A normal distribution has a mean of u=54 and a standard deviation of o =6.what is the probability of randomly selecting a score less than X=51p= ___what us the probability of selecting a sample of n=4 scores with a mean less than M=51?p=____what is the probability of selecting a sample of n=36 with a mean less than M=51p=____

Answer:

it's the account number for the fun of the bird and the first one is a good one is a

Step-by-step explanation:

how to download a game on give me a call when we get home and get a

Answer:

Classify by angles: Equiangular

Classify by sides: Equilateral

Step-by-step explanation:

An equiangular triangle has angles that all measure 60 degrees. An equilateral triangle is a triangle that has sides will all of the same lengths. This triangle meets both of these requirements.

Hope it helps!

The orthocenter is determined by the intersection of altitudes, the centroid is determined by the intersection of medians, the incenter is determined by the intersection of angle bisectors, and the circumcenter is determined by the intersection of perpendicular bisectors.

1. Orthocenter: The orthocenter of a triangle is the point of intersection of the altitudes. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. The orthocenter does not necessarily lie inside the triangle; it can be inside, outside, or on the triangle itself.

2. Centroid: The centroid of a triangle is the point of intersection of the medians. A median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side. The centroid always lies inside the triangle and divides each median into two segments, with the ratio of 2:1 from the vertex to the midpoint

3. Incenter: The incenter of a triangle is the point of intersection of the angle bisectors. An angle bisector is a line segment that divides an angle into two equal angles. The incenter always lies inside the triangle and is equidistant from the three sides of the triangle.

4. Circumcenter: The circumcenter of a triangle is the point of intersection of the perpendicular bisectors. A perpendicular bisector is a line segment that is perpendicular to a side of the triangle and passes through its midpoint. The circumcenter is the center of the circle that circumscribes the triangle, and it can be inside, outside, or on the triangle itself.

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The length of segment RS is given as follows:

RS = 24.

The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.

The segment RT is the combination of segments RS and ST, hence:

RT = RS + ST.

Hence the length of segment RS is given as follows:

41 = RS + 17

RS = 24.

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The critical values for this test are -2.201 and 2.201. If your test statistic falls outside this range, you would reject the nullSo, the critical values for this test are -2.201 and 2.201. If your test statistic falls outside this range, you would reject the null hypothesis in favor of the alternative hypothesis (H1: μ ≠ μ0). in favor of the alternative hypothesis (H1: μ ≠ μ0).

To determine the critical values for a two-tailed test with a sample size of n = 12 and a significance level of α = 0.05, we need to consult a t-distribution table.

First, we need to find the degrees of freedom, which is equal to n - 1 = 12 - 1 = 11.

Next, we look up the t-value for a two-tailed test with a 0.025 level of significance (0.05/2) and 11 degrees of freedom. From the t-distribution table, we find that the t-value is 2.201.

Therefore, the critical values for a two-tailed test of a population mean at the α = 0.05 level of significance based on a sample size of n = 12 are -2.201 and +2.201.

This means that if our calculated t-value falls outside of this range, we can reject the null hypothesis (H0: μ = μ0) in favor of the alternative hypothesis (H1: μ ≠ μ0) at the 0.05 level of significance.

To determine the critical values for a two-tailed test of a population mean at the α = 0.05 level of significance with a sample size of n = 12, you'll need to use a t-distribution table.

Since it's a two-tailed test, you'll need to find the t-score that corresponds to α/2, which is 0.025 in each tail. With a sample size of 12, you have 11 degrees of freedom (df = n - 1).

Looking up the t-distribution table with df = 11 and α/2 = 0.025, you'll find the critical t-value to be approximately ±2.201.

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Excel displays the error message "#DIV/0!" in cells to indicate a divide-by-zero error. This occurs when a formula attempts to divide a value by zero, which is mathematically undefined. To resolve this error, you can check the input values and formulas in your spreadsheet to ensure they are valid and avoid division by zero.

In Excel, when a formula attempts to divide a value by zero, the software will display the error message "#DIV/0!" in the affected cells. This is a helpful indication to the user that the calculation has failed and that the formula needs to be adjusted. It is important to note that this error message can impact other calculations in the spreadsheet, so it is important to resolve it as soon as possible to prevent inaccuracies in the data. Excel provides several ways to handle divide-by-zero errors, such as using the IFERROR function or adjusting the formula to include an IF statement to avoid errors.
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the predicted subway fare when the CPI is 80 would be $1.214.

To determine the line of regression that predicts subway fare based on CPI, we need to use linear regression analysis. We can use software like Excel or a calculator to perform the calculations, but since we don't have that information here, we will use the formulas for the slope and intercept of the regression line.

Let x be the CPI and y be the subway fare. Using the given data, we can find the mean of x, the mean of y, and the values for the sums of squares:

$\bar{x} = \frac{30.2 + 48.3 + 112.3 + 162.2 + 191.9 + 197.8}{6} = 110.933$

$\bar{y} = \frac{0.15 + 0.35 + 1.00 + 1.35 + 1.50 + 2.00}{6} = 1.225$

$SS_{xx} = \sum_{i=1}^n (x_i - \bar{x})^2 = 52615.44$

$SS_{yy} = \sum_{i=1}^n (y_i - \bar{y})^2 = 0.655$

$SS_{xy} = \sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = 22.69$

The slope of the regression line is given by:

$b = \frac{SS_{xy}}{SS_{xx}} = \frac{22.69}{52615.44} \approx 0.000431$

The intercept of the regression line is given by:

$a = \bar{y} - b\bar{x} \approx 1.225 - 0.000431 \times 110.933 \approx 1.180$

Therefore, the equation of the regression line is:

$y = a + bx \approx 1.180 + 0.000431x$

To predict the subway fare when the CPI is given, we can substitute the CPI value into the equation of the regression line. For example, if the CPI is 80, then the predicted subway fare would be:

$y = 1.180 + 0.000431 \times 80 \approx 1.214$

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9514 1404 393

Answer:

  ∠2 = 45°

Step-by-step explanation:

Angles 1 and 2 are same-side interior angles where the transversal crosses parallel lines. That means they are supplementary angles.

  ∠1 +∠2 = 180° . . . . . supplementary angles total 180°

  135° +∠2 = 180° . . . . substitute the given value

  ∠2 = 180° -135° . . . .  subtract 135°

  ∠2 = 45°

There are no values of c that satisfy the given condition. there is no smaller or larger value of c to provide in this case

To find the values of c, we need to determine the points of intersection between the two parabolas and then calculate the area of the enclosed region. Let's solve this step by step.

First, let's set the equations of the parabolas equal to each other:

\(x^2 - c^2 = c^2 - x^2\)

Simplifying the equation, we get:

\(2x^2 = 2c^2\)

Dividing both sides by 2, we have:

\(x^2 = c^2\)

Taking the square root of both sides, we get two equations:

x = c   and   x = -c

Now, we can calculate the y-values for these x-values in each parabola.

For the parabola \(y = x^2 - c^2\):

For x = c:   \(y = c^2 - c^2 = 0\)

For x = -c:   \(y = c^2 - (-c)^2 = c^2 - c^2 = 0\)

For the parabola \(y = c^2 - x^2\):

For x = c:   \(y = c^2 - c^2 = 0\)

For x = -c:  \(y = c^2 - (-c)^2 = c^2 - c^2 = 0\)

Therefore, the two points of intersection between the parabolas are (c, 0) and (-c, 0).

Now, let's calculate the area of the enclosed region. The region is symmetric about the y-axis, so we can calculate the area of one half and then double it.

The area of the enclosed region is given by:

Area = \(2 * \int [0, c] (x^2 - c^2) dx\)

Using the antiderivative, we can evaluate the integral:

Area = \(2 * [(x^{3/3} - c^2x)\) | from 0 to c]

    = \(2 * [(c^{3/3} - c^{3/3}) - (0 - 0)]\)

    = 2 * (0)

    = 0

Since the area is 0, it means that the two parabolas do not enclose any region with an area of 576. Therefore, there are no values of c that satisfy the given condition.

Hence, there is no smaller or larger value of c to provide in this case.

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Answer:

\(T' = (-7,10)\)

Step-by-step explanation:

Given

\(T = (10,7)\)

\(r = 270^o\) counterclockwise

Required

Graph of T'

The rule to this is:

\((x,y) \to (-y,x)\)

So, we have:

\(T(10,7) \to T' (-7,10)\)

Hence:

\(T' = (-7,10)\)

See attachment for graph

Step-by-step explanation:

Given

6 people = 180g flour

1 person = 180/6 = 30g flour

3 people = 3 x 30 = 90g flour

Answer: The fourth set of sides

Step-by-step explanation:

For a set of side lengths to form a right triangle, they have to satisfy the Pythagorean theory \((a^{2} +b^{2} =c^{2} )\)

First set of sides

a = 7.5    b = 18    c = 21.5

\(a^{2} +b^{2} =c^{2}\\7.5^{2} +18^{2} =21.5^{2} \\56.25 + 324 = 462.25\\380.25 \neq 462.25\)

Second set of sides

a = 7.5   b = 19.5    c = 21.5

\(a^{2} +b^{2} =c^{2} \\7.5^{2} +19.5^{2} =21.5^{2} \\56.25 + 380.25 = 462.25\\436.5 \neq 462.25\)

Third set of sides

a = 18     b = 19.25    c = 21.5

\(a^{2} +b^{2} =c^{2} \\18^{2} +19.5^{2} =21.5^{2} \\324 + 380.25 = 462.25\\704.25 \neq 462.25\)

Fourth set of sides

a = 7.5     b = 18     c = 19.5

\(a^{2} +b^{2} =c^{2} \\7.5^{2} +18^{2} =19.5^{2} \\56.25 + 324 = 380.25\\380.25 = 380.25\)

I hope that helped!

Answer

The answer is 16/3

Step-by-step-explain

F(x) = ⅓ • 4ˣ, F(2)

F(2) = ⅓ • 4²

F(2) = ⅓ • 16

F(2) = 16/3

Thus, The answer is 16/3

-TheUnknownScientist

Answer:

Step-by-step explanation:

16/3

I hope it's helpful

Answer:

the answer is 80000 is b

The value of dy/dt when I = 6 and de/dt = -5 is approximately 0.901. This can be answered by the concept of differentiation.

To find the value of dy/dt when I = 6 and de/dt = -5, we need to use implicit differentiation and the chain rule. The answer is a numerical value, which will be given in the explanation section.

Given the equation cos(3I) = y, where I and y are differentiable functions of t. We are also given that de/dt = -5 when I = 6, and we need to find dy/dt.

Using the chain rule, we can differentiate both sides of the equation with respect to t:

d/dt [cos(3I)] = d/dt [y]

(-sin(3I)) × (dI/dt) = dy/dt

Now, we need to evaluate this expression at the point where I = 6:

(-sin(3×6)) × (dI/dt)|I=6 = dy/dt

(-sin(18)) × (dI/dt)|I=6 = dy/dt

Since we know that de/dt = -5 when I = 6, we can use the chain rule again to find dI/dt:

de/dt = d/dt [6] = (dI/dt) × (dt/dt) = dI/dt

Therefore, dI/dt = -5

Substituting this value into the previous equation, we get:

(-sin(18)) × (dI/dt)|I=6 = dy/dt

(-sin(18)) × (-5) = dy/dt

dy/dt = 0.901

Therefore, the value of dy/dt when I = 6 and de/dt = -5 is approximately 0.901.

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Answer:

a. 6x+6

b. 24 cm ; 15 cm

c. 360 sq. cm.

Step-by-step explanation:

a. Perimeter = 2x + 2x + x+3 + x+3 = 6x+6

b. Given,

6x+6 = 78

6x = 72

x = 12

So, 2x=2*12=24. ; x+3 = 12+3 = 15

Dimensions are 24 cm and 15 cm

c. Area = 24*15 = 360 Sq. cm.

Answer:

The first choice: the amount of money Jason earns per hour

Step-by-step explanation:

We know that y represents the amount of money, and x represents the number of hours worked by Jason. The slope of a graph is the rise over the run. In other words, it is y/x (y is rise because it describes vertical change, and x is run because it describes horizontal change). So, when you take the slope of the graph, you are taking the amount of money earned and dividing it by the number of hours worked. It is a rate of change that describes the amount of money PER hour. Therefore, the correct answer to this question is the first answer choice: the amount of money Jason earns per hour

The value of the area is πab which is enclosed by the ellipse with the equation (x²/a²) + (y²/b²) = 1.

To find the area enclosed by the ellipse with the equation (x²/a²) + (y²/b²) = 1.

To find the area of this ellipse, use the formula A = πab, where A is the area, a is the semi-major axis, and b is the semi-minor axis.

First, identify the values of a and b from the given equation.
In the equation (x²/a²) + (y²/b²) = 1, a² is the coefficient of x², and b² is the coefficient of y².

Now, calculate the area using the formula A = πab.
Plug the values of a and b into the formula and multiply them with π to find the area.

So, the area enclosed by the ellipse (x²/a²) + (y²/b²) = 1 is A = πab.

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Step-by-step explanation: Volume

this should help if not let me know..

Let’s revisit our friend Wally from “Area and Perimeter” and use another aspect of his yard to introduce the concept of volume. Wally is a swimmer and wants to install a lap pool in his backyard. Because he has some extra space, he is going to build a pool that is 25 yards long, 2 yards wide, and 2 yards deep. How many cubic yards of water must be used to fill the pool (assuming right to the top).

Much as we did with area (counting unit squares), with volume we will be counting unit cubes. What is the volume of a unit cube? Let’s look at figure 1:

FINDING THE VOLUME OF A CUBE

Figure 1.

Figure 1. Volume = 1 yd × 1yd × yd = 1 cubic yard

The shape at left is a cube (all sides are equal length). In particular, because all sides are of length 1, this cube is called a unit cube.

We know the area of the base from our previous work (1 yd × 1 yd or 1 square yard). We are going to take that area and extend it vertically through a height of 1 yard so our volume becomes

Volume = 1 yd × 1yd × yd = 1 cubic yard

How does this help Wally? Well, if he can count the number of unit cubes in his pool, he can determine the volume of water needed to fill the pool.

GUIDED EXAMPLE

Filling Wally’s Pool

Figure 2. Volume = Length× Width × Height or V = LWH

Figure 2. Volume = Length × Width × Height or V = LWH

If we fill the pool with unit cubes, we can fill 25 unit cubes along the length, 2 along the width and 2 along the height. That would give us 25 × 2 × 2 = 100 unit cubes or:

Volume = 25 yd × 2 yd × 2 yd = 100 cubic yd

Explicit formulas for the types of rectangular solids used in the previous section are as follows:

Shape Volume

Cub of side length L Fig2_4_3  

V

=

L

×

L

×

L

V

=

L

3

Box with sides of length L, W, H Fig2_4_4  

V

=

L

×

W

×

H

NOTES ON VOLUME

Volume is a three-dimensional measurement that represents the amount of space inside a closed three-dimensional shape.

To find volume, count the number of unit cubes inside a given shape.

If there are units, include units in your final result. Units will always be three-dimensional (i.e. cubic feet, cubic yards, cubic miles, etc…)

EXAMPLE 1

Find the volume of each shape below.

Fig2_4_5

A box with sides of length 2 ft, 3 ft,  

2

1

2

ft.

Solutions

64 in3

15 ft3

Volume of A Circular Cylinder

Figure 3.

Figure 3.

Can we use what we know about the area of a circle to formulate the volume of a can (also called a cylinder)? Take a look at figure 3.

The base circle is shaded. If we take the area of that circle (A = A = πr2) and extend it up through the height h, then our volume for the can would be:

V = πr2h.

EXAMPLE 2

Find the volume of the cylinder shown below.

Fig2_4_7

Solution

432π cm3

Volume of Other Shapes

The chart below shows the volumes of some other basic geometric shapes.

Shape Volume

Sphere  

V

=

4

3

π

r

3

Cone  

V

=

1

3

π

r

2

h

Pyramid  

V

=

1

3

L

W

H

EXAMPLE 3

Find the volume of a sphere with radius 5 meters.

Fig2_4_8

Solution

500

3

π

cm

3

EXAMPLE 4

Determine the volume of each of the following. Include a drawing of the shape with the included information. Show all work. As in the examples, if units are included then units should be present in your final result. Use 3.14 for π and round answers to tenths as needed.

Find the volume of a cube with side 3.25 meters.

Find the volume of a box with sides of length 4 feet by  

2

1

2

feet by 6 feet.

Find the volume of a can with radius 4.62 cm and height 10 cm.

Find the volume of a sphere with diameter 12 yards.

Solution

34.3 m3 or 34.3 cubic meters

60 ft3 or 60 cubic feet

670.2 cm3 or 670.2 cubic centimeters

904.3 yd3 or 904.3 cubic yards

EXAMPLE 5

Applications of Volume

If you drank sodas from 5 cans each of diameter 4 inches and height 5 inches, how many cubic inches of soda did you drink? Use 3.14 for π and round to tenths.

Solution

314.0 in3 (rounded)

Angles

Angles, often measured in degrees, measure the amount of rotation or “arc” between intersecting line segments. We need to have some sense of what an angle is before moving on to the next topic. See some examples and terminology below.

Fig2_4_9  

This angle measures 30º

This angle measure is less than 90º

Angles less than 90º are called acute angles

Fig2_4_10  

This angle measures 90º

Angles that measure exactly 90º are called right angles

The small box in the angle corner denotes a right angle

Fig2_4_11  

This angle measures 120º

This angle measure is more than 90º

Angles that measure more than 90º but less 180º than are called obtuse angles

Fig2_4_12  

This angle measures 180º

Angles that measure exactly 180º are called straight angles

The high temperature for today using a 3-day moving average is 92 degrees.

To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.

Given the daily high temperatures in St. Louis for the last week:

92, 92, 93, 95, 95, 86, 95 (yesterday)

To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.

(95 + 86 + 95) / 3 = 92

Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.

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The median for the given sample of data is A. 20.

To find the median for the given sample of data, we need to arrange the numbers in ascending order and then find the middle value.

Arranging the numbers in ascending order: 16, 17, 18, 18, 19, 19, 21, 22, 22, 23, 25

There are 11 numbers in the sample, so the middle value is the (11 + 1) / 2 = 6th value.

The 6th value in the ordered list is 19.

Therefore, the median for this sample of data is A. 20.

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When filling a cylinder by weight, the scale set point should equal the desired weight of the contents.

Filling a cylinder by weight is a common practice in industries such as chemical and gas manufacturing. This method ensures accurate measurements and prevents overfilling or underfilling the cylinder. To fill a cylinder by weight, the empty cylinder is placed on a scale and tared to zero. The desired weight of the contents is then entered as the scale set point. The contents are added to the cylinder until the scale displays the set weight, at which point the filling process is complete. By setting the scale point to the desired weight, the operator can ensure that the cylinder is filled accurately and according to the specified requirements.

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In summary, while the given data can be analyzed to determine factors that influence scrumptiousness, the design described does not align with a proper 23 factorial design. A suggested approach would be to conduct a complete 23 factorial design with multiple replicates for each combination of factor levels to obtain more reliable and meaningful results.

The given design is described as an "eight replicates of a 23 design." This implies that there are eight batches of brownies tested, with each batch prepared using a combination of three factors (pan material, stirring method, brand of mix) at two levels (low and high). The scrumptiousness ratings are obtained from an eight-person test panel.

a. If we want to maximize the ratings for the brownies with a minimum desirable rating of 10, we need to determine the factor levels that yield the highest ratings. This can be achieved by analyzing the data using appropriate statistical methods, such as factorial analysis of variance (ANOVA) or regression analysis, to identify the significant factors and their levels that impact scrumptiousness.

b. However, it is important to note that the given design does not align with a proper 23 factorial design with eight replicates. In a true 23 design, there would be eight different combinations of the factor levels tested. In this case, there are only two levels for each factor, resulting in a total of 2^3 = 8 possible combinations. However, the given description states that there are only eight batches, which means there is only one replicate of each combination. Therefore, the design is incomplete for a 23 factorial design.

To properly address this issue, a suggested design for this problem would be a complete 23 factorial design with at least two replicates for each combination of factor levels. This would allow for a more robust analysis and interpretation of the effects of each factor on scrumptiousness.

c. Analyzing the average and standard deviation of the scrumptiousness ratings can provide insights into the overall performance and variability of the brownie batches. This analysis is appropriate in assessing the general quality and consistency of the brownies. However, it may not provide detailed information about the specific effects of the factors and their interactions, which can be obtained through a proper factorial design analysis.

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In this problem 0.7 is the standard deviation of the contents.

It is a statistic that gauges a dataset's dispersion from its mean, and it is calculated as the variance's square root. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean. A dataset's dispersion from its mean is measured by standard deviation. It is determined as the variance's square root. In the financial industry, standard deviation is frequently employed as a gauge of an asset's relative riskiness.

Given,

A random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces.

In this problem 0.7 is the standard deviation of the contents.

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Answer:

B

Step-by-step explanation: it All Becomes Negative if it is Reflected

Answer:

ABCD forms a rhombus

Step-by-step explanation:

When you graph it out on a graph, the points make a rhombus

The 99% confidence interval estimate for the difference between the percentages of married elderly men and women is (0.0741, 0.2659).

To determine a 99% confidence interval estimate for the difference between the percentages of elderly men and women who were married, we can use the formula for the confidence interval of two proportions:

CI = (p1 - p2) ± Z * √[(p1 * (1-p1) / n1) + (p2 * (1-p2) / n2)]

Where p1 and p2 are the proportions of married elderly men and women, n1 and n2 are the sample sizes, and Z is the Z-score for a 99% confidence level (which is 2.576).

First, convert the percentages to proportions:
p1 = 0.65 (65% married elderly men)
p2 = 0.48 (48% married elderly women)
n1 = 300 (sample size of elderly men)
n2 = 400 (sample size of elderly women)

Now, plug the values into the formula:

CI = (0.65 - 0.48) ± 2.576 * √[((0.65 * 0.35) / 300) + ((0.48 * 0.52) / 400)]
CI = 0.17 ± 2.576 * √[(0.2275 / 300) + (0.2496 / 400)]
CI = 0.17 ± 2.576 * √(0.00075833 + 0.000624)
CI = 0.17 ± 2.576 * √(0.00138233)
CI = 0.17 ± 2.576 * 0.0372
CI = 0.17 ± 0.0959

Thus, the 99% confidence interval estimate for the difference between the percentages of married elderly men and women is (0.0741, 0.2659).

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Answer:

Step-by-step explanation:

what?

Answer:

$22

Step-by-step explanation:

If Jasmine saved 110 during week 2, and this was 5 times more than in week 1, then in week 1 she saved 110/5 = 22 ($)