How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a 45% solution of acid?

Answer:

The answer is 1 inch per second

Answer:

i think its the last one

Step-by-step explanation:

i think its the last on ig

The true statements from the given statements are -

Two triangles are congruent when they have exactly the same three sides and exactly the same three angles.

Given is a triangle as shown in the image.

It is clear that the measure of ∠MNP is less than ∠ONP as

∠MNP = 38°  <   ∠ONP = 39°

The line NP ≅ NP as it is common to both sub - triangles and has same length.

OP > PM since ∠ONP = 39° > ∠MNP = 38°

Therefore, the true statements from the given statements are -

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Answer:

Instructions are below.

Step-by-step explanation:

Giving the following information:

Fixed costs= 4,000 + 10,000= $14,000

Unitary variable cost= $5.5

Selling price= $7.2

To calculate the number of units to be sold to break-even, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 14,000 / (7.2 - 5.5)

Break-even point in units= 8,235 units

In dollars:

Break-even point (dollars)= fixed costs/ contribution margin ratio

Break-even point (dollars)= 14,000 / (1.7/7.2)

Break-even point (dollars)= $59,294

Now, imagine the company requires a profit of $50,000:

Break-even point in units= (fixed costs + desired profit) / contribution margin per unit

Break-even point in units= 64,000/1.7

Break-even point in units= 37,647 units

Break-even point (dollars)= (fixed costs + desired profit) / contribution margin ratio

Break-even point (dollars)= 64,000 / (1.7/7.2)

Break-even point (dollars)= $271,059

Answer:

r < 3

Step-by-step explanation:

Step 1: Write out inequality

5r + 2 < 17

Step 2: Subtract 2 on both sides

5r + 2 - 2 < 17 - 2

5r < 15

Step 3: Divide both sides by 5

5r/5 < 15/5

r < 3

In this case, r has to be smaller than 3. So anything like -2, -15, or even -12413573875942 works as r, as long as it's smaller than 3.

Answer:

Scaline Triangle

Step-by-step explanation:

All sides are different. So it is known as Scaline triangle. If only two sides are equal then it is isosceles triangle and if all sides are equal then ut us equilateral triangle.

If the columns of matrix B are linearly dependent, then the columns of AB are also linearly dependent.

Suppose the columns of matrix B are linearly dependent, which means there exist constants c₁, c₂, ..., cₙ (not all zero) such that c₁b₁ + c₂b₂ + ... + cₙbₙ = 0, where b₁, b₂, ..., bₙ are the columns of B.

Now, let's consider the product AB. Suppose A is an m × n matrix.

The jth column of AB is given by the product AB(:, j) = A(b₁j) + A(b₂j) + ... + A(bₙj), where b₁j, b₂j, ..., bₙj are the jth columns of B.

Substituting the linear dependence relation for the columns of B into the expression for AB(:, j), we get:

AB(:, j) = A(c₁b₁ + c₂b₂ + ... + cₙbₙ)

         = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

Since matrix multiplication distributes over column vectors, we have:

AB(:, j) = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

This shows that the jth column of AB can be expressed as a linear combination of the columns of A, multiplied by the corresponding coefficients c₁, c₂, ..., cₙ. Therefore, if the columns of B are linearly dependent, the columns of AB are also linearly dependent.

In conclusion, if the columns of matrix B are linearly dependent, then so are the columns of the product AB.

Complete Question:

Show that if the columns of B are linearly dependent, then so are the columns of AB.

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Answer:

Step-by-step explanation:

1, sec theta  * sin theta = 1/cos * sin = sin/cos =tan theta

2. cosec theta * cos theta = 1/ sin * cos = cos/sin = cot theta

3, tan theta * cosec theta =sin/cos * 1/sin = 1/cos

4, cot theta * sec theta = cos /sin * 1/cos= 1/sin

5, 1 - cos^2 theta = sin ^2 theta

6, sec^2 theta - 1 =tan ^2 theta

7 , cosec^2 theta - cot^2 theta = 1

8, 1 - sin^2 theta = cos^2

please mark me as the brainliest.........please

Answer

0.6

Step-by-step explanation:

here is the working out! Can i get brainliest

Answer:

Look at the image!!

Step-by-step explanation:

Hope this helps!!

Sorry for the bad righting XD

If you want to learn more search Mathisfun.com!!

Answer:

B

Step-by-step explanation:

1/5 as a a decimal would be 0.20 because if you multiply 0.20 by 5 you get 1

Answer:

B

Step-by-step explanation:

First convert \(\frac{1}{5}\) to a decimal : 0.2

y represents how many strawberries Zoe ate

x represents how many strawberries Nora ate

If you take the equation- y = 0.2x and plug how many strawberries Nora ate you would claculate how many Zoe ate.

       For example: say Nora ate 10 strawberries the equation would be- y(how many strawberries Zoe ate) = 0.2 · 10 ( the naumber of strawberries Nora ate)

I hope this help :)

Answer:

b^5

Step-by-step explanation:

Answer:

The answer will be b5

Step-by-step explanation:

Multiply b-6 by b11 by adding the exponents

Answer:

0.18

Step-by-step explanation:

Answer:

-5/6, -2/5, 2/5, 5/6

Step-by-step explanation:

put the fractions in your calculator and then click the fraction to decimal button and press enter.

Answer:

Number c

Step-by-step explanation:

Because the bottom denomonator matches up with the highest expression, and then you have to add up the X and Y values to each other to get youre answer.

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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The number of students received the text message at 10 am is 25 and at 11 am is 125.

Given,

Lets solve this using exponential expressions;-

Number of students received same text message at 9 am = 5¹ = 5

At 10 am each of this 5 students send the same text message to another 5 students;

That is, 5 x 5 = 5² = 25

Now,

At 11 am  each of this 25 students send the same text message to another 5 students;

So, 5 x 5 x 5 = 5³ = 125

Therefore,

The number of students received the text message at 10 am is 25 and at 11 am is 125.

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Using the rules of complementary angles we calculate that the value of x is  12° .

Pairs of complementary angles have measures which are one right angle.

The two given angles are 29° and ( 5x + 1 )°.

There are a pair of complementary angles.

Therefore 29° + ( 5x + 1 )° = 90 °

or, 5x + 30° = 90 °

or, 5x = 60

or, x = 12°

Therefore using the rules of complementary angles we calculate the value of x is 12°.

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The area of the one rectangular panel is equal to 220 ft².

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Generally speaking, the opposites sides of a rectangle are equal;

DN = WF

12x + 4 = 20x - 8

20x - 12x = 8 + 4

8x = 12

x = 3/2.

Side DN = 12x + 4 = 12(3/2) + 4 = 22 feet.

DW = NF

5y - 5 = 2y + 4

y = 3

Side DW = 5y - 5 = 5(3) - 5 = 10 feet.

Area of rectangular panel = DN × DW

Area of rectangular panel = 22 × 10

Area of rectangular panel = 220 ft².

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Answer:

2 1/3 ; 9 1/3

Step-by-step explanation:

Given that:

Outside temperature increases by 3 1/2 degrees every 1 1/2 hours

The rate per hour of temperature increase will be :

Let rate per hour = x

3 1/2 = 1 1/2

x = 1

Cross multiply :

1 1/2 * x = 3 1/2 * 1

3x/2= 7/2

Multiply both sides by 2/3

3x/2 * 2/3 = 7/2 * 2/3

x = 14/ 6

x = 2 2/6

x = 2 1/3

Hence, outside temperature increases at the rate of 2 1/3 degrees per hour.

2.) Temperature increase after 4 hours :

(Temperature rate per hour * number of hours)

(2 1/3) * 4

(7/3) * 4

28 / 3

= 9 1/3

Hence, temperature increase after 4 hours = 9 1/3

2 1/3 ; 9 1/3

Step-by-step explanation:

Given that:

Outside temperature increases by 3 1/2 degrees every 1 1/2 hours

The rate per hour of temperature increase will be :

Let rate per hour = x

3 1/2 = 1 1/2

x = 1

Cross multiply :

1 1/2 * x = 3 1/2 * 1

3x/2= 7/2

Multiply both sides by 2/3

3x/2 * 2/3 = 7/2 * 2/3

x = 14/ 6

x = 2 2/6

x = 2 1/3

Hence, outside temperature increases at the rate of 2 1/3 degrees per hour.

2.) Temperature increase after 4 hours :

(Temperature rate per hour * number of hours)

(2 1/3) * 4

(7/3) * 4

28 / 3

= 9 1/3

Hence, temperature increase after 4 hours = 9 1/3

I know because i am in the future

Answer:

cost price of a table=$9000

profit%=20%

Let profit be x

to find profit use formula,

profit%=profit/cost price*100

20%=x/$9000*100

20*$9000=100x

$180000/100=x

$1800=x

Now to find selling prie os a table use formula,

cost price +profit

$9000+$1800

$91800

therefore selling price of a table is $91800

Step-by-step explanation:

Hope this helps u!!

Answer:

B

Step-by-step explanation:

from ΔABC to ΔA'B'C' the lengths of all corresponding sides change by a scale factor of 1/2 (just look at the base and the height).  In other words, the transformed triangle,  ΔA'B'C', is half as big as the original triangle, ΔABC.  The corresponding angles are the same.

As per the distance concept, the speed of the buses are 79 km/h and 69km/h if the two buses leave a station at the same time and travel in opposite directions.

Distance

Distance refers the physical length or an approximation based on other physics or common usage considerations.

Given,

Two buses leave a station at the same time and travel in opposite directions. One bus travels 10 slower than the other. If the two buses are 276 miles apart after 2 hours,

Here we need to find the rate of each bus.

Let us consider the speed of the first bus is x km/h.

Then the speed of the other bus = (x - 10) km/h

We know the formula of distance is,

Distance = time × speed

When we combined speed then we get,

=> x + x - 10 = (2x - 10) km/h

=> 2(2x - 10) =276

When we expand the equation, then we get,

4x - 40 = 276

4x = 316

After calculating,

x = 79 km/h

The speed of first bus x = 79 km/h

Speed of the second bus = x - 10 = 79 - 10 = 69 km/h

Therefore, the speed of the buses are 79 km/h and 69/km/h if the two buses leave a station at the same time and travel in opposite directions.

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The interval of convergence is (-18/5, 18/5).

To express f(x) as a power series, we first need to decompose it into partial fractions:

f(x) = 11/(x^2 - 7x - 18) = 11/[(x - 9)(x + 2)]

Using partial fractions, we can write:

11/[(x - 9)(x + 2)] = A/(x - 9) + B/(x + 2)

Multiplying both sides by the denominator (x - 9)(x + 2), we get:

11 = A(x + 2) + B(x - 9)

Setting x = 9, we get:

11 = A(9 + 2)

A = 1

Setting x = -2, we get:

11 = B(-2 - 9)

B = -1

Therefore, we have:

f(x) = 1/(x - 9) - 1/(x + 2)

Now, we can write the power series of each term using the formula for a geometric series:

1/(x - 9) = -1/18 (1 - x/9)^(-1) = -1/18 * sigma^n=0 to infinity (x/9)^n

1/(x + 2) = 1/11 (1 - x/(-2))^(-1) = 1/11 * sigma^n=0 to infinity (-x/2)^n

So, putting everything together, we get:

f(x) = 1/(x - 9) - 1/(x + 2) = -1/18 * sigma^n=0 to infinity (x/9)^n + 1/11 * sigma^n=0 to infinity (-x/2)^n

The interval of convergence can be found using the ratio test:

|a_n+1 / a_n| = |(-x/9)^(n+1) / (-x/9)^n| + |(-x/2)^(n+1) / (-x/2)^n|

= |x/9| + |x/2|

= (|x|/9) + (|x|/2)

For the series to converge, we need |a_n+1 / a_n| < 1. This happens when:

(|x|/9) + (|x|/2) < 1

Solving for |x|, we get:

|x| < 18/5

Therefore, the interval of convergence is (-18/5, 18/5).

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In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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The seamstress can cover a banner of **72 square inches** with the fabric.

The length of the fabric is 2 yards, which is equal to 72 inches. The width of the fabric is 36 inches. To find the size of the banner that the seamstress can cover with the fabric, we need to multiply the length and width.

```

72 inches * 36 inches = 2592 square inches

```

Therefore, the seamstress can cover a banner of 2592 square inches with the fabric.

Here is an explanation of the steps involved in finding the answer:

1. We convert the length of the fabric from yards to inches.

2. We multiply the length and width of the fabric.

3. We simplify the result to get the size of the banner in square inches.

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Answer:

1,428.36$

Step-by-step explanation:

The balance after 5 years when the interest is compounded quarterly is  $5,593.60

Compound Interest:

Compound interest is the principal plus interest on a loan or deposit, or in other words, principal plus interest. It is the result of reinvesting interest, or adding it to the principal borrowed instead of paying it, or demanding payment from the borrower so that the next installment of interest is principal plus previously accrued interest. Compound interest is the norm in finance and economics.

Lets use the compound interest formula provided to solve this:

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 2.25% into a decimal:

2.25% > 2.25/100 > 0.0225

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

      \(A = (1+\frac{0.0225}{4} )4(5)\\\)

Or, A = 5593.60

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