Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup. How many grams of 25% sugar syrup did Samantha use?

[tex](3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13[/tex]

The required covariance between the variable and correlation coefficient are -2.8 and -0.38.

a. To calculate the covariance, we'll first find the mean of both variables, x and y:

mean of x = (11 + 13 + 27 + 22 + 30) / 5 = 20

mean of y = (28 + 26 + 25 + 20 + 16) / 5 = 22

Next, we'll find the deviations of each x and y value from their respective means:

x deviations: -9, -7, 7, 2, 10

y deviations: 6, 4, 3, -2, -6

Finally, we'll multiply the deviations of x and y for each pair of values and take the average of these products:

covariance = ( (-9 * 6) + (-7 * 4) + (7 * 3) + (2 * -2) + (10 * -6) ) / 5 = -2.8

So, the covariance between the variables x and y is -2.8.

b. To calculate the correlation coefficient, we'll divide the covariance by the standard deviation of x and y:

standard deviation of

x = [tex]\sqrt{\frac{(((11 - 20)^2 + (13 - 20)^2 + (27 - 20)^2 + (22 - 20)^2 + (30 - 20)^2)}{5} }[/tex] = 8.3666

standard deviation of

y = [tex]\sqrt{\frac{(((28 - 22)^2 + (26 - 22)^2 + (25 - 22)^2 + (20 - 22)^2 + (16 - 22)^2)}{5} }[/tex]= 3.87298

correlation coefficient = covariance / (standard deviation of x * standard deviation of y) = -2.8 / (8.3666 * 3.87298) = -0.381

So, the correlation coefficient between the variables x and y is -0.38.

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To derive the distribution of W, we need to find the cumulative distribution function (CDF) of W, F_W(w), and then find its probability density function (PDF), f_W(w).

a) The distribution of the random variable W = Y^2:

The cumulative distribution function (CDF) of W is given by F_W(w) = P(W <= w), where W is the random variable defined as W = Y^2.

Since Y has a uniform distribution on the interval (0,1), its CDF is given by:

F_Y(y) = 0, for y < 0.

= y, for 0 <= y <= 1.

= 1, for y > 1.

Therefore, the CDF of W = Y^2 is:

F_W(w) = P(Y^2 <= w)

= P(0 <= Y <= sqrt(w))

= F_Y(sqrt(w))

= sqrt(w), for 0 <= w <= 1.

= 1, for w > 1.

Thus, the CDF of W is a monotonically increasing function that maps the interval [0, 1] to [0, 1].

The probability density function (PDF) of W is given by f_W(w) = dF_W(w)/dw. The PDF of W can be found by differentiating the CDF:

f_W(w) = dF_W(w)/dw

= d(sqrt(w))/dw

= 1/(2*sqrt(w))

f_W(w) is defined only for 0 <= w <= 1.

b) The distribution of the random variable W = Y^(1/2):

The CDF of W = Y^(1/2) is given by F_W(w) = P(W <= w), where W is the random variable defined as W = Y^(1/2).

Using the same argument as in part (a), we have:

F_W(w) = P(Y^(1/2) <= w)

= P(0 <= Y <= w^2)

= F_Y(w^2)

= w^2, for 0 <= w <= 1.

= 1, for w > 1.

The PDF of W = Y^(1/2) can be found by differentiating the CDF:

f_W(w) = dF_W(w)/dw

= d(w^2)/dw

= 2w

f_W(w) is defined only for 0 <= w <= 1.

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Graph A is not a function as its ordered pairs have the same first coordinate for different y coordinates.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is not a function if two distinct ordered pairs have the same first coordinate, (a, b), (a, c) is not a function.

The graph of A has an x value of - 3 and has different y values hence it is not a function.

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Answer: B = 9 cm, C = 15 cm

Step-by-step explanation:

If the ratio of A to B to C is 2:3:5, we can write:

A = 2x

B = 3x

C = 5x

and all we have to do is solve for x.

Since we know A = 2x = 6, we have 2x = 6 and x = 3.

So for B we can plug in 3x = 3(3) = 9 cm

And for C we can plug in 5x = 5(3) = 15 cm

If you put these numbers in a ration, 6:9:15 and reduce as much as possible, you'll see you get 2:3:5.

Answer:uhhhh

Step-by-step explanation:

So yeah

A repeating decimal like 0.222222222..... is a rational number and can be written as the fraction 2/9

A stopping decimal like 0.22 is a rational number and can be written as the fraction 22/100 or 11/50

A non-stopping and non-repeating decimal like 0.1234567891011... or 0.121121112... is an irrational number can not be written as the fraction

The square root of a perfect square is a rational number and also a whole number.

The square root of a imperfect square is an irrational number.

Rational numbers are the numbers that can be expressed in the form of a ratio (i.e., P/Q and Q≠0) and irrational numbers cannot be expressed as a fraction. But both the numbers are real numbers and can be represented in a number line.

Given,

Fill in the blanks,

By the properties of irrational numbers,

Irrational numbers are non terminating and non-recurring decimal numbers and any square root that is not perfect root is irrational number.

Rational numbers the numbers that can be written as fraction.

Hence, rational, 2/9, 11/50, irrational, can not be written as fraction, perfect square and imperfect square are the words to fill in the blanks.

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The solution to the given equation 5x - 2 + x = 9 + 3x + 10 is x = 7.

Given the equation in the question;

5x - 2 + x = 9 + 3x + 10

Solve for x, first collect and add like terms

5x - 2 + x = 9 + 3x + 10

5x + x - 2 = 3x + 10 + 9

Add 5x and x

6x - 2 = 3x + 10 + 9

Add 10 and 9

6x - 2 = 3x + 19

Add 2 to both sides

6x - 2 + 2 = 3x + 19 + 2

6x = 3x + 21

Subtract 3x from both sides

6x - 3x = 3x - 3x + 21

3x = 21

Divide both sides by 3

3x/3 = 21/3

x = 21/3

x = 7

Therefore, the value of x is 7.

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Answer:

  no

Step-by-step explanation:

You want to know if the equation y = 3x +1/5 represents a proportional relation.

A proportional relation has the equation ...

  y = kx

for some constant of proportionality k.

The added constant +1/5 in the given equation means the relation is Not Proportional.

<95141404393>

Answer:

36 3/16

Step-by-step explanation:

63 1/2 -27 5/16

= 63 8/16 -27 5/16

= 36 3/16

Order of fractions from smallest to largest:

If sorted we first equate the denominator to 40.

21/40, 29/40, 34/40, 30/40, 32/40

So if sorted from smallest to largest, the order becomes:

21/40, 29/40, 3/4, 4/5, 17/20

If sorted we first equate the denominator to 35. it becomes:

40/35, 65/35, 84/35, 98/36, 37/35

So if sorted from smallest to largest, the order becomes:

37/35, 8/7, 13/7, 12/5, 14/5

If sorted we first equate the denominator to 30. it becomes:

20/30, 24/30, 12/30, 21/30, 27/30

So if sorted from smallest to largest, the order becomes:

2/5, 2/3, 7/10, 4/5, 9/10

If sorted we first equate the denominator to 30. it becomes:

126/30, 65/30, 125/30, 66/30, 39/30

So if sorted from smallest to largest, the order becomes:

13/10, 13/6, 11/5, 25/6, 21/5

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The average velocity is 0.1 meters per second.

The displacement of a body during a period of time divided by the passage of time yields the average velocity of the body during that period. Therefore, if a particle travels along a specific displacement vector AB between times t₁ and t₂, its average speed is:

Here we have

At time t in seconds, a particle's distance s(t), in cm, from a point is given in the table.  

t     0    3     6    10     13

s(t)  0   72   92   144  180    

As we know

Average velocity = [ Total distance ]/[ Total time]    

From the given table,

The total distance traveled up to t = 10, = 144 - 72 = 72

As we know 100 cm = 1 meter

=>  72 cm = 72 × 1/100 = 0.72 m

The total time from t = 3 to t = 10, = 10 - 3 = 7  

Average distance = 0.72/7 = 0.10 meter per sec  

Therefore,

The average velocity is 0.1 meters per second.  

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The lifeguard covered distance of 14 feet to save the victim. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, also referred to as "arithmetic operations," are said by mathematicians to be able to describe all real numbers. The four mathematical operations of division, multiplication, addition, and subtraction result in the terms quotient, product, sum, and difference, respectively.

We are given that a life guard is sitting 8 feet on the observation chair and he notices someone struggling at 6 feet beneath the pool.

So, the total distance he travelled is 8 + 6 = 14 feet

Hence, the lifeguard covered distance of 14 feet to save the victim.

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The function is positive in the interval of (-∞, -1). Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The intersection point of the curve and x-axis is at (-1, 0).

Then the function is positive in the interval of (-∞, -1) and the the function is negative in the interval of (-1, ∞).

Thus, the correct option is C.

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The required, we end up paying 60% of the original price.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
If an item is marked down by 25%, then its sale price is 75% of its original price.

If the sale offers an additional 20% off clearance items, then the final sale price is 80% of the sale price.

Multiplying these two percentages, we get:

Final price = 80% of 75% of the original price

Final price = 0.80 × 0.75 × original price

Final price = 0.6 × original price

So the final price that you pay is 60% of the original price.

Therefore, we end up paying 60% of the original price.

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Answer: Let's call the number of percussionists on the sideline "x".

Since the ratio of percussionists to marching instruments is 2 to 13, for every 2 percussionists, there are 13 marching instruments.

So the total number of band members is 2x + 13x = 15x.

We know that the total number of band members is 150, so we can write an equation to solve for x:

15x = 150

Dividing both sides by 15:

x = 10

So there are 10 percussionists on the sideline.

Step-by-step explanation:

Answer:

3 dollars for

Step-by-step explanation:

The cost of a donut is $0.5.

The cost of donut holes is $0.041

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 6 is an equation.

We have,

x = cost of a donut

y = cost of donut holes

Cleo:

$25 to purchase 2 bags of donut holes and 4 dozen donuts.

This can be written as,

(2 x 12)y + (4 x 12)x = 25

24y + 48x = 25 ______(1)

Gavin:

$20 to buy 4 bags of donut holes and 3 dozen donuts.

This can be written as,

(4 x 12)y + (3 x 12)x = 20

48y + 36x = 20 ________(2)

Now,

From (1) and (2),

Multiplying 2 on (1).

48y + 96x = 50

48y + 36x = 20

(-)     (-)       (-)

        60x = 30

             x = 30/60 = 1/2 = 0.5

Now,

24y + 48x = 25

Substituting x = 1/2

24y + 48 x 1/2 = 25

24y + 24 = 25

24y = 25- 24

y = 1/24

y = 0.042

Thus,

$0.5 = cost of a donut

$0.042 = cost of donut holes

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Answer: The statement "d. The total cost is $4,950.00 since $27.50×180 = $4,950.00" is incorrect.

The first step is to convert the dimensions of the floor from feet to yards. Since 1 yard = 3 feet, the length of the floor is 15 feet / 3 feet/yard = 5 yards, and the width of the floor is 12 feet / 3 feet/yard = 4 yards. The total area of the floor is 5 yards * 4 yards = 20 square yards.

The total cost per square yard for carpet and installation is $27.50 + $4.15 = $31.65.

The total cost for carpet and installation for the entire floor is 20 square yards * $31.65/square yard = $633.00.

So, the statement "b. The total cost is $633.00 since $31.65×20 = $633.00" is correct.

