HELP ASAP PLEASE!!!!!!!!!!!!

What is the measure of ∠CED and ∠ACD?

Answer:

  $6 for a 1-minute call

Step-by-step explanation:

For duration "d" the costs of the plans are identical when ...

  5 +1d = 1 +5d

  4 = 4d . . . . . . . . add -1-1d to both sides

  1 = d  . . . . . . . . . divide by 4. Duration in minutes.

Then the cost for this 1-minute call is ...

  5 + 1·1 = 6 . . . . dollars

Each plan will charge $6 for a 1-minute call.

Answer:

Step-by-step explanation:

Let x represent the call duration that would cost the same amount with either plans.

On her plan, christina pays $5 just to place a call and $1 for each minute. This means that the total cost of x minutes on this plan is

x + 5

When brenna makes an international call, she pays $1 to place the call and $5 for each minute. This means that the total cost of x minutes on this plan is

5x + 1

For both costs to be the same, the number of minutes would be

x + 5 = 5x + 1

5x - x = 5 - 1

4x = 4

x = 4/4 = 1

A call duration of 1 minute would cost exactly the same under both plans. The cost of the call would be

5 × 1 + 1 = $6

Final answer:

To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight. The probability is 0.1525.

Explanation:

To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight.

First, we need to calculate the probability that a passenger shows up for the flight. Since the airline believes that 5% of passengers fail to show up, the probability that a passenger shows up is 1 - 0.05 = 0.95.

Next, we can use the binomial distribution to calculate the probability that more than 265 passengers show up. The formula for the binomial distribution is P(X > k) = 1 - P(X <= k), where X is the number of passengers who show up and k is the maximum number of passengers the plane can hold (265).

Using the binomial distribution, we can calculate the probability that more than 265 passengers show up as P(X > 265) = 1 - P(X <= 265) = 1 - binomcdf(275, 0.95, 265) = 0.1525.

Answer: the bill for a glass of apple juice is $0.7 and the bill for a salad is $1.5

Step-by-step explanation:

Let x represent the bill for a glass of apple juice.

Let y represent the bill for a salad.

The bill for five glasses of apple juice and four salads is $9.50. It means that

5x + 4y = 9.5 - - - - - - - - - - - 1

The bill for four glasses of apple juice and five salads is $10.30. This means that

4x + 5y = 10.30- - - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

20x + 16y = 38

20x + 25y = 51.5

Subtracting, it becomes

- 9y = - 13.5

y = - 13.5/-9

y = 1.5

Substituting y = 1.5 into equation 1, it becomes

5x + 4 × 1.5 = 9.5

5x + 6 = 9.5

5x = 9.5 - 6 = 3.5

x = 3.5/5 = 0.7

The bill for a glass of juice and a salad would be $2.20.

To find the cost of a glass of apple juice and a salad, we need to set up a system of equations using the given information. Let's assign variables to the cost of a glass of apple juice and a salad. Let x be the cost of a glass of apple juice and y be the cost of a salad.

From the first sentence, we can write the equation 5x + 4y = 9.50. From the second sentence, we can write the equation 4x + 5y = 10.30.

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method. Multiply the first equation by 4 and the second equation by 5 to eliminate x:

20x + 16y = 38.00

20x + 25y = 51.50

Subtract the first equation from the second:

9y = 13.50

Divide both sides by 9:

y = 1.50

Substitute this value of y into one of the original equations (let's use the first equation):

5x + 4(1.5) = 9.50

5x + 6 = 9.50

Subtract 6 from both sides:

5x = 3.50

Divide both sides by 5:

x = 0.70

Therefore, the bill for a glass of juice and a salad would be $0.70 + $1.50 = $2.20.

Answer:

Step-by-step explanation:

w = Henry's weight

e = Eric's weight

e = w - 12

The algebraic expression that represents Eric's weight in pounds is [tex]\( w - 12 \)[/tex].

1. We're given that [tex]\( w \)[/tex] represents Henry's weight in pounds. This means we're using the variable  [tex]\( w \)[/tex]  to stand for whatever Henry's weight is.

2. The problem states that Eric weighs 12 pounds less than Henry. So, if Henry weighs  [tex]\( w \)[/tex]  pounds, then Eric's weight would be [tex]\( w - 12 \)[/tex] pounds because he's 12 pounds lighter than Henry.

