Pure acid is to be added to a 10% acid solution to obtain 90L of 84% solution. How many liter of 10% solution should be in the mixture?

Answer:

Step-by-step explanation:

5x + 7x - 1/2x + 1/4 = 6

move x to one side move numbers to the other side

5x + 7x - 1/2 x = 6 - 1/4

add x and numbers

23/2x = 23/4

divide both side by 23/2

x = (23/4)/(23/2)

  = 1/2

plug it in to check the answer

5/2 + 7/2 - 1/4 + 1/4 = 6

12/2 = 6

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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A statement that describes the median of a triangle include the following: A. a segment drawn from a vertex to the midpoint of the opposite side.

In Mathematics and Geometry, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

In Mathematics and Geometry, the median of a triangle can be defined as a line segment with end points that is typically drawn from a vertex to the midpoint of the opposite side of the triangle.

In this context, we can logically deduce that a line segment with end points at the vertex and the midpoint of the triangle's opposite side simply refers to the median of a triangle.

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Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

Answer:

\( \frac{4}{7} \times 42 \\ = 24 \: storms\)

Answer:

This is  called a mid segment theorem in which the al ine segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side.

Step-by-step explanation:

Suppose we have a triangle ABC. Then the midpoints can be located as D, E and F. If we join D , E and F another triangle is formed.

From the figure we can see that

AE≅ CE

AD≅DB

BF≅CF  

BECAUSE  all the given points are the midpoints which divide the lines into two equal halves.

If we increase the line DE to a point L we find out that DL is parallel to BC i.e. it does not meet at any point with BC. ( the two lines do not meet)

(1)

If we join C with L we find out that the the line DE is half in length to the line BC.

AS

AE= CE  (midpoints dividing into equal line segements.)

LE= DE

Triangle CEL= Triangle DEF

so

DL= BC

But DE = 1/2 DL

therefore

DE= 1/2 BC (2)

Therefore from 1 and 2 we find that a line segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side

The monthly revenue is $1037

What is a linear equation in one variable?

A linear equation in one variable is equation whose degree is one and there is only one variable present.

We are given the monthly revenue received from selling a pair of earrings at a cost of d dollars is given by equation \(-7d^{2}+180d\)

We have to find the monthly revenue received when the cost is $17

That is d=17

Now we substitute d=17 in the given equation to find the monthly revenue

We get,

\(-7d^{2}+180d\\\)

⇒\(-7(17^{2})+180(17)\\\)

⇒ -2023+3060

⇒1037

Hence the monthly revenue earned is $1037

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The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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first off, let's take a peek at the picture above

hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.

now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.

\(\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}\)

9514 1404 393

Answer:

  y =1/8(x -1)^2

Step-by-step explanation:

The vertex is halfway between the focus and directrix, so has y-coordinate (2-2)/2 = 0. The x-coordinate of the vertex is the same as that of the focus. The focus-vertex distance (p) is 2-0 = 2. Where the vertex is (h, k), the equation is ...

  y = 1/(4p)(x -h)^2 +k

For p=2, (h, k) = (1, 0), the equation of the parabola is ...

  y = 1/8(x -1)^2

Answer: The answer is B and im 100% correct

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.

The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).

For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.

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The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.

The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).

For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.

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Answer:

The function f(x) = -2∛x represents a cube root function that is multiplied by -2.

As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.

As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.

Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.

Answer:

The function f(x) = -2∛x represents a cube root function that is multiplied by -2.

As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.

As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.

Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

If we increase each value by 7 grams, we get: {2507, 2707, 2807, 2907, 3107} this would change the rage median iqr of the data set.

what is the median?

The median is a measure of central tendency in a set of data, which represents the middle value of the data when it is arranged in order.

If each birth weight needs to be increased by 7 grams due to a calibration error in the scale being too low, this would affect all the values in the dataset equally, without changing the distribution of the data. Therefore, the range and median of the data set would be increased by 7 grams, while the IQR (interquartile range) would remain the same since it is calculated based on the middle 50% of the data.

For example, suppose we have the following birth weight data set:

{2500, 2700, 2800, 2900, 3100}

The range of the data set was originally 600 (3100 - 2500) but now it is 607 (3107 - 2507), an increase of 7. Similarly, the median of the data set was originally 2800 but now it is 2807, an increase of 7. However, the IQR of the data set, which is the difference between the third quartile (Q3 = 3000) and the first quartile (Q1 = 2700), remains the same at 300 - 270 = 30.

