The solution is, the two dimensions will be 2121.32 by 1414.2.
Here, we have,
let X and Y be the two dimensions.
Area will be X times Y.
XY = 3000000
Y = 3000000 / X
Perimeter = 2x + 3y
substituting the values:
Perimeter = 2x + 3*3000000 / x
= 2x + 9000000 / x
so, we get,
2 = 9000000 / x^2
x^2 = 9000000 / 2 = 4500000
x = sqrt(4,500,000)
= 2121.32
= 1000 sqrt (4.5)
y = 3000000 / 2121.32
= 1414.2
= 1000 sqrt(2)
so the dimensions will be 2121.32 by 1414.2 .
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complete question:
A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
The value of Q₃ of the data represented by the box plot is,
⇒ Q₃ = 30
Given that;
A box plot is shown in figure.
Now, We have been given an image of a box plot and we are asked to find the value of third quartile represented by our given box plot.
Since, we know that the upper or 3rd quartile is represented by the last line of the box.
We can see that 1st line of our box is at 20 ,so it will be 1st or lower quartile.
And, The middle line is at 25, so median for our given box plot is 25.
The last line of the box is at 30, which is representing the upper or third quartile of our given box plot.
Therefore, the third quartile, is 30 for our given box-plot.
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A set of data items is normally distributed with a mean of 80 and a standard deviation of 9. Convert 71 to a z-score.
271 = 0
(Type an integer or a decimal.)
The z-score for 71 is -1.
Understanding Z-score calculationz-score is a measure of how many standard deviations an observation or data point is away from the mean of a distribution.
It is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation: z = (x - μ) / σ
A positive z-score means that the data point is above the mean, while a negative z-score means that it is below the mean.
Applying the formula to solve our question
Here is a proven formula to use:
z = (x - μ) / σ
where:
x = the data item (x = 71)
μ = the mean of the distribution (μ = 80)
σ = the standard deviation of the distribution (σ = 9)
Substituting the values, we get:
z = (71 - 80) / 9
z = -1
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A pyramid-shaped building is 318 ft tall and has a square base with sides of 580 ft. The sides of the building are made
from reflective glass. What is the surface area of the reflective glass?
The surface area of the glass is _____ ft².
(Round the final answer to the nearest whole number as needed. Round all intermediate values to four decimal places
as needed.)
Answer:
499,237 ft²
Step-by-step explanation:
You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.
AreaTo find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:
A = 1/2bh
There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:
4A = 4(1/2bh) = 2bh
Slant heightThe slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)
h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet
Glass arealateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²
The surface area of the glass is about 499237 square feet.
What function is represented in the graph?
Select one:
y = 2(.5^x)
y = 2(3^x)
y = 3(.5^x)
y = 3(2^x)
The exponential function represented by the given graph is:
y = 2(.5^x)
What function is represented by the graph?Here we have an exponential decay, the general form of these functions is:
y = A*(b)^x
Where A is the initial value and b is the base, and it is a decay if 0 < b < 1.
Now let's look at the y-intercept, we can see that it is y = 2, then:
2 = A*(b)^0
2 = A
The function is of the form:
y = 2*(b)^x with 0 < b < 1.
The option that meets these conditions is the first one: y = 2(.5^x)
So that is the correct option.
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A
Select the correct answer.
Which system of linear inequalities is represented by this graphed solution?
OA y> -+2
V≤ 32-1
OB V<= +2
v2 32-1
Ocy> -2x + 2
vs-1
OD S-2 +2
v < 30-1
The two inequalities of the graph are:
y ≥ 3x - 1
y < -¹/₂x + 4
How to identify inequality graph?
The general form of the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The first inequality with a solid line has a y-intercept of -1 and since it is shaded above the line, we will use ≥.
Two coordinates on the line are: (0, -1) and (1, 2)
The slope = (2 + 1)/(1 - 0) = 3
Thus, inequality is:
y ≥ 3x - 1
The second inequality with a dashed line has a y-intercept of 4 and since it is shaded below the line, we will use <.