3. Therefore, the expression [tex]\( w - 12 \)[/tex] represents Eric's weight in pounds. We subtract 12 from Henry's weight  [tex]\( w \)[/tex]  to get Eric's weight. This expression tells us Eric's weight in terms of Henry's weight.

The distance between (-3, 2) and (3, -8) is approximately 11.66.

To find the distance between two points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, (-3, 2) can be denoted as (x1, y1) and (3, -8) can be denoted as (x2, y2). Substituting these values in the formula:

d = sqrt((3 - (-3))^2 + (-8 - 2)^2)

d = sqrt(6^2 + (-10)^2)

d = sqrt(36 + 100) = sqrt(136)

The distance between (-3, 2) and (3, -8) is approximately 11.66.

Final answer:

To calculate the distance between (-3, 2) and (3, -8), one must find the differences in both the x and y coordinates, square these differences, sum them, and take the square root of this sum, which yields approximately 11.66.

Explanation:

To find the distance between the points (-3, 2) and (3, -8), we use the Pythagorean Theorem. The distance d is calculated as the square root of the sum of the squares of the difference in the x-coordinates and the y-coordinates.

First, find the differences:
Δx = [tex]x_2 - x_1[/tex] = 3 - (-3) = 6
Δy = [tex]y_2 - y_1[/tex] = -8 - 2 = -10

Then calculate the distance squared:
d² = (Δx)² + (Δy)²
d² = (6)² + (-10)²
d² = 36 + 100
d² = 136

Take the square root of the distance squared to find the distance:
d = [tex]\sqrt{136}[/tex]
d ≈ 11.66

Answer:

Step-by-step explanation:

The large screen television is rectangular in shape. The diagonal divides the rectangle into two equal right angle triangles. The diagonal represents the hypotenuse of the right angle triangle.

He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches. To determine the height,h of the triangle which is also the width of the rectangle, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

42.1² = 34.3² + h²

h² = 1772.41 - 1176.49 = 595.92

h = √595.92 = 24.41 inches.

Area of rectangle = Length × width

Area of Television = 34.3 × 24.41 = 837.3 inches²

Answer:

I feel bad for you I really would like to help you but I haven't even learn that stuff yet

Answer:

The heart is located in the middle of the 2 lung's in the middle of the chest and slightly to the left side of the chest.

Step-by-step explanation:

The heart is a muscular organ of the size of a fist just behind and to the left of the breastbone. The cardiovascular system is the heart pumping blood across the artery and vein network.Behind your sternum and between your two lungs your heart is found. The heart lies closer to the front of the chest and in the front of the spine. Your diaphragm, stomach and liver are underneath your heart.

Step-by-step explanation:

The given four sides of quadrilateral = (2, 4), (3, 5), (4, 6) and (5,8)

To find, the area of the quadrilateral = ?

We know that,

The area of quadrilateral [tex]=\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]

[tex]=\dfrac{1}{2} [2( 5-6)+3( 6-8)+4( 8-4)+5(4-5)][/tex]

[tex]=\dfrac{1}{2} [2(-1)+3(-2)+4(4)+5(-1)][/tex]

[tex]=\dfrac{1}{2} (-2-6+16-5)[/tex]

[tex]=\dfrac{1}{2} (16-13)[/tex]

= [tex]\dfrac{3}{2}[/tex] units

Thus, the area of the quadrilateral is [tex]\dfrac{3}{2}[/tex] units.

Step-by-step explanation:

We have,

[tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]

To find, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex] = ?

∴ [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]

= [tex]\dfrac{7x.x}{(x-4)(x+7)}[/tex]

= [tex]\dfrac{7x^2}{(x(x+7)-4(x+7)}[/tex]

= [tex]\dfrac{7x^2}{x^2+7x-4x-28}[/tex]

= [tex]\dfrac{7x^2}{x^2+3x-28}[/tex]

Thus, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7} = \dfrac{7x^2}{x^2+3x-28}[/tex].

Answer:

179.2km

Step-by-step explanation:

The distance from their house to the beach is 448km. Now they have to drive to and from the beach. The total distance traveled by the family is 448km + 448km.

