language course decreases exponentially over time. This data can be modelled by the function
N(t) = axb-t + 450,
where a and b are positive constants, and t is the time in years since a student completed the French
language course.
Immediately after completion, a student remembers 4200 French words.
a) Find the value of a.
After 4 years a student remembers only 1600 French words.
b) Find the value of b, rounded to 2 decimal places.
The number of French words a student remembers never decreases below a certain number of words, n.
c) Write down the value of n.

The dot plots are plotted and the heights are compared

Given data ,

The heights of the tennis and badminton teams are given

Tennis team’s height (in inches): 66, 67, 69, 70, 71, 73, 73, 74, 75, 75, 76

Range: 10

Mean: 71.73

Median: 73.00

Mode: [73,75]

Badminton team’s heights (in inches): 62, 62, 65, 66, 68, 71, 73

Range: 11

Mean: 66.71

Median: 66.00

Mode: [62]

Now , each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value.

So , the frequency of the plots are given

Hence , the dot plots are plotted and the graph is given

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Answer:

Step-by-step explanation:

Answer:

P=-1

Step-by-step explanation:

Blank 1: In this study, 5 treatment conditions were compared
Blank 2: There were 60 individuals who participated in the entire study

The Independent Samples t Test is extended by the One-way ANOVA (In independent samples t test used to compare the means between two independent groups, whereas in one-way ANOVA, means are compared among three or more independent groups).

Whereas a two-way ANOVA employs two independent variables, a one-way ANOVA just uses one.

Example of One-Way ANOVA You want to examine how three different fertilizer combinations affect crop yield as an agricultural researcher.

ANOVA comes in two primary flavours: one-way (also known as unidirectional) and two-way. ANOVA can also take several forms.

The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the values of two categorical variables

Blank 1: In this study, 5 treatment conditions were compared (the number of conditions is one more than the first number in the F-statistic, which is 4).

Blank 2: There were 60 individuals who participated in the entire study (you can calculate this by adding the two numbers in the F-statistic and then adding 1,

so 4 + 55 + 1 = 60).

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Applying the definition of a linear pair, the value of n is calculated as: n =  41.33.

A linear pair consist of two angles that are on a straight line and also have a sum of 180 degrees.

The missing diagram is in the attachment provided below which shows the angles in question.

Angle 1 and (3n - 6) are two angles on a straight line, therefore, they are a linear pair. This also implies that they will have a sum of 180 degrees.

Therefore, we have:

62 + 3n - 6 = 180

Solve for the value of n:

56 + 3n = 180

3n = 180 - 56

3n = 124

n = 124/3

n = 41.33

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Answer:

$1,500

Step-by-step explanation:

167 x 9 = 1,503 rounded is 1,500 dollars

Hope this helps Good Luck

The amount of interest earned from the Mega Millions winnings after 7 years of investing in the PNC Bank money market account at 6% interest every half-year is $25,218.08.

The interest rate is increased to 12% because 6% every half-year translates to 12% annually.

The compounding period is 14 semi-annual periods because in 7 years there are 14 compounding periods.

N (# of periods) = 14 semi-annual periods (7 years x 2)

I/Y (Interest per year) = 12% (6% x 2)

PV (Present Value) = $20,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $45,218.08

Total Interest = $25,218.08

Thus, from the investment of $20,000 at 6% every half- year, you earn an interest of $25,218.08.

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The graph of the inequality is x + 2 ≥ 6 is plotted

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

x + 2 ≥ 6

Subtracting 2 on both sides , we get

x ≥ 4

So , the inequality is x ≥ 4 and the graph is plotted

Hence , the inequality is x ≥ 4

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The equation of the line, in point-slope form, that passes through (1, -7) and has a slope of -2/3 is y + 7 = -2/3 (x − 1).

Option A is the correct answer.

