Q3. (Calculator)

Abox contains only red, blue and green pens.

The ratio of red pens to blue pens is 5:9.

The ratio of blue pens to green pens is 1:4.

Calculate the percentage of pens that are blue.

Answer:

a = 191/81

Step-by-step explanation:

a+ 1 1/6 = 11 7/9

1 1/6 = 7/6

11 7/9 = 106/9

So, our equation is

a + 7/6 = 106/9

Subtract 7/6 from both sides

a = 191/81

So, the answer is

a = 191/81

Answer:

8.41

Step-by-step explanation:

8.14+3.45=11,59

20-11,59=8.41

Step-by-step explanation:

A=7x+3+13x-7

B=2x+3-3x

P=x+3+2x+2-x-1(hope those are the numbers)

C=?

7x+3+13x-7+2x+3-3x+C=x+3+2x+2-x-1

22x-1+C=2x+4

C=2x+4-22x+1

C=-20x+3

Answer:

1 1/12

Step-by-step explanation:

3/4 + 1/3

Get a common denominator of 12

3/4 * 3/3 = 9/12

1/3 * 4/4 =4/12

9/12 + 4/12

13/12

12/12 + 1/12

1 1/12

Answer:

yes because When you are given an equation and a specific value for x, there should only be one corresponding y-value for that x-value. For example, y = x + 1 is a function because y will always be one greater than x. Equations with exponents can also be functions.

Step-by-step explanation:

The notation y = f(x) defines a function named f. This is read as “ y is a function of x.” The letter x represents the input value, or independent variable. The letter y, or f(x), represents the output value, or dependent variable.

The value of the iterated integral is (-π/4) (cos(64) - 1).

To evaluate the iterated integral by converting to polar coordinates, we need to use the given terms:

- The integral bounds: 0 to 8 (for x), -8 to 8 (for y)
- The integrand: sin(x² + y²)
- The conversion factor for polar coordinates: rdrdθ

First, we convert the integral bounds and integrand to polar coordinates.

In polar coordinates, x = rcos(θ) and y = rsin(θ), so:

x² + y² = r²cos²(θ) + r²sin²(θ) = r²

because sin²(θ) + cos²(θ) = 1.

Now we rewrite the integrand in polar coordinates:
sin(x² + y²) = sin(r²)

The integral bounds in polar coordinates are 0 to 8 (for r), and 0 to π/2 (for θ) as the given bounds cover the first quadrant.

Now we can write the iterated integral:
\(\int_{0} ^ {\pi/2} \int_{0} ^{ 8}  sin(r^2) r dr d\theta\)

To evaluate the inner integral with respect to r, we use substitution:
Let u = r², so du = 2r dr

Now the inner integral becomes:

\((1/2)\int_{0}^ {64} sin(u) du\) = (-1/2) [cos(64) - cos(0)] = (-1/2) (cos(64) - 1)

Now we evaluate the outer integral with respect to θ:

\(\int_{0}^ {\pi/2} ((-1/2)  (cos(64) - 1)) d\theta\) = (-1/2) (cos(64) - 1) [θ] evaluated from 0 to π/2

Finally, substitute the limits of integration:

((-1/2) (cos(64) - 1)) (π/2 - 0) = (-π/4) (cos(64) - 1)

So, the value of the iterated integral is (-π/4) (cos(64) - 1).

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Answer:

1. List (in order) the five phases a single 2 solar mass will go through in its life.

2. List (in order) the five phases a single 25 solar mass will go through in its life.

3. List (in order) the five phases a single 60 solar mass will go through in its life.

Phase options (can be used more than once, some may not be used at all):

Type II Supernova

Protostar

White Dwarf

Giant Phase

Main sequence

Neutron Star

Brown Dwarf

Black Hole

Type 1a Supernova

Planetary Nebula

Step-by-step explanation:

Answer:

1. 240 oz

2. 6000lb

3. 20 lb

4. 368 oz

5. 12000 lb

6. 9 lb

7. 30000 lb

8. 22

9. 288

Step-by-step explanation:

Answer:

1. 240

2. 6613.87

3. 20

4. 368

5. 13227.7

6. 9

7. 33069.3

8. 22

9. 288

Step-by-step explanation:

Answer:

A. x = 3

Hope this helps!! <3

Circumference = 2 x radius x Pi

Circumference = 2 x 15 x 3.14

Circumference = 30 x 3.14

Circumference = 94.2 feet

Answer:

\( \huge{ \boxed{ \sf{94.2 \: ft}}}\)

Step-by-step explanation:

\( \underline{ \sf{Given}} : \)

\( \star{ \sf{ \: Radius \: of \: a \: circle \: ( \: r \: ) \: = \: 15 \: ft}}\)

\( \star{ \sf{ \: pi \: (\pi) = 3.14}}\)

\( \boxed{ \sf{ \: Circumference \: of \: a \: circle \: = \: 2 \: \pi \: r}}\)

Plug the values and multiply them

\( \mapsto{ \sf{Circumference = \: 2 \:* \: 3.14 \: * \: 15}}\)

\( \mapsto{ \sf{Circumference \: = \: 94.2 \: ft}}\)

Hope I helped!

