Cormac uses milk and water when he makes tea. He
makes sure to never have more than 2 cups of milk and
water combined. He also likes the amount of milk to be
less than the amount of water. He writes the system
of inequalities shown below to represent this situation.
x+y≤2
x< ½ y
The point (1) is a solution to Cormac's system of
inequalities. Which statement explains what the point
(1) represents?
Cormac could use
oup of mik and
Cormac could use
cup of milk and
Smes as much
water
Cormac could use
cup of milk and
cups of water,
Cormac could ve
cup of milk
mixture with a lotal of
1

Answer:

To solve this problem, we can set up a proportion:

9.5 cups of flour / 18 cookies = 15 cups of flour / x cookies

To solve for x, we can cross-multiply:

9.5 cups of flour * x cookies = 18 cookies * 15 cups of flour

Dividing both sides by 9.5 cups of flour gives us:

x cookies = 18 cookies * 15 cups of flour / 9.5 cups of flour

x cookies ≈ 28.42

Since we can't make a fraction of a cookie, we'll round down to the nearest whole number. Therefore, Lan can make about 28 cookies with 15 cups of flour using the same recipe.

The correct slope and y-intercept for the linear equation y=2x+7 are 2 and 7, respectively.

The y-intercept of a graph is the point where the graph crosses the y-axis. It is written as (0, b), where b is the y-intercept. The y-intercept is the value of y when x is equal to zero. It can be used to determine the equation of a line when two points on the line are known.

The slope of a linear equation is the coefficient of the x variable, which is 2 in this case. The y-intercept is the constant term, which is 7 in this case.

So, the slope is 2 and the y-intercept is 7.

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Answer:

8 - w

Step-by-step explanation:

In my opinion, an expression for eight minus w would be 8 - w. Thanks.

Hope it helps.

If the mean of x, y and z is 88 1/3% of 360. The range of x, y and z is 2,852.

To solve this problem, we need to use the given ratios and proportions to find the values of x, y, and z, and then use the given mean to find their range.

From the first ratio, we have:

x:y = 5:3

This can be written as:

x = (5/3) * y

Substituting this value of x into the second ratio, we get:

y:2 = 11:6

Multiplying both sides by 3, we get:

3y = 22

y = 22/3

Substituting this value of y into the equation for x, we get:

x = (5/3) * (22/3) = 110/9

To find z, we can use the mean of x, y, and z:

(1/3)(x + y + z) = (8/3) * 360

x + y + z = 2880

Substituting the values we found for x and y, we get:

(110/9) + (22/3) + z = 2880

Multiplying both sides by 9, we get:

110 + (66/3) + 9z = 25920

110 + 22 + 9z = 25920

9z = 25788

z = 2864

Therefore, the values of x, y, and z are:

x = 110/9

y = 22/3

z = 2864

To find the range, we need to subtract the smallest value from the largest value:

Range = z - x = 2864 - (110/9) = 2,852

Therefore, the range of x, y, and z is 2,852.

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The answer is ((81c^(8))/(16d^((32)/(5)))).

To simplify ((3c^(2))/(2d^((8)/(5))))^(4), we can use the power of a power rule and distribute the exponent of 4 to each term inside the parentheses.

((3c^(2))/(2d^((8)/(5))))^(4) = (3^(4))(c^(2*4))/(2^(4))(d^((8*4)/(5)))

Simplifying further, we get:

= (81)(c^(8))/(16)(d^((32)/(5)))

= (81c^(8))/(16d^((32)/(5)))

This is the simplified answer with no variables. It cannot be simplified further. Therefore, the answer is ((81c^(8))/(16d^((32)/(5)))).

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Answer: The inequality is:

1.2 + m ≤ 5.5

This inequality can be read as "the sum of 1.2 and m is less than or equal to 5.5."

To solve for m, you need to isolate it on one side of the inequality symbol.

1.2 + m ≤ 5.5

Subtract 1.2 from both sides:

m ≤ 5.5 - 1.2

Simplify:

m ≤ 4.3

Therefore, the solution to the inequality is m ≤ 4.3.

Step-by-step explanation:

The value of the expression c^(2)-5c+2 when c = 3 is -4.

Evaluating a quadratic expression involves substituting the given value of the variable into the expression and simplifying. In this case, we are given that c=3 and the expression is c^(2)-5c+2. We will substitute 3 in for c and simplify.

Step 1: Substitute 3 in for c: (3)^(2)-5(3)+2
Step 2: Simplify the expression: 9-15+2
Step 3: Combine like terms: -4

Therefore, the value of the expression when c=3 is -4.

A quadratic term is any expression that has in its unknowns (in which letters are used) one that is squared (or two), these terms are part of a quadratic function.

For a term to be quadratic it must be multiplied by itself (twice), for example:

a² + a + 1

We can see that it is a quadratic function and that its literal term is a while the quadratic term is a², i.e. a*a.

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Answer:

Step-by-step explanation:23.80*34=809.20

Answer:

66%

Step-by-step explanation:

"of the" something = means denominator of a fraction

of the tickets sold = denomination here

question asked about child tickets , so child tickets = numerator here

what percentage? = fraction x 100%

answer:

2640 / (2640+1360) x 100

The slope of the line in simplest form is 1/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = rise/run

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 + 5)/(9 - 0)

Slope, m = 3/9

Slope, m = 1/3

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Hence, the shape is rectangular prism with the dimensions 10mm, 8mm, and 8mm has a surface area of 448mm2.

We must first calculate the surface area of each face of a rectangular prism with 10mm, 8mm, and 8mm measurements before adding them all up.

The top and bottom faces, which are both rectangles with measurements of 10 mm by 8 mm, are first measured for area:

Area of the top and bottom faces is equal to 2 (10 x 8 mm) or 160 mm2.

The area of the front and back faces, which are both rectangles measuring 10 mm by 8 mm, is then determined: Area of the front and back faces is equal to 128mm2 (8mm x 8mm).

The area of the two side faces, which are both rectangles with dimensions of 10 mm by 8 mm, is then determined: Area of the side sides is equal to 2 (10mm x 8mm) = 160mm2.

We add up the areas of all the faces to determine the overall surface area:

Whole surface area equals the sum of the areas of the top and bottom faces, the front and back faces, and the side faces.

Surface area total = 160 mm2 + 128 mm2 + 160 mm2

448 mm2 is the total surface area.

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Answer:

The answer is 13.

Step-by-step explanation:

First, we must find the hypotenuse for right angle:

[tex]c^{2} = a^{2} + b^{2}\\ \\\\c^{2} = 12^{2} + 5^{2} \\c^{2} 144 + 25 \\c^{2} = 169 \\c^{2} =\sqrt{169}\\c^{2} = 13[/tex]

Answer: a = 3, b = 2

Step-by-step explanation:

When a system of linear equations has no solution, they are parallel and do not share the same y-intercept.

Parallel lines have the same slope so a must equal 3.

The first equation's y-intercept is -2, so the only other option is b = 2.

Hope this helps!

The probability of A) 3 arrivals in an hour is approximately 0.1404, of B) at least 2 arrivals an hour is 0.918, of C) at most 1 arrival in an hour is 0.0821, and of D) no arrivals in an hour is 0.0067.

a. The probability of 3 arrivals in an hour can be calculated using the Poisson distribution formula: [tex]P(X = 3) = (e^{-5} * 5^3) / 3! = 0.1404[/tex]

b. The probability of at least 2 arrivals in an hour can be calculated by finding the complement of the probability of 0 or 1 arrival: [tex]P(X \geq 2) = 1 - P(X = 0) - P(X = 1) = 1 - e^{-5} * (5^0 / 0!) - e^{-5} * (5^1 / 1!) = 0.918[/tex]

c. The probability of at most 1 arrival in an hour can be calculated by adding the probabilities of 0 and 1 arrival: [tex]P(X \leq 1) = P(X = 0) + P(X = 1) = e^{-5} * (5^0 / 0!) + e^{-5} * (5^1 / 1!) = 0.0821[/tex]

d. The probability of no arrivals in an hour can be calculated by using the Poisson distribution formula: [tex]P(X = 0) = e^{-5} * (5^0 / 0!) = 0.0067[/tex]

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The area of the triangle with the given vertices is 4.47.

To find the area of the triangle with the given vertices, we can use the formula:
Area = (1/2) * |(B-A) x (C-A)|
Where "x" represents the cross product of two vectors.
First, we need to find the vectors B-A and C-A:
B-A = (1-5, 1-(-1), 0-(-2)) = (-4, 2, 2)
C-A = (3-5, 2-(-1), -1-(-2)) = (-2, 3, 1)
Next, we need to find the cross product of these two vectors:
(B-A) x (C-A) = (2*1 - 2*3, 2*(-2) - (-4)*1, (-4)*3 - 2*(-2)) = (-4, 0, -8)
Finally, we can find the area of the triangle by plugging in the values into the formula:
Area = (1/2) * |(-4, 0, -8)|
Area = (1/2) * √((-4)^2 + 0^2 + (-8)^2)
Area = (1/2) * √(80)
Area = (1/2) * 8.94
Area = 4.47
Therefore, the area of the triangle with the given vertices is 4.47.

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Answer:

42 minutes are not spent on instructions

Step-by-step explanation:

First, we must find out how many minutes is in [tex]\frac{7}{8}[/tex] hour

[tex]60*\frac{7}{8}=\frac{60*7}{8} =\frac{420}{8} =52.5[/tex]

In [tex]\frac{7}{8}[/tex] hour, there is about 52 [tex]\frac{1}{2}[/tex] minutes

Then we must add up the fractions that are NOT the instructions

[tex]\frac{1}{2} +\frac{3}{10} =\frac{5}{10} +\frac{3}{10} =\frac{8}{10} =\frac{4}{5}[/tex]

[tex]\frac{4}{5}[/tex] of the total time (52 [tex]\frac{1}{2}[/tex] minutes) is not spent on instructions

Then we must multiply the fraction of time spent on other things ([tex]\frac{4}{5}[/tex]) by total time (52 [tex]\frac{1}{2}[/tex] minutes) in order to find out how many minutes weren't spent on instructions.

[tex]\frac{4}{5}*52 \frac{1}{2} =\frac{4}{5}* \frac{105}{2}=\frac{420}{10} =42[/tex]

42 minutes are not spent on instructions

The solutions to the given equations are T1 = 0.2 and T = 4.5.

To solve the given equations, we will use algebraic methods to isolate the variable on one side of the equation.

First, let's solve the equation 0.2=1−(1−T1​).

0.2 = 1 - (1 - T1)
0.2 = 1 - 1 + T1
0.2 = T1

So, T1 = 0.2

Next, let's solve the equation 30T=135.

30T = 135
T = 135/30
T = 4.5

So, T = 4.5

Therefore, the solutions to the given equations are T1 = 0.2 and T = 4.5.

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With an APR of 6.75% over a 20-year period, the annual payment for the loan will be $81,371.52.

To find the annual payment for the loan, we need to first find the total cost of the land and the amount of the loan.

Total cost of the land = 245 acres x $4,700/acre = $1,151,500

Down payment = 25% of total cost = 0.25 x $1,151,500 = $287,875

Loan amount = Total cost - Down payment = $1,151,500 - $287,875 = $863,625

Next, we need to use the loan amount, APR, and loan term to find the annual payment. We can use the following formula:

Annual payment = (Loan amount x APR) / (1 - (1 + APR)^(-Loan term))

Plugging in the values we have:

Annual payment = ($863,625 x 0.0675) / (1 - (1 + 0.0675)^(-20))

Annual payment = $58,294.69 / (1 - 0.2837)

Annual payment = $58,294.69 / 0.7163

Annual payment = $81,371.52

Therefore, the annual payment for the loan is $81,371.52.

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AB =

BC = 2x

T.P. =>

4x² = x² + 6²

3x² = 36

x² = 12

=> x = 2sqrt3

This is the final factored form of the original expression. = (4x^(2)-x-265)/((4(x-9)(x+6)))

To find the factored form of (x^(2)-64)/(x^(2)-3x-54)-(x^(2)-81)/(4x^(2)-12x-216), we will first factor each of the expressions in the numerator and denominator.

The factored form of x^(2)-64 is (x+8)(x-8).

The factored form of x^(2)-3x-54 is (x-9)(x+6).

The factored form of x^(2)-81 is (x+9)(x-9).

The factored form of 4x^(2)-12x-216 is (2x-18)(2x+12).

Now, we can substitute the factored forms back into the original expression:

((x+8)(x-8))/((x-9)(x+6))-((x+9)(x-9))/((2x-18)(2x+12))

Next, we will simplify the expression by canceling out common factors:

((x+8)(x-8))/((x-9)(x+6))-((x+9)(x-9))/(2(x-9)(2x+12))

= ((x+8)(x-8))/((x-9)(x+6))-(1/2)((x+9)/(2x+12))

= ((x+8)(x-8))/((x-9)(x+6))-(1/2)((x+9)/(2(x+6)))

= ((x+8)(x-8))/((x-9)(x+6))-(1/4)((x+9)/(x+6))

Now, we will find a common denominator and combine the two fractions:

= ((4(x+8)(x-8))-(x+9))/((4(x-9)(x+6)))

= ((4x^(2)-256)-(x+9))/((4(x-9)(x+6)))

= (4x^(2)-x-265)/((4(x-9)(x+6)))

This is the final factored form of the original expression.

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The area under the curve is 4.55 square units.

Here we have to find the area,

That lies under the curve y -x + 1 between x = 0 and x = 10

Therefore,

To estimate the area that lies under the curve y = -x + 1 between x = 0 and x = 10,

Use the Riemann Sum method,

Divide the interval [0, 10] into n subintervals of equal width,

And let Δx be the width of each subinterval.

Then, we can estimate the area under the curve as the sum of the areas of n rectangles with heights given by the function.

The formula for the Riemann Sum is,

⇒ Δx [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]

where Δx = (b-a)/n, a = 0, b = 10, and f(x) = -x + 1.

Let's choose,

n = 100 for a reasonably accurate estimate.

Then, Δx = (10-0)/100 = 0.1

Put it into the formula, we get.

⇒ 0.1[1 + 0.9 + 0.8 + ... + 0.1]

Evaluating the sum using the formula for the sum of an arithmetic series, we get:

⇒ 0.1(0.5)[2 + (99)(-0.9)]

Simplifying, we get,

⇒ 4.55

Therefore, the required area be 4.55 square units.

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Answer: 8.5 by 11 inches.

Step-by-step explanation:

The standard 8.5″ x 11″ or Letter size so prevalent in full sized notebooks.

Find a positive value of c so that the following trinomial is factorable. [tex]x^2-4x+c[/tex], The value of [tex]c[/tex] will be given by [tex]c=4[/tex].

To find a positive value of c so that the trinomial [tex]x^2-4x+c[/tex] is factorable, we need to use the formula for the sum of two squares. This formula states that [tex](a-b)^2=a^2-2ab+b^2[/tex].

In this case, we can let [tex]a=x[/tex] and [tex]b=2[/tex], so the formula becomes [tex](x-2)^2=x^2-4x+4.[/tex]

Comparing this formula to the given trinomial, we can see that the value of c must be 4 in order for the trinomial to be factorable.

Therefore, the positive value of c that makes the trinomial [tex]x^2-4x+c[/tex] factorable is [tex]c=4[/tex].

In factored form, the trinomial becomes [tex](x-2)^2[/tex].

Answer: [tex]c=4.[/tex]

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Using graph it is seen that the solution of the linear system  is found as (-1, 1).

The points for the two intersecting lines are-

Red points:  (0, 5), (-1, 1), and (-3, -6)

Green points: (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5).

Graph of there points are plotted.

Thus, it is seen that the solution of the linear system graphically  is found as (-1, 1).

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The correct question is-

Estimate the solution of the linear system graphically and check the solution algebraically:

A line graph showing 2 intersecting lines, the first line passes through the points (0, 5), (-1, 1), and (-3, -6) and the second line passes through the points (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5).

The volume of the cone in terms of π is [tex]90.312\ inches^{3}[/tex].

A cone is a three-dimensional body with a flat base that is connected to a pointed top.

The formula for the volume of a cone is :

[tex]Volume,V = \frac{\pi r^{2}H }{3}[/tex]

It is given that height, H = 15 inches.

The formula for the circumference of the base is = [tex]2\pi r[/tex]

So, we can say that :

[tex]2\pi r=8.5\pi[/tex]

[tex]r=\frac{8.5}{2} =2.25[/tex] inches

Therefore, the volume of the cone is, V:

[tex]=\pi \times 4.25^{2} \times 15\\ =90.312\ \text{inches}^{3}[/tex]

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c = 3.

a) A is linearly dependent for any value of c because the vectors are not linearly independent.

This means that one of the vectors can be written as a linear combination of the others.

For example, the vector (1,2,c) can be written as (2,2,0) + (-1,0,c-0) = (1,2,c).

This means that the set of vectors is linearly dependent.

b) For c = 0, Vector (A) is the set of all linear combinations of the vectors (2,2,0), (1,2,0), (0,0,0), and (1,0,0).

This means that Vect (A) is the set of all points in the xy-plane, or the set of all vectors in R^2.c).

To find all the values of c for which (4,1,3) is in Vect (A),

we need to solve the equation (4,1,3) = a(2,2,0) + b(1,2,c) + d(0,0,c) + e(1,0,0) for the scalars a, b, d, and e.

This gives us the system of equations:4 = 2a + b + e1 = 2a + 2b3 = bc + dc.

Solving this system of equations gives us the values of a, b, d, and e in terms of c.

We can then use these values to find the values of c for which (4,1,3) is in Vect (A).

After solving the system of equations, we find that c = 3 and a = 1, b = -1, d = 0, and e = 2.

Therefore, the value of c for which (4,1,3) is in Vect (A) is c = 3.

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Answer:

To express the value 0.0000547 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point.

0.0000547 = 5.47 × 10^(-5)

The exponent -5 indicates that we moved the decimal point 5 places to the right.

Step-by-step explanation:

I am going to assume this is a quadratic so

[tex]f(x) = {ax}^{2} + bx + c[/tex]

When 3 is c

[tex] {ax}^{2} + bx + 3[/tex]

When x is 7,

[tex]a( {7}^{2} ) + b(7) + 3 = 13[/tex]

[tex]49a + 7b = 10[/tex]

When x is 9,

[tex]a(9) {}^{2} + 9b + 3 = - 11[/tex]

[tex]81a + 9b = - 14[/tex]

We have two system, let's eliminate the b variable by multiplying the second system by

[tex] \frac{7}{9} [/tex]

[tex]63a + 7b = - \frac{98}{9} [/tex]

Bring down the first system

[tex]49a + 7b = 10[/tex]

Subtract the two system,

[tex]14a = \frac{ - 188}{9} [/tex]

[tex]a = - \frac{94}{63} [/tex]

Plugging in a, we will eventually get

[tex]b = \frac{748}{63} [/tex]

So our quadratic is

[tex] - \frac{94}{63} {x}^{2} + \frac{748}{63} x + 3[/tex]

Answer:

Below

Step-by-step explanation:

f(-5) = 85 * .95^(-5)   = 109.9 mg remaining after -5 hours   this does not fit the context of the problem  

 ( domain ( values of 'x')  should be   0 ---> infinity)

f(24) = 85 * .95^24 = 24.8 mg remaining after 24 hours   this does fit the context of the problem

Yes, the production manager should be concerned about production rate variations. Based on the data provided, the standard deviation of the daily production rate of fiberglass boats from Dhaka Glass is 4.6 boats, which is higher than the threshold of 3 boats a day set by the production manager. This indicates that there are significant variations in the production rate of fiberglass boats, which should be a cause for concern.

To further explain, the standard deviation measures the spread of a set of data. In this case, the data provided shows that the daily production rate of fiberglass boats can vary from 17 to 32 boats a day. The large standard deviation of 4.6 boats suggests that the daily production rate can vary significantly from the average, and this can lead to instability in production.

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