please please help!!!
Katie needs 60 mL of a 10% acid solution for a science experiment. She has available a 8% solution and a 20% solution.
How many milliliters of the 8% solution and how many milliliters of the 20% solution should she mix to make the 10%
solution?

The area of the given figure is 39 square inches.

To find the area of the given figure, we can break it down into separate rectangles and then add up their areas.

The figure consists of two rectangles:

The larger rectangle with dimensions 7 in by 5 in:

Area = length × width = 7 in × 5 in = 35 in²

The smaller rectangle with dimensions 2 in by 2 in:

Area = length × width = 2 in × 2 in = 4 in²

Now, we can add the areas of these two rectangles to find the total area of the figure:

Total Area = Area of the larger rectangle + Area of the smaller rectangle

= 35 in² + 4 in²

= 39 in²

for more such questions on area

https://brainly.com/question/25292087

#SPJ8

The solution is:

The inverse of the given equation is ±sqrt(x+1).

Here, we have,

given equation is :

y = x^2 -1

now, we have to find the inverse of the given equation

so, we have,

Exchange x and y, we get,

x = y^2 -1

Solve for y, we get,

Add 1 for each side

we get,

x+1 = y^2-1+1

x+1 = y^2

Take the square root of each side

we get,

±sqrt(x+1) = sqrt(y^2)

±sqrt(x+1) = y

The inverse is ±sqrt(x+1)

Hence, The solution is:

The inverse of the given equation is ±sqrt(x+1).

To learn more on function click:

brainly.com/question/21145944

#SPJ1

complete question:

If f(x) = x^2 -1, what is the equation for f–1(x)?

Answer:

The standard deviation is of 8.586.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have a genetic mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

About 9% of the population has a particular genetic mutation.

This means that \(p = 0.09\)

900 people are randomly selected.

This means that \(n = 900\)

Find the standard deviation for the number of people with the genetic mutation in such groups of 900.

\(\sqrt{V(X)} = \sqrt{900*0.09*0.91} = 8.586\)

The standard deviation is of 8.586.

Answer: 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Acellus

Step-by-step explanation:

Therefore, the first five multiples of 17 are 17 , 34 , 51 , 68 and 85 .

Answer:

\( \frac{ 56}{ - 4} = - 14\)

Hope it helps...........................

Answer:

\(\frac{7}{15}\) or 46.6667%

Step-by-step explanation:

  9 chocolates

 14 gumballs

+ 7  mints        

30 pieces of candy in the jar

\(\frac{14}{30}\) of those candies are gumballs.

This can be simplified to \(\frac{7}{15}\)

As a percentage: 46.6667%

Hope this helps~!

Answer:

7/15

Step-by-step explanation:

30 pieces of candy

14/30

actual 7/15

As a percentage 46.66%

Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

asking what I don't see a question

Step-by-step explanation:

Answer:

where is the question

Step-by-step explanation:

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

Learn more on age word problems here;

https://brainly.com/question/17043336

#SPJ1

Answer:

2(x² + 5)

Step-by-step explanation:

To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:

2x² + 10 = 2(x² + 5)

We can't factor anymore, so the answer is:

2(x² + 5)

Answer:

2(x² + 5)

Step-by-step explanation:

To factorise this, do the distributive property backwards. In other words:

2x² + 10

2x² ÷ 2 + 10 ÷ 2

x² + 5

2(x² + 5)

∴ 2(x² + 5) is the answer

The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

To know more about equation refer to:

brainly.com/question/187506

#SPJ1

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

For more such questions on explicit

https://brainly.com/question/30394385

#SPJ8

The volume of the solid generated when the region R is rotated around y = -5 is 7π/4. so the correct answer is (b).

To find the volume , we can use the method of cylindrical shells.

Consider a vertical slice of R at x = a, where a is a point on the x-axis. Let h be the height of this slice and r be the distance from the line y = -5 to the point (a, h). Then the volume of the cylindrical shell generated by rotating this slice around the line y = -5 is given by:

V(a) = 2πrh Δa

where Δa is the thickness of the slice. Note that we multiply by 2 because the slice can generate a shell both above and below the line y = -5.

To find the values of h and r in terms of x, we can use the fact that the centroid of R is (4, 3), which means that the equation of the line passing through the centroid and the point (x, h) is given by:

(y - 3) = m(x - 4)

where m is the slope of the line. Since the line passes through the point (x, h), we have:

(h - 3) = m(x - 4)

Solving for h, we get:

h = mx - (4m - 3)

To find the slope m, we can use the fact that R has area 1. Since R lies in quadrant I, we know that m > 0. Then we have:

1 = ∫[0, 4] h dx = ∫[0, 4] (mx - (4m - 3)) dx

Simplifying, we get: 1 = (1/2) m(4^2) - (4m - 3)(4)

Solving for m: m = 1/8

Substituting this into the equation for h, h = (x/8) - 11/8

To find the distance r from the line y = -5 to the point (x, h), we have:

r = h + 5 = (x/8) - 3/8

Now we can integrate V(a) over the interval [0, 4] to get the total volume:

V = ∫[0, 4] V(a) da = ∫[0, 4] 2πr(h + 5) Δa

Substituting for r and h, we get:

V = ∫[0, 4] 2π[(x/8) - 3/8][(x/8) - 11/8 + 5] Δx

Simplifying, V = π/2 ∫[0, 4] (x^2/64) - (27/64)x + 2.25 Δx

Integrating, V = π/2 [(1/192)x^3 - (27/128)x^2 + 2.25x] [0, 4]

V = (π/2) [(1/12) - (27/32) + 9]

V = 7π/4

Therefore, the volume of the solid generated when the region R is rotated around y = -5 is 7π/4. Answer: (b)

To know more about volume:

https://brainly.com/question/11168779

#SPJ4

Check the picture below.

the answer is D

The figure can be divided into a rectangle and 2 triangles

(a) Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39
(b) The function is y = 3  (1.1)ˣ.

(c) It would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) It would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

(a)

Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39

(b) Let x be the number of clicks and y be the width of the door on the screen. Then, we can write the algebraic rule as:

y = 3  (1.1)ˣ

(c) To make the door approximately 3 feet wide on screen, we need to convert 3 feet to inches, which is 36 inches. Then, we need to solve for x in the equation:

3 (1.1)ˣ = 36

Dividing both sides by 3, we get:

(1.1)ˣ = 12

Taking the logarithm of both sides (with base 1.1), we get:

x = log(12) / log(1.1) ≈ 14.7

So, it would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) To transform the display of the door from 3 feet wide back to a width of approximately 3 inches, we need to find the number of clicks of the zoom-out button that will result in a width of approximately 3 inches. We can use the same formula as before, but with the initial width of 36 inches (since we are zooming out):

36 (0.9)ˣ = 3

Dividing both sides by 36, we get:

(0.9)ˣ = 1/12

Taking the logarithm of both sides (with base 0.9), we get:

x = log(1/12) / log(0.9) ≈ 11.5

So, it would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

To learn more about the exponential function;

https://brainly.com/question/14344314

#SPJ1

The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

Learn more about y-intercept at

https://brainly.com/question/10606087

#SPJ1

9514 1404 393

Answer:

  A, M, N, F

Step-by-step explanation:

I find it easier to look at the graph, rather than mess with the coordinate transformations. Each image point is the same distance from the line of reflection that its pre-image point is. The line joining the two points is perpendicular to the line of reflection.

See attached for the reflected points.

__

The red and turquoise dashed lines are the lines y=x and y=-x, respectively. The same-colored arrows show the reflection of the relevant point.

_____

The transformations of interest are ...

  (x, y) ⇒ (y, x) . . . . reflection over y = x

  (x, y) ⇒ (-x, y) . . . . reflection over y-axis

  (x, y) ⇒ (x, -y) . . . . reflection over x-axis

  (x, y) ⇒ (-y, -x) . . . . reflection over y = -x

Answer:

2/10

Step-by-step explanation:

Answer:

(1/2)x + 4 - 4 = 10 - 4

2(1/2)x = 6 * 2

x = 12

Answer:

15

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

bResponses

y = 8

y, = 8

y = 3

y, = 3

y=−3

Answer:

Step-by-step explanation:

The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.

To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.

So, the growth rate of the investment is:

1.035 - 1 = 0.035

0.035 * 100 = 3.5%

Therefore, the growth rate of the investment is 3.5%.

The option that is not true about polynomial functions is:

Option D. The deg (f ^ 3) = 3m​

For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:

Option A: deg(f + g) = max(m, n)

This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.

Option B: deg(f * g) <= m + n

This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.

Option C: If g is a factor of f, then deg(f) <= m

This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.

D. The deg(f ^ 3) = 3m

This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.

Read more about Degree of Polynomials at: https://brainly.com/question/1600696

#SPJ1

Answer:

6.2

Step-by-step explanation:

every minute 6.2 gallons fill into the pool.

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

Learn more about numbers in https://brainly.com/question/24908711

#SPJ1