Therefore, If we increase each value by 7 grams, we get:

{2507, 2707, 2807, 2907, 3107}

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Complete Question:

You realize your scale was calibrated too low by 7 grams meaning each birth weight needs to be increased by 7 grams. How would this change the rage median IQR of the data set?

Answer:

The acceleration is 466.7m/s^2

Step-by-step explanation:

Given

\(u = 0m/s\) -- Initial Velocity

It is 0 because the plane starts from a standstill

\(v = 350mi/h\) -- final velocity

\(t = 45s\) -- time

Required

Determine the acceleration

This is calculated using Newton's first equation of motion

\(v = u + at\)

Convert time to hour

\(t = 45s\)

\(t = \frac{45}{60}hr\)

\(t = 0.75hr\)

Substitute values for v, u and t

\(350 = 0 + a*0.75\)

\(350 = 0.75a\)

Divide both sides  by 0.75

\(\frac{350}{0.75} = a\)

\(466.67 = a\)

\(a=466.67m/s^2\)

Hence, the acceleration is 466.7m/s^2

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Using the z-distribution, as we are working with a proportion, the 99% confidence interval is given by:

a) (0.733, 0.927).

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, we have a 99% confidence level, hence\(\alpha = 0.99\), z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The other parameters are p = 0.83, n = 100, hence the bounds of the interval are given as follows.

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.83 - 2.575\sqrt{\frac{0.83(0.17)}{100}} = 0.733\)

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.83 + 2.575\sqrt{\frac{0.83(0.17)}{100}} = 0.927\)

Hence option a is correct.

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9514 1404 393

Answer:

  A, B, D

Step-by-step explanation:

A. Multiplication is the same as repeated addition.

B. Multiplying a fraction by an integer effectively multiplies only the numerator. The denominator remains unchanged.

C. (false -- see B)

D. A product is unchanged if a factor is removed from the multiplicand and is applied to the multiplier. (The associative property of multiplication tells you this.)

  4 × 1/6

  = (2 × 2) × 1/6 = 2 × (2 × 1/6)

  = 2 × 1/3

As the margin of error decreases, the width of the confidence interval decreases.

So option B is correct option.

A confidence interval is a method used to estimate the population parameter of interest based on a random sample from the population. It is a range of values that contains the true population parameter with a certain degree of confidence.

To determine the accuracy of the estimate, the confidence interval is calculated as a range of values within which we are reasonably certain the true population parameter lies. The confidence interval is calculated based on the sample statistics (e.g. sample mean) and the sample size.

The margin of error (also known as the confidence interval half-width) determines the width of the confidence interval. It is the amount of uncertainty associated with the estimate. It is calculated as the product of the critical value (z*) and the standard error of the statistic.

The width of the confidence interval is inversely related to the margin of error. When the margin of error decreases, the width of the confidence interval decreases, and when the margin of error increases, the width of the confidence interval increases.

Therefore, the correct answer is b. Decreases.

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Answer:

49 prizes each, with 5 left

Step-by-step explanation:

985/20 is 49 with 5 left over.

Answer:

y=60

Step-by-step explanation:

1) Find x

All the interior angles of a triangle add up to 180 degrees. Knowing this, we can construct the following equation:

\(180=x+35+25\\180=x+60\)

Subtract 60 from both sides

\(180-60=x+60-60\\120=x\)

2) Find y

A straight line has an angle measure of 180 degrees as well. Knowing this, we can construct the following equation:

\(180=x+y\\180=120+y\)

Subtract 120 from both sides of the equation

\(180-120=y+120-120\\60=y\)

There is also a second way to solve for y: An exterior angle of a triangle is equal to the sum of the opposite interior angles. y, in this case, would be the exterior angle and 35 and 25 degrees would measure the opposite interior angles. To solve for y, we just add 35 and 25, getting us 60 degrees.

I hope this helps!

The correct answers are:

1) 1/2

2) 1/10

3) 3/4

Step-by-step explanation:

\(\boxed{50=0.5\\}\\\boxed{10=0.1\\\\\\} \boxed{75=0.75}\)

50% means 0.5. This 0.5 was (multiplied before by 100) to get this percentage.

