Which of the following is not the test of congruence of two triangles ? ASA test ,
AAS test, SSA test , SAS test.

The months when both of these plans would pay off the same amout of money for the new phone is 8 months.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the number of months be x

You can pay a one-time charge of 200$ and then an additional $15 per month. This will be 200 + 15x. The second option is not paying any money at this time and having a monthly bill of 40$ a month. This will be 40x.

The equation will be

200 + 15x = 40x

Collect like terms

40x - 15x = 200

25x = 200

Divide

x = 200/25

x = 8

The number of months is 8.

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Theoretical centre-to-centre distance (C)=3.25 which is the distance between the centers of the pinion and gear

Given data:

No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

The rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.

The rotational speed of the gear(NG)=544 rev/min or 544 rpm.

To calculate:

No. of teeth on gear(TG) & theoretical centre-to-centre distance(C).

We know that;

Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP

Pittiong the values in above eq.

8 teeth/in =17/DP =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

(NP/NG)=(TG/TP)

1120/544 =TG/17 =>TG=35

therefore No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

1120/544=DG/2.125

DG=4.375 in.

In figure I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre-to-centre distance(C)

From fig.,

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

C=(DP+DG)/2 {\large \because Diameter =2*radius}

C=(2.125+4.375)/2 in. =3.25 in.

therefore Theoretical centre to centre distance (C)=3.25

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David's speed in still water 2 mile per hour , using downstream and upstream concept in river .

What is downstream and upstream in river?

Downstream : Towards the river where flow ends

In this river speed get added in rowing boat speed.

Upstream : Opposite to the flow of river

In this river speed gets subtracted from rowing boat speed.

In given que , one time boat is rowed by David in upstream and got back to original place i.e. case of downstream.

Speed of river = 1mile per hour

Let speed of David = x mile per hour.

Total time taken = 4 hour

As we know time = total distance / speed

Total distance covered by David = 3+3 = 6 miles

In upstream speed = x-1

In downstream speed = x+1

So, time = 3/(x-1 )+ 3/(x+1)

            4/3 = 1/x-1  + 1/x+1

Solving this we get,

2x^2 - 3x - 2 = 0

Solution for this eq will be

x  = 2, -1/2

But speed can't be negative.

So, x= 2mile per hour.

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Answer:

B) 4%

Step-by-step explanation:

The total is

.8 + 4 + .2 = 5

[tex]\frac{r}{t}[/tex] = [tex]\frac{.2}{5}[/tex] = 0.04 = 4%  To change a decimal to a percent multiply by 100%

A university surveys its student-athletes about their experience in college sports. The survey only includes student-athletes with scholarships. This is an example of sampling bias.

In the field of statistics, sampling bias is a type of bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of the population where all individuals, or instances, were not equally likely to have been selected. If this is not corrected, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. Here as the sample of the survey only includes the student athletes with scholarship, it becomes biased.

Therefore, sampling bias is the type of bias when a university surveys its student-athletes about their experience in college sports. the survey only includes student-athletes with scholarships.

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Answer:

Step-by-step explanation:

balls

The required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

Given that,
At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
let y be the total cost for each different item
cost of the shirt = s - 10 and pair of pants = 2p
According to the question,
y = s - 10 / 2  and y = 2p / 2

Thus, the required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

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Answer:

x = 50

Step-by-step explanation:

we have 110, so

180 - 110 = 70

sum of all angles is 180

60 + 70 + x = 180

x = 180 - 60 - 70

x = 50

The slope of the line that contains the points: (-7, 8) and (12, 8) is 0

From the question, the points are given as

(-7, 8) and (12, 8)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) =  (-7, 8) and (12, 8)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) =  (-7, 8) and (12, 8)

Substitute the known values in the above equation

So, we have the following equation

Slope = (8 - 8)/(12 + 7)

Evaluate

Slope = 0

Hence, the slope of the line is 0

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The number in between 10 and 15 and having prime factors of 2 and 3 is 12.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

The integer between 10 and 15 are,

11,12,13,14

The prime factors of 2 and 3 will be given as,

[tex]2^{a} \times 3^{b}[/tex] where a and b can be positive.

Since, 12 = 2² × 3¹

Thus, 12 is the only number that is the prime factor of 2 and 3 both.

Hence "The number between 10 and 15 and having prime factors of 2 and 3 is 12".

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Answer:

the answer is B

Step-by-step explanation:

Answer:

$125

Step-by-step explanation:

600 - 475 = 125

Answer:

600-475

275

Step-by-step explanation:

The amount borrowed is subtracted from the amount paid back gives the remaining debt.

Therefore the amount to be paid back is 275

Answer:

t ≈ 7.7

Step-by-step explanation:

                   r         ^nt

A = P ( 1 + ------- )

                  n

A = 3000

P = 1500

n = 12

r = 0.09

t = ?

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

                               12

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

÷1500  ÷1500         12

              0.09        

2 =  ( 1 + ------- ) ^(12)(t)

               12

Change into logs and divide

  log 2

----------------------    =   12t

              0.09

log (1 + ----------)

               12

multiply both sides by (1/12)

                 log 2

(1/12) ----------------------    =   12t (1/12)

                    0.09

      log (1 + ----------)

                     12

7.7304805 = t

7.7 ≈ t

I hope this helps!

The sample mean is 5.0833 and the standard deviation is 3.476 and the confidence interval is (2.87, 7.29).

In the given question, a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period).

Using these data to create a 95% confidence interval for the population mean days absent for sickness

2   5   3   7   10   0   6   8   5   11   3   1

a) We have to find the sample mean and the standard deviation (round to two decimal places).

The sample mean;

X = 2+5+3+7+10+0+6+8+5+11+3+1/12

X = 61/12

X = 5.0833

Now the standard deviation

SD = √[{x(1)-X)^2+(x(2)-X)^2…………….(x(12)-X)^2}/N]

After solving using that formula;

SD = 3.476

b) 95% confidence in interval for the population mean days absent for sickness.

Lower Bound = X - t(α/2)*s/√n

Upper Bound = X + t(α /2)*s/√n

where

α /2 = (1 - confidence level)/2 = 0.025

X = sample mean = 5.083333333

t(α/2) = critical t for the confidence interval = 2.20098516

s = sample standard deviation = 3.476108936

n = sample size = 12

df = n - 1 = 11

Thus,

Lower bound = 2.874719086

Upper bound = 7.291947581

Thus, the confidence interval is (2.87, 7.29).

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The right question is:

How healthy are the employees at direct marketing industry? A random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). Use these data to create a 95% confidence interval for the population mean days absent for sickness.

2   5   3   7   10   0   6   8   5   11   3   1

a) Find the sample mean and the standard deviation (round to two decimal places)

b) 95% confidence in interval for the population mean days absent for sickness.

[tex]\displaystyle\\\\ Answer: A=\frac{2P}{xV^3}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\P=\frac{1}{2} xAV^3\\[/tex]

Multiply both parts of the equation by 2:

[tex]2P=xAV^3[/tex]

Divide both parts of the equation by xV³:

[tex]\displaystyle\\\frac{2P}{xV^3} =A[/tex]

[tex]\displaystyle\\\\Thus,\ A=\frac{2P}{xV^3}[/tex]

The value of 0.88 in the exponential function p(x) = 8500(0.88)ˣ is the rate of growth

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = aˣ

In the exponential function given;

p(x) = 8500(0.88)ˣ

Where;

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Therefore, option (c)normality assumption is checked when looking at a  Q–Q plot in one-way ANOVA model.

In statistics, a Q–Q plot is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. A point on the plot corresponds to one of the quantiles of the second distribution plotted against the same quantile of the first distribution

Here,

normality assumption is checked when looking at a Q–Q plot in one-way ANOVA model.

Explanation: The core tenet of the assumption of normality states that the sample mean distribution (across independent variables) is normal. Technically speaking, the Assumption of Normality asserts that the mean's sampling distribution or the distribution of means among samples is normal.

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The probability that the number in a sample of 127 who do so differs from the expected value is 0.6198.

How to calculate probability?

The critical value, according to the data, is 84. the following will be the mean:

= np = 127 × 2/3 = 84.6

The standard deviation is also 5.3748. The corresponding z score will be:

= (84 - 86.67)/5.3748

= -0.50.

Therefore, the left tailed area will be:

P(z < -0.50) = 0.3099

Since, it's two tailed, we'll multiply by 2. This will be:

= 2 × 0.3099

= 0.6198

In conclusion, the probability is 0.6198.

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Answer:

a₂₅ = 157

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = 6 , then

a₂₅ = 13 + (24 × 6) = 13 + 144 = 157

Yes, the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.

Average:

In math average refers mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

Here we have the data of the national health and nutrition examination survey contains data on 2,263 US. adults. one of the variables is total cholesterol. total cholesterol levels less than 200 milligrams per deciliter (mg/dl) are considered desirable for adults. a reading between 200 and 239 mg/dl is considered borderline high and a reading of 240 mg/dl and above is considered high.

And we need to find that does the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.

