Every real root of a polynomial with rational coefficients is also a root of a polynomial with integer coefficients.
Suppose that c is a root of the polynomial equation:
[tex]q_n[/tex] × [tex]x^n[/tex] + q_{n-1} × [tex]x^{n-1}[/tex] + ... + q1 × x + q0 = 0
where [tex]q_i[/tex] are rational coefficients. Since c is a root of this polynomial equation, we have:
[tex]q_n[/tex] × [tex]c^n[/tex] + [tex]q_{n-1}[/tex] × [tex]c^{n-1}[/tex] + ... + q1 × c + q0 = 0
Multiplying both sides of the equation by the common denominator of the coefficients [tex]q_i[/tex], we can obtain an equation with integer coefficients. Let d be the least common multiple of the denominators of the coefficients [tex]q_i[/tex]. Then we can write:
d × ([tex]q_n[/tex] × [tex]c^n[/tex] + [tex]q_{n-1}[/tex] × [tex]c^{n-1}[/tex] + ... + q1 × c + q0) = 0
Expanding the left-hand side of the equation, we obtain a polynomial with integer coefficients:
d × [tex]q_n[/tex] × [tex]x^n[/tex] + d × [tex]q_{n-1}[/tex] × [tex]x^{n-1}[/tex] + ... + d × q1 × x + d × q0 = 0
Since c is a root of the original polynomial equation, it is also a root of this polynomial with integer coefficients. Therefore, we have shown that if c is a root of a polynomial with rational coefficients, then it is also a root of a polynomial with integer coefficients.
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22 and 28 are two numbers Express the smallest number as a percentage of the sum of the two numbers
Answer: 44%
Step-by-step explanation:
22 is the smallest of the two numbers, and you want that number as a percentage of the sum of the two numbers. So basically it is asking you to put 22/(22+28) as a percentage. The step by step is as follows:
1. Simplify denominator
22+28 = 50
2. Rewrite the fraction so that the numerator is out of 100
22/50 = 44/100
3. Convert this new fraction to percentage
44/100= 44%
Hope this helps!!
What is the probability that a 58% free-throw shooter will miss her next free throw?
James placed an online order for an item that costs US$75 via the Internet. Shipping and handling costs were charged at US$39. Given the exchange rate of US$1.00 to S$1.65, how much, in Singapore dollars, would James have to pay altogether?
James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.
What is prοbability?Prοbability is a measure οf the likelihοοd οf an event οccurring. It is a numerical value between 0 and 1, where 0 means the event is impοssible and 1 means the event is certain tο οccur. Fοr example, the prοbability οf flipping a fair cοin and getting heads is 1/2 οr 0.5.
Tο calculate the tοtal cοst in Singapοre dοllars, we need tο cοnvert the US dοllars tο Singapοre dοllars using the given exchange rate, and then add the twο cοsts tοgether.
The cοst οf the item in Singapοre dοllars is:
75 USD * 1.65 SGD/USD = 123.75 SGD
The shipping and handling cοst in Singapοre dοllars is:
39 USD * 1.65 SGD/USD = 64.35 SGD
The tοtal cοst in Singapοre dοllars is the sum οf these twο cοsts:
Tοtal cοst = 123.75 SGD + 64.35 SGD = 188.10 SGD
Therefοre, James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.
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Values of the Born exponents for Rb+ and l-are 10 and 12, respectively. The Born exponent for Rbl is therefore: O A. 2 O B.22 C. 1/11 OD. 11
The Born exponent or interatomic potential energy for Rbl is 11 ( approximately). The correct option is D).
The Born exponent for RbI can be calculated using the relationship between the Born exponent and the interionic distance. The Born exponent is defined as the ratio of the repulsive to attractive contributions to the interatomic potential energy, and it depends on the charges and sizes of the ions.
For Rb+ and I-, the Born exponents are 10 and 12, respectively. This means that the repulsive interaction between Rb+ and I- is weaker than the attractive interaction, as the repulsion is proportional to Rb+^10 and the attraction is proportional to I^-12. Therefore, the attractive interaction dominates.
For RbI, we can use the relationship between the Born exponent and the interionic distance to calculate the Born exponent. This relationship is given by:
B = (1/d) * ln[(l1 + l2)/|l1 - l2|]
where B is the Born exponent, d is the interionic distance, and l1 and l2 are the ionic radii of the cation and anion, respectively.
Assuming the ionic radii of Rb+ and I- are additive, we have:
l1 + l2 = l(RbI) = l(Rb+) + l(I-) = 1.52 + 1.81 = 3.33 Å
|l1 - l2| = |l(Rb+) - l(I-)| = |1.52 - 1.81| = 0.29 Å
Substituting these values into the equation for B, we get:
B = (1/d) * ln[(l1 + l2)/|l1 - l2|] = (1/d) * ln[3.33/0.29] ≈ 11.02
Therefore, the Born exponent for RbI is approximately 11.02.
The correct answer is D).
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Classify each statement according to whether it describes a regression or a coefficient of determination Regression Coefficient of determination represented as R models the relationship between two variables describes how well data points fit a line values range from 0 to 1 can be positive or negative can be described by the linear equation YmX + b
The claims under "Regression" are as follows: 1. can be described by the l
Regression is a statistical technique that connects one or more independent (explanatory) variables to a dependent variable. If there is a relationship between changes in one or more of the explanatory factors and changes in the dependent variable, it can be shown using a regression model.
Y = mx + b is how the slope-intercept form of the equation for a straight line is expressed.
In the equation y = mx + b, m denotes the slope of the line and b its intercept. The distance between the line and the x- and y-axes is denoted by the letters x and y, respectively.
The first of the following claims, "Is used to assess the fit of a model," is true.
b) By including more factors, the result may be overstated.
called the coefficient of determination.
d.) Indicates the proportion of the variation in y that the model can account for.
e.) It is equivalent to the correlation coefficient r2 in basic linear regression.
What is Regression Analysis?
A collection of statistical procedures known as regression analysis is used to estimate the correlations between a dependent variable and one or more independent variables.
SS(res) + SS(reg) = SS, R2 1 - SS(res) / SS(tot) (tot)
R2 is defined as (SS(reg)/SS(tot) = (SS(reg)/n)/(SS(tot)/n)
Where SS(tot) = (y - y(bar)), the total sum of squares (proportional to the variance of the data), 2 • The explained sum of squares, also known as the regression sum of squares, is SS(reg) = (f(i)-y(bar)). SS(res) = (y(i) - f(i))2 = e2 is the sum of squares of residuals, often known as the residual sum of squares (i)
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6th grade math, is this correct?
Answer:
No, it is y = - 3x + 7
( negative 3x not positive )
Hope this helps!
Step-by-step explanation:
1. Subtract both sides by 3x
3x + y - ( 3x ) = 7 - ( 3x )
2. Combine like terms
( 3x - 3x ) + y = 7 - ( 3x )
0 + y = 7 - ( 3x )
y = 7 - ( 3x )
y = -3x + 7
My cookbook's pancake recipe states that it makes 12 standard sized pancakes. The nutritional information says 2 pancakes is a serving containing 150 calories. For breakfast, I prepared half a recipe, but made smaller sized pancakes, so ended up preparing 8 pancakes. I ate 4 of them. How many calories did I consume?
Answer:
225 calories
Step-by-step explanation:
1 recipe makes
12 standard sized pancakes
2 pancakes are 1/6 of the recipe
1/6 of the recipe has 150 calories
6 × 150 calories = 900 calories
The full recipe of 12 pancakes has 900 calories
1/2 recipe was made
1/2 recipe has 1/2 × 900 calories = 450 calories
1/2 recipe made 8 pancakes
4 pancakes are half of the half recipe or 1/4 recipe
1/4 × 900 calories = 225 calories
In a large study designed to compare the risk of cardiovascular disease (CVD) between smokers and nonsmokers, random samples from each group were selected. The sample proportion of people with CVD was calculated for each group, and a 95 percent confidence interval for the difference (smoker minus nonsmoker) was given as (-0.01, 0.04). Which of the following is the best interpretation of the interval? We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the sample is between -0.01 and 0.04. We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the population is between -0.01 and 0.04. We are 95% confident that the proportion of all smokers with CVD is greater than the proportion of all nonsmokers with CVD because the interval contains more positive values. The probability is 0.95 that for all random samples of the same size, the difference in the sample proportions for smokers and nonsmokers with CVD will be between -0.01 and 0.04. long Pa Docs The probability is 0.95 that there is no difference in the proportions of smokers and nonsmokers with CVD because o is included in the interval -0.01 and 0.04 D Submit hips..
