The ratio of green to yellow
candies is 2:5. If there are 32
green candies, how many green
and yellow candies are there
altogether?

The parabola \(y = √(x - 4)\) opens upward.

The parabola y = √(x - 4) represents the square root function of x minus 4. To determine the direction in which the parabola opens, we examine the behavior of the square root function.

The square root function (√x) returns non-negative values for non-negative inputs. Since the expression inside the square root, (x - 4), must be non-negative for real solutions, we have x - 4 ≥ 0. Solving this inequality, we find x ≥ 4.

This means that the parabola is defined for x values greater than or equal to 4. As we increase x from 4, the value of √(x - 4) will also increase. Therefore, the graph of the parabola opens upward.

The parabola \(y = √(x - 4)\) opens upward.

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Using it's concept, it is found that the probability that a randomly selected student is in music/drama is:

P(Music/Drama) = 0.25.

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

In this problem, the number of students is given by:

N = 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100.

Of those, the number involved in music/drama is:

D = 7 + 13 + 5 = 25.

Hence the probability is given by:

p = 25/100 = 0.25.

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Answer:

yes

Step-by-step explanation:

A statistical question is one that can be answered by collecting data and where there will be variability in that data.

because not every father would be born on the same day this is a statistical question.

It will take approximately 4.08 years for an investment of P8,000 to amount to P16,000 at a 10% interest rate compounded monthly.

Using the compound interest formula, we can determine how long it will take for an investment of P8,000 to grow to P16,000 at a monthly interest rate of 10%:

Where: A = the ultimate sum (in this case, P16,000);

\(A = P(1 + r/n)^(nt)\)

P is equal to the principal ($8,000 in this case).

r = the yearly interest rate (decimalized as 10% or 0.10)

n is the number of times each year (monthly, thus 12) that interest is compounded.

t is the number of years.

By rearranging the equation to account for t, we get at: \(t = (1/n) * log(A/P) / log(1 + r/n)\)

By entering the specified values, we obtain:

\(t = (1/12) * log(16,000/8,000) / log(1 + 0.10/12)\)

When we calculate this statement using a calculator, we see that t is roughly 4.08 years (rounded to the next hundredth).

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The sample space is (a) watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

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

2 watermelon, 3 lemon-lime, and 5 grape gumballs

Rewrite the items according to their frequencies

So, we have the following representation

watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

The above represents the sample space

Hence, the sample space is (a)

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Answer:

16

Step-by-step explanation:

it doubles every time    2,4,8. 16

Answer:

a) About 68% of the data would be between 305 grams to 395 grams

b) About 95% of organs weighs between 260 grams and 440 ​grams

c)About 5% of organs weighs less than 260 grams or more than 440 ​grams

d) About 97% of organs weighs between 215 grams and 440 ​grams

Step-by-step explanation:

The empirical rule formula:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

​(a) About 68​% of organs will be between what​ weights?

We would be applying the First rule of the Empirical formula to this.

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

Mean = 350 grams

Standard deviation = 45 grams

Hence,

350 grams - 45 grams

= 305 grams

350grams + 45grams

= 395 grams

Therefore about 68% of the data would be between 305 grams to 395 grams

​(b) What percentage of organs weighs between 260 grams and 440 ​grams?

Let try the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ - 2σ

= 350 - 2(45)

= 350 - 90

= 260

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Therefore, about 95% of organs weighs between 260 grams and 440 ​grams

​(c) What percentage of organs weighs less than 260 grams or more than 440 ​grams? ​

Let try the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ + 2σ

= 350 - 2(45)

= 350 - 90

= 260

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Since, about 95% of organs weighs between 260 grams and 440 ​grams, the percentage of organs weighs less than 260 grams or more than 440 ​grams is calculated as:

100% - 95%

= 5%

Therefore, percentage of organs weighs less than 260 grams or more than 440 ​grams is 5%

(d) What percentage of organs weighs between 215 grams and 440 ​grams?

For 215 grams, we apply the 3rd rule to confirm

= 3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

Mean = 350 grams

Standard deviation = 45 grams

μ - 3σ

= 350 - 3(45)

= 350 - 135

= 215.

Hence, 99% of the organs weigh 215 grams

For 440, from the solve questions above, we know the second rule applies.

Hence,

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Hence,

99% + 95%/ 2

= 194% / 2

= 97%

Therefore, about 97% of organs weighs between 215 grams and 440 ​grams

Answer:

85° and 95°

Step-by-step explanation:

Let's begin noting that a triangle is isosceles if and only if two of its angles are congruent. We can thus find the angle <ABP, recalling that the sum of the interior angles of a triangle is equal to 180°.

\( \angle \: ABP = \frac{180 - 80}{2} = 50 \degree\)

Finally, let point K be the intersection between segments BC and PQ, and let's note that the triangle PQB is a right isosceles triangle, since all the angles in a square are equal to 90°, and the two triangles APB and BQC are congruent.

Therefore, the angle BKQ is equal to 180-50-45=85°.

Of course angle BKP=180-85=95°.

Hope this helps :)

\(0.5 - ( - 10.5 \times 5) + 40.5\) = \(\boxed{93.5}\)

A. 93.5 ✅

Step-by-step explanation:-

\(0.5 - ( - 10.5 \times 5) + 40.5 \\ = 0.5 - ( - 52.5) + 40.5 \\ = 0.5 + 52.5 + 40.5 \\ = 93.5\)

Note:-

\(\sf\purple{BODMAS\: rule.}\)

B = Brackets

O = Orders

D = Division

M = Multiplication

A = Addition

S = Subtraction

\(\sf\red{(-\:x\:-)\:=\:+}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

Answer:

93.5

Step-by-step explanation:

See the steps below:)

The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.

To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:

a/5 = b/3

5/a = 3/b (multiplying both sides by 5/a)

5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)

5/a = 1

Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

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Given:

\(\tan A=\dfrac{1}{5}\)

\(\tan B=\dfrac{1}{4}\)

To find:

The value of \(\tan^2(A-B)\).

Solution:

We know that,

\(\tan (A-B)=\dfrac{\tan A-\tan B}{1+\tan A\tan B}\)

Putting the given values, we get

\(\tan (A-B)=\dfrac{\dfrac{1}{5}-\dfrac{1}{4}}{1+\dfrac{1}{5}\cdot \dfrac{1}{4}}\)

\(\tan (A-B)=\dfrac{\dfrac{4-5}{20}}{1+\dfrac{1}{20}}\)

\(\tan (A-B)=\dfrac{\dfrac{-1}{20}}{\dfrac{20+1}{20}}\)

\(\tan (A-B)=\dfrac{-1}{21}\)

Taking square on both sides, we get

\(\tan^2 (A-B)=\left( \dfrac{-1}{21}\right)^2\)

\(\tan^2 (A-B)=\dfrac{1}{441}\)

Therefore, the value of \(\tan^2(A-B)\) is \(\dfrac{1}{441}\).

Answer:

10 m

Step-by-step explanation:

Using the circumference equation C=2r

We are given that C=20

Plug it into the equation!

20=2r

r=10

Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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Answer:

\(a^{2} +b^{2} =c^{2}\)

Step-by-step explanation:

C is the horisontal and a or b can be the height, plug in the numbers and you solve for length.

Answer:

(sqr) 30^2/100^2+3^2

Step-by-step explanation:

Answer:

The answer is -4-2 = -6

Answer:

-6 is the answer hope that helps

Answer:

Not sure but I think the answer is 129

Step-by-step explanation:

first, substitute the value of x in the expression like this

18(3*2+1)+3

after substituting, our work has made easier

18(6+1)+3

18(7)+3 or simply 18*7+3

126+3

129

#10. In order to find a ratio, all we need to do is set up a simple equation and then cross-multiply!

I'll show you !

In this case, we'll take the already established ration (14 : 8 ) and find the equivalent ratio where 7 is in place of 14 (7: x)

x will be the other table value we are looking for!

Now let's set up the equation and cross-multiply!

\(\frac{14}{8} = \frac{7}{x}\)

cross multiply 14 and x, then 8 and 7

We get:  14x = 56

solve to find x!

x = 56/14

x = 4 blankets

Now let's use the ratio 7: 4 to find what goes with 16 in the table!

\(\frac{7}{4} = \frac{x}{16}\)

4x = 112

x = 112/4

x = 28 towels

_________________________________________________-

#11. : Using the same method, I'll fill in the values of the table on #11

16 forks, 10 spoons

8 forks, 5 spoons,

48 forks, 30 spoons

_____________________________________________

#12. If the neighbor pays you $17 for every 2 hours of work, we need to find how many times 2 hours goes in 8 hours of work

We do this by dividing

8/2 = 4 times

2 hours of work goes into 8, 4 times!

Now we multiply 4 by $17 to find how much your neighbor owes you!

$17 × 4 = $68

Your neighbor owes you $68 !!!

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

Answer:

The answer is B. X > -2

if you click the image it will show you how to solve the equation. I hope this helps you.

Thus, the cardinal number of the set E is found to be: N(E) = 6.

A cardinal number describes or expresses how many of anything are present.

So all natural numbers are often refereed to as cardinal numbers. Cardinal numerals have been used for counting. When an ordinal number is an integer that represents the location or place of an object.

The description of a cardinal number is really a number that is used to express quantity in whole numbers. Decimals and fractions are not regarded as cardinal numbers. Natural numbers and numbering numbers constitute cardinal numbers. Each of them is a positive integer.

Given data:

N(CxE) = 18

C = {4, 5, 6)

In which N is the cardinal number, that is the total elements present in the set.

So,

N(C) = 3

Given that: N(CxE) = 18

The formula for the Cartesian product is:

N(CxE) = N(C) * N(E)

18 = 3* N(E)

N(E)  = 18 /3

N(E) = 6

Thus, the cardinal number of the set E is found to be: N(E) = 6.

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Complete questions:

Find N(E), Given That N(CxE) = 18 And C = {4, 5, 6).

Α. 6

B. 9

C. 3

D. 5

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

\(Area = \int\limits^b_a {y} \, dy\)

\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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Answer:

\(d=9.21954\)

Step-by-step explanation:

Distance Formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Simply plug in the 2 coordinates into the distance formula to find distance d:

\(d=\sqrt{(-1-5)^2+(9-2)^2}\)

\(d=\sqrt{(-6)^2+(7)^2}\)

\(d=\sqrt{36+49}\)

\(d=\sqrt{85}\)

\(d=9.21954\)

Answer:

I think it a triangle

Answer:

  about 1.1%

Step-by-step explanation:

Given a moon has a diameter of 22% of the diameter its planet, you want the volume of the moon as a percent of the planet's volume.

The ratio of moon diameter to planet diameter is given as 22%. The ratio of moon volume to planet volume will be the cube of this scale factor:

  moon volume / planet volume = (0.22)³ ≈ 0.0106 = 1.06%

The volume of the moon is about 1.1% of the volume of the planet.

<95141404393>

Answer:

3880 ÷ 960 = 4.041

ratio = 4:1