Express as a product "1 - sin(a) - cos (a)"

The measure οf the equal sides οf the triangle is 8√3 cm and the perimeter οf the triangle is apprοximately 49.9 cm.

The current carried by the third resistοr is 2.4A is the tοtal current is 8A what current is carried by the third resistοr.

A fractiοn is a mathematical term that represents a part οf a whοle οr a ratiο between twο quantities.

a. Tο find the fractiοn οf tοtal current carried by the twο resistοrs, we need tο add up the currents and divide by the tοtal current. Let I be the tοtal current, and let I1 and I2 be the currents carried by the first twο resistοrs, respectively. Then we have:

I1 = 1/5I

I2 = 1/2I

The tοtal current is:

I = I1 + I2 = (1/5 + 1/2)I = 7/10I

Therefοre, the fractiοn οf tοtal current carried by the twο resistοrs is:

(I1 + I2)/I = (1/5I + 1/2I)/I = (7/10I)/I = 7/10

b. Let I3 be the current carried by the third resistοr. Then we have:

I3 = I - (I1 + I2) = I - 7/10I = 3/10I

Therefοre, the fractiοn οf tοtal current carried by the third resistοr is:

I3/I = (3/10I)/I = 3/10

c. If the tοtal current is 8A, then we have:

I = 8A

The current carried by the third resistοr is:

I3 = 3/10I = 3/10 x 8A = 2.4A

Therefοre, the current carried by the third resistοr is 2.4A.

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the answer is 1 5/8 inches shorter. To find the difference between the initial length of the pencil and the final length after the project, we need to subtract the final length from the initial length.

Initial length of the pencil = 7 1/2 inches

Final length of the pencil = 5 7/8 inches

To subtract these two values, we need to convert the mixed numbers to improper fractions.

7 1/2 = 15/2

5 7/8 = 47/8

Now we can subtract:

15/2 - 47/8

To subtract these fractions, we need to find a common denominator. The least common multiple of 2 and 8 is 8, so we can convert both fractions to have a denominator of 8.

15/2 = 60/8

47/8 = 47/8

Now we can subtract:

60/8 - 47/8 = 13/8

So the pencil is 13/8 inches shorter after the project. To write this as a mixed number, we divide the numerator by the denominator:

13 ÷ 8 = 1 with a remainder of 5

So the answer is 1 5/8 inches shorter.

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The area of triangle ABC is 249.36 sq ft while the area of ΔACD and ΔBCD is 124.68 sq ft

The area of a triangle can be calculated using the formula:

Area = (1/2) x base x height

where "base" is the length of the base of the triangle and "height" is the perpendicular distance from the base to the opposite vertex.

Lets find altitude with with Pythagoras formula:

[tex]\rm a^2 + b^2 = c^2[/tex]

[tex]\rm a^2 + 12^2 = 24^2[/tex]

[tex]\rm a^2 = 24^2 -12^2[/tex]

[tex]\rm a^2 = 576 - 144[/tex]

[tex]\rm a^2 = 432[/tex]

a = √432

a =

​a = 20.78

To find the area of a triangle, we use the formula A = 1/2 × base × height.

In this case, the base of the triangle is 24 ft and the height is 20.78 ft.

Therefore,

A = 1/2 × 24 ft × 20.78 ft

A = 249.36 sq ft

Hence, The area of each triangle is 249.36 square feet.

Now, Both tringles are 1/2 of the area as base = 12 = 1/2 × 24

ΔACD =  1/2 × 249.36

ΔACD =  124.68 sq ft

ΔBCD =  1/2 × 249.36

ΔBCD =  124.68 sq ft

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Complete question:

What is the area of each triangle Base = 24 ft 20 ft

To calculate the compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly, we need first to calculate the quarterly interest rate and the number of compounding periods.

Quarterly interest rate = Annual interest rate / 4

= 20% / 4

= 5%

Number of compounding periods = (Time in months) / (Number of months per compounding period)

= 9 / 3

= 3

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

where,

A = final amount

P = principal amount

r = annual interest rate

n = number of compounding periods per year

t = time in years

Plugging in the values, we get:

A = 16000(1 + 0.05/4)^(4*3/12)

A = 16000(1 + 0.0125)^1

A = 16000(1.0125)

A = 16180

Therefore, the compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs 1800 (i.e., A - P = 16180 - 16000).

The area of the composite figure using area formula is 45unit².

Option b is the correct option.

The space that any composite shape occupies is referred to as the area of composite shapes. In order to create the desired shape, a few polygons are connected to create a composite shape. These figures or forms can be constructed using a variety of geometrical elements, including triangles, squares, quadrilaterals, and others.

To determine the area of a composite object, divide it into simple shapes like a square, triangle, rectangle, or hexagon. In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.

In the question, we can see that the composite figure comprises of a triangle and a rectangle.

Now, length of the rectangle as per the vertices is, l = 6 units.

Breadth of the rectangle as per the vertices is, b = 6 units.

As the length and breadth of the rectangle as per the vertices are equal it's a square with side a = 6 units

Area of square = a²

= 6²

=36unit².

Now in the triangle,

Base, b = 6 units

Height, h = 3 units.

Area = 1/2 × b × h

= 1/2 × 6 × 3

= 9unit².

Therefore, the total area of the figure is 36 + 9 = 45unit².

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The mean of the sampling distribution of all possible samples of size 16 will be 42.5, the correct option is D.

Normal distribution with mean μ = 42.5 inches and standard deviation σ = 2.5 inches. Let x₁, x₂, ..., xₙ be a random sample of size n = 16 from X, and let x be the sample mean

The sampling distribution of the mean x is also Normal, with mean μ and standard deviation σ/√n.

f(x) = (1/√(2π) × (σ/√n)) × exp[-(x - μ)² ÷ (2 × (σ/√n)²)]

we integrate

Mean of x = ∫(-∞ to ∞) x × f(x) dx

Mean of x = 2 × ∫(μ to ∞) x × f(x) dx

Next, we substitute

u = (x - μ) / (σ/√n):

Mean of x = 2 × ∫(0 to ∞) (u × (σ/√n) + μ) × (1/√(2π) × (σ/√n)) × exp(-u² / 2) du

Simplifying this expression gives:

Mean of x = μ

Therefore, the mean of the sampling distribution of all possible samples of size 16 is equal to the population mean μ, which is 42.5 inches.

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The complete questions is :

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the mean of the sampling distribution of all possible samples of size 16?

A 2.66

B 10.63

C 17

D 42.5

16.8 gallons

2.85 dollars/gallons

[tex]16.8 \times \frac{2.85 \: dollars}{gallons} = 47.88 \\ [/tex]

Alyssa paid a total of $47.88 for 16.8 gallons of gas when each gallon costs $2.85

The subject of this question is mathematics. Let's start by identifying what we know. We know that Alyssa filled her tank with 16.8 gallons of gas and that the cost of gas is $2.85 per gallon.

To find out how much Alyssa paid in total, we need to multiply the number of gallons by the cost per gallon:

Now, we are asked to round to the nearest cent. Rounding $47.88 doesn't change anything because the digits following the decimal point are 88, which is less than 100. So, the total amount Alyssa paid is $47.88.

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Step-by-step explanation:

oil change. palm trees oil

In the percentage , the statement is the best prediction about the scoops of ice cream the college will need is D)The college will have about 1,440 students who prefer ice cream.

What is percentage?

percentage. Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Here then given, Total number of students = 4000

Sample number of students = 225.

In 225 students 81 students prefer ice cream.

Now to find percentage then,

=> [tex]\frac{81}{225}\times100[/tex]

=> 0.36*100

=> 36%.

Now Number of students who prefer ice cream = 36% of 4000

=> 36/100 * 4000

=> 1440.

Hence the correct option is D)The college will have about 1,440 students who prefer ice cream.

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1) the JK does not form the line segment.

2) NL line segment is different from other three options.

It is a part of line having two ends points.

The simplest definition of a line is an arrangement of points that extends in opposite directions to infinity, while a ray is a section of a line that has one endpoint and extends continuously in one direction, while a segment of a line is a section of a line between two endpoints.

1) Like a line can be expressed in liner form such as y=mx+c where as, a line segment will consist of two coordinates such as A(x₁,y₁) and B(x₂,y₂).

Here, the JK does not form the line segment as there is no connecting line between them.

2) Here, NL line segment is different from other three options as is formed the line JL.

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To determine the correct inequality that represents the shaded area below the diagonal curve, we need to identify the equation of the line that passes through the two endpoints of the curve, which are (-2, 5) and (3, -5).

First, we need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-5 - 5) / (3 - (-2))

slope = -10 / 5

slope = -2

Next, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points on the line.

Using the point (-2, 5), we have:

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

y - 5 = -2(x + 2)

y - 5 = -2x - 4

y = -2x + 1

So the equation of the line passing through the endpoints of the curve is y = -2x + 1.

To determine which inequality represents the shaded area below the curve, we can test a point that is not on the line, such as (0, 1).

Plugging in (0, 1) into the equation of the line, we get:

1 = -2(0) + 1

1 = 1

Since 1 is equal to 1, the point (0, 1) is on the line. Therefore, the inequality that represents the shaded area below the curve is y < -2x + 1, since the points below the line satisfy this inequality.

So the correct answer is C. y < -2x + 1.

Miss x baked 286 loaves of bread on Saturday and 208 loaves of bread on Sunday. To calculate the total loaves of bread baked on both days, we can subtract 78 from 286 to get the number of loaves of bread baked on Sunday.

Miss x baked 286 loaves of bread on Saturday. We know that she baked 78 fewer loaves of bread on Sunday than Saturday. To calculate the total loaves of bread baked on both days, we can subtract 78 from 286 to get the number of loaves of bread baked on Sunday. This gives us 208 loaves of bread baked on Sunday. Adding this to the 286 loaves of bread baked on Saturday, we get a total of 494 loaves of bread baked on both days. Therefore, Miss x baked 286 loaves of bread on Saturday and 208 loaves of bread on Sunday.

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The equation with SLOPE: -3/4 and Y-intercept (0,5) is Y = (-3/4)x + 5 and graphed below.

The pοint οn a line's graph where it crοsses the x-axis is knοwn as the x-intercept.

The pοint where a line's graph crοsses the y-axis is knοwn as the y-intercept.

On any graph, the x and y -intercepts are crucial lοcatiοns. The graphs οf linear equatiοns will be the main tοpic οf this chapter. Hοwever, at this pοint, we may utilize these cοncepts tο identify nοnlinear graph intercepts. Always keep in mind that intercepts are οrdered pairs that shοw where the graph and axes cοnnect.

The fοrmula οf slοpe-intercept is y=mx+b.

By using this fοrmula

Y=(-3/4)x+b

Using the given pοint we get,

5=(-3/4)0+b

Or, b=5

The answer is Y=(-3/4) x+5

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In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

To find the annual rate of change between 1992 and 2006, we can use the formula:

r = [tex](V_2/V_1)^{1/n}-1[/tex]

where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.

=>r = -0.0839

Therefore, the rate of change between 1992 and 2006 is -0.0839.

To express the rate of change in percentage form, we can multiply the result from part A by 100:

=>r = -0.0839 x 100

=> r = -8.39%

Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.

From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:

where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.

=>V = 11792.51

Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).

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The value of the two numbers are 43 and 218

From the information given, we have;

Let the numbers be x and y

Then,

The difference between the numbers = x - y

The sum of the numbers = x + y

Substitute the values

x + y = 261

x - y = 175

Let's solve the simultaneous equations

Make 'x' the subject from 1

x = 261 - y

Substitute the value in 2

261 - y - y= 175

collect the like terms

-2y = - 86

y = 43

Substitute to determine the value of x

x = 261 - y = 261 - 43 = 218

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The total cost of the metal which will be used to construct the metal tank would be = $82.5

To calculate the area of the metal tank, the formula for the area of the cylinder is used which would be;

= 2πr (h+r)

Where

R = 12/2 = 6 ft

h = 4ft

π = 3.14

area = 2×3.14×6(4+6)

= 37.68×10

= 3.75 ft²

But 1ft² = $22

3.75ft² = X

make X the subject of formula;

X = 22× 3.75 = $82.5

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Step-by-step explanation:

on Monday:340ML

on Tuesday:1.5L

total millilitres?so we have to get the to get the total of water in Millilitres (ML)

step 2:we have to convert the 1.5L to ML

we know 1L=1000ML

and 1000ML=1ML

so 1.5L =1500ml

Step 3

340 +1500=1840ML

The expression "[tex]r_i \ o \ r_j = r_{i+j},[/tex]for all i and j" represents a mathematical relationship involving a binary operation "o" and a sequence of elements denoted by "[tex]r_i[/tex]", where "i" and "j" are integers.

The expression states that for any two integers "i" and "j", the result of applying the binary operation "o" to the elements "r_i" and "r_j" is equal to the element "[tex]r_{i+j}[/tex]" in the sequence that is the sum of the indices "i" and "j".

In other words, if we have a sequence of elements "r_1, r_2, r_3, ..." and a binary operation "o", then this expression tells us that the result of applying the operation "o" to any two elements in the sequence is equal to the element in the sequence whose index is the sum of the indices of the two original elements.

For example, as given in the polygon, a sequence of numbers {1, 2, 3, 4, ...} and the binary operation is addition (+), then the expression "[tex]r_i \ o \ r_j = r_{i+j}[/tex], for all i and j" tells us that the sum of any two numbers in the sequence is equal to the number whose index is the sum of the indices of the two original numbers.

For instance, 1 + 2 = 3, which is the same as r_1 o r_2 = r_{1+2} = r_3.

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Side A and Side B are both equal to 32/3, which is 10 2/3 centimeters and the total number of hours the girls spent cleaning is 15 hours.

The perimeter of a shape can be found by adding up the lengths of all its sides.

The perimeter of a triangle is the sum of the lengths of its three sides, so in this case the equation to solve for the length of each of the two sides is:

Perimeter = 2 x Side A + Side B

32 = 2x + x

3x = 32

x = 32/3

Therefore, Side A and Side B are both equal to 32/3, which is 10 2/3 centimeters.

Kelsey and her 4 sisters spent an equal amount of time cleaning their home. To find the total number of hours the girls spent cleaning, we can write and solve a division equation. Let c be the total number of hours the girls spent cleaning.

c / 5 = 3

c = 15

Therefore, the total number of hours the girls spent cleaning is 15 hours.

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Answer: 41 degrees

Step-by-step explanation: To determine the angle at which the pizza was cut, we need to use the formula for the area of a sector of a circle:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a constant (approximately equal to 3.14), and r is the radius of the circle.

In this case, we know that the area of the sector that corresponds to the slice of pizza that was eaten is 17 square inches. We also know that the pizza has a diameter of 14 inches, which means that the radius is 7 inches.

Substituting these values into the formula, we get:

17 = (θ/360)π(7²)

17 = (θ/360)49π

θ/360 = 17/(49π)

θ = (17/49π) * 360

θ ≈ 41 degrees (rounded to the nearest whole number)

Therefore, the pizza was cut at an angle of approximately 41 degrees.

Answer:

a dilatation centred at the origin with scale factor 3

Step-by-step explanation:

under a dilation centred at the origin with scale factor k

a point (x, y ) → (kx, ky )

here

A (2, 4 ) → A' (3(2), 3(4) ) → A' (6, 12 )

B (1, 6 ) → B' (3(1), 3(6) ) → B' (3, 18 )

C (5, 3 ) → C' (3(5), 3(3) ) →C' (15, 9 )

thus the transformation for Δ ABC → Δ A'B'C'

is a dilatation centred at the origin with scale factor 3

One possible set of four lengths that meets the given requirements is:

3 inches, 4 inches, 5 inches, 7 inches

To show that this set of lengths meets all the requirements, we need to demonstrate that:

Each length is different: We can see that all four lengths are different.

Each length is a whole number: We can see that all four lengths are whole numbers.

No matter which three you choose, you will always be able to make a triangle: To show this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For example, if we choose the lengths 3, 4, and 5, we can see that 3 + 4 = 7, which is greater than 5. Therefore, we can make a triangle with sides of length 3, 4, and 5. Similarly, if we choose the lengths 3, 4, and 7, we can see that 3 + 4 = 7, which is still greater than 7. Therefore, we can make a triangle with sides of length 3, 4, and 7.

We can repeat this process with any combination of three lengths from the set, and we will always find that we can make a triangle. Therefore, we have shown that the set of lengths {3 inches, 4 inches, 5 inches, 7 inches} meets all the requirements.

Thus, the amount of money Richard owe (in dollars) after 1 year on his credit card is $2,016.19.

Compounding interest on both the principal and the accrued interest is expressed by the term "monthly compound interest," which refers to interest that is compounded over month. The principal amount times one plus the interest rate divided by a number of periods, raised to the power of such number of periods, is how monthly compounding is computed.

Formula for amount after compounding:

A = P[tex](1 + r/n)^{nt}[/tex]

A = amount after compounding

P is principal (=$1,597.57)

r is rate of interest (23.5%)

n is the number of times compounded (= 12)

t is time in years (1 year)

A = 1597.57* [tex](1 + 0.235/12)^{12*1}[/tex]

A = 1597.57* 1.26

A = 2,016.19

Thus, the amount of money Richard owe (in dollars) after 1 year on his credit card is $2,016.19.

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The estimated fox population in the year 2008 is 19498.

A function is a mathematical concept that describes the relationship between two sets of variables, where each input value (independent variable) corresponds to a unique output value (dependent variable).

(a) The continuous growth rate of 5% per year means that the fox population is increasing at a rate proportional to its current size. Let P(t) be the fox population t years after 2000. Then, we can model the population using the differential equation:

dP/dt = kP

where k is the constant of proportionality. To solve this differential equation, we can separate the variables and integrate:

dP/P = k dt

ln|P| = kt + C

where C is the constant of integration. To find the value of C, we use the initial condition that the population in the year 2000 (t=0) was 12500:

ln|12500| = 0 + C

C = ln|12500|

Therefore, the solution to the differential equation is:

ln|P| = kt + ln|12500|

Simplifying, we get:

P(t) = [tex]e^(kt + ln|12500|)[/tex]

P(t) = 12500 [tex]e^(kt)[/tex]

where P(t) is the fox population t years after 2000.

We know that the population grows at a continuous rate of 5% per year, so we can use this information to find the value of k. Since the continuous growth rate is given by r = 0.05, we have:

k = ln(1 + r) = ln(1.05)

As a result, the following function represents the fox population t years after 2000:

p(t) = 12500 [tex]e^(0.05t)[/tex]

(b) Since t is the number of years after 2000, we must determine the value of p(8) in order to calculate the fox population in 2008. We have the following using the function from section (a):

p(8)  = 12500 [tex]e^(0.05(8))[/tex]

       = 19498

Therefore, the estimated fox population in the year 2008 is 19498.

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Answer:

56.7%

Step-by-step explanation:

Total number of students = 30

Number of boys in the class = 13

Number of girls in the class = 30 - 13 = 17

Now we have to find the percent of girls of the class

Therefore

[tex]\dfrac{\text{Number of girls}}{\text{Total students}} \times100[/tex]

[tex]=\dfrac{17}{30}\times100=56.67\%[/tex]

[tex]56.67\implies56.7\%[/tex]

Hence, girls are 56.7% of the class.

The relationship shown on the table is such that C. The relationship is not linear.

To determine if the relationship is linear, we can check if the differences in the y-values are constant for equal differences in the x-values.

Calculate the differences between the x-values and the y-values:

Δx1 = 7 - 1 = 6

Δy1 = -7 - (-4) = -3

Δx2 = 13 - 7 = 6

Δy2 = 10 - (-7) = 17

Δx3 = 19 - 13 = 6

Δy3 = -13 - 10 = -23

The differences in x-values are constant (Δx1 = Δx2 = Δx3 = 6), but the differences in y-values are not (Δy1 ≠ Δy2 ≠ Δy3). Therefore, the relationship is not linear.

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Answer:

3.5

Step-by-step explanation:

Answer: 3.5

Step-by-step explanation: In this scenario, the vertex would be the peak of the baseball throw. We can find the x value of the vertex by using -b/2a. With your equation of 112x-16x^2 we need to change the x^2 value to the front to make it -16x^+112x so that it is in standard form. Now take your b value (112), make it negative (-112), and divide that by 2 times -16. to get 3.5.

I should also include that the x value of the vertex is equal to t which is seconds.