Kristin made a scatter plot to represent the relationship between the temperature and the number of bottles of water sold at her concession stand at a soccer tournament. Which is a description of the location of the point Kristin will add to represent the 13 bottles of water that were sold when the temperature was 39 degrees Fahrenheit? Select one:
O Top left of the scatter plot
OBottom right of the scatter plot
O Top right of the scatter plot
OBottom left of the scatter plotâ

Answer:

x = 8 since 3 × 8 = 24

Answer:

95

Step-by-step explanation:

To find the average you take the sum of the scores and then divide it by the number of exams. Let x equal the score Lucy must obtain on the next math test.

\(\frac{85+64+76+x}{4} =80\)

Add the scores and multiply both sides by 4

225 + x = 320

Subtract 225 from both sides

x = 95

The value of quadratic function is,

⇒ y = 9x² + 54x - 63

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ y = 9 (x - 1) (x + 7)

Now, We can find the quadratic equation as;

⇒ y = 9 (x - 1) (x + 7)

⇒ y = 9 (x² + 7x - x - 7)

⇒ y = 9 (x² + 6x - 7)

⇒ y = 9x² + 54x - 63

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If the area and perimeter of a right triangle are 30 cm² and 30 cm, respectively, the length of the hypotenuse is 13 cm.

Given that, the area of the right-angled triangle is 30 cm² and the perimeter is 30 cm.

Let a, b, and c be the lengths of the sides and assume that c is the hypotenuse.

Area = 30 cm²

1/2×a×b = 30

ab = 60.

Perimeter = 30 cm

Perimeter is the sum of the sides of the triangle.

a + b + c = 30.

a + b = 30 - c

Squaring on both sides

a²+b²+2ab = 900+c²-60c

In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.

So, a²+b²=c²

c²+2ab = 900 + c²-60c

c²+120 = 900+c²-60c    [we know that ab=60]

Subtracting c² on both sides.

60c = 780

c = 13.

Therefore, the length of the hypotenuse is 13 cm.

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Step-by-step explanation:

a) here,

diametre = 19 cm

Area = ?

Now,

Area = pie d

= 22/7 *19

59.71 cm2

Therefore, area = 59.71 sq.cm.

b)

here,

Area = 1000 sq.cm

diametre = ?

Now ,

Area = pie d

1000 = 22/7 *d

7000 = 22 * d ( cross multiply between 7&1000)

7000/22 = d

318.18 = d

Therefore, diametre = 318.18 cm .

Given,

The diagram of the circle is,

Required

The radius of the circle O.

The radius of the circle is the line segment that join the center of the circle to any point on the circle.

In the circle, AO, FO, EO, CO and DO joins the center of the circle to the point on the circle. Hence AO, FO, EO, CO and DO are radius.

So, option D( All of the listed choice ) is correct.

Answer:

Median - 15.5

Lower Quartile - 13

Upper Quartile - 22.5

Steps to calculate Median:

1. Orchestrate your numbers in mathematical request.  

2. Check the number of numbers you have.  

3. On the off chance that you have an odd number, partition by 2 and gather together to get the situation of the middle number.  

4. On the off chance that you have a considerably number, partition by 2. Go to the number around there and normal it with the number in the following higher situation to get the middle.

Steps to calculate Upper and Lower Quartile:

1. Request your informational index from most minimal to most elevated qualities.  

2. Track down the middle. This is the second quartile Q2.  

3. At Q2 split the arranged informational collection into equal parts.  

4. The lower quartile Q1 is the middle of the lower half of the information.  

5. The upper quartile Q3 is the middle of the upper portion of the information.

Answer:          IQR = 16

Step-by-step explanation:

The given data is 25 th percentile is 64, 50th percentile is 74 and 75 th percentile is 80.

percentage : 25    50   75

 score        : 64    74    80

Median:- The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is odd, then the median is  observation

term

If the number of observations is even, then the median is  observation and  observations.

given n=3, middle term is '74'

In this given data the median is (M) = 74

Interquartile range IQR = median of upper half-median of lower half

                                      = 80-64

                                      = 16

                           IQR = 16

Answer:

3, text time get a better pic

Step-by-step explanation:

Answer:

11+0.48+0.23=11.71.

The graph of g(x) with the graph of f(x): Option D, which is a shift of 2 units to the left, is correct.

What is Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

We are aware that the graph of the modified function is:

for every parent function f(x).

g(x) = f(x + a)

is a left- or right-shift of the parent function f(x), depending on the value of a.

The shift is 'a' units to the left if a>0.

The shift is 'a' units to the right if a0.

Here, G(x) has been changed as follows:

G(x) = F(x + 2)

i.e. a=2>0.

2 units up: G(x) = F(x) + 2.

2 units down: G(x) = F(x) - 2.

2 units to the left: G(x) = F(x + 2).

