Solve the equation.

3(k−6) = 15

k = ____?

To find out how many servings are in a 15 cup bag of pasta when serving size is 3/4 cup per person, divide 15 by 3/4, which equals 20 servings.

Firstly, convert the mixed fraction into an improper fraction for easier division: 3/4 remains the same since it is already a proper fraction.

Now, carry out the division: 15 ÷ (3/4)
= 15 × (4/3) (You multiply by the reciprocal of 3/4)

Then, multiply the numbers:
= 15 × 4 ÷ 3
= 60 ÷ 3
= 20

Therefore, there are 20 servings in a 15 cup bag of pasta when the serving size is 3/4 cup per person.

Answer:

So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)

Step-by-step explanation:

When you graph all of the constraint functions, the vertices of the shape that is made are at the points above. Now you plug those points into the function equation C=5x-4y and see where you get a max or min.

(0,1)

(1.5,1.5)

(0,0)

(3,0)

(1,1)=C=1

(1.5,1.5)=C=1.5

(0,0)=C=0

(3,0)=C=15

So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)

Final answer:

To find the value of k so that the line containing the points (-5,k) and (2,10) is parallel to the line containing the points (5,5) and (1,-4), we need to find the slope of the second line and use it to find the value of k.

Explanation:

To find the value of k so that the line containing the points (-5, k) and (2, 10) is parallel to the line containing the points (5, 5) and (1, -4), we need to find the slope of the second line and use it to find the value of k. Firstly, let's find the slope of the second line:

The formula we apply is the slope

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

slope = -9 / -4 = 9/4;

slope = (-4 - 5) / (1 - 5)

The lines now have the same slope since they are parallel.

So, the slope of the line passing through (-5, k) and (2, 10) should also be 9/4. We can find the slope using the formula:

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

Substituting the coordinates (-5, k) and (2, 10):

9/4 = (10 - k) / (2 - (-5))

By simplifying the equation, we get:

9 = 7(10 - k)

Now, let's solve for k:

90 - 9k = 63

-9k = 63 - 90

-9k = -27

k = 3

To find the probability that the average weight of four babies will be more than 7.5 pounds, we calculate the z-score and look it up in the standard normal distribution table. The probability is approximately 0.2843, or 28.43%.

To find the probability that the average weight of four babies will be more than 7.5 pounds, we need to calculate the z-score and look it up in the standard normal distribution table.

First, we convert the weight of 7.5 pounds to ounces: 7.5 pounds * 16 ounces = 120 ounces.

Next, we calculate the z-score using the formula: z = (x - &μ) / &σ, where x is the given weight, &μ is the mean weight, and &σ is the standard deviation. In this case, z = (120 - 112) / 14 = 0.571.

Finally, we can look up the probability using the z-score in the standard normal distribution table. The probability of the average weight of four babies being more than 7.5 pounds is approximately 0.2843, or 28.43%.

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The slope of a line perpendicular to the given line is -5/2.

The equation of the line given is 5y = 10 + 2x. To find the slope of this line, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m represents the slope. Dividing both sides of the equation by 5, we get y = 2/5x + 2. Comparing this equation to the slope-intercept form, we can see that the slope is 2/5.

To find the slope of a line perpendicular to this line, we use the fact that the product of the slopes of two perpendicular lines is -1. Therefore, the slope of the perpendicular line is the negative reciprocal of the slope of the given line. The negative reciprocal of 2/5 is -5/2.

Therefore, the slope of a line that is perpendicular to the line with the equation 5y = 10 + 2x is -5/2.

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We have that if the sin 30 degrees is 1/2 then the cos __60=1/2.__

Option C

Question Parameters:

The sin 30 degrees is 1/2

Generally, the Trigonometry of a right angle triangle gives values for sin, cos, tan.

Using the triangle we have that

if the sin 30 degrees is 1/2 then the cos60=1/2

Therefore, if the sin 30 degrees is 1/2 then the cos __60=1/2__.

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The expected number of ticket holders that will fail to show for the flight is 11.

Given that,

Based on the above information,

= 276%

= 2.76

Now the number of ticket holders who fail for presenting the flight should be

[tex]= 2.76\times 4[/tex]

= 11

Therefore we can conclude that the expected number of ticket holders that will fail to show for the flight is 11.

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The sum of three consecutive integers is 90. So you know that 3 numbers that are next to each other in numerical order equals 90.

First step: Make an equation:

Let's take x as the smallest of the three numbers.

[tex]x +(x+1)+(x+2)=90[/tex]

2nd step: Open the brackets:

[tex]x+x+1+x+2=90[/tex]

3rd step: Simplify:

[tex]3x+3=90[/tex]

4th step: Keep similar integers on one side of the equation

[tex]3x+3-3=90-3[/tex]

5th step: Solve for x:

[tex]3x=87[/tex]

[tex]\frac{3x}{3} =\frac{87}{3}[/tex]

[tex]x=29[/tex]

So if the numbers are consecutive, they have to be next to each other.

Answer: 29, 30, 31

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The two numbers are 8 and 12.

What is Algebraic expression ?

Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables.

Let us assume first number be = x

and, let the second number be = y

the,

One number is 4 less than a second number means :

x = y - 4........(1)

Twice the second number is 16 less than 5 times the first means :

2y = 5x - 16.......(2)

Substitute x equals from the first equation in the second equation.

2y = 5(y - 4) - 16

2y = 5y - 20 - 16

-3y = -36

y = 12

Now use the first equation for find x.

x = y - 4

x = 12 - 4

x = 8

Thus, The numbers are 8 and 12.

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Answer:

Rational.

Step-by-step explanation:

We are asked to determine the type of number 0.5.

We can see that our given number is a decimal.

We can also see that our given number is a terminating decimal, so we can represent it as a fraction.

[tex]0.5\times \frac{10}{10}=\frac{5}{10}=\frac{1}{2}[/tex]

Therefor, our given number is a rational number as we can represent it as a fraction.

Answer:

A black-tailed jackrabbit can hopes 36 in 5 seconds.

Step-by-step explanation:

Consider the provided information.

Black tailed jackrabbit hopes 51 feet in one second.

Therefore, in 5 second Black tailed jackrabbit covers a distance of:

51×5=255  feet

So, in 5 seconds a black-tailed jackrabbit will travel 255 feet.

In one hops Black tailed jackrabbit covers 7 feet.

Now find the number of hops, we need to divide the distance by the length of one hop:

[tex]255\div 7=\frac{255}{7}\approx36[/tex]

Hence, A black-tailed jackrabbit can hopes 36 in 5 seconds.