Use the diagram and the given angle measure to find the other three measures

Given.

The distance covered by the snail in 4 minutes is 10 cm.

The speed of snail is,

The distance covered by snail in 6 minute is,

Hence, the distance covered by the snail is 15 cm.

Speed :

Speed is defined as the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling.

Hence , speed can be calculated by using the formula,

               Speed = [tex]\frac{Distance-travelled}{Time-taken}[/tex]

Given data :

Distance travelled by the snail = 10 cm = 0.1 m

Time taken by the snail to travel a distance of 10 cm = 4 min = 240 s

Then , speed of the snail = [tex]\frac{10}{4}[/tex] = 2.5 cm/min = 0.0004 m/s

If the time taken by the snail is 6 min = 360 s

Then, the distance travelled by the snail in 6 min

         = speed x time taken

          = 2.5 cm/min  x 6 min

          = 15 cm = 0.15 m.

Therefore, the snail travels a distance of 15 cm in 6 min.

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Answer:

nothing but B2. 0 hours

The bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.

Speed can be thought of as the rate at which an object covers distance.

i.e.

Speed = distance traveled/time taken

After arranging the equation we get,

Time taken = Distance traveled/Average speed

Here distance traveled by bus = 90 km

The average speed of the bus = 60 km/hr

So total time taken = 90/60 = 1.5 hours

So the bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.

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P : Principal amount deposited : $600

r : interest rate : 5 % = 0.05 ( decimal form)

n : number of compounding periods in a year : 4 (4 times in a year)

t : years

Apply compound interest formula:

A= P (1+r/n)^nt

Replace by the values given:

A = 600 (1+0.05/4)^(4.3)

A = 600 ( 1.0125) ^12

A =$ 696.45

Answer:

y=5

Step-by-step explanation:

RS  +    ST   =    RT

9y+2     +     2y+3       =   60

11y         +      5         = 60

11y   =     55

Y = 5

Answer:

3x + 5 + (8x - 3) = 180

11x + 2 = 180

11x = 178

x = 16.18

= 16.2

In a sample of 10 nucleotides, the likelihood of drawing 10 consecutive adenines at random is 0.000006.

Probability: The probability of an occurrence is defined as the ratio between the number of favorable outcomes to a certain event and the entire number of potential outcomes.

The following calculation shows the likelihood of picking 10 consecutive adenines at random from a sample of 10 nucleotides:

According to the information provided, there are 10 adenines and a likelihood of 0.30 that DNA contains them. n = 10 and p = 0.30

Therefore, Probability = (0.30)10 = 0.000006

The likelihood of randomly selecting 10 consecutive adenines from a sample of 10 nucleotides is calculated by multiplying the likelihood that DNA contains adenines by 10 times.

Therefore, The probability of picking 10 consecutive adenines at random from a sample of 10 nucleotides is 0.000006.

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Answer:what photo

Step-by-step explanation:

where

Answer:

The translation rule is;

Explanation:

Given the graph attached;

Let us pick a corresponding edge(point) on the preimage and image respectively;

The change on the x and y axis is;

Therefore, the translation rule is;

The equation is, 4x - y = -5

The equation is, x + 2y = 6

The equation is, [tex][tex]y = -\frac{3}{4}x + \frac{29}{4}[/tex][/tex]

The equation is, y = -2x + 5

What is standard form of equation of line?

When A and B are not both zero, a line has the usual form Ax + By = C. The standard form of equation with slope and the point is,[tex][tex]y - y_{1} = m(x - x_1)[/tex][/tex] ...(1)

1. Given:[tex][tex]x_1 = -3, y_1 = -7, m = 4[/tex][/tex]

Plug these values in the above equation,

[tex][tex]y - (-7) = 4(x - (-3)\\ y + 7 = 4(x + 3)\\\\y + 7 = 4x + 12\\y = 4x + 5\\\\4x - y = -5[/tex][/tex]

This is the equation in standard form of line.