Two coordinates on the line are: (4, 0) and (0, 2)
The slope = (2 - 0)/(0 - 4) = -1/2
Thus, inequality is:
y < -¹/₂x + 4
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How many permutations do I have it I select 4 things from a total of 9 with replacement? (9P4)
There are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
It is required to find the number of permutations when 4 things are selected from a total of 9 with replacement.
Use the formula for permutations with replacement, which is:
= [tex]^np_r[/tex]
Here n is the total number of items and r is the number of selections.
As per the question, n = 9 and r = 4.
So, the number of permutations is:
= ⁹p₄
= 9!/5!
= 9 x 8 x 7 x 6
= 3024
Thus, there are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
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El 60% de número de hombres es igual al 40% de mujeres. ¿qué tanto por ciento del total representa las mujeres?
The percentage of the total that women represent, would be 60% of the total.
How to find the percentage ?Given that 60 % of men is equal to 40 % of women, we have :
0. 6 M = 0. 4 W
Solving for women in terms of Men gives:
W = ( 0.6 x M) / 0.4
= 1.5 x M
We can then find the percentage of women to be:
= (W / Total ) x 100
= ((1.5 x M) / (2.5 x M)) x 100
= (1.5 / 2.5) x 100
= 0.6 x 100
= 60%
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solve the proportion for x pls help image attached
[tex]\cfrac{10}{x}=\cfrac{x}{7}\implies 70=x^2\implies \sqrt{70}=x[/tex]
3
2
A ABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of
create A A'B'C'.
The center of dilation is the point (5,
(5,
-6).
What are the coordinates of vertex.
B'₂
Enter your answers, as decimals, in the boxes.
9
The coordinates of vertex B' are (76, -86).
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 9 centered at the point D (-5, 5) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate B, we have;
Coordinate B = (4, -4) → (9(4 - (-5)) + (-5), 9(-4 - 5) + (-5))
Coordinate B = (4, -4) → (9(9) - 5, 9(-9) - 5)
Coordinate B = (4, -4) → (81 - 5, -81 - 5)
Coordinate B' = (76, -86).
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Complete Question:
ΔABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of 9 to create ΔA'B'C'. The center of dilation is the point (5, -6).
What are the coordinates of vertex B'?
Pls help thanks!!!!!!!!!!!
Answer:
Put your calculator in degree mode.
sin(13°) = 500/x
x sin(13°) = 500
x = 500/sin(13°) = 2,222.7 miles
Using a trigonometric relation we can see that x = 2,222.7 ft
How to find the value of x?We can see a right triangle, there we can see that one of the angles has a measure of 13°.
The opposite cathetus has a measure of 500ft, and we want to find x, which is the hypotenuse.
Then we can use the relation:
sin(a) = (opp cathetus)/hypotenuse
Replacing what we know, we will get:
sin(13°) = 500/x
Solving that for x:
x = 500/sin(13°) = 2,222.7 ft
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In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
The percentage of pennies in the roll is A = 30 %
Given data ,
Let the percentage of pennies in the roll made before 1985 be A
Now , the total number of pennies be = 50 pennies
And , the number of pennies made before 1985 is = 15 pennies
So , the percentage is A = ( 15 / 50 ) x 100
On simplifying the equation , we get
A = 3/10 x 100
A = 30 %
Hence , the percentage is 30 %
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What is the measure of angle b?
A
90o
B
180o
C
43o
D
47o
Answer:
b
Step-by-step explanation: makes sense
complete the table on the relation
The triangles below are similar. Find the value of X. The image is not to scale
Answer:
x is 25
Step-by-step explanation:
There is a common ratio between the sides. In this case, 35/28 is 1.25. This is the number you have to multiply to 20. 1.25 * 20 = 25.
The volume of the tank is cubic feet and it will be completely filled with water at the end of minutes.
Answer:
there is missing information needed to provide a solution to this problem.
