Answer:
310.8m²
Step-by-step explanation:
GIVEN :-
Diameter = 9m ⇒ Radius (r) = 9/2 = 4.5mSlant height (l) = 13mTO FIND :-
Surface area of the whole figure.FORMULAES TO KNOW BEFORE SOLVING :-
Curved surface area of cone = \(\pi rl\) (where r = radius & l = slant height)Curved surface area of hemisphere = \(2\pi r^2\) (where r = radius)PROCEDURE :-
In the figure , the cone is mounted on a hemisphere.
⇒ Radius of cone = Radius of hemisphere = 4.5m
Total surface area of the figure = Curved surface area of both cone & hemisphere.
⇒
Curved surface area of cone = \(\pi rl = 3.14 \times 4.5 \times 13 = 183.69m^2\) ≈ 183.7m²Curved surface area of hemisphere = \(2\pi r^2 = 2 \times 3.14 \times (4.5)^2 = 127.17m^2\) ≈ 127.1m²∴ Total surface area = 183.7 + 127.1 = 310.8m²
There are 14 marbles, 8 marbles, and 12 green marbles in a jar.What is the ratio of the total number of marbles to the number of red marbles?
Answer:
22\12 in total there is 22 marbles and 12 green marbles in total
14. Write the point-slope form of the function that has a slope of -3 and passes through the
point (11,2).
Answer:
y-2=-3(x-11)
Step-by-step explanation:
point-slope form is y-y1=m(x-x1), where (x1,y1) is the ordered pair of the coordinates given, and m is the slope of the line.
y-2=-3(x-11)
Ms. Emily had a total of 428.5 ounces of pretzels to put into 5 bowls for a party. She put an equal number of ounces of pretzels into each bowl. How many ounces of pretzels did Ms. Emily put into each bowl?
Answer:
85.7 ounces.
Step-by-step explanation:
428.5/5 = 85.7
Therefore, Ms. Emily put 85.7 ounces of pretzels into each bowl.
Answer:
85.7 ounces
Step-by-step explanation:
428.5 ounces ÷ 5=85.7 ounces
can someone please help me on this. been stuck on it for a hour.
Answer:
The answer is in the picture
Step-by-step explanation:
I evaluated the expression the picture showes the answer
Hope it helped you brainiest plz
√32×^2y^2
simplify square roots
Answer:
5.656854x^2y^2
Step-by-step explanation:
√32x^2y^2
Simplifies to:
5.656854x^2y^2
=5.656854x^2y^2
Match each expression with its greatest common factor. 4a + 8 2a2 + 8a 12a2 − 8a 4 − 6a Greatest Common Factor Expression 4 : 2 : 2a : 4a :
Answer:
see explanation
Step-by-step explanation:
4a + 8 4
2a² + 8a 2a
12a² - 8a 4a
4 - 6a 2
Match each expression with its greatest common factor as follows;
4a + 8 4
2a² + 8a 2a
12a² - 8a 4a
4 - 6a 2
What is the greatest common factor?The largest number that is found in the common factors is called the greatest common factor.
The given expression are;
4a + 8
2a² + 8a
12a² - 8a
4 - 6a
The greatest common factor of the expression are as follows;
4a + 8 = 4(a+2) = common factor = 4
2a² + 8a = 2a(a+4a) = common factor = 2a
12a² - 8a = 4a(3a-2) = common factor = 4a
4 - 6a = 2(2-3a) = common factor = 2
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Which system of equations has one solution?
On a coordinate plane, 2 lines intersect at one point.
On a coordinate plane, 2 lines are parallel to each other.
On a coordinate plane, a line has a positive slope.
Answer:
A
Step-by-step explanation:
Hence, the option (A) is the correct answer i.e., On a coordinate plane, two lines intersect at one point
What are the one solution ?
One Solution Equation is when an equation has only one solution. This means that when you solve an equation, the variable can only be subsituted by one number to make an equation true.
So, when the two lines passes and intersect at one point it forms one solution so that is why option (A) is correct i.e., On a coordinate plane, two lines intersect at one point.
Hence, the option (A) is the correct answer i.e., On a coordinate plane, two lines intersect at one point
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Thesis statement for an ancient greek argumentative essay about how the greeks influenced ancient rome in religion and architecture.