Step-by-step explanation:

The farmer should place the two fence pieces at an angle of 90 degrees (perpendicular) against the barn wall to maximize the area of the resulting triangular enclosure.

When all the sides are the same length, or when the object is genuinely a square, the area will be at its greatest for a given perimeter.

But a square is still a rectangle! Therefore, to find the length of each side if you know the perimeter, divide it by four. To get the area, multiply the length by the breadth.

For the problem, a right triangle with legs of equal length will have the maximum area among all right triangles with equal perimeter.

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The y - intercept of the graph is,  5

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 5) and (8, -2).

Now,

Since, The equation of line passes through the points (0, 5) and (8, -2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 2 - 5) / ( 8 - 0)

m = - 7 / 8

Thus, The equation of line with slope - 7/8 is,

⇒ y - 5 = - 7/8 (x - 0)

⇒ y - 5 = - 7/8x

⇒ y = - 7/8x + 5

Therefore, The y - intercept of the graph is,  5

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The expression for the number of sundaes shop owner needs to sell in September is 3x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, the ice cream shop owner wants to triple her sale of sundaes from August to September.

If the ice cream shop owner sold x sundaes in August, then she will sell

3×x=3x sundaes in September.

Therefore, number of sundaes shop owner sold in September is 3x.

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The solution for the given system of equation is (x, y, z) is = (0 , (3-4t) , t) by Gaussian elimination method.

In the question ,it is given that the system of equations are ,

3x + 3y + 6z = 9

x + y + 2z = 3

2x + 5y + 10z = 15

-x + 2y + 4z = 6

we have to solve the equations for x, y , z.

writing the given equations in augmented matrix form , we get

[tex]\left[\begin{array}{ccc}3&3&6\\1&1&2\\2&5&10\\-1&2&4\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}9\\3\\15\\6\\\end{array}\right][/tex]

Applying R₁ → 1/3R₁

[tex]\left[\begin{array}{ccc}1&1&2\\1&1&2\\2&5&10\\-1&2&4\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}3\\3\\15\\6\\\end{array}\right][/tex]

Apply R₂ → R₂ - R₁

[tex]\left[\begin{array}{ccc}1&1&2\\0&0&0\\2&5&10\\-1&2&4\\\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}3\\0\\15\\6\\\end{array}\right][/tex]

After applying more row operations in the above matrix ,to make the lower triangle matrix 0 ,we get ,

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&2\\0&0&0\\0&0&0\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}0\\3\\0\\0\\\end{array}\right][/tex]

The above result can be expressed as x = 0 and y + 2z = 3 .

So , the system of equations have infinite solutions .

So , the solution x, y, and z expressed in terms of the parameter t is

(0 , (3-2t) , t)  .

Therefore , the solution is (x, y, z) is = (0 , (3-2t) , t) .

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This question is incomplete. The complete question is

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x, y, and z in terms of the parameter t.)

3x + 3y + 6z = 9

x + y + 2z = 3

2x + 5y + 10z = 15

−x + 2y + 4z = 6

Therefore, the annual simple interest rate charged by the pawnbroker is 5%

To determine simple interest, divide the balance by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a percent of the principal amount.

Here,

To find the annual simple interest rate, we need to use the formula:

Simple interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate, and Time is the time period in years.

In this case, the Principal is $270, and the amount paid back is $276.75, which means the interest paid is:

Interest = Amount paid back - Principal = $276.75 - $270 = $6.75

The time period is 5/360 years, since there are 360 days in a year and Elisa had the loan for 5 days.

Plugging these values into the formula, we get:

$6.75 = $270 x Rate x 5/360

Solving for Rate, we get:

Rate = $6.75 / ($270 x 5/360) = 0.05 or 5%

Therefore, the annual simple interest rate charged by the pawnbroker is 5%

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The value of the angle m/G is 118 degrees

It is important to note that the sum of the angles in a triangle is equivalent to 180 degrees.

From the information given, we have that;

Add the angles, we get;

8x + 14 + 3x - 6 + x + 16 = 180

collect like terms

8x + 3x + x = 180- 14 + 6 - 16

add or subtract like terms, we get;

12x = 156

Make 'x' the subject of formula by dividing both sides by the coefficient

x = 156/12

Divide the values

x = 13

m/G = 8(13) + 14

m/G = 118 degrees

Hence, the angle is 118 degrees

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The domain of the given inequality is y>1.

What do you mean by inequality?

A fundamental idea in social justice theories is inequality, which is the state of not being equal, especially with regard to status, rights, and opportunities.

                              Due to the fact that it frequently has diverse meanings to different people, it can become confusing in public discourse. But there are some similarities as well.

y<√x+3+1

This equation is defined if

    x + 3 ≥ 0

     x ≥ -3

So, the domain of the given inequality is x>-3.

     √x+3 ≥ 0

     √x+3 + 1 ≥ 0 + 1

             y ≥ 1

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

So, the domain of the given inequality is y>1.

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A. The probability that a randomly selected person aged 40 years or older is female and smokes is 0.05841.

B. No, it would not be unusual to randomly select a person aged 40 years or older who is female and smokes.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

When given an event A and an event B, the conditional probability that A will occur given than B has occurred is calculated using this formula -

P(A|B) = P(A and B) / P(B)

Let A be that the person is female and B be that they smoke. It is known that P(B) = 0.295 and let P(A|B) = 0.198.

Use the formula for conditional probability -

0.198 = P(A and B) / 0.295

P(A and B) = 0.198 × 0.295

P(A and B) = 0.05841

The probability that a person aged 40 years or older is female and smokes would happen is 0.05841, which is not less than the usual benchmark of 0.05 to be considered unusual.

Therefore, no, this would not be unusual.

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Suppose there is a 29.5% probability that a randomly selected person aged 40 years or older is a smoker. In addition, there is a 19.8% probability that a randomly selected person aged 40 years or older is a smoker. A. What is the probability that a randomly selected person aged 40 years or older is female and smokes? B. Would it be unusual to randomly select a person aged 40 years or older who is female and smokes?

Answer:

-22

Step-by-step explanation:

-9x^0-13

=-9×1-13

=-9-13

=-22

Answer:

-22

Step-by-step explanation:

To solve the expression

Let's start by finding the value of 'x'

[tex] - 9 {x}^{0} - 13[/tex]

Hint: Any number raised to power 0 is always 1.

Therefore x⁰ = 1

let's rewrite the expression by substituting where x is with 1

[tex] - 9(1) - 13[/tex]

[tex] - 9 \times 1 = - 9[/tex]

[tex] - 9 -13 = - 22[/tex]

Answer:

60th term is 347

Step-by-step explanation:

This is an arithmetic sequence with common difference = -1 - (-7) = 5 - (-1) = 11 -5 = 6

The nth term for such a series is given by
aₙ = a₁ + d(n-1) where d = common difference and a₁ is the first term

Here d = 6, a₁ = -7

So

aₙ = -7 + 6(n-1)

aₙ = -7 + 6n-6

aₙ = 6n-13

60th term is

a₆₀ = 6(60) - 13 = 360 - 13 = 347

The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is​ R9,338.80.

The future payment to be made at the end of the seventh year is determined by computing the future values in two stages.

The first stage computes the future value before the payment at the end of the first year.  The second stage computes the future value for six years.  

The future value is computed by compounding the present value at an interest rate.

Current debt = R6,421,00

Compound interest rate = 11% per year

Compounding period = Quarterly

N (# of periods) = 4 quarters (1 year x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R6,421.00

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R7,156.98

Total Interest = R735.98

Future Value (FV) = R7,156.98

Payment in one year's time = R2,287.00

Balance = R4,869.98

N (# of periods) = 24 quarters (6 years x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R4,869.98

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R9,338.80

Total Interest = R4,468.82

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