Assignment Active
The Economic Effect of Snowsheds
With so many snowsheds along the line, annual
maintenance soared. By 1910 many of the original
wooden structures needed replacing, and heavy snows in
the winter of 1912-13 crushed others. That year the
railway hired 1,800 workers to make shed improvements
along just 8 miles of track, and the need for additional
sheds was clear....
While making repairs on the Cascade Mountain
snowsheds in 1917, the Great Northern Railway used over
35 million board feet of timber that cost triple what it had
just eight years earlier. By this time, snowsheds and
tunnels covered 6.7 of the 9 track miles between
Wellington and Scenic.
According to this passage, how did snowsheds affect
the railroad in the long term?
O They decreased delays, which lowered the railroad
costs.
They required frequent repairs, which added to the
railroad costs.
They reduced the need for bridges, which lowered
the railroad costs.
O They required many workers to operate them,
which added to the railroad costs.
help help help help help
The Winberg apartment complex rents out units at $200x monthly for each of their 9 units. The Hensing apartment complex has 3x more units and rents out each unit for $20 less monthly.
Which of the following equations could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out?
A. y = $(600x^2 - 180)
B. y = $(600x^2)
C. y = $(600x^2 + 1,740x - 180)
D. y = $(600x^2 + 1,860x - 180)
The equation that could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out is A. y = $(600x^2 - 180).
How to calculate the equationThe Hensing apartment complex rents out each unit for $20 less monthly than the Winberg complex, so the rent for each unit is $200x - $20 = $180x.
The equation that represents this situation is: y = $(600x^2 - 180
So the answer is (A) y = $(600x^2 - 180).
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A slide at a water park with a constant slope sends riders traveling a distance of 45 feet to the pool at the bottom of the slide. If the depth of the pool is 12 feet, and the angle of depression from the top of the slide is 45 ° what is the vertical distance from the top of the slide to the bottom of the pool? Round answers to the nearest tenth.
The required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.
We can use trigonometry to solve this problem. Let's call the vertical distance from the top of the slide to the bottom of the pool "h" (in feet). We can use the angle of depression (45°) to find the horizontal distance from the top of the slide to the bottom of the pool. Since the slide has a constant slope, the angle between the slide and the ground is also 45°. It implies that the vertical height is equal to the horizontal projection of the slide.
Apply Pythagorean theorem,
45² = h² + h²
h = 45/√2
h = 31.8
Now, as mentioned that depth of the pool is 12 feet so, the total vertical height is given as,
= h + 12
= 31.8 + 12
= 43.8 feet
Thus, the required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.
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Given that NL HI and NM JK, find the radius of circle N if JK=14. Round the answer to the hundredths place. A. 12.56 B. 12.57 C. 13.03 D. 13.04
The value of the radius is 13.04
What is Pythagoras theorem?Pythagoras theorem states that: The sum of square of the two legs of a right triangle is equal to the square of the other side.
Therefore c² = a² + b²
Since MN is perpendicular to JK , this means MK = JM = JK/2
= 14/2 = 7
HI = JK, therefore LI is also 7
and MN = LN = 11
Therefore,
NI =√ LN)² + LI)²
NI = √ 11² + 7²
NI = √121+49
NI = √ 170
NI = 13.04( nearest hundredth)
therefore the radius of the circle is 13.04
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In a greenhouse, Brazil is grown in planters that have a base of 4 1/5 In by 1 1/3 in. If there is a 3 x 3 array of these planters with no space between them, what is the area covered by the planters
Answer:
The area of one planter is:
4 1/5 in × 1 1/3 in = (21/5) in × (4/3) in = 28/5 in²
In a 3 x 3 array, there are 3 planters in each row and 3 planters in each column, so there are a total of 9 planters.
The area covered by the planters is:
9 × (28/5) in² = 252/5 in² ≈ 50.4 in²
Therefore, the area covered by the planters is approximately 50.4 square inches.
Step-by-step explanation:
mark brainliest
find the mean of the set of data 3,5,4,4,5,7,7
Answer:
mean=5
Step-by-step explanation:
To find the mean of a set of data, we add up all the values in the set and then divide by the number of values.
