The histograms display the frequency of temperatures in two different locations in a 30-day period.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.

When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?

Answer:25.2

Step-by-step explanation:

To find the value of x, we first need to find the missing angle value, which is 180-90-59, making it 31.

Now that we have that value, we can use SOH to find the hypotenuse.

The equation would look something like this:

[tex]\sin\left(31\right)=\frac{13}{x}[/tex]

Which we can change to get the x value like this:

[tex]\frac{13}{\sin\left(31\right)}=x[/tex]

This makes the X value equal to 25.241.

Since you need it as the nearest tenth, you can round it down to 25.2.

The test statistic for testing the hypotheses H0: μ=100 vs Ha: μ<100 using the given sample results x = 91.7, s= 12.5 with n = 30 is -2.17 and the p-value is 0.019. We can reject the null hypothesis H0: μ=100 in favor of the alternative hypothesis Ha: μ<100 at a 5% level of significance.

(a) The test statistic for testing the hypotheses H0: μ=100 vs Ha: μ<100 using the given sample results x = 91.7, s= 12.5 with n = 30 can be calculated as:

t = (x - μ) / (s / sqrt(n))
= (91.7 - 100) / (12.5 / sqrt(30))
= -2.17 (rounded to two decimal places)

Using a t-table with 29 degrees of freedom (n - 1 = 30 - 1 = 29) and a 5% significance level (or 0.05), the corresponding p-value for a one-tailed test is found to be 0.019 (rounded to three decimal places). Therefore, the p-value for the given test statistic is 0.019.

(b) Since the p-value (0.019) is less than the significance level (0.05), we can reject the null hypothesis H0: μ=100 in favor of the alternative hypothesis Ha: μ<100. This implies that there is sufficient evidence to conclude that the population means μ is less than 100 at a 5% level of significance. In other words, the sample provides strong evidence that the true population mean is lower than the hypothesized value of 100.

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The total radius of a cone with a radius of 4in and a height of 12in is 8in.

The total radius of a cone is the sum of the radius of the base and the slant height of the cone. The slant height of a cone can be found using the Pythagorean theorem, which states that the square of the slant height is equal to the sum of the square of the height and the square of the radius of the base.

So, to find the total radius of the cone, we need to calculate the slant height and add it to the radius of the base.

Slant height = sqrt(radius² + height²)

= √(4² + 12²)

= √(160)

= 12.65in (rounded to two decimal places)

Total radius = radius + slant height

= 4in + 12.65in

= 16.65in

≈ 8in (rounded to two decimal places)

Therefore, the total radius of the cone is approximately 8 inches.

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The relation "a-b a mod 4 = b mod 4" means that for any two numbers a and b, if their difference is divisible by 4, then they belong to the same equivalence class. To find the equivalence class of -, we need to find all the numbers that have the same modulus as - when divided by 4.

We can start by listing out some numbers with the same modulus as -. For example, we have {-9, -5, -1, 3, 7, ...}, since these numbers are all congruent to -1 mod 4. Similarly, we have {0, 4, 8, 12, ...} for numbers that are congruent to 0 mod 4, and {1, 5, 9, 13, ...} for numbers that are congruent to 1 mod 4.

Therefore, the equivalence class of - is {-9, -5, -1, 3, 7, ...}, which contains all the negative numbers that are congruent to -1 mod 4.

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Using BODMAS, where x =  x = 22 + 10-((5/25)*100), x is 12. (Option  D)

Bracket, Of, Division, Multiplication, Addition, and Subtraction are abbreviated as BODMAS.

The BODMAS is used to describe the sequence in which a mathematical equation operates. The BODMAS is also known as PEDMAS in certain places, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction.

Sure, using BODMAS, we get

x = 22 + 10 - ((5/25) x 100)

= 22 + 10 - (0.2 x 00)

= 22 + 10 -20

= 12

Thus, x is equal to 12. (Option D)

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The correct interpretation of the given confidence interval is C. We are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

The confidence interval is given as (-0.13, 0.09), which represents the range within which the true difference in proportions (p1 - p2) is likely to fall with a confidence level of 98%.

The negative value of -0.13 indicates that the proportion of obese clients losing weight under strategy 1 may be 13% less than the proportion under strategy 2.

The positive value of 0.09 indicates that the proportion of obese clients losing weight under strategy 1 may be 9% more than the proportion under strategy 2.

Since the confidence interval includes both positive and negative values, it suggests that the true difference in proportions could be either positive or negative.

The confidence level of 98% means that if we were to repeat the study and construct 100 different confidence intervals, about 98 of those intervals would capture the true difference in proportions (p1 - p2).

Therefore, we can conclude that we are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

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The level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect.

In this experiment, the effectiveness of a new allergy medication is being tested. Sixty people with allergies were randomly assigned to two groups: the first group received the new medication, and the second group received a placebo.

By randomly assigning participants to the two groups, the researchers ensured that any observed differences between the groups could be attributed to the medication and not to some other factor.

After a certain period, the level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect. This is because the comparison of symptoms between the two groups allows the researchers to determine if the medication had a significant effect compared to the placebo.

Therefore, the benefit of comparison in this experiment is to determine the effectiveness of the new allergy medication.

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The level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect, accurately describes the benefit of comparison in the experiment. The correct answer is A.

The benefit of comparison in the experiment shown in the design web is that the level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect.

By randomly assigning participants to either the treatment group (who receive the new allergy medication) or the control group (who receive a placebo), researchers can compare the difference in allergic symptoms between the two groups.

If the treatment group experiences a significant reduction in symptoms compared to the control group, then it suggests that the new medication is effective in reducing allergy symptoms.

Therefore, the correct answer is "the level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect." The correct answer is A.

Your question is incomplete but most probably your full question was attached below

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a.) The hire purchase price would be =$3,933.6

b.) The amount of each monthly instalment would be =$218.5

C.) The difference between the price for hire purchase and cash price would be = $953.6

To hire purchase price for the video recorder would be = initial down payment + interest + cash price.

The initial down payment = 20/100×2980

= 59600/100 = $596

The interest = 15 % of outstanding balance

outstanding balance = 2980- 596 =$2,384

Therefore, 15/100 × 2,384

= 35760/100 = $357.60

Thet hire purchase price = 2980+596+357.60=$3,933.6

The amount for each month installment over the next 18 months = $3,933/18 = $218.5

The difference between hire purchase and cash price = $3,933.6- $2980 = $953.6

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The vertical component of the release velocity for the soccer ball is 6.32 m/s and the horizontal component of the release velocity is 21.64 m/s.

To resolve the release vector of the soccer ball, we can use trigonometry. The vertical component of the release velocity can be found by multiplying the initial velocity (23 m/s) by the sine of the angle of release (18 degrees):

Vertical component = 23 m/s x sin(18 degrees)
Vertical component = 6.32 m/s

Similarly, the horizontal component of the release velocity can be found by multiplying the initial velocity (23 m/s) by the cosine of the angle of release (18 degrees):

Horizontal component = 23 m/s x cos(18 degrees)
Horizontal component = 21.64 m/s

Therefore, the vertical component of the release velocity for the soccer ball is 6.32 m/s and the horizontal component of the release velocity is 21.64 m/s.

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The population of interest in this study is all births in southern California between the years 1989 and 1993. The sample in this study is 143,196 births for which length of gestation data and air pollution exposure during gestation were collected.

The results of this study cannot be generalized to the entire population of births in southern California beyond the years 1989 to 1993. However, the findings of the study can still provide valuable insights into the relationship between air pollutants and preterm births in this specific population and time period. It is also important to note that this study alone cannot establish causal relationships between air pollutants and preterm births, as other factors may contribute to preterm births that were not measured or accounted for in this study. Further research and analysis would be needed to establish causal relationships.

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The tables are completed as follows:

For Table 1, we have an exponential function defined as follows:

f(x) = b^x.

We have that when x = 0.699, f(x) = 5, hence the base b is obtained as follows:

b^0.699 = 5

b = 5^(1/0.699)

b = 10.

Hence, when x = 1.477, the value of f(x) is given as follows:

f(x) = 10^1.477

f(x) = 30.

Table 2 is the inverse of table 1. For Table I, we have that when x = 1.301, f(x) = 20, hence for table 2, we have that f(x) = 1.301 when x = 20.

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The inverse function of the function f(x) = -3x/8 is f⁻¹(x) = -8x/3

To find the inverse of a function, we need to switch the roles of x and y and then solve for y.

Let's begin by rewriting the function f(x) in terms of y:

y = f(x) = -3x/8

Now, let's switch x and y:

x = -3y/8

Next, we'll solve for y:

x = -3y/8

8x = -3y

y = -8x/3

So the inverse function of f(x) = -3x/8 is f⁻¹(x) = -8x/3

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There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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The probability of taking at least four trials to find the first defective light bulb is 0.073 (rounded to 3 decimal places).

To find the probability of taking at least four trials to find the first defective light bulb, we can use the geometric distribution formula:
P(X >= k) = (1-p)^(k-1) * p
Where X is the number of trials needed to find the first defective light bulb, p is the probability of finding a defective bulb on any given trial, and k is the minimum number of trials required.
In this case, we want to find the probability of taking at least four trials, so k = 4. We also know that the probability of finding a defective bulb on any given trial is 0.1 (since there is a 10% chance of any given bulb being defective). Therefore, we can plug in these values:
P(X >= 4) = (1-0.1)^(4-1) * 0.1
P(X >= 4) = 0.729 * 0.1
P(X >= 4) = 0.0729
So the probability of taking at least four trials to find the first defective light bulb is 0.073 (rounded to 3 decimal places).

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Step-by-step explanation:

The y-axis intercept occurs when x = 0

put in 0 for 'x' and compute the intercept as

(0+2)(0-2)(0-A)   = 12

      -4 ( -A) = 12

       4A =12

         A = 3

If we choose ε > 0, we can find a δ such that ||f – ft||1 < ε for all t with 0 < |t - 1| < δ, and we have shown that lim||f - ft||1 = 0 as t -> 1.

(a) To prove that lim||f – ft||1 = 0 as t -> 0, we need to show that for any ε > 0, there exists a δ > 0 such that ||f – ft||1 < ε for all t with 0 < |t| < δ.

We have:

||f – ft||1 = ∫|f(x) – f(x – t)| dx

By the continuity of f, we know that for any ε > 0, there exists a δ > 0 such that |f(x) – f(x – t)| < ε whenever |t| < δ. Therefore:

||f – ft||1 = ∫|f(x) – f(x – t)| dx < ε∫dx = ε

This holds for all t with 0 < |t| < δ, so we have shown that lim||f – ft||1 = 0 as t -> 0.

(b) To prove that lim||f - ft||1 = 0 as t -> 1, we need to show that for any ε > 0, there exists a δ > 0 such that ||f – ft||1 < ε for all t with 0 < |t - 1| < δ.

We have:

||f – ft||1 = ∫|f(x) – f(tx)| dx

Using the change of variables y = tx, we can write this as:

||f – ft||1 = (1/t)∫|f(y/t) – f(y)| dy

Since f is integrable, it is also bounded. Let M be a bound on |f|. Then we have:

||f – ft||1 ≤ (1/t)∫|f(y/t) – f(y)| dy ≤ (1/t)∫M|y/t – y| dy = M|1 – t|

This holds for all t with 0 < |t - 1| < δ, where δ = ε/2M. Therefore, if we choose ε > 0, we can find a δ such that ||f – ft||1 < ε for all t with 0 < |t - 1| < δ, and we have shown that lim||f - ft||1 = 0 as t -> 1.

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The equation of the line in slope intercept form is: y = 3x - 5

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph given, we see that the y-intercept which is the point where the line crosses the y-axis is at: y = -5

To get the slope, we will use two points namely:

(0, -5) and (1, -2)

Thus:

Slope = (-2 + 5)/(1 - 0)

Slope = 3

Thus, the equation is:

y = 3x - 5

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Answer:

The sum of two dice can range from 2 to 12. To get a sum of 3, the only possible combinations are (1,2) and (2,1), since there is only one way to get each of those sums.

There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled, since each die has 6 possible outcomes.

Therefore, the probability of rolling a sum of 3 is:

P(D1 + D2 = 3) = number of ways to get a sum of 3 / total number of possible outcomes

P(D1 + D2 = 3) = 2 / 36

Simplifying by dividing both the numerator and denominator by 2, we get:

P(D1 + D2 = 3) = 1 / 18

Therefore, the probability of rolling a sum of 3 with two standard dice is 1/18.

Step-by-step explanation:

in answer :)

Answer:

1/18

Step-by-step explanation:

got it right

The function that has a constant additive rate of -14 is y = -14x + 2

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

Constant additive rate of change of -14

A function that has a constant rate is a linear function

And linear functions take the form

y = mx + c

Where

Rate = m

So, we have

y = -14x + c

Assuming any value for c, we have

y = -14x + 2

Hence, the function is y = -14x + 2

The table of values are not clear. so the question is solved generally

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The total volume of ice cream in term of π is 42π³

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space.

The total volume of the ice cream = volume of cone + volume of half sphere

volume of a cone = 1/3 πr²h

= 1/3 × π × 3² × 8

= π×3 ×8

= 24π in³

volume of the half sphere = 4/6πr³

= 4/6 ×π × 3³

= 108π/6

= 18π in³

therefore the total volume of the ice cream

= 24π + 18π

= 42π in³

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The probability that a randomly selected adult has an IQ greater than 134.4 is 0.025 or 2.5%

To find the probability that a randomly selected adult has an IQ greater than 134.4, we need to calculate the z-score and then find the corresponding area under the standard normal distribution curve.

The z-score is calculated as: [tex]z= \frac{x-μ}{σ}[/tex]

where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

Substituting the given values, we get:

[tex]z = \frac{(134.4 - 101.1)}{17}[/tex]

z = 1.96

Using a standard normal distribution table, we find that the area to the right of z = 1.96 is approximately 0.025. Therefore, the probability that a randomly selected adult has an IQ greater than 134.4 is 0.025 or 2.5%.

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The value of the expression is 4y.

Given is an expression, [tex]12x^{2} y/ 3x^2[/tex], we need to simplify it,

[tex]12x^{2} y/ 3x^2[/tex]

= 12 × x² × y / 3 × x²

= 4 × x² × y / x²

= 4y

Hence, the value of the expression is 4y.

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The probability that she will get a white button and a blue button is 18/30 * 3/29 = 9/145 or approximately 0.062.

The total number of buttons is 18 + 9 + 3 = 30. The probability of getting a white button on the first draw is 18/30. After drawing a white button, there are 29 buttons left, including 3 blue buttons, so the probability of getting a blue button on the second draw is 3/29.

To find the probability of both events happening, we multiply the probabilities:

18/30 * 3/29 = 9/145

Therefore, the probability that she will get a white button and a blue button is 9/145 or approximately 0.062.

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Answer:

-3 times n+7>-17

Step-by-step explanation:

Answer:

[tex] \frac{168}{120} = \frac{21}{15} = \frac{7}{5} = 1.4[/tex]

So the percent increase is 40%.

The percentage increase from 120 to 168 is 40%. This is calculated by finding the increase (48), dividing it by the original number (120), and multiplying the result by 100.

The question asks for the percentage increase from 120 to 168. To find this, we first determine the increase in the number, which is 168 - 120 = 48. The percentage increase is then calculated by dividing this increase by the original number (120 in this case), and then multiplying the result by 100 to get the percentage. So, the calculation would be (48/120) * 100 = 40. Therefore, the percentage increase from 120 to 168 is 40%.

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The length of the lake of 4.042 miles in yards is 7113.92 yards

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

Lake has a length of 4.042 mi.

This means that

Length = 4.042 miles

From the table of values:

To convert inches to feet, we multiply the length value by 1760

So, we have

Length = 4.042 * 1760 yards

Evaluate

Length = 7113.92 yards

Hence, the length is 7113.92 yards

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The area of the triangles are: (a) 8.4 square units. (b) 526.1 square units. (c) 96.7 square units.

(a) Area = (1/2)ab*sin(y)

where y is the angle opposite to side c.

using the law of sines:

b/sin(B) = a/sin(a)

b/sin(16°) = 6/sin(16°)

b = 6*sin(16°)/sin(16°) = 6 units

Now, the sum of the angles in a triangle is 180°:

y = 180° - a - B

y = 180° - 16° - 16°

y = 148°

Finally,

Area = (1/2)66*sin(148°)

Area ≈ 8.4 square units

Therefore, the area of the triangle is approximately 8.4 square units.

(b) using the law of sines:

b/sin(B) = c/sin(y)

b/sin(180°-a-B) = 27.55/sin(56°)

b/sin(76°) = 27.55/sin(56°)

b ≈ 21.94 units

Now,

Area = (1/2)48sin(56°)*21.94/sin(76°)

Area ≈ 526.1 square units (rounded to the nearest tenth)

Therefore, the area of the triangle is approximately 526.1 square units.

(c) using the law of cosines:

b^2 = a^2 + c^2 - 2accos(B)

12.5^2 = 14^2 + c^2 - 214ccos(53°)

c ≈ 13.3 units

Now, the sum of the angles in a triangle is 180°:

y = 180° - a - B

y = 180° - 53° - arcsin(c*sin(53°)/14)

y ≈ 74.8°

Finally,

Area = (1/2)1413.3*sin(74.8°)

Area ≈ 96.7 square units

Therefore, the area of the triangle is approximately 96.7 square units.

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The exponential regression equation for the set of data is given as follows: y = 931.61(1.1)^x.

The number of bacteria after 16 hours is given as follows:

4,281 bacteria.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

For exponential regression, we must insert the points of a data-set into an exponential regression calculator.

The points for this problem are given as follows:

(0, 940), (1, 1034), (2, 1105), (3, 1223), (4, 1352), (5, 1520).

Inserting these points into a calculator, the equation is given as follows:

y = 931.61(1.1)^x.

The number of bacteria after 16 hours is given as follows:

y = 931.61 x (1.1)^16

y = 4,281 bacteria.

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The experimental probability that the next time Audra rolls the number cube, she will roll a 2 is 3/22.

Experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted. In this case, we want to find the experimental probability of rolling a 2.

Looking at the data provided, we can see that Audra rolled a 2 three times out of the total 22 rolls. So, the experimental probability of rolling a 2 can be calculated as:

Experimental probability = number of times the event occurred / total number of trials

Experimental probability of rolling a 2 = 3 / 22

Therefore, the correct option is (B) 3/22. This means that based on Audra's experiment, the probability of rolling a 2 is approximately 0.136 or 13.6%. It is important to note that this is the experimental probability based on a small sample size, and the actual probability of rolling a 2 in a large number of rolls may differ.

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