.201x109

=4.85x103

Step-by-step explanation:

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Answer:

0.2857

Step-by-step explanation:

We want to determine,

The probability that the battery life is at least 11 hours is 0.2857.

Answer:

x = 7/2

Step-by-step explanation:

The whole triangle is an equilateral triangle--all the sides are the same: 7, 7, 7 and all the angles are equal: 60°, 60°, 60°.

So the line thru the triangle makes two 30°-60°-90° triangles. The shortest side of the right triangle is half the length of the hypotenuse. Also, the line cuts the angle in half (30° and 30°) and also the side: 7/2

The sample mean of data is 24.19 and median is 3.54. The sign test and hypothesis testing. The boxplot for observation is present above figure. Yes, it support assumption that we are sampling from a normal distribution.

We have a sample data with values 1.48, 4.10, 2.02, 56.59, 2.98, 1.51, 76.49, 50.25, 43.52, 2.96. Also, here consider a sample from a normal distribution with unknown mean and variance, and the hypothesis that the population median (which is the same as the mean in this case) is 3.

Hypothesis testing parameters are

\(Н_0 : \mu = 3 \)

\(H_a : \mu ≠ 3 \)

The sample mean is called the average and it is defined as the ratio sum of data values divided by number of data values.

Median is a statistical measure. It is equals to the middle data value obtained by ordering the data values in ascending order. In case of odd number of data values it is middle value and in case of even number of data values it become mean of two middle values. Here we use Excel function to determine the mean and median values. So, see the above figure, excel command for mean is

'= mean (column contain data values)' and for median '= median ( same column)'. So, mean = 24. 19 and median

= 3.54 . The sign test for hypothesis testing of observations also present in above figure. P-value of test = 0.623 > 0.05 , That is no evidence to reject the null hypothesis. So, population mean = 3. The boxplot of observations also present in above figure.

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Answer:2.a

Step-by-step explanation:

The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.

This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.

It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.

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Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

Neil is growing sugar crystals for his science fair experiment. He wants to find out if the amount of sugar affects the size of the crystal. Neil adds 18 tablespoons of sugar to his first bowl of water. He plans to add less sugar to the second bowl.

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Stephen's hourly pay will be $10.42 in two years, calculated by plugging the principal amount of $9.45, the rate of interest of 5%, and the number of times interest is compounded per year of 1 into the compound interest formula.

Stephen's current hourly pay is $9.45. In order to calculate his hourly pay in two years time, we need to use the compound interest formula. The formula is A = P (1 + r/n)^nt, where A is the amount after n years, P is the principal or initial amount, r is the rate of interest, and n is the number of times interest is compounded per year. In this case, the principal is $9.45, the rate of interest is 5%, and the number of times interest is compounded per year is 1. Plugging these into the formula yields A = 9.45(1 + 0.05/1)^2*1, which equals $10.42. That means Stephen's hourly pay will be $10.42 in two years.

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Answer:

um tbh me dont know

Step-by-step explanation:

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

First one, true

Second one, 23/45

Third one, 11/29

Step-by-step explanation:

There's thy answer for thy self t-t

Answer:

1.)true

2.) 23/45

3.)11/29

Step-by-step explanation:

Answer:

In 3/4 of an hour, she would have ran 5.1 miles.

Hope this helps!

  (a). Perimeter of the drawing = 28 in.

  (b). Perimeter of the actual flower bed = 672 in.

  (c). Perimeter of the actual flower bed is 24 times the perimeter of the

       drawing.

           Perimeter = 2(Length + Width)

Given in the question,    

             the length and width in the drawing.

a). Perimeter of the drawing = 2(length + width)

                                                = 2(6 + 8)

                                                = 28 in.

b). Length of actual flower bed = 24(Length of the flower bed in drawing)

                                                    = 24(6)

                                                    = 144 in

   Width of the actual flower bed = 24(width of the flower bed in drawing)

                                                        = 24(8)

                                                        = 192 in

    Perimeter of the actual bed = 2(144 + 192)

                                                    = 672 in.

c). \(\frac{\text{Perimeter of the flower bed in drawing}}{\text{Perimeter of the actual flower bed}}\) = \(\frac{28}{672}\)

    \(\frac{\text{Perimeter of the flower bed in drawing}}{\text{Perimeter of the actual flower bed}}=\frac{1}{24}\)                  

    Perimeter of the actual flower bed = 24(perimeter of the flower bed in drawing)              

    Therefore, (a) Perimeter of the the drawing = 28 in.

                       (b) Perimeter of the actual flower bed = 672 in.

                       (c) Perimeter of the actual flower bed is 24 times the

                           perimeter of the drawing.

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Answer:

25

Step-by-step explanation:

Answer:

25!!

Step-by-step explanation:

One side(s) = x+6

Perimeter (4s)= 124

4(x+6) = 124

4x + 24 = 124

4x = 124-24

x = 100/4 = 25

I hope im right!! ;)

Answer:

1 1/2

Step-by-step explanation: