help with this math questions

15 liters of the 10% acid solution must be used

55 liters of the 80% acid solution must be used

Let the volume of the 10% acid solution be x

Let the volume of the 80% acid solution be y

The combination of the two solutions gives 70 liters

x + y = 70..............................(1)

The 70 liters solution is equivalent to 65%

10x + 80y = 70(65)

10x + 80y = 4550..........................(2)

Make x the subject of the formula in equation (1)

x = 70 - y...............................(3)

Substitute equation (3) into equation (2)

10(70 - y) + 80y = 4550

700 - 10y + 80y = 4550

70y = 4550 - 700

70y = 3850

y = 3850/70

y = 55 liters

Substitute y = 55 into equation (3)

x = 70 - 55

x = 15 liters

16 ounces volume is equivalent to 473.176 milliliters.

To convert ounces (oz) to milliliters (ml), you can use the conversion factor of 1 oz = 29.5735 ml. So to convert 16 oz to ml, you would multiply 16 by 29.5735. This gives you the equivalent volume of 473.176 ml.

It's worth noting that the ounce is a unit of volume commonly used in the United States and the United Kingdom, while the milliliter is the standard unit of volume in the International System of Units (SI) and widely used across the world. It's important to use the correct unit of measurement when working with volumes in different contexts.

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The given expression:

The expression can be written as :

Take 9 common :

Since 3 x 3 = 9

Apply the property of factorization:

So, the expression can be written as :

So, the factorization is : 9(x + 3) (x - 3)

Answer :

To prepare a 1000 mL of a 1:32 ratio bleach solution, you would need to mix 31.25 mL of bleach with 968.75 mL of water.

To calculate the amount of bleach needed to make a 1000 mL solution, we can set up the following proportion:

1 part bleach / 32 parts water = X mL bleach / 1000 mL total solution

Cross-multiplying, we get:

32X = 1000

Solving for X, we get:

X = 1000 / 32 = 31.25 mL of bleach

Therefore, to prepare a 1000 mL 1:32 bleach solution, you would need to mix 31.25 mL of bleach with 968.75 mL of water.

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Answer:

√36 = 6

3√1,000 = 10

Answer: 192,000

Step-by-step explanation:

..

Answer:

x = 12 cm

y = 2 cm

Step-by-step explanation:

Length is G are 3 times the lengths in H.

Lengths in H are 1/3 the lengths in G.

x = 3 × 4 cm = 12 cm

y = 6 cm / 3 = 2 cm

Answer:

(2) 0.6

Step-by-step explanation: Common sense should tell you that Choices (3) and (4) might be approximate answers in kilometers per hour, not minute.

To change from miles to kilometers, multiply by 1.609. To change hours to minutes, divide by 60. 22.7 * 1.609 / 60 = 0.608..., which is approximately 0.6.

The 22.7 miles per hour in the km per hour is 0.6 km per minute option (2) is correct.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.

We have:

Sarah travels on her bicycle at a speed of 22.7 miles per hour.

The speed of the Sarah = 22.7 miles per hour

As we know:

1 miles per hour = 1.609 km per hour

and 1 hour = 60 minutes

22.7 miles per hour in km per minute:

= (22.7×1.609)/60

= 0.6 km per minute

Thus, the 22.7 miles per hour in the km per hour is 0.6 km per minute option (2) is correct.

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Statistical significance refers to the likelihood that the association between two variables is not due to chance alone. In other words, it is a measure of the probability that the observed relationship between two variables is real and not just a result of random variation or sampling error.

When analyzing data, researchers often use statistical tests to determine whether there is a significant association between two variables. A p-value is calculated, which represents the probability that the observed relationship between the variables is due to chance. If the p-value is less than a predetermined threshold (usually 0.05), the results are considered statistically significant, and the researchers can conclude that there is a real association between the variables. It's important to note that statistical significance does not necessarily imply practical significance. Just because a relationship is statistically significant does not mean that it is important or meaningful in real-world terms. Additionally, statistical significance only tells us about the strength of the relationship between two variables, not about causation or directionality. Therefore, it is always important to interpret statistical significance in the broader context of the research question and study design.

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The dimensions of the box that minimize the amount of material used are a square base with side length 4√2 cm and a height of 2√2 cm..

To minimize the amount of material used, we need to minimize the surface area of the box.
Let's call the height of the box "h" and the length of each side of the square base "x".
The volume of the box is given by V = x^2 * h = 32 cm^3.
We want to minimize the surface area, which consists of the area of the base (x^2) and the four sides (4xh). So the surface area is given by:
A = x^2 + 4xh
We can solve for h in terms of x using the volume equation:
h = 32 / x^2
Substituting this into the surface area equation, we get:
A = x^2 + 4x(32/x^2)
Simplifying this equation, we get:
A = x^2 + 128/x
To minimize the surface area, we need to find the value of x that makes the derivative of A with respect to x equal to zero:
dA/dx = 2x - 128/x^2 = 0
Solving for x, we get:
x = 4√2 cm
Substituting this value back into the equation for h, we get:
h = 2√2 cm
So the dimensions of the box that minimize the amount of material used are a square base with side length 4√2 cm and a height of 2√2 cm.

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the series is convergent or divergent. [infinity] k = 1 k2 k2 − 2k 9 convergent divergent if it is convergent, find its sum. (if the quantity diverges, enter diverges.) is convergent.

To determine whether the series is convergent or divergent, we can use the limit comparison test. We can compare the given series with the p-series 1/k^2, which is a known convergent series.

Using the limit comparison test, we have:

lim (k→∞) (k^2/(k^2-2k+9))/(1/k^2) = lim (k→∞) k^4/(k^2-2k+9)

Using L'Hopital's rule, we can evaluate the limit as:

lim (k→∞) 4k^3/(2k-2) = ∞

Since the limit is greater than zero, we can conclude that the given series converges if and only if the p-series 1/k^2 converges. Since the p-series converges, the given series also converges.

The series is convergent. However, we are not asked to find the sum of the series in this question.

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Infinite discontinuity

The given equation is:

The function will be undefined at the point x + 1 = 0

x = -1

This means that x = -1 is a point of discontinuity

Substituting x = -1 into the equation:

This is an infinite discontinuity

The total value of all the coins in Uncle Ralph's pocket is $3.35, which is represented by the number of each sort of coin.

addressing a problem by a method or action; giving a justification for the remedy. a number of different variable values that all agree with an equation, specifically The solution is any value of a variable in an equation that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal and so fulfills the equality. The act of solving an equation entails locating its solution or solutions. One approach to express a solution's concentration is as a percentage of a solute in the solvent. The mass of the solute to the mass of the solution ratio or the mass of the solute to the mass of the solution ratio are two other ways to calculate the percentage.

given

q represents the number of quarter

17 - q represents the number of dimes

0.25q + 0.10(17 - q) = 3.35

The total value of all the coins in Uncle Ralph's pocket is $3.35, which is represented by the number of each sort of coin.

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An approximate size which does not represent any of the actual dimensions of the unit is nominal value.

The phrase "nominal number" is said to be quite new and rarely used. It seems to have come from the statistical phrase "nominal data," which is reportedly defined as data revealing "...merely declarations of qualitative category of membership," as it is used in school textbooks. The meaning of the word "nominal" in this use is "name."

Nominal numbering is mathematically a one-to-one and onto function from a set of named objects to a set of numbers, which may change (typically growing) over time. It is a function because each named object is assigned a single number; it is one-to-one because different objects are assigned different numbers; and it is onto because every number in the set at a given time has a single named object associated with it.

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Answer:

For part A, you could decompse the figure into a rectangle and two triangles.

for Part B, its the first one.

Step-by-step explanation:

If you split up the figure into two parts then you will get 2 triangles and a rectangle. The area of 1 triangle is

A=1/2xbh

but there are two triangles so it would be 2(1/2x bh).

you can then multiply tht by the areaof the rectangle and get

2(1/2x12*5)+(16*12)

The integral ∫₀¹ \([(7te^{5t^2})i + (e^{-6t})j + (1)k]\) dt evaluates to (1/10)e - \((1/36)e^{-36}\) + t + C, where C is the constant of integration.

To evaluate the given integral, we need to integrate each component separately. Let's start with the i-component. The integral of 7te^(5t^2) with respect to t can be solved using the u-substitution method, where u = 5t^2 and du = 10t dt. After substituting, we get (1/10)∫e^u du, which simplifies to (1/10)e^u. Plugging back in the original variable, we have (1/10)e^(5t^2) for the i-component.

Moving on to the j-component, we have the integral of e^(-6t). This integral can be evaluated directly using the power rule for integration, giving us (-1/6)e^(-6t) for the j-component.

Lastly, the k-component is a constant, so its integral is simply tk + C. Since we are integrating from 0 to 1, the k-component evaluates to 1.

Putting it all together, we have (1/10)e^(5t^2)i - (1/6)e^(-6t)j + tk + C. Evaluating the limits of integration, we get (1/10)e - (1/36)e^(-36) + t + C. The constant of integration, C, represents the arbitrary constant that appears when integrating, and its specific value would depend on additional information or initial conditions given in the problem.

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Answer:  480 and 253.2

Step-by-step explanation:

For the first one we want to do (12 x 5 / 2) x 16 which equals 480.

