To decorate a cake, you make a shade of purple icing using 12 drops of red food coloring for every 18 drops of blue.

How many drops of blue food coloring would you need if you use 6 drops of red food coloring?

Answer:

  x = 9

Step-by-step explanation:

You want the length of the hypotenuse in the right triangle with one hypotenuse segment of length 4 and altitude to the hypotenuse of length 2√5.

The altitude of the triangle is the geometric mean of the segments of the hypotenuse:

  2√5 = √(4·(x-4))

  4·5 = 4·(x -4) . . . . . . square both sides

  5 = x -4 . . . . . . . divide by 4

  9 = x . . . . . . . add 4

The length of x is 9 units.

<95141404393>

Answer:

d) 5.88×10^9

Step-by-step explanation:

Answer:

d) 5.88 × 10⁻⁹

Explanation:

\(\rightarrow \sf \left(1.2\cdot 10^7\right)\left(4.9\cdot 10^2\right)\)

\(\sf apply \ exponent \ rule : a^b + a^c = a^{b + c}\)

\(\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7}\cdot \:10^{2}\)

\(\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7+2}\)

\(\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^9\)

\(\rightarrow \sf 5.88 \cdot \:10^9\)

The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².

To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:

Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.

So, the integral for the area of the region is given by:

A = ∫a b [x₂(y) - x₁(y)] dy

Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10

So,

A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy

=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy

=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2

=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]

=> A = 174/3

Hence, the area of the region enclosed by the curves is 174/3 units².

Know more about area here:

https://brainly.com/question/15122151

#SPJ11

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

Learn more about index here :-

https://brainly.com/question/32793068

#SPJ11

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

For more questions on adjacent sides, click on:

https://brainly.com/question/28394984

#SPJ8

No, it is not a probability function because ∫f(x) dx ≠ 1.

To check if F(x) = x on [0, 6] is a probability density function, we need to verify two conditions:

1. f(x) ≥ 0 for all x in the domain.
2. ∫f(x) dx = 1 over the domain [0, 6].

For F(x) = x on [0, 6], the first condition is satisfied because x is greater than or equal to 0 in this interval. However, to check the second condition, we calculate the integral:

∫(from 0 to 6) x dx = (1/2)x² (evaluated from 0 to 6) = (1/2)(6²) - (1/2)(0²) = 18.

Since ∫f(x) dx = 18 ≠ 1, F(x) is not a probability density function.

To know more about probability density function click on below link:

https://brainly.com/question/30403935#

#SPJ11

Answer:

29.52cm sqauared

Step-by-step explanation:

length x width = area of rectangle

Answer: 29.52cm2

Step-by-step explanation:

8.2 times 3.6=...

The probability of getting at least one tail when a coin is tossed 9 times is 0.8438. This can be calculated by adding the probability of getting 0 tails, 1 tail, 2 tails, 3 tails, 4 tails, 5 tails, 6 tails, 7 tails, 8 tails, and 9 tails together:

P(at least one tail) = P(0 tails) + P(1 tail) + P(2 tails) + P(3 tails) + P(4 tails) + P(5 tails) + P(6 tails) + P(7 tails) + P(8 tails) + P(9 tails)
= 0.0019 + 0.0156 + 0.0781 + 0.2051 + 0.3086 + 0.3086 + 0.2051 + 0.0781 + 0.0156 + 0.0019
= 0.8438

Therefore, the probability of getting at least one tail when a coin is tossed 9 times is 0.8438, which can be expressed as a decimal rounded to four decimal places.
The probability of getting at least one tail in a coin toss is 1 minus the probability of getting all heads.
The probability of getting a head in one toss is 0.5, so the probability of getting all heads in 9 tosses is 0.5^9 = 0.001953125.

So the probability of getting at least one tail is 1 - 0.001953125 = 0.998046875.
As a fraction, this can be written as 998046875/1000000000, which can be simplified to 511/512.
So the probability of getting at least one tail in 9 tosses is 0.9980 or 511/512.