This is equal to 896km. Now we have 5 adults who took their turns to drive and they drove the same distance. The total distance traveled by each adult will be 896/5 = 179.2km

Hence, each adult in the family drove a distance of 179.2km

Answer:

13 r 3

Step-by-step explanation:

Answer:

Option E is the correct answer (As the)

Step-by-step explanation:

Option A indicates that Joan, for 18 years, was the former chair; it is inappropriate to think that she would be attending meetings while she was the former chair. The sentence indicates that Joan served for 18 years as the chair lady, and during this time she attended meetings. Thus, option E is clearer and precise in its meaning than option A.

Answer:

a) 375m/s2

b) F = 0.045N

c) F/T =  0.00096

d) Tension = 46.9N

Step-by-step explanation:

The step by step calculation is as shown in the attached file.

Answer:

break even units for both the cases will be 5

Step-by-step explanation:

Data provided in the question:

For the case 1

Variable cost = $20 each

Selling cost = $50

Rent for the booth fair = $150

Now,

Let break even units be x

At break even

Total cost = Total revenue

Thus,

$20x + $150 = $50x

or

$50x - $20x = $150

or

$30x = $150

or

x = 5

Case 2

Variable cost = $15 per unit

Thus,

At break even

Total cost = Total revenue

Thus,

$15x + $150 = $50x

or

$50x - $15x = $150

or

$35x = $150

or

x = 4.28 ≈ 5

The break even point will still remain the same.

The break-even point is calculated by setting total cost equal to total revenue and solving for the number of units produced and sold (denoted as 'units').

Given the current variable cost per unit ($20), the sale price per unit ($50), and the fixed cost (booth rent - $150), we can set up the equation as follows:

Total Cost = Fixed cost (booth rent) + variable cost per unit * units
Total Revenue = sale price per unit * units

Setting these two equal to each other, we get:

150 + 20*units = 50*units

By rearranging this equation, we find:

units = 150 / (50 - 20)

This calculates out to 5 units. Therefore, Ray needs to sell 5 units to break even with his current costs.

If Ray is able to reduce his variable cost to $15 per unit, we will repeat the same calculation with the new variable cost:

units = 150 / (50 - 15)

This calculates out to approximately 4.29 units. Since Ray cannot sell a fraction of a unit, he would have to sell 5 units to fully cover his costs, but he would begin to make a profit sooner than with his current variable cost. In fact, from the 5th unit sold, part of the revenue would go towards profit. Therefore, with the reduced variable cost, his break-even point would be closer to 4 units, but practically still 5 units.

In conclusion, with his current costs, Ray's break-even point is at 5 units. If he is able to reduce his variable cost to $15 per unit, his break-even point would theoretically be lower at approximately 4.29 units, but practically still would round up to 5 units.

#SPJ3

Answer:

Step-by-step explanation:

The sum of the two angles is ...

  m∠L + m∠M = 42° +48° = 90°

__

A calculator can show you the sines of these angles.

  sin(42°) ≈ 0.66913

  sin(48°) ≈ 0.74314

_____

The two acute angles of a right triangle always have a sum of 90°.

In triangle LNM, the sum of angles L and M is 90°. The sine values for angles L and M are approximately 0.6691 and 0.7431 respectively.

The sum of the measures of angles L and M can be calculated as follows:

m∠L + m∠M = 42° + 48°

                      = 90°

For a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. Therefore, using trigonometry:

sin(L) = sin(42°)

         ≈ 0.6691

sin(M) = sin(48°)

           ≈ 0.7431

Thus, the sum of angles L and M is 90°, and the sine values are approximately 0.6691 and 0.7431 respectively.

System of inequalities are,  [tex]x+y<10[/tex]  and [tex]5x+8y\geq 56[/tex]

Let us consider, He does house cleaning job for x hours and sales job for y hours.

Since, he can work a total of not more than 10 hours each week at  two jobs.

So, inequality are,   [tex]x+y<10[/tex]

Since, house cleaning job pays $5. per hour and  sales job pays $8 per hours.

Thus, Total earn = 5x + 8y

But he need to earn at least $56 each week

So, inequality are , [tex]5x+8y\geq 56[/tex]

Learn more:

https://brainly.com/question/15816805

Final answer:

The variables x and y represent the hours worked at the house cleaning and sales jobs, respectively. The system of inequalities x + y ≤ 10, 5x + 8y ≥ 56, and x ≥ 0, y ≥ 0 reflects the constraints on work hours and minimum earnings.

Explanation:

To solve the problem, we need to define two variables representing the hours worked at each job:

Let x be the number of hours worked at the house cleaning job.

