A Girl Scout is selling cookies to raise money for her troop. She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day. The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.


Girl Scout Cookie Fundraiser
Time (in days) 1 3 4 7
Number of Boxes 24 18 15 6


Which of the following graphs shows the relationship given in the table?
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 21
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 23 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 25 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 23

Out of the given three sets, only set a and C are valid vector spaces because A produces vectors in the same subspace on calculative operations and C produces a 0 on one of its function's values.

Because A is a subspace of [tex]R^{4}[/tex] (a vector space), it satisfies the requirement that vector addition and scalar multiplication produce vectors in the same subspace, making it a vector space. The zero vector's inclusion in the set is a further given. The zero-function is not a part of the set; hence B is not a vector space.

F(x)=0 on the range [-1,1] implies that f(x)=0 someplace on that range, hence C must be a vector space. We know that continuous functions satisfy the requirements for a subspace of a vector space since they have clearly defined function addition and scalar multiplication.

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Complete question is:

Determine if the following sets with operations defined over the given fields are valid vector spaces.

A = {(a,b,c,d) ∈ R4: a+5c+d=0}

B = {f ∈ C [0,1]: f (0) =1}

C = {f ∈ C [−1,1]: ∫1−1 f(x) dx=0}

Answer:

Step-by-step explanation:

At least 75% of the data fall in the interval from the first quartile (Q1) to the third quartile (Q3).

At least 88.9% of the data fall in the interval from the first decile (D1) to the ninth decile (D9).

At least 93.8% of the data fall in the interval from the second percentile (P2) to the 98th percentile (P98).

Note: The quartiles, deciles, and percentiles divide a set of data into 100 equal parts and provide information about the distribution of the data. The first quartile (Q1) is the 25th percentile, the third quartile (Q3) is the 75th percentile, the first decile (D1) is the 10th percentile, the ninth decile (D9) is the 90th percentile, the second percentile (P2) is the 2nd percentile, and the 98th percentile (P98) is the 98th percentile.

Answer:

You would use one quart of red paint and 2.4 quarts of blue paint.

Step-by-step explanation:

You first want to make 3 2/5 into a decimal. To do that you multiply 3x5 and add 2 which equals 17/5. Then you divide 17 by 5 and you get 3.4. So, now you know that you want your blue paint plus your red paint to equal 3.4 So, add 4/5 and 1/3 which equals 1.13333333333. Multiply 1.13333333333 and 3 which equals 3.4. So use the equation (4/5+1/3)x3 and you'll get 3.4. This shows that everything that you do was right.Then multiply just 1/3 x 3 and you'll get your answer which is 1. Then multiply just 4/5 x 3 and you'll get 2.4.

The mean of the data set is 58.3. The standard deviation of the data set is 10.8.

In descriptive statistics, the standard deviation measures how widely the data points vary from the mean. It describes how values are distributed throughout the data sample and measures how widely apart data points are from the mean.

Sum of all values divided by the number of values.

Mean = ( 64 + 46 + 54 + 47 + 70 + 78 ) / 6

Mean = 58.3

The mean of the data set is 58.3.

The square root of the sum of the difference squared between each value and the mean is divided by the number of values subtracted by 1. So

[tex]\sigma =\sqrt{\dfrac{(X-\bar X)^2}{n- 1 }[/tex]

[tex]\sigma = \sqrt{\dfrac{(64 - 58.3)^2+(46 - 58.3)^2+(54 - 58.3)^2+(47-58.3)^2+(70-58.3)^2+(78-58.3)^2}{6-1}\\[/tex]

σ = 10.8

The standard deviation of the data set is 10.8.

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double average = (double)(num1 + num2 + num3) / 3;

1. Declare and assign a double variable named avg

double avg;

2. Calculate the average of the variables num1, num2, num3 and assign that value to avg

avg = (double)(num1 + num2 + num3) / 3;

double avg;  Declare and assign a double variable named avg

int num1, num2, num3;  Declare three int variables

Assign values to the three int variables

num1 = 10;

num2 = 20;

num3 = 30;

Calculate the average of the three int variables and assign that value to the double variable avg

avg = (double)(num1 + num2 + num3) / 3;  Typecast the result of the addition to a double to get the accurate value

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Answer: The inner rectangles area is forty cubic feet, and the outer rectangles area is eighty cubic feet.

The probability that one or more of the children is a carrier of the recessive allele is 0.988.

The probability that one or more of the children is a carrier of the recessive allele can be calculated using the binomial theorem. The binomial theorem states that the probability of a success in a given trial is the sum of all probabilities of success minus the probability of none of the successes.

For the given scenario, we can assume that the probability of each child being a carrier is 0.25 (since each parent is known to be a carrier). The probability of one or more of the children being a carrier is then[tex](1-0.25^4) = 0.988.[/tex]

To calculate this, we first calculate the probability of none of the children being a carrier, which is [tex](1-0.25)^4 = 0.316[/tex]. We then subtract this from 1 to get the probability of one or more of the children being a carrier:[tex](1-0.25)^4 = 0.316[/tex]

Therefore, the probability that one or more of the children is a carrier of the recessive allele is 0.988.

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The frequency table for the histogram is (d)

From the question, we have the following parameters that can be used in our computation:

82, 83, 89, 67, 65, 88, 66, 69, 83, 81, 94, 68, 82, 69, 86, 83, 88, 62, 64, 93

To plot the dataset on a histogram, the data points must be represented on equal intervals

From the list of options, the histogram for the given data set can be made using the interval, 60–75, 75–90, and 90–105 this is because in this case none of the intervals has a frequency of 0.

Hence, the correct option is D.

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Complete question

Fiona has to plot a histogram of the given data. 82, 83, 89, 67, 65, 88, 66, 69, 83, 81, 94, 68, 82, 69, 86, 83, 88, 62, 64, 93

Which frequency table should she use for the histogram?

A. Interval 60–70 70–80 80–90 90–100 Frequency 8 0 10 2

B. Interval 56–63 63–70 70–77 77–84 84–91 91–98 Frequency 1 7 0 5 5 2

C. Interval 50–70 70–80 80–85 85–90 90–100 Frequency 8 0 6 4 2

D. Interval 60–75 75–90 90–105 Frequency 8 10 2

Answer:

This equation is not complete please

Or it is a simultaneous linear equation

Answer:

[tex]4x + y = 5[/tex]

[tex]4x + y - y = 5 - y[/tex]

[tex]4x = 5 - y[/tex]

[tex] \frac{4x}{4} = \frac{5 - y}{4} [/tex]

[tex]x = \frac{5 - y}{4} [/tex]

x = 13

y = 13√2

Special right triangles are right triangles with specific angle measurements whose side lengths follow a certain pattern.

45-45-90 Triangle

A 45-45-90 special right triangle is a triangle that has two 45-degree angles and one 90-degree angle. Remember that in a right triangle, the two shorter sides are called the legs. Additionally, the longest side that is directly across from the right angle is the hypotenuse. In a special right triangle, the legs are equal. Additionally, the hypotenuse is √2 times the leg length. So, if x is the leg, then the hypotenuse is x * √2.

Solving For x and y

In the problem above, x represents one of the legs and y is the hypotenuse. Since this is a 45-45-90 triangle we know that the legs are equal, and one of the legs is 13 units. So, x must equal 13 as well. Then, we know that y must equal x * √2. So, y equals 13√2. This radical cannot be simplified any further, so the final answers are:

Answer:

l=24, w=8

Step-by-step explanation:

64/2=32 for one length and one width

l=3w

l+w=32

3w+w=32

4w=32

w=8

8*3=24=l

An equation for the arithmetic sequence is aₙ=14.6-0.6n.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, Zariah's dash times for her first four races were 14, 13.4, 12.8, and 12.2.

Here, first term (a)=14 and common difference (d)= 13.4-14= -0.6

Now, aₙ=14+(n-1)×(-0.6)

aₙ=14-0.6n+0.6

aₙ=14.6-0.6n

Therefore, an equation for the arithmetic sequence is aₙ=14.6-0.6n.

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Answer:

Step-by-step explanation:

For 66 cups, 9 boxes are needed.

For 72 cups, 9 boxes are also needed.

For 84 cups, 9 boxes are also needed.

