Marcus keeps a record of the money he has in his checking account. In January he wrote checks totaling $45. In February he made a deposit of $100. In March he did not deposit any money nor did he write any checks. Use integers to describe each month's activity in the account.

Answer:

4w + 6

Step-by-step explanation:

Group like terms

7w - 3w + 6 = 4w + 6

Hope this Helps :)

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Answer:

This graph is Greater than to because the graph has a y int at 1 and so does your formula given just make x=0 to find it by plugging that in and that one has a y int at 1. You can also see the line going up.

Step-by-step explanation:

Answer:

Greater Than

Step-by-step explanation:

The y-intercept of the function is 2

The y-intercept of the function represented in the graph is -2

2>-2

I know this is late, but just to help other people :)

All the true statements about the data include the following:

B. The median average temperature was 12°C.

C. The range in temperatures was 8°C.

D. The average temperature was between 11°C and 15°C on half of the days.

F. The data are univariate and numerical.

In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Range = 17 - 9

Range = 8°C

In conclusion, we can logically deduce that the median of the data set is 12 and it has no outlier.

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\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Question:

Solution:

A translation is called a rigid transformation or isometry because the image is the same size and shape as the pre-image. In this translation that maps ΔABC to ΔA'B'C', the distances from the pre-image points to the image points are equal, and the segments representing these distances are parallel.

Then we can conclude that the correct answers are:

The last two options.

Answer:

5.93

Step-by-step explanation:

\(Average= \frac{9+5/9+7+2/9+2+7/36+4+3/4}{4} = 5.930555\) or \(\frac{427}{72}\)

Answer:

13 hours

Step-by-step explanation:

8:00 plus 4 is twelve ( 12 o'clock )

then you have 9hrs left.

( 4+9=13 )

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

y = 1/3x - 4

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Identify

Slope m = 1/3

y-intercept b = -4

Step 2: Write Equation

Substitute variables into general form

y = 1/3x - 4

Answer:

\(\large\boxed{\textsf{Option D.}}\)

Step-by-step explanation:

\(\textsf{For this problem, we are asked to compare the areas between Kristin's and Ben's circle.}\)

\(\textsf{To start, we should know that the Radius plays an important role for the area.}\)

\(\Large\underline{\textsf{What is the Radius?}}\)

\(\textsf{The \underline{Radius} is a \underline{line segment} that starts at the \underline{center} of the circle, and ends at}\)

\(\textsf{a point on the \underline{circumference} of the circle. (\underline{Arc})}\)

\(\large\underline{\textsf{Area of a Circle:}}\)

\(\mathtt{Area = \pi (radius)^{2}}\)

\(\textsf{The Radius \underline{determines} what the area of the circle is.}\)

\(\textsf{Because Kristin's radius is 1/2 of Ben's radius, \underline{the area will be 1/2 of Bens}.}\)

\(\large\boxed{\textsf{Option D.}}\)

The equation for the graph above is y = 5sin(2x/3).

In Mathematics and Geometry, a sine wave is sometimes referred to as a sinusoidal wave, or sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave can be represented or modelled by this mathematical equation:

y = asin(bx)

Where:

Based on the graph of this sine wave, we have:

Amplitude, a = 5.

Periodicity, b = 2π/period = 2π/(3π) = 2/3

Therefore, the required sine wave function is given by;

y = asin(bx)

y = 5sin(2x/3)

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9514 1404 393

Answer:

  b.  60

Step-by-step explanation:

The list of factors is 2, 3, 5, 7. The list of common factors is 2, 3, 5. The lowest exponents on those factor are ...

  2^2 × 3^1 × 5^1 = 60

The GCF of 720 and 2100 is 60.

_____

Additional comment

You can verify this using Euclid's method of finding the GCF.

  2100/720 = 2 r 660

  720/660 = 1 r 60

  660/60 = 11 r 0 . . . . 60 is the GCF

Find the remainder from the division. If it is zero, the divisor is the GCF. If it is non-zero, replace the largest number with the remainder, and repeat.

Answer:

help

Step-by-step explanationnn:

Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

Find minutes per mile by dividing time by distance:

45 minutes / 6 miles = 7.5 minutes per mile

Now multiply his speed by each distance:

7.5 x 9 = 67.5 minutes

7.5 x 15 = 112.5 minutes

Now subtract the two:

112.5 - 67.5 = 45 minutes more

It will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.

Jesper's running speed is 6 miles in 45 minutes.

To find out how long it will take him to complete the races, you can use the formula:

Time = Distance / Speed

Let's calculate the times for both races:

For the 9-mile race:

Time = 9 miles / (6 miles/45 minutes)

= 9 × (45/6)

= 67.5 minutes

For the 15-mile race:

Time = 15 miles / (6 miles/45 minutes)

= 15 × (45/6)

= 112.5 minutes

The difference in time between the 15-mile race and the 9-mile race will be:

Difference = Time for 15-mile race - Time for 9-mile race

= 112.5 minutes - 67.5 minutes

= 45 minutes

So, it will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.

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Answer:

300

Step-by-step explanation:

10% of 250 is 25. so 20% is 50

250 + 50 = 300

Answer:

4 1/2 inches

Step-by-step explanation:

Hi! I hope this helps!:

Since Ms. Henderson's plant is 6 1/3, all we need to do is subtract 1 5/6 from it! We do this because it says, "1 5/6 inches taller than Megan's plant".

For the next steps, you can change the mixed numbers into decimals or into improper fractions! 6 1/3 would be 19/3. 1 5/6 would be 11/6. You can find a common denominator for both. I would make 19/3 to 38/6.

Lastly, you need to subtract and make it into simplest form! 38/6 - 11/6 = 27/6.

You could simplify it to 9/3, 4.5, or 4 1/2 inches.

Answer:

The is 4 1/2. just like

ChocoWaffoALT said.

Answer:

hello your question is incomplete below is the complete question

Case-Control Calculation Enter only numeric values into the answer line. Place a leading 0 before the decimal and remember to round to two decimal places. Note your answers for the next short essay question. Swine Influenza (SI) is a growing concern at the local Broncoville Health Department in Lawrence, Kansas. You are working for a pharmaceutical company which is developing a human vaccine against SI. You are in charge of testing the vaccine’s effectiveness. You need to determine if one or two doses of vaccine is required to provide immunity. You field test and collect the following information about the vaccine status of persons who did and did not contract SI after getting either one or two doses of vaccine. Develop a 2 x 2 table with the following information: Of the 727 cases of SI, 203 received two doses of vaccine. Of 1,239 controls, 771 received two doses of vaccine for SI. What is the likelihood of contracting SI with only one dose of vaccine?

1. Calculate the incidence of persons with one dose of vaccine for SI

2. Calculate the incidence of persons with two doses of vaccine for SI

3. Calculate the odds ratio of developing SI among those with one dose of vaccine for SI

answer : 1) ≈ 0.53 , (2)  ≈ 0.21,  (3)  ≈ 1.12

Step-by-step explanation:

cases of SI = 727

number of SI cases that received two doses of vaccine = 203

number of SI cases that received one dose of vaccine = 727 -203 = 524

controls = 1239

number of controls that received two doses of vaccine = 771

number of controls that received one dose of vaccine = 1239 - 771 = 468

I) The incidence of persons with one dose of vaccine for SI

= 524 / 992 = 0.528 ≈ 0.53

2) The incidence of persons with two doses of vaccine for SI = 203/974 = 0.208 ≈ 0.21

3) The Odds of SI in one dose group

=  524/468 = 1.119 ≈ 1.12

Answer:460

Step-by-step explanation:

The image point of the coordinate X after the rotation is (-1, 5).

When a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.

So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).

Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).

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The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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Bode plots depict the frequency response, or the magnitude and phase changes as a function of frequency. This is accomplished using two semi-log scale plots. Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below.

(a) The first function is:

G1(s) = (1 + s)/(1 + 2s)

MATLAB Code:

%G1(s)

n1 = [1 1]                %coefficients of numerator

d1 = [2 1]               %coefficients of denominator

sys1 = f(n1,d1)      %the transfer function

bode(sys1)           %bode plot

grid on

Command Window:

>> Untitled

n1 = 1 1

d1 = 2 1

sys1 = (1 + s)/(1 + 2s)

Continuous-time transfer function.

(b) The second function is:

G(s) = (1 - s)/(1 - 2s)

MATLAB Code:

%G2(s)

n2 = [-1 1]                    %coefficients of numerator

d2 = [2 1]                   %coefficients of denominator

sys2 = f(n2, d2)       %the transfer function

bode(sys2)               %bode plot

grid on

Command Window:

>> Untitled

n2 = -1 1

d2 = 2 1

sys2 = (1 - s)/(1 - 2s)

Continuous-time transfer function.

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The complete question is:

Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below:

G1(s) = (1 + s)/(1 + 2s)

G2(s) = (1 - s)/(1 - 2s)

Note that the second transfer function is a non-minimum phase system; meaning it has a zero on the right-half plane. Note how the phase plot is affected.

Answer:

Since there are 2 possibilities for each bat (hit or out), the amount of total possibilities is 2 * 2 * 2 = 8. There is only one possibility out of those eight that gives us three hits, therefore the probability is 1 / 8 or 0.125.

Answer:

It Is!

Step-by-step explanation:

"For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages."

Answer:

\(\frac{8}{5} -= p\)

Step-by-step explanation: 3p -3 =8p + 5                                                              3 +5 =8p -3p                                                                                                                                    8=5p                                                                                                                                   \(\frac {8}{5}- = p\)

Answer:p=-8/5

Step-by-step explanation:simplify

subtract -8p from both sides

simplify

divide by -5

p=-8/5

The solution is (FoF) (0) = -8, when f(x) = 3x-2.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

f(x) = 3x-2

i.e. fof(x)

 =3(3x-2)-2

=9x-8

so. fof(0)

   =9*0-8

   = -8

Hence, The solution is (FoF) (0) = -8, when f(x) = 3x-2.

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