Given the graph of y=f(x) below, find the value f(4).

Answer: Area=3.125 square feet

Step-by-step explanation:

2.5x2.5=6.25

6.25/2= 3.125

Answer:

A = 50 ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

given that 1 inch equals 4 feet , then

b = 2.5 in = 2.5 × 4 feet = 10 feet

h = 2.5 in = 2.5 × 4 feet = 10 feet

then

A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²

Answer:

D. Quadratic

Step-by-step explanation:

The vertex of the parent function y = x2 lies on the origin. It also has a domain of all real numbers and a range of [0, ∞). Observe that this function increases when x is positive and decreases while x is negative

Answer: ∠EGF and/or ∠CGB

Step-by-step explanation:

Starting Angle: ∠CGE

Possible Supplements: ∠EGF and ∠CGB

The Sum of interior angles of the given polygon is: 540°

The value of the angle x is: 85°

The interior angle-sum formula for an irregular polygon is the same as the sum of interior angle in a regular polygon.

Sum of interior angles in a n-sided polygon is:

Sum = (n - 2)180

where:

n is the number of sides of the irregular polygon.

This is a 5-sided irregular polygon

Thus:

Sum = (5 - 2)180

Sum = 540°

Thus:

x + 115 + 115 + 130 + 95 = 540

x + 455 = 540

x = 540 - 455

x = 85°

Read more about Interior angle of Polygon at: https://brainly.com/question/224658

#SPJ1

[ rate 5stars~ and give thanks for more po! welcome! ]

Step-by-step explanation:

We have the triple integral:

∫∫∫E x^2 + y^2 + z^2 dV

where E is the ball x^2 + y^2 + z^2 ≤ 81.

In spherical coordinates, the volume element is given by:

dV = ρ^2 sin φ dρ dθ dφ

where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).

Substituting into the integral, we get:

∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ

= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π

= (2π/5)(9^5)(-(-1 - 1))

= (4π/5)(9^5)

≈ 114413.73

Therefore, the value of the triple integral is approximately 114413.73.

To the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.

We can use the formula for compound interest:

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

where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

We know P = 8000, r = 0.0475, and we want A = 20400. We also know that the interest is compounded daily, so n = 365.

Let's solve for t:

20400 = 8000[tex](1 + 0.0475/365)^{(365t)}[/tex]

2.55 = [tex](1.00013)^{(365t)}[/tex]

Taking the natural logarithm of both sides, we get:

after solving

Using a calculator, we find:

t ≈ 15.5

So, to the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.

to know more about bank

brainly.com/question/14042269

#SPJ1

The estimated number of quarts of blood the individual with the given weight will have would be = 2.7 quarts.

The body weight of the first individual = 200 pounds

The volume of blood = 6 quarts.

Therefore a person of 90 pounds = X quarts.

That is;

200 pounds = 6 quarts

90 pounds = X quarts

make X quarts the subject of formula;

X = 90×6/200

= 540/200

= 2.7 quarts

Learn more about volume here:

https://brainly.com/question/27710307

#SPJ1

Answer:

A. 4.5 hours

Step-by-step explanation:

We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:

117 miles / x hours = 13 miles / 0.5 hours

We can cross-multiply to get:

117 miles * 0.5 hours = 13 miles * x hours

Simplifying:

58.5 = 13x

x = 58.5 / 13

x = 4.5 hours

Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.

Hope this helps!

Answer:

A. 4.5 hours

Step-by-step explanation:

We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:

117 miles / x hours = 13 miles / 0.5 hours

We can cross-multiply to get:

117 miles * 0.5 hours = 13 miles * x hours

Simplifying:

58.5 = 13x

x = 58.5 / 13

x = 4.5 hours

Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.

Hope this helps!

23. By the diagram, the triangle is a [tex]45^\circ - 45^\circ-90^\circ[/tex] triangle. Therefore, the triangle is isosceles, so [tex]x=6.[/tex] And by the Pythagorean theorem, [tex]y^2=x^2+6^2=6^2+6^2=72,[/tex] and taking the square root yields [tex]y = 6\sqrt{2}.[/tex]

24. Notice that by the diagram, the triangle is a [tex]30^\circ-60^\circ-90^\circ[/tex] triangle. It is well known that in these special types of triangles, if [tex]a[/tex] is the side length opposite the [tex]30^\circ[/tex] angle, then the side length opposite the [tex]90^\circ[/tex] angle is [tex]2a,[/tex]  and finally the side length opposite the [tex]60^\circ[/tex]  is [tex]a\sqrt{3}.[/tex] This is shown in the image I've attached below, and can also be easily proven by the fact that two of these triangles combine to form an equilateral triangle.

So using this fact, we know that [tex]x = \frac{8}{2} = 4,[/tex] and [tex]y = x\sqrt{3} = 4\sqrt{3}.[/tex]

25. Tell whether the given side lengths can represent the sides of a right triangle: 10, 12, 20

For this question, we simply use the converse of the Pythagorean theorem. One part of its statement says that if a triangle has sides of length [tex]a, b, c[/tex] such that [tex]a^2 + b^2 = c^2[/tex], and [tex]c[/tex] is the longest side, then the angle opposite the side of length [tex]c[/tex] is a right angle.

Thus, if the triple [tex](a, b, c)[/tex] does not satisfy the equation, the triangle it forms is not a right triangle. In our case, the corresponding values for [tex](a, b, c)[/tex] are [tex](10, 12, 20),[/tex] because [tex]20[/tex] is the largest number in this triple. But [tex]10^2+12^2=244\neq 400 = 20^2,[/tex] so the triangle with side lengths [tex]10, 12, 20[/tex] is not a right triangle.

26. Another statement of the converse of the Pythagorean theorem is that if a triangle has side lengths [tex]a, b, c[/tex] such that [tex]c^2 > a^2+b^2[/tex] , with [tex]c[/tex] being the longest side, then the triangle is an obtuse triangle. So the corresponding values for [tex]a, b, c[/tex] are [tex]10, 11, 14,[/tex] and because [tex]14^2 = 196 < 221 = 10^2+11^2,[/tex] the triangle is an obtuse triangle.

Answer:

Step-by-step explanation:

The surface area of this cylinder is 942 millimeter square

The formula for the surface area of a cylinder is expressed as;

SA = 2πr h + 2πr²

Given that the parameters are identified as;

From the information given, we have that;

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 10²

Find the square values

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 100

Multiply the values

Surface area = 314 + 628

Now, add the values

Surface area = 942 mm²

Learn more about cylinders at: https://brainly.com/question/9554871

#SPJ1

As a result, the item's final price is $53.50 and the sales tax is $3.50.

The government levies a consumption tax known as sales tax on the purchase of goods and services. The seller often calculates it as a percentage of the purchase price and collects it. After then, the vendor transfers it to the government .. The funding of government services and programmers comes from sales tax

We can multiply the item's price by the applicable sales tax rate to determine the sales tax:

Price of Item  x   Sales Tax Rate equals Sales Tax

Sales Tax: $50.00 x 7% = $3.50

We can multiply the item's price by the applicable sales tax to determine the entire cost of the purchase, including tax:

Price of Item + Sales Tax = Total Cost

$50.00 plus $3.50 equals $53.50 as a total

To know more about sales tax visit :

brainly.com/question/29751934

#SPJ1

Answer:

The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.

Step-by-step explanation:

Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.

It can be calculated as:

[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]

where:

c is the speed of light (c = 332m/s)

all the subscripted s is related to the Source (frequency, velocity);

all the subscripted o is related to the Observer (frequency, velocity);

As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.

So, the frequency perceived by the observer:

[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]

[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]

[tex]f_o=460(1.247)[/tex]

[tex]f_o= 573.6 \ \text{Hz}[/tex]

At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz

Answer:

The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time

The perceived frequency you hear is

370.9 Hertz

The function is given as:

[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x  [tex]f_{s}[/tex]

From the question

[tex]c=332[/tex] --- speed of the sound

[tex]V_{o} =32[/tex] ---current speed of the train

[tex]V_{s} = 40[/tex] --- speed of the opposite train

[tex]f_{s} =460[/tex] --- frequency of the sound wave

This gives:

[tex]f_{o}= \frac{332-32}{332+40}[/tex]  ×[tex]460[/tex]

[tex]f_{o}= \frac{300}{372} x460[/tex]

Rewrite as:

[tex]f_{o}= \frac{300x460}{372}[/tex]

[tex]f_{o}= 370.9[/tex]

Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.

Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean or median of that dataset. It measures the dispersion or variability of the data points in relation to the central tendency of the dataset.

To calculate the MAD, you first find the mean or median of the dataset, and then you calculate the absolute difference between each data point and the mean or median. The absolute differences are then averaged to give the mean absolute deviation.

MAD is expressed in the same units as the original data and is commonly used in finance, economics, and other fields to measure the variability of financial returns, economic indicators, or other datasets. MAD is a robust measure of dispersion that is less sensitive to extreme values or outliers compared to other measures of dispersion such as standard deviation.

Let's say the times taken by the four people are:

Diane: 2 minutes

Friend 1: 1.5 minutes

Friend 2: 2.5 minutes

Friend 3: 1.75 minutes

The mean of these times is:

Mean = (2 + 1.5 + 2.5 + 1.75) / 4 = 1.9375 minutes

Next, we need to find the absolute deviations of each time from the mean. To do this, we subtract the mean from each time and take the absolute value of the result:

|2 - 1.9375| = 0.0625

|1.5 - 1.9375| = 0.4375

|2.5 - 1.9375| = 0.5625

|1.75 - 1.9375| = 0.1875

Then, we find the mean of these absolute deviations:

MAD = (0.0625 + 0.4375 + 0.5625 + 0.1875) / 4 = 0.3125 minutes

Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.

To know more about absolute deviations, visit:

https://brainly.com/question/10528201

#SPJ1

Okay, here are the steps to solve this problem:

* Jen earns a weekly salary of $250

* She gets a 10% bonus on any sales

* In the past 4 weeks, she sold $312 worth of phones and accessories

* 10% of $312 is $31.20

* So in 4 weeks, her bonus would be $31.20 * 4 = $124.80

* Her weekly salary is $250

* So in 4 weeks, her salary would be $250 * 4 = $1000

* Her total income over 4 weeks is $1000 + $124.80 = $1124.80

* The choices are:

** $1,031.20 ** $562.00 ** $312.00 ** $281.20 ** $31.20

So the correct choice is $1,031.20.

Given

ABCΔ  is a triangle.

D is a point on [BC]

|BD|=4

|AD|=|CD|

m(CBAˆ)=α=30∘

m(ACBˆ)=β=20∘

To Find

What is |AC|=x?

Solution

Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b

and applying law of cosines to all three triangles yields;

respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4

The complete question is -

In the given diagram find the value of x

a) 1

b) 2

c) 3

d) 4

Learn more about from the given link

brainly.com/question/30239338

the greatest common factor of 72 and 96 is 24

a. K = E + (x + y). This implies that Kofi is (x + y) older than Esenam.

b. (i) Adoma = (5 + y) years

   (ii) Kofi = (5 + (x+y)) years

Word problem is a topic that requires the transformation of a mathematical statement into an equation, such that the variable is to be determined.

In the given question, we have;

Let the age of Kofi, Adoma, and Esenam be represented by K, A and E respectively. So that;

K = A + x ...... i

A = E + y........ ii

substitute i into ii

K = (E + y) + x

  = E + (x + y)

K = E + (x + y) ........ iii

Thus,

a. From equation iii, we can deduce that Kofi is (x + y) years older than Esenam.

b. The age of Adoma = 5 + y years

ii. The age of Kofi = 5 + (x + y) years

Learn more about word problem at https://brainly.com/question/28075643

#SPJ1

the balance after 6 years is approximately $926.45.

What is Continuous compounding ?

Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.

We can use the formula for continuous compounding to find the balance after 6 years:

[tex]F = Pe^{(rt)}[/tex]

where F is the future value, P is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this problem, P = $550, r = 8.5% = 0.085 (note that we need to use the decimal form of the interest rate), and t = 6 years.

[tex]F = 550e^{(0.085*6)}[/tex]

F ≈ $926.45

Therefore, the balance after 6 years is approximately $926.45.

To know more about Continuous compounding visit,

https://brainly.com/question/30460031

#SPJ1

Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean so option A is correct.

In mathematics, the absolute value (also known as modulus) of a real number is its distance from zero on the number line. It is denoted by enclosing the number between two vertical bars, such as |x|.

For example, the absolute value of 5 is 5, because 5 units to the right of zero on the number line is at a distance of 5 units from zero. Similarly, the absolute value of -5 is also 5, because 5 units to the left of zero on the number line is at a distance of 5 units from zero.

To determine which Z-score represents the location closest to the mean, we need to know the sign of each Z-score, as well as the absolute value of each Z-score.

The sign of the Z-score indicates whether the location is above (+) or below (-) the mean. The absolute value of the Z-score indicates how far away the location is from the mean, measured in standard deviations.

Looking at the options provided, we see that:

A. Z=+0.5 is positive, indicating a location above the mean, and has an absolute value of 0.5.

B. Z=+1.0 is positive, indicating a location above the mean, and has an absolute value of 1.0.

C. Z=-1.5 is negative, indicating a location below the mean, and has an absolute value of 1.5.

D. Z=-0.3 is negative, indicating a location below the mean, and has an absolute value of 0.3.

Since we want to find the Z-score closest to the mean, we should look for the option with the smallest absolute value. Therefore, the answer is A. Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean.

To know more about the absolute value visit:

brainly.com/question/29764645

#SPJ1

Answer:

The correct equation is C. d = 163t.

This equation shows a direct proportionality between the amount of time worked (t) and the amount of money earned (d). For each hour worked, Rajindri earns $163, so the total amount earned (d) is equal to the hourly rate of $163 multiplied by the number of hours worked (t).

Step-by-step explanation:

The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.

SSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.

By sine rule,

Y = sin156.78 × 44 / 34

= 29

sin Y = 0.499

Y = 29.93°

By the angle sum property. The last angle will be:

180 - 156.78 - 29.93

= 6.67°

Learn more about triangles on

https://brainly.com/question/21629009

#SPJ1

It will take 4. 09 weeks for the tires to be rotated at the current rate.

When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.

25, 200 rotations / day x 7 days / week = 176, 400 rotations per week

To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:

C = 2πr

Rotation per mile is:

1 mile / 87.96 inches / rotation = 72.26 rotations / mile

Number of weeks:

10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations

722, 600 rotations / 176, 400 rotations/week = 4.09 weeks

Find out more on tire rotations at https://brainly.com/question/3471381

#SPJ1

Answer:

------------------------------

We are given three sides and need to find one of angles.

Use the law of cosines:

  [tex]cos(A) = \cfrac{ b^2 + c^2 - a^2}{2bc}[/tex]

Here we are given:

Substitute above values into the given equation:

   [tex]cos(R) = \cfrac{ 52^2 + 41^2 - 59.7^2}{2*52*41} =0.1925[/tex]

Find m∠R: