I think the answer is A
The question about the number of cities with more than 2 inches of snow is a statistical question as it involves data collection and analysis. Hence option a is correct.
The question, 'How many cities had more than 2 inches of snow?' is considered a statistical question. This is because it deals with the collection, analysis, interpretation, and presentation of data regarding the amount of snow that fell in various cities. Statistics is an area of mathematics that pertains to data analysis, and this question would likely require the processing and summarization of snowfall data from a number of cities.
Help fast please!!!!!!!!
Step-by-step explanation:
The area is
[tex] {x}^{2} - 110x + 2800 \\ = {x}^{2} - 40x - 70x + 2800 \\ = x(x - 40) - 70(x - 40) \\ = (x - 40)(x - 70)[/tex]
Since the width is
[tex]x - 40 \: (feet)[/tex]
Then, the length will be
[tex]x - 70 \: (feet)[/tex]
Adante begins to evaluate the expression 3 1/3 x 5 1/4 using the steps below
Answer:
[tex]\frac{35}{2}[/tex]
Step-by-step explanation:
To solve this problem we need to write the mixed fraction as a fractional number, as follows:
[tex]3 1/3 = 3 + \frac{1}{3} = \frac{9+1}{3} = \frac{10}{3}[/tex]
[tex]5 1/4 = 5 + \frac{1}{4} = \frac{20+1}{4} = \frac{21}{4}[/tex]
Then, evaluating the expression:
[tex]\frac{10}{3}[/tex]×[tex]\frac{21}{4}[/tex] = [tex]\frac{210}{12}[/tex]
→ [tex]\frac{35}{2}[/tex]
Answer:
35 over 2
Step-by-step explanation:
The deer population in a region is expected to decline 1.1% from 2010-2020. Assuming this continued how many deer would there be in the region in the year 2060 if the 2010 population was 1,578?
1,406
1,510
1,493
1,385
Answer:
Option C. 1,493
Step-by-step explanation:
If the deer population in a region is expected to decline 1.1% from 2010 to 2020. Assuming this continued, we can say that the deer population decreases 1.1% each ten years.
From 2010 to 2060 there are 50 years. If the deer population decreases 1.1% each ten years, then it will decrease 5.5% in 50 years.
If the population in 2010 was 1,578. Then, the population in 2060 is going to be:
Using the rule of three:
If 1578 ----------------> Represents 100%
X <----------------- 5.5%
X = (5.5%x1578)/100% = 86.79 ≈ 87
Then the total population in 2060 is: 1578 - 87 = 1491
None of the answers equal to 1491. That's why I assume the correct answer must be Option C. 1,493. Given that it's the closest answer!
Answer:
The population would be 1,493.
Step-by-step explanation:
Given,
The initial population, P = 1,578, ( In 2010 )
Also, the decline rate per 10 years, r = 1.1 %,
And, the number of the periods of 10 years since, 2010 to 2060, n = 5,
Hence, the population in 2060 would be,
[tex]A=P(1-\frac{r}{100})^n[/tex]
[tex]=1578(1-\frac{1.1}{100})^5[/tex]
[tex]=1493.09849208\approx 1493[/tex]
Option third is correct.
Which polynomial expression represents a sum of cubes?
(6 – s)(s2 + 6s + 36)
(6 + s)(s2 – 6s – 36)
(6 + s)(s2 – 6s + 36)
(6 + s)(s2 + 6s + 36)
Answer:
(6 + s)(s² - 6s + 36)Step-by-step explanation:
[tex]\text{The sum of cubes:}\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\text{Therefore}\\\\\text{for}\ a=6\ \text{and}\ b=s:\\\\6^3+s^3=(6+s)(6^2-6s+s^2)=(6+s)(36-6s+s^2)[/tex]
Answer: (6 + s)(s^2 – 6s + 36)
Step-by-step explanation:
6th Grade Math! Complete the function table and write the function rule. Please explain, since this is a written answer. Tysm!
Answer:
Its subtract 12.
Step-by-step explanation:
The first question mark is positive 6.
6-12= -6
The second question mark is -22.
Negative 10 minus 12 equals negative 22
Once you understand integers, it will be really easy. I was in 6th grade last year.
7. Prepaid expenses require what type of adjusting entry?
A. Matched
B. Accumulated
C. Accrued
D. Deferral
Answer:
B
Step-by-step explanation:
Adjusting entries for prepaid expenses are classified as a (D) deferral. They gradually recognize the cost as expense over the period of benefit. This involves decreasing the prepaid asset account and increasing the corresponding expense account.
