please write the question number and then answer the question plzz

The statement for the congruency of the triangles and the corresponding sides are as follows:

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .

In other words, triangles that have exactly the same size and shape are called congruent triangles.

Let's write a congruency statement for the triangles and identify the pair of congruent corresponding side.

Therefore,

ΔPQR ≅ ΔCBA

Hence,

∠Q = ∠B

∠R = ∠A

∠P = ∠C

PQ = BC

QR = AB

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Hello!

\(\large\boxed{4 : 3 \text{ and } 16 : 12}\)

We can go through each answer to verify whether each is equivalent to 8 : 6.

4 : 3 is equivalent to 8 : 6 because reducing the ratio 8 : 6  by a factor of 2 yields 4 : 3.

6 : 8 is not equivalent to 8 : 6 because the ratio is reversed.

16 : 12 is equivalent to 8 : 6 because the ratio is increased by a factor of 2.

10 : 8 is not equivalent to 8 : 6. We can verify this by checking whether each term was scaled equally:

10 ÷ 8 = 1.25

8 ÷ 6 = 1.33. Therefore, they are unequal.

7 : 5 is not equal to 8 : 6 for the same reason.

The only correct choices are:

4 : 3 and 16 : 12.

Answer:

9.33π

Step-by-step explanation:

the formula to solve for the volume of a cone is V=πr^2 * h/3

r = radius of base (2mi)

h = height (7mi)

plug in the numbers

V=π2^2 * 7/3

V=π4*2.33333333

V=9.33π

Both statements are true. When events A and B are mutually exclusive, meaning they cannot occur simultaneously, you can use the special rule of addition.

If events A and B are not mutually exclusive, meaning they can occur together, you should use the general rule of addition. The specific rule of addition can only be used when dealing with mutually exclusive events, while the general rule of addition can be used for any two events, whether they are mutually exclusive or not. The specific rule of addition states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities, while the general rule of addition states that the probability of event A or event B occurring is equal to the sum of their individual probabilities minus the probability of their intersection (if they are not mutually exclusive).

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The dimensions of the rectangle whose length and width must have a sum of 70 are 35 cm and 35 cm respectively.

A rcetangle is a plane shape that has pair of opposite side equal and parallel.

To calculate the dimension of rectangle that will have the maximum area, we find the first derivation of the  function representing the area of the rectangle, and then equate it to zero.

At the maximum area,

Therefore,

Solve for x

The dimensions of the rectangle are

Hence, the dimensions of the rectangle are 35 cm and 35 cm respectively.

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Using it's concept, it is found that the probability that the first student chosen is a senior and the second student chosen is a sophomore is given by:

\(p = \frac{11}{320}\)

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, we have that there are:

31 juniors, 10 sophomores, 17 juniors, 22 seniors.

Then:

The events are independent, hence the probability of both is given by:

\(p = p_1p_2 = \frac{11}{40} \times \frac{1}{8} = \frac{11}{320}\)

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Explanation:-

Total number of families are surveyed = 1500

Total number of possible outcomes = 1500

Number of part time maids = 860

Number of favourable outcomes to part time maids = 860

Number of only full time maids = 370

Number of favourable outcomes to only full time maids = 370

Number of both type of maids = 250

Number of favourable outcomes to both type of maids = 250

From all families selecting a family randomly is an event then

We know that

Probability of an event =

Number of favourable outcomes/Total number of possible outcomes

1⟩ Probability of getting both type of maids

⇛250/1500

⇛25/150

⇛1/6

Probability of a family has both type of maids= 1/6.

2⟩ Probability of getting Part time maids

= 860/1500

⇛86/150

⇛43/125

Probability of getting Part time maids = 43/125.

3⟩. Number of part time maids =n(P only )=860

Number of only full time maids =n(F only) = 370

Number of both type of maids = n(PnF)= 250

Total number of families are surveyed= n(PUF)

= 1500

number of no maids =

n(PUF)= n(only P)+n(only F)+n(PnF)

= 1500-(860+370+250)

⇛1500-(1480)

⇛20

Number of no maids = 20

Probability of getting no maid = 20/1500

⇛2/150

⇛1/125

Probability of getting no maid = 1/125.

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The wage of 2001 in terms of wage in 2012 is option A $14.97

Given,

Mack's wages in 2001 = $7 per hour

Mack's wages in 2012 = $12 per hour

The CPI in 2001 = 94

The CPI in 2012 = 201

We have to fins the wage of 2001 in terms of wage in 2012;

CPI;- Consumer Price Index

The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.

Here,

The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year

= (201 / 94) x 7

= 14.97

That is,

The wage of 2001 in terms of wage in 2012 is option A $14.97

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We have the iterated integral:

∫

�

=

0

2

∫

�

=

1

5

5

(

�

+

�

)

(

2

−

�

2

)

�

�

�

�

∫

y=0

2

​

∫

x=1

5

​

5(x+y)(2−y

2

)dxdy

To convert this to polar coordinates, we need to express $x$ and $y$ in terms of $r$ and $\theta$. Since the region of integration is defined by $0 \leq y \leq 2$ and $1 \leq x \leq 5$, we see that $1 \leq r \leq 5$ and $0 \leq \theta \leq \pi$. Then we have:

�

=

�

cos

⁡

�

and

�

=

�

sin

⁡

�

x=rcosθandy=rsinθ

The Jacobian of the transformation is $\frac{\partial(x,y)}{\partial(r,\theta)} = r$, so we have:

\begin{align*}

\int_{y=0}^{2} \int_{x=1}^{5} 5(x+y)(2-y^2) ,dx,dy &= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5(r\cos \theta + r\sin \theta)(2 - r^2\sin^2 \theta) ,r,dr,d\theta \

&= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\cos \theta ,dr,d\theta + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\sin \theta \cos \theta ,dr,d\theta \

&\quad + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^3\sin \theta ,dr,d\theta - \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^5\sin^3 \theta ,dr,d\theta \

&= \int_{\theta=0}^{\pi} \left[ \frac{10}{3}r^3\cos \theta \right]{r=1}^{r=5} ,d\theta + \int{\theta=0}^{\pi} \left[ \frac{5}{2}r^3\sin^2 \theta \right]{r=1}^{r=5} ,d\theta \

&\quad + \int{\theta=0}^{\pi} \left[ \frac{5}{4}r^4\sin \theta \right]{r=1}^{r=5} ,d\theta - \int{\theta=0}^{\pi} \left[ \frac{5}{6}r^6\sin^4 \theta \right]{r=1}^{r=5} ,d\theta \

&= \int{\theta=0}^{\pi} \frac{1240}{3}\cos \theta + \frac{60}{2}\sin^2 \theta + \frac{155}{4}\sin \theta - \frac{2480}{6}\sin^4 \theta ,d\theta \

&= \left[ \frac{1240}{3}\sin \theta - \frac{60}{2}\frac

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Answer: 2.87 hours

Step-by-step explanation:

There may be a typo in the question because 55 hours in a day is not logical so you must have meant 5.5 hours.

In that case, the hours he will require on the third day would require the distance left to calculate. Get this distance from the first 2 days.

Day 1 distance travelled = Time * Speed

= 5.5 * 66

= 363 miles

Day 2 distance travelled = Time * Speed

= 5.5 * 58

= 319 miles

Total distance remaining

:= 840 - 363 - 319

= 158 miles

Travelling at 55 miles per hour, the time to be taken is:

= Distance remaining / Speed

= 158 / 55

= 2.87 miles per hour

The experimental probability of the coin landing heads up is calculated by dividing the number of times the coin landed heads up (16) by the total number of flips (40). So the experimental probability of the coin landing heads up is:

P(heads up) = 16/40

Simplifying the fraction by dividing both the numerator and denominator by 8, we get:

P(heads up) = 2/5 or 0.4

Therefore, based on the results, the experimental probability of the coin landing heads up is 0.4 or 2/5.

To find the experimental probability of the coin landing heads up, you'll need to use the following formula:

Experimental probability = (Number of successful outcomes) / (Total number of trials)

In this case, the successful outcome is the coin landing heads up, which occurred 16 times. The total number of trials is 40 flips. So, the experimental probability would be:

Experimental probability (heads up) = (16 successful outcomes) / (40 total flips)

Now, divide 16 by 40 to get the probability:

Experimental probability (heads up) = 16/40 = 0.4 or 40%

So, based on the results, the experimental probability of the coin landing heads up is 40%.

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The Laplace transform can be used to solve the given initial-value problem, where y'' − 4y' + 4y = t, with initial conditions y(0) = 0 and y'(0) = 1.

To solve the initial-value problem using the Laplace transform, we first apply the transform to both sides of the differential equation. Taking the Laplace transform of the given equation yields:

s^2Y(s) - sy(0) - y'(0) - 4(sY(s) - y(0)) + 4Y(s) = 1/s^2,

where Y(s) represents the Laplace transform of y(t) and s represents the Laplace variable. Substituting the initial conditions y(0) = 0 and y'(0) = 1 into the equation, we have:

s^2Y(s) - 1 - 4sY(s) + 4Y(s) = 1/s^2.

Simplifying the equation, we can solve for Y(s):

Y(s) = 1/(s^2 - 4s + 4) + 1/(s^3).

Using partial fraction decomposition and inverse Laplace transform techniques, we can obtain the solution y(t) in the time domain.

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Answer:

...I think this was what you needed?...

Step-by-step explanation:

Input 10 as x,

Add everything in your parenthesis,

and then multiply by 4.

On substituting the value of x left-hand side is equal to the right-hand side.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is  4(x+3)=52. To prove put the value of x = 10,

4(x+3)=52

4 ( 10 + 3 ) = 52

4 x 13 = 52

52 = 52

Hence, the expression is true for the value of x = 10.

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The calculated summation value with the message "Summation: " preceding it. The program assumes that the user will provide valid numerical inputs (integers) when prompted.

Here's a Python program that calculates the sum using a loop based on the user's input values for `i` and `k`. The program handles cases where `i` is larger than `k` and continuously asks for proper values until valid inputs are provided.

```python

while True:

   i = int(input("Enter value for i: "))

   k = int(input("Enter value for k: "))

   if i <= k:

       break

   else:

       print("Error: i cannot be greater than k.")

summation = 0

for x in range(i, k+1):

   summation += 2 * x

print("Summation:", summation)

```

In this program, we use a `while` loop to repeatedly prompt the user for values of `i` and `k`. We convert the inputs to integers using `int()` for numerical comparison. If the condition `i <= k` is satisfied, we break out of the loop; otherwise, an error message is displayed, and the loop continues.

Once we have valid values for `i` and `k`, we initialize the `summation` variable to 0 and use a `for` loop with `range(i, k+1)` to iterate through the values of `x` from `i` to `k` (inclusive). We accumulate the sum by adding `2 * x` to `summation` in each iteration.

Finally, we print the calculated summation value with the message "Summation: " preceding it.

Note: The program assumes that the user will provide valid numerical inputs (integers) when prompted.

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The mean of a sample is computed by summing all the data values and dividing the sum by the number of items.

The mean of a sample is a measure of central tendency of a sample and represents the average value of the sample.The formula for computing the mean of a sample is as follows:μ = (x₁ + x₂ + x₃ + ... + xₙ) / nwhere μ is the mean, x₁, x₂, x₃, ..., xₙ are the data values and n is the number of items in the sample. The mean of a sample is an estimate of the mean of the population from which the sample was taken. If the sample is representative of the population, the mean of the sample will be similar to the mean of the population.

the mean of a sample is not always equal to the mean of the population, especially if the sample is not representative of the population. In addition, the mean of a sample is not always smaller than the mean of the population. Therefore, options A and B are incorrect.On the other hand, option C is incorrect as well because the formula given is for the computation of the sample variance, not the mean. The formula for the sample variance is as follows:s² = ∑(x - μ)² / (n - 1)where s² is the sample variance, x is a data value, μ is the sample mean and n is the number of items in the sample.Option D is correct because it gives the correct formula for computing the mean of a sample.

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The integration of the function ∫(1 + 2x²)\(e^{x} ^{2}\) is -

\($\frac{i\sqrt{\pi}\; erf(ix) }{2} +\) \($\frac{2i\sqrt{\pi}\;erf(ix) }{4} + \frac{xe^{x}^{2} }{2} +C\).

Integration is the process of finding the area under the graph of the function f(x), between two specific values in the domain. We can write the integration as -

I = ∫f(x) dx

Given is to integrate the function -

∫(1 + 2x²)\(e^{x} ^{2}\)

We have the function as -

I = ∫(1 + 2x²)\(e^{x} ^{2}\)

I = ∫\(e^{x} ^{2}\)  +  ∫2x²\(e^{x} ^{2}\)

I =  \($\frac{i\sqrt{\pi}\; erf(ix) }{2} +\) \($\frac{2i\sqrt{\pi}\;erf(ix) }{4} + \frac{xe^{x}^{2} }{2} +C\)

Therefore, the integration of the function ∫(1 + 2x²)\(e^{x} ^{2}\) is -

\($\frac{i\sqrt{\pi}\; erf(ix) }{2} +\) \($\frac{2i\sqrt{\pi}\;erf(ix) }{4} + \frac{xe^{x}^{2} }{2} +C\).

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Answer:

Step-by-step explanation:

2.8 × (-11) - 3 × 8 =

-30.8 - 24 =

-54.8 ( in fraction -274/5)

Answer:

n/2 - 6 + 10

8/2 - 6 + 10

4 - 6 + 10

= 8

Step-by-step explanation:

Answer:

It's B

Step-by-step explanation:

I just took the test, sorry if I didn't come on time.

In mathematics, every integer is a rational number, hence a whole number 8 can be written as 8/1. 1/3 x 8 = 8/3 in fraction form. 1/3 x 8 = 2.6667 in decimal form.

The simplest form is given as 3/8.

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.

The number a is called as the numerator and b is the denominator.

Two fractions can be multiplied by taking the product of their numerators and denominators respectively.

The given expression is 1/3 x 8.

It can be simplified as follows,

1/3 x 8

Write 8 in the fraction form as 8 = 8/1

= 1/3  x 8/1`

Multiply the numerators and denominators to obtain,

(1 x 8)/(3 x 1)

= 8/3

The given expression can be simplified as 8/3.

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The angle of depression is the angle formed with the horizontal, when an object is viewed below the horizontal level. Thus, the height of the cliff is approximately 123.86 m.

Let the height of the cliff be represented by h, so that:

From the triangle 1, we have:

tan \(32^{o}\) = \(\frac{h}{x}\)

⇒ h = tan \(32^{o}\)*x

    h = x tan \(32^{o}\) ............. 1

Also, from the bigger triangle, we have:

tan \(24^{o}\) = \(\frac{h}{80 + x}\)

⇒ h = tan \(24^{o}\) (80 + x) .........  2

Now equating the expressions for h in equations 1 and 2, we have:

x tan \(32^{o}\) = tan \(24^{o}\) (80 + x)

0.6249x = 0.4452 (80 + x)

               = 35.616 + 0.4452x

0.6249x - 0.4452x = 35.616

0.1797 x = 35.616

x = \(\frac{35.616}{0.1797}\)

x = 198.2 m

Substitute the value of x in equation 1;

h = x tan \(32^{o}\)

  = 198.2 * 0.6249

 = 123.8552

h = 123.86 m

Therefore, the height of the cliff is approximately 123.86 m.

A sketch to this question is attached.

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a = 55°, b = 97°, c = 83°

Explanation:

Larger triangle:

a° + 44° + 28° + 53° = 180° (sum of angles in a triangle)

a + 125 = 180

a = 180 -125

a = 55°

The smaller triangle by the left:

a° + b° + 28° = 180° (sum of angles in a triangle)

55 + b + 28 = 180

83 + b = 180

b = 180 -83

b = 97°

The smaller triangle by the right:

53° + 44° + c° = 180° (sum of angles in a triangle)

97 + c = 180

c = 180 -97

c = 83°

Answer:

The Domain is X and Range is Y

Step-by-step explanation:

Top values are domain and bottom values are Range

Answer:

remove parentheses by multiplying factors.

use exponent rules to remove parentheses in terms with exponents.

combine like terms by adding coefficients.

combine the constants.

Step-by-step explanation:

Answer:

  100.9 yards

Step-by-step explanation:

One circuit of the track is a distance of ...

  C = 2πr = 2π(60 yd) = 120π yd.

At Alex's running rate, the distance covered in 20 minutes is ...

  (4 yd/s)(20 min)(60 s/min) = 4800 yd

The number of circuits will be ...

  (4800 yd)/(120π yd/circuit) = 40/π circuits ≈ 12.7324 circuits

The last of Alex's laps is more than half-completed, so the shortest distance to his starting point is 13 -12.7324 = 0.2676 circuits,

That distance is (0.2676 circuits)×(120π yd/circuit) ≈ 100.88 yd

The shortest distance along the track to Alex's starting point is about 100.9 yards.

_____

Additional comment

The exact distance is 120(13π-40) yards. The distance will vary according to your approximation for pi. If you use 3.14, this is about 98.4 yards.

Answer: The area is 6.5

Answer:

The answer is below

Step-by-step explanation:

The rocket is made up of square pyramid and a rectangular prism. Hence the volume of the rocket is the sum of the volume of the square pyramid and the volume of the rectangular prism.

Volume of square pyramid = a²h/3

a = base length = 1.1 in, h = height of pyramid = 2.1 in

Volume of square pyramid = a²h/3 = 1.1² * 2.1/3 = 0.847 in³

Volume of rectangular prism = length * breadth * height = 1.1 * 1.1 * 8.2 = 9.922 in³

Volume of rocket = volume of prism + volume of pyramid = 0.847 + 9.922 = 10.769 in³