Tara has 8.7 feet of fabric. She wants to make table runners that are all 1.45 feet long. How many table runners can she make?

Answer:

Step-by-step explanation: the answer is option c

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

to know more about unitary method

https://brainly.com/question/28276953

Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

Answer:

Step-by-step explanation:

3x - 4y = 13 (1)

2x + y = 5 (2)

——————

3x - 4y = 13

4(2x + y = 5) (2) times 4

——————-

3x - 4y = 13

8x + 4y = 20

——————-

11x = 33

x = 33/11

x = 3

Plug x = 3 in (2):

2(3) + y = 5

6 + y = 5

y = 5-6

y = -1

Thus, x = 3 and y = -1

Answer:

f(6) = 51

Step-by-step explanation:

f(x)= x² + 3x - x/2

In order to find f(6) ,we need to substitute

x by 6 in the expression of f :

f(6) = (6)² + 3(6) - (6)/2

    = 36 + 18 - 3

    = 54 - 3

    = 51

Then

f(6) = 51

Answer:

f(6) = 51

Step-by-step explanation:

Simplify:

  Substitute the value of x

\(\sf f(x) =x^2 + 3x -\dfrac{x}{2}\\\\f(6)=6^2 + 3*6 -\dfrac{6}{2}\\\\\)

        = 36 + 18 - 3

        =  51

Answers:

A, B, D, E

Nearly everything except choice C is true.

====================================================

Explanation:

Answer:

Counter Clockwise Torque = 360 Nm

Clockwise Torque = 240 Nm

Step-by-step explanation:

Using relations in a right triangle, it is found that the measure of angle DHG is of 116º.

The relations in a right triangle are given as follows:

In this problem, angle DHG is the sum of measures a and b.

Angle a is adjacent to a side of 33 cm, while the hypotenuse is of 49 cm, hence:

\(\cos{a} = \frac{33}{49}\)

\(a = \arccos{\left(\frac{33}{49}\right)}\)

\(a = 47.66^\circ\)

Angle b is opposite to a side of 39 cm, while the hypotenuse is of 42 cm, hence:

\(\cos{b} = \frac{39}{42}\)

\(b = \arccos{\left(\frac{39}{42}\right)}\)

\(b = 68.21^\circ\)

Then:

a + b = 47.66º + 68.21º = 115.87º

Rounding, the measure of angle DHG is of 116º.

More can be learned about relations in a right triangle at https://brainly.com/question/26396675

Answer:

(2,-9)

Step-by-step explanation:

Equation Form:

x = 2  

y = − 9

Answer:

this is a wild guess but  10.

Step-by-step explanation:

Not sure if you're allowed to do this but i added the x's

7x+3x= 10x

   10x+20.

I then subtracted 10 by both sides. That leaves me with 10.

  x =10

 this is a guess i apologize if it's wrong

The number of days the family were on vacation is 20 days.

The number of days the family were on vacation is calculated as follows;

Let's consider morning and afternoon as a half day.

From the question we will have the following equation;

12 mornings +  13 afternoons = 25  half days.

25 - 15 days of raining = 10  half days

10  half days = 5  mornings and 5 afternoons with no rain.

The number of days they stayed is calculated as;

15 + 5 = 20  days.

Learn more about number of days at vacation here: https://brainly.com/question/19260584

#SPJ1

Answer:

H0 : μ ≥ 98.6

H1 : μ < 98.6

Step-by-step explanation:

The population mean temperature, μ = 98.6

The null hypothesis takes up the value of the population mean temperature as the initial truth ;

The alternative hypothesis on the other hand is aimed at using a sample size of 109 to establish if the mean temperature is less than the population mean temperature.

The hypothesis ;

Null hypothesis, H0 : μ ≥ 98.6

Alternative hypothesis ; H1 : μ < 98.6

The fraction of the area of the tray occupied by the blondies is 1/9.

To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.

Let's calculate the area of each individual blondie:

The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.

Now, let's calculate the area occupied by the blondies in each row:

Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.

So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.

Next, let's determine the area occupied by the brownies:

The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.

Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.

Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.

Now, let's calculate the total area of the tray:

Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:

Total area of the tray - Area occupied by the brownies = Area occupied by the blondies

648 square inches - 576 square inches = 72 square inches.

So, the fraction of the area of the tray occupied by the blondies is:

Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:

72 square inches / 648 square inches = 1/9.

Therefore, the blondies' percentage of the tray's surface area is 1/9.

for such more question on fraction

https://brainly.com/question/1622425

#SPJ8

Answer:

i am the first person to answer mark me brainliest! :D

Step-by-step explanation:

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.

Given that-

Volume of cylinder = πr²h

Volume of cylinder = 3.14 *5²*18

Volume of cylinder = 3.14*25*18

Volume of cylinder = 1413 ft³

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

Know more about the cylinder:

https://brainly.com/question/23935577

#SPJ1

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

For more questions on algebraic fraction:

https://brainly.com/question/11875858

#SPJ8

Answer: D) 12 units

Explanation:

There are 12 spaces between T and S.

You can count the spaces out, or subtract and use absolute value.

You could use the distance formula, but it's a bit overkill in this situation. The distance formula is only ever needed whenever we don't have horizontal or vertical line segments.

Edit: The solution has been corrected to the correct value.

Answer:

50% chance.

Step-by-step explanation:

There are 3 numbers that are either greater than 4 or less than 2. They are 1, 5, and 6. There is a 3/6 chance you roll one of them or 50% chance.

Hey there! :)

Answer:

P(greater than or less than 2) = 50%.

Step-by-step explanation:

Numbers greater than 4: 5, 6

Numbers less than 2: 1

Total of 3 numbers that fit the criteria. Therefore:

P(greater than 4 or less than 2) = # of numbers / total

P(greater than 4 or less than 2) = 3 / 6 = 1 / 2

Convert fraction to percent:

1/2 × 100 = 50%

The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:

Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory

Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.

5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:

Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead

Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:

Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor

Without knowing the value for direct labor, we cannot compute the overhead cost.

https://brainly.com/question/30198250

#SPJ1

Answer:

Step-by-step explanation:

Temperature change:

Sal is wrong as the difference should be calculated as subtraction of the two values and absolute value of the result should be taken as the answer

Answer:

Sal was wrong as the change of temperature is 26°F

Step-by-step explanation:

recorded temperature at 7:30 A.M. = -4°F

                                             at noon = 22°F

change of temperature = 22 - (-4) = 26°F

therefore, Sal was wrong as the change of temperature is 26°F

Answer:

If a candle shop is offering a 20% off sale, the prices of all candles will be reduced by 20%. This will affect the mean, median, and mode cost per type of candle in the following ways:

Hope this helps!

Answer:

Mean: The mean is calculated by adding up all the prices of the candles and dividing by the total number of candles. When the prices are reduced by 20%, the new mean will also decrease by approximately 20%. This is because each price is being multiplied by 0.8, and then the total is divided by the same number of candles.

Median: The median is the middle value when all the candle prices are listed in order from lowest to highest. When the prices are reduced by 20%, the relative position of each price will remain the same. However, the actual values will decrease by 20%. Therefore, the new median will also decrease by approximately 20%.

Mode: The mode is the most common value in the set of candle prices. When the prices are reduced by 20%, it is possible that the mode will change, depending on the original distribution of prices. For example, if there are originally two or more prices that are tied for the most common value, then the mode may remain the same. However, if there is only one most common value, and this value is reduced by 20%, then a different value may become the new mode.

Step-by-step explanation:

============================================================

Explanation:

Ignore the portions that are 12 and 13 units long.

The base of triangle ABC is 8 units long. The height is 5 units. The base and height are always perpendicular.

The area is base*height/2 = 8*5/2 = 40/2 = 20 square units

---------

Side note:

You could find the area of triangle ABD, where D is at the 90 degree angle location, and then subtract off the area of triangle ACD. This is a slightly longer approach compared to the first section above.

Answer: let's try the Second one ( sorry if i get it wrong)

Step-by-step explanation:

Each number in the sequence is called a term. In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on. The notation a 1, a 2, a 3,… a n is used to denote the different terms in a sequence. The expression a n is referred to as the general or nth term of the sequence.

Answer:

it is the first one

Step-by-step explanation:

Answer:

14. x=30, y=15, z=165

15. x=10, y=25

Step-by-step explanation:

Answer:

1)

x= 30

y=15

z=150

2)

x= 10

y=25

Step-by-step explanation:

1)

2x+90+x=180

3x+90=180

x= 90/3=30

2y= x

2y=30

y= 30/2=15

2y+z= 180

30+z= 180

z= 150  

2)

3x= 5x-20

5x-3x=20

x=20/2=10

2y+4y+ (5x-20) = 180

6y+30= 180

y= 150/6= 25

I hope im right!!

The features of the logarithmic function are given as follows:

a) Domain: x > 0.

b) Range: all real values.

c) End behavior: as x -> ∞, f(x) -> ∞.

d) The x-intercept is at x = 1.

e) The function does not have an absolute maximum, as it is never decreasing.

The domain of the function is given by the set of input values, hence it is composed by the values of x assumed by the graph.

In this problem, the function is not defined for negative numbers, and has a vertical asymptote at x = 0, meaning that the function is not defined at this point, hence the domain is:

x > 0.

The range is the values of y of the graph, which are the output values of the function. The function assumes all value of y, hence the range is of all real values.

The end behavior of the function is given by the limit when x goes to infinity. The function is only defined for positive numbers, and it increases to right, hence the end behavior is:

As x -> ∞, f(x) -> ∞.

The x-intercept of the function is the value of x at which the function crosses the x-axis, hence it is given by:

x = 1.

An absolute maximum is a point in which the function changes from increasing to decreasing. In this problem, the function is increasing over it's entire domain, hence it contains no absolute maximum.

More can be learned about logarithmic functions at https://brainly.com/question/25537936

#SPJ1

Answer:

a.) The domain of the function is x > 0

b.) The range of the function is all real values.

c.) The end behavior of the function is as x approaches infinity, f(x) approaches infinity.

d.) Written as an ordered pair, the x-intercept of the function is (1,0).

e.) No, the function does not have an absolute maximum because the function is constantly increasing and never decreasing, meaning an exact absolute maximum is impossible to pinpoint. An absolute maximum is a point in which the function changes from increasing to decreasing. This function represents a constant increase over the entire domain. Therefore, the function contains no absolute maximum.

Hope that is super helpful! Have an amazing rest of your day! Please consider giving me the Brainliest! :)

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

Given:

In Δ\(WXY,m < Y=90^o,WY=3,XW=5\) and \(YX=4\).

To find:

The ratio represents the cosine of ∠\(W\).

Solution:

In Δ\(WXY,m < Y=90^o\). It means the opposite side of angle Y, i.e., XW is the hypotenuse of the triangle.

In a right angle triangle,

\(cos0=\frac{Base}{Hypotenuse}\)

In the given triangle,

\(cosW=\frac{XY}{YW}\)

\(cosW=\frac{3}{5}\)

Therefore, the required cosine ratio is \(\frac{3}{5}\).

Answer:

BC = 21 cm

Step-by-step explanation:

In similar triangles the corresponding sides are in same proportion.

Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.

      \(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)

     \(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)

Part A: The total area of the brick paver border is \(960\) square feet.

Part B: The total cost of the brick pavers needed for this project is $\(7,680\).

Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.

The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.

Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).

Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).

Note: The calculations provided assume that the border consists of a single layer of brick pavers.

For more such questions on area:

https://brainly.com/question/2607596

#SPJ8

Answer:

33/100

Step-by-step explanation:

E = 99/3

p = E/S = 33/100