Prepaid expenses are costs that have been paid in advance for services or goods that will be received in the future. In accounting, prepaid expenses are considered assets because they provide future economic benefits to the company. When adjusting entries for prepaid expenses, the necessary adjusting entry is a ( D) deferral.
This means that the initial payment is recorded in a prepaid asset account, and then as the expense is incurred over time, it is gradually recognized as an expense on the income statement. For example, if a company pays a year's worth of rent in advance, each month, a portion of that prepaid rent would be moved from the prepaid asset account to the rent expense account, reflecting the usage of the space.
An adjusting entry for a deferral decreases the prepaid asset account and increases the expense account. The goal of this type of entry is to apportion the expense to the periods in which the benefits from the prepaid cost are actually realized.
consider the function,
Answer:
If x= 4 then f(x) = 4x -5 is 11.
Step-by-step explanation:
f(x) = 4x -5
We need to find the domain value that corresponds to the output f(x) = 11
In this question, we need to solve the expression for value of x such that the answer is 11.
if x= 3
f(3) = 4(3) -5
= 12 -5
= 7
Since we want the answer 11 so we cannot take x= 3
if x = 4
f(4) = 4(4)-5
= 16 - 5
= 11
So, if x= 4 then f(x) = 4x -5 is 11.
write a polynomial of least degree with rational coefficients and with the root -19-5 square root 2.
Write your answer using variable x and in standard form with leading coefficients of 1.
Answer:
y = x² + 38x + 311
Step-by-step explanation:
If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.
y = (x − (-19-5√2)) (x − (-19+5√2))
y = (x + 19+5√2) (x + 19−5√2)
Use FOIL to distribute:
y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)
y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)
y = x² + 38x + (19+5√2)(19−5√2)
Use FOIL to distribute the last term:
y = x² + 38x + 19² − 95√2 + 95√2 − 50
y = x² + 38x + 361 − 50
y = x² + 38x + 311
The required polynomial would be y = x² + 38x + 311.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
Given that least degree with rational coefficients and with (-19-5√2)
We know that if a polynomial has both rational and irrational roots, the roots must be conjugate pairs.
y = (x − (-19-5√2)) (x − (-19+5√2))
y = (x + 19+5√2) (x + 19−5√2)
Apply the distributive property,
y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)
y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)
y = x² + 38x + (19+5√2)(19−5√2)
y = x² + 38x + 19² − 95√2 + 95√2 − 50
y = x² + 38x + 361 − 50
y = x² + 38x + 311
Thus, the required polynomial would be y = x² + 38x + 311.
Learn more about the polynomial here:
brainly.com/question/11536910
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Lindsay was going to visit her grandma, shop at the mall, and then return home. The route she took was in the shape of a triangle. The distance between each place she visit was 10 miles. What type of triangle is formed by the route she traveled.
Answer:
Is an equilateral triangle
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal internal angles measures 60 degrees each
so
In this problem the triangle formed by the route has three equal sides (10 miles)
therefore
Is an equilateral triangle
The Earth completely rotates on its axis once every 24 hours.
A) How long does it take for it to rotate 310 degrees?
B) How long does it take to rotate 5 radians?
C) The diameter of the Earth is approximately 7920 miles. How far will a point on the equator rotate in 2 hours?
Show all work. Give answers to the nearest hundredth. Include the units in your response.
Answer:
A)
62/3 = 20.67 hours
B)
60 hours
C)
2074.29 miles
Step-by-step explanation:
If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.
A)
In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;
(24/360) = (x/310)
solving for x;
x = (24/360) * 310 = 62/3 = 20.67 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;
(24/2π radians) = (x/5π radians)
Solving for x;
x = (24/2π radians)*5π radians = 60 hours
C)
If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;
circumference = 2*π*R = π*D
= 7920π miles
Therefore, the speed of the earth is approximately;
(7920π miles)/(24 hours) = 330π miles/hr
The distance covered by a point in 2 hours will thus be;
330π * 2 = 660π miles = 2074.29 miles
Answer:
Part A). In 20 hr 24 minutes earth rotate 310°.
Part B). In 19 hr 6 minutes earth rotate 5 radians
Part C). 2072.4 miles point on equator rotates in 2 hours.
Step-by-step explanation:
Degree that earth rotate in 24 hour = 360°
Number of radian that earth rotate in 24 hour = 2π radian
Part A).
Time taken to rotate 360° = 24 hours
Time taken to rotate 1° = [tex]\frac{24}{360}=\frac{1}{15}\,hours[/tex]
Time taken to rotate 310° = [tex]310\times\frac{1}{15}=20\frac{2}{5}=20\,hr\:24\,minutes[/tex]
Part B).
Time taken to rotate 2π radian = 24 hours
Time taken to rotate 1 radian = [tex]\frac{24}{2\pi}=\frac{12}{\pi}\,hours[/tex]
Time taken to rotate 5 radian = [tex]5\times\frac{12}{\pi}=\frac{60}{\pi}=19.1\.hr=19\,hr\:6\,minutes[/tex]
Part C).
Diameter of Earth = 7920 miles
Radius of earth, r = 3960 miles
Degree of rotation in 1 hours = [tex]\frac{360}{24}=15^{\circ}[/tex]
Degree of rotation in 2 hours , [tex\theta[/tex] = 15 × 2 = 30°
Length of the arc for angle 30° of circle with radius 3960 miles = Distance covered by point in 2 hours.
Length of the arc = [tex]\frac{\theta}{360^{\circ}}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]
Therefore, Part A). In 20 hr 24 minutes earth rotate 310°.
Part B). In 19 hr 6 minutes earth rotate 5 radians
Part C). 2072.4 miles point on equator rotates in 2 hours.
Choose the correct description of the graph of the compound inequality x − 2 > −4 and 3x less than or equal to 15.
Answer:
A number line with an open circle on −2, a closed circle on 5, and shading in between
Step-by-step explanation:
solve it you get x>-2
and 3x <=15
x<=5
so its close on 5 and open on -2
PLEASE HELP ME SOLVE THIS
Answer:
y = 90°
Step-by-step explanation:
The left side base angle of the triangle and the angle of 110° form a straight angle and are supplementary, thus
base angle = 180° - 110° = 70°
The right base angle is also 70° , thus the triangle is isosceles
The line segment from the vertex is a perpendicular bisector, hence
y = 90°
A shopper seeking a bargain combined a 25% off coupon and brought enough money to cover 25% of the base price. Why did this shopper go home disappointed?
Let's pretend the base price is $100
If the shopper brings enough money to cover 25% of the base price then they are bringing $25
The bargain promises 25% off of the base price of $100, meaning that the bargain price will be $75
The shopper cannot purchase the item because they only brought $25 when they should have brought $75
The shopper went home disappointed because combining a 25% off coupon and paying 25% of the base price results in a net discount of 0%, not the expected 50%.
The shopper went home disappointed because they assumed that by combining a 25% off coupon with paying 25% of the base price, they would get a 50% discount on the item. However, these discounts are applied sequentially, so the actual discount is less than 50%. In this case, the final discount would be 25% off the base price minus 25% of the base price, resulting in a net discount of 0%. The shopper didn't get the expected bargain they were hoping for because the discounts do not add up linearly but are applied to the remaining amount after the previous discount.
To know more about discount, refer here:
https://brainly.com/question/34935576
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Please help will give brainliest
Answer:
4
Step-by-step explanation:
The sum of the measures of all interior angles in triangle is always equal to 180°. So,
∠A+∠B+∠C=180°
∠B=180°-63°-49°=68°
Now use the sine rule:
[tex]\dfrac{c}{\sin \angle C}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{3}{\sin 49^{\circ}}=\dfrac{b}{\sin 68^{\circ}}\\ \\b=\dfrac{3\sin 68^{\circ}}{\sin 49^{\circ}}\approx 3.685\approx 4[/tex]
how to graph from linear standered form 2x-6y=12?
Answer:
See graph below for answer
Step-by-step explanation:
Step 1) Change to y-intercept form
6y = 2x - 12
y = 1/3x - 2
Step 2) Graph.
See graph below for answer
Which of the following is a valid comparison between the possible minimum and maximum values of the function y = -x2 + 4x - 8 and the graph below?
The maximum value of the equation is 1 less than the maximum value of the graph.
The minimum value of the equation is 1 less than the minimum value of the graph.
The minimum value of the equation is 1 greater than the minimum value of the graph.
The maximum value of the equation is 1 greater than the maximum value of the graph.
Answer:
The maximum value of the equation is 1 less than the maximum value of the graph
Step-by-step explanation:
We have the equation [tex]y=-x^2+4x-8[/tex].
We can know that this graph will have a maximum value as this is a negative parabola.
In order to find the maximum value, we can use the equation [tex]x=\frac{-b}{2a}[/tex]
In our given equation:
a=-1
b=4
c=-8
Now we can plug in these values to the equation
[tex]x=\frac{-4}{-2} \\\\x=2[/tex]
Now we can plug the x value where the maximum occurs to find the max value of the equation
[tex]y=-(2)^2+4(2)-8\\\\y=-4+8-8\\\\y=-4[/tex]
This means that the maximum of this equation is -4.
The maximum of the graph is shown to be -3
This means that the maximum value of the equation is 1 less than the maximum value of the graph
Answer:
The maximum value of the equation is 1 less than the maximum value of the graph
Step-by-step explanation:
I need help with this question someone please help and explain. Find the sum of the first twenty-seven terms of an arithmetic series whose first term is -8 and the sum of the first seven-term is 28.
Answer:
The sum of the first twenty-seven terms is 1,188
Step-by-step explanation:
we know that
The formula of the sum in arithmetic sequence is equal to
[tex]S=\frac{n}{2}[2a1+(n-1)d][/tex]
where
n is the number of terms
a1 is the first term
d is the common difference (constant)
step 1
Find the common difference d
we have
n=7
a1=-8
S=28
substitute and solve for d
[tex]28=\frac{7}{2}[2(-8)+(7-1)d][/tex]
[tex]28=\frac{7}{2}[-16+(6)d][/tex]
[tex]8=[-16+(6)d][/tex]
[tex]8+16=(6)d[/tex]
[tex]d=24/(6)=4[/tex]
step 2
Find the sum of the first twenty-seven terms
we have
n=27
a1=-8
d=4
substitute
[tex]S=\frac{27}{2}[2(-8)+(27-1)(4)][/tex]
[tex]S=\frac{27}{2}[(-16)+(104)][/tex]
[tex]S=\frac{27}{2}88][/tex]
[tex]S=1,188[/tex]
20 POINTS
(SSS)
If the lengths of the ______sides of two triangles are______, then the triangles are similar.
(SAS)
If an angle of one triangle is______to an angle of a second triangle and the lengths of the sides including these angles are______, then the triangles are similar.
Answer:
can you make it more specific please?
Step-by-step explanation:
I honestly don't get what you're saying in what subject this is?
A building that is 100 for tall casts a shadow that makes a 30 degree angle. Approximately how long in feet is the shadow across the ground?
Answer: 173.20 ft
Step-by-step explanation:
Observe the attached image. To know how long the shadow is, we must find the length of the adjacent side in the triangle shown. Where the opposite side represents the height of the building
By definition, the function [tex]tan (x)[/tex] is defined as
[tex]tan(x) = \frac{opposite}{adjacent}[/tex]
So
[tex]opposite = 100\ feet\\x=30\°[/tex]
[tex]adjacent = l[/tex]
Then
[tex]tan(30\°) = \frac{100}{l}[/tex]
[tex]l = \frac{100}{tan(30\°)}[/tex]
[tex]l = 173.20\ ft[/tex]
The answer is:
The shadow is 173.20 feet
Why?To solve the problem, we need to calculate the projection of the building's shadow over the ground.
We already know the height of the building (100 feet), also, we know the angle of elevation (30°), so, we can use the following formula to calculate it:
[tex]Tan(\alpha)=\frac{y}{x}=\frac{height}{x}\\\\x=\frac{height}{Tan(\alpha) }[/tex]
Now, substituting the given information and calculating, we have:
[tex]x=\frac{height}{Tan(\alpha) }[/tex]
[tex]x=\frac{100feet}{Tan(30\°) }=173.20feet[/tex]
Have a nice day!
Please answer right away!!!
Answer:
22.9m
Step-by-step explanation:
Using Pythagorean theorem, we can get two equations using the angles.
From Point A:
∠A = 20°
AB = 20m
From Point B:
∠B = 29°
BD = x
What we are looking for is the opposite side of each right triangle, each person makes because we have one adjacent side. We also know that both opposite sides will be equal.
So we use this formula for both point of views:
[tex]Tan\theta=\dfrac{Opposite}{adjacent}[/tex]
Where:
Opposite = height of the building
Adjacent = distance from the building
We are looking for the opposite side so we can tweak our formula to get an equation for the height
[tex]height=(Tan\theta)(distance)[/tex]
Using our given, we can solve for the distance of point B to D:
[tex](Tan20)(20+x) = (Tan29)(x)\\\\(0.3640)(20+x) = (0.5543)(x)\\\\\dfrac{(7.28+0.3640x)}{0.5543}=x\\\\13.1337 + 0.6567x = x\\\\13.1337 = x - 0.6567x\\\\13.1337 = 0.3433x\\\\\dfrac{13.1337}{0.3433}=x\\\\38.2572 = x[/tex]
The distance of point B to D is 38.2572 m.
Now that we know the distance of BD we can solve for the height of the building using only the given from point B.
[tex]height=(Tan\theta)(distance)[/tex]
[tex]height=(Tan29)(38.2572m)[/tex]
[tex]height=(0.5543)(38.2572m)[/tex]
[tex]height=21.21m[/tex]
But this is only the height from the line of sight. To get the height of the building from the ground, we just add the height of the viewer, which is 1.7m.
21.21m + 1.7m = 22.91m
The closest answer is: 22.91 m
Solve the inequality.
2(4 + 2x) < 5x + 5?
X<_____
Answer:
x > 3
Step-by-step explanation:
Given
2(4 + 2x) < 5x + 5 ← distribute left side
8 + 4x < 5x + 5 ( subtract 5 from both sides )
3 + 4x < 5x ( subtract 4x from both sides )
3 < x ⇒ x > 3
what is the leading coeffcient of this polynomial
3x^2
Answer:
3
Step-by-step explanation:
The leading coefficient is the number in front of the highest power term.
We only have one term, so the leading coefficient is 3
Tx^2+3x-7=0 has two real solutions. What can be deduced from value of T?
Answer:
T > -9/28
Step-by-step explanation:
A quadratic has two real solutions when the discriminant (b² - 4ac) is positive.
b² - 4ac > 0
3² - 4(T)(-7) > 0
9 + 28T > 0
28T > -9
T > -9/28
You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?
Answer:
26 2/3
Step-by-step explanation:
if you walked that distance 4 times last week then you walked 6 2/3 x 4
and that = 26 2/3
4. How many solutions does the system of equations have?
y= 5x + 7 and y= 5x + 8
A) one
B)two
C)none
D)infinitely many
Answer:
C) none
Step-by-step explanation:
The two lines are parallel (have the same slope (x-coefficient), but different y-intercepts). They have no point in common, hence there is no solution to the system of equations.
___
Another way to think about this: subtract the first equation from the second. You get ...
0 = 1
There are no values of the variables that will make this be true, hence no solutions.
Help pleaseee I need it todayyyyyyt
Answer:
D. (0,5)
Step-by-step explanation:
Any points on the dashed line is not a solution. In this case, any points in the shade or above the dashed line is a solution.
For this case we must locate each of the points in the graph and see if they are in the region.
The border of the region is dotted, therefore equality is not included. That is, the points (-3,1) and (3,3) do not belong to the region.
On the other hand, we observe that the point (0,0) does not enter the region either.
Finally, it is observed that the point (0,5) if it is located within the region.
Answer:
(0,5)
Create a table of values then graph the following equation:
x + 2 = y
Answer:
The table in the attached figure N 1
The graph in the attached figure n 2
Step-by-step explanation:
we have
x+2=y
we know that
To graph a linear equation the best way is plot the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
For x=0
0+2=y
y=2
The y-intercept is the point (0,2)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
For y=0
x+2=0
x=-2
The x-intercept is the point (-2,0)
Find additional points to create a table (is not necessary for plot the line)
For x=1
1+2=y
y=3
For x=2
2+2=y
y=4
The table in the attached figure N 1
Graph the linear equation ------> plot the intercepts a joined the points
see the attached figure N 2
Creating a table of values for the equation \( x + 2 = y \):
To create a table of values, we can choose arbitrary values for \( x \), and then calculate the corresponding \( y \) values using the equation. Let's pick a few values for \( x \) and solve for \( y \).
Here's the table:
\[
\begin{array}{cc}
\textbf{x} & \textbf{y (= x + 2)} \\
\hline
-3 & -1 \\
-2 & 0 \\
-1 & 1 \\
0 & 2 \\
1 & 3 \\
2 & 4 \\
3 & 5 \\
\end{array}
\]
For each value of \( x \), taking the equation \( x + 2 = y \) we just add 2 to \( x \) to find \( y \).
Now, let's graph these points on a coordinate plane:
1. Draw a horizontal line for the \( x \)-axis and a vertical line for the \( y \)-axis, ensuring they intersect at the origin (0,0).
2. Mark the scale on both axes. For simplicity, we can choose each grid unit to represent 1.
3. Plot the points from the table onto the graph:
- (-3, -1)
- (-2, 0)
- (-1, 1)
- (0, 2)
- (1, 3)
- (2, 4)
- (3, 5)
4. Once all the points are plotted, draw a straight line through the points, extending the line as far as the graph allows on both ends since the equation represents a linear relationship without bounds.
5. Label the line with the equation \( x + 2 = y \).
The graphical representation would show a straight line with a slope of 1 (since for every unit increase in \( x \), \( y \) increases by 1) and a \( y \)-intercept at \( y = 2 \) (since when \( x = 0 \), \( y = 2 \)).
The coordinates of A, B, and C in the diagram are A(p,4), B(6,1), and C(9,q). Which equation correctly relates p and q?
Hint: Since is perpendicular to , the slope of × the slope of = -1.
ANSWER
[tex]p + q= 7[/tex]
EXPLANATION
We determine the slope of each line using the slope formula;
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
The slope of BC is
[tex] = \frac{ q - 1}{9 - 6} [/tex]
[tex] \frac{ q - 1}{3} [/tex]
The slope of AB is
[tex] = \frac{1 - 4}{6 - p} [/tex]
[tex] = - \frac{3}{6 - p} [/tex]
The two lines are perpendicular so the product of their slopes is -1.
[tex] - \frac{3}{6 - p} \times \frac{ q - 1}{3} = - 1[/tex]
This implies that,
[tex]\frac{q - 1}{6 - p} = 1[/tex]
[tex]q - 1=6 - p[/tex]
[tex]q + p = 6 + 1[/tex]
[tex]p + q= 7[/tex]
.
If f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)}, what is the range? {2, 5, 3, 9} {3, 7, 3, 4, 1} all whole numbers {1, 3, 4, 7}
Answer:
Range : {1, 3, 4, 7}
Step-by-step explanation:
Given function is defined as f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},
Now we need to find about what is the range of the given function f.
we know that y-value corresponds to the range.
since each point is written in (x,y) form so we just need to collect y-values of
f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},
Hence required range is {3, 7, 3, 4, 1}
But we need to remove repeated values
so correct choice is {1, 3, 4, 7}
A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on the top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder. The farmer would like the height of the silo’s cylinder portion to be 4 times the diameter of the base of the cylinder. What should the radius of the silo be if the silo is to hold 35,500pie cubic feet of grain?
Answer:
The radius of the silo should be [tex]16\ ft[/tex]
Step-by-step explanation:
we know that
The volume of the grain silo is equal to the volume of the cylinder plus the volume of a hemisphere
[tex]V=\pi r^{2} h+\frac{4}{6}\pi r^{3}[/tex]
we have
[tex]V=35,500\pi\ ft^{3}[/tex]
[tex]h=4D=8r[/tex]
substitute the values and solve for r
[tex]35,500\pi=\pi r^{2} (8r)+\frac{4}{6}\pi r^{3}[/tex]
Simplify
[tex]35,500=r^{2} (8r)+\frac{4}{6}r^{3}[/tex]
[tex]35,500=8r^{3}+\frac{2}{3}r^{3}[/tex]
[tex]35,500=\frac{26}{3}r^{3}[/tex]
[tex]r^{3}=35,500*(3)/26[/tex]
[tex]r=16\ ft[/tex]
To find the radius of the silo, we need to calculate the volume of the cylinder and hemisphere components of the silo, and then set their sum equal to the desired volume of grain. By substituting the given relationship between the height and radius, we can express the volumes in terms of the radius, and solve for the value of r that satisfies the equation.
Explanation:To find the radius of the silo, we can start by calculating the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height. In this case, we are given that the height of the cylinder is 4 times the diameter of the base, so we can write h = 4r. The volume of the cylinder portion would then be V_cylinder = πr²(4r) = 4πr³.
The volume of the hemisphere on top can be calculated using the formula for the volume of a sphere, which is V = (4/3)πr³. Since the radius of the hemisphere is the same as the radius of the base of the cylinder, this volume would be V_hemisphere = (4/3)πr³.
The total volume of the silo is the sum of the cylinder volume and the hemisphere volume. So we have the equation V_total = V_cylinder + V_hemisphere = 4πr³ + (4/3)πr³ = (16/3)πr³. We know that the silo is to hold 35,500π cubic feet of grain, so we can set up the equation (16/3)πr³ = 35,500π and solve for r. Dividing both sides by (16/3)π, we get r³ = 35,500/((16/3)π), and taking the cube root of both sides, we find r = ∛(35,500/((16/3)π)). Evaluating this expression, we find that r ≈ 5.02 feet.
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