On a sunny day, the tree in your backyard casts a shadow of 16 feet. At the same time, you cast a shadow of 4 feet. You
are 5 feet 3 inches tall.
How tall is the tree?
21.21 ft
17.3ft ft
12.2 ft
21 ft

Answer:

0.08333333333

Step-by-step explanation:

because 1/3 divided by 4 equals 0.08333333333

Answer:

3.1 miles

Step-by-step explanation:

2.5 + 4.4 = 6.9

10 - 6.9 = 3.1

Answer: 1 To find the sampling distribution of the sample mean, we need to use the Central Limit Theorem. According to the Central Limit Theorem, for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

In this case, the population has a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes. Since the sample size is large (25), we can assume that the sampling distribution of the sample mean will be approximately normally distributed with the same mean but a smaller standard deviation.

To calculate the standard deviation of the sampling distribution (also known as the standard error), we divide the population standard deviation by the square root of the sample size:

Standard Error = Population Standard Deviation / √(Sample Size)

Standard Error = 22 / √(25)

Standard Error = 22 / 5

Standard Error = 4.4 minutes

Therefore, the sampling distribution of the sample mean has a mean of 87 minutes (same as the population mean) and a standard deviation of 4.4 minutes.

3 To determine the sample size needed to achieve a desired margin of error and confidence level, we can use the formula:

Sample Size = (Z-score)^2 * (p * (1 - p)) / (E^2)

In this case, the desired margin of error is 3% (0.03) and the confidence level is 90%, which corresponds to a Z-score of 1.645.

Sample Size = (1.645)^2 * (0.5 * (1 - 0.5)) / (0.03^2)

Sample Size = 2.705 * 0.25 / 0.0009

Sample Size = 6.762 / 0.0009

Sample Size = 7513.33

Therefore, approximately 7514 students should be surveyed to achieve a 90% confidence level with a margin of error of 3%.

5. To test the hypothesis about the population mean lifetime of batteries, we can perform a one-sample t-test.

Null hypothesis (H0): The population mean lifetime of batteries is 50 hours.

Alternative hypothesis (H1): The population mean lifetime of batteries is not 50 hours.

We are given that the sample mean lifetime for a sample of nine batteries was 48.2 hours. The population standard deviation is 3 hours.

Using a significance level of 0.01, we can calculate the t-value and compare it to the critical t-value from the t-distribution with (n-1) degrees of freedom.

t-value = (Sample Mean - Population Mean) / (Sample Standard Deviation / √n)

t-value = (48.2 - 50) / (3 / √9)

t-value = -1.8 / (3 / 3)

t-value = -1.8

With a significance level of 0.01 and (n-1) degrees of freedom (n-1 = 9-1 = 8), the critical t-value is approximately ±2.896.

Since the calculated t-value (-1.8) does not exceed the critical t-value of ±2.896, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population mean lifetime of batteries is significantly different from 50 hours at the 0.01 level of significance.

6.To test the hypothesis about the proportion of customers who cannot distinguish the wine producer's product, we can perform a one-sample proportion test.

Null hypothesis (H0): The proportion of customers who cannot distinguish the product is 0.09 or less.

Alternative hypothesis (H1): The

Step-by-step explanation:

Answer:

meteor hitting earth

Step-by-step explanation:

not sure of actual probability but i believe one that would cause mass extinction is quite improbable

The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

To learn more about binomial expansion click :

https://brainly.com/question/3537167

#SPJ1

Answer:

-4

Step-by-step explanation:

So we have the function:

\(h(x)=-3x-4\)

To find h(0), substitute 0 for x. Thus:

\(h(0)=-3(0)-4\)

Multiply:

\(h(0)=0-4\)

Subtract:

\(h(0)=-4\)

And we're done!

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

Answer:

24

Step-by-step explanation:

angle = 38

opposite of angle = 15

hypotenuse = c

sohcahtoa

sin utilizes both opposite and hypotenuse

thus,

sin(38) = 15/c

multiply both sides by c to make it a numerator

csin(38) = 15

divide both sides by sin(38) to get c

c = 15/sin(38) ≈ 24

Answer:

$17.20

Step-by-step explanation:

You need to print (130)(17) = 2210 pages.

This means you need 2210/500 reams, which rounds up to 5.

So, the cost is 5(3.44) = $17.20

Answer:

7602.40

Step-by-step explanation:

Based on the given conditions

Formulate:

3.44×30×17

447.2×17

7602.4

Round 7062.4

=7062.40

Answer:

7

Step-by-step explanation:

to find the circumference of a circle the equation is C=πd where C is circumference, d is diameter, and using 3.14 for π

once we plug in the known information we are left with

22=(3.14)d

all that's left is to solve for d

22=(3.14)d

22/3.14=(3.14)/3.14 d

7=1d

7=d

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

Answer:

maybe ; the length of ab is 6

The value that each term can be multiplied by to eliminate the decimals in the equation is 4

The equation is given as

0.5x + 1 = 0.75x

Represent the terms as a fraction

So, we have

1/2x + 1 = 3/4x

The denominators in th​e above fractions are

2 and 4

The LCM of 2 and 4 is 4

Hence, the value that each term can be multiplied by to eliminate the decimals in the equation is 4

Read more about equations at

https://brainly.com/question/13763238

#SPJ1

The quadratic model using regression for the given time(seconds) and height (feet) is given by y = 1.287x + 3.602.

Ball will be at 3.28feet when time is equal to 0.43seconds

As given in the question,

From the given time (seconds) and height(feet):

let x be the time and y be the height,

from the table consider two points get the equation of line:

( 0.01, 1.88) and (0.11 , 3.05)

(y - 1.88)/ (x - 0.01) = (3.05 - 1.88)/ (0.11- 0.01)

⇒ y= 11.7x -1.763

Using regression model calculator,

Quadratic model of the data is given by:

y = 1.287x + 3.602

When y = 3.28feet

Then 3.28 = 11.7x - 1.763

⇒x = 0.43seconds

Therefore, the quadratic model of the data using regression is given by y = 1.287x + 3.602 and ball will be at height 3.28feet when time is 0.43seconds.

Learn more about regression here

brainly.com/question/7656407

#SPJ4

Answer:

To my best knowledge from what I can see the answer is A.

Step-by-step explanation:

The perimeter and area of the square are; 24√2 units and 12 units² respectively

Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance AS = 6√2

The perimeter of the square = 4 (6√2)

Perimeter = 24√2 units

The area of the square = l²

Area of the square = (6√2)²

Area of square = 12 units²

Learn more on perimeter of square here;

brainly.com/question/25092270

#SPJ1

Answer:

Step-by-step explanation:

The diagonals of a rectangle have the same midpoint, so for points A, B, C, D, we must have ...

  (A+C)/2 = (B+D)/2

  D = A + C - B

  D = (-2, -8) +(8, 2) -(-2, 2) = (-2+8+2, -8+2-2)

  D = (8, -8)

__

The side lengths are 2-(-8) = 10, and 8-(-2) = 10. The area is the product of the side lengths, so is 10×10 = 100 square units.

_____

Comment on side lengths

When the end points of one side are on the same vertical line, the length of that side is the difference of y-coordinates. When the points lie on the same horizontal line, the side length is the difference of x-coordinates.

Answer:

the last vertex is (8,-8)

the area of the rectangle is 100 square units

Step-by-step explanation:

The value of x with the given condition is 10

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

D(7,2), E(1, 9), F(4,8), and G(x, 1),

Also, we have

DE || FG

This means that the lines DE and FG are parallel lines and they have equal slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(9 - 2)/(1 - 7) = (1 - 8)/(x - 4)

Evaluate the difference

-7/6 = -7/(x - 4)

So. we have

x - 4 = 6

Evaluate

x = 10

Hence. the value of x is 10

Read more about slope at

https://brainly.com/question/3493733

#SPJ1

Answer:

The answer is 4...

Hope it helps! ^^

Answer:

No

1/1000

Step-by-step explanation:

The place digits is .713.

The seven is the tenths.

The one is the hundredths.

The three is the thousandths.

So the three would be in the thousandths place

Answer:

Step-by-step explanation:

1/2 ÷ 2/3 = 1/2 x 3/2 = 3/4 -_- so easy

Answer:

The first one is three the second is four

Step-by-step explanation:

1/2÷2/3 (do copy, dot, flop)

1/2·3/2

1·3=3

2·2=4

3/4

The two numbers in bold are the answers

Answer:125-1/3 can be written as : none of these

Answer:

Step-by-step explanation:

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

Answer:

I think it is 3600

Step-by-step explanation:

Answer:

be yourself

Step-by-step explanation:

that's the only thing that i can say

Answer:

Just let her.

Step-by-step explanation:

The image point of the coordinate X after the rotation is (-1, 5).

When a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.

So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).

Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).

Read mroe about transformation at

https://brainly.com/question/27224272

#SPJ1

The potential roots of f(x) = 3x³ - 13x² - 3x + 45 are given as follows:

A. +1/3

B. +5

C. +5/3

D. +9

E. +1

F. +15

G. +3

To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Hence the possible roots are given as follows:

±1/3, ±1, ±3, ±5, ±5/3, ±9, ±5, ±15.

More can be learned about the rational zeros theorem at brainly.com/question/28782380

#SPJ1

To find the volume of the solid, you need to calculate the area of each cross-section and then multiply that by the thickness of the section (which is the distance along the y-axis).

(a) Squares: The cross-sections are squares with sides of length y. The area of a square is side^2, so the area of each square is y^2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the square cross-sections is y^2 * y

(b) Semicircles: The cross-sections are semicircles with radii of length y. The area of a semicircle is (pi * r^2) / 2 , so the area of each semicircle is (pi * y^2) / 2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semicircular cross-sections is (pi * y^2) / 2 * y

(c) Equilateral triangles: The cross-sections are equilateral triangles with side length of y. The area of an equilateral triangle is (s^2 * √3)/4. so the area of each equilateral triangle is (y^2 * √3) / 4. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the equilateral triangle cross-sections is (y^2 * √3) / 4 * y

(d) Semi-ellipses: The cross-sections are semi-ellipses whose heights are twice the lengths of their bases. The area of a semi-ellipse is πab/2, where a and b are the lengths of the semi-major and semi-minor axes respectively. Therefore the area of each semi-ellipse will be (πy^2)/2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semi-ellipse cross-sections is (πy^3)/2

It is important to note that this is a theoretical volume calculation, as the shape of the solid does not have a closed form representation by these functions, but rather, these are an approximation.

Also, for any of these volumes to be meaningful, we have to integrate over the range of the variable y, since it is bounded by the equations y=x, y=0 and x=1, the variable y is limited.

To know more about volume of the solid refer to:

brainly.com/question/21036176

#SPJ4