Answer: 12.72 ft.
Step-by-step explanation:
[tex]\frac{6}{8.3} = \frac{x}{17.6} \\\\ 8.3x= 105.6\\\\x= 12.72[/tex]
Twenty rubber spheres were compressed with varying amounts of force. The widths
and heights of the resulting shapes were measured. Here is a scatter plot that shows the
measurements for each sphere.
1. Label the vertical axis of the scatter plot.
Art gass
2. If a compressed rubber sphere has a 6-inch width, is its height closer to 5 inches or to
sla 11 inches? Explain your reasoning.
The vertical axis of the scatter plot is the height; on the other hand, if the sphere is 6 inches, the height is closer to 5 inches than to 11 inches.
What is the vertical axis?In this scatter plot, the horizontal axis is the width; however, we know the second variable is the height and this should be in the vertical axis.
What is the height if the width is six inches?Following the trend of the graph, it can be concluded the height if the width is six inches is approximately 5 rather than 11 inches.
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Hello can you help me solve
Answer:
(p o q) = 54
(q o p) = 68
Step-by-step explanation:
Another way to write is (p o q)(3) is p(q(3)). As you can see, you start with the inner function and 3 is an input in the q(x) function. Then, the output of this becomes the input of p(x) (the outer function), which yields a final output and the answer:
[tex]p(x) = 4x + 2\\q(x)=5x-2\\\\p(q(3))\\\\q(3)=5(3)-2=13\\p(13)=4(13)+2=54[/tex]
You do the same process for (q o p)(3), which can be written as q(p(3)), where you start with p(3) and then plug in this result as the input for q(x):
[tex]p(x)=4x+2\\q(x)=5x-2\\\\q(p(3))\\\\p(3)=4(3)+2=14\\q(14)=5(14)-2=68[/tex]
When rolling 2 number cubes what is the probability of rolling a 6
Answer:
Step-by-step explanation:
To find the probability of rolling a 6 on two number cubes, we need to calculate the number of favorable outcomes (rolling a 6 on either or both of the cubes) divided by the total number of possible outcomes.
Each cube has 6 sides, numbered 1 through 6. So, the total number of possible outcomes when rolling two cubes is 6 x 6 = 36.
The number of favorable outcomes is 2, because there are two ways to roll a 6: either rolling a 6 on the first cube and a 6 on the second cube, or rolling a 6 on one of the cubes.
So, the probability of rolling a 6 is:
favorable outcomes / total outcomes = 2 / 36 = 1/18
Therefore, the probability of rolling a 6 on two number cubes is 1/18 or approximately 5.56%.
Differentiate y=sin x using first principles
Answer:
[tex]\dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]
Step-by-step explanation:
Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]
The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)).
As h gets smaller, the distance between the two points gets smaller.
The closer the points, the closer the line joining them will be to the tangent line.
To differentiate y = sin(x) using first principles, substitute f(x + h) = sin(x + h) and f(x) = sin(x) into the formula:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x+h)-\sin(x)}{(x+h)-x}\right][/tex]
Use the sin addition formula to expand sin(x + h).
[tex]\boxed{\sin(A + B) = \sin A \cos B + \cos A \sin B}[/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)+\cos(x)\sin(h)-\sin(x)}{(x+h)-x}\right][/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)-\sin(x)+\cos(x)\sin(h)}{h}\right][/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)+\cos(x)\sin(h)}{h}\right][/tex]
Separate the sin(x) and cos(x) terms into two fractions:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)}{h}+\dfrac{\cos(x)\sin(h)}{h}\right][/tex]
When h gets really small, we can use the small angle approximation to rewrite cos(h).
[tex]\boxed{\cos (h) \approx 1-\dfrac{1}{2}h^2}[/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(1-\dfrac{1}{2}h^2-1\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(-\dfrac{1}{2}h^2\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]
Cancel the common factor, h:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[-\dfrac{1}{2}h\sin(x)+\cos(x)\right][/tex]
As h → 0, the first term → 0:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]
Eighteen low-fat wheat crackers have 3 grams of fat. How many grams of fat do 63 of these crackers have?
Answer:
10.5
Step-by-step explanation:
18/3 = 63/x
18 * x = 63
18 * 3.5 = 63
3 * 3.5 = 10.5
Use the distributive property to evaluate 4(2x - 1) when x = 6.
O44
04
40
O 47
The value of the expression 4(2x - 1) when x = 6 is 44. Option A
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of coefficients, terms, variables, factors and constants.
They are also identified with arithmetic operations, such as;
AdditionMultiplicationDivisionSubtractionBracketParenthesesFrom the information given, we have that;
4(2x - 1)
expand the bracket, we get;
8x - 4
Substitute the value of x as , we have;
8(6) - 4
Multiply
48 -4
Subtract the values
44
Hence, the value is 44
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Are girls better at spelling than boys? An SRS of 200 boys and an SRS of 150 girls was administered a
spelling test. The average score for boys was 48.4 with standard deviation 12.96. The girls had an average score
of 48.9 with standard deviation 11.85. Construct and interpret a 95% confidence interval to estimate the true
mean difference in the scores of the spelling test between boys and girls. Does this interval suggest a
difference? Explain.
Based on the information, it should be noted that the difference between the scores of the girls and boys aren't significant.
How to explain the informationFrom the information, the average score for boys was 48.4 with standard deviation 12.96 and the girls had an average score
of 48.9 with standard deviation 11.85.
The computed upper limit = 2.1119
The computed lower limit = -3.1119
Since the interval (-3.1119, 2.1119) contains the between the value 0 thus the difference of boys and girls scores isn't significant.
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suppose that you have an alphabet of 26 letters. (a) how many possible simple substitution ciphers are there? (b) a letter in the alphabet is said to be fixed if the encryption of the letter is the letter itself. how many simple substitution ciphers are there that leave: (i) no letters fixed? (ii) at least one letter fixed? (iii) exactly one letter fixed? (iv) at least two letters fixed?
A. There are 25^26 possible simple substitution ciphers.
How did we arrive at this assertion?(a) A simple substitution cipher is a substitution of one letter for another. In a simple substitution cipher, each letter in the alphabet can be mapped to one of the 25 other letters. Therefore, for each letter in the alphabet, there are 25 possible substitutions. The total number of possible simple substitution ciphers is the number of possible substitutions for each letter, raised to the power of the number of letters in the alphabet:
25^26 = 25 × 25 × 25 × ... × 25 (26 times)
So, there are 25^26 possible simple substitution ciphers.
(b) (i) If no letters are fixed, then each letter can be mapped to one of the 25 other letters. Therefore, the number of simple substitution ciphers that leave no letters fixed is:
25 × 24 × 23 × ... × 2 × 1 = 25!
(ii) If at least one letter is fixed, then for each letter in the alphabet, there are 24 possible substitutions. Therefore, the number of simple substitution ciphers that leave at least one letter fixed is:
25 × 24 × 23 × ... × 2 × 1 = 25!
(iii) If exactly one letter is fixed, then there are 26 possible letters that could be fixed. For each of these 26 possibilities, there are 24 possible substitutions for each of the remaining 25 letters. Therefore, the number of simple substitution ciphers that leave exactly one letter fixed is:
26 × 24^25 = 26 × 24 × 24 × ... × 24 (25 times) = 26 × 24!
(iv) If at least two letters are fixed, then the number of ways to choose the two fixed letters, multiplied by the number of ways to arrange the other 24 letters, gives the number of ciphers that have exactly two fixed letters. The number of ways to arrange 24 letters is 24!, and there are 26 choose 2 ways to choose two letters from 26:
26 choose 2 × 24! = 325 × 24!
However, this counts ciphers with exactly two fixed letters twice: once for each of the two fixed letters. So, to find the number of ciphers with at least two fixed letters, we need to subtract the number of ciphers with exactly two fixed letters and divide by 2:
(25! - 325 × 24!) / 2 = (25! - 325 × 24!) / 2.
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If n = 200 and (p-hat) = 0.45, construct a 90% confidence interval.
Give your answers to three decimals
__ < p < __
Answer:
0.392 < p < 0.508
Step-by-step explanation:
[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.45\pm 1.645\sqrt{\frac{0.45(1-0.45)}{200}}\\\\CI_{90\%}\approx0.45\pm0.058\\\\CI_{90\%}=\{0.392,0.508\}[/tex]
Thus, we are 90% confident that the true population proportion [tex]\hat{p}[/tex] is between 0.392 and 0.508, assuming conditions are met.
last month maria hiked a total of 90 miles on two trails a 5 mile mountain trail and a 10 mile canal trail let x represent the number of times maria hiked the mountain trail and let y represent the number of times maria hiked the canal trail. which equation can be used to find the number of times maria hiked each trail
Answer:
5x + 10y = 90
Step-by-step explanation:
x represents the mountain trail which she walked 5 miles
y represents the canal trail which she walked 10 miles
An entire 6 inch personal pizza has 620 calorie. Estimate the number of calories in a
16 inch pizza
Answer: 1,652.8 calories
Step-by-step explanation:
620 divided by 6 = 103.3 calories per inch
103.3 times 16 inches = 1,652.8 calories
Conrad is reading a blue print to make a shed. On the blue print, the length of the shed is 12 inches and the ramp attached to the shed is 1 inch. He wants to convert the total length of the shed and ramp from inches to yards. Select all of the expressions which correctly show how to convert the length of the shed and ramp from inches to yards using the ratio 36 inches to 1 yard.
To convert inches to yards, we need to divide by 36, since 36 inches make 1 yard. Therefore, to convert the length of the shed and ramp from inches to yards, we can use the following expressions: (12 + 1) / 36 = 0.3611... yards, (12 / 36) + (1 / 36) = 0.3611... yards, 13 / 36 = 0.3611... yards
What are expressions?An expression in mathematics is a grouping of variables, numbers, and actions that can be evaluated to yield a value. A wide range of mathematical notions, from basic arithmetic computations to intricate algebraic formulas and beyond, are represented by expressions.
These components can be used to combine expressions in a wide range of different ways. For instance, we can construct straightforward arithmetic phrases such as "2 + 3" or "5 * 4" or more intricate algebraic expressions such as "3x2 + 2x + 1" or "sin(x) + cos(x)". In each instance, the expression denotes a mathematical idea that may be tested to provide a certain value.
Expressions play a significant role in mathematics and are utilized in a wide range of fields in science, engineering, and finance. By being aware of how expressions work, we can better understand and solve a wide variety of mathematical problems.
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A salesperson's weekly paycheck is 25% more than a second salesperson's paycheck. The two paychecks total $1225. Find the amount of each paycheck. (Round your answers to the nearest cent.) first salesperson's paycheck $ second salesperson's paycheck
On solving the provided question we can say that the equation is p + 1.25p = 1225 => 2.25p = 1225 => p = 544.44
What is equation?A formula is a formula that connects two statements and uses the equal sign (=) to indicate equality. A formula that proves the equality of two formulas is called an equation in algebra. For example, in the expression 3x + 5 = 14, the equal sign separates the variables 3x + 5 and 14. The relationship between the two sentences on either side of the letter is represented by a mathematical formula. In many cases, only one variable can also act as a symbol. For example, 2x – 4 = 2.
the equation is
p + 1.25p = 1225
2.25p = 1225
p = 544.44
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12) Identify the trigonometry ratio that would be used to find x.
B
11
37°
A) sine
OB) cosine
OC) tangent
The required trigonometry ratio that would be used to find x is cosine. Option B is correct.
If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
Consider the triangle ACB, in order to determine the measure of x, we can use the cosine operator of the trigonometric ratio.
So,
cosB = BC/AB
cos37 = 11/x
0.8 = 11/x
x = 11 / 0.8
x = 13.75
Thus, the required trigonometry ratio that would be used to find x is cosine. Option B is correct.
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Fill in the blank to complete the sentence below.
In a standard deck of 52-cards, there are 13 spades and 4 aces, and thus there are
(Type a whole number.)
cards are neither spades nor aces.
Answer: 35
Step-by-step explanation: 52-13-4
Find the volume of the solid that results when the region enclosed by the given curves is revolved about the x-axis. Round the answer to at least two decimal places.
[tex]y=e^{x}, y=0,x=0,x=ln(3)[/tex]
Answer:
Step-by-step explanation:
Two different investment companies offer college savings plans, one at 8.4% compounded continuously and the other at 8.6% compounded quarterly. Which is the better investment?
The 8.4% compounded quarterly is the better investment because it gives a good return.
What is compound interest?You can earn interest on interest, which is known as compound interest. Mathematically, if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year. Compound interest is calculated by multiplying the initial principle amount by the annual interest rate multiplied by the number of compound periods minus one.Next, the value obtained is reduced by the full initial loan amount. Katherine Kerpel 2019. Investopedia, "Copyright."The word "compound interest" refers to interest that is charged on both a loan and a deposit. It is the concept that we apply most frequently in daily life. Compound interest is calculated as the sum of the interest and principal that have accrued over time. Compound interest and simple interest differ primarily in this way.(i)
S = P
S = P(1.0854) (1.0854)
AP(1) = 1.0846 - 1
AP(1)= 0.08546 or 8.546%
(ii)
r = 0.084/4
AP(2) = (1 + 0.084/4)⁴ -1
AP(2) = 1.08688 - 1
AP(2) = 8.668%
The 8.4% quarterly investment is therefore preferable.
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Solve the equation for the specified variable.
W = F(r + B), for r
The required equation in terms of r is r = (W - FB) / F
What is an equation?An equation is a mathematical statement given by connecting two expressions by equal sign.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example: 3x=9y, 67x = 90+39y
Given that an equation W = F(r + B) we need to solve the equation for r,
Therefore, rearranging for r,
W = F(r + B)
Using the distributive law,
W = Fr+FB
Transposing FB to the LHS
Fr = W - FB
Diving the equation by F
r = (W - FB) / F
Hence, the equation in terms of r is r = (W - FB) / F
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If M = {distinct letters in the word mathematics} and N = {distinct letters in the word nevertheless}, what is |M × N|?
|M × N| =
The value of the expression represented by |M × N| is 64
How to determine the value of |M × N|?from the question, we have the following parameters that can be used in our computation:
M = {distinct letters in the word mathematics} N = {distinct letters in the word nevertheless}Using the above as a guide, we have the following:
M = 8 i.e. {m, a, t, h, e, i, c, s}.
N = 8 i.e. {n, e, v, r, t, h, l, s}.
So, we have
|M × N| = 8 * 8
Evaluate
|M × N| = 64
Hence, the value of |M × N| is 64
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help please asapppppp
Answer: The answers are both B and C
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:15n + 3 = 153
Step-by-step explanation:
15n + 3 = 153
product of 15 and a number n is 15n, and 3 more gets the plus 3, and it said all of this is 153
n=10 also as subtract 3 both sides then get 15n=150 get n by itself by dividing both sides by 15 and get n=10
Find the value of 15 - 8-2.
3.5
04
11
Answer:
Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0) which is not in the given options, so none of them are the correct answer.
Given the function f ( r ) = ( r − 6 ) ( r + 3 ) ( r − 1 ) its f -intercept is its r -intercepts are
The f -intercepts and r -intercepts of the function are (0, 180) and (6, 0), (-6, 0),(5, 0)
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x)
At y-axis, we've got x = 0, so putting it will give us the y-intercept.
Thus, y-intercept of y = f(x) is y = f(0)
We are given that;
The function is f ( r ) = ( r − 6 ) ( r + 3 ) ( r − 1 )
Now,
Substituting r=0 for f -intercept
f(0) = (0-6)(0+6)(0-5)
f(0) = 180
The f-intercept is (0, 180);
Solving for the r-intercepts;
Set the function equal to 0.
0 = (r-6)(r+6)(r-5)
(r-6) = 0
r = 6
(r+6) = 0
r = -6
(r-5) = 0
r = 5
Therefore, the r-intercepts will be (6, 0), (-6, 0), and (5, 0)
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How do I find the correct answer to this question?
The direction and slope of line A'B' would still be the same as that of line AB, but the positioning of A'B' would depend on the location of line AB with respect to the origin and the value of g.
What is a scale factor ?
A scale factor is a number that scales or multiplies the size or dimensions of an object or a geometric figure by the same amount in all directions. It can be used to describe changes in size or magnification of an object or figure, and is often expressed as a ratio or a percentage.
When line AB is dilated with a scale factor of 3 and a center of dilation at the origin, the resulting line A'B' will be three times as long as line AB and will pass through the origin.
The direction and slope of line A'B' will be the same as that of line AB, but it will be positioned closer to the origin.
If line AB were dilated with a scale factor of g, then the resulting line A'B' would be g times as long as line AB and would also pass through the origin.
Therefore, The direction and slope of line A'B' would still be the same as that of line AB, but the positioning of A'B' would depend on the location of line AB with respect to the origin and the value of g.
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What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning
The approximate angle of elevation if Brendan looks up at the tower is 20.03°
What is an elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
We know that, sinθ = opposite/hypotenuse
Here, sinx° = 50/146
sinx° =0.34246575342
x = sin⁻¹(0.34246575342)
x = 20.0271724581
x = 20.03°
Therefore, the approximate angle of elevation if Brendan looks up at the tower is 20.03°
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"Your question is incomplete, probably the complete question/missing part is:"
Amelia and Brendon are both on the ground looking at The top of a tower point D. Amelia is at point A and Brendan is at point B.
What is the approximate angle of elevation in Brendan looks up at the tower explain your reasoning.
NEEDED TODAY THANK YOU
All numbers less than 17 and greater than or equal to -8. into SET BUILDER NOTATION!!
In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:
{x | -8 <= x < 17}
Explanation of set builder notation?
A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | }, where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.
In this case,
the set comprises of all figures higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint
-8 <= x < 17,where x is a real value. This predicts that x must exceed or equal to -8 and must be less than 17 to be a part of the set.
Thus, in set builder form, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows: {x | -8 <= x < 17}
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Given f(x) = -3(x + 2), what is the value of f(−7)?
Answer:
f(-7) = 15
Step-by-step explanation:
Subsitute x = - 7 into f (X) = - 3 (x+2)
f(-7) = -3 x (-7+2)
calculate the sum or difference
f(-7) =-3 x (-5)
determine the sign for multiplication or division
f(-7)=3x5
calculate the product or quotient
f(-7)=15
final awnser f(-7)=15
You deposit $3000 in a savings account at Yorktown Bank, which has a
rate of 5%. Find the interest at the end of the first year.
Answer:
$150
Step-by-step explanation:
Interest = Principal x Rate x Time (in years)
I = 3000(.05)(1)
I = 150
two inches is what percent of the length of a ruler
The percent of two inches to the length of a ruler is 16.7 percent.
How to find the percent length?The length of a standard ruler is 12 inches. Therefore, the percent of two inches to the length of a ruler can be calculated as follows:
percent length = 2 / 12 × 100
Hence,
percent length = 200 / 12
percent length = 16.6666666667
percent length = 16. 7 %
Therefore, the percent length of 2 inches to the length of a ruler(12 inches) is 16.7 percent.
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