Approximate the area under the curve graphed below from z=1 to z = 6 using a Left Endpoint
approximation with 5 subdivisions.

Which of the following is correct for this approximation?
O The rectangles are circumscribed because the function is increasing.
O The rectangles are circumscribed because the function is decreasing.
O The rectangles are inscribed because the function is increasing.
O The rectangles are inscribed because the function is decreasing.

The measure of sides a and b are 10 and √116 respectively.

Similar triangles are triangles that have the same shape, but their sizes may vary. The ratio of corresponding sides of Similar triangles are equal.

This means for two triangles to be similar the corresponding angles of the triangles must be equal.

Therefore;

b/29 = 4/b

b² = 29 × 4

b² = 116

b = √116

using Pythagorean theorem,

b² = a²+4²

116 = a² +16

a² = 116-16

a² = 100

a = 10

therefore the measure of both sides a and b are 10 and √116 respectively.

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

The area of the sector is 229.92 square inches and the length of the arc is 32.99 inches.

How to find area of the sector?

Follow is the formula of area of the sector,

Area of sector = [tex] \frac{θ}{360} \times πr²[/tex]

where θ is the angle of the sector in degrees, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14159.

Substituting the given values,

Area of sector

[tex]= \frac{135}{360} \times π \times 14² \\ = 0.375 \times π \times 196 \\ = 73.0875π[/tex]

≈ 229.92 square inches (rounded to two decimal places)

How To find the length of the arc?

The formula for the arc is [tex]Length \: of \: arc = \frac{θ}{360} \times 2πr[/tex]

Substituting the given values,

Length of arc = (135/360) × 2π × 14

= 0.375 × 2π × 14

= 32.9856

≈ 32.99 inches (rounded to two decimal places)

Therefore, the area of the sector is approximately 229.92 square inches and the length of the arc is approximately 32.99 inches.

Learn more about sector here,

https://brainly.com/question/31540457

#SPJ1

Answer:

the vertex is the highest or lowest point on theparabola. (0,3)

The focus is (0,4)

The directrix is the fixed line. Equation y=2

by definition, all points on the parabola are equidistant from a fixed point (focus) and fixed line (directrix)

Step-by-step explanation:

The total out-of-pocket expense for one month is $677. The correct option is D.

The first step is to calculate the amount of the prescription costs that will be covered by the insurance plan.

Since the family will fill 6 prescriptions per month and the total cost is $850, the average cost per prescription is $850/6 = $141.67 per prescription.

The insurance plan covers 90% of the first $450 in prescription costs, which is $450 * 0.9 = $405.

The remaining $141.67 - $405 = -$263.33 of the first prescription is not covered, since it is below the $450 threshold. This means that the family will have to pay the full cost of the first prescription, and the insurance will not contribute anything to it.

For the remaining 5 prescriptions, the insurance will cover 80% of the cost, since they are over the $450 threshold. The remaining 20% will be the family's responsibility.

The cost of the remaining 5 prescriptions is $141.67 x 5 = $708.35.

The insurance will cover 80% of this amount, which is $708.35 x 0.8 = $566.68.

The family will be responsible for the remaining 20% of the cost, which is $708.35 x 0.2 = $141.67.

Adding up all the costs, the total out-of-pocket expense for one month is:

$405 (first prescription) + $141.67 (20% of remaining prescription costs) + $48 (monthly premium) = $594.67

Therefore, the correct answer is option D: $677.

To know more about an expression follow

https://brainly.com/question/31407377

#SPJ1

Answer:

The area of triangle APB is 240 m².

Step-by-step explanation:

We are told that PA and PB are equal in length. Therefore, triangle APB is an isosceles triangle with base AB.

As PQ is perpendicular to the base (signified by the right angle symbol), point Q is the midpoint of AB. This means that:

As triangle PQB is a right triangle, use Pythagoras Theorem to find the length of QB:

[tex]\implies PQ^2+QB^2=PB^2[/tex]

[tex]\implies 24^2+QB^2=26^2[/tex]

[tex]\implies 576+QB^2=676[/tex]

[tex]\implies 576+QB^2-576=676-576[/tex]

[tex]\implies QB^2=100[/tex]

[tex]\implies \sqrt{QB^2}=\sqrt{100}[/tex]

[tex]\implies QB=10[/tex]

As AQ = QB, and QB is 10 m, then AQ is also 10 m.