2 units to the right: G(x) = F(x - 2).

Hence, Option D, which is a shift of 2 units to the left, is correct.

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Answer:

A and D

Step-by-step explanation:

Answer:

A andD

Step-by-step explanation:

==================================================

Work Shown:

C(x+2) - (x+2)(x-2) = 0

(x+2)(C-(x-2)) = 0

(x+2)(C-x+2) = 0

x+2 = 0 or C-x+2 = 0

x = -2 or x = C+2

If we want one solution only, then we must make C+2 = -2 which solves to C = -4

If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)

The probability that the sample mean is within 1 inch of the population mean is approximately 0.1935 for California and approximately 0.1724 for New York.

a. The probability distribution of the sample mean annual rainfall for California can be approximated using the normal distribution. Given that the population mean is 23 inches and the standard deviation is 4 inches, the sample mean can be represented as x with a standard deviation of σ/√n, where n is the sample size. In this case, n = 30. By calculating the z-scores for various values of x using the formula z = (x- μ) / (σ/√n), we can find the corresponding probabilities using a z-table.

b. To find the probability that the sample mean for California is within 1 inch of the population mean, we need to calculate the z-score for x = 22 (one inch below the mean). Using the formula z = (x - μ) / (σ/√n), we get z = (22 - 23) / (4/√30) ≈ -0.866. Looking up this z-score in the z-table, we find the corresponding probability to be approximately 0.1935.

c. Similarly, to find the probability that the sample mean for New York is within 1 inch of the population mean, we need to calculate the z-score for x = 50 (one inch below the mean). Using the formula z = (x - μ) / (σ/√n), we get z = (50 - 51) / (4/√45) ≈ -0.9487. Looking up this z-score in the z-table, we find the corresponding probability to be approximately 0.1724.

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a) The critical value F for the test is approximately 4.26.

b) The observed value F for the test is approximately 5.4.

c) Since the observed value of F is greater than the critical value F, we reject the null hypothesis and conclude that there is a significant difference in the mean weights of a single species of fish in the three different lakes at the 0.05 significance level.

Step-by-step explanation:

a) To find the critical value F, we first need to calculate the degrees of freedom (d.f.) for Treatment and Error. Since there are three different lakes, the d.f. for Treatment is (3-1)=2. We already have the d.f. for Error, which is 9. The Total d.f. is (2+9)=11. Now, using an F-distribution table or calculator with a significance level of 0.05 and d.f. 2 and 9, the critical value F is approximately 4.26.

b) To find the observed value of F, we need to calculate the Mean Square (MS) for Treatment and Error. We already have the Sum of Squares (SS) for Treatment, which is 17.04. The Total SS is 31.23, so the Error SS is (31.23-17.04)=14.19. Now, we can find the MS for Treatment and Error by dividing SS by the respective d.f.:

MS Treatment = SS Treatment / d.f. Treatment = 17.04 / 2 = 8.52

MS Error = SS Error / d.f. Error = 14.19 / 9 = 1.577

Now, we can calculate the observed value of F as the ratio of MS Treatment to MS Error:

Observed F = MS Treatment / MS Error = 8.52 / 1.577 ≈ 5.4

c) Since the observed value of F (5.4) is greater than the critical value F (4.26), we reject the null hypothesis. This means there is a significant difference in the mean weights of a single species of fish in the three different lakes at the 0.05 significance level.

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Answer:

\( {20}^{2} + 6(9 + 3) \\400 + 54 + 18 = 472\)

I hope I helped you^_^

To find out how many of the cars traveled less than 75 miles per hour, we need to add up the frequency of the first three categories: 45 up to 55, 55 up to 65, and 65 up to 75.

50 + 325 + 275 = 650
So, 650 cars traveled at a speed less than 75 miles per hour.
Based on the provided frequency distribution, we can determine the number of cars traveling less than 75 miles per hour by adding the frequencies of the relevant speed ranges:
- 45 up to 55: 50 cars
- 55 up to 65: 325 cars
- 65 up to 75: 275 cars
To calculate the total number of cars traveling less than 75 miles per hour, add the frequencies:
50 cars (45-55 mph) + 325 cars (55-65 mph) + 275 cars (65-75 mph) = 650 cars
So, 650 cars traveled less than 75 miles per hour.

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a. Based on the sample data, the mean price in dollars for a gallon of unleaded gasoline in San Francisco is $3.72.

b. The sample standard deviation in dollars is $0.3589.