Adding up the values in the set, we get:
3 + 5 + 4 + 4 + 5 + 7 + 7 = 35
There are 7 values in the set, so we divide the sum by 7 to get the mean:
mean = sum of values / number of values
mean = 35 / 7
mean = 5
What is angle CAB
Enter your answer in the box
The measure of the angle CAB in a right angled triangle ABC using given measurements is equal to 37°.
In the triangle ABC,
From the figure we have,
Measure of angle ABC = 90 degrees
Measure of angle ACB= 53 degrees
Sum of all the interior angles of a triangle is equal to 180 degrees .
⇒Measure of angle ABC + Measure of angle ACB + Measure of angle CAB = 180 degrees
⇒ 90° + 53° + Measure of angle CAB = 180°
⇒143° + Measure of angle CAB = 180°
⇒ Measure of angle CAB = 180° - 143°
⇒ Measure of angle CAB = 37°
Therefore, the measure of the angle CAB is equal to 37°.
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WHATS THE 2ND TO THE POWER OF THE 4TH
Answer:
16.
Step-by-step explanation:
3
Q
The diagram shows three shapes that are mathematically similar.
The heights of the shapes are in the ratio small: medium: large = 1:5:8.
Find the ratio shaded area : total unshaded area.
Give your answer in its simplest form.
NOT TO
SCALE
The ratio of the shaded area to the total unshaded area can be found to be 5 : 9.
How to find the ratio ?The three shapes are similar to each other which means that their areas must be similar as well.
The only shape that is shaded is the second largest shape and it has the value of 5 in the ratio. This means that the other two shapes are not shaded and their ratio values are 1 and 8.
This then means that the ratio of shaded area to unshaded area can be written as :
Shaded area : Unshaded area
5 x width : ( 1 x width) + ( 8 x width )
5 : 1 + 8
5 : 9
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Classifying the polynomial
Answer: Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2x3+3x2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.
Find the distance between (-2.1,80°) and (-1.8,-70°)
Answer:
15,136 km
Step-by-step explanation:
Im not 100% sure but everyone meses up sometimes/
(CLASSKICK) HELP ASAPPPP!
The value of the angle 3 as solved is 52 degrees.
What is the sum of the angles on a straight line?
The sum of the angles on a straight line is always 180 degrees, and this property is true for any pair of opposite angles formed by two intersecting lines.
We can see that what we have is the angles that are on a straight line
We have from the question that;
< 1= 90
<2 = 38
Thus;
<6 = 180 - (90 + 38) - Sum of angles on a straight line
<6 = 52°
Now;
<4 = 90 degrees (Vertically opposite angles)
<5 = 38 degrees (Vertically opposite angles)
Then;
<3 = 180 - (90 + 38) - Sum of angles on a straight line
<3 = 52°
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The boxplot displays the total cost of attendance for all US public and private universities.
Use this graphic to complete the statements.
Both distributions of the total cost of attendance are
. The average cost of attendance is higher for
universities. The costs of more than
% of the public institutions were within the costs of the lowest 25% of private institutions. Both the range and IQR was higher for
universities. Both distributions have
outliers.
Both distributions of the total cost of attendance are skewed right
The average cost of attendance is higher for private universities.
The costs of more than 75 % of the public institutions were within the costs of the lowest 25% of private institutions.
Both the range and IQR was higher for private universities
Both distributions have outliers.
What is a box plot?A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile [Q1], median, third quartile [Q3] and “maximum”).
It can tell you about your outliers and what their values are
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Answer:
skewed right private 75 private do have outliers
Step-by-step explanation:
plot a point to represent the approximation sqrt(20)
To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.
|---------------------|---------------------|
0 4.472
We have,
To plot the point representing the approximation of √(20), we need to first find the approximate value of √(20):
√(20) ≈ 4.472
This means that the point we want to plot is located approximately 4.472 units to the right of the origin on the number line.
To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.
The resulting point represents the approximation of √(20).
Thus,
A rough sketch of what the plot could look like:
|---------------------|---------------------|
0 4.472
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