A tiny songbird called the blackpoll warbler migrates each fall from North America. A tracking study showed one bird flew from Vermont at map coordinates (63,45) to Venezuela at map coordinates (67,10) in three days. If each map coordinate represents 75 kilometers, how far did the bird travel? Round to the nearest kilometer.

The  production department factory overhead rates for Cut and sew department is 89 and Pattern is 67.

a. Pattern Department            

Factory overhead rate=Total Overhead Cost/Direct Labor Hours

Factory overhead rate= 140,700/2700

Factory overhead rate=67

Cut and sew Department

Factory overhead rate=231,400/2600

Factory overhead rate=89

b.  Factory overhead per unit

Pattern Department:      

Small glove=.04 x 67

Small glove=2.68    

Medium glove= .05 x 67

Medium glove=3.35

Large glove= .06 x 67

Large glove=4.02

Cut and sew Department:      

Small glove=.07 x 89

Small glove=6.23    

Medium glove=.09 x 89

Medium glove=8.01  

Large glove=.11 x 89

Large glove=9.79

Therefore the  production department factory overhead rates for Cut and sew department is 89 and Pattern is 67.

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The complete question is:

Handy Leather, Inc., produces three sizes of sports gloves: small,

medium, and large. A glove pattern is first stenciled onto leather in the Pattern Department. The stenciled patterns are then sent to the Cut and Sew Department, where the glove is cut and sewed together. Handy Leather uses the multiple production department factory overhead rate method of allocating factory overhead costs. Its factory overhead costs were budgeted as follows:

Pattern department Overhead                $140,700

Cut and sew Department overhead        $231,400

Total    $372100

Direct labor labor estimated for each department was as follows:

Pattern   Dept. -                       2100 direct labor hours

Cut and Sew Department      2600

Total                                          4700 direct labor hours

Direct labor hours are used to allocate the production department overhead to the products. The direct labor hours per unit for each product for each production department were obtained from the engineering records as follows:

Production Departments        Small Glove    Medium Glove          Large Glove

Pattern dept. 0.04         0.05                          0.06

cut and sew dept.                             0.07                 0.09                          0.11

direct labor hours per unit               0.11                   0.14                          0.17

If required, round all per unit answers to the nearest cent.

a. Determine the two production department factory overhead rates.

Cut and sew department and Pattern

b. Use the two production department factory overhead rates to determine the factory overhead per unit for each product.

small glove, medium glove and large glove

Answer:

5/6.

Step-by-step explanation:

This is (7/9 + 8/9) / 2

= 15/9 / 2

= 15/9 * 1/2

= 15/18     Now, dividing top and bottom by 3, we get:

5/6.

The required fraction midway between 7 / 9 and 8 / 9 is 5/6.

Given that,
To determine the fraction that lies between the fraction 7/9 and 8/9.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Fraction is defined as the number of compositions that constitute the Whole.

Here,
According to the question,
Fraction midway to the fractions, 7 / 9 and 8 / 9
= [7 / 9 + 8 / 9] / 2
= 15/9/2
= 15 / 9 * 2
= 15 / 18
= 5 / 6

Thus, the required fraction midway between 7 / 9 and 8 / 9 is 5/6.

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Answer:

a= 6/25

Step-by-step explain

because it probably is

Answer:

30 degrees

Step-by-step explanation:

There are 360 degrees of longitude ( 360 degrees is a complete circle)

   It takes 24 hours to complete a complete rotation of the earth

       360 degrees / 24 hours = 15 degrees / hr

15 degrees/ hr * 2 hr = 30 degrees

Answer:

21,000$

Step-by-step explanation:

part to whole method

20/100 and 4,200/

How many 20s to get to 4,200?

Answer:

x=2.5

Step-by-step explanation:

Answer:

12.7

Step-by-step explanation:

Mean is total/the amount of numbers

Total: 11+14+11+5+17+28+3=89

Amount: 7

89/7=12.7142857

Answer:

12.7

Step-by-step explanation:

Mean = sum/count

Sum = 89

Count = 7

mean = 89/7

mean = 12.7142857143

Rounded

12.7

Answer:

sam rode further because 5 kilometers is 5000 metres and pam rode 4000 metre therefore sam rode 1kilometres further

Step-by-step explanation:

1km= 1000metres

Answer:

P(x) =x³-4x²-31x+70

Step-by-step explanation:

The function is expressed as:

P(x) = (x+5)(x-2)(x-7)

P(x) =(x²-2x+5x-10)(x-7)

P(x) = (x²+3x-10)(x-7)

P(x) = x³-7x²+3x²-21x-10x+70

P(x) =x³-4x²-31x+70

Hence the polynomial is P(x) =x³-4x²-31x+70

The final expression is

sqrt (39y9) = y4 • sqrt(39y) assuming y as positive.

Rewrite

39 y ^9 as ((y^2)^2)^2 . 39 y

Factor out y^8.

√39(y^8 . y).

Rewrite   \(y^8 as (y^4)^2\)

 √39(y^4)^2 . y).

Rules for simplifying variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

    sqrt(x8)=x4

    sqrt(x-6)=x-3

  (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     sqrt(x5)=x2•sqrt(x)

     sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

SQRT(y9) = y4 • SQRT(y)

Therefore, sqrt (39y9) = y4 • sqrt(39y)

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Answer:

Step-by-step explanation:

The circumference of a circle can be calculated using the formula C = πd, where d is the diameter of the circle and π is the mathematical constant pi (approximately 3.14).

In this case, the diameter of the crater is 680 m. So, the circumference can be calculated as:

C = πd = 3.14 × 680 = 2139.2 m

To convert this to kilometers, we can divide by 1000:

C = 2139.2 m ÷ 1000 = 2.1392 km

Rounding this to one decimal place, the circumference of the rim of the crater is approximately 2.1 km.

Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

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The amount that she owes after she factors in interest will be $33,455.64.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.

Then the amount is given as,

A = $25,000 x (1 + 0.06)⁵

A = $25,000 x (1.06)⁵

A = $25,000 x 1.3382

A = $33,455.64

The amount that she owes after she factors in interest will be $33,455.64.

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1 yard is equivalent to 3 feet. Then to convert 3.2 yards to feet​ we can use the next proportion,

Solving for x,

3.2 yards is equivalent to 9.6 feet​

Answer:

true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

10 since its the longest part of the triangle ig

Step-by-step explanation:

Answer: 10 centimeters

Step-by-step explanation:

Because it's longer than both the other sides so it has to be 10.

The height of the tree is 4.15m

We are given that

Height of Joshua, h=1.85 m

Length of tree's shadow, L=39.55 m

Distance between the tree and Joshua=35.4 m

We have to find the height of the tree.

BC=35.4 m

BD=39.55m

CD=BD-BC

CD=-35.4 m=4.15 m

EC=1.45 m

All right triangles are similar. When two triangles are similar then the ratio of their corresponding sides is equal.

\(\triangle ABD=\triangle ECD\)

\(\frac{AB}{EC}=\frac{BD}{CD}\)

Substitute the values

\(\frac{AB}{1.45}=\frac{39.55\times 1.45}{4.15} \\\\AB=20.39\)

Hence, the height of the tree=20.39 m

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The domain and range of the given graph is \([-3,-2) \sqcup (-1,5]\) and \([-5,4)\) respectively .

From the graph , we can see that the left most point is when x = -3 and this point is closed in endpoint, so we will include this value of x in the domain.

Whereas its another point is on x = -2 which is not filled up so , we will not consider this value of x in the domain. In the interval , domain can be represented by \(-3\leq x < -2\)  .This interval can be written as \([-3,-2)\)

Now , the right most point is when x = 5 which is filled up so we will include this value of x in the domain. Whereas it's another endpoint is at x = - 1 , we will not consider this value of x in the domain as it is not filled up. In the interval , domain can be represented by \(-1 < x\leq 5\) .This interval can be written as \((-1,5]\) .

In order to get the full domain of the function we will use union symbol

 \([-3,-2) \sqcup (-1,5]\)

For the range , we will observe the values of y . The lowest point is when y = -5 which is filled up so we will include this value of y in the range.

Whereas the highest point is when y = 4 which is not filled up so , we will not consider this value of y in the range . In the interval , range can be represented by \(-5\leq y < 4\) .Since there are no gaps in the range, we don't use any union symbols here and hence range is \([-5,4)\)

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x is equal to 2 or -5

y is equal to 1 or 8

Step-by-step explanation:

first put your first equation in a format of y = x + _

here it will be :

\(y = - \times + 3\)

now go and substitute this in your second equation. just like the picture. the pictures explain further

Hello there!

We are given the simultaneous equations:

\( \displaystyle \large{ \begin{cases} x + y = 3 \\ {x}^{2} - 3y = 1 \end{cases}}\)

There are many methods to solve the equation but the best way for this problem is Substitution Method.

First, we have to isolate one-degree variable. I will choose the first equation to isolate. We are going to isolate y-variable so we can substitute the first equation in the second.

\( \displaystyle \large{ \begin{cases} x + y = 3 \\ {x}^{2} - 3y = 1 \end{cases}}\)

Subtract x both sides for first equation.

\( \displaystyle \large{ \begin{cases} x - x+ y = 3 - x \\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} - 3y = 1 \end{cases}}\)

After isolating y-term, we can finally substitute y = 3-x in the second equation.

\( \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} - 3(3 - x) = 1 \end{cases}}\)

Expand -3 in. Recall that negative × negative = positive and negative × positive = negative.

\( \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 + 3x= 1 \end{cases}}\)

Notice that the second equation is in quadratic pattern. We are going to convert in the standard form to solve the equation.

Subtract both sides by 1.

\( \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 - 1 + 3x= 1 - 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -10 + 3x= 0 \end{cases}}\)

Arrange the expression in ax^2+bx+c = 0.

\( \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 - 1 + 3x= 1 - 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} + 3x - 10= 0 \end{cases}}\)

Factor the expression.

What two numbers add or subtract each others and equal to 3? (These numbers must not multiply each others and be greater than 10)

What two numbers multiply each others and equal to -10?

Check the number above and multiply two numbers.

Two numbers would be 5 and -2. Factor the expression in two brackets.

\( \displaystyle \large{(x + 5)(x - 2) = 0}\)

Then we solve like a linear equation, isolate both x.

\( \displaystyle \large{x= - 5,2}\)

We've got two x-values. But we are not done yet.

We are going to use these values to substitute in the simultaneous equation. You can substitute in any equations; the first or second. I will choose to substitute x = -5 or x = 2 in the first equation since it is faster.

\( \displaystyle \large{ \begin{cases} y= 3 - x \\ {x}^{2} - 3y = 1 \end{cases}}\)

Substitute x = -5

\( \displaystyle \large{ \begin{cases} y= 3 - ( - 5)\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 3 + 5\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 3 - ( - 5)\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 8\\ {x}^{2} - 3y = 1 \end{cases}} \)

When we substitute x = -5, y = 8.

Next, substitute x = 2

\( \displaystyle \large{ \begin{cases} y= 3 -2\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 1\\ {x}^{2} - 3y = 1 \end{cases}}\)

When we substitute x = 2, y = 1.

Therefore,

OR

Let me know if you have any questions!

Topic: Simultaenous Equations

The value of x, considering the consecutive interior angles in this problem, is given as follows:

x = 30.

We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.

Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of x can be found as follows:

3x - 8 + 4x - 22 = 180

7x - 30 = 180

7x = 210

x = 210/7

x = 30.

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To write a number in exponential form, we look at the main number, then see how much is it repeated by.

Our main number is 0.75.

How many times 0.75 is repeating is 5 times.

Therefore, our answer is: \(0.75^5\).

Optional: 0.75 to the power of 5 is: 0.2373046875.

we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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Answer:

Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

Step-by-step explanation:

hourly pay: $5/hour

number of hours: 24 hours

total pay = hourly pay × number of hours

total pay = $5/hour × 24 hours

total pay = $120

MP3 player costs $100.

Total pay is $120.

Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

D. dP/dt = 0.02P - N

The correct differential equation is dP/ dt = 0.02 P-N.

To decide the differential equation that describes the relationship between P and t, we can use the formula for continuously compounded interest

P = Pe^(rt)

where P is the balance of the account at time t, r is the periodic interest rate, and e is the fine constant e.

Now, we know that Ana is withdrawing money from the account continuously at a rate of N bones per time. This means that the rate of change of the balance, dP/dt, is equal to the difference between the interest earned and the money withdrawn

dP/dt = 0.02P - N

This is because the interest earned is 0.02P ( since the interest rate is 0.02 and the balance is P), and the plutocrat withdrawn is N.

Thus, the correct differential equation is dP/ dt = 0.02 P-N.

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Answer:

2.5 cups of flour per cup of water.

Step-by-step explanation:

We can divide the entire recipe by two, to get the amount of flour to 1 cup of water.

5/2 = 2.5

2/2 = 1

Therefore, 2.5 cups of flour needs 1 cup of water.

Answer:

There are 2.5 cups of flour per cup of water

Step-by-step explanation:

Step 1:  Find the ration

Cups of Flour : Cups of Water

5 : 2

2.5 : 1

Answer:  There are 2.5 cups of flour per cup of water

Answer:

(0, 0)

Step-by-step explanation:

f(x) = (x-4)(x+4)

Let f(x) = 0

Therefore,

(x-4)(x+4) = 0

x - 4 = 0 or x + 4 = 0

x = 4 or x = - 4

Hence x - intercepts are (-4,0) & (4, 0)

Mid point of x - intercepts = (- 4 + 4) /2, (0+0)/2= 0/2 , 0/2 = (0, 0)

Each corsages sell for $22. And Each boutonnieres sell for $21.

Brittany sold 12 corsages and 17 boutonnieres last year in total of $621.

And she sold 19 corsages and 16 boutonnieres this year for a total of $754.

First, we will create the system of equation from given information

So, the equations are

12x+17y=621..…(1)

19x+16y=754..…(2)

Where,

X=cost of one corsage

Y=cost of one boutonniere

Make y the subject of equation (1)

y=(621-12x)/17

Put this value of y in equation (2)

Therefore

19x+16((621-12x)/17)=754

19x+(9936-192x)/17=754

(323x+9936-192x)/17=754

131x+9936=12818

131x=12818-9936

131x=2882

x=2882/131

x=22

So, the cost of one corsage is $22.

Now, put this value of x in equation (1)

12×22+17y=621

264+17y=621

17y=621-264

y=357/17

y=21

The cost of one boutonniere is $21.

Thus, the cost of each corsages and boutonnieres are $22 and $21.

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The expression for the simplified polynomial would be - x² - 10x - 24.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the polynomial ( x + 5 )² is subtracted from 1. The simplified polynomial can be written as:-

Polynomial = 1 - ( x + 5 )²

Polynomial = 1 - ( x² + 10x + 25 )

Polynomial = 1 - x² - 10x - 25

Polynomial = -x² - 10x - 24

Hence, the polynomial can be written as -x² - 10x - 24.

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A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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