3. The number of goals by Jaromir Jagar in each of his 19 NHL seasons is recorded below 27,32,34,32,32,62,47,35,44,42,52,31,36,31,54,30,25,19,16 a) Construct a steam-and-leaf plot to display the data.[2] b) Determine the percent of seasons where greater than 35 goals were scored.[2]

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

9514 1404 393

Answer:

  CB = √6 cm

Step-by-step explanation:

The diagonal of a square is √2 times the edge length, so the length AB will be (1/2)√2(2 cm) = √2 cm.

Then the length CB is given by the Pythagorean theorem as ...

  CB = √(AC^2 +AB^2) = √((2 cm)^2 + (√2 cm)^2) = √(4 +2) cm

  CB = √6 cm

Answer:

10/4

Step-by-step explanation:

Answer:

0 is your y intercept and 5 is the x intercept

Answer: -46 15/100

Explanation: (see pic attached)

Answer:

46 3/20

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

46.15=46.15/1

Multiply to remove 2 decimal places. Here, you multiply top and bottom by 10^2 = 100

46.15/1 x 100/100= 4615/100

Find the Greatest Common Factor (GCF) of 4615 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 5

4615/100 divided by 5/5= 923/20

Simplify the improper fraction

46 3/20

In conclusion

46.15= 46 3/20

I hope that helped ;)

X is an algebraic variable which has no defined value. X is kind of universe variable taken in most of the equations.

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

Solution:

Given: - 5x - 15 > 10 + 20x

Let us solve the inequality by isolating the variable x.

Add 5x on both sides

- 5x - 15 + 5x > 10 + 20x + 5x

- 15 > 10 + 25x

Subtract 10 from both sides

- 15 - 10 > 10 - 10 + 25x

- 25 > 25x

Divide both sides by - 25

-1 > x

x < - 1

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

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Answer:

-2

Step-by-step explanation:

i did it

Answer: number 4 is +(positive) because the exponent is even.

Number 5 is -(negative) because the exponent is odd.

Step-by-step explanation:

7) Solution:

→ (2)³

→ 2 × 2 × 2 {Expanded form}

→ +8

Ans: Positive

4) Solution:

→ (-6)⁴

→ -6 × -6 × -6 × -6

→ +1296

Ans: Positive

5) Solution:

→ (-3)⁷

→ -3 × -3 × -3 × -3 × -3 × -3 × -3

→ -2187

Ans: Negative

Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?

Step-by-step explanation:

EDGE2021

The information provided is insufficient to calculate the probability without knowing the specific probability distribution of molecule speeds.

In order to calculate the probability of finding a molecule with a specific speed range, we need to know the probability distribution of molecule speeds. The given expression ml(2kt) = 5.62 x s2/m2 relates the mass (m) and the speed (s) of the molecules, but it does not specify the distribution. Different distributions can have different shapes and characteristics, and they affect how probabilities are calculated.

To proceed, we need information about the specific probability distribution that governs the molecule speeds. For example, the distribution could be Gaussian (normal), exponential, or another specific distribution. Additionally, we would need any parameters or assumptions associated with that distribution, such as the mean and standard deviation.

Once we have the necessary information about the distribution, we can use it to calculate the probability of finding a molecule with a z-component speed between 400 and 401 m/s. Without the specific distribution or additional details, we cannot proceed with the calculation.

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Answer:

2x²+2x

Step-by-step explanation:

you have f(x)= x+1 and g(x)= 2x

you must multiply the 2 polynomials

(1x·2x) +( 1·2x)

1·2=2  x^1·x^1=x²

2x²

1·2x=2x

The interest she earn in 7years is £287

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

The total amount to earn after a specified time if compound interest is :

A = P( 1+r/100)^t

where P is the principal, r is the rate and t is the time

A= 700( 1+ 5/100)⁷

A = 700( 1+0.05)⁷

A = 700(1.05)⁷

A= 700× 1.41

A = £ 987

interest =Amount - Principal

I = 987-700

I = £287

Therefore the interest she will earn in 7years is £287

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If the shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches then, the perimeter of the shape is 91.4 inches.

To find the perimeter of the shape, we need to know the length of the curved boundary (the circumference of the half-circle) and the length of the straight boundary (the perimeter of the equilateral triangle).

The radius of the half-circle is half the length of the side of the equilateral triangle, which is 10 inches. Therefore, the circumference of the half-circle is:

C = πr = π(10) = 31.4 inches.

The perimeter of the equilateral triangle is 3 times the length of one side, which is 20 inches. Therefore, the perimeter of the triangle is:

P = 3s = 3(20) = 60 inches

Finally, the perimeter of the entire shape is the sum of the lengths of the curved and straight boundaries:

Perimeter = C + P = 31.4 + 60 = 91.4 inches.

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Complete Question

This shape is made up of one half-circle attached to a square with side lengths 11 inches. Find the perimeter of the shape.

You can use 3.14 as an approximation for π. help i don't know it.

Answer:

x°=113°

y°=67°

z°=49°

Step-by-step explanation:

Looking at the right triangle exclusively, we know that it must have 180° in total.

Set up an equation that represents this:

28°+39°+x°=180°

Simplify:

67°+x°=180°

Solve:

x°=113°

Now, we also know that x°+y°=180°, because they form a line. Now that we know the value of x°, plug it in to this equation:

113°+y°=180

Solve:

y°=67°

Finally, apply the same logic with the first triangle with the other triangle:

64°+67°+z°=180°

Simplify:

131°+z°=180°

Solve:

z°=49°

Answer:

Step-by-step explanation:

Area = length x width Area = 12 feet x 14 feet Area = 168 square feet So the area of Jacinda's bedroom is 168 square feet.

Answer:

168 ft²

Step-by-step explanation:

area of rectangle = length × width

A = LW

A = 12 ft × 14 ft

A = 168 ft²

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer:

12 feet.

Step-by-step explanation:

1 inch = 4 feet.

Multiply 3 by 4.

3×4=12

I multiplied 3 by 4 because 1-inch equals 4 feet, which means if we multiply both terms by 3, you will get 3 inch = 12 feet.

Hope this helps!

Answer:

               Yes, it is.

Step-by-step explanation:

For each x we get y, and no two xes give the same y

On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = \(-1 < y < 1\)

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The Range of the given function, f(x) = sin(x)

\(-1 < y < 1\)

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In this simplex tableau, x₄, x₅, and z are the basic variables, while x₁, x₂, x₃, x₆, x₇, and x₈ are the nonbasic variables. The values of all the variables associated with this basic feasible solution are x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, and z = 620.

In this tableau, the basic variables are x₄, x₅, and z, while the nonbasic variables are x₁, x₂, x₃, x₆, x₇, and x₈.

The basic variable associated with row 1 is x₄, the basic variable associated with row 2 is x₅, and the basic variable associated with row 3 is z.

The values of all the variables associated with this basic feasible solution are:

x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, z = 620.

Note that these values correspond to the entries in the tableau in the "BV" column.

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The missing tableau is in the image attached below

Answer:

QUESTION:

You start at (1,-5). You move left 5 units. Where do you end?​

ANSWER:

You end at (-4,-5)

Step-by-step explanation:

Hope that this helps you out! :)        

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The functions have been arranged in ascending order from the least to the highest value below

This is used in mathematics as well as other disciplines to explain the order by which values are arranged. This arrangement is usually done in such a way that the smallest value would come first and continue to climb till we get to the value that is the highest.

The values here have been arranged in this order in such a way that the smallest values came first while the bigger values are at the end.

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The equation that shows the amount of water in gallons remaining in the water tank in terms of time t is A = 50 - t/2.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

As per the given,

Amount of water initially = 50 gallons

Leakage of water in 2 hours = 1 gallon.

Leakage in t hour = t/2 gallons.

Thus,

Amount = 50 - t/2

A = 50 - t/2

Hence "The equation that shows the amount of water in gallons remaining in the water tank in terms of time t is A = 50 - t/2".

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The students who audition will be in the play is 40%

percentage, a relative value indicating hundredth parts of any quantity.

Given that Students are auditioning for a school play

Only 18 of the 45 students auditioning will get a part in the play.

We need to find the percent of the students who audition will be in the play.

45x=18

Divide both sides bby 45

x=18/45

x=0.4

Now multiply with 100 as it is hundredth part

0.4×100=40%

Hence, the students who audition will be in the play is 40%

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Answer:

A)

this is a corect answer for this question:)

The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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If the patient must receive 0.190 millicuries of Na-24 per kilogram of body weight, 10.4928 millicuries of Na-24 should be given to a patient who weighs 55.2 kilograms.

To calculate the number of millicuries that should be given to a patient, you have to multiply the dose per kilogram of body weight by the patient's body weight in kilograms.  

Here is the formula:

Millicuries to be given = dose per kilogram of body weight × body weight in kilograms

So, if the patient must receive 0.190 millicuries of Na-24 per kilogram of body weight, 10.4928 millicuries should be given to a patient who weighs 55.2 kilograms.

That is,0.190 millicuries /kg × 55.2 kg = 10.4928 millicuries

Therefore, 10.4928 millicuries of Na-24 should be given to a patient who weighs 55.2 kilograms.

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Answer:

If a table of values shows a constant rate of change, it is linear. ANSWER: Sample answer: A non-vertical graph that is a straight line is linear. An equation that can be written in the form y = mx + b is linear. If a table of values shows a constant rate of change, it is linear

The point between the hour and miniature hands is 52.5 degrees. 

To illuminate this issue, we need to begin with figure out the positions of the hour and miniature hands.

At any given time, the miniature hand will point to the number of minutes past the hour times 6 (since there are 60 mins in an hour and 360 ranges in a circle, every miniature speaks to six ranges).

Additionally, the hour hand will point to the number of hours past midnight times 30 (since there are 12 hours on a clock and 360 degrees in a circle, each hour represents 30 degrees).

Let's expect that it could be a standard 12-hour clock and the time is given in hours and minutes. We'll call the current hour "h" and the current miniature "m". At that point:

Position of the miniature hand = 6m degrees

Position of the hour hand = 30h + 0.5m degrees

Presently ready to calculate the point between the hands by taking the absolute contrast between their positions and subtracting it from 360 degrees (since the hands are on the same side of the clock, we have to discover the littler point between them).

So the equation for the angle between the hands is:

| 0.5(60h - 11m) | degrees

Stopping within the values given within the issue, we get:

| 0.5(60h - 11m) | = | 0.5(603 - 1115) | = | 0.5(-105) | = 52.5 degrees

Subsequently, the point between the hour and miniature hands is 52.5 degrees. 

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f(x) = 30•2^x

Then answer is

Initially there are 30 beettles

What is happening to beetle population?

Is doubling, every week.