For the next question, the answer is 253.2 because 2πrh is the formula of lateral area. If we just plug in the numbers it's (2 x 3.14 x 4.8 x 8.4) = 253.2cm

Answer:4

Step-by-step explanation:

The Mean Absolute Deviation is 4 from the data given

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

The slope of the line that contains these points is 0.75.

The slope of a line is the change in y-values divided by the change in x-values. In other words, it is the rise over the run. We can use the points given to calculate the slope.

Let's take the first two points (9, -24) and (13, -21) and use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

slope = (-21 - (-24)) / (13 - 9)

slope = (3) / (4)

slope = 0.75

We can do the same with the other two points (17, -18) and (21, -15):

slope = (-15 - (-18)) / (21 - 17)

slope = (3) / (4)

slope = 0.75

Since the slope is the same for both sets of points, we can conclude that the slope of the line that contains these points is 0.75.

The slope of the line that contains these points is 0.75.

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Answer:

x = 55, y = 70, z = 125

Step-by-step explanation:

125 and x are adjacent angles and are supplementary, then

x = 180 - 125 = 55

The triangle is isosceles ( 2 congruent sides ) thus the base angles are congruent, both 55

The sum of the 3 angles in the triangle = 180° , thus

y = 180 - (55 + 55) = 180 - 110 = 70

55 and z are adjacent and supplementary, so

z = 180 - 55 = 125

Answers:

x = 55

y = 70

z = 125

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

Explanation:

The tick marks indicate those two lines are the same length. We have an isosceles triangle. One base angle is x. The other missing base angle is also x, which is adjacent to angle z. The base angles of any isosceles triangle are always congruent.

Since the 125 and x degree angle form a straight line, they must add to 180

x+125 = 180

x = 180-125

x = 55

We can use this to find y

x+x+y = 180 .... three angles of any triangle always add to 180

2x+y = 180

2(55)+y = 180 .... plug in x = 55

110+y = 180

y = 180-110

y = 70

And,

x+z = 180

55+z = 180 ... plug in x = 55

z = 180-55

z = 125

Starting with the least likely event, the chances of a politician fulfilling all his or her campaign promises can be quite low due to the complexities of politics and the potential for unforeseen circumstances.

Next, while full moons are relatively common, they occur approximately once a month, making it more likely than the politician's scenario but less likely than the other events.

Rolling a die and getting a 6 has a higher likelihood as there is a 1 in 6 chance of rolling a 6 on a fair six-sided die. The safe arrival of a person in New York City from Chicago is more probable than the previous events but still has an element of uncertainty regarding the fate of their luggage.

Randomly selecting an ace from a regular deck of 52 playing cards has a higher probability compared to the previous events, as there are four aces in a deck. The likelihood increases further when randomly selecting the queen of hearts, which is only one specific card out of the 52-card deck.

Finally, selecting a black card from a regular deck has the highest probability among the listed events since there are 26 black cards in the deck, including all the clubs and spades.

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from Keith as Joaquin.

solve.

Answer:

x = - \(\frac{3}{2}\), x = 1

Step-by-step explanation:

Given

2x² + x - 1 = 2 ( subtract 2 from both sides )

2x² + x - 3 = 0 ← in standard form

(2x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - \(\frac{3}{2}\)

x - 1 = 0 ⇒ x = 1

Answer:

x= -3/2 or 1

Step-by-step explanation:

2x^2 +x-1=2

2x^2 +x-3=0

(2x+3)(x-1)=0

2x+3=0   x-1=0

2x= -3     x=1

x= -3/2    x=1

Matrix A represents the amount of each type of material required for each plant when multiplied with the matrix from part (a).

Let's create a matrix A to represent the amount of each type of material required for each plant.

The columns of matrix A represent the different types of materials (plush, stuffing, trim), and the rows represent the different types of animals (Giant Pandas, Saint Bernard, Big Birds). The entries in the matrix represent the amount of each material required for each animal.

| 1.5   30   5  |

| 2     35   8  |

| 2.5   25   15 |

By multiplying matrix A with the matrix from part (a) (representing the number of animals produced in each plant), we will obtain a matrix representing the amount of each type of material required for each plant.

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The number that can each terms of the equation be multiplied by to eliminate the decimals before solving is 100

The equation is

5.6j + 0.12 = 4 + 1.1j

The equation is defined as the mathematical expression that shows the relationship between one expression and another expression with equal sign. The equation consist of mathematical operator like addition, subtraction, division and multiplication

The equation is

5.6j + 0.12 = 4 + 1.1j

Here three term has fractional part.

In 0.12 there are two digits after the decimal point to eliminate the decimal number we have to multiply the number with 100 .

Then the equation will become

560j + 12 = 400 + 110j

Therefore, the number is 100

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The given question is incomplete, the complete question is

Which number can each term of the equation be multiplied by to eliminate the decimals before solving?

5.6j + 0.12 = 4 + 1.1j