Standard deviation,

Mean (the simple average of the numbers

Data and Calculations:

Average price of a gallon of unleaded gasoline in U.S. = $3.28

Number of gasoline and convenience stores for the U.S. average price = 90,000

Sample of San Francisco gasoline and convenience stores = 20

Prices of a gallon of gasoline in 20 San Francisco stores are as follows:

S/N.     Prices Difference in Mean  Difference Squared

1.          $3.59             -$0.13                     0.0169

2.           3.39                -0.33                     0.1089

3.           4.79                 1.07                      1.1449

4.           3.56               -0.16                      0.0256

5.           3.35              -0.37                      0.1369

6.           3.71               -0.01                     0.0001

7.           3.85              0.13                     0.0169

8.           3.40              -0.32                     0.1024

9.           3.55              -0.17                      0.0289

10.         3.76             0.04                      0.0016

11.          3.77             0.05                        0.0025

12.         3.39             -0.33                      0.1089

13.         3.75              0.03                       0.0009

14.         3.79              0.07                      0.0049

15.         4.19              0.47                       0.2209

16.        4.15             0.43                      0.1849

17.        3.66              -0.06                      0.0036

18.        3.93              0.21                       0.0441

19.        3.41              -0.31                       0.0961

20.      3.57              -0.15                       0.0225

Total $74.40                                          2.5765

Mean = $3.72 ($74.40/20)                 $0.12885 ($2.27394/20)

Standard deviation = square root of $0.12885

= $0.3589

Thus, in San Francisco, the price per gallon of unleaded gasoline is $0.03589 .

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To find the average price of unleaded gasoline in San Francisco, add up all the given prices and divide by the total number of prices. The standard deviation, indicating spread around this average price, is computed by finding the square root of the average of the squared deviations from the mean.

To estimate the mean price of a gallon of unleaded gasoline in San Francisco, you need to add up all the 20 given prices, then divide by the number of terms (20) in this case. The mean gives us the average value of the data set.

The standard deviation is a measure of how spread out the prices are from the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

Remember, these calculations provide estimates, as the sample might not represent the entire population of gasoline prices in San Francisco. It's also important to note that external factors, such as changes in crude oil prices or regional taxes, can impact the cost of unleaded gasoline in diverse regions.

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The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

Below

Step-by-step explanation:

Domain    'x' can be any value except 10 <====which would make the denominator = 0 which is not allowed

   (-∞, 10 )  U (10 , +∞)

Range :   horizontal asymptote    the degree of the numerator and the denominator is the same : 1     so the horizontal asymptote will be

          3 / -1 = -3    ( The coefficients of 'x' in the num and den)

   the vertical asymptote occurs at x = 10 ...then the value of y goes to + inf

        so range is   ( -3, +∞)

Inverse Does exist , switch x's and y's in the original equation

   x = (3y+1) / (10-y)     now solve for   y

     and you will get  f^-1 (x) = (10x-4) / (x+3)

Here is graph of f(x) , f^-1(x)   and  x=y :

The ordered pairs that would graph the function are (a) (-3, 21), (-2, 16), (0, 6), (1, 1), (2, -4)

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

y = 6 - 5x

Using has the domain values shown in the table we have the following y values

y = 6 - 5(-3) = 21

y = 6 - 5(-2) = 16

y = 6 - 5(0) = 6

y = 6 - 5(1) = 1

y = 6 - 5(2) = -4

So, we have the following ordered pairs

(-3, 21), (-2, 16), (0, 6), (1, 1), (2, -4)

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Answer:

We need to find the value of f(g(10)) when k = 3, where f(x) = 6x - 2 and g(x) = 5x - kx + 15.

First, we need to evaluate g(10) when k = 3:

g(x) = 5x - kx + 15

g(10) = 5(10) - 3(10) + 15

g(10) = 50 - 30 + 15

g(10) = 35

Now that we know g(10) = 35, we can evaluate f(g(10)):

f(x) = 6x - 2

f(g(10)) = 6(35) - 2

f(g(10)) = 208

Therefore, when k = 3, f(g(10)) = 208.

It took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

Let L(t) be the amount of undeveloped land in acres at time t, where t is measured in years since 2002. Then, we can write:

L(t) = 30 * (7/8)^t

We know that the amount of undeveloped land we are interested in is approximately 15.39 acres. Therefore, we can set up the following equation:

15.39 = 30 * (7/8)^t

To solve for t, we can first divide both sides by 30:

0.513 = (7/8)^t

Next, we can take the natural logarithm of both sides:

ln(0.513) = ln[(7/8)^t]

ln(0.513) = t * ln(7/8)

t = ln(0.513) / ln(7/8)

t ≈ 5.3

Therefore, it took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

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Since -1 ≤ cos A ≤ 1, this triangle does not exist, as the cosine of an angle cannot be less than -1.

In a triangle, given a = 6, b = 2 and c = 5, we need to find the angle measures.

We can use the law of cosines to find the unknown angle:

cos A = (b² + c² - a²) / 2bc

Now we can substitute the given values and simplify:

cos A = (2² + 5² - 6²) / (2×2×5)

cos A = -15/20

cos A = -0.75

Since -1 ≤ cos A ≤ 1, this triangle does not exist, as the cosine of an angle cannot be less than -1.