Let y be the number of hours worked at the sales job.

Given the conditions of the problem, we can formulate the following system of inequalities:

The total working hours from both jobs cannot exceed 10 hours per week: x + y ≤ 10.

The total earnings must be at least $56 to pay bills: 5x + 8y ≥ 56.

The number of working hours cannot be negative: x ≥ 0 and y ≥ 0.

This system of inequalities represents the constraints on the number of hours you can work at each job and the minimum earnings required to pay your bills.

Answer:

$2925

Step-by-step explanation:

To find the cost, we need to get the area of the triangular sale. This can be obtained by using the area of a triangle.

This is A = 1/2 * b * h

Where in this case, b = 12ft and h = 25ft

The area is thus 1/2 * 12 * 25 = 150sq.ft

Now we know that 1sq.ft is $19.50, 150 will be 150 * 19.5 = $2925

Answer:

Since the Option of equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.

[tex]x^2+15^2=17^2[/tex]

[tex]x^2=17^2-15^2[/tex]

OR

[tex]x^2+225=289[/tex]

[tex]x^2=289-225[/tex]

Step-by-step explanation:

Given:

Length of One leg = x

Length of other Leg= 15

Hypotenuse = 17

We need to find the equation used to determine the value of x.

Solution:

Assuming Triangle to right angled triangle.

So we will apply Pythagoras theorem which sates that;

"The square of sum of two legs of right angle triangle is equal to square of the length of hypotenuse."

so we can say that;

[tex]x^2+15^2=17^2[/tex]

[tex]x^2=17^2-15^2[/tex]

OR

[tex]x^2+225=289[/tex]

[tex]x^2=289-225[/tex]

Since the equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.

[tex]x^2+15^2=17^2[/tex]

[tex]x^2=17^2-15^2[/tex]

OR

[tex]x^2+225=289[/tex]

[tex]x^2=289-225[/tex]

Answer:

b

Step-by-step explanation:

Answer:

(1) -0.833

(2) 0.80

(3) 0.70

(4) 390

(5) 90

(7) 48

Step-by-step explanation:

Given:

E (X) = 100, E (Y) = 120, E (Z) = 130

Var (X) = 9, Var (Y) = 16, Var (Z) = 25

Cov (X, Y) = -10, Cov (X, Z) = 12, Cov (Y, Z) = 14

The formulas used for correlation is:

[tex]Corr (A, B) = \frac{Cov (A, B)}{\sqrt{Var (A)\times Var(B)}} \\[/tex]

(1)

Compute the value of Corr (X, Y)-

[tex]Corr (X, Y) = \frac{Cov (X, Y)}{\sqrt{Var (X)\times Var(Y)}} \\=\frac{-10}{\sqrt{9\times16}} \\=-0.833[/tex]

(2)

Compute the value of Corr (X, Z)-

[tex]Corr (X, Z) = \frac{Cov (X, Z)}{\sqrt{Var (X)\times Var(Z)}} \\=\frac{12}{\sqrt{9\times25}} \\=0.80[/tex]

(3)

Compute the value of Corr (Y, Z)-

[tex]Corr (Y, Z) = \frac{Cov (Y, Z)}{\sqrt{Var (Y)\times Var(Z)}} \\=\frac{14}{\sqrt{16\times25}} \\=0.70[/tex]

(4)

Compute the value of E (3X+4Y-3Z)-

[tex]E(3X+4Y-3Z)=3E(X)+4E(Y)-3E(Z)\\=(3\times100)+(4\times120)-(3\times130)\\=390[/tex]

(5)

Compute the value of Var (3X-3Z)-

[tex]Var (3X-3Z)=[(3)^{2}\times Var(X)]+[(-3)^{2}\times Var (Z)]+(2\times3\times-3\times Cov(X, Z)]\\=(9\times9)+(9\times25)-(18\times12)\\=90[/tex]

(6)

Compute the value of Var (3X+4Y-3Z)-

[tex]Var (3X+4Y-3Z)=[(3)^{2}\times Var(X)]+[(4)^{2}\times Var(Y)]+[(-3)^{2}\times Var (Z)]+[(2\times3\times4\times Cov(X, Y)]+[(2\times3\times-3\times Cov(X, Z)]+[(2\times4\times-3\times Cov(Y, Z)]\\=(9\times9)+(16\times16)+(9\times25)+(24\times-10)-(18\times12)-(24\times14)\\=-230[/tex]

But this is not possible as variance is a square of terms.

(7)

Compute the value of Cov (3X, 2Y+3Z)-

[tex]Cov(3X, 2Y+3Z)=Cov(3X,2Y)+Cov(3X, 3Z)\\=6Cov(X, Y)+9Cov(X,Z)\\=(6\times-10)+(9\times12)\\=48[/tex]

The correct answers to the given set of data are:

This refers to the measurement of spread between numbers which can be found in a set of data.

Hence, to compute the variance and covariance

Using the variance formula we can see that the given sets of data are:

Read more about variance here:
https://brainly.com/question/25639778

Answer:

Correct option (B).

Step-by-step explanation:

A 95% confidence interval for a population parameter implies that there is 0.95 probability that the population parameter is contained in that interval.

Or, if 100, 95% confidence intervals are created then 95 of those intervals would contain the population parameter with probability 0.95.

In this question the 95% confidence interval was created for population proportion of all United States citizens who were optimistic about the economy.

Then this 95% confidence interval implies that if 100 such confidence intervals were created then 95 of those would consist of the true proportion of US citizens who were optimistic about the economy..

Thus, the correct option is (B).

Answer:

We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.

Step-by-step explanation:

Answer:

The solution is (5, −2)

Step-by-step explanation :

x + y = 3 => y = 3 - x

                  y = x - 7  } =>

=> 3 - x = x - 7 => 3 + 7 = x + x => 2x = 10 => x = 5

x + y = 3

5 + y = 3

y = 3 - 5

y = - 2

Final answer:

Marie used 4 1/2 cups of flour for the bread and had 6 1/2 cups left for the muffins. By adding these amounts together, we find that the original bag of flour contained 11 cups of flour in total.

Explanation:

To determine how much flour was initially in the bag, we need to add together the amount of flour used for the bread and the muffins.

Marie baked two loaves of bread, with each loaf requiring 2 1/4 cups of flour. Therefore, the total flour used for bread is:

2 loaves × 2 1/4 cups/loaf = 4 1/2 cups

After baking the bread, she used the remaining 6 1/2 cups of flour to make muffins. To find the initial amount of flour in the bag, we add the flour used for the bread to the flour used for the muffins:

4 1/2 cups + 6 1/2 cups = 11 cups

Therefore, the bag originally had 11 cups of flour.

Answer:

It will cost is $828.75.

Step-by-step explanation:

Given:

Davis is putting tile in his rectangular kitchen. His kitchen is 13 feet long, and 17 feet wide. The tile davis is installing is $3.75 per square foot.

Now, to find the total cost.

Davis is putting tile in his rectangular kitchen.

Length = 13 feet.

Width = 17 feet.

So, to get the area of kitchen:

Area = length × width

Area = 13 × 17

Area = 221 square foot.

As, the unit rate is given.

Cost per square foot = $3.75.

Now, to get the total cost by using unitary method:

If cost of 1 square foot = $3.75.

So, the cost of 221 square foot = $3.75 × 221

                                                    = $828.75.

Therefore, it will cost  $828.75.

To find the total cost of tiling Davis' kitchen, we need to find the area of the kitchen in square feet by multiplying its length and width, then multiply the area by the cost per square foot. In this case, it will cost Davis $828.75 to tile his kitchen.

The question is about Davis installing tiles in his rectangular kitchen and how much the cost will be at $3.75 per square foot. First, we need to determine the total area of the kitchen. In this case, the kitchen is rectangular in shape and the area of a rectangle is calculated by multiplying the length by the width. Here, length is 13 feet and the width is 17 feet, hence the area of the kitchen is 13 x 17 = 221 square feet.

Now, the cost per square foot of tile is given as $3.75. So, we multiply the total area by the cost per square foot to determine the overall cost of the tile. The calculation is as follows, 221 square feet x $3.75 = $828.75.

