A path is 288.3 feet long. Jamie wants to walk the length of the path taking 100 equal steps. How long should each step be? A. 0.2883 foot B. 2.883 feet C. 28.83 feet D. 288.3 feet

The side length of the unknown segment x in the triangle has a value of 40.1cm

To find the unknown side x, we use the sine rule

The Law of Sines (or Sine Rule) is very useful for solving triangles:

a/sin A = b/sin B = c/sin C

It works for any triangle and it says that:

When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C

To find the third angle in the triangle, we use the known rule of the sum of angles in a triangle which is equal to 180°

unknown angle = 180° - 90°- 55° = 35°

Using the sine rule let us find the side x

23/sin35 = x/sin90

23/0.5736 = x/1

from here we cross multiply to get

0.5736x = 23

We can find the value of x by dividing both sides by 0.5736

x = 23/0.5736

x = 40.1cm

Hence, the value is 40.1 cm

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Answer:

Step-by-step explanation:

Use the figure to complete the transformations.

1. Reflect the triangle across the y-axis.

2. Reflect the image across the x-axis.

The final image is the same as what single transformation?

a translation 2 units to the left and 2 units down

a reflection across the y-axis

a 180° rotation about the origin

a clockwise rotation 90° about the origin

Answer:

6,400,500 = 660,000(0.66)^t

Step-by-step explanation:

The tοtal return οn investment after 20 years is $55,275.00.

By dividing the tοtal number οf shares οutstanding by the number οf shares that a sharehοlder οwns, and multiplying the result by 100, a sharehοlder can determine hοw much οf a firm they οwn.

a. Tο cοmplete the table, we plug in the values οf x and evaluate the fοrmula:

Investment Balance

Years          (x)

3             $14,157.00

5             $18,564.38

10            $32,435.85

20           $67,275.00

b. Tο find the tοtal return οn investment after 20 years, we need tο calculate the difference between the investment balance after 20 years and the initial investment οf $12,000:

Tοtal return = Investment balance after 20 years - Initial investment

Tοtal return = $67,275.00 - $12,000

Tοtal return = $55,275.00

Therefοre, the tοtal return οn investment after 20 years is $55,275.00.

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We use the additiοn prοperty οf equality tο simplify this tο FA = RN, which is what we wanted tο prοve.

The substitutiοn prοperty οf equality states that if twο expressiοns are equal, then οne can be substituted fοr the οther in any equatiοn οr expressiοn withοut changing the truth οf that equatiοn οr expressiοn.

Step:

The prοοf starts with the given that FRAN. We want tο prοve that FARN is true. We start by using the segment additiοn pοstulate tο add RA tο bοth sides οf FR tο get FR + RA = FR + RA.

We then use the additiοn prοperty οf equality tο simplify this tο FR + RA = FR + RA. Next, we use the segment additiοn pοstulate again tο add AN tο bοth sides οf FR + RA tο get FR + RA + AN = FR + RA + AN.

We then use the substitutiοn prοperty οf equality tο replace AN with FR, which gives us FR + RA + FR = FR + RA + FR.

We simplify this tο FR + RA = FR + RA + FR and then use the segment additiοn pοstulate again tο add FA tο bοth sides οf RA tο get RA + FA = RA + FA.

Finally, we use the additiοn prοperty οf equality tο simplify this tο FA = RN, which is what we wanted tο prοve.

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Answer:

500 Milliliters

Step-by-step explanation:

Because a liter is 100x a milliliter so 0.5x100=500

Therefore , the solution of the given problem of equation comes out to be  ratio of y to x is not constant in this situation, y does not directly change with x.

The use of the same variable word in mathematical formulas frequently ensures agreement between two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate expression the equality of many academic figures. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the sample of y + 6 instead.

Here,

Checking whether there is a fixed ratio between y and x will help us determine whether y directly changes with x.

In general, straight variation is calculated as follows:

=>  y = kx

where k is the variational constant.

Let's split both sides by x to check if the equation 3y = -7x - 18 can be expressed in this way:

=>  3y/x = -7 - 18/x

Now, 3y/x ought to equal some constant k if the relation between y and x is constant:

=>  3y/x = k

When we add this to the solution we previously determined, we get:

=> k = -7 - 18/x

Since the ratio of y to x is not constant in this situation, y does not directly change with x.

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Answer:

8

Step-by-step explanation:

square the whole equation to get

[tex] {m}^{2} + \frac{1}{ {m}^{2} } = 9[/tex]

then minus one from both sides of the equation to get 8

Answer: To construct a 99% confidence interval for the mean number of books people read, we can use the following formula:

CI = X ± Z*(S/sqrt(n))

where:

X = sample mean (11.3)

S = sample standard deviation (16.6)

n = sample size (1005)

Z = the z-score for the confidence level (99%)

To find the z-score for the 99% confidence level, we can look up the value in a standard normal distribution table or use a calculator. The z-score for a 99% confidence level is 2.576.

Substituting the values into the formula, we get:

CI = 11.3 ± 2.576*(16.6/sqrt(1005))

CI = 11.3 ± 2.576*(0.524)

CI = 11.3 ± 1.35

Therefore, the 99% confidence interval for the mean number of books people read is (9.95, 12.65). We can be 99% confident that the true population mean falls within this interval.

Step-by-step explanation:

Answer:

The value of m that satisfies the equation 6200 = 200^m is approximately 1.94.

Step-by-step explanation:

To find the value of m, we can take the logarithm of both sides of the equation:

log(6200) = log(200^m)

By the laws of logarithms, we can simplify this to:

log(6200) = m log(200)

Now we can solve for m by dividing both sides by log(200):

m = log(6200) / log(200)

Using a calculator, we can evaluate this expression to find:

m ≈ 1.94

Therefore, the value of m that satisfies the equation 6200 = 200^m is approximately 1.94.

Hopefully this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

Therefore , the solution of the given problem of expressions comes out to be  the expression's precise number is 8/15.

There is a need for calculations like variable multiplication, dividing, joining, and currently removing. If you combined them, you'd get the following: A mathematical formula, some data, and an equation. Values, elements, mathematical operations like equation additions, deductions, errors, and subdivisions, as well as mathematical formulas, make up a statement of truth. It is possible to assess and analyse words and sentences.

Here,

A right triangle with an opposite side of 8 and a hypotenuse of 17 can be completed by adding the missing side using the Pythagorean equation. Make x the neighbouring side. Then:

=> x² + 8² = 17²

=> x² = 17² - 8²

=> x² = 225

=> x = 15

The triangle therefore has edges of 8, 15, and 17. As a result, the neighbouring angle's tangent is 15/8 and the sine of the angle across from the side of length 8 is 8/17. (since tangent is opposite over adjacent). In order to determine the cotangent, we can take the inverse of this tangent:

Coefficient

=> [sin⁻¹ 8/17] = 8/15

As a result, the expression's precise number is 8/15.

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The simplified form of each rational equation is:

Case 1: f(x) = (6 · x³ + 11 · x² - 5 · x - 12) / (3 · x + 4) → f(x) = 2 · x² + x - 3

Case 2: f(x) = (6 · x⁴ + 7 · x³ - 9 · x² + 13 · x - 12) / (3 · x² - x + 3) → f(x) = 2 · x² + 3 · x - 4

Herein we find two rational equations, whose simplified form has to be found. Rational equations are algebraic equations of the form:

R(x) = P(x) / Q(x)

Where:

The procedure to simplify a rational equation is summarized below:

Case 1

f(x) = (6 · x³ + 11 · x² - 5 · x - 12) / (3 · x + 4)

f(x) = [(x - 1) · (3 · x + 4) · (2 · x + 3)] / (3 · x + 4)

f(x) = (x - 1) · (2 · x + 3)

f(x) = 2 · x² - 2 · x + 3 · x - 3

f(x) = 2 · x² + x - 3

Case 2

f(x) = (6 · x⁴ + 7 · x³ - 9 · x² + 13 · x - 12) / (3 · x² - x + 3)

f(x) = [6 · (x + 3 / 4 - √41 / 4) · (x + 3 / 4 + √41 / 4) · (x - 1 / 6 - i √ 35 / 6) · (x - 1 / 6 + i √35 / 6)] / [3 · (x - 1 / 6 - i √ 35 / 6) · (x - 1 / 6 + i √35 / 6)]

f(x) = 2 · (x + 3 / 4 - √41 / 4) · (x + 3 / 4 + √41 / 4)

f(x) = 2 · [x² + (3 / 2) · x + [(3 / 4)² - (√41 / 4)²]]

f(x) = 2 · [x² + (3 / 2) · x - 2]

f(x) = 2 · x² + 3 · x - 4

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Answer:

[tex]2\frac{7}{24}[/tex]

Step by step explanation:

just do the math it aint hard tbh

Answer:

[tex]2\frac{7}{24}[/tex]

Step-by-step explanation:

To work this out, we first need to change the fractions into mixed numbers...

Now we have to flip the second fraction around so our question will turn into a multiplication...

Now solve...

Hope this helps, have a lovely day! :)

Answer:

the answer is (-infinity,1/3)Union (1/3,infinity)

A graph of the equation -5 < x < -3 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Next, we would rewrite the given compound inequality in pairs as follows;

-5 < x < -3 ≡ x > -5 or x < -3

In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below.

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The given sequence is a geometric sequence, where the common ratio (r) between any two consecutive terms is:

r = 3/1.5 = 2

We need to find the sum of the first 10 terms of this sequence. Let's denote the first term (a₁) as 1.5 and the tenth term (a₁₀) as a.

The formula to find the sum of the first n terms of a geometric sequence is:

Sₙ = a(1 - rⁿ)/(1 - r)

Substituting the values, we get:

a = 1.5 x 2^9 = 768

S₁₀ = 1.5(1 - 2¹⁰)/(1 - 2) = 1.5(1 - 1024)/(-1) = 1.5 x 1023

Therefore, the sum of the first 10 terms of the given sequence is 1.5 x 1023, which is approximately equal to 1.53 x 10³=1534,5

The total feet of steel wire needed to secure the pole is 26 using Pythagoras Theorem.

What is Pythagorean Theorem?

A fundamental idea in mathematics pertains to the lengths of the sides of a right triangle and is known as the Pythagorean theorem. It claims that the hypotenuse's square length, which is the side that faces the right angle, equals the sum of the squares of the lengths of the other two sides of any right triangle. The Pythagorean theorem, which is named after the ancient Greek mathematician Pythagoras who originally proved the theorem, has extensive applications in areas including geometry, trigonometry, and physics.

Let the length of the wire = x.

Using Pythagoras Theorem we have:

x² = 12² + 5²

x² = 144 + 25

x² = 169

x = √(169)

x = 13

For two steel wires:

2(13) = 26 ft.

Hence, the total feet of steel wire needed to secure the pole is 26.

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the rate of change of the angle of elevation teta is  ∅ = tan⁻¹ 2.1275

Angle of Elevation is an equation used in math to describe the angle formed between the horizontal line and the line of sight when an observer looks upwards. It is always at a height that is greater than the height of the observer

Using ∅ = tan⁻¹ (x/2000)

Then we are to find the angle teta

Where x = 4255 ( substitution)

∅ = tan⁻¹ (4255/2000)

∅ = tan⁻¹ 2.1275

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Answer:

8 seconds

Step-by-step explanation:

-2t^2+9t+56=0

-2t^2+16t-7t+56=0

-2t(t-8)-7(t-8)=0

(-2t-7)(t-8)=0

-2t-7=0 or t-8=0

t-8=0

t=8

The area of the triangles are 81.77 square units, 333.50 square units, 207 square units and 52.21 square units

Given the triangles as the parameters, the area can be calculated as

Area = 1/2absin(C)

Using the above formula as a guide, we have the following equations

Triangle 7 = 1/2 * 15 * 13 * sin(57 degrees)

Triangle 7 = 81.77 square units

Triangle 8 = 1/2 * 28 * 24 * sin(83 degrees)

Triangle 8 = 333.50 square units

Triangle 9 = 1/2 * 23 * 18 * sin(90 degrees)

Triangle 9 = 207 square units

Triangle 10 = 1/2 * 15 * 7 * sin(96 degrees)

Triangle 10 = 52.21 square units

Hence, the area of triangle 10 is 52.21 square units

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The area of the triangle in the diagram is 87.55 squared centimeters.

A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.

The area of a triangle is expressed as;

Area A= 1/2 × b × h

Where b is the base and h is the height of the trinagle.

From the image;

Plug the given values into the above formula and solve for the area of the triangle.

Area = 1/2 × base × height

Area = 1/2 × 17cm × 10.3cm

Area = 87.55 cm²

Therefore, the area is 87.55 squared centimeters.

Option D) 87.55 cm² is the correct answer.

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Answer:

B) [tex]\frac{3}{2}[/tex] % of 400

Step-by-step explanation:

A) 2% of 150 = 3

Start by expressing the percent as a decimal by dividing the percent by 100

2% -> 0.02

Next multiply the percent by the number given

0.02 * 150 = 3

B)  [tex]\frac{3}{2}[/tex] % of 400 = 6

Start by expressing the percent as a decimal by dividing the percent by 100

3/2% -> 0.015

Next multiply the percent by the number given

0.015 * 400 = 6

C) 5% of 60

Start by expressing the percent as a decimal by dividing the percent by 100

5% -> 0.05

Next multiply the percent by the number given

0.05 * 60 = 3

D) 6% of 50

Start by expressing the percent as a decimal by dividing the percent by 100

6% -> 0.06

Next multiply the percent by the number given

0.06 * 50 = 3

After calculating all of the questions, we can see that the common product is 3, making B) the one that is not equal to the rest.

Hence, 7200 units were produced throughout the period equivalently as WIP multiplied by the percentage of completion.

The percentage sign (%) is used to indicate it. When a student receives a score of 80% on a test, for instance, it signifies that 80 of the 100 questions were properly answered by the student. Alternatively, the result can also be expressed as a fraction of 80/100, or as 0.8 in decimal form. In order to express a portion or component of a whole, percentages are utilized. It is a practical technique to contrast values of various magnitudes on an equivalent scale.

given

The steps to determine the equivalent production are as follows:

Total units input: 8000

A typical loss is 400 units, or 5% of 8000 units.

Consider there to be no anomalous loss because none has been reported.

Counted in total units: 8000 - 400 = 7600 units

Units completed: 7600 less 1000 (closing WIP) equals 6600 units.

Equivalent production equals completed units plus closing WIP multiplied by the percentage of completion, which equals 6600 + 1000 x 60%, or 6600 + 600, or 7200 units.

Hence, 7200 units were produced throughout the period equivalently as WIP multiplied by the percentage of completion.

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We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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Answer:

θ = arctan(10/62) ≈ 8.8°

Step-by-step explanation:

Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:

tan(θ) = 10/x

We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.

You do not have enough baking powder.

A mixed number is a value that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is 1 1/2.

In order to determine if you have enough baking powder, multiply 2 1/4 by 9. The teaspoons of baking powder that is needed for 4 1/4 servings = teaspoons needed for one serving x number of serving

2 1/4 x 4 1/4

= 9/4 x 17/4 = 153 / 16 = 9 9/16

9 9/16 is greater than 9 so you do not have enough baking powder.

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Answer:64

Step-by-step explanation:

27.5------100%

17.6--------x

x=64

(a) Keiko's monthly payment is $536.82. (b) The total amount Keiko will repay is approximately $64,419.19 over the 10-year term. c. (c) The total amount is approximately $14,419.19 in interest.

(a) To find Keiko's monthly payment, we can use the formula for the monthly payment of an amortized loan:

P = (r * A) / (1 - (1+r)^(-n))

where:

P = monthly payment

A = loan amount

r = monthly interest rate (annual interest rate / 12)

n = total number of payments

Plugging in the values we have:

A = $50,000

r = 0.055 / 12

n = 10 * 12 = 120

P = (r * A) / (1 - (1+r)^(-n))

P = (0.055/12 * $50,000) / (1 - (1+0.055/12)^(-120))

P ≈ $536.82

Therefore, Keiko's monthly payment is $536.82.

(b) If Keiko pays the monthly payment each month for the full term of 10 years (120 months), her total amount to repay the loan will be:

Total amount = P * n

Total amount = $536.82 * 120

Total amount ≈ $64,419.19

Therefore, Keiko will repay a total amount of approximately $64,419.19 over the 10-year term.

(c) If Keiko pays the monthly payment each month for the full term of 10 years (120 months), the total amount of interest she will pay can be calculated as:

Total interest = P * n - A

= $536.82 * 120 - $50,000

Total interest ≈ $14,419.19

Therefore, Keiko will pay a total of approximately $14,419.19 in interest over the 10-year term.

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The length of the curve y=1/3x³/2-x⁻¹/² from (1, -2/3) to (4, 2/3) is approximately 0.236 units.

what is curve?

In mathematics, a curve refers to a continuous and smooth line or a geometric object that is formed by joining an infinite number of points. Curves can be defined algebraically or geometrically, and they can have different shapes and properties. Some examples of curves include lines, circles, ellipses, parabolas, hyperbolas, and spirals.

Curves are often used in various fields of mathematics, science, and engineering to represent real-world phenomena, such as the trajectory of a moving object, the shape of a surface, or the behavior of a system over time. They are also important in computer graphics and design, where they are used to create visual effects, animations, and models.

In calculus, the study of curves is an essential part of differential and integral calculus. The concepts of limits, derivatives, integrals, and differential equations are used to analyze the properties and behavior of curves, such as their slope, curvature, area, and length.

To find the length of the curve y=1/3x³/2-x¹/² from (1, -2/3) to (4, 2/3), we can use the formula for arc length:

L = ∫[a,b] √(1 + (dy/dx)²) dx

where a and b are the x-coordinates of the starting and ending points of the curve.

First, we need to find the derivative of y:

dy/dx = (d/dx) (1/3 x^³/²- x¹/²) = (1/2) x⁻¹/² - (1/2) x⁻¹/²= x⁻¹/²

Next, we need to find the definite integral of the square root of 1 + (dy/dx)² from 1 to 4:

L = ∫[1,4] √(1 + (x⁽⁻¹/²⁾⁾²) dx

L = ∫[1,4] √(1 + 1/x) dx

To evaluate this integral, we can use the substitution u = 1 + 1/x, which gives du/dx = -1/x²and dx = (1/u) du.

Substituting, we get:

L = ∫[u(1),u(4)] √u (1/u²) du

L = ∫[u(1),u(4)] u⁻¹/² du

L = 2(u(4)¹/²- u(1)¹/²

To find u(1) and u(4), we substitute x=1 and x=4 into the equation for u:

u = 1 + 1/x

u(1) = 2 and u(4) = 1.25

Substituting these values into the expression for L, we get:

L = 2(1.118 - 1)

L = 0.236

Therefore, the length of the curve y=1/3x³/²-x¹/²from (1, -2/3) to (4, 2/3) is approximately 0.236 units.

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