A chemical solution contains 5.8 ml of water. A chemist adds more water t the solution at a rate of 0.07 ml/s. 9.900 XP 1 How many seconds will it take for the solution to contain 10 ml of water? If your answer is a decimal, give it to 2 d.p.​

Answer:

Volume V = 18.735 m3

Step-by-step explanation:

hope this helps

We have a line that passes through the point P:

P = (2, -1)

And that has a slope m = 5. Using the point-slope form of the linear equation:

(y - y0) = m*(x - x0) ...(1)

Where x0 and y0 are the coordinates of any point contained in the line. In particular, if the point is P:

x0 = 2

y0 = -1

Then, replacing these values on (1):

(y - (-1) = 5*(x - 2)

y + 1 = 5x - 10

Finally:

y = 5x - 11

Answer: 66%

Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, \(\frac{1}{4}\) is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.

hope this helps!

please give brainliest!

The weighted average length of a nail from the carpenter's box whose distribution is give in image is: 3.5cm.

What is weighted average ?

Weighted average is a type of average that takes into account the relative importance or weight of each data point. In a weighted average, each data point is multiplied by a corresponding weight, which reflects its relative importance, and the products are then summed and divided by the sum of the weights.

To find the weighted average length of a nail, we need to multiply each nail length by its percent abundance, then add up all the products and divide by the total percent abundance.

Let's start by calculating the product of each nail length and its percent abundance:

Short nail: (2.5 cm) x (70.5%) = 1.7625 cm

Medium nail: (5.0 cm) x (19%) = 0.95 cm

Long nail: (7.5 cm) x (10.5%) = 0.7875 cm

Now, we add up all the products:

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

Finally, we divide by the total percent abundance:

70.5% + 19.0% + 10.5% = 100%

Therefore, the weighted average length of a nail from the carpenter's box is: 3.5 cm ÷ 100% = 3.5cm

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The additional 60 men, the provisions will last for approximately 20 weeks.

To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.

Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.

Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.

To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:

Provisions last = Total person-weeks / Number of men

= 9200 / 460

≈ 20 weeks (rounded to the nearest whole number)

The additional 60 men will extend the supply's shelf life to around 20 weeks.

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Thus, the given set of triangles ABC and DEF are not found to be similar triangles.

If the matching sides and angles of two polygons are proportional, then the polygons are comparable. If any two polygons meet the following two criteria, they are said to be similar.

For the given triangles ABC and DEF to be similar, the ratios of their sides muse be equal.

AB/DE = BC/EF = AC/DF

6/8 = 4/6 = 6/8

3/4 = 2/3 = 3/4

But,

3/4 ≠ 2/3  ≠ 3/4

Thus, the given set of triangles ABC and DEF are not found to be  similar triangles.

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The value of x will be;

⇒ x = 6

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The expression is,

⇒ 5 1/2x + 2/3x = 37

Now,

Since, The expression is,

⇒ 5 1/2x + 2/3x = 37

Solve for x as;

⇒ 11/2x + 2/3x = 37

⇒ (33 + 4)x/6 = 37

⇒ 37x = 37 × 6

⇒ x = 6

Thus, The value of x = 6

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Answer:

yes I just checked it

Step-by-step explanation:

Answer:

She would be able to buy

4 Chicken Salads &

2 Egg Salads

Step-by-step explanation:

4x5=20

leaving 8 dollars

2x4=8

Answer: she will spend 3 orders of chicken salad, and 3 orders of egg salad the total it will be $27.

Step-by-step explanation:

Problem 34

Answer: \(\boldsymbol{n(B) = 3}\)

Reason:

We count the number of items inside set B. In this case there are 3 values, so that is why n(B) = 3

===========================================================

Problem 36

Answer:  \(\boldsymbol{n(A \cap C) = 1}\)

Reason:

To be able to count the number of items inside set \(A \cap C\), we first need to determine what this set looks like. In other words, we need to know the number(s) inside this set.

The upside down U symbol is the intersection symbol. It indicates we want to find what the sets A and C have in common. In this case, it's the value "4" and nothing else. This number is in both set A and set C at the same time. It might help to draw a venn diagram as you see below. I'm ignoring set B entirely since your teacher is not asking about the set in this problem.

We can then say \(A \cap C = \{4\}\)

There's only one item inside this set, which is why \(n(A \cap C) = 1\)

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Fixed cost to produce gizmo = $1000

Cost to produce each gizmo = $5

Fixed cost to produce gadget = $750

Cost to produce each gizmo = $3

A.) Expression to make x gizmo:

Fixed cost + 5x

$1000 + 5x

B.)Expression for cost of making y gadget:

Fixed cost + 3y

$750 + 3y

C.) Cost of making x gizmo and y gadget :

($1000 + 5x) + ($750 + 3y)

D.) $1750 + 5x + 3y

The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

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Answer:

option D 12 is correct..

in second question the student didn't multiply -3 with 4. that's the mistake he did.

hope it helps

Answer:

D. 12

Step-by-step explanation:

4(3x+2)

=(4)(3x+2)

=(4)(3x)+(4)(2)

=12x+8

Answer:

c

Step-by-step explanation:

Answer:

the answer is 5

Step-by-step explanation:

On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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The length of line segment DL of the system of similar triangles is 4√3. The length of line segment BD of the system is √3.

