Find the length x of QR

Answer:

Step-by-step explanation:

You want the slope, y-intercept, and equation for a line that passes through the points (2, -2) and (8, 1).

The slope formula is used to find the slope:

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-2))/(8 -2) = 3/6 = 1/2

The slope-intercept equation can be rearranged to give the y-intercept:

  b = y - mx

  b = 1 -(1/2)(8) = 1 -4 = -3 . . . . . . using (x, y) = (8, 1)

The slope-intercept form equation is ...

  y = mx +b . . . . . . where m is the slope, and b is the y-intercept

Using the found values, the equation is ...

  y = 1/2x -3

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

for such more question on volume

https://brainly.com/question/6204273

#SPJ8

Answer:

HELLO?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability Mrs. Walker will pick all 32 of the first round games correctly is given by:

0.56^32 = 1.56789e-10

To find the probability that Mrs. Walker will pick exactly 8 games correctly in the first round, we can use the binomial formula:

P(x=8) = 32 choose 8 * 0.56^8 * (1-0.56)^(32-8)

Where 32 choose 8 is the number of ways to choose 8 games out of 32.

To find the probability that Mrs. Walker will pick exactly 28 games incorrectly in the first round, we can use the same formula as in 2:

P(x=4) = 32 choose 4 * 0.56^4 * (1-0.56)^(32-4)

Given

To find

Let the purchase value be P,

ATQ,

P -3 x 0.1P = Rs 43,740

P-0.3P = Rs 43,740

0.7P = Rs 43,740

P = Rs 43,740/0.7

P = Rs 62,486 (approx)

Hence, the purchase value of the machine would be Rs 62,486

Answer:

0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

North Catalina:

Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:

\(\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188\)

Chapel Mountain:

Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:

\(\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735\)

What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?

We want that: \(N - C > 5\)

Distribution N - C:

The mean is:

\(\mu = \mu_N - \mu_C = 130 - 120 = 10\)

The standard deviation is:

\(s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937\)

This probability is 1 subtracted by the pvalue of Z when X = 5. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{5 - 10}{7.3937}\)

\(Z = -0.68\)

\(Z = -0.68\) has a pvalue of 0.2483

1 - 0.2483 = 0.7517

0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students

Answer:

28.274

Step-by-step explanation:

Use the circle formula

A=pi(r)^2

Radius is 3

A=pi(3)^2=28.274

Hope this helps : )

Solution:

The leaf and the stem for the data provided is as below :

Leaf (American)                        Stem                                Leaf (French)

                                                   8              1  

0 0 0 1 1  2 3 4 5 5 5 7               9              0 0 2 3 4 5 6 6

                         9 4 3 2              10             2 3 5 6

                         6 6 3 0              11              1 3 6 9

                             8 5 0             12             2 2 3 5 5 8

                                   8              13             7

                                                    14

                                                    15             8

                                    2              16

Some of the important features of the leaf and the stem plot are as :

1. Most of the American and the French movies have have a time range of 90 - 99 minutes most likely.

2. American movies are unimodal strongly positively skewed, while French movies are bimodal.

3. The median of the American movies is 102 minutes and that of French movies is 106 minutes.

Answer:

24 games.

Step-by-step explanation:

( 3 / 4 ) x = 18

3 x / 4 = 18

3 x = 4 * 18 = 72

x = 72 / 3 = 24

Answer: try well the answer will be 200

Answer:

8¹⁵

Step-by-step explanation:

When multiplying powers with the Same Base,

1. Keep the Base

2. Add the exponents

P(same number on both) = 10/60 = 1/6 and P(odd, even) or P(even, odd)  = 1/4

There are 10 possible outcomes on the 10-sided die and 6 possible outcomes on the 6-sided die

The total number of possible outcomes is 10 x 6 = 60.  

To get the same number on both, we need to get one of the 10 numbers on the first toss and then get the same number on the second toss. There are 10 ways to do this. Therefore, the probability of getting the same number on both is:

P(same number on both) = 10/60 = 1/6

b. To get an odd and an even number, we need to get an odd number on the first toss and an even number on the second toss, or vice versa.

There are 5 odd numbers and 5 even numbers on the 10-sided solid, and 3 even numbers and 3 odd numbers on the 6-sided solid.

Therefore, the probability of getting an odd and an even number, or an even and an odd number, is:

P(odd, even) or P(even, odd) = (5/10) x (3/6) + (5/10) x (3/6) = 1/4

Learn more about probabilities at:https://brainly.com/question/13604758

#SPJ1

If one can make 48 donuts in 2 hours then the number of donuts made in 8 hours is 192 donuts.

The unitary method is the technique used to solve the given question. In this method, we calculate the number of a unit by division. Then the given amount is calculated by multiplying by the given number.

Given in the question,

Number of donuts made in 2 hours = 48

The number of donuts made in 1 hour is calculated by dividing the above number by 2

Thus, the number of donuts made in 1 hour = 48 ÷ 2

= 24

To calculate the number of donuts made in 8 hours we have to multiply 24 by 8

Hence, the number of donuts made in 8 hours = 24 * 8

= 192

Learn more about the Unitary method:

https://brainly.com/question/24587372

#SPJ1

Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.

Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.

On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.

Learn more about workers in: https://brainly.com/question/30203906

#SPJ1

Answer: no

Step-by-step explanation:

117% equals 1.17 and 50/33 equals 1.51 repeating so they aren’t equal.

The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

for more search question distance

https://brainly.com/question/30395212

#SPJ8

Step-by-step explanation:

Area=Length ×Width

so take 625×235=

which is..

146875 square cm

Answer:

C. 8√3

Step-by-step explanation:

* = multiply or times

To find √192 in its simplest form we need to divide it by a square number like 64.

192/64 = 3

√192 = √64 * √3 = 8√3

Answer:

~ 7 years

Step-by-step explanation:

2 = (1 + .1/4)^(4t)

2 = (1.025)^(4t)

Take the log of both sides

log2 = 4t * log1.025

divide both sides by log1.025

log2/log1.025 = 4t

28.07103452593863 = 4t

Divide both sides by 4

7.017758631484657 = t

~ 7 years

Answer:

a line has arrow on both sides indicating that it goes forever in both directions.

Let A(t) denote the amount of salt (in kg) in the tank at time t.

At the start, there are 80 kg of salt in the tank, so A(0) = 80.

Solution flows into the tank at a rate of 8 L/min at a concentration of 0.04 kg/L, so that salt flows in at a rate of

(8 L/min) * (0.04 kg/L) = 0.32 kg/min

Solution flows out at the same rate, but its concentration depends on the amount of salt in the tank. The concentration of the solution is the proportion of salt in the liquid to the total volume of the liquid. Solution flows in and out at 8 L/min, so the volume of liquid (1000 L) stays the same. A(t) is the amount of salt in the tank, so the concentration is A(t)/1000 kg/L. Hence salt flows out at a rate of

(8 L/min) * (A(t)/1000 kg/L) = 0.008 A(t) kg/min

The net rate at which salt flows through the system is then given by the differential equation,

dA(t)/dt = 0.32 - 0.008 A(t)

(Don't forget to include the initial condition)

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

Learn more about the angle bisector of an equilateral triangle here:

https://brainly.com/question/30341397

#SPJ1

Answer:

71 %

Step-by-step explanation:

250/350 = 0.714285    

71.4285   move decimal 2 places to the right

71 %  rounded to whole percent

Answer:

good luck

.............

Answer: the third one. filled circle for 4 ,5,6,7,8,9, open circle 10

Step-by-step explanation:

Answer:

  117

Step-by-step explanation:

You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).

The cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.

  u×v = (12)(11) -(-3)(-5) = 132 -15

  u×v = 117

<95141404393>

Answer:

1. (a)  [-1, ∞)

   (b)  (-∞, -1) ∪ (1, ∞)

2. (a)  (1, 3)

    (b)  (-∞, 1) ∪ (3, ∞)

3. (a)  9.6 m and 0.4 m

   (b)  03:08 and 15:42

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Part (a)

When x < 0, the function is f(x) = x².

Since the square of any non-zero real number is always positive, the range of the function f(x) for x < 0 is (0, ∞).

When x ≥ 0, the function is f(x) = sin(x).

The minimum value of the sine function is -1 and the maximum value of the sine function is 1.  As the sine function is periodic, the function oscillates between these values.  Therefore, the range of function f(x) for x ≥ 0 is [-1, 1].

The range of function f(x) is the union of the ranges of the two separate parts of the function.  Therefore, the range of f(x) is [-1, ∞).

Part (b)

The domain of the function g(x) = ln(x² - 1) is the set of all real numbers x for which (x² - 1) is positive, since the natural logarithm function (ln) is only defined for positive input values.

Find the values of x:

\(\implies x^2-1 > 0\)

\(\implies x^2 > 1\)

\(\implies x < -1, \;\;x > 1\)

Therefore, the domain of function g(x) is (-∞, -1) ∪ (1, ∞).

Part (a)

To determine the interval where f(x) < 0, we need to find the values of x for which the quadratic is less than zero.

First, set the function equal to zero and solve for x:

\(\begin{aligned} x^2-4x+3&=0\\x^2-3x-x+3&=0\\x(x-3)-1(x-3)&=0\\(x-1)(x-3)&=0\\ \implies x&=1,\;3\end{aligned}\)

Therefore, the function is equal to zero at x = 1 and x = 3 and so the parabola crosses the x-axis at x = 1 and x = 3.

As the leading coefficient of the quadratic is positive, the parabola opens upwards. Therefore, the values of x that make the function negative are between the zeros.  So the interval where f(x) < 0 is 1 < x < 3 = (1, 3).

Part (b)
Since the square root of a negative number cannot be taken, and dividing a number by zero is undefined, function f(x) has to be positive and not equal to zero:  f(x) > 0.

As the parabola opens upwards, the values of x that make the function positive are less than the zero at x = 1 and more than the zero at x = 3.

Therefore the domain of g(x) is (-∞, 1) ∪ (3, ∞).

Part (a)

The range of a sine function is [-1, 1]. Therefore, to calculate the maximal and minimal possible water depths of the bay, substitute the maximum and minimum values of sin(t/2) into the equation:

\(\textsf{Maximum}: \quad 5+4.6(1)=9.6\; \sf m\)

\(\textsf{Maximum}: \quad 5+4.6(-1)=0.4\; \sf m\)

Part (b)

To find the times when the depth is maximal, set sin(t/2) to 1 and solve for t:

\(\implies \sin \left(\dfrac{t}{2}\right)=1\)

\(\implies \dfrac{t}{2}=\dfrac{\pi}{2}+2\pi n\)

\(\implies t=\pi+4\pi n\)

Therefore, the values of t in the interval 0 ≤ t ≤ 24 are:

Convert these values to times:

If a 4-yard dumpster cost $95.00 monthly, the total cost for the year is $1,140.

The total cost for the year of the dumpster is the product of the multiplication of the monthly cost and 12.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

In any multiplication, there must be the multiplicand (the number being multiplied), the multiplier (the number multiplying the multiplicand), and the product (or the result).

The monthly cost of the 4-yard dumpster = $95.00

1 year = 12 months

The total annual cost = $1,140 ($95 x 12)

Thus, using the multiplication operation, we can find that none of the options is correct as the total annual cost but $1,140.

Learn more about mathematical operations at https://brainly.com/question/20628271.

#SPJ1

Answer:

x = [12]

Step-by-step explanation:

=> \( \frac{x}{6} = \frac{6}{3} \)

=> x = 2 × 6

=> x = 12

Answer: magnitude of an earthquake with an energy release of 7.079 X 10^26 =8

Step-by-step explanation:

Given that the magnitude M of an earthquake can be expressed by the equation

M=(2/3)log E - 9.9

Given that Energy release , E=7.079 X 10^26

Magnotude , M=(2/3)log E - 9.9

=2/3 log7.079 X 10^26 -9.9

2/3 x 2.8499719  -9.9

17.8999813 -9.9

=7.9999

rounded to 8 magnitude

Given:

There are given the expression:

Explanation:

To find the simplified expression, we need to multiply the above-given expression.

So,

From the expression:

Then,

Then,

Final answer:

Hence, the correct option is C.

Answer:

20.6 cm (im pretty sure lol)

Step-by-step explanation:

sine rule:

(ab = x)

13.5/sin41 = x/sin90

13.5sin90/sin41 = x

x = 20.57741667

ab = 20.6cm