Therefore, the answer is true

Answer:

A. 78

Step-by-step explanation:

7 x 4 is the bottom and the bottom is the same as the top so I got 28 x 2 which is 56. 4 x 1 is one side. The other side is the same so I got 4 x 2 which is 8. 1 x 7 is the front and back. I got 7 x 2 is 14. i wrote 56 + 14 + 8 and got 78

hope this helps :)

The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

Given,

When using re-grouping to solve 25 x 45, we have to find the problems that would be calculated to find the final answer;

Here,

25 × 45 = 1125

Now,

This is simply multiplicity;

1. 20 x 40: 20 x 5: 40 x 5

800 ; 100 ; 200

1100

This is not the problem.

2. 20 x 40; 5 x 40; 20 x 5 ; 5 x 5

800 ; 200 ; 100 ; 25

1125

This is the problem

3. 20 x 40 ; 5 x 20 ; 20 x 5 ; 5 x 5

800 ; 100 ; 100 ; 25

1025

This is not the problem

4. 20 x 20 ; 40 x 40 ; 20 x 5 ; 5 x 5

400 ; 1600 ; 100 ; 25

2125

This is not the problem

Therefore,

The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

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Answer:

$12.50

Step-by-step explanation:

25 (bookmarks) x $0.50(price) = $12.50(profit)

Answer:

$12.50

Step-by-step explanation:

hope it hels u

plzz plzz plzz mark as brainliest

Angle L's in the triangle LMN is,

⇒ L = 72.54°

We have to given that;

A triangle LMN is shown in figure.

And, The sides are,

Since, We know that;

A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Since, We know that;

⇒ sin L = Opposite / Hypotenuse

And, cos L = Base / Hypotenuse

Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, We can use trigonometry formula to find the value of angle l we get;

⇒ sin L = Opposite / Hypotenuse

⇒ sin L = LM / LN

⇒ sin L = 18/60

Taking arc sin both side, we get;

⇒ L = 72.54°

Therefore, The value of measure of angle L is triangle LMN is,

⇒ L = 72.54°

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Cody will need to paint 1600 square inches of surface area on the box for his art project.

Given that:

Length, L = 20 in

Width, W = 20 in

Height, H = 10 in

The surface area of each face can be calculated as follows:

Top and bottom faces: Length * Width = 20 in * 20 in = 400 in² each.

Front and back faces: Length * Height = 20 in * 10 in = 200 in² each.

Side faces: Width * Height = 20 in * 10 in = 200 in² each.

Now, let's calculate the total surface area:

Total surface area = 2 * (top and bottom) + 2 * (front and back) + 2 * (sides)

Total surface area = 2 * 400 in² + 2 * 200 in² + 2 * 200 in²

Total surface area = 800 in² + 400 in² + 400 in²

Total surface area = 1600 in²

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The complete question is given below:

Cody is painting the box shown for part of his art project. If he paints all of the surfaces, how many square centimeters will he paint? Use the net to find the surface area of the right rectangular prism.

Length, L = 20 in

Width, W = 20 in

Height, H = 10 in

The equation (i), (ii), and (v) are the equivalent.

What is the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

We have,

2 + x = 5

x + 1 = 4

9 + x = 6

x + (-4) = 7

-5 + x = -2

If we take x =3,

the sums would be true.

for the equation (i) take x = 3,

2 + x = 5

2 + 3 = 5

LHS = RHS = 5

for equation (ii) take x = 3,

x + 1 = 4

3 + 1 = 4

LHS = RHS = 4

for equation (iii) take x = 3,

9 + x = 6

9 + 3 = 6

12 ≠ 6

LHS ≠ RHS

for the equation (iv) take x = 3,

x + (-4) = 7

3 + (-4) = 7

-1 ≠ 7

LHS ≠ RHS

for the equation (v) take x = 3,

-5 + x = -2

-5 + 3 = -2

-2 = -2

LHS = RHS = -2

Hence, if If we take x =3, the sums would be true. the equation (i), (ii), and (v) are the equivalent.

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Answer:

x=20, Angles are 70° and 110°

Step-by-step explanation:

Angles are supplementary, so their sum is 180°

5x-30+x+90 = 180

6x+60 = 180

6x = 180-60

6x = 120

x = 20

5x-30 = 5*20 - 30 = 100 -30 = 70°

x+90 = 20 + 90 = 110°