If the points A,B and C have the coordinates A (5,2), B (2,-3) and C (-8,3) show that the triangle ABC is a right angled triangle.

The test statistic z ≈ -2.59 falls into the rejection region (z < -1.96).

Therefore, we reject the null hypothesis (H₀) in favor of the alternative hypothesis (H₁).

a) Null and alternative hypothesis:

The null hypothesis (H₀) states that there is no significant difference between the claimed weekly production volume and the actual production volume.

The alternative hypothesis (H₁) states that there is a significant difference between the claimed weekly production volume and the actual production volume.

H₀: μ = 370 units (the claimed weekly production volume is true)

H₁: μ ≠ 370 units (the claimed weekly production volume is not true)

b) Critical value:

Since we're using a two-tailed test at α = 0.05 significance level, we'll look for the critical value (z-score) that corresponds to the 2.5% in each tail (5% total) of the standard normal distribution.

The critical value for a two-tailed test at α = 0.05 is ±1.96. The rejection region consists of the areas where the z-score is less than -1.96 or greater than 1.96.

c) Test statistic:

To calculate the test statistic, we will use the following formula:

z = (X - μ) / (σ / √n)

z = (355 - 370) / (19 / √30) = -15 / (19 / √30) ≈ -2.59

d) Conclusion:

The test statistic z ≈ -2.59 falls into the rejection region (z < -1.96).

Therefore, we reject the null hypothesis (H₀) in favor of the alternative hypothesis (H₁).

This means that there is significant evidence to suggest that the claimed weekly production volume of 370 units is not true.

The Vice President's suspicion about the statement appears to be correct, and further investigation should be conducted to determine the actual production volume.

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Answer:

let the children be x

let the dog be y

for the heads

x+y = 14 --- eqn 1

for the legs

2x + 4y = 40 ----- eqn2

since the children have 2 legs each and the dogs have 4 legs each

x + y = 14

2x+4y=40

through elimination method

multiply eqn1 by 2 and multiply eqn2 by 1

2x + 2y = 28

2x + 4y = 40 , then subtract

-2y = -12

to get y divide both sides by -2

y = 6

since in eqn 1

x+y=14

x = 14-y = 14-6 = 8

x = 8, y = 6

the children are 8 while the dogs are 6

Answer: 16-4√x/16-x is the answer.

Step-by-step explanation:

=> 4/4+√x*4-√x/4-√x

=> 4(4-√x)/(4)²-(√x)²  {using identity - (a+b) (a-b)=a² - b²}

=> 16-4√x/16-x

Answer:

logb28 ≈ 1.634.

Step-by-step explanation:

logb28 = (log428)/(log47)

We can then substitute the given values for logb4 and logb7:

logb28 = (log428)/(log47) = (log28)/(log24 + log27) = (log28)/(1.386 + 1.946)
1.386+1.946=3.332

logb28/3.332
logb28 ≈ 1.634.

Answer:

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

Given:

Use the following identity to find [tex]log_b28[/tex]:

Apply the identity to the given:

Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units;   MN = 49.5 units.

To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.

a. HZ * HW = HX * HY [based on the intersecting secants theorem]

Plug in the values:

16.8 * HW = 14 * 42

HW = 588/16.8

HW = 35 units

b. VK * VJ = VM * VN [based on the intersecting chords theorem]

Plug in the values:

27 * 18 = 36 * VN

VN = 486/36

VN = 13.5 units

MN = VM + VN = 36 + 13.5

MN = 49.5 units

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The general formula for f'(x) would be f' (x) = - 8 sin (x) + C.

The most general formula based on the first would be f(x) = 8 cos ( x ) + Cx + D.

To find the most general formula for f ' ( x ), we need to integrate f'' ( x ) with respect to x:

f'' ( x ) = - 8 cos (x)

f' (x) = ∫ ( -8cos(x)) dx

f ' (x) = - 8 sin(x) + C, where C is an arbitrary constant.

We need to integrate f'( x ) with respect to x to find the most general formula for f ( x ):

f'(x) = - 8 sin(x) + C

f(x) = ∫ ( - 8sin ( x ) + C) dx

f(x) = 8 cos ( x ) + Cx + D, where D is another arbitrary constant.

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Answer:

period :  π ; amplitude : 2

Step-by-step explanation:

Correct me if I'm wrong!!

Answer:

how many points will you give?

Step-by-step explanation:

The surface area of the triangular pyramid is 147.6 cm².

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the triangular pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

cos 2x

f(x)=4•sin(x)•cos(x)

Step-by-step explanation:

Answer:

To write 1/4 (x - 12) in words, you would say "one-fourth of the quantity obtained by subtracting 12 from x."

Answer:

last choice:  2b²/a³

Step-by-step explanation:

2a⁻³/b⁻² = 2·(1/a³) / (1/b²) = 2·(1/a³)(b²) = 2b²/a³

Answer:

Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

Step-by-step explanation:

My apologies for the confusion. Let's analyze how Elin arrived at her answer.

According to the given information, car A travels 221.5 km at a given time. Elin interpreted the statement "car B travels 1.2 times the distance car A travels at the same time" to mean that the distance traveled by car B is 1.2 times the distance traveled by car A.

To calculate the distance traveled by car B, Elin multiplied the distance of car A (221.5 km) by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

Note that in order to map A onto B, Kyle would have to dilate the given figure by a scale factor or 3.

A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.