Therefore, we can calculate the length of the base AB:

[tex]\begin{aligned}\implies AB &= AQ + QB\\&=10 + 10 \\&= 20\; \sf m\end{aligned}[/tex]

Now we have the length of the base of the triangle and the height of the triangle, we can calculate the area of triangle APB:

[tex]\begin{aligned}\textsf{Area of triangle $APB$}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2} \cdot AB \cdot PQ\\\\&=\dfrac{1}{2} \cdot 20 \cdot 24\\\\&=10 \cdot 24\\\\&=240\; \sf m^2\end{aligned}[/tex]

Therefore, the area of triangle APB is 240 m².

The total surface area of the figures are 897.5in², 230cm², 217in² and 192in²

1. The net surface area of to the figure can be calculated using the formula;

TSA = (s + s + s)l * bh

s = side length

TSA = (15 + 17 + 8) * 17 + 14.5 * 15

h = 14.5 from Pythagorean theorem

Substituting the values into the formula

TSA = 897.5 in²

2. The total surface area of the figure is calculated as

TSA = (lw + wh + lh)

TSA = [(13 * 8) + (8 * 6) + (13 * 6)]

TSA = 230 cm²

3. The total surface area of the figure is

TSA = (lw + wh + lh)

TSA = [(11 * 2) + (2 * 15) + (15 * 11)]

TSA = 217 in²

4. The total surface area of the figure is

TSA = (lw + wh + lh)

TSA = (8 * 8) + (8 * 8) + (8 * 8)

TSA = 192in²

Learn more on total surface area here;

https://brainly.com/question/22744289

#SPJ1

The measure of the angle m∠RTS in the circle is drives to be equal to 105°.

Any two angles that have the same endpoint that lie on the same segment of the circle, that is the region between the chord joining the endpoints of the angle and the arc not containing the angle are said to be equal in measure.

Thus;

m∠QPT = m∠RST

so; m∠RST = 34°

Considering the triangle RST, we can solve for m∠RTS as follows:

m∠RTS = 180° - (34 + 41)° {sum of interior angles of a triangle}

m∠RTS = 180° - 75°

m∠RTS = 105°

Therefore, the measure of the angle m∠RTS in the circle is drives to be equal to 105°

Read more about circle here:https://brainly.com/question/1553817

#SPJ1

Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.

Given that, line XY is parallel to line segment AC.

Consider triangle XBY and triangle ABC,

∠X=∠A (Corresponding angles are equal)

∠Y=∠C (Corresponding angles are equal)

By AA similarity, triangle XBY and triangle ABC are similar.

Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.

To learn more about the similar triangles visit:

https://brainly.com/question/25882965.

#SPJ1

Answer:

Divide by two is the term-to-term rule.

Step-by-step explanation:

64/2=32

32/2=16

16/2=8

8/2=4

The exponential function described is f(x) = 3*(5)^x

A general exponential function can be written as:

f(x)=  A*(b)^x

Where A is the initial value and b is the base.

Here we know that the function contains the point (0, 3), then:

f(0) = 3 = A*(b)^0

        3 = A

We also know that the function contains (2, 75), then:

f(2) = 75 = 3*(b)^2

        75/3 = b^2

           25 = b^2

           √25 = b = 5

The exponential function is.

f(x) = 3*(5)^x

Learn more about exponential functions at.

https://brainly.com/question/2456547

#SPJ1

Answer:

Step-by-step explanation:

7 horses were left

The coordinates of point M divides the line segment AB int he ratio 3 : 4 is given by ( 1, 0).

Ratio in which line segment AB divides m : n = 3 : 4

Let us consider the coordinates of A be ( x₁ , y₁ )  = ( 7, -3 )

Let us consider the coordinates of B be ( x₂ , y₂ )  = ( - 7 , 4)

Let us consider the coordinates of M be ( x , y )  

Using the formula of line segment divides in the ration m: n we have,

x = ( mx₂ + nx₁ ) / ( m + n )

y = ( my₂ + ny₁ ) / ( m + n )

Substitute the values we have,

x = ( 3 × (-7) + 4 × 7 ) / ( 3 + 4 )

  = ( -21 + 28 ) / 7

  = 1

y = ( 3 × (4) + 4 × -3 ) / ( 3 + 4 )

  = ( 12 - 12 ) / 7

  = 0

Therefore, the coordinates of point M which partition the line segment AB is equal to ( 1, 0).

learn more about coordinates here

brainly.com/question/14780868

#SPJ1

The above question is incomplete, the complete question is:

Find the coordinate of point M that partitions the segment AB in the ratio 3:4,if A (7,-3) and B (-7,4).

The correct answer for the distance between two points is 3.5 units.

To find the distance between two points on a coordinate plane, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

The two points given are (-3,0) and (0.5,0). Plugging these values into the formula, we get:

distance = sqrt((0.5 - (-3))^2 + (0 - 0)^2)

Simplifying the expression inside the square root:

distance = sqrt(3.5^2)

distance = sqrt(12.25)

distance = 3.5

Therefore, the distance between the two points is 3.5 units.

Learn more about coordinates here:

https://brainly.com/question/20282507

#SPJ1

a. The figure that has at least one line of symmetry is rectangle.

b. Another name for <XYZ in the figure is <Y.

A given straight line drawn from one edge to another edge of a figure in such a way that it divides a given figure into two equal parts with the same characteristics is known as the line of symmetry. Thus a given figure may have more than one line of symmetry, depending on the figure.

Considering the given figures in the question, we have;

ai. Rectangle: This is a quadrilateral in which opposite sides are equal and parallel. It has more than one line of symmetry.

ii. Right trapezoid: This is a trapezium in which one of its internal angles is a right angle. It has only one line of symmetry.

iii. Parallelogram: This is a quadrilateral in which the opposites are equal but slant, while the top and base are equal and not slant. It does not have a line of symmetry.

b. In the given figure, another name that can be given to <XYZ is <Y.

Learn more about line of symmetry at https://brainly.com/question/27746983

#SPJ1

"∠Y" is the answer of which you seek.

I want you guys to be able to answer your questions with assurance that my answer will work for you guys. I hope this helps you guys get 100% on that k12 diagnostic!

SCREENSHOT

To multiply mixed numbers, we first need to convert them to improper fractions, then we can multiply them and simplify the result back to a mixed number.

Converting the first mixed number to an improper fraction:

-3 5/7 = -3 × 7/7 + 5/7 = -21/7 + 5/7 = -16/7

Converting the second mixed number to an improper fraction:

-2 1/2 = -2 × 2/2 + 1/2 = -4/2 + 1/2 = -3/2

Multiplying the two improper fractions:

(-16/7) × (-3/2) = (16/7) × (3/2) = 48/14 = 24/7

Simplifying the result to a mixed number:

24/7 = 3 3/7

Therefore, -3 5/7 x -2 1/2 = 3 3/7.

Answer:

a. The quadratic function for the data can be expressed in function notation as follows, rounding the coefficients to two decimal places:

#(x) = 0.23x^2 - 0.46x + 7.54

b. To find the year when the number of households living in poverty was at a minimum, we need to find the vertex of the parabola given by the quadratic function. The x-coordinate of the vertex is given by:

x = -b/(2a)

Substituting the values for a and b given in the problem, we get:

x = -(-0.4599459636)/(2*0.2299729818) ≈ 1

This means that the minimum occurs one year after 1999, i.e., in the year 2000.

c. To find the number of households living in poverty in the year 2000, we can substitute x = 1 in the function:

#(1) = 0.23(1)^2 - 0.46(1) + 7.54 ≈ 7.4

This means that there were about 7,400 households living in poverty in Asturias in the year 2000.

Step-by-step explanation:

S = {1, 2, 3, 4, 5, 6} is the sample space Aryonna rolls a standard number cube once

The sample space for rolling a standard number cube once consists of all the possible outcomes or numbers that could appear on the face of the cube.

Since a standard number cube has six faces, numbered 1 through 6, the sample space is:

S = {1, 2, 3, 4, 5, 6}

Each element in this set represents a possible outcome of rolling the number cube once.

Therefore, S = {1, 2, 3, 4, 5, 6} is the sample space Aryonna rolls a standard number cube once

Learn more about Sample Space here

https://brainly.com/question/29163145

#SPJ1

Answer:

[tex]x = 1.68[/tex]

Step-by-step explanation:

We have the equation
9ˣ = 40 and we have to solve for x

Take logs on both sides
[tex]\ln(9^x) = \ln(40)\\\\\ln(9^x) = x ln(9) \\\\\therefore x \ln(9) = \ln(40)\\\\x = \dfrac{\ln(40)}{\ln(9)}\\\\\text{Using a calculator, this works out to: }\\\\x=1.67888139\dots \\\\\text{Rounded to the nearest hundredth, }\\x = 1.68\\\\[/tex]

Thus, Maricopa invested $60000 in stocks, $70000 in bonds, $40000 in CDs.

A system of linear equations that can be solved using algebraic methods. In the provided problem, we have three unknowns (the amounts invested in CDs, bonds, and stocks) and three equations based on the supplied data (the total investment amount, the interest rates of each investment, and the total annual income from the investments).

We can ascertain the values of the unknowns, i.e. the amounts invested in each account, by setting up and solving these equations.

Let the principal amount invested in CDs be 'p' :

CDs:

Bonds:

Stock:

Total interest:

[tex](0.05p) + (0.041p + 1230) + (8710 - 0.134p) = \$8220[/tex] (given)

[tex]-0.043p + 9940 =8220\\-0.043p = -1720[/tex]

Solving further for p:

p = $40,000

Putting value of p in (1), (2) and (3), we get;

[tex]CDs:\\Principal = p = \$40,000\\Bonds:\\Principal = p + 30000 = 40,000 + 30000 = \$70,000\\Stocks:\\Principal = 140000 - 2p = 140000 - 80000= \$60000\\[/tex]

Learn more about linear equations here:

https://brainly.com/question/29739212

#SPJ1

For given problem, (A.) Independent variable is x, Dependent variable is y. (B.) Amplitude=5 feet, Period= 12 hours, frequency= 1/12 cycles per hour, midline is y= 10 feet, Vertical shift= 0, phase shift = 3 hours and trigonometric function that models the ocean tide is

                          [tex]y= 5 sin(\pi x/6-\pi /2)+10[/tex]

E. At x=63, Height of tide= y=10

A.Independent variable: x, representing time in hours since the first high tide occurred at x = 3.

Dependent variable: y, representing the height of the tide above or below the average sea level in feet.

B.

a. Amplitude: The amplitude is the distance from the average sea level to the highest point of the tide, or from the average sea level to the lowest point of the tide. In this scenario, the amplitude is 5 feet.

b. Period: The period is the time it takes for one complete cycle of the tide, from high tide to high tide or from low tide to low tide. In this scenario, the period is 12 hours (6 hours from high tide to low tide, and another 6 hours from low tide to high tide.

c. Frequency: The frequency is the number of cycles per unit of time. In this scenario, the frequency is 1/12 cycles per hour.

d. Midline: The midline is the horizontal line representing the average sea level. In this scenario, the midline is y = 10 feet.

e. Vertical Shift: The vertical shift is the amount that the graph of the function is shifted up or down from the midline. In this scenario, the vertical shift is 0, since the high tide is 5 feet above the average sea level and the low tide is 5 feet below the average sea level, so the average of the high and low tides is at the midline.

f. Phase Shift: The phase shift is the horizontal shift of the graph of the function. In this scenario, the first high tide occurs at x = 3, which is 3 hours after the starting point (x = 0). So the phase shift is 3 hours.

C. Using the standard form of a trigonometric function, we can model the tide as:

[tex]y = A\; sin(2\pi ft -\phi ) + B[/tex]

where A is the amplitude, f is the frequency,[tex]\phi[/tex] is the phase shift, B is the  vertical shift and the function 'sin' represents the sine of an angle in radians.

Substituting the values we found in part B, we get:

[tex]y = 5\;sin(2\pi \;(1/12)\;x-\pi/2) + 10[/tex]

Therefore, the trigonometric function that models the ocean tide is:

[tex]y= 5 sin(\pi x/6-\pi /2)+10[/tex]

D. Graph of [tex]y=5\sin(\pi\left(x/6\right)-\left(\pi/2)\right)+10[/tex] ( refer to image attached )

E. Height of tide at x=63,

[tex]y=5\sin(\pi\left(63/6\right)-\left(\pi/2)\right)+10[/tex]

[tex]y=5\sin(21\left(\pi/2\right)-\left(\pi/2)\right)+10\\\\y=5\sin(20\left(\pi/2\right))+10\\\\y=5\sin(10\left(\pi\right))+10\\\\y=10[/tex](∵Sin (nπ) = 0)

Learn more about trigonometric function here:

https://brainly.com/question/6904750

#SPJ1

Answer: 4000 millilitres

Step-by-step explanation:

One liter is equal to 1000 millilitres.

So since to get 4 from one, you multiply 1 x 4.

To get to the number of millilitres, you multiply 1000 x 4.

1000 x 4 is 4000.

The answer of the given question based on the percent is , 20.49 trillion is about 52.84% larger than 13.4 trillion.

Percentage is a way of expressing a quantity or value as a fraction of 100. It is a widely used method for describing proportions, rates, changes, and comparisons in various fields such as mathematics, economics, statistics, science, and everyday life. The term "percent" literally means "per hundred", and it is represented by the symbol "%". To convert a number to a percentage, we multiply it by 100 and add the symbol "%".

To find the percent larger that 20.49 trillion is to 13.4 trillion, we can use the following formula:

Percent change = (New value -Old value) /Old value * 100%

Plugging in the values we have:

Percent change = (20.49 trillion - 13.4 trillion) / 13.4 trillion * 100%

= 7.09 trillion / 13.4 trillion * 100%

= 52.84%

Therefore, 20.49 trillion is about 52.84% larger than 13.4 trillion.

To know more about Fraction visit:

https://brainly.com/question/11947917

#SPJ1

Answer:

D

Step-by-step explanation:

Answer:

B. (0, 6), (5, 1)

Step-by-step explanation:

y=6−x

y=x2−6x+6

6 - x = x² - 6x + 6

x² - 5x = 0

x(x - 5) = 0

x = 0 or x = 5

x = 0; y = 6 - 0; y = 6

x = 5; y = 6 - 5; y = 1

Answer: (0, 6), (5, 1)

Answer: 15.888

Step-by-step explanation:

You should use SOH CAH TOA or 30-60-90 rules.  Since they are asking for approximate they probably want you to use SOH CAH TOA

They have given you the opposite of the angle and hypotenuse.  The hypotenuse is always across from the right angle

You will use SOH

Sin 60 =y/18        mult both sides by 18

18 sin 60 =y

y=15.588

Answer:

Since Giovanna deposited half of the money into each account, she deposited $1600 / 2 = $800 into each account.

Let's assume that First Oak offers an annual interest rate of r1, and West United offers an annual interest rate of r2. The amount of interest earned on each account after 5 years would be:

Interest earned on First Oak = $800 * r1 * 5

Interest earned on West United = $800 * r2 * 5

The total interest earned from both accounts would be the sum of these two amounts:

Total interest earned = $800 * r1 * 5 + $800 * r2 * 5

Total interest earned = $4000 * (r1 + r2)

We are not given the interest rates, so we cannot calculate the exact amount of interest earned. However, we can use the given information to make some observations.

Since we are looking for the total interest earned from both accounts, we can simplify the problem by assuming that the interest rates for both accounts are the same. In this case, we have:

Total interest earned = $4000 * 5 * r

Total interest earned = $20000 * r

To find the interest earned, we need to know the value of r. If, for example, the annual interest rate is 4%, then:

r = 0.04

Total interest earned = $20000 * 0.04

Total interest earned = $800

Therefore, if the interest rates for both accounts are the same and equal to 4%, Giovanna would have earned $800 in interest from both accounts at the end of 5 years. However, if the interest rates are different, the total interest earned would be different as well.

Without knowing the interest rates for the two accounts Giovanna deposited her money in, it's not possible to calculate the total interest she'd earn in 5 years. Normally, you would need to use the Simple Interest formula for each account and then add the two results together.

This is a Mathematics question about simple interest, which can be solved using the formula: Interest = Principal × Rate × Time. Given that Giovanna divided her money equally into two accounts at First Oak and West United, she put $800 into each account. However, without information about the annual interest rates for both accounts, we can't calculate the amount of interest Giovanna would earn after 5 years. Once the specific interest rates for the two accounts are provided, one could use the Simple Interest formula for each account and then add the interest from both to get the total.

Learn more about Simple Interest here:

https://brainly.com/question/32543341

#SPJ2

The calculated value of the  reciprocal of the number -7 is -1/7

From the question, we have the following parameters that can be used in our computation:

Number = -7

As a general rule, the reciprocal of a number x is 1/x

Using the above as a guide, we have the following:

Reciprocal = -1/7 given that Number = -7

To check, we have

-1/7 * -7

Evaluate

Result = 1

Hence, the reciprocal is 1

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

26 kids can come on the budget of 470.

first subtract the 80 for the room then divided the rest by 15

The composite functions and their domains are (f . g)(x) = √(4x - 1)/(5x² + 3) and [tex](f + g)(x) = \frac{5x^2\sqrt{4x-1}+3\sqrt{4x-1}+1}{5x^2+3}[/tex]

Domain: x ≥ 1/4

Given that

f(x) = 1/(5x² + 3)

g(x) = √(4x - 1)

For the first pair, we have

(f . g)(x) = f(x) * g(x)

So, we have

(f . g)(x) = 1/(5x² + 3) * √(4x - 1)

Evaluate

(f . g)(x) = √(4x - 1)/(5x² + 3)

For the domain, we have

4x - 1 ≥ 0

x ≥ 1/4

Next, we have

(f . g)(x) = f(x) * g(x)

So, we have

(f + g)(x) = 1/(5x² + 3) + √(4x - 1)

Evaluate

[tex](f + g)(x) = \frac{5x^2\sqrt{4x-1}+3\sqrt{4x-1}+1}{5x^2+3}[/tex]

For the domain, we have

4x - 1 ≥ 0

x ≥ 1/4

Read more about composite functions at

https://brainly.com/question/10687170

#SPJ1