2. Given:

[tex][tex]x_1 = 10, y_1 = -2, m = -\frac{1}{2}[/tex][/tex]

Plug these values in the equation (1),

[tex][tex]y - (-2) = -\frac{1}{2} (x - 10)\\y + 2 = -\frac{1}{2} x + 5\\[/tex][/tex]

Multiply both sides by 2.2y + 4 = -x + 10x + 2y = 6

This is the equation in standard form of line.

3. Given:

[tex][tex]x_1 = -1, y_1 = 8, m = -\frac{3}{4}[/tex][/tex]

Plug these values in the equation (1),[tex][tex]y - 8 = -\frac{3}{4}(x - (-1))\\ y -8 = -\frac{3}{4}(x + 1)\\ y - 8 = -\frac{3}{4}x - \frac{3}{4}[/tex][tex]y = -\frac{3}{4}x -\frac{3}{4} + 8\\ y = -\frac{3}{4}x + \frac{29}{4} \\[/tex][/tex]

This is the equation in point slope form.

4. Given:[tex][tex](x_1, y_1) = (-3, 11), (x_2, y_2) = (6, -7)[/tex][/tex]

First to find the slope from the given two points.

[tex][tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{-7-11}{6-(-3)}\\ m = \frac{-18}{9\\}\\ m = -2[/tex][/tex]

Now plug m = -2 and one of the given point in the equation (1), we ge[tex]t[tex]y - 11 = -2(x - (-3))\\y - 11 = -2(x + 3)\\y - 11 = -2x - 6\\y = -2x + 5[/tex][/tex]

This is the equation in slope intercept form.

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Work done in stretching spring from 36 cm to 38 cm is 0.333J.

The work needed to stretch a spring is given by the formula mentioned below:

[tex]W_{s}[/tex] = (1/2) K × [tex]x^{2}[/tex]

Here,  k is spring constant and x is the elongation.

So, x = [tex]x_{f} - x_{i}[/tex]

When spring is stretched from 40 cm to 34 cm

x = 40 - 34  = 6cm = 0.06 m

We need to know the spring constant so that we can calculate work.

3 = (1/2) K × [tex](0.06)^{2}[/tex]

K = 1666.67

Now, when spring is stretched from 36 cm to 38 cm

x = 38 - 36 = 2 cm = 0.02 m

[tex]W_{s}[/tex] = (1/2) × (1666.67) × [tex](0.02)^{2}[/tex]

[tex]W_{s}[/tex] = 0.333J

So, 0.333J work is done in stretching spring from 36 cm to 38 cm.

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We cannot conclude that working in a digital workplace caused employees to be happier from the survey.

How is the conclusion from the survey explained?

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Approximately, all of the signatures in the sample of 3000 signatures are invalid . We get this outcome by using binomial distribution .

This problem it is said that 30% of 10000 signatures on certain recall petition are invalid . So, here is the two outcomes possible one is the signatures are invalid and other signature are valid .

Probability of Success (signature are valid ) = p = favourable outcomes / total outcomes

Favourable outcomes for Success = 70% of 10,000= 7000

Total number of possible outcomes = 10,000

P = 7000/10,000 = 7/10

Probability of failure (signature are invalid ) = q= 1- p = 1- 7/10 = 3/10

We have to find out probability of getting invalid signature from a sample of 3000 signatures..

Using the binomial distribution,

P(X = x ) = ⁿ C ₓ pˣ (1- p)⁽ⁿ⁻ˣ⁾

n = 3000 , x= 0 for none of signatures from 3000 are invalid.

P(X=0) = ³⁰⁰⁰C ₀ (3/10)⁰ ( 7/10) ³⁰⁰⁰

= 1 . 1 . (7/10)³⁰⁰⁰ = (7/10)³⁰⁰⁰ = 0

Probability of getting invalid signature out of sample 3000 is

1 – ( 7/1000)³⁰⁰⁰ = 1

This implies that all the signatures in sample of 3000 are invalid.

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One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials.

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials. In other words, the results of one trial do not influence those of the others.

An experiment with a fixed number of independent trials and just two results is referred to as a binomial experiment.

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Investor purchased 50 shares of stock in a company for $40.

So, the total initial amount he invested is

Then the rate of return is:

So, the requied rate of return is 10.0%.

Answer:

A. k ≥ 8.14

Step-by-step explanation:

Hope this helps! :))

Rainfall anually table data

Then

Option A)

Half of the data are between 6 and 18

TRUE , because there are 8/2 = 4 data in the box plot

Option B)

Data point 27 ,could be an outlier

FALSE, because 27 is a black point. It means it belongs, is not out

Option C)

More points between 6,9 that between 9,18

FALSe,. Area between 6,9. Is smaller than area between 9,18

Option D)

Data are less spread out to the left

TRUE, because box plot is ubicated at left

Option E)

Only one data point is less than 6

TRUE, is data point 3

The angle in the fourth quadrant associated with trigonometric function is 314.415°. The exact values of the six trigonometric functions are listed below:

In this problem we find the exact form of a trigonometric function and the related quadrant on a Cartesian plane. By definition of the sine function and the features of the sine, the exact value has the following form and conditions:

y / √(x² + y²) = - 5 / 7, x > 0, y < 0

Then,

y = - 5, √(x² + y²) = 7

√[x² + (- 5)²] = 7

x² + 25 = 49

x² = 24

x = √24

x = 2√6

Then, the angle associated to the trigonometric function is:

θ = tan⁻¹ (y / x)

θ = tan⁻¹ (- 5 / 2√6)

θ ≈ 314.415°

And the five other trigonometric functions are:

cos θ = 2√6 / 7

tan θ = - 5 / 2√6

cot θ = - 2√6 / 5

sec θ = 7 / 2√6

csc θ = - 7 / 5

The angle associated with trigonometric function is 314.415°.

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Answer: 55

Step-by-step explanation: 180-78 to get the complementary angle. 180-157 to get complementary angle. 180-102+23 to get the last angle inside the triangle. 180-125 and get 55

The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)

Given,

The equation: 8 ( 5 + 2) = (__×___) + (___×__)

Distributive property:

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Here,

8 (5 + 2)

Using distributive property open the brackets:

8 (5 + 2) = (8 × 5) + (8 × 2)

Now,

8 (5 + 2) = 40 + 16

That is,

8 (5 + 2) = 56

So,

The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)

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The correct option regarding the symmetry of the distribution is given as follows:

The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.

To find the symmetry of the distribution, the mean and the median need to be calculated and compared, if they are equal or which is greater.

A dot plot shows the number of times that each observation appears in the data-set, hence the complete data-set of heart beats per minute is given as follows:

62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.

The mean is the sum of all these observations divided by the number of observations, which is of 20, hence:

Mean = (62 + 3 x 68 + 69 + 2 x 70 + 3 x 72 + 2 x 75 + 76 + 2 x 78 + 3 x 80 + 2 x 89)/20 = 74.55.

The median is the middle value of the data-set, the value which 50% of the observations are less than and 50% are greater than. The cardinality of 20 in this data-set is an even number, hence the median is the mean of the 10th and of the 11th element, as follows:

Median = (72 + 75)/2 = 73.55.

When the mean is greater than the median, as is the case in this problem, the distribution is right skewed, which is the reason for the correct option.

The problem is given by the image at the end of the answer.

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Answer:

proportional!!!!!!

Step-by-step explanation:

The linear function is y = -3x -5 with f(3)=-4 and f(1)=2.

The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields. The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. Any function with the formula f(x) = mx + b—where m and b are constants—is said to be linear. Because the graphs of these functions are lines in the plane, we refer to them as linear.

