7. Find (i) the length of an arc and (ii) the area of a sector in a circle of radius 7 meters subtended by the central angle of 85°.

The exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]

A manufacturer earned $55 per hour of labor when it opened.

Each year the manufacturer earns an additional 7% per hour.

Since the manufacturer earns an additional 7% per hour each year, the amount earned per hour can be represented as follows:

[tex]A(t) = 55(1 + 0.07)^t[/tex]

where t is the number of years after the plant opened. T

This can be simplified as function:

[tex]A(t) = 55(1.07)^t[/tex]

Therefore, the exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]

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If Justin mowed 45% of her garden in 18 minutes, then we can set up a proportion to find how long it would take him to mow 100% of the garden:

45/100 = 18/x

where "x" is the unknown number of minutes it would take to mow 100% of the garden.

To solve for "x," we can use cross-multiplication:

45x = 100 * 18

Simplifying the right-hand side:

45x = 1800

Dividing both sides by 45:

x = 40

Therefore, it would take Justin 40 minutes to mow all of his garden at the same rate of 45% in 18 minutes.

To explain this, we used the fact that the amount of work done (mowing a certain percentage of the garden) is directly proportional to the time it takes to do that work. This means that if Justin mowed 45% of the garden in 18 minutes, he would take proportionally longer to mow the entire garden. The proportion we set up allows us to find the unknown amount of time it would take to mow the entire garden. Solving the proportion, we found that it would take Justin 40 minutes to mow all of his garden at the same rate he mowed the 45%.

Answer:

y=14

Concept Used:

Slope of a line:  [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where (x1,y1) and (x2,y2) are passing points

Step-by-step explanation:

On substitution:

[tex]4 = \frac{y-(-10)}{2-(-4)}[/tex]

Solving for y:

y = 14

Step-by-step explanation:

I think you mean the sun's mass is 1.99 × 10³⁰ kg.

70% of that is hydrogen :

1.99 × 10³⁰ × 0.7 = 1.393 × 10³⁰ kg

a.

13% of that is in the core :

1.393 × 10³⁰ × 0.13 = 0.18109 × 10³⁰ = 1.8109 × 10²⁹ kg

b.

600 000 000 000 kg = 6.0 × 10¹¹ kg/s

so, 1.8109 × 10²⁹ kg will last

1.8109 × 10²⁹ / (6.0 × 10¹¹) = 0.301816666... × 10¹⁸ =

= 3.01816666... × 10¹⁷ seconds

60 seconds per minute.

60 minutes per hour.

24 hours per day.

365 days per year.

1 000 000 000 years.

that is

31,536,000,000,000,000 seconds in 1 billion years =

= 3.1536 × 10¹⁶ seconds in 1 billion years

so, this will go on for

3.018166666... × 10¹⁷ / 3.1536 × 10¹⁶ billion years =

= 0.957054372... × 10¹ = 9.57054372... billion years.

c.

the sun has already "spent" 4.6 billion years, so, that leaves about

9.6 - 4.6 = 5 billion years

According to the information, the total mass of hydrogen available for nuclear fusion in the Sun's core is 10^29 kg, the duration of the oroginal supply of hydrogen of the sun is 3.02 × 10^17 seconds, and the left time of the sun is 4.98 billion years.

a. The total mass of hydrogen available for nuclear fusion in the Sun's core is:

0.7 × 1.99 × 10^30 kg × 0.13 = 1.81 × 10^29 kg

How long the sun's original suply of hydrogen can last?

t = (1.81 × 10^29 kg) / (6 × 10^11 kg/s) = 3.02 × 10^17 seconds

Converting to billions of years:

t = (3.02 × 10^17 s) / (3.15 × 10^16 s/billion years) = 9.58 billion years

c. The Sun has already burned for 4.6 billion years, so the amount of time it has left before it runs out of fuel is:

9.58 billion years - 4.6 billion years = 4.98 billion years

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Answer:The sample space that satisfies the definition of a continuous random variable is: ×=[0,500]

Step-by-step explanation:

The sample space that satisfies the definition of a continuous random variable is: ×=[0,500]

A continuous random variable is a variable that can take on any value within a certain range of values, typically a continuous interval. This means that there are an infinite number of possible values that the variable can take on, and the probability of any particular value is zero.

In contrast, the other sample spaces listed are all discrete random variables, meaning that they can only take on a finite or countable number of values. For example, the first sample space x={odd integers between 5 and 15} can only take on 6 possible values (5, 7, 9, 11, 13, or 15), and the third sample space x=[0,1,2,3] can only take on 4 possible values.

The fourth sample space x=[the number of days in the week that have the letter "r"] is also a discrete random variable, as it can only take on values of 0, 1, 2, or 3 (depending on how many days of the week have the letter "r").

Therefore, the only sample space that satisfies the definition of a continuous random variable is ×=[0,500].

The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100

The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.

The specified equations obtained from the constraints in slope intercept form are;

y = -0.5·x + 7; The region below the graph is shaded

y = -0.75·x + 9; The region below the graph is shaded

x = 0; The region to the right of the line x = 0 is shaded

y = 0; The region above the line y = 0 is shaded

The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9

Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3

The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)

The value of the function g for each of the feasible region are therefore;

g(0, 0) = 8 × 0 + 12 × 0 = 0

g(0, 7) = 8 × 0 + 12 × 7 = 84

g(8, 3) = 8 × 8 + 12 × 3 = 100

g(12, 0) = 8 × 12 + 12 × 0 = 96

Please find attached the graph of the inequalities showing the feasible region created with MS Excel

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The number of real zeros for the function whose graph is shown include the following: D. 0.

In Mathematics and Geometry, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

This ultimately implies that, a polynomial graph touches the x-axis at real zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can reasonably and logically deduce that the real zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and it is non-existent on the graph above.

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The ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.

A circle is a two-dimensional shape that is defined as the set of all points in a plane that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference, and the distance across the circle passing through the center is called the diameter.

The circumference of a circle with radius r is given by the formula:

C = 2πr

The area of a circle with radius r is given by the formula:

A = π×r²

Therefore, the ratio of the circumference of a circle with radius r to its area is:

C/A = (2πr) / (πr²)

Simplifying the expression by canceling out π and r from the numerator and denominator, we get:

C/A = 2/r

Therefore, the ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.

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The complete question is:

Find the following ratio.

The ratio of circumference of circle with radius r to its area.

To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:

[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]

The solution provided above uses a method of matrix called Echelon.

Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.

By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.

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The height of the school building is approximately 4.38 meters (rounded to the nearest hundredth).

JX / BX = JM / BT

Substituting the known values, we get:

(d1 + d2) / h = d1 / (h - 1.75)

(d1 + d2) * (h - 1.75) = d1 * h

d1 * h + d2 * h - 1.75 * d1 - 1.75 * d2 = d1 * h

d2 * h - 1.75 * d1 - 1.75 * d2 = 0

h = (1.75 * d1 + 1.75 * d2) / d2

h = (1.75 * 8.75) / 3.5

h = 4.375

The height of the school building is approximately 4.38 meters

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The systems of linear equations can be classified as "consistent dependent," "consistent independent," or "inconsistent" as follows:

A. System A = Inconsistent (No solution)

B. System B = Consistent dependent (Indefinitely many solutions)

C. System C = Consistent independent (A unique solution)

To identify the systems of linear equations, you first need to note the meaning of the different systems of equations. First, the Consistent dependent has two equations that represent the same line, so they intersect at infinitely many points and any point on the line represents a solution to the system.

Next, the Consistent independent has the two equations represented by two distinct non-parallel lines, so they intersect at exactly one point, which is the unique solution to the system.

Finally, the Inconsistent has two equations that are represented by two distinct parallel lines, so they do not intersect, and there is no solution to the system.

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The graphs are:

1) not one-to-one

2) one-to-one

3) not one-to-one

A graph represents an one-to-one function only if.

We can't draw a vertical line that touches the graph twice or more.

We can't draw an horizontal line that touches the graph twice or more.

For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.

Similarly forthe third graph, the line y = 0 touches two points-

So these two are not one-to-one.,

For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.

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Answer: The answer is false

Answer:

False

Step-by-step explanation:

If you were asking true or false it is false

If the Amethyst Woodstar species of hummingbird beats its wings about 80 times per second and there are 60 seconds in a minute, it beats its wings D. 43,200 times in 9 minutes.

The number of times that the Amethyst Woodstar species of hummingbird beats its wings in 9 minutes can be determined using the mathematical operation of multiplication.

The number of times it beats its wings = 80 seconds per second

The total number of minutes involved = 9 minutes

1 minute = 60 seconds

The total number of times it beats in 9 minutes = 43,200 (80 x 60 x 9)

Thus, using multiplication operation, the number of times the bird beats its wings is Option D.

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Answer:

The statement that is best supported by the information in the box plots is:

* The 8th graders completed more community service hours than the 7th graders.

The 8th grade box plot is shifted to the right of the 7th grade box plot, which indicates that the 8th graders had a higher median number of community service hours. The 8th grade box plot also has a wider spread, which indicates that there was more variation in the number of community service hours completed by the 8th graders.

However, it is important to note that the box plots do not provide information about the total number of community service hours completed by each group of students. It is possible that some 7th graders completed more community service hours than some 8th graders.

Step-by-step explanation:

Answer:The 8th graders completed more community service hours than the 7th graders

Step-by-step explanation:

For circle O, For circle O, m CD=125° and m∠ABC = 55°. In the figure, ∠ ABO and ∠ BCO have measures equal to 35°.

For circle O, m(arc CD) = 125° and m∠ABC = 55°.

First, we use central angle to find that ∠COB is 125°,

give that ∠COB = arc CD

Next, we use complementary angles to find that ∠BCA is 35°,

given that ∠ABC +  ∠BCA = 90°.

Then, we use the sum of interior angles in a triangle to find that ∠CBO is 20°; given that:

∠CBO + ∠COB + ∠BCO = 180°.

∠BCO = ∠BCA = 35°

∠COB = 125°

125° + 35° = 160°

180° +  160° =  20°

Finally, we use angle addition postulate to find that ∠ABO is also 35°.

Therefore, <ABO and <BCO both have measures of 35° in the figure.

The above answer is in response to the question below;

For circle O, and m∠ABC = 55°. In the figure, ∠_____ and ∠____ have measures equal to 35°.

a. the first could be AOB, ABO, or BOA

b. the second could be BCO, OBC, or BOC

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Using trigonometric ratio, the value of x in the figure is 2.61 units

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In this problem, we have the adjacent side and we need to find the opposite side.

The ratio that gives us room to find this is the tangent to the angle

tanθ = opposite / adjacent

tan 43 = x / 2.8

x = 2.8 * tan 43

x = 2.61

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The equation of the line passing through the given points is y = 6x

Given that are the values of x and y coordinates we need to find the equation of the line using them,

So, considering the points (4, 24) and (5, 30),

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),

Therefore, the required equation is =

y-24 = 30-24/5-4 (x-4)

y-24 = 6(x-4)

y-24 = 6x-24

y = 6x

Hence, the equation of the line passing through the given points is y = 6x

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The cost of ending inventory using the weighted-average method is $198.24.

An ending inventory is often derived by adding new purchases to beginning inventory and then subtracting the cost of goods sold.

To calculate it using the weighted-average, we must compute the weighted average cost per unit and then multiply the weighted average cost per unit by the number of units in ending inventory to get the cost of ending inventory.

The total cost of goods available for sale is:

= (4 x 1.50) + (11 x 2.00) + (11 x 2.50) + (16 x 2.75) + (17 x 3.50) + (21 x 3.70) + (31 x 3.90) + (17 x 4.30)

= $430.7

The total units available for sale is:

= 4 + 11 + 11 + 16 + 17 + 21 + 31 + 17

= 128

The weighted average cost per unit is:

= $430.70 / 128 units

= $3.36484375

= $3.36

The cost of ending inventory will be:

= 59 units x $3.36

= $198.24

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__________________________________

The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.

Given: cosθ = -1/3 and θ is in quadrant III.

This means that sinθ = ± √(1 - (cosθ)2).

We know that cosθ is negative, so sinθ will be negative.

Therefore, sinθ = -√(1 - (-1/3)2 )

sinθ = - √(1 - 1/9)

sinθ = -√8/9

tanθ = sinθ/cosθ

tanθ = (-√8/9)/-1/3

tanθ = √8/3

secθ = 1/cosθ

secθ = 1/-1/3

secθ = -3

cscθ = 1/sinθ

cscθ = 1/-√8/9

cscθ = -√9/8

cotθ = cosθ/sinθ

cotθ = -1/3/-√8/9

cotθ = √9/8

Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.

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Answer: 18 feet.

Step-by-step explanation:

Average of bases = (22 + 14.75) / 2

Average of bases = 18.375

18.375 to the nearest tenth is = 18ft

Therefore, the average of the two bases of the trapezoid is 18 feet.

Answer:

a= Acute

b=Obtuse

c= Acute

d= Right

Answer:

a quotient is the result obtained by dividing one quantity by another.

Answer:

Step-by-step explanation:

vertex form = y=a(x-h)^2+k

standard form = y=ax^2+bx+c

the most straightforward way to solve it is to expand the vertex form

we get :

-(x+1)(x+1)-1

= -(x^2+x+x+1) - 1

note: remember to leave the negative sign out of the parentheses and distribute it after - otherwise you may mix up signs

= (-x^2-x-x-1) - 1

= -x^2-2x-1-1

= -x^2 - 2x - 2

So, in standard form, it is y=-x^2-2x-2

Hope this helps!

Answer: 5.3 repeated portions or about 5 portions

Step-by-step explanation: 25 pounds = 400 ounces

400/75 = 5.3 repeated

Answer:33

Step-by-step explanation:

48 labels can be made if the company has a total of 4521.6in² of paper available.

We can calculate the number of labels by finding the surface area of the side of the can.

The surface area of the side of the can is the circumference of the base times the height:

C = πd

C = 3.14 x 6

C = 18.84 in

Area = C x h

Area = 18.84 x 5

Area = 94.2 in²

Therefore, each label requires 94.2 in² of paper.

To find the number of labels that can be made, we divide the total amount of paper by the amount needed per label:

Number of labels = Total area of paper / Area per label

Number of labels = 4521.6 / 94.2

Number of labels = 48

Therefore, 48 labels can be made using a total of 4521.6in² of paper.

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The simplest form of log5+log6-log2​ is:  log15.

Let us simplify log5 + log6 - log2 by making use  logarithmic rules:

log a + log b = log (ab)

log a - log b = log (a/b)

So,

log5 + log6 - log2

= log (5 x 6) - log2

= log30 - log2

Now let make use of the  logarithmic rule:

log a - log b = log (a/b) = log a - log b

log30 - log2

= log (30/2)

= log15

Therefore the simplest form is log15.

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