The ancient Greeks had a profound impact on ancient Rome in terms of religion and architecture. From the Roman adoption of Greek gods and goddesses to the construction of grand temples and amphitheaters, the influence of Greek culture can be seen throughout the city of Rome.
Through an examination of key examples of Roman religious and architectural practices, it becomes clear that the ancient Greeks played a crucial role in shaping the cultural identity of ancient Rome. In this argumentative essay, the thesis statement establishes the main focus of the essay, which is to examine the influence of the ancient Greeks on ancient Rome in the areas of religion and architecture.
The thesis statement highlights the two specific aspects that will be explored: the adoption of Greek religious practices by the Romans and the integration of Greek architectural styles in Roman structures. The essay will delve into the historical and cultural context to demonstrate how the Greeks' religious beliefs and architectural techniques permeated Roman society, showcasing the interplay between the two civilizations.
By presenting this thesis statement, the essay sets a clear direction and provides an overarching argument that will guide the subsequent analysis and evidence presented in the essay.
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HELP ASAP !!! I need the answer bad
Answer:
Sum of real parts: 12
Sum of imaginary parts: 3
Step-by-step explanation:
(22 − 5i) + (−10 + 8i)
Combine the real and imaginary parts in numbers 22 − 5i and −10 + 8i
22 − 10 + (−5 + 8)i
Add 22 to −10. Add −5 to 8
12 + 3i
So, the answer is:
Sum of real parts: 12
Sum of imaginary parts: 3i
The real part is 12, the imaginary part is 3
In parallelogram PQRS, the measure of angle P is five times the measure of angle Q. What is the measure of angle R , in degrees?
The measure of angle R, in degrees, is 150°.
A parallelogram is a quadrilateral or four-sided shape, that has opposite sides that are parallel to each other. The opposite sides of a parallelogram are equal in length, and the opposite angles are also equal in measure.
In a parallelogram, opposite angles are equal, so if the measure of angle P is five times the measure of angle Q, then the measure of angle R must also be five times the measure of angle Q.
Let's call the measure of angle Q "x". Then the measure of angle P is 5x, and the measure of angle R is 5x.
Therefore, the measure of angle R in degrees is 5x degrees.
We know,
All of the angles added together = 360°
∠5Q +∠Q+∠5Q+∠Q = 360 Solve for Q
∠12Q = 360
⇒ ∠Q = 30°
then ∠P = ∠5Q = 5(30) = 150°
and,
∠P = ∠R
⇒ ∠R = 150°
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Problem 5. (a) Find ged(18675, 20112340) (b) Factor both numbers from (b) above. (c) Find the lem of the two numbers from (b) above.
a) The last non-zero remainder will be the gcd of the two numbers. In this case, the gcd is 5. b) The prime factors of 18675 are 3, 5, 5, 5, 5, and 5. The prime factors of 20112340 are 2, 2, 5, 53, 761, and 769. c) In this case, the lcm is 60336724860.
It involves three problems related to number theory. (a) The task is to calculate the greatest common divisor (gcd) of two numbers: 18675 and 20112340. (b) The objective is to factorize both of these numbers. (c) The goal is to calculate the least common multiple (lcm) of the two numbers.
a) Finding the gcd of 18675 and 20112340, we can use the Euclidean algorithm. By repeatedly dividing the larger number by the smaller number and taking the remainder, we can continue this process until the remainder becomes zero. The last non-zero remainder will be the gcd of the two numbers. In this case, the gcd is 5.
b) To factorize the numbers 18675 and 20112340, we need to find their prime factors. This can be done by dividing the numbers by prime numbers and their multiples until the resulting quotient becomes a prime number. The prime factors of 18675 are 3, 5, 5, 5, 5, and 5. The prime factors of 20112340 are 2, 2, 5, 53, 761, and 769.
c) For calculating the lcm of 18675 and 20112340, we can use the formula: lcm(a, b) = (a * b) / gcd(a, b). By multiplying the two numbers and dividing the result by their gcd (which is 5), we can obtain the lcm of the two numbers. In this case, the lcm is 60336724860.
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PLEASE HELP!!
The shortest side of a right-angled triangle is 6cm.