Answer:

Step-by-step explanation:

The volume of a swimming pool can be calculated as follows:

Volume = Length * Width * Depth

In this case, the length is 20 m, the width is 6 m, and the depth is 3 m, so the volume is:

Volume = 20 m * 6 m * 3 m = 360 m^3

To convert this volume to cubic feet, we can use the conversion factor:

1 m^3 = 35.3147 ft^3

So, 360 m^3 = 360 * 35.3147 ft^3 = 12611.32 ft^3

Rounding to 3 significant figures, the volume of the swimming pool in cubic feet is:

12611.32 ft^3 ≈ 12611 ft^3

Therefore, the volume of the swimming pool in cubic feet to 3 significant figures is 12611 ft^3.

The volume of the swimming pool is 12,800 ft^3.

To find the volume of the swimming pool in cubic feet, we need to convert the measurements to feet and then multiply them together. One meter is equal to approximately 3.281 feet. So, the length in feet is 20 m × 3.281 ft/m = 65.62 ft, the width is 6 m × 3.281 ft/m = 19.68 ft, and the depth is 3 m × 3.281 ft/m = 9.84 ft.

Now, multiply the length, width, and depth together: 65.62 ft × 19.68 ft × 9.84 ft = 12,848.156 ft3.

Rounding to 3 significant figures, the volume of the swimming pool is approximately 12,800 ft3.

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This is an example of descriptive statistics. Descriptive statistics involves summarizing and describing the main features of a set of data. In this case, the data consists of the responses from 85 randomly selected fifty-year-old Americans about the amount of money they have saved for their retirement.

The statistics provided, such as the average ($25,000), minimum ($0), and maximum ($1,200,000), are all examples of descriptive statistics that summarize the data and provide information about its distribution.

Inferential statistics, on the other hand, involves making inferences about a population based on a sample. Inferential statistics allow us to use the information from a sample to make educated guesses about the characteristics of the population from which the sample was drawn.

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Answer:

C

Step-by-step explanation:

The actual value of the function is: [tex]$$y(1.3) = \frac{1.3^6}{6} + 8.6835 = 11.6375$$[/tex]

The exact solution to the differential equation can be found using separation of variables. We first integrate both sides of the equation with respect to x and obtain: [tex]$$\int \frac{x^5}{y}dx = \int 1\,dy$$$$\frac{x^6}{6} + c = y$$[/tex]

where c is a constant. From the initial conditions, we can solve for c to get: [tex]$$c = 9 - \frac{0.3^6}{6} = 8.6835$$[/tex]

Therefore, the exact solution is:[tex]$$y(x) = \frac{x^6}{6} + 8.6835$$[/tex]

At x = 1.3, the actual value of the function is: [tex]$$y(1.3) = \frac{1.3^6}{6} + 8.6835 = 11.6375$$[/tex]

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Solving an exponential equation we will see that the correct option is C.

We know that if the 1is P ( a percentage) and the initial value is A, then the value after x years is:

A' = A*(1 + P/100%)^x

We want the value $70 to be doubled after 5 years, sowe can write the equation:

$140 = $70*(1 +  P/100%)^5

Now we need to solve that for P.

$140/$70 = (1 +  P/100%)^5

2 = (1 +  P/100%)^5

2^(1/5) = 1 +  P/100%

(2^(1/5) - 1)*100% = P

14.8% = P

Then the correct option is C.

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The bearing here is given as 54.89 degrees degrees

The distance that the puffin flies is 38 km due to the east

Then the distance is 54 km due to the north

We would have the height h = √(p²+b²)

We would have to solve this out such that :

=√54²+38²

h = 66.03 units

From here we would have to solve for sine θ

sin θ = 54 / 66.03

sine θ = 0.818

θ = sin ⁻¹0.818

= 54.89 degrees

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A graph that best represents these ordered pairs is: C. Graph C.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:

Since the values on the x-coordinate (abscissa) increases by 1/2 and the values on the y-coordinate (ordinate) increases by 1, the most appropriate scale 0.5:1, which is best represented by the data points in graph C.

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Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.

The process of statistical analysis involves the collection of data, organizing it, and summarizing it in an understandable way. After summarizing the data, the analyst can then use a variety of techniques to analyze the data. For example, the analyst may use descriptive statistics such as the mean, median, and mode to describe the data. The analyst may also use inferential statistics such as chi-square tests or correlation tests to determine the relationships between variables. Finally, the analyst may use regression analysis to predict future outcomes based on the data. All of these techniques involve the use of mathematics, primarily algebra and calculus, to solve equations and generate the desired results. Ultimately, the goal of statistical analysis is to draw meaningful conclusions from the data that can be used to inform decision-making.

Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.

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Answer: A, and B

A) 894

B) 728

Step-by-step explanation:

When pentagon ABCDE is translated 2 units down, dilated by a scale factor of 1/2 units and reflected over the x-axis, it will map into pentagon FGHIJ. This proves that the pentagons are similar.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The transformations to this problem are given as follows:

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The diameter of the back wheel is 163.68 inches.

Diameter is a straight line passing through the center of a circle, connecting two points on the circumference of a circle. It is the longest possible distance between any two points on the circle and is used to measure the size of a circle. The length of the diameter is twice the radius of the circle. The diameter is also the measure of the distance across a circle, rather than the circumference.

To do this, we first need to calculate the circumference of the front wheel, which is the distance around the edge of the wheel. The circumference of a circle is calculated using the formula C = π x D, where C is the circumference and D is the diameter. Therefore, the circumference of the front wheel is 3.14 x 52 = 163.68 inches.

Next, we need to divide the circumference of the front wheel by the number of spokes on the back wheel. Since there is only one spoke on the back wheel, we can divide the circumference of the front wheel by 1. Therefore, the diameter of the back wheel is 163.68 inches.

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Answer:

20 because the breathe is 18 to get it length

Answer:

169m^2

Step-by-step explanation:

8m x 8m =64m^2

(the area of square = side length x side length)

15m x 7m= 105m^2

(the area of parallelogram= length x height)

so the are of the figure is: 64m^2 + 105m^2= 169m^2

The combined inequality for the conditions is 2x + 3y > 7.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given inequalities,

-2x + 5 < 2 and 3y - 3 > 1

-2x + 5 < 2

subtract 2 from both sides

-2x + 5 - 2 < 2 - 2

-2x + 3 < 0

multiply by -1 to change the sign,

-1(-2x + 3) > 0

2x - 3 > 0 .......(1)

and 3y - 3 > 1

subtract 1 from both sides

3y - 3 - 1 > 1 - 1

3y - 4 > 0..........(2)

since both equations are greater than zero we can add both equations,

2x - 3 + 3y - 4 > 0

2x + 3y > 7

Hence combined equation is 2x + 3y > 7.

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The complete question is -2x + 5 < 2 and 3y - 3 > 1,

find the combined equations.

The value of the variable 'x', 'y', and 'z' will be -6, -9, and -1, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

x - y - z = 4

z = x - y - 4                           ....1

3x - 2y = 0

y = 1.5x                                ....2

-2x + 4y + 4z = - 28            ....3

From equations 1, 2, and 3, then we have

-2x + 4(1.5x) + 4(x - 1.5x - 4) = - 28

- 2x + 6x + 4x - 6x - 16 = - 28

2x = - 12

x = -6

Then the value of 'y' is given as,

y = 1.5(-6)

y = - 9

Then the value of 'z' is given as,

z = - 6 - (-9) - 4

z = - 10 + 9

z = -1

The value of the variable 'x', 'y', and 'z' will be -6, -9, and -1, respectively.

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The amount of tip is $ 6.40 and the total amount including the tip is given by the equation A = $ 38.40

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount including the tip for family be A

Now , the equation will be

The total amount of the bill without the tip = $ 32.00

The percentage of tip = 20 %

So , the amount of tip is = percentage of tip x total amount of the bill without the tip

Substituting the values in the equation , we get

The amount of tip is = ( 20/100 ) x 32

The amount of tip is = $ 6.40

Now , the total amount including the tip A = total amount of the bill without the tip + amount of tip

Substituting the values in the equation , we get

The total amount including the tip A = $ 32.00 + $ 6.40

The total amount including the tip A = $ 38.40

Hence , the equation is A = $ 38.40

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The future value F of the given principal under compound interest for the

time period and interest rate specified is $17,149.99.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = the number of times compounded in a year.

We have,

t = 13 years

r = 2.75%

Compounded monthly

This means,

n = 12

P = $12,000

Now,

A = P [tex](1 + r/n)^{nt}[/tex]

A = 12000 [tex](1 + 0.00229)^{156}[/tex]

A = $17,149.99

Thus,

The future value is $17,149.99.

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