Thus, we would enter NA in each answer area.

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The triangle ABC is not valid since the sum of the angles of the triangle must be exactly 180°.

Given data: a = 6, b = 2, c = 5To solve the triangle, we can use the law of cosines.

The law of cosines states that for any triangle ABC with sides a, b, and c, and angle A opposite side a, the following formula holds:

c² = a² + b² - 2abcos( A) Similarly, b² = a² + c² - 2accos( B) And, a² = b² + c² - 2bccos( C)

Solving for the angle A:

cos( A) = (b² + c² - a²)/(2bc)

cos( A) = (2² + 5² - 6²)/(2×2×5)

cos( A) = (4+25-36)/20

cos( A) = -0.35A = cos⁻¹ (-0.35)A

≈ 109.47°

Solving for the angle B:

cos( B) = (a² + c² - b²)/(2ac)

cos( B) = (6² + 5² - 2²)/(2×6×5)

cos( B) = (36+25-4)/60

cos( B) = 0.85B

= cos⁻¹ (0.85)B

≈ 31.8°

Solving for the angle C:

cos( C) = (a² + b² - c²)/(2ab)

cos( C) = (6² + 2² - 5²)/(2×6×2)

cos( C) = (36+4-25)/24

cos( C) = 0.25C

= cos⁻¹ (0.25)C

≈ 75.5°

The angles of the triangle ABC are A ≈ 109.47°, B ≈ 31.8°, and C ≈ 75.5°.

The sum of the angles of the triangle is 216.77°, which is slightly more than 180°.

Therefore, the triangle ABC is not valid since the sum of the angles of the triangle must be exactly 180°.

Therefore, the triangle does not exist. Thus, the answer is NA.

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To find the rate of the boat you divide the distance by the time:

Going upstream is s

The binary number 1011011 is equal to the denary number 91.

1011011two is converted to  denary by writing the numbers and assigning powers of 2 from zero to the number of digits available. For the problem, we have zero to six. then multiply out and add

= 1 x 64 + 0 x 32 + 1 x 16 + 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1

this results to

= 64 + 0 + 16 + 8 + 0 + 2 + 1

then the addition is equal to

= 91.

hence, the binary number 1011011 is equal to the denary number 91.

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When using the partition algorithm, the goal is to divide a set of elements into two subsets based on a chosen pivot element. This pivot element is typically chosen as the median of the set or a close approximation to it.

To find the median of the set, we first divide it into groups of 5 (or any other fixed number). We then find the median of each group, which will give us a set of medians. We can then recursively find the median of this set of medians, which will give us an approximate median for the entire set.

Once we have the pivot element, we can compare it to each element in the set and divide them into two subsets based on whether they are greater or less than the pivot element. However, we do not need to compare the pivot element to every element in the set.

We only need to compare the pivot element to the elements that we do not already know how they compare. These are the elements that are in different subsets than the pivot element.

For example, if the pivot element is greater than a certain element, we know that this element is in the subset that contains elements less than the pivot. Therefore, we do not need to compare the pivot element to this element.

In general, we only need to compare the pivot element to approximately half of the elements in the set. This is because each comparison will divide the set into two subsets, one of which we already know the relationship to the pivot element.

In conclusion, when using the partition algorithm, we only need to compare the median of medians to approximately half of the elements in the set, those that we do not already know how they compare.

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Answer:

(-6,10)

Step-by-step explanation:

This is simple, you just subtract 8 from the x value, and add 4 to the y value.

Hope this helps

Melanie is a researcher who wishes to estimate the mean birthweight of full-term babies in her hospital. What minimum number of babies should she sample if she wishes to be at least 99% confident that the mean birth- weight of the sample is within 150 grams of the mean birthweight of all babies? Assume that the distribution of birthweights at her hospital is normal with a standard deviation of 600 g.

The sample size needed is 45.6. The researcher will need a sample size of 46 babies if she wishes to be at least 99 percent confident that the sample's mean birth weight is within 150 grams of the population's mean birth weight. We'll use the formula zα/2 (σ/√n) to solve this issue.Zα/2 = 2.576, σ = 600, and E = 150 are the inputs used in the formula.

The formula for solving for n is rewritten as follows:(Zα/2)^2 (σ^2 )/E^2where Zα/2 is the z-score at the α/2 level of the confidence level (0.005 in this case) and E is the error, which is given as 150 in the question. Zα/2 is 2.576, while σ is 600, which gives us:(Zα/2)^2 (σ^2 )/E^2 = (2.576)^2 (600)^2 /(150)^2 = 45.6.We get a sample size of 46 babies by rounding up to the nearest whole number. Therefore, if Melanie wants to be at least 99 percent confident that the mean birth weight of the sample is within 150 grams of the population mean birth weight, she will require a sample size of 46 babies.

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