You can read more about probability at https://brainly.com/question/24756209

#SPJ11

Answer:

8 weeks per painting

Step-by-step explanation:

1/4 of a painting in 2 weeks

Multiply everything x 4

4/4 or 1 painting in 8 weeks

The proportion shows that the time taken to do the same job by Mrs. Squirrel is 6 hours.

From the information given, the ratios are:

Turtle / Squirrel = Squirrel / Pigeon

3/x = x/(1/48)

x² = 1/16

x = 1/4

The number of days will be:

= 1/4 × 24

= 6 hours.

Learn more about proportion on:

brainly.com/question/24372153

#SPJ1

Answer:

y = e^x

Step-by-step explanation:

The fastest way to do this is to use a graphing calc or an online graphing platform and check to see which graph matches the one given.

The graph of the exponential function approaches zero as the value of x approaches negative infinity. Then the correct option is C.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The graph of the logarithm function approaches the infinity as the value of x approaches zero. So the given graph can not be a logarithm graph.

The graph of the exponential function approaches zero as the value of x approaches negative infinity. And at x = 0, the value of the function is 1.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

A correlation does not simply mean that two or more variables are present together. The statement is false.

Correlation can be positive, negative, or zero.
Positive correlation means that as one variable increases, the other variable also increases. For example, there is a positive correlation between the amount of studying and exam scores.

Negative correlation means that as one variable increases, the other variable decreases. For example, there is a negative correlation between the number of hours spent watching TV and physical activity levels.

Zero correlation means that there is no relationship between the variables. For example, there is zero correlation between the number of pets someone owns and their height.

It's important to note that correlation does not imply causation. Just because two variables are correlated does not mean that one variable causes the other to change.

To summarize, a correlation measures the statistical relationship between variables, whether positive, negative, or zero. It is not simply the presence of two or more variables together. The statement is false.

Know more about correlation here,

https://brainly.com/question/30116167

#SPJ11

Answer:

1,029

Step-by-step explanation:

The total number of girls in Class B is 7

Let's solve the problem step by step:

We know that the number of boys in both classes is 26. Since the problem states that there are 4 more girls than boys in Class A, we can subtract 4 from the total number of students in Class A to find the number of boys in Class A. This gives us (26 - 4) = 22 boys in Class A.

Since the total number of boys and girls in both classes is 49, we can subtract the number of boys from this total to find the number of girls. Thus, there are (49 - 26) = 23 girls in both classes.

Now, we are given that in Class B, there are twice as many boys as girls. So, let's assume the number of girls in Class B is 'x'. Therefore, the number of boys in Class B would be 2x.

Adding the number of girls and boys in Class B, we get x + 2x = 3x.

We know that the total number of girls in both classes is 23, so we can set up the equation 3x = 23.

Dividing both sides of the equation by 3, we find x = 23/3 ≈ 7.67.

Since the number of girls must be a whole number, we round down to the nearest whole number. Therefore, the number of girls in Class B is 7.

Know more about number here;

https://brainly.com/question/24908711

#SPJ11

The net outward flux across the boundary of the tetrahedron is: 5, using the concept of gradient of function.

The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).

Given vector field:

F = ( -x, 3y, 2 z )

Δ . F = (i δ/δx + j δ/δy + k δ/δz) (-x, 3y, 2 z )

Δ . F = [δ/δx(-x)] + δ/δy (3y) + δ/δz (2z)]

Δ . F = - 1 + 3 + 2

Δ . F = 4

According to divergence theorem;

Flux =  ∫∫∫ Δ . (F) dv

x+y+z = 1; so, 1st octant

∫₀¹∫₀¹⁻ˣ∫₀¹⁻ˣ⁻y (4) dz dy dx

= 4 ∫₀¹∫₀¹⁻ˣ (1 - x - y) dy dx

= 5

Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: 5

To learn more about the gradient of a function refer to:

brainly.com/question/6158243

#SPJ4

Answer: i will put the answer as a comment but what are you rounding to

Step-by-step explanation:

Answer:

Depends on what you're round to. Read below.

Step-by-step explanation:

To the 100,000 place:

100,000

To the 10,000 place:

110,000

To the 1,000 place:

107,000

To the 100 place:

106,500

To the 10 place:

106,510

To the 1 place:

106,513

f(x) = -2x

-2x = 0

x = 0/-2

x = 0

Now putting 0 as x in g(x)

g(x) = 8x^2 - 5x + 7

g(0) = 8(0)^2-5(0)+7

= 0 - 0 + 7

= 7

Answered by Gauthmath must click thanks and mark brainliest

Answer:

x=-2 y=-5

x=5 x=2

The conversion of decimal number directly to binary number will be faster.

The number conversion deals with the operation to change the base of the number.

Binary number - It contains only 2 numbers that are 1 and 0.

Decimal number - It contains 10 numbers that are from 0 to 9.

Hexadecimal number - It contains 16 numbers that are from 0 to F.

Convert the decimal number 431 to binary will be

431 / 2 = 215 with 1 remainder

215 / 2 = 107 with 1 remainder

107 / 2 = 53 with 1 remainder

53 / 2 = 26 with 1 remainder

26 / 2 = 13 with 0 remainder

13 / 2 = 6 with 1 remainder

6 / 2 = 3 with 0 remainder

3 / 2 = 1 with 1 remainder

1 / 2 = 0 with 1 remainder

The decimal number 431 to binary number will be 110101111.

Convert first to hexadecimal and then from hexadecimal to binary. Then we have

(431)₁₀ = (1AF)₁₆ = (110101111)₂

More about the conversion of the number system link is given below.

https://brainly.com/question/655411

#SPJ1

The histogram is attached.

Given that, we need to draw a histogram,

Data :-

1-3        3, 2, 3     Frequency = 3

4-6       4, 6, 5     Frequency = 3

7-9       7, 8, 8, 7  Frequency = 4

10-12    10, 10       Frequency = 2

Hence, you can draw the histogram according to the table.

Learn more about histogram, click;

https://brainly.com/question/30354484

#SPJ1

Answer:

answer

Step-by-step explanation:

80/100 - 80%

D. 62% of women in the sample are the primary investor in their household.Inference: Women in the United States are likely to be the primary investors in their households.

The answer to this question is D. 62% of women in the sample are the primary investor in their household. This is an example of the descriptive branch of statistics because it summarizes the data collected in the survey. The inference based on the results of the survey is that women in the United States are likely to be the primary investors in their households.

62% of women in the sample are the primary investor in their household.

Inference: Women in the United States are likely to be the primary investors in their households.

Learn more about sample here

https://brainly.com/question/25894237

#SPJ4

Always use alpha=0.05 since it's the most commonly used one. Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H0.

When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha. Generally speaking, you should reject the null hypothesis less frequently when there is a greater risk of doing so, which happens as you lower the significance level.

Know more about null hypothesis at:

https://brainly.com/question/4436370

#SPJ4

Answer:

Justin did not eat 7/12 of the pizza

Step-by-step explanation:

Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over

Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over

Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over

Justin eats 10.

24 - 10 = 14

Justin did not eat 14/24 = 7/12

If you know the angle in radians, then the length of the arc is

(measure of the angle in radians) x (radius of the circle) .

In this circle, we know the angle and we know the radius.

Arc AB = ( π/4) x (16")

Arc AB = 4π inches

Arc AB =  about 12.566... inches

Answer:

6 pie correct on edge

Step-by-step explanation:

This relates to combination and permutations and the number of distinct arrangements that are possible will be 6.

From the information, a mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row.

Let 1 = IMO

Let 0 = IPho.

Therefore, the number of arrangement will be:

0011

0110

1100

1010

0101

1001

Therefore, the number of arrangement will be 6.

Learn more about permutations and combination on:

brainly.com/question/4658834

#SPJ1

Answer:

Area = 3.14  yards squared

Circumference = 6.28 yards

Step-by-step explanation:

If the diameter is 2, the radius is 1.

Area = πr²

3.14(1²)=3.14 yards squared

Circumference = 2πr or πd

3.14x2=6.28 yards