Best regards! :D

~\( \text{TheAnimeGirl}\)

the probability of that there will be 2 defective items among them is 0.476 or 47.6%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Calculating the possibility of an event occurring is the focus of the math discipline of probability. Probability gauges the likelihood of an event occurring.

there are 4 defective items in a lot consisting of 10 items.

from this lot we select 5 items at random.

The number of ways in which 55 items can be selected 10 C 5 = 252.

Number of ways in which 2 defective systems and 3 non-defective systems can be selected

4C2 * 6C3 = 6*20=120

The probability = 120 / 252 = 0.476

Hence the probability of that there will be 2 defective items among them is 0.476 or 47.6%.

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The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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It is true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.

A parabola is a quadratic function graph .A parabola is a curve equation in which a point on the curve is equidistant from a fixed point and a fixed line.

The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie on the fixed line.

A parabola is a locus of any point that is equidistant from a given point (focus) and a given line (directrix). The parabola is a significant curve of the coordinate geometry's conic sections.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex.

The standard equation of a regular parabola is y² = 4ax.

It's true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.

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Answer:

Yes!

Step-by-step explanation:

Yes, every diameter of a circle is also a chord because a chord of a circle is any line connecting 2 parts of the circle's circumference.

The algorithm described is the Insertion Sort Algorithm.

The given algorithm is the Insertion Sort Algorithm. It is used to sort an array of elements in ascending order.

The algorithm iterates through the array from index 2 to n, where n represents the size of the array.

At each iteration, it selects the element at the current index (x) and compares it with the previous elements in a backward manner.

If the element at the previous index (A[j]) is greater than x, it shifts that element to the right (A[j+1] = A[j]) until it finds the correct position for x.

This shifting process continues until either j becomes 0 or the element at A[j] is not greater than x.

x is placed at the correct position in the sorted portion of the array (A[j+1] = x).

The algorithm continues this process until all elements are sorted.

This approach resembles the way we sort playing cards in our hands, hence the name "Insertion Sort."

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Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Answer:

m∠XBC = 135

Step-by-step explanation:

What is the measure of ∠XBC?

m∠XBC = m∠BAC + m∠BCA

3p – 6 = p + 4 + 84

3p – 6 = p + 88

2p – 6 = 88

2p = 94

From the simplified expression, we need to find the value of p first

From the last line we can see that;

2p =94

Divide both sides by 2:

2p/2 =94/2

p = 47

From the expression, m∠XBC =3p-6

m∠XBC = 3(47)-6

m∠XBC = 141 -6

m∠XBC = 135

Hence the measure of m∠XBC is 135

Answer:

425

Step-by-step explanation:

Answer:

f(-4)=85

Step-by-step explanation:

Given function

f(x)= 2x^2-10x+13

Now put x= -4, We get

f(-4)=2(-4)^2-10(-4)+13

f(-4)=2(16)+40+13

f(-4)=32+53

f(-4)=85

Answer:

It's 18 days

Step-by-step explanation:

Answer:

6%

Step-by-step explanation:

The probability of picking a maths student = 21% = 21/100

The probability of picking a science student = 15% = 15/100 = 3/20

The probability of picking in both = 6/100 = 3/50

The probability that the student is in maths or science = 21/100 - 15/100 = 6/100 = 6%.

Answer:

105⁰

Step-by-step explanation:

Please refer to the attachment.

Hope it helps :)

Answer:

It is mode

Step-by-step explanation:

Answer: 6 candies

Step-by-step explanation:

So if the teacher buys 12 packs of 8 candies she will have 96 candies in total giving each of the 30 students 3 candies. That leaves her with 6 candies to enjoy by herself.

The required volume of the given solid is (√16 - r²) -(-√16 - r²).

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

The digit 8 in Carla’s number represents 10 times of what the digit 8 represents in Travis’ number.

The number written by Carla = 814,247

The number written by Travis = 683,571

The place value of digits starting from left is ones, ten's, hundreds, thousands, ten thousand, hundred thousand and so on.

As per this sequence of values, we can see that digit 8 in Carla's number is at hundred thousand place value. Also, digit 8 in Travis' number is at ten thousand place value. So, representing these place value in numeral form and finding the number of times one is greater than other.  

Digit 8 in Carla's number: 100,000

Digit 8 in Travis' number: 10,000

Finding the answer -

Value = 100,000 ÷ 10,000

Cancelling common zeroes from numerator and denominator

Value = 10

Hence, digit 8 in Carla’s number represents 10 times of what the digit 8 represents in Travis’ number.

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The correct question is -

Carla wrote this number: 814,247

Travis wrote this number: 683, 571

The digit 8 in Carla’s number represents how many times what the digit 8 represents in Travis’ number?

A. 10

B. 100

C. 1000

D. 1/10

Answer:

Step-by-step explanation:

it is 2x

Answer:

h

Step-by-step explanation:

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