What are the slope and y-intercept of the line?



The slope is 3 and the y-intercept is 2.



The slope is 1.33 and the y-intercept is 2.



The slope is 2 and the y-intercept is 3.



The slope is 2 and the y-intercept is 1.33.

Answer:

10,781 voters

Step-by-step explanation:

In election poll, if 4 out of 7 voters will vote for a certain political party, the total voters will be 7 and 3 out of 7 will not vote for the political party

If there are 25 156 voters, we are to find the number of voters that will not vote for that party. Hence the number of people that will not vote is expressed as;

= 3/7 * 25,156

= 75,468/7

= 10,781

Hence approximately 10,781 voters will not vote for the party.

The true statement about the function represented by this graph  is "The function f(x) has an inverse because it passes the horizontal line test." Option B.

This is further explained below.

Generally, In mathematics, the set of ordered pairs that satisfy the condition "display style f(x)=y" is referred to as the graph of the function f. These pairings, which are Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane, are found under the usual scenario in which both x and f(x) are real values.

In conclusion, The assertion that "The function f(x) has an inverse since it passes the horizontal line test" is accurate with regards to the function that is being represented by this graph.

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A p-value for correlation which is statistically significant implies the correlation is due to random chance. The correct solution to this is False.

A p-value for correlation which is statistically significant implies that it is unlikely that the observed correlation is due to random chance alone. In other words, it suggests that there is evidence to support the presence of a true correlation between the two variables being studied. The p-value is a measure of the strength of evidence against the null hypothesis (i.e., that there is no correlation between the two variables), and a smaller p-value indicates stronger evidence against the null hypothesis.

Interpretation of the intercept: The intercept in a linear regression model represents the value of the dependent variable when all independent variables are equal to zero. It is the value of the dependent variable when there is no effect of the independent variable(s) on it. For example, in a regression model predicting height based on age, the intercept would represent the expected height of a person at age zero (which is not a realistic scenario).

Interpretation of a residual: A residual is the difference between the actual observed value of the dependent variable and the predicted value of the dependent variable based on the regression model. It represents the part of the dependent variable that the model was not able to explain. A positive residual means that the actual value is greater than the predicted value, while a negative residual means that the actual value is smaller than the predicted value.

Interpretation of r-squared: R-squared is a measure of how much of the variation in the dependent variable is explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. Specifically, it represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. For example, if r-squared is 0.75, it means that 75% of the variability in the dependent variable is explained by the independent variable(s) in the model.

Interpretation of the slope: The slope in a linear regression model represents the change in the dependent variable that is associated with a one-unit increase in the independent variable, holding all other variables constant. It reflects the average change in the dependent variable for each unit change in the independent variable. For example, in a regression model predicting height based on age, the slope would represent the average change in height for each additional year of age.

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Answer: 450 cm³ is the volume

Step-by-step explanation:

Volume of pyramid = L x W x H divide by 3

The required volume of the given square pyramid is 20,250 cubic centimeters.

Given that,
The side length of the base of a square pyramid is 30 centimeters. The height of the pyramid is 45 centimeters. The volume of the pyramid in cubic centimeters is to be determined.

Volume is defined as the ratio of the mass of an object to its density.

Here,
The volume of the square pyramid is given as,
= 1/2 area of base × height
= 1/2[30×30]×45
= 900 × 45 / 2
= 20,250 cubic centemeters.

Thus, the required volume of the given square pyramid is 20,250 cubic centimeters.

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Answer:

1,2,5,10

Step-by-step explanation:

hope this helps

The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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The given statement "the irregular variation component of a time series measures the over-all general directional movement over a long period of time." is true because the overall behavior of the series and make more accurate predictions about future trends.

The irregular variation component of a time series can be defined as the part of the series that is not explained by any of the other components, such as the trend, seasonal, or cyclical components. This means that it represents the random fluctuations in the series that are not due to any underlying pattern or trend. In other words, it measures the extent to which the series deviates from its expected value at any given point in time.

Mathematically, the irregular variation component can be expressed as the difference between the observed value of the time series at a particular point in time and the expected value of the series at that same point in time, given the other components of the series.

The irregular variation component is important because it can provide insight into the underlying causes of the random fluctuations in the time series.

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Answer:

27°C

Step-by-step explanation:

The temperature on February 9th 1934 = -15°C

The next day the temperature rose 42 degrees.

We need to find an expression for the temperature on February 10th.

February 10th temperature = -15 + 42

= 27°C

So, the temperature on February 10th is 27°C.

Answer: it would be 42+(-15)

Step-by-step explanation:

Got it right

Answer:

Step-by-step explanation:

3245

An equation that best fits the data above is y = 3 - 0.5x.

There is no correlation between the data.​

In this exercise, we would plot the x-values on the x-axis (x-coordinates) of a scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.

Based on the scatter plot shown below, which models the relationship between the x-values and y-values, an equation for the line of best fit is modeled as follows:

y = 3 - 0.5x

Correlation coefficient, r = -1

In conclusion, there is no correlation between the data because the correlation coefficient (r) is less than 0;

0＜|r| ≤ 0.2  (no correlation)

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Answer:

A. \( 25x² - 64 \)

B. \( (5x + 8)(5x - 8) \)

Step-by-step explanation:

A. The area of the shaded region = area of the whole large square - area of the 4 smaller squares

= (5x*5x) - 4(4*4)

Area of shaded region = \( 25x^2 - 64 \)

B. The expression, \( 25x^2 - 64 \), is the difference of two perfect squares, 25x² and 64. Therefore, apply the rule of factoring difference of two perfect squares.

Thus, \( a^2 - b^2 = (a + b)(a - b) \)

Therefore, the expression of the are of the shaded region can be expressed in factored form as:

\( 25x^2 - 64 = (5x + 8)(5x - 8) \)

Answer:

B:

Distribute –4 to get –8x – 1 > 5 – 3x.

We find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139. Any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps. The middle 70% of her laps are between 119 and 131 seconds.

To answer your questions, we first need to have some context on what we're dealing with. You mentioned "her laps," so I assume we're talking about a person who is running or swimming laps. We also need to know the distribution of her lap times (i.e., are they normally distributed, skewed, etc.) in order to answer these questions accurately. For now, let's assume that her lap times are normally distributed.
To find the proportion of her laps that are completed between 127 and 130 seconds, we need to calculate the area under the normal distribution curve between those two values. We can do this using a calculator or a statistical software program, but we need to know the mean and standard deviation of her lap times first.

Let's say the mean is 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139.
To find the fastest 2% of laps, we need to look at the upper tail of the distribution. Again, we need to know the mean and standard deviation of her lap times to do this accurately. Let's say the mean is still 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 98th percentile (i.e., the fastest 2% of laps) is about 2.05. We can then use the formula z = (x - mu) / sigma to find that x = z * sigma + mu, where x is the lap time we're looking for. Plugging in the numbers, we get x = 2.05 * 5 + 125 = 135.25 seconds.

Therefore, any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps.
Finally, to find the middle 70% of her laps, we need to look at the area under the normal distribution curve between two values, just like in part However, we need to find the values that correspond to the 15th and 85th percentiles, since those are the cutoffs for the middle 70%. Using the same mean and standard deviation as before, we can use a standard normal distribution table or calculator to find that the z-scores corresponding to the 15th and 85th percentiles are -1.04 and 1.04, respectively.

We can find that the lap times corresponding to those z-scores are 119 seconds and 131 seconds, respectively. Therefore, the middle 70% of her laps are between 119 and 131 seconds.

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Answer: The ratio of the side lengths of two similar figures is 2:5.

Let's assume that the dimensions of the smaller figure are 2x, 2y, and 2z, where x, y, and z are some constants. Then, the dimensions of the larger figure will be 5x, 5y, and 5z.

The ratio of the volumes of two similar figures is the cube of the ratio of their corresponding side lengths.

So, the ratio of the volumes of the smaller and larger figures will be:

(2x)^3 : (5x)^3

8x^3 : 125x^3

We can simplify this ratio by dividing both sides by the common factor of x^3:

8 : 125

Therefore, the ratio of the volumes of the smaller and larger figures is 8:125.

Step-by-step explanation:

Answer:

a(66) = -10 + 17(65) = 1095

Step-by-step explanation:

We know that this is an arithmetic sequence.  Subtracting -10 from 7 results in 17; subtracting 7 from 24 also results in 17.  Thus, the common difference, d, is 17.  The first term is -10.

The general form of an arithmetic sequence is a(n) = a(1) + d(n - 1).

Substituting -10 for a(1) and 17 for d, we get:

a(n) = -10 + 17(n - 1)

Now let n = 66:  a(66) = -10 + 17(66 - 1), or    a(66) = -10 + 17(65) = 1095

Tony should buy the paint from Ready-Steady-Paint because it would be cheaper, costing him £28.05 compared to £30 from Paint-O-mine.

To determine which shop Tony should buy the paint from, let's compare the total cost of 12 tins of paint from both shops.

Paint-O-mine:

The cost of 3 tins of paint from Paint-O-mine is £7.50.

Cost of 1 tin = £7.50 / 3 = £2.50 per tin.

Since Tony needs 12 tins, the total cost from Paint-O-mine would be: £2.50 × 12 = £30.

Ready-Steady-Paint:

The normal price of a box of 4 tins from Ready-Steady-Paint is £11. However, there is a 15% discount on the normal price.

To calculate the discounted price, we multiply the normal price by (100% - 15%):

Discounted price = £11 × (100% - 15%) = £11 × 85% = £9.35.

So, the cost per tin from Ready-Steady-Paint is

= £9.35 ÷ 4

= £2.3375

Since Tony needs 12 tins, the total cost from Ready-Steady-Paint would be: £2.3375 × 12 = £28.05.

Comparing the total costs:

The total cost from Paint-O-mine is £30.

The total cost from Ready-Steady-Paint is £28.05.

Therefore, Tony should buy the paint from Ready-Steady-Paint because it would be cheaper, costing him £28.05 compared to £30 from Paint-O-mine.

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Answer: x=15

Step-by-step explanation: Since 3x+5 is equal to 50, you can write 3x+5=50, and 3x=45, x=15.

Step-by-step explanation:

it is geometric  

so we will use this equation:

a(n)=a1*(r)^(n-1)

and we have a(1)=75 , