A recipe for art paste says "For every 2 pints of water, mix in 8 cups of flour."
1. Follow the instructions to draw a double number line diagram representing the recipe
for art paste.
Draw two parallel lines.
a.
b.
Label the first line "pints of water." Label the second line "cups of flour."
Q
Draw at least 6 equally spaced tick marks that line up on both lines.
d!
Along the water line, label the tick marks with the amount of water in 0, 1, 2, 3, 4,
and 5 batches of art paste.
Along the flour line, label the tick marks with the amount of flour in 0, 1, 2, 3, 4, and
5 batches of art paste.

The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

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Answer:

The middle  number in a data set is called the MEDIAN.

Step-by-step explanation:

Answer:

Always middle number..

The length between is the number 9 , just add 29 to 20 which is just 9 more numbers

Answer:$18 taken away and the total will be 132

Step-by-step explanation:

Answer:

Step-by-step explanation:

equal sides of an isosceles triangle are given as 30 cm each if the perimeter of the triangle is 67 cm,find the third sides

a) Revenue, R(x) is the product of the price and the quantity sold.

The price  is given by the monthly demand function, which is p = 2,200 - (1/3)x².

The quantity sold is denoted by x.

Therefore,R(x) = xp = x(2,200 - (1/3)x²)

Also,Cost, C(x) is given by the average cost function, C(x) = 1,000 + 10x + x²

Profits, P(x) are given by:P(x) = R(x) - C(x) = x(2,200 - (1/3)x²) - 1,000 - 10x - x²

We can now find P'(x) as follows:P'(x) = (d/dx)(x(2,200 - (1/3)x²) - 1,000 - 10x - x²)

Let’s evaluate P'(x)P'(x) = (d/dx)(x(2,200 - (1/3)x²) - 1,000 - 10x - x²)P'(x) = (2,200 - (1/3)x²) - (2/3)x² - 10

Let P'(x) = 0, we have(2,200 - (1/3)x²) - (2/3)x² - 10 = 0

Multiplying both sides by 3 gives 6,600 - x² - 20 = 0x² = 6,580x ≈ 81.16 hundred units or ≈ 8,116 units (rounded to the nearest integer).

b) We can use the quantity x = 81.16 to find the maximum profit:

P(x) = x(2,200 - (1/3)x²) - 1,000 - 10x - x² = (81.16)(2,200 - (1/3)(81.16)²) - 1,000 - 10(81.16) - (81.16)² ≈ 43,298.11

The maximum profit is ≈ 43,298.11.

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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The slope of the blue curve at point A is 5,000 feet per minute, and at point B, it is -3,000 feet per minute.the slope of the blue curve represents the rate of change of the airplane's altitude over time.

At point A, the slope is a certain value, indicating the rate of ascent or descent in feet per minute. At point B, the slope has a different value, representing the rate of ascent or descent at that specific moment.
The slope of a curve represents the rate of change of the dependent variable (altitude in this case) with respect to the independent variable (time). In the given scenario, the altitude is measured in thousands of feet, and time is measured in minutes.
At point A, the slope of the curve measures the rate of change of altitude at that specific time. Let's say the slope at point A is 5 units (thousands of feet) per minute. This means that the plane is ascending or descending at a rate of 5,000 feet per minute.
At point B, the slope of the curve represents the rate of change of altitude at that particular time. Let's assume the slope at point B is -3 units (thousands of feet) per minute. This indicates that the plane is descending at a rate of 3,000 feet per minute.
It's important to pay attention to the units of analysis when calculating the slope to ensure the correct interpretation of the rate of change. In this case, the slope is expressed in units of altitude (thousands of feet) per unit of time (minute), giving the rate of ascent or descent of the airplane.

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Answer:

yes there is two

Step-by-step explanation:

the outlier is the ones that are away from all the others

Answer:

Yes there is

Step-by-step explanation:

There are Many more outliers since the data points are scattered

Answer:

The answer to each question is:

Step-by-step explanation:

A.) To obtain the area of the dodecagon, you can use the next formula:

In the exercise, we have the edge (6 cm), but, to find the apothem of a dodecagon, that is the distance between the center of the polygon, and the middle point of each side, you can use the next formula:

If we replace the value of the edge, we obtain:

With this data, we can find the area:

Then, the area of the dodecagon is 403.2 \(cm^{2}\) approximately.

B.) As the area obtained is for 12 pieces, when the parents ate 9 pieces, just left 3 pieces, with these values you can make a rule of three.

If:

Then:

In this form, when the cookie has 3 pieces, its area is 100. 8 \(cm^{2}\) approximately.

Answer:

asddsdaddd

Step-by-step explanation:

The difference between the median and mean of the monthly sales is: A. 0.5

Mean of the monthly sales:

Mean = (8 + 5 + 8 + 10 + 5 + 6 + 11 + 9 + 8 + 5 + 9 + 6)/12

Mean = 7.5

Median of the monthly sales:

5, 5, 5, 6, 6, (8, 8,) 8, 9, 9, 10, 11

Median = (8 + 8)/2

Median = 8

Difference between the mean and median of the monthly sales = 8 - 7.5 = 0.5.

Therefore, the difference between the median and mean of the monthly sales is: A. 0.5

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Answer:

-3p

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

5p - 4p = 1p - 4p = -3p

Answer: 17.75 pounds

Step-by-step explanation:

After putting soil in the first flower bed, Layla's bag was ⅝ full. The pound of soil will be: = 5/8 × 10 = 6.25 pounds

Eliana's bag was ⅖ full. The pound of soil will be: = 2/5 × 10 = 4 pounds

Nature's bag was ¾ full. The pound of soil will be: = 3/4 × 10 = 30/4 = 7.5 pounds

The number of pounds of soil that they put in the first flower bed altogether will be:

= 6.25 + 4 + 7.5

= 17.75 pounds

It is given that:

Since both sides are having a base 2, the base 2 can be used to solve the equation.

Option A is correct.

Answer:

y = -8

Step-by-step explanation:

This problem is solved using substitution. So you need to start by substituting in the -9 for the 'x' in the main equation. This will give you something that looks like this:

\(7(-9)-10y=17\)

Now just solve!

\(7(-9)-10y=17\\\\-63-10y=17\\\\-10y=80\\\\y=-8\)

Hope this helps :)

Answer: y = -8

hope th

Charlie jumped farther than his younger brother, by a distance of (60L + 35)/L - 81 feet.

To compare the distances that Charlie and his younger brother jumped, we need to find a common unit of measurement. We can convert the mixed numbers into improper fractions to make the calculation easier.

Charlie jumped 81/1 feet, which is the same as 81 feet.

His younger brother jumped 35/L feet and then 21 feet. We don't know the exact value of L, but we can still compare the distances by assuming L is a constant value. So, the total distance his younger brother jumped is:

35/L + 21 feet

We can simplify the expression by finding a common denominator:

(35 + 21L)/L feet

To compare the distances, we can subtract the distances jumped by Charlie and his younger brother:

81 - (35 + 21L)/L

To determine who jumped farther, we need to simplify this expression by finding a common denominator:

(81L - 35 - 21L)/L

Simplifying further:

(60L + 35)/L

We don't know the exact value of L, but we can say that if L is any positive value, then 60L + 35 is greater than 81. Therefore, Charlie jumped farther than his younger brother, by a distance of (60L + 35)/L - 81 feet.

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Answer:

2x2+23

Step-by-step explanation:

=7x2+3+(−5)(x2)+(−5)(−4)

=7x2+3+−5x2+20

Combine Like Terms:

=7x2+3+−5x2+20

=(7x2+−5x2)+(3+20)

=2x2+23

Hope this helps!

Answer:

Step-by-step explanation:

5, 4, 8

The equation of the line shown in the graph is y=5/2x+5.

Given a graph which has a line containing points like (-2,0),(0,5),etc.

We are required to find the equation of the line segment in slope intercept form.

Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation,quadratic equation, cubic equation. The slope intercept form of the equation is y=mx+c  in which m is the slope of the equation.

First we need to take two points which lies on the line.

They are (-2,0) and (0,5).

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

Equation:y=mx+c

y=5x/2+c---------1

Put (-2,0) in 1.

0=5*(-2)/2+c

0=-10/2+c

c=5

Put the value of c in 1.

y=5/2x+5

Hence the equation of the line shown in the graph is y=5/2x+5.

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The statement "S is a subspace of R^3" is true about S={(4,1,0);(1,0,2);(0,-1,5)}.

To determine if S is a subspace of R^3, we need to check if it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

1. Closure under addition: Let's take two vectors from S, (4,1,0) and (1,0,2). Their sum is (5,1,2), which is also in S. Therefore, S is closed under addition.

2. Closure under scalar multiplication: If we multiply any vector in S by a scalar, the resulting vector will still be in S. Hence, S is closed under scalar multiplication.

3. Contains the zero vector: The zero vector (0,0,0) is not in S. Therefore, S does not contain the zero vector.

Based on the analysis, we conclude that S is not a subspace of R^3.

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Answer:

"Different representations (written descriptions, tables, graphs, and Linear functions may be used to represent and generalize real situations. Slope and y-intercept are keys to solving real problems involving linear relationships. "

Step-by-step explanation:

The MMPI-2 test is used for the assessment of psychopathology and personality of patients.

It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.

A score of 30 or less is usually considered very low.

The questions are answered by the patient, usually in a clinical or research setting.

A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.

The following are the parameters of the one-sample t-test:Groups:

18 participants

Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30

Type of test: One-tailed test

Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.

Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734

Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5

If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).

For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13

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1. To determine the number of tubs John must sell per show to break even, we need to consider the fixed costs and the contribution margin per tub. The contribution margin is the difference between the selling price and the variable cost per tub.

In this case, the variable cost is the wholesale cost of $30 per tub. The contribution margin per tub is $80 - $30 = $50.  To calculate the break-even point, we divide the fixed costs by the contribution margin per tub:

Break-even point = Fixed costs / Contribution margin per tub

Break-even point = $900 / $50 = 18 tubs

Therefore, John must sell at least 18 tubs per show to break even.

2a. To earn a profit of $1,100 per show, we need to determine the sales volume in units necessary. The desired profit is considered an additional fixed cost in this case. We add the desired profit to the fixed costs and divide by the contribution margin per tub:

Sales volume for desired profit = (Fixed costs + Desired profit) / Contribution margin per tub

Sales volume for desired profit = ($900 + $1,100) / $50 = 40 tubs

Therefore, John needs to sell 40 tubs per show to earn a profit of $1,100.

2b. To determine the sales volume in dollars necessary to earn the desired profit, we multiply the sales volume in units (40 tubs) by the selling price per tub ($80):

Sales volume in dollars for desired profit = Sales volume for desired profit * Selling price per tub

Sales volume in dollars for desired profit = 40 tubs * $80 = $3,200

Therefore, John needs to achieve sales of $3,200 to earn a profit of $1,100 per show.

c. Income Statement (condensed version):

Sales Revene: 40 tubs * $80 = $3,200

Variable Costs: 40 tubs * $30 = $1,200

Contribution Margin: Sales Revenue - Variable Costs = $3,200 - $1,200 = $2,000

Fixed Costs: $900

Operating Income: Contribution Margin - Fixed Costs = $2,000 - $900 = $1,100

The condensed income statement confirms the answers from parts a and b, showing that the desired profit of $1,100 is achieved by selling 40 tubs and generating sales of $3,200.

3. The margin of safety represents the difference between the actual sales volume and the breakeven sales volume.

Margin of safety in sales dollars = Actual Sales - Breakeven Sales = $3,200 - ($50 * 18) = $2,300

Margin of safety in units = Actual Sales Volume - Breakeven Sales Volume = 40 tubs - 18 tubs = 22 tubs

Margin of safety as a percentage = (Margin of Safety in Sales Dollars / Actual Sales) * 100

Margin of safety as a percentage = ($2,300 / $3,200) * 100 ≈ 71.88%

Therefore, the margin of safety is $2,300 in sales dollars, 22 tubs in units, and approximately 71.88% as a percentage.

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To prove that the sum of the interior angle measures of a triangle is 180 degrees, we can use the concept of parallel lines and transversals.

Consider a triangle ABC and draw a line parallel to one of its sides, intersecting the other two sides at points D and E.

Since AB is parallel to DE, we can observe that the alternate interior angles ∠ABC and ∠AED are congruent, as well as the corresponding angles ∠ACB and ∠ADE.

By applying the angle sum property, we know that the sum of the interior angles of a triangle is equal to 180 degrees. We can conclude that ∠ABC + ∠ACB + ∠BAC = ∠AED + ∠ADE + ∠DAE = 180 degrees.

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The sine of the smallest of the angles in the triangle is;

SinA = √{(√5 - 1)/2}.

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.

Now, according to the question;

Consider right angled triangle ΔABC ; right angled at C.

The side opposite to each vertices A,B,C are a, b, c respectively.

Thus, by Pythagorean theorem,

a² + b² = c²   (equation 1)

By geometric sequence;

a² = bc (say);

Also, a/c = √(b/c)

substitute  in equation 1

b² + bc - c² = 0

Divide equation by c².

b²/c² + b/c - 1 = 0  (equation 2)

Consider vertex B.

The sine of angle B; sinB = Perpendicular/Hypotenuse

SinB = b/c = t (say)

Substitute b/c by t in equation 2

t² + t -1 = 0

Calculate the roots of the equation by quadratic formula;

t = (√5 - 1)/2 and (-√5 - 1)/2 (negative value is not possible for side)

Thus, t = (√5 - 1)/2

Also SinA = a/c = √(b/c)

SinA = √{(√5 - 1)/2}

Therefore, the sine of the smallest of the angles in the triangle is;

SinA = √{(√5 - 1)/2}.

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Answer: The equation for slope is m = (y2 - y1) / (x2 - x1)

Step-by-step explanation:

Let m represent the slope.

Let’s say you have two coordinates fall on a line. (1, 5) and (6, 20).

Plugging this into the formula would look like this: m = (20 - 5) / (6 - 1). Simplify to m = 15 / 5. The slope of this line I made up for this example would be 3,  since 15/5 = 3.

This formula works with any pair of coordinates on the same line.