The original point of figure A which has 4 points are


(0,02)
(-1, 2)
(0, 1)
(1, 2)

Multiply all th e points by 3, and you get,

(0,02) x 3 = (0, -6) =
(-1, 2) x 3 = (-3, 6)
(0, 1) x 3 = (0, 3)
(1, 2) x3 = (3, 6)

Plotting the new values will give us the transformation (dilation) required. See the attached image.

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1. The probability that P(X > 979) = 0.567

2. The probability that P(M > 979) = 0.956

To calculate the probability that  a single randomly selected value is more than 979 dollars.

 979-1016

= -37/209

= -0.177

P(X > -0.177) = 0.5675

Therefore P(X > 979) = 0.568

To calculate that a sample of size is randomly selected with a mean that is more than 979 dollars.

209 / √94 = 21.557

-37/ 21.557 = -1.7164

P(Z > -1.714) = 0.9564

therefore P(M > 979) = 0.956

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Answer: 27.33

Step-by-step explanation: If you use a calculator to do the hard stuff the rest is a breeze

Answer:

123 feet/41 yards

Step-by-step explanation:

When solving problems like this, we need to understand and note down what we already know to make our lives easier.

- He walks 13 different dogs

- the park is a perfect square

- he takes each dog for one full lap

- That day, he walked 6396ft

- He takes each dog the same distance

Now, let's find the unit value (how much ft does he walk if he takes JUST ONE dog around Greenpoint Park?)

Just divide: 6396 / 13 = 492 ft

Meaning, that when Harrold takes JUST ONE dog around the park, which is a perfect square, he walks 492 feet.

One full lap around the square shaped park is just 4 sides of the square.

So, he walks 492 ft every 4 sides.

However, the question specifically asked for one side.

Just divide again to get your answer:

492 / 4 = 123 ft

Therfore, the length of one side of the park is 123 feet, which is 41 yards.

Wwe can reject the null hypothesis and deduce that there is sufficient empirical evidence to validate the presumption that seatbelts are competent for mitigating fatalities.

Null Hypothesis: There is no discernible distinction between the proportion of fatalities among occupants wearing seat belts and those without.

Alternative Hypothesis: The portion of fatalities experienced by those in vehicles donning seatbelts will be demonstrably lower in comparison to individuals not utilizing them.

The z-value was computed, finding that (0.0113 - 0.0024) / √(0.0047 * (1 - 0.0047) * (1/2915 + 1/7848)) = 12.43.

For a two-tailed test at a 0.05 significance level with 2915 plus 7848 less 2 = 10761 degrees of freedom, the critical value range would be ±1.96. With the calculated z-value of 12.43 surpassing the critical threshold, we can reject the null hypothesis.

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Therefore, there are 3,628,800 different routes possible for the delivery truck to visit all 10 locations only once.

Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by an exclamation mark (!) placed after the number. Factorial notation is often used in combinatorics to calculate the number of possible permutations and combinations of a set of objects.

Here,

The number of different routes possible for the delivery truck can be calculated using factorial notation.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

This simplifies to:

10! = 3,628,800

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Answer: C

Step-by-step explanation:

We need to turn 50% into a fraction first to make it easier,

50% is equal to 1/2 because 50/100 is simplified to 1/2.

Now let's multiply!

24 x 1/2 = 24/2 = 12/1 = 12

The value of f(2020) is 39/100.

Given function is,

f(25) = 80

And f(xy) = f(x)/y²   .....(i)

Since

f(25) = 80

Then we define function as

f(x) = x + 55   .....(ii)

Now we can write 2020 = 101 x 20

So f(2020) = f(101x20) = f(101)/20²                from (i)

                                    =  (101 + 55)/400       from(ii)

                                    = 156/400

                                    = 39/100

Hence, f(2020) = 39/100

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The probability of selecting all defective transistors is 1/560.

The probability of selecting all defective transistors can be calculated as:

P(all defective) = (number of ways to select 3 defective transistors) / (total number of ways to select 3 transistors)

The number of ways to select 3 defective transistors is simply the number of combinations of 3 defective transistors out of the total of 3, which is 1. The total number of ways to select 3 transistors out of 16 is:

total number of ways = number of combinations of 3 transistors out of 16

= (16 choose 3)

= 560

Therefore, the probability of selecting all defective transistors is:

P(all defective) = 1 / 560

To simplify the answer, we can write it as a fraction in lowest terms:

P(all defective) = 1 / 560 = 1/ (161514/321) = 1/560

Therefore, the probability of selecting all defective transistors is 1/560.

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Answer:

"B".  Domain is all real numbers, and the Range is all positive real numbers

Step-by-step explanation:

It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form [tex]y=a*b^x[/tex] where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.

Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).

The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.

The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.

Since "a" is positive, the Range is positive numbers only.

Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.

Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero".  There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0".  So, the Range is written as { y | y>0 }.

Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.

Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"

Answer: 189 m^2

Step-by-step explanation:

Area = (Diagonal 1 x Diagonal 2) ÷ 2

Answer:6.25%

Step-by-step explanation:

The probability that a student is a graduate student given they are a history major is approximately 0.16.

The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.

We are given the following information:

Total number of students who are history major: 463

Total number of graduate students: 261

Number of graduate students who are history major: 73

We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:

P(graduate | history) = P(graduate and history)/P(history)

P(graduate | history) = 73/463

P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)

Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.

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The sequence 1, 6, 30, 60, . . . is not a geometric sequence

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

1, 6, 30, 60, . . .

To check if the sequence is geometric, we calculae the common ratio of the sequence using

r = next term/previous term

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

r = 6/1 = 6

r = 30/6 = 5

r = 60/30 = 2

The common ratios of the sequence calculated above are different

This means that the sequence is not geometric

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