Two triangles are similar if they have congruent angles and if their sides are not congruent though proportional. The statement of the problem can be described by following equations:

Proportion formula

AD / BD = DL / AD

DL = 4 · BD

Then, we find the formula for line segment DL:

AD / BD = 4 · BD / AD

AD² = 4 · BD²

BD = √(AD / 2)

If we know that AD = 6, then the length of line segment DL:

BD = √3

DL = 4√3

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14.05 at most

If it is saying at least, than it would be in the cooler for longer than it should be and drop below 60.5

If saying more than 14.05, it is basically the same thing where it is inside the cooler for longer than it should be

If saying at most, that means that 14.05 is the max it would be in the cooler and keeps the liquid above 60.5

Answer: im late but here you go

12/2/22

Step-by-step explanation:

Answer:

a) \(n=\frac{0.5(1-0.5)}{(\frac{0.02}{2.58})^2}=4160.25\)  

And rounded up we have that n=4161

b) \(n=\frac{0.96(1-0.96)}{(\frac{0.02}{2.58})^2}=639.01\)  

And rounded up we have that n=640

Step-by-step explanation:

Part a

The confidence level is 99% , our significance level would be given by \(\alpha=1-0.99=0.01\) and \(\alpha/2 =0.005\). And the critical value would be given by:

\(z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58\)

The margin of error for the proportion interval is given by this formula:  

\( ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\)    (a)  

And on this case we have that \(ME =\pm 0.02\) and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

\(n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}\)   (b)  

Since we don't have prior info for the true proportion we can use \(\hat p=0.5\). And replacing into equation (b) the values from part a we got:

\(n=\frac{0.5(1-0.5)}{(\frac{0.02}{2.58})^2}=4160.25\)  

And rounded up we have that n=4161

Part b

For this case we have a prior estimation ofr the proportion:

\( \hat p=0.96\)

And replacing we got:

\(n=\frac{0.96(1-0.96)}{(\frac{0.02}{2.58})^2}=639.01\)  

And rounded up we have that n=640

Answer:

8

Step-by-step explanation:

a² + b² = c²

c² = a² + b²

c² = 5² + (√39)²

c² = 25 + 39

c² = 64

c = 8

Answer:

386.75

Step-by-step explanation:

added in the picture

The cost of joining the gym for 6 months is 386.75.

Given,

The function G(m) = 49.5m + 89.75 represents the cost of joining the gym in addition to the one-time membership fee.

The cost, G, is measured in dollars for m months.

We need to find the value of G(6).​

Here,

The one-time membership = 89.75.

Now,

Putting m = 6 months in:

G(m) = 49.5m + 89.75

G(6) = 49.5 x 6 + 89.75

       = 297 + 89.75

       = 386.75

Thus the cost of joining the gym for 6 months is G(6) = 386.75.

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The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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The that will represent the exponential function is given in image

What are exponential functions, exactly?

A mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is referred to as the function's base and must be greater than zero. The most commonly used exponential function basis is the transcendental number e, which is approximately equivalent to 2.71828.

Exponentially increasing growth

In Exponential Growth, the amount expands incredibly slowly at first, then rapidly. With the passage of time, the rate of change quickens. The rate of growth quickens as time passes. The fast growth is supposed to indicate a "exponential ascent".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the proportion of increase.

Now,

As the function y=10x² represents the number of gummies after x months

the the graph will be  

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Alexa and Raymond spent the same amount of money at the art store.

Alexa bought a paint brush for $8 and 4 jars of pant.

Raymond bought a paintbrush for $5 and 6 jars of paint

Let the cost of each jar of paint be x

For Alexa,

Since, she bought a paintbrush for $8 and 4 jars of paint

Total cost = y

Total cost = cost of paint brush + number of jars of paint x cost of each jar of paint

Since the cost of each jar of paint = x

total cost = 8 + 4 * x

y = 4x + 8----------- Alexa total cost equation

For Raymond,

He bought a paint brush for $5 and 6 jars of paint

Since, the cost of each jar of paint = x

Total cost = y

y = 6 * x + 5

y = 6x + 5 ---------- Raymond equation

The x - variable is the cost of each jar of paints

Answer:

1.57ft

Step-by-step explanation:

The circumference is twice the radius times pi.

C=2πr

C=2·π·5

C=10π

C=31.4159265359

We know that KL is 18° of that (180-162).

So we get the formula

31.4159265359÷360x18=1.57

Answer:

its b little dude

Step-by-step explanation:

Answer:

d = 48.8

Step-by-step explanation:

Subtract 71.2 from both sides:

71.2 + d - 71.2 = 120 - 71.2

Group like terms:

d + 71.2 - 71.2 = 120 - 71.2

Simplify the arithmetic:

d = 120 - 71.2

Simplify the arithmetic:

d = 48.8

Answer:

D. 0.34

Step-by-step explanation:

0.24²+0.31²=x² then you find the square root

Answer:

the answer is 0.28, Because of SEGEMENT FH IS HALF OF FG BECAUSE ITS A RIGHT ANGLE.