Given:
a) The radius is doubled.
b) The radius is tripled.
To find:
The changes to the surface area of a sphere
Explanation:
Let us take the original radius as r.
The surface area of the original sphere is,
[tex]A=4\pi r^2[/tex]a) The new radius will be,
[tex]R=2r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(2r)^2 \\ =4\pi(4r^2) \\ A=4(4\pi r^2) \\ A=4\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes four times the original surface area if the radius is doubled.
b) The new radius will be,
[tex]R=3r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(3r)^2 \\ =4\pi(9r^2) \\ A=9(4\pi r^2) \\ A=9\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is tripled.
what is a root of a parabola?
The roots of a prabola is where the function intersects the x-axis.
2. The polygon on the grid represents the floor plan of a factory. The manager labeled each side to describe it. For example, N1 means North 1. у 84 5 N1 W1 E1 S2 --10-8-8-7-6-5-4-3-2-11 B 1 2 3 W2 2 -3 si -6 (a) The polygon has six sides. Find the length of each side of the polygon. (b) Each unit on the grid represents 25 feet. Find the perimeter of the factory. Show your work. Denne
Solution:
Given:
A polygon on a grid.
Question 2a:
The length of each side of the polygon on the grid is given by;
[tex]\begin{gathered} N1=13\text{units} \\ E1=7\text{units} \\ S1=5\text{units} \\ W2=4\text{units} \\ S2=8\text{units} \\ W1=3\text{units} \end{gathered}[/tex]Question 2b:
Perimeter is the sum of the outer sides enclosing a shape.
Hence, the perimeter of the factory is;
[tex]P=N1+E1+S1+W2+S2+W1[/tex]Thus,
[tex]\begin{gathered} P=N1+E1+S1+W2+S2+W1 \\ P=13+7+5+4+8+3 \\ P=40\text{units on the grid} \\ \\ \text{But each unit on the grid represents 25 f}eet. \\ \text{Hence, } \\ P=40\times25 \\ P=1000\text{feet} \end{gathered}[/tex]Therefore, the perimeter of the factory is 1000 feet.
I need help with homework I got the picture with the questions
We have the following:
[tex]\begin{gathered} \text{CAE}=135-45=90\degree \\ \text{EAF}=45-15=30\degree \\ \text{CAF}=\text{CAE}+\text{EAF}=90+30=120\degree \end{gathered}[/tex]Becky a sales women is offered two salary plans. Plan 1 is 400 per week salary plus 2% commission sales. Plan 2 is a 300 per week salary plus a 18% commission of sales. How much would Becky need to make in sales for the salary to be the same from both plans?
Let the commission sales = X
Salary Plan 1
salary per week = $400
commission sales = 2%
[tex]\text{Commision sales = 2\%}\times X=\text{ \$0.02X}[/tex]Salary Plan 2
salary per week = $300
commission sales = 18%
[tex]\text{ Commission sales = 18\%}\times X=\text{ \$0.18X}[/tex]Becky's salary for both plans (inclusive of commission sales) would be:
Plan 1:
[tex]\text{ \$400+0.02X}[/tex]Plan 2:
[tex]\text{ \$300+0.18X}[/tex]In order to find how much Becky needs to make in sales for salary to be the same from both plans would be:
[tex]\begin{gathered} \text{ \$400+0.02X= \$300+0.18X} \\ \text{collect like terms} \\ 0.18X-0.02X=400-300 \\ 0.16X=100 \\ X=\frac{100}{0.16}=625 \end{gathered}[/tex]Therefore, the commission sales should be $625
I need help solving an answering this practice problems from my pre-calculus prep guide
The general formula of a geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]where,
n = 6
a₁ = -8100
r = -0.1
Replacing on the formula:
[tex]\begin{gathered} a_6\text{ = -8100}\times(-0.1)^{6-1} \\ a_6\text{ = 0.081} \end{gathered}[/tex]
Help step by step pleaseeee
The graphic below includes the graph of the provided question.
The horizontal axis is x-axis
The vertical axis is y-axis.
How do collinear points work?Points that are situated along the same straight line but within a single line are known as collinear points. Two or more points in Euclidean geometry are said to be collinear if they are situated on a line that is either close to or far from one another.
In light of the information provided:All the points necessary to solve the equation will be positive and negative in turn, and that point will form a straight line through the origin, indicating that all the points are collinear.
You can change the value to fit your graph in the diagram that corresponds to the graph for the question that is attached below.
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name a number that is not a whole number
Whole numbers are the numbers 0, 1, 2, 3, 4, etc. (the natural numbers and zero). Negative numbers are not considered whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
For example.
- 2, - 10
A rectangular driveway is 9 feet wide, and it has an area of 135 square feet. How lo g is the driveway
Area of a Rectangle
Given a rectangle of length L and width W, the area is calculated as follows:
A = L.W
We are given the area of A=135 square feet and the width is W= 9 ft. Solving for L:
[tex]L=\frac{A}{W}=\frac{135ft^2}{9ft}=15ft[/tex]The driveway is 15 feet long
Noah operates an orange juice stand. On Monday he used 3 3/10 bags of oranges. On Tuesday he used 1/6 as many oranges as on Monday. How many bags of oranges did Noah use on Tuesday?
Write your answer as a fraction or as a whole or mixed number.
The number of bags of oranges Noah used on Tuesday as required to be determined in the task content is; 11/20 bags of oranges.
What is the number of bags of oranges used by Noah on Tuesday?It follows from the task content that Noah used 3 3/10 bags of oranges on Monday.
Hence, by expressing the mixed number, 3 3/10 as a fraction; we have; 33/10.
Therefore, since he uses 1/6 as many oranges as on Monday on Tuesday;
The number of bags of oranges used on Tuesday is; (1/6) × 33/10
= 33/60
= 11/20.
Therefore, the number of bags of oranges Noah uses on Tuesday is; 11/20.
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Describe a series of transformations Matt can perform to device if the two windows are congruent
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
Define transformations.There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
Given Data
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. The direction of a rotation, whether it be in a clockwise or counterclockwise counterclockwise. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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The length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.Which function defines the area of the rectangle?Hint: A=l⋅w
The area of a rectangle is calculated using the formula:
[tex]A=l\times w[/tex]where l is the length and w is the width.
The functions for the length and width are given to be:
[tex]\begin{gathered} l(x)=2x+1 \\ w(x)=x+4 \end{gathered}[/tex]Therefore, the area of the rectangle will be:
[tex]A=(2x+1)(x+4)[/tex]We can apply the FOIL Method:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Therefore, we have:
[tex]\begin{gathered} \left(2x+1\right)\left(x+4\right)=2x\cdot x+2x\cdot\:4+1\cdot\:x+1\cdot\:4 \\ =2x^2+8x+x+4 \end{gathered}[/tex]Simplifying, the area is:
[tex]a(x)=2x^2+9x+4[/tex]The SECOND OPTION is correct.
I’m trying to do my homework help
The average rate of change f(x) on the interval -6 ≤ x ≥ 2 is; 5
What is the Average Rate of Change of the function?
Average rate of change is a measure of how much the function changed per unit, on average, over that interval. This is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Now, the formula for the average rate of change over the interval (a, b) is;
f'(x) = [f(b) - f(a)]/(b - a)
Now, we are given the interval as -6 ≤ x ≥ 2.
From the given polynomial graph, we see that;
f(2) = 0 and f(-6) = 40
Thus;
f'(x) = [f(-6) - f(0)]/(2 - (-6))
f'(x) = (40 - 0)/8
f'(x) = 5
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In december 2004 35% of student in the high school were satisfied with the lunches supplies through the school of the 856 survey, 265 inducted they were satisfied does this suggests the proportion of student satisfied with the quality of lunches has decreased
What does it means to make a type 2 error for the test
When one fails to reject a null hypothesis that is actually wrong, this error is known statistically as a type II error. This term is used in the context of hypothesis testing.
A type II error, often called an error of omission, results in a false negative. When the patient is infected, a disease test, for instance, can return a negative result. This is a type II error because, despite being wrong, we accept the test's negative conclusion.
The difference between a type I and type II error is that a type I error refers to the failure to reject a valid null hypothesis, whereas a type II error refers to the failure to do so. Despite the fact that the error does not happen by accident, it rejects the alternative theory.
The likelihood of mistakenly failing to reject the null hypothesis when it does not apply to the entire population is known as a type II error.
In essence, a type II error is a false negative.
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What subset of real numbers does 1/2 belongs to?
Answer:
It belongs to the sets of natural numbers, {1, 2, 3, 4, 5, …}.
It is a whole number because the set of whole numbers includes the natural numbers plus zero. It is an integer since it is both a natural and whole number.
Answer: rational numbers if thats an answer
Step-by-step explanation:
A survey showed that of college students read internet news on a regular basis and that of college students regularly watch the news on TV. The survey also showed that of college students both follow TV news regularly and read internet news regularly.
(a)What is the probability that a student watches TV news regularly, given that he or she regularly reads internet news? Round your answer to the nearest hundredth.
(b)What is the probability that a randomly selected college student reads internet news regularly, given that he or she watches TV news regularly? Round your answer to the nearest hundredth.
For the given values, the probability that a student watches TV news regularly is 0.833, the probability that a randomly selected college student reads internet news regularly is 0.240.
According to a survey, 83% of college students routinely watch the news on television, while 24% of college students read newspapers on a regular basis.
Additionally, the survey revealed that 20% of college students routinely read newspapers and watch TV news.
(A) Given that a student reads newspapers frequently,
The answer is [P(TV and newspapers)/P] where P(watches TV|reads newspapers) (newspapers)
= 0.20/0.24 = 0.833
(b) Given that a randomly chosen college student watches TV news frequently
The answer is that P(newspapers | watches TV) = [P(newspapers and TV)] / P. (TV)
= 0.20/0.83 = 0.240
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fastest answer gets brainlyest
Answer:
see my photo bro. hope it can help.
Answer:
[tex]\textsf{(a)} \quad \overline{v}=-8t-4h-2[/tex]
[tex]\textsf{(b)} \quad v(t)=-8t-2[/tex]
[tex]\textsf{(c)} \quad L(t)=-26t+41[/tex]
(d) See attachment.
Step-by-step explanation:
Given equation for displacement:
[tex]s(t)=-4t^2-2t+5[/tex]
Part (a)Average velocity formula:
[tex]\boxed{\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}[/tex]
where:
[tex]\overline{v}[/tex] = average velocitys(t₁) = position function at t₁s(t₂) = position function at t₂t₁ = initial timet₂ = final timeTo find the average velocity of s(t) between the inputs t and t+h:
[tex]\textsf{Let}\;t_1 = t[/tex][tex]\textsf{Let}\; t_2 = t+h[/tex]Find expressions for s(t) at t₁ and t₂:
[tex]\implies s(t_1)=s(t)=-4t^2-2t+5[/tex]
[tex]\begin{aligned}\implies s(t_2)=s(t+h)&=-4(t+h)^2-2(t+h)+5\\&=-4(t^2+2th+h^2)-2t-2h+5\\&=-4t^2-8th-4h^2-2t-2h+5\end{aligned}[/tex]
Substitute the found values into the average velocity formula:
[tex]\begin{aligned}\implies \overline{v} =\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}&=\dfrac{(-4t^2-8th-4h^2-2t-2h+5)-(-4t^2-2t+5)}{(t+h)-t}}\\\\&=\dfrac{-4t^2-8th-4h^2-2t-2h+5+4t^2+2t-5}{t+h-t}\\\\&=\dfrac{-8th-4h^2-2h}{h}\\\\ &=-8t-4h-2\\\\ \end{aligned}[/tex]
Therefore, the average velocity between the inputs t and t+h is:
[tex]\boxed{\overline{v}=-8t-4h-2}[/tex]
Part (b)To find the equation for instantaneous velocity v(t), differentiate the equation for displacement:
[tex]\begin{aligned}\implies v(t)&=s'(t)\\&=2 \cdot -4t^{(2-1)}-1 \cdot 2t^{(1-1)}+0\\&=-8t-2\end{aligned}[/tex]
Part (c)Find the value of s when t = 3:
[tex]\begin{aligned}\implies s(3)&=-4(3)^2-2(3)+5\\&=-4(9)-6+5\\&=-36-6+5\\&=-42+5\\&=-37\end{aligned}[/tex]
To find the gradient of s(t) at t = 3, substitute t = 3 into the differentiated function:
[tex]\begin{aligned}\implies s'(3)=v(3)&=-8(3)-2\\&=-24-2\\&=-26\end{aligned}[/tex]
Substitute the found gradient and found point (3, -37) into the point-slope form of a linear equation to find the equation of the tangent line L(t):
[tex]\begin{aligned}\implies s-s_1&=m(t-t_1)\\s-(-37)&=-26(t-3)\\s+37&=-26t+78\\s&=-26t+41\\\implies L(t)&=-26t+41\end{aligned}[/tex]
Part (d)See attachment.
in the equation 8x - 1 = 3x + 4 the variable x represents the same value. Which value of x is the solution of the equation; x = 0, 1, 2, or 3? Explain.
Given the following expression:
a.) 8x - 1 = 3x + 4
Let's determine the value of x,
8x - 1 = 3x + 4
8x - 1 + 1 - 3x = 3x + 4 + 1 - 3x
8x - 3x = 4 + 1
5x = 5
5x/5 = 5/5
x = 1
Therefore, x = 1.
If y = 2x2 – 4, what is its inverse?
The inverse of the function y = 2 · x² - 4 is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4. (Correct choice: B)
How to find the inverse of a function
In this problem we have a quadratic function, whose inverse has to be found. First, we make the following substitution on the function:
y = x
x = y⁻¹
Now we proceed to clear y⁻¹ by using algebra properties:
x = 2 · (y⁻¹)² - 4
x + 4 = 2 · (y⁻¹)²
(x + 4) / 2 = (y⁻¹)²
√[(x + 4) / 2] = y⁻¹
y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4
The inverse of the function is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4.
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For each graph below, state whether it represents a function.
Graph 1: No, because it fails the vertical line test.
Graph 2: No, because it fails the vertical line test.
Graph 3: Yes, because it passes the vertical line test.
Graph 4: Yes, because it passes the vertical line test.
Graph 5: No, because it fails the vertical line test.
Graph 6: Yes, because it passes the vertical line test.
While studying abroad, Alan wants to make 6 batches of his mothers enchilada recipe to feed his classmates. The recipe calls for 20oz of cheese for each batch. The local market sells cheese by the gram. How many grams of cheese alan should by. USE 1 oz = 28 g AND DON'T ROUND ANY COMPUTATIONS.
The total cheese used by Alan to make 6 batches of recipe is 3360 g
What is an equation?An equation is an expression that is used to show the relationship between two or more numbers and variables.
1 oz = 28 g
The recipe calls for 20 oz. of cheese for each batch. Hence:
Total cheese in gram for each recipe = 20 oz. * 28 g per oz. = 560 g
There are 8 batches, hence:
Total cheese = 560 g * 6 batches = 3360 g
The total cheese is 3360 g
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The students in Cassie's class got to choose between pizza and burgers for the celebration on the last day of school. 8 students picked the pizza. If there are 10 students in all in Cassie's class, what percentage of the students picked the pizza? Write your answer using a percent sign (%).
Four year after a maple tree was planted its height was 9 feet. By 8 years is grew to 12 feet. What is the growth rate and how tall was it when it was planted!
The Growth rate is 3/4 ft/year
What is Growth rate ?
Growth rates are computed by dividing the difference between the ending and starting values for the period being analyzed and dividing that by the starting value. Formula is, Growth rate = Absolute change / Previous value.
growth rate = (12-9)/(8-4)
= 3/4 ft/year
Therefore, The Growth rate is 3/4 ft/year
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Select all the figures that have sides that to be perpendicular
A
B
C
D
E
HELP
The figures that have sides that to be perpendicular are figures A and E.
What is defined as the perpendicular?Perpendicular lines are two distinct lines that intersect at 90°, or a right angle.The symbol " represents perpendicular lines. If m and n are two lines that intersect at 90°, they are perpendicular to one another and are symbolized as m ⊥ n. The intersection of two perpendicular lines is known as the foot of a perpendicular.Perpendicular Line PropertiesThese lines are always at right angles when they intersect.If two lines have become perpendicular to each other, they are parallel and will not intersect.Adjacent square and rectangle sides always are perpendicular to the other.For the given question;
As we can see that the only in figures A and E, there are two lines making an angle of 90 degrees.
Thus, only figures A and E have the sides perpendicular to each other.
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Which words describe the polynomial? (Select all that apply) * (1 Point)
f (x) = x^4 - 2
quartic
trinomial
cubic
quadratic
binomial
A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
What is meant by Quartic polynomial?A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
Quartic in mathematics refers to something that is of the "fourth order," such as a function. One of the following is possible: Quartic function, a fourth-degree polynomial function. Quartic polynomial, a polynomial equation of degree 4, where an is a nonzero polynomial that defines the quartic equation.
A quartic equation, also known as an equation of the fourth degree, is an equation of the form that reduces a quartic polynomial to zero. A quartic function's derivative is a cubic function.
Therefore, the correct answer is option a) quartic.
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ng waffles for breakfast. The recipe calls for 1/2 cups of water for every 2Jemina pancake mix. How many cups water would he need for only oneake mix? Show your work
Ratio:
cups of water / pancake mix = (1/2) / 2
For 1 pancake mix, x cups of water:
x / 1 = (1/2) / 2
Solve for x, cross multiply:
2x = ( 1/2) 1
2x = 1/2
Divide both sides by 2
2x/2 = (1/2) / 2
x = 1/4
Answer:
She would need 1/4 cups of water
Can somebody please help me right now??? i’m stuck and i need help with this bad
Answer:
Is wolfgang Mozart's
Step-by-step explanation:
The central traits of the Classical style are all present in Mozart's music. Clarity, balance, and transparency are the hallmarks of his work, but simplistic notions of its delicacy mask the exceptional power of his finest masterpieces, such as the Piano Concerto No. 24 in C minor, K.
Which expression can be used to determine the number of downloads on the meh day after the game was available
we have the sequence
1,790 2,555 3,320 4,085 4,850
so
a1=1,790 ----> first term
a2=2,555
a3=3,320
a4=4,085
a5=4,850
Find out the difference between consecutive terms
a2-a1=2,555-1,790=765
a3-a2=3,320-2,555=765
a4-a3=4,085-3,320=765
a5-a4=4,850-4,085=765
This is an arithmetic sequence
The common difference is d=765
so
[tex]a_n=a_1+d\left(n-1\right)[/tex]we have
d=765
a1=1,790
substitute
[tex]\begin{gathered} a_n=1,790+765(n-1) \\ a_n=1,790+765n-765 \\ a_n=1,025+765n \end{gathered}[/tex]The answer is option BUsing synthetic division what is the first row for the dividend (divided) and the divisor value using synthetic division process:
2x3−10x+2/x−4
Using synthetic division, the solution to the polynomial fraction expression is; 2x² - 10 + 12/(x - 4)
How to use Synthetic Division?We are given the polynomial fraction as;
(2x³ - 10x + 2)/(x- 4)
This means that we want to divide the polynomial (2x³ - 10x + 2) by (x - 4) using synthetic division.
For the divisor, we have x - 4, and that means x - 4 = 0, x = 4
So, we'll be using 4 for the synthetic division and we have;
-1 | 2 0 -10 2
× 0 0 10
-------------------------
2 0 -10 12
Now we will form the expression in the form of fraction again;
2x² - 10 + (12/(x - 4))
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Use the above data to calculate the correlation coefficient Answer Choices.0.890.94-0.89-0.94
Using the table, we have the following points:
(x1, y1) ==> (2.5, 3), (3.5, 4.5), (5, 4.8), (5.5, 5.2), (6, 5.5)
Let's find the correlation coefficient.
To find the correlation coefficient, apply the formula:
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-\Sigma(x)^2)(n}\Sigma y^2-\Sigma(y)^2)}[/tex]Where:
n = 5
Σx = 2.5 + 3.5 + 5 + 5.5 + 6 = 22.5
Σy = 3 + 4.5 + 4.8 + 5.2 + 5.5 = 23
Σxy = 2.5⋅3 + 3.5⋅4.5 + 5⋅4.8 + 5.5⋅5.2 + 6⋅5.5 = 108.85
Σx² = 2.5² + 3.5² + 5² + 5.5² + 6² = 109.75
Σy² = 109.6
Plug in values in the formula and solve for r.
We have:
[tex]\begin{gathered} r=\frac{5(108.85)-(22.5)(23)}{\sqrt{(5(109.75)-22.5^2)(5(109.6)-(23)^2}} \\ \\ r=0.94 \end{gathered}[/tex]Therefore, the coefficient is 0.94
ANSWER:
0.94
What do the 2 points on the graph mean in terms of the situation
Coordinates - A pair of integers that show the location of a point on a graph. The first number represents the x-axis, while the second represents the y-axis.
Other names for this type of pair are ordered pair and numbered pair. A proportionate connection is one in which the values are all connected by the same constant value. A proportionate connection is also known as a linear relationship in mathematics.
Assume f(x) and g(x) are two functions that accept a real number as input and return a real number as output.
The intersection points of f(x) and g(x) are then those x values for which f(x)=g(x).
The precise numbers can sometimes be discovered by algebraically solving the equation f(x)=g(x).
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