Therefore, it will cost Davis $828.75 to tile his kitchen.

https://brainly.com/question/30694298

Answer: the height after 10 hours is 21 cm

Step-by-step explanation:

Assuming the rate at which the height of the candle is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

If after seven hours of burning, a candle has high of 22.5 Centimeters, the expression is

22.5 = a + (7 - 1)d

22.5 = a + 6d - - - - - - - - - -1

If after 26 hours of burning, it's height is 13 cm. The expression is

13 = a + (26 - 1)d

13 = a + 25d - - - - - - - - - - - 2

9.5 = - 19d

d = 9.5/ - 19

d = - 0.5

Substituting d = - 0.5 into equation 1, it becomes

22.5 = a + 6 × - 0.5

22.5 = a - 3

a = 22.5 + 3

a = 25.5

The linear expression becomes

Tn = 25.5 - 0.5(n - 1)

The height of the candle after 10 hours would be

25.5 - 0.5(10 - 1)

= 25.5 - 4.5

= 21 centimeters

Answer:

a.) 10

b.) -2

c.) 6

d.) y = 6

e.) T = π

f.) y = -6cos(2t) + 4

Step-by-step explanation:

a.) Max value is the highest value in the y-axis. It peaks at y=10

b.) Min value is the lowest value in the y-axis. Peaks at y=-2

c.) Amplitude is how high the peak is from the midpoint. It could be found by taking the average of the peaks. (10 - (-2))/2 = 6

d.) y = 6

e.) T = π

f.) General equation for a sinusoidal wave is

y = Acos(ωt - Ф) + k

y = Acos((2π/T)t - Ф) + k

The graph started at it's min, so the amplitude must had been fliped upsidedown because it normally starts at the max. Therefore I must make my equation negative to flip it.

y = -Acos((2π/T)t - Ф) + k

y = -(6)cos((2π/(π))t - (0)) + (4)

y = -6cos(2t) + 4

Answer:

84

Step-by-step explanation:

Area of a rectangle : A = bh

5 x 6 = 30

Area of a trapezoid : A = 1/2 (b1 + b2) h

b1: 7 + 5 = 12

b2:  15

h: 10 - 6 = 4

12 + 15 = 27

27 x 4 x .5 = 54

Add the areas up:

30 + 54 = 84

Answer: 1 2/3 ounces of cinnamon is needed.

Step-by-step explanation:

1/3 ounce is cinnamon is needed for each 1 and 1/2 cups of flour. Converting 1 and 1/2 cups to improper fraction, it becomes 3/2 cups.

It means that the number of ounces of cinnamon need for 1 cup of flour would be

(1/3)/(3/2) = 1/3 × 2/3 = 2/9 ounces of cinnamon.

Converting 7 and 1/2 cups of flour to improper fraction, it becomes 15/2 cups of flour.

Therefore, the ounces of cinnamon needed to bake cookies with 15/2 cups of flour is

2/9 × 15/2 = 15/9 = 5/3

= 1 2/3 ounces of cinnamon

Answer:

[tex]2\frac{1}{4} inches.[/tex]

Step-by-step explanation:

Hi,

We see the plot line below, which shows that three crosses above [tex]\frac{3}{4} - inch[/tex] buttons, that means we have three such buttons available with us.

To find their total lengths, we have two methods:

[tex]\frac{3}{4} \times 3\\ = \frac{3 \times 3}{4}\\= \frac{9}{4}[/tex]

changing this improper fraction into a mixed fraction: [tex]2\frac{1}{4} inches.[/tex] will be the total length of three buttons lined up.

The answer is in the attachment

Final answer:

Using the Pythagorean theorem, the calculation shows that the wire should be attached 10 feet up the pole to support it if the wire is 26 feet long and attached to the ground 24 feet away from the base of the pole.

Explanation:

The question asks how high up the pole a wire should be attached if the pole is supported by a wire that is 26 feet long and is attached to the ground 24 feet away from the base of the pole. This scenario forms a right triangle with the ground and the pole as the perpendicular sides, and the wire as the hypotenuse. To solve for the height of the pole where the wire should be attached (the vertical side of the triangle), we can use the Pythagorean theorem which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): [tex]a^2 + b^2 = c^2[/tex].

Given that the distance from the pole to the point where the wire is attached to the ground (b) is 24 feet and the length of the wire (c) is 26 feet, we can set up the equation as follows:

[tex]24^2 + a^2 = 26^2[/tex]
576 + [tex]a^2[/tex] = 676
[tex]a^2[/tex] = 676 - 576
[tex]a^2[/tex] = 100
a = [tex]\sqrt{100}[/tex]
a = 10
Thus, the wire should be attached 10 feet up the pole.