We have,

The point-slope form of a linear equation is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Now,

Given that the line passes through the point (1, -7) and has a slope of -2/3, we can substitute these values into the point-slope form:

y - (-7) = (-2/3)(x - 1)

Simplifying the equation:

y + 7 = (-2/3)x + (2/3)

Subtracting 7 from both sides:

y = (-2/3)x - (19/3)

So,

y + 7 = -2/3 (x - 1)

Thus,

The equation of the line, in point-slope form, that passes through (1, -7) and has a slope of -2/3 is y + 7 = -2/3 (x − 1).

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Answer:

likely

Step-by-step explanation:

Probability is a measure of the likelihood of an event occurring. In this case, the event is selecting a chocolate chip cookie from the batch of chocolate chip, oatmeal raisin, and sugar cookies made by the baker.

The probability of selecting a chocolate chip cookie is given as P(chocolate chip) = 0.75.

This means that out of all the cookies in the batch, 75% are chocolate chip cookies.

Since this probability is greater than 0.5 (which represents an event that is equally likely and unlikely), we can interpret it as indicating that it is likely to randomly select a chocolate chip cookie from the batch. In other words, if we were to randomly select a cookie from the batch, it is more likely that we would get a chocolate chip cookie than any other type of cookie.

Therefore, the correct answer is B) Likely.

The likelihood of randomly selecting a chocolate chip cookie is B. Likely.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

From the information, the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 75%.

The likelihood of randomly selecting a chocolate chip cookie from the batch is 0.75. This implies that it is likely.

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Probabilities are calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, we need to know what the experiment or event is, and what the probability distribution of the outcomes looks like. Space directors refer to the three coordinate axes x, y, and z, which are used to describe three-dimensional space. Vectors are quantities that have both magnitude and direction and can be represented by arrows or line segments in space.

To find the probabilities of getting the values +1 and -1 for each of the space directors (x, y, z) and each of the vectors (luz, ld, liz, 107, 117, 18), follow these steps:

1. Determine the total number of possible outcomes for each vector. For example, if luz has 3 possible outcomes (+1, 0, -1), the total number of outcomes is 3.

2. Count the number of occurrences of +1 and -1 in each vector. For example, if luz has 1 occurrence of +1 and 1 occurrence of -1, then there are 2 occurrences of interest.

3. Calculate the probabilities by dividing the number of occurrences of interest by the total number of outcomes. For example, for luz, the probability of getting +1 or -1 is 2 occurrences of interest / 3 total outcomes = 2/3 or approximately 0.67.

Repeat these steps for each of the space directors (x, y, z) and vectors (ld, liz, 107, 117, 18) to find the probabilities of getting the values +1 and -1.

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Answer:

23 ft^3

Step-by-step explanation:

The volume would be the little box plus the big rectangle. The volume of the little box is 2*2*2 which equals 8. The volume of the second box is 1*3*5 which equals 15. The volume of the whole shape is 8+15=23ft^3.

The values of the variables for the parallelogram include the following;

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In this context, we can reasonably infer and logically deduce that this parallelogram has both pairs of opposite sides parallel to each other and the opposite angles (vertical angles) are equal and congruent.

By CPCTC, the variable x can be calculated as follows;

15x = 45°

x = 45°/15

x = 3

Since the diagonals of a parallelogram are perpendicular to each other, we have:

m<1 = 3y - 9 = 90

3y = 99

y = 33

15x = 18z

15(3) = 18z

45 = 18z

z = 45/18

z = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

It's D.

We can use the recurrence relation for Bessel functions on the terms involving J_(n+2)(x):

x^2J"n(x) = (n^2 - n)J_n(x) - xJ_(n+1)(x) + (n+2)x^2J_n(x) + 2nxJ_(n+2)(x) + (d/dx)^(n-2) [xJ_n(x) +

To prove the given identity, we will start with the following expression:

x^2J_(n+1)(x) = xJ_n(x) + xJ_(n+2)(x) (Recurrence relation for Bessel functions)

Now, let's differentiate both sides of the above equation n times with respect to x:

(d/dx)^n [x^2J_(n+1)(x)] = (d/dx)^n [xJ_n(x)] + (d/dx)^n [xJ_(n+2)(x)]

Using the Leibniz rule for differentiating products, we can expand each term on the right-hand side:

(d/dx)^n [x^2J_(n+1)(x)] = x(d/dx)^n [J_n(x)] + n(d/dx)^(n-1) [J_n(x)] + (d/dx)^(n-2) [J_n(x)] + x(d/dx)^n [J_(n+2)(x)] + 2n(d/dx)^(n-1) [J_(n+2)(x)] + (d/dx)^(n-2) [J_(n+2)(x)]

Now, we can use the recurrence relation for Bessel functions on the terms involving J_n(x) and J_(n+2)(x):

(d/dx)^n [x^2J_(n+1)(x)] = xJ_(n-1)(x) + nJ_(n-1)(x) + (d/dx)^(n-2) [J_n(x)] + xJ_(n+3)(x) + 2nJ_(n+3)(x) + (d/dx)^(n-2) [J_(n+2)(x)]

We can simplify the above expression using the following identity:

(d/dx)^n [xJ_n(x)] = xJ_(n-n)(x) + nJ_(n-1)(x)

Substituting this identity into the above equation, we get:

(d/dx)^n [x^2J_(n+1)(x)] = xJ_n(x) + nJ_n(x) - nJ_(n-1)(x) + xJ_(n+2)(x) + 2nJ_(n+2)(x) + (d/dx)^(n-2) [J_n(x) + J_(n+2)(x)]

Next, we can multiply both sides of this equation by x^2 and simplify using the identity:

(n+1)J_n(x) = xJ_(n+1)(x) + xJ_(n-1)(x)

Multiplying both sides by x and substituting the resulting expression into the previous equation, we obtain:

x^2J"n(x) = (n^2 - n)J_n(x) - xJ_(n+1)(x) + x^2J_(n+2)(x) + 2nxJ_(n+2)(x) + (d/dx)^(n-2) [xJ_n(x) + xJ_(n+2)(x)]

Now, we can use the recurrence relation for Bessel functions on the terms involving J_(n+2)(x):

x^2J"n(x) = (n^2 - n)J_n(x) - xJ_(n+1)(x) + (n+2)x^2J_n(x) + 2nxJ_(n+2)(x) + (d/dx)^(n-2) [xJ_n(x) +

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Answer:

z = -95

Step-by-step explanation:

You simplify both sides of the equation, then isolate the variable.

The median of the data-set 3, 3, 5, 7, 9, 9, 10, 10 is given as follows:

C. 8.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The data-set for this problem is given as follows:

3, 3, 5, 7, 9, 9, 10, 10.

The data-set has an even cardinality, hence the median is given by the mean of the two middle elements, as follows:

Median = (7 + 9)/2

Median = 8.

The data-set for this problem is given as follows:

3, 3, 5, 7, 9, 9, 10, 10.

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A ray is a half-infinite line. The pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.

Since, We know that;

A half-infinite line (also known as a half-line) with one of the two points and is commonly used to represent a ray. It is assumed to be infinite.

A straight line has an angle of measurement of 180°. And a 90° angle is made when two lines are perpendicular to each other.

As we can see the line EGH is a straight line, and FG is another line that is perpendicular to line EH,

Therefore, it will form two angles measuring 90°. These angles will be ∠FGE and ∠FGH.

Hence, the pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.

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Exponential kind of function best models the set of data points (-3, 18), (-2, 6), (-1, 2), (0, 11), and (1,27).

To figure out which sort of capability best models the given arrangement of pieces of information, we can plot them on a chart and outwardly review the state of the bend that interfaces them.

After plotting the given pieces of information, we can see that the bend that best fits them is certainly not a straight line (direct) or a parabola (quadratic), as it seems to bend all the more steeply. The bend that best fits these focuses is likewise not a steady capability (nothing unless there are other options), as the upsides of y change concerning x.

Consequently, the capability that best models the given arrangement of information focuses is a dramatic capability, which has a bend that increments or diminishes at a speeding up rate. An overall condition for a dramatic capability is:

y =[tex]ab^x[/tex]

where an and b are constants. We can utilize the given focuses to track down the upsides of an and b, and in this manner get the particular condition that models the data of interest.

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The equilibrium quantity of a follower firm in a market with a leading firm that produces the monopoly quantity is determined by the follower's reaction function. Specifically, the follower will choose a quantity that maximizes its profit given the quantity chosen by the leader.

Assuming that the follower's cost function is linear, the equilibrium quantity can be expressed as a function of the leader's quantity. Let Qf denote the quantity chosen by the follower and Ql denotes the quantity chosen by the leader. The follower's profit function can be written as:

πf = (P(Qf) - c)Qf

where P(Q) is the market price as a function of the total quantity produced (Q = Qf + Ql) and c is the follower's unit cost. The first-order condition for profit maximization is:

∂πf / ∂Qf = P(Qf) + Qf ∂P / ∂Q - c = 0

Solving for Qf, we get:

Qf = (1 / 2) (Qm - Ql)

where Qm is the monopoly quantity produced by the leader. This expression shows that the follower's equilibrium quantity is half of the deviation between the monopoly quantity and the quantity chosen by the leader. In other words, the follower's quantity is determined by the leader's deviation from the monopoly quantity.

Overall, the expression for the equilibrium quantity of a follower firm in a market with a leader that produces the monopoly quantity is Qf = (1 / 2) (Qm - Ql), where Qm is the monopoly quantity and Ql is the quantity chosen by the leader. This result highlights the strategic interdependence between the leader and the follower and the importance of anticipating each other's actions in a competitive market.

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(NM)v_i = N(Mv_i) = Nv_i = v_i.

Thus, MN = NM = I, as required.

Yes, such a matrix N exists.

Since M^2 = M, we can write M(M - I) = 0. Therefore, the only possible eigenvalues of M are 0 and 1.

If M has any eigenvalue equal to 0, then the determinant of M is 0, which is not possible according to the problem statement. Hence, all eigenvalues of M are 1.

Since M is a 10 x 10 matrix, it must have a basis of 10 linearly independent eigenvectors corresponding to the eigenvalue 1. Let v1, v2, ..., v10 be such eigenvectors.

Now, we can define N as follows:

For any i and j, if i = j, then Nv_i = v_i.

For any i and j, if i ≠ j, then Nv_i = v_j.

It is easy to verify that this N satisfies MN = NM = I, the identity matrix.

To see this, note that for any i,

(MN)v_i = M(Nv_i) = Mv_i = v_i

and

(NM)v_i = N(Mv_i) = Nv_i = v_i.

Thus, MN = NM = I, as required.

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Answer:

8

Step-by-step explanation:

diameter=radius×2=4×2=8

Answer:

x=4

Step-by-step explanation:

as it's an equilateral each side will equal the same so the 12x will be the same as 10x+8

12x=10x+8

2x=8

x=4

if u substitute x into each equation

12×4=48

10×4+8=48

they equal the same

so x=4

To calculate the percentage of the 250 ha paddock that can be sowed with 12.560 kg of wheat seed, we first need to determine how much seed is needed per hectare and this will give the answer 0.063%.

Given that the showing rate is 79.62 kg/ha, we can divide the total seed amount by the showing rate to get the number of hectares that can be sown with the given amount of seed:

12.560 kg / 79.62 kg/ha = 0.1576 ha

This means that 0.1576 hectares of land can be sown with 12.560 kg of wheat seed.

To calculate the percentage of the 250 ha paddock that can be sown, we can divide the sown land area by the total paddock area and then multiply by 100:

0.1576 ha / 250 ha x 100% = 0.063%

Therefore, you can sow approximately 0.063% of the 250 ha paddock with 12.560 kg of wheat seed, assuming a showing rate of 79.62 kg/ha.

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The large drain can empty the tank on its own in 10 hours, while the small drain can empty the tank on its own in 16 hours.

Let's assume that the large drain can empty the tank in x hours. Then, according to the problem statement, the small drain can empty the same tank in x + 6 hours.

When both the large and small drains are opened together, they can empty the tank in 4 hours. This means that their combined rate of emptying the tank is 1/4 tank per hour.

We can set up two equations based on the rates of the individual drains and their combined rate:

1/x + 1/(x+6) = 1/4

Solving for x, we get x = 10 hours, which is the time it takes for the large drain to empty the tank on its own.

To find the time it takes for the small drain to empty the tank on its own, we substitute x = 10 in x+6, which gives us 16 hours.

Therefore, the large drain can empty the tank on its own in 10 hours, while the small drain can empty the tank on its own in 16 hours.

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The 2.65 × 10²⁵ atoms of Fluorine into moles of F atoms after conversions are 4.406 moles of F atoms.

To convert 2.65 × 10²⁵ atoms of Fluorine into moles of F atoms, we can use Avogadro's number, which is the number of particles (atoms or molecules) in one mole of a substance. Avogadro's number is approximately 6.022 × 10²³ particles per mole.

The conversion factor between atoms and moles is,

1 mole = 6.022 × 10²³ atoms

In order to convert Fluorine atoms to moles, we may do the following steps: multiply the number of atoms by Avogadro's number to obtain the molecular weight,

2.65 × 10²⁵ atoms / 6.022 × 10²³ atoms/mole

= 4.406 moles

Round the answer to an appropriate number of significant figures, if necessary. Therefore, 2.65 × 10²⁵ atoms of Fluorine is equal to 4.406 moles of F atoms.

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Complete question - Convert 2.65 × 10²⁵ atoms of Fluorine into moles of F atoms.

The actual sum of the quarter dollars is determined as $ 1.25.

The actual sum of the quarter dollars is calculated by summing up all the individual coins.

For the diagram given, we have a total of;

1 quarter dollar + 1 quarter dollar  + 1 quarter dollar  + 1 quarter dollar + 1 quarter dollar = 5 quarter dollars

A quarter dollar  or 1 quarter dollar = 25 cent = $0.25

The total sum of the quarter dollars is calculated as;

= $0.25 + $0.25 + $0.25 + $0.25 + $0.25

= $ 1.25

Thus, the total sum of the quarter dollars has been obtained in dollar equivalent.

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About 4.24% of all samples of 26 of today's women in their 20s have mean heights of at least 63.36 inches.

Since the sample size is 26, we can use the central limit theorem and assume that the distribution of sample means is approximately normal with a mean of 62.8 inches and a standard deviation of 1.65 inches / sqrt(26) = 0.323 inches.

To find the percentage of samples with mean heights of at least 63.36 inches, we need to find the z-score corresponding to this value:

z = (63.36 - 62.8) / 0.323 = 1.74

Using a standard normal distribution table or calculator, we can find that the percentage of samples with z-scores greater than or equal to 1.74 is about 4.24%. Therefore, about 4.24% of all samples of 26 of today's women in their 20s have mean heights of at least 63.36 inches.

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The various terms of the circle are matched accordingly:

C - Center

CI = Radius

DE - Diameter

HJ - Tangent Line

AB = Chord

GF - Secant

IE - Arc

The region bound by CI, CE, and IE - Sector.

Note that these are all various way in which parts of a circle may be described.

There are also rules and principles guiding the relationship with each of them.

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The volume of the tank that is shown here is 282.31

In mathematics, the capacity of a 3D object is denoted by its volume. Volume is typically computed in cubic units like cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³) or cubic inches (in³). Depending on an object's form, various formulas can be used to calculate its volume.

15 - 6 = 9

Radius = 6 / 2

= 3

Then the volume =

4 / 3 π (3)³ + π (3)²6

= 112.75 + 169.56

= 282.31

The volume is 282.31

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