Given Data

f(3) = -4

f(1) = 2

The ordered pairs are (3,-4) and (1,2)

The equation of the line :

y - y₁ = [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex](x - x₁)

y + 4 = [tex]\frac{2+4}{1-3}[/tex] (x-3)

y + 4 = -3(x -3)

y + 4 = -3x + 9

3x + y = -5

y = -3x -5

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Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Solve the problem?

Given that a card is selected from a 52-card deck that has been thoroughly shuffled without being replaced, the following card is drawn.

A: The top card is a 4, and B: The next card is an ace.

Probability =A∩B

After this first card is pulled, if 10is drawn, we have 51 cards left with 4 aces in them. This is the probability we need to discover for

P(A). =  10/52  

P(B) = number of aces in 51 cards divided by 51, thus = 4/51

Hence A∩B =10/52×10/51

=   100/2652

(From this, we can see that, after changing the card count, A and B are independent.

Additionally, we multiply the probability for both.)

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Answer:

First, find x.

(12x + 20) + (6x + 70) = 180 (sum of angles on straight line = 180°)

18x + 90 = 180

18x = 90

x = 5

Next, find z.

z = 12x + 20 (vertically opposite angles)

Substitute x = 5 into equation.

z = 12(5) + 20

= 80

8.27 is the normally distributed value of the shelf life which falls under 16% of the battery shelf life.

Because the shelf life of a battery manufactured by one big business is known to be regularly distributed, we would use the normal distribution formula, which is stated as

z = (x - µ) ÷ σ

Where

x = shelf life of a battery in years.

µ = mean shell life

σ = standard deviation

Based on the facts provided,

µ = 8 years

σ = 0.3 years

The z score corresponds to a p-value of 16% in the normal distribution table,

(16 ÷ 100 = 0.16) is - 0.9.

Therefore,

- 0.9 = (x - 9) ÷ 0.3

0.3 × (- 0.9) = x - 8

0.27 = x - 8

x = 0.27 + 8

x = 8.27

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Answer:  [tex]132000 \le f(t) \le 264000[/tex]

Explanation:

The domain is [tex]3 \le t \le 6[/tex] to represent the time values between 3 and 6 hours, including the endpoints. This represents the set of possible inputs to the function.

The function f(t) = 44000t is an increasing function. This means the smallest range value corresponds to the smallest domain value.

Plug in t = 3 to find that:

f(t) = 44000t

f(3) = 44000*3

f(3) = 132000

This says he mows 132,000 sq ft of lawn in 3 hours.

Now plug in the largest domain value to find the largest range value

f(t) = 44000t

f(6) = 44000*6

f(6) = 264000

He mows 264,000 sq ft of lawn in 6 hours.

The range is the set of f(t) values between 132,000 and 264,000

We can write that as [tex]132000 \le f(t) \le 264000[/tex]

Answer: The daily cost of production in a factory is calculated using

c(x) = 200 +16 x, where x is the number of complete products manufactured.

Complete products manufactured will can not be a decimal or fraction number.

The domain of function c(x) will be the set of  values x can take.x will be a set of whole numbers. Whole numbers are positive numbers, including zero, without any decimal or fractional parts.

Option D) whole numbers is the right answer.

(4) f(1) = 3, f(n+1)=3f(n) - 2

Step-by-step explanation: I hope this helps.

Answer:

See attached worksheet

Step-by-step explanation:

Answer:

The value of x is 65 degrees.

Explanation:

To solve for x, we use the formula for an angle formed by a tangent and a secant.

Next, solve the equation for x:

The value of x is 65 degrees.

In a performance there will be 5 songs and 3 dances

Total objects 5+3 = 8

Number of ways of arranging this objects is 8! = 40,320...........(1)

If all the dances must be next to each other than all dances should take as an object as 3!

Number of ways of arranging performing taking dance to each other

is = (5+1)! 3!

    = 6! 3!

    = 4320 ....................(2)

Number of ways to arrange the shows if all dances can not be next to each other = (1) - (2)

         = 40320-4320

         = 3600 ways

Number of ways to arrange the shows if all the dances must be next to each other is 4320 ways.

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