The best interpretation of the confidence interval is We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the population is between −0.01 and 0.04 that is option B.
Confidence interval is estimate of Parameter were parameter is difference in proportion of smokers and non smokers in population.
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
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Create a trigonometric function that models the ocean tide..
Explain why you chose your function type. Show work for any values not already outlined above.
Answer:
One possible function that models the ocean tide is:
h(t) = A sin(ωt + φ) + B
where:
h(t) represents the height of the tide (in meters) at time t (in hours)
A is the amplitude of the tide (in meters)
ω is the angular frequency of the tide (in radians per hour)
φ is the phase shift of the tide (in radians)
B is the mean sea level (in meters)
This function is a sinusoidal function, which is a common type of function used to model periodic phenomena. The sine function has a natural connection to circles and periodic motion, making it a good choice for modeling the regular rise and fall of ocean tides.
The amplitude A represents the maximum height of the tide above the mean sea level, while B represents the mean sea level. The angular frequency ω determines the rate at which the tide oscillates, with one full cycle (i.e., a high tide and a low tide) occurring every 12 hours. The phase shift φ determines the starting point of the tide cycle, with a value of zero indicating that the tide is at its highest point at time t=0.
To determine specific values for A, ω, φ, and B, we would need to gather data on the tide height at various times and locations. However, typical values for these parameters might be:
1. A = 2 meters (representing a relatively large tidal range)
2. ω = π/6 radians per hour (corresponding to a 12-hour period)
3. φ = 0 radians (assuming that high tide occurs at t=0)
4. B = 0 meters (assuming a mean sea level of zero)
Using these values, we can write the equation for the tide as:
h(t) = 2 sin(π/6 t)
We can evaluate this equation for various values of t to get the height of the tide at different times. For example, at t=0 (the start of the cycle), we have:
h(0) = 2 sin(0) = 0
indicating that the tide is at its lowest point. At t=6 (halfway through the cycle), we have:
h(6) = 2 sin(π/2) = 2
indicating that the tide is at its highest point. We can also graph the function to visualize the rise and fall of the tide over time:
Tide Graph
Overall, this function provides a simple and effective way to model the ocean tide using trigonometric functions.
(please mark my answer as brainliest)
In a certain region of space the electric potential is given by V=+Ax2y−Bxy2, where A = 5.00 V/m3 and B = 8.00 V/m3.1) Calculate the magnitude of the electric field at the point in the region that has cordinates x = 1.10 m, y = 0.400 m, and z = 0.2)Calculate the direction angle of the electric field at the point in the region that has cordinates x = 1.10 m, y = 0.400 m, and z = 0.( measured counterclockwise from the positive x axis in the xy plane)
The direction angle of the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0) is approximately 74.5 degrees clockwise from the positive x-axis in the xy plane.
To calculate the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0), we need to take the negative gradient of the electric potential V:
E = -∇V
where ∇ is the del operator, which is given by:
∇ = i(∂/∂x) + j(∂/∂y) + k(∂/∂z)
and i, j, k are the unit vectors in the x, y, and z directions, respectively.
To calculate the magnitude of the electric field at the point, we first need to find the partial derivatives of V with respect to x and y:
∂V/∂x = 2Axy - By^2
∂V/∂y = Ax^2 - 2Bxy
Substituting the values of A, B, x, and y, we get:
∂V/∂x = 2(5.00 V/m^3)(1.10 m)(0.400 m) - (8.00 V/m^3)(0.400 m)^2 = 0.44 V/m
∂V/∂y = (5.00 V/m^3)(1.10 m)^2 - 2(8.00 V/m^3)(1.10 m)(0.400 m) = -1.64 V/m
Next, we can calculate the magnitude of the electric field:
E = -∇V = -i(∂V/∂x) - j(∂V/∂y) - k(∂V/∂z)
= -i(0.44 V/m) + j(1.64 V/m) + 0k
= (0.44 i - 1.64 j) V/m
The magnitude of the electric field is given by:
|E| = sqrt((0.44 V/m)^2 + (-1.64 V/m)^2) = 1.70 V/m
Therefore, the magnitude of the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0) is 1.70 V/m.
To calculate the direction angle of the electric field, we need to find the angle that the electric field vector makes with the positive x-axis in the xy plane.
The angle can be found using the arctan function:
θ = arctan(Ey/Ex)
Substituting the values of Ex and Ey, we get:
θ = arctan(-1.64 V/m / 0.44 V/m) = -1.30 radians
The negative sign indicates that the direction angle is measured counter clockwise from the negative x-axis, which is equivalent to measuring clockwise from the positive x-axis.
Converting to degrees, we get:
θ = -1.30 radians * (180 degrees / pi radians) = -74.5 degrees
Therefore, the direction angle is approximately 74.5 degrees clockwise in the xy plane.
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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.
Answer:
[tex]\dfrac{4096\pi}{5}\approx 2573.593\; \sf (3\;d.p.)[/tex]
Step-by-step explanation:
The shell method is a calculus technique used to find the volume of a solid revolution by decomposing the solid into cylindrical shells. The volume of each cylindrical shell is the product of the surface area of the cylinder and the thickness of the cylindrical wall. The total volume of the solid is found by integrating the volumes of all the shells over a certain interval.
The volume of the solid formed by revolving a region, R, around a vertical axis, bounded by x = a and x = b, is given by:
[tex]\displaystyle 2\pi \int^b_ar(x)h(x)\;\text{d}x[/tex]
where:
r(x) is the distance from the axis of rotation to x.h(x) is the height of the solid at x (the height of the shell).[tex]\hrulefill[/tex]
We want to find the volume of the solid formed by rotating the region bounded by y = 0, y = √x, x = 0 and x = 16 about the y-axis.
As the axis of rotation is the y-axis, r(x) = x.
Therefore, in this case:
[tex]r(x)=x[/tex]
[tex]h(x)=\sqrt{x}[/tex]
[tex]a=0[/tex]
[tex]b=16[/tex]
Set up the integral:
[tex]\displaystyle 2\pi \int^{16}_0x\sqrt{x}\;\text{d}x[/tex]
Rewrite the square root of x as x to the power of 1/2:
[tex]\displaystyle 2\pi \int^{16}_0x \cdot x^{\frac{1}{2}}\;\text{d}x[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x[/tex]
Integrate using the power rule (increase the power by 1, then divide by the new power):
[tex]\begin{aligned}\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x&=2\pi \left[\dfrac{2}{5}x^{\frac{5}{2}}\right]^{16}_0\\\\&=2\pi \left[\dfrac{2}{5}(16)^{\frac{5}{2}}-\dfrac{2}{5}(0)^{\frac{5}{2}}\right]\\\\&=2 \pi \cdot \dfrac{2}{5}(16)^{\frac{5}{2}}\\\\&=\dfrac{4\pi}{5}\cdot 1024\\\\&=\dfrac{4096\pi}{5}\\\\&\approx 2573.593\; \sf (3\;d.p.)\end{aligned}[/tex]
Therefore, the volume of the solid is exactly 4096π/5 or approximately 2573.593 (3 d.p.).
[tex]\hrulefill[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Power Rule of Integration}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}(+\;\text{C})$\\\end{minipage}}[/tex]
Samir bought three pounds of strawberries for $12.00. What is the price, in dollars
per ounce of strawberries?
1 pound = 16 ounces
Before you try that problem, answer the question below.
How many ounces of strawberries did Samir buy?
Solve please geometry, solve for x
Answer: The answer is D
Step-by-step explanation:
Pythagorean theorem: a²+b²=c²
x²+x²=14²
2x²=196
Evaluate...
x=7√2
Rewrite without absolute value for the given condition: |(square root 2) +3 -5|
Answer: We can simplify the expression inside the absolute value first:
|(sqrt(2) + 3 - 5)|
= |(sqrt(2) - 2)|
Since sqrt(2) > 2, we know that sqrt(2) - 2 is negative. Therefore, we can rewrite the absolute value as a negative:
|sqrt(2) - 2| = -(sqrt(2) - 2)
So the expression without absolute value is:
-(sqrt(2) - 2)
Step-by-step explanation:
You applied for k40 000.00 for a bank loan and you where given a flat rate interest of 9% for 2½ years. What is the amount he will pay the bank?
Answer:
The formula to calculate the amount of loan with flat rate interest is:
Amount = Principal + (Principal x Rate x Time)
Where,
Principal = the amount of loan
Rate = the interest rate per year
Time = the time period in years
Given,
Principal = K40,000.00
Rate = 9% per year
Time = 2.5 years
Substituting the values in the formula, we get:
Amount = K40,000.00 + (K40,000.00 x 0.09 x 2.5)
Amount = K40,000.00 + K9,000.00
Amount = K49,000.00
Therefore, the amount he will pay the bank is K49,000.00.
find the smallest value of n that you can for which s n has an element of order greater than or equal to 100
The value of n that yields the smallest S_n element having an order of at least 100 is 101.
To find the minimum value of n for which the set S_n contains an element with an order equal to or greater than 100, the formula S_n = n!/r!(n-r)! can be used. This formula calculates the number of permutations in a set with n elements, where r elements are chosen at a time. By substituting r=100 into the formula, it is determined that n must be at least 101 to contain an element with an order of 100 or greater. Therefore, the smallest value of n for which S_n contains an element with an order of 100 or greater is 101.
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Complete question:
Find the smallest value of n that you can for which S_n has an element of order greater than or equal to 100
Jenny took the car, the bus, and the train to get home in time.
What form of punctuation is missing?
O A. No punctuation is missing.
OB.
A period
OC.
A comma
OD. A semicolon
Last three times I have tried to take a picture of my question. Nothing comes up that resembles any of it. I don’t know what’s wrong with this app but it’s not helping.
According to the question. A. No punctuation is missing.
What is punctuation ?Punctuation is the use of symbols to indicate the structure and organization of written language. It is used to help make the meaning of sentences clearer and to make them easier to read and understand. Punctuation marks can also be used to indicate pauses in speech, to create emphasis, and to indicate the speaker’s attitude. There are many different types of punctuation marks, each with its own purpose. The most commonly used punctuation marks are the period, comma, question mark, exclamation mark, quotation marks, and the apostrophe.
Quotation marks are used to enclose quoted material, while the apostrophe is used to indicate possession or to replace missing letters in a word or phrase. By using punctuation correctly, writers can ensure that their messages are correctly understood by their readers.
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The figure below displays the SAT scores of three students, but each chart looks different. The two charts have the same data, but the difference seems larger for the graph on the left. Why?
Answering the presented question, we may conclude that This greater expressions scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
The difference in look between the two charts is due to the choice of the scales on the x and y-axes. In the left chart, the y-axis starts offevolved at 800 and has a range of only 200 points, whilst the x-axis starts offevolved at 1300 and has a vary of 200 points. This compressed scale makes the variations between the ratings of the three students appear larger than they absolutely are.
On the other hand, the proper chart has a y-axis that starts at zero and has a vary of 800 points, whilst the x-axis begins at 1200 and has a range of 800 points. This greater expanded scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.
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Write the sentence as an equation. j plus 309 equals 313
Answer:j+309=313
Step-by-step explanation:
313-309=4
J=4
A boat can travel 29mph in still water. If it travels 342 miles with the current in the same length of time it travels 180 miles against the current, what is the speed of the current?
29 = speed of the boat in still water
c = speed of the current
t = time it took each way
when going Upstream, the boat is not really going "29" fast, is really going slower, is going "29 - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "29" fast, is really going faster, is going "29 + c", because the current is adding its speed to it.
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&180&29-c&t\\ Downstream&342&29+c&t \end{array}\hspace{5em} \begin{cases} 180=(29-c)(t)\\\\ 342=(29+c)(t) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{180=(29-c)t\implies \cfrac{180}{29-c}=t} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{342=(29+c)\left( \cfrac{180}{29-c} \right)}\implies \cfrac{342}{29+c}=\cfrac{180}{29-c} \\\\\\ 9918-342c=5220+180c\implies 4698-342c=180c\implies 4698=522c \\\\\\ \cfrac{4698}{522}=c\implies \boxed{9=c}[/tex]
Suppose an unknown radioactive substance produces 16000 counts per minute on a Geiger counter at a certain time, and only 1000 counts per minute 13 days later. Assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance.
The radioactive substance has a half-life of __ days.
The radioactive material has a half-life of roughly 11.8 days.
What exactly does half-life mean?The amount of time it takes for an active component of a medication to degrade by half in your body is referred to as the half-life.
Let's apply the exponential decay formula:
N(t) = N0 e(-kt)
Let's calculate the decay constant using the information provided:
At time t=0, the number of counts per minute is N0 = 16000.
At time t=13 days, the number of counts per minute is N(13) = 1000.
When we enter these numbers into the equation, we obtain:
N(13) = N0 e(-k*13)
1000 = 16000 e(-k*13)
e(-k*13) = 1000/16000
When we take the natural logarithm of both sides, we obtain:
ln(e(-k*13)) = ln(1000/16000)
-k*13 = ln(1000/16000)
k = -ln(1000/16000)/13
k ≈ 0.0585
We may use the half-life formula now that we know the decay constant:
t1/2 = ln(2)/k
Substituting k = 0.0585, we get:
t1/2 = ln(2)/0.0585
t1/2 ≈ 11.8
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Some friends went out for a meal. The restaurant added a 10% service charge to the cost of the meal. The total bill was £126.50 including the service charge. What was the cost of the meal? Give your answer in pounds (£). Receipt Cost of the meal: £ Service charge: +10% Total: £126.50
Answer:
Let's start by setting up an equation to represent the problem. Let x be the cost of the meal:
x + 0.1x = 126.50
Simplifying the left side of the equation:
1.1x = 126.50
Dividing both sides by 1.1:
x = 115
Therefore, the cost of the meal was £115.
Is the function represented by the following table linear, quadratic or exponential?
The function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
What is function in mathematics?Function in mathematics is a relation between two sets, where one set is the input and the other set is the output. Functions are an important tool in mathematics and can be used to describe and model real-world phenomena. Functions take inputs, manipulate them and produce outputs. They can be used to represent relationships between two or more variables, or to represent a complex process. Functions allow us to break down complex problems into smaller, more manageable pieces and to study how changes in one variable affect other variables.
The function represented by the table is linear. It can be determined by the fact that the y-values change by the same amount every time the x-values increase by one unit. In this case, the y-values decrease by 2 each time the x-values increase by one unit. This is an example of a linear function.
Linear functions have the shape of a straight line and are characterized by having a constant rate of change. The constant rate of change is represented by the slope of the line, which in this case is -2. This means that for every one unit increase in the x-values, the y-values decrease by two.
A quadratic function is the opposite of a linear function, as it has a rate of change that is not constant. Quadratic functions are characterized by their parabolic shape and their rate of change increases as x-values increase. Exponential functions are characterized by their curved shape and increase exponentially as x-values increase.
In conclusion, the function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
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Tara bought 12 yards of fabric to make tote bags. Each bag requires 1.25 yards of fabric. Write an equation that shows how the number of yards or fabric remaining, depends on the number of tote bags Tara sews, x.
Answer: y = 12 - 1.25x
Step-by-step explanation:
Let y be the number of yards of fabric remaining after Tara sews x tote bags.
Initially, Tara has 12 yards of fabric. For every tote bag she sews, she uses 1.25 yards of fabric. Therefore, the total amount of fabric used after sewing x tote bags is 1.25x yards.
The number of yards of fabric remaining is the difference between the initial amount of fabric and the total amount of fabric used:
y = 12 - 1.25x
This equation shows how the number of yards of fabric remaining depends on the number of tote bags Tara sews, x. As she sews more tote bags, the amount of fabric remaining decreases.
Answer:
5.75 yds left
1.25 yards each bag multiplied by 5 bags is 6.25 yards utilized
Tara's yardage was 12-6.25 = 5.75.
She has 5.75 yards to go.
Step-by-step explanation:
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A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.
x 0 1 2 3 4 5 6
p(x) 0.10 0.15 0.20 0.25 0.20 0.05 0.05
Calculate the probability of each of the following events.
(a) {at most three lines are in use}
(b) {fewer than three lines are in use}
(c) {at least three lines are in use}
(d) {between two and five lines, inclusive, are in use}
(e) {between two and four lines, inclusive, are not in use}
(f) {at least four lines are not in use}
The probability of each of the events of {at most three lines are in use}, {fewer than three lines are in use}, {at least three lines are in use, {between two and five lines, inclusive, are in use}, {between two and four lines, inclusive, are not in use} and {at least four lines are not in use} are 0.70, 0.45, 0.55, 0.80, 0.35 and 0.40 respectively.
The problem involves finding probabilities of different events for a mail-order company with six telephone lines. The probability mass function (pmf) is given, and we use it to calculate the probabilities of different events such as "at most three lines are in use" or "between two and five lines, inclusive, are in use".
To calculate these probabilities, we use basic probability formulas such as the addition rule, subtraction rule, and the complement rule.
P(X ≤ 3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70
P(X < 3) = 0.10 + 0.15 + 0.20 = 0.45
P(X ≥ 3) = 1 - P(X < 3) = 1 - (0.10 + 0.15 + 0.20) = 0.55
P(2 ≤ X ≤ 5) = P(X ≤ 5) - P(X < 2) = (0.10 + 0.15 + 0.20 + 0.25 + 0.20) - 0.10 = 0.80
P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.20 = 0.65, so P(2 ≤ X ≤ 4)ᶜ = 1 - 0.65 = 0.35
P(X ≥ 4) = 0.20 + 0.05 + 0.05 = 0.30, so P(X ≤ 3) = 1 - P(X ≥ 4) = 0.70 - 0.30 = 0.40
These formulas are applied based on the given events to determine the probabilities.
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What is the code to this I need help asap.
Based on the information in the image, the values of the symbols in order would be: 5, 9.86, 9.93, 7.91. 10.56.
How to find the equivalent value of each symbol?To find the equivalent value of each symbol we must apply the Pythagorean theorem and find the value of the hopotenuse of all triangles as shown below:
Triangle 1:
4² + 3² = c²16 + 9 = c²c = 5Triangle 2:
5² + 8.5² = c²25 + 72.25 = c²c = 9.86Triangle 3:
9.86² + b² = 14²b² = 14² - 9.86²b² = 98.78b = 9.93Triangle 4:
a² + 6² = 9.93²a² = 9.93² - 6²a² = 62.60a = 7.91Triangle 5:
7.91² + 7² = c²62.56 + 49 = c²111.56 = c²10.56 = cAccording to the above, the values of the symbols in order would be:
5, 9.86, 9.93, 7.91. 10.56.
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the annual rainfall in 2017 in opuwo was 420mm.
the annual rainfall in 2018 was 12% more than in 2017.
Answer:
470.4 mm
Step-by-step explanation:
Given: the annual rainfall in 2017 in opuwo was 420 mm, the annual rainfall in 2018 was 12% more than in 2017.
First, find 12% of 420 mm:
12% of 420 mm
[tex]\frac{12}{100}[/tex] x 420 mm
1.2 x 420 mm
= 50.4 mm
Then add 50.4 mm to the previous annual rainfall of 420 mm:
50.4 mm + 420 mm
= 470.4 mm
Therefore, the annual rainfall in opuwo in 2018 is 470.4 mm.
mr Li wishes to give each of his five relatives in China 500 renminbi (RMB) Find the amount he would need in Singapore dollars, if the exchange rate is S$100 to RMB510.20
Exchange rate calculation.
To find out the amount in Singapore dollars that Mr Li would need to give each of his five relatives 500 RMB each, we can follow these steps:
Calculate the total amount in RMB that Mr Li needs to give:
500 RMB/relative x 5 relatives = 2500 RMB
Convert the total amount in RMB to Singapore dollars using the given exchange rate:
2500 RMB x (S$100/RMB510.20) = S$490.64 (rounded to the nearest cent)
Therefore, Mr Li would need S$490.64 to give each of his five relatives 500 RMB each, given the exchange rate of S$100 to RMB510.20.
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Suppose A and B are nxn matrices such that B and AB are both invertible. Prove that A is also invertible.
Hint: Show that A can be multiplied (on either side) by some other matrix or matrices to equal I
Matrix B and AB both are invertible implies that A is invertible as a matrix C such that AC = CA = I.
For matrix A to be invertible,
Show that there exists a matrix C such that AC = CA = I,
where I is the identity matrix.
Since B and AB are both invertible,
There exist matrices D and E such that ,
BD = DB = I
And ABE = EAB = I.
Multiplying both sides of the equation ABE = I by D on the left and E on the right, we get,
ADEBE = DE
Since BD = I, we can simplify this to,
ADE = DE
Multiplying both sides of this equation by B on the left and B^(-1) on the right, we get,
AD = DB^(-1)
Now, let C = DB^(-1).
Then we have,
AC
= ADB^(-1)
= ABEB^(-1)
= AI
= A
and
CA
= DB^(-1)A
= DB^(-1)ABE
= DI
= I
Therefore, A is invertible as a matrix C such that AC = CA = I.
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Lucy is trying to find the radius of a circle. She is stuck on this step: 121=r
2
What is the radius?
Answer:
I am not good at this but i gess itis 11 √121 equals 11