The triangle has a perimeter of 24cm and an area of 24cm squared.
Find the lengths of the other two sides (x and y).
Answer:
8 and 10
Step-by-step explanation:
Our first step is to set x as the other side length, and y as the hypotenuse. We get that 6 + x + y = 24, and x + y = 18. The area gives us that 6x = 24(2) = 48. We then divide both sides by 6 and we get x = 8. We have x = 8 so we plug that into the equation x + y = 18 and we get that y = 10. So the other side lengths are 8 and 10.
a container with 3 1 2 gallons of weed killer can spray 2 1/4 lawns. how many gallons would it take to spray 2 lawns
Answer:
Step-by-step explanation:
my answer is 3 1/9 gallons
Given: a container with 3 1/2 gallons of weed killer can spray 2 1/4 lawns.
No. of gallons required to spray 2 lawns = x
So, first of all we should divide 3 1/2 with 2 1/4
now this division we should equalise with x/3
(3 1/2 ÷ 2 1/4) = x ÷ 2
after doing this we have got the value of x = 28/9 or 3 1/9
hence, 3 1/9 gallons is required to spray 2 lawns.
So . this question is related to capacity.
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WHATS THE ANSWER TO THIS PLS TIME IS RUNNING OUT
Answer:
ectangles, rhombuses (also called rhombi) and squares are all more specific versions of parallelograms, also called special parallelograms. A quadrilateral is a rectangle if and only if it has four right (congruent) angles.
Step-by-step explanation:
i hope it's right
Data was collected for a city that indicates that crime increases as median income decreases. The relationship was moderately strong. What would be an appropriate value for the correlation
In the given case, where data was collected for a city that indicates that crime increases as median income decreases, and the relationship was moderately strong, an appropriate value for the correlation is the Pearson correlation coefficient. Pearson's correlation coefficient is a measure of the strength of a linear relationship between two variables.
It is a statistical measure that quantifies the degree of association between two variables, in this case, crime and median income. The Pearson correlation coefficient is a number between -1 and 1, where -1 indicates a perfectly negative correlation, 0 indicates no correlation, and 1 indicates a perfectly positive correlation. In the given case, as the relationship was moderately strong, the appropriate value for the correlation would be close to -1.
To find the Pearson correlation coefficient between crime and median income, we use the following formula:
r = (NΣxy - (Σx)(Σy)) / sqrt((NΣx² - (Σx)²)(NΣy² - (Σy)²))
Where,r = Pearson correlation coefficient, N = Number of pairs of scores, x = Scores on the independent variable (Median Income), y = Scores on the dependent variable (Crime), Σ = Sum of the values in parentheses
The correlation coefficient will be between -1 and 1. The closer the value is to -1 or 1, the stronger the correlation. The closer the value is to 0, the weaker the correlation.
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Shipping to or within the United States
Nalue of Order Shipping, Packing, and
Handling Charge
$0.00 - 25.00
$3.50
$25.01 - 75.00
$5.95
$75.01 - 125.00
$7.95
$125.01 and up
$9.95
What type of function is described?
Answer:
linear function
Step-by-step explanation:
Answer:
A step function is described by the situation
Step-by-step explanation:
I just did it on edge
Evaluate t-⅓=8 no like please and thanks
Answer:
If its t to the power - 1/3 then it is 1/512
Step-by-step explanation:
t^-1/3=8
(1/t) ^1/3 =8
1/t = 8 ^3
t=1/512
An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in shape. The builder is making trim for the windows and needs to know the length of the arc of the outer rim of the window. If the central angle is 270 degrees, and the radius of the partial circle is 30 inches, how much trim is needed for each window? Round your answer to the nearest inch, and enter the number only.
The amount of rim needed for each window is 141.4 in
How to find the length of the outer rim?Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.
What is an arc?An arc is part of section of the circumference of a circle
What is the length of an arc?So, length of arc, L = Ф/360 × 2πR where
Ф = central angle of arc and R = radius of circle.Gven that for the window rim
Ф = angle of the rim = 270° and R = radius of the rim = 30 inSubstituting the values of the variables into the equation for L, we have
L = Ф/360 × 2πR
L = 270°/360° × 2π × 30 in
L = 3/4 × 2π × 30 in
L = 3/2 × π × 30 in
L = 3 × π × 15 in
L = 45π in
L = 141.37 in
L ≅ 141.4 in
So, the amount of rim needed for each window is 141.4 in
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(1 pt) Let A = [-16 8]
[12 -6]
find bases of the kernel and image of a (or the linear transformation T(x)=Ax).