While we looking into the given question,

Total number pf participants = 2,263

Desirable level of cholesterol = less than 200 milligram

Border line level of cholesterol = Between 200 and 239 mg

Higher level of cholesterol = 240 mg

So, based on the given details, we know that at least 25% of people must have the desirable.

Therefore, the given level is a desirable one.

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Given √24−x when x = 6 in simple radical form is 3*√2.

Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc.

Additionally, it entails eliminating any radicals from a fraction's denominator.

The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414.

So, we have:

√24−x when x = 6
Thus we must now calculate the square root of 18.

The square root, if you're allowed to use a calculator, is 4.242.

If not, however, let's come as close as we can:

√(9 * 2)

Since 3 is the square root of 9:

3*√2

Therefore, given √24−x when x = 6 in simple radical form is 3*√2.

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The value of ∠WXY = 20.

What is Exterior angle theorem?

The exterior angle theorem describes the connection between the two remote angles in a triangle and the external angle created by an extended side outside the triangle.

Given: Measure of angle YWX = (3x + 17) °

Measure of angle WXY = (3x + 2) °

Measure of angle XYZ = (10x − 5) °

Therefore, m∠XYZ = m∠YWX + m∠WXY (exterior angle theorem)

⇒ (10x − 5) ° = (3x + 17) ° + (3x + 2) °

Solve for x,

⇒ 10x - 5 = 3x + 17 + 3x + 2

⇒ 10x - 6x = 17 + 7

⇒ 4x = 24

⇒ x = 6

∴ ∠WXY = (3x + 2) = 18 + 2 = 20

Hence, value of ∠WXY = 20.

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Answer:(29.85km/h)

Step-by-step explanation:

1000m=1km

200m=x  [x=(200m/1000m)x1km]

x=0.2km

3600second= 1 hour  

24 seconds =b   [b=(24s/3600s)x1 hour ]

b=0.0067(in 2 decimal place)

velocity in km/h will be

0.2km/0,0067secs

=29.85(in 2 decimal place)

Answer:

speed = 30 km/h

Step-by-step explanation:

We are told that a 200 metres race is run by an athlete in 24 seconds. The question then asks us to calculate the athlete's speed in km/h.

To do this, let's first convert the given data into the required units:

• Converting from metres to kilometres:
To convert from 200 metres to kilometres, we have to divide it by 1000:

200 m = 200 m ÷ 1000 m/km

           = 0.2 km

• Converting from seconds to hours:
To convert 24 seconds to hours, we have to divide it by 3600:

24 s = 24 s ÷ 3600 s/h

        = [tex]\frac{24}{3600}[/tex] h

Now that we have the data in the appropriate units, we can use the following formula to calculate speed:

[tex]\boxed{\mathrm{speed = \frac{distance}{time}}}[/tex]

⇒ speed = [tex]\mathrm{\frac{0.2 \ km}{24/3600 \ h}}[/tex]

⇒ speed = 30 km/h

Therefore, the speed of the athlete is 30 km/h.

Answer: 780

Step-by-step explanation:

Two times 2 is 4

4 + 89 = 93

93 +765 = 858

858 - 78 = 780

The transformations from the parent function are

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

g(x) = -|x + 3| - 4

The above function is an absolute value function

Next, we plot the graph using a graphing calculator

See attachment for the graph

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

f(x) = |x| --- the parent function of an absolute value function

g(x) = -|x + 3| - 4 -- the transformed function

First, we have the transformation to be:

From f(x) = |x| to f'(x) = |x + 3|

This means the function is translated left by 3 units

Next, we have:

From f'(x) = |x + 3| to f'(x) = -|x + 3|

This means the function is reflected across the x-axis

Lastly, we have:

From f'(x) = -|x + 3| to g(x) = -|x + 3| - 4

This means the function is translated down by 4 units

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Answer: A+B+C=π⇒A+B=π−C

Step-by-step explanation: I think not sure hope this helps :)

The slopes of the lines are 2/3, 5, 5/6 and 1 respectively

The slope of a line is a measure of its steepness or incline. It is defined as the ratio of the vertical change (called the "rise") to the horizontal change (called the "run") between two points on the line.

The slope of a line can be expressed using the following formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

1.  P₁(0,2) and P₂(3,4):

Slope = (4-2)/(3-0) = 2/3

2.  P₁(1,2) and P₂(3, 7):

Slope = (7-2)/(3-2) = 5/1 = 5

3. P₁(-1,1) and P₂(5,6):

Slope = (6-1) / (5-(-1)) = 5/6

4. P₁(-1,-2) and P₂(10,11)

Slope = (11-(-1)) / (10-(-2)) = 12/12 = 1

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