The kernel (null space) and image (column space) of the matrix A can be determined as follows:
Kernel (Null space):
To find the kernel of A, solve the equation Ax = 0, where x is a vector in the null space. The basis of the kernel is the set of vectors that satisfy this equation.
Image (Column space):
The image of A, also known as the column space, is the set of all possible linear combinations of the columns of A. The basis of the image is a set of linearly independent vectors that span the column space.
To find the basis of the kernel and image of the matrix A, we can start by performing Gaussian elimination or row reduction on A to obtain its row-echelon form or reduced row-echelon form.
The given matrix A can be written as:
A = [[-16, 8],
[12, -6]]
By performing row reduction, we can find the row-echelon form of A:
A = [[4, -2],
[0, 0]]
From the row-echelon form, we can see that the second row consists of all zeros. This implies that the equation Ax = 0 has a non-trivial solution, indicating that the matrix A has a non-trivial kernel.
To find the basis of the kernel, we can express the variables in terms of free parameters. In this case, we have one free parameter, let's say t, and we can express the kernel as:
Kernel (Null space)
:
x = t[2, 1]
(where t is a scalar)
The vector [2, 1] represents a basis for the kernel of A.
Next, to find the basis of the image (column space), we can observe that the first column of A is a multiple of the second column. This implies that the columns of A are linearly dependent, and the column space will be spanned by a single vector.
Image (Column space):
The basis of the image is a vector that spans the column space of A. In this case, we can take the first column of A as the basis vector for the image:
Image (Column space):
Basis = [2, 12]
In summary, the basis of the kernel (null space) of A is [2, 1], and the basis of the image (column space) is [2, 12]. These vectors represent the linearly independent vectors that characterize the kernel and image of the matrix A.
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I need help with this honestly
Answer:
D.(-4,-8) and(2,4)
Step-by-step explanation:
y=-2x
y=x²-8
this means that the two equations are equal because they both add up to y
thus; x²-8=-2x
formulae=Ax²+bx+c=0
x²+2x-8=0
find two numbers which multiplied will give you x² and when added will give you 2x that is x and x
x²+x+x-8=0
x(x+1)+1(x-8)=0
(x+1)(x-8)=0
1)x+1=0. x= -1
further explanation on answers1)y=-2x
y=-2(-1)=2
y=2
2)y=x²-8
y=1²-8= -8
y= -8
note*this means that the answer should have both 2 and -8 thus d is the answer
2+2+2......
please help ASAP................
Answer:
6
Step-by-step explanation:
2*3=6
I did the test
A plane takes off at a speed of 300 km/h and rises at an angle of 36°49′. After 3 minutes the plane levels off and continues flying at a constant altitude. Calculate the distance in metres that the plane flies through the air, before reaching it's cruising altitude
The plane flies approximately 13,773 meters through the air before reaching its cruising altitude.
To calculate the distance that the plane flies through the air before reaching its cruising altitude, we need to find the horizontal component of the distance traveled during the initial climb.
Speed of the plane = 300 km/h
Angle of climb = 36°49′
Time of climb = 3 minutes.
First, let's convert the angle of climb from degrees and minutes to decimal degrees for ease of calculations.
36°49′ = 36 + (49/60) ≈ 36.817°
Now, we can calculate the horizontal component of the distance traveled during the climb using trigonometry
The horizontal distance (d) can be found using the formula:
\(d = v \times t \times cos(\theta)\)
Where:
v is the speed of the plane,
t is the time of climb, and
theta is the angle of climb in radians.
Converting the speed from km/h to m/s:
\(300 km/h = (300 \times 1000) / (60 \times 60) m/s \approx 83.33 m/s\)
Converting the time of climb from minutes to seconds:
\(3 $ minutes = 3 \times 60 $ seconds = 180 seconds\).
Converting the angle of climb from degrees to radians:
\(36.817= (36.817 \times \pi ) / 180 $ radians \approx 0.642 $ radians\)
Now, we can calculate the horizontal distance:
\(d = 83.33 m/s \times 180 s \times cos(0.642 radians) \approx 13,773 meters\)
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the radius of the base of a cylinder is 7cm and height is 8cm find the volume and surface area of the solid cylinder
Answer:
Volume=1232cm Surface area=660cm
Step-by-step explanation:
Volume=π x r² x t
=22/7 x 7 x 7 x 8
=1232cm
Surface area=2 x π x r x (r+t)
=2 x 22/7 x 7 x (7+8)
=44 x 15
=660cm
SORRY IF I AM WRONG, I'M TRYING MY BEST
help please help help help
Answer:
area = 32
perimeter = 30
Step-by-step explanation:
Formulas:
Area of a parallelogram: A = bh
Perimeter of a parallelogram: P = 2 ( b + s )
Where h = height s = slant height and b = base length
Define:
b = 8
h = 4
s = 7
Plug in given values into formulas and calculate
A = (8)(4)
8 * 4 = 32
A = 32
P = 2 ( 8 + 7 )
8 + 7 = 15
2(15) = 30
P = 30
given a sample of size of 36 how large does the population standard deviation have to be in order for the standard error to be
If you provide the desired standard error value, I can help you calculate the corresponding population standard deviation.
The standard error is a measure of the variability or uncertainty of a sample mean. It is calculated by dividing the population standard deviation by the square root of the sample size. Therefore, if we want the standard error to be smaller, the population standard deviation should be larger.
To determine how large the population standard deviation needs to be, we need to specify a desired standard error value. Without that information, it is not possible to provide a specific answer. The relationship between the population standard deviation and the standard error is inversely proportional, so as the population standard deviation increases, the standard error decreases.
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The figure shows ∆ABC with m∠ABC = 90°.
The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. Match the remaining steps to their correct sequence in the proof.
Statement Reason
1. Draw . construction
2. ∠ABC ≅ ∠BDC Angles with the same measure are congruent.
4. ∠BCA ≅ ∠DCB Reflexive Property of Congruence
4. AA criterion for similarity
5. Corresponding sides of similar triangles are proportional.
6. BC2 = AC × DC cross multiplication
7. ∠ABC ≅ ∠ADB Angles with the same measure are congruent.
8. ∠BAC ≅ ∠DAB Reflexive Property of Congruence
9. AA criterion for similarity
10. Corresponding sides of similar triangles are proportional.
11.
12.
13.
14.
15.
AB2 + BC2 = AC2
Reason: multiplication
AB2 + BC2 = AC × AC
Reason: segment addition
AB2 = AC × AD
Reason: cross multiplication
AB2 + BC2 = AC(AD + DC)
Reason: Distributive Property
AB2 + BC2 = AC × AD + AC × DC
Reason: addition
11
arrowBoth
12
arrowBoth
13
arrowBoth
14
arrowBoth
15
arrowBoth
Answer:
Hello,
Please, see the attached file.
Thanks.
Step-by-step explanation:
The remaining steps can be ∆ABC ∼ ∆DBA AA criterion for similarity Corresponding sides of similar triangles are proportional, AB/AC = AD/AB, and AB2 = AC × AD.
What is triangle?Triangles are closed two-dimensional geometric figures with three straight sides and three angles. The sum of the three angles in any triangle is always 180 degrees.
The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. The remaining steps to their correct sequence in the proof are:
Draw . construction∠ABC ≅ ∠BDC Angles with the same measure are congruent.∠BCA ≅ ∠DCB Reflexive Property of CongruenceAA criterion for similarityCorresponding sides of similar triangles are proportional.BC2 = AC × DC cross multiplication∠ABC ≅ ∠ADB Angles with the same measure are congruent.∠BAC ≅ ∠DAB Reflexive Property of CongruenceAA criterion for similarityCorresponding sides of similar triangles are proportional.∆ABC ∼ ∆DBA AA criterion for similarityCorresponding sides of similar triangles are proportional.AB/AC = AD/AB Reason: corresponding sides of similar triangles are proportionalAB2 = AC × AD Reason: cross multiplicationThese steps follow logically from the previous statements in the proof. In step 11, the Pythagorean Theorem is applied to the right triangle ADB.
Thus, this can be the match for the given scenario.
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Show that ∑
i=1
6
(dx
i
+e)=d(∑
i=1
6
x
i
)+6e 2. Show the equation below in a Sigma operator notation: (5x
3
+4)+(5x
3
+5)+(5x
3
+6)+(5x
3
+7)+(5x
3
+8)+(5x
3
+9)
Since both sides are equal, we have shown that ∑(i=1 to 6) (dx_i + e) = d(∑\((i=1 to 6) x_i\)) + 6e. This represents the summation of the terms \((5x_3 + i)\) for i = 1 to 6.
To show that ∑(i=1 to 6) \((dx_i + e)\)= d(∑(i=1 \(x_i\)) + 6e, we can expand both sides and compare.
Left-hand side:
∑\((i=1 to 6) (dx_i + e) = (dx_1 + e) + (dx_2 + e) + (dx_3 + e) + (dx_4 + e) +\)(dx_5 + \(e) + (dx_6 + e)\)
= \(dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6 + e + e + e + e\)+ e + e
= \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6) + 6e\)
Right-hand side:
d(∑\((i=1 to 6) x_i)\)+ 6e = d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\)+ 6e
Now, let's compare the two sides:
Left-hand side: \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6)\) + 6e
Right-hand side: d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\) + 6e
Since both sides are equal, we have shown that ∑\((i=1 to 6) (dx_i + e)\) = d(∑(i=1 to 6)\(x_i)\) + 6e.
To represent the equation\((5x_3 + 4) + (5x_3 + 5) + (5x_3 + 6) + (5x_3 +\)7) + \((5x_3 + 8) + (5x_3 + 9)\) using a Sigma operator notation, we can write it as:
∑\((i=1 to 6) (5x_3 + i)\)
This represents the summation of the terms \((5x_3 + i)\)for i = 1 to 6.
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Question 1: A certain county has 1,000 farms. Corn is grown on 100 of these farms but on none of the others. In order to estimate the total farm acreage of corn for the country, two plans are proposed. Plan I: a) Sample 20 farms at random. b) Estimate the mean acreage of corn per farm in a confidence interval. c) Multiply both ends of the interval by 1,000 to get an interval estimate of the total. Plan II: a) Identify the 100 corn-growing farms. b) Sample 20 corn-growing farms at random. c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval. d) Multiply both ends of the interval by 100 to get an interval estimate of the total. On the basis of the information given, which of the following is the better method for estimating the total farm acreage of corn for the county? *
Answer:
Plan II
Step-by-step explanation:
A certain county has 1,000 farms.
Corn is grown on 100 of these farms but on none of the others.
Since corn is grown on only 100 of these farms, the population of interest is the 100 farms on which corn is grown.
Therefore, a better method for estimating the total farm acreage of corn for the county is Plan II.
a) Identify the 100 corn-growing farms.
b) Sample 20 corn-growing farms at random.
c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval.
d) Multiply both ends of the interval by 100 to get an interval estimate of the total.
The graph of f(x) = 3.2x-3 is shown below. g(x) is a transformation of f(x).
How would you write the equation for the function g(x)?
Answer:
C. g(x) = 3·2^x +2
Step-by-step explanation:
The graph of g(x) appears to be a translation upward of the graph of f(x).
__
To find the equation of g(x), we can add 5 to f(x), since the translation appears to be 5 units. (The y-intercept of f(x) is 0; the y-intercept of g(x) is 5.)
g(x) = f(x) +5
g(x) = (3·2^x -3) +5
g(x) = 3·2^x +2
__
You can also determine the correct choice by looking at the value at x=0:
A. g(0) = 3 +6 = 9
B. g(0) = 1 +3 = 4
C. g(0) = 3 +2 = 5 . . . . matches g(0) on the given graph
D. g(0) = 3
Solve the equation. -5x + 1 = 31 x=
we get that:
\(\begin{gathered} -5x+1=31\rightarrow-5x=31-1=30 \\ x=-\frac{30}{5}=-6 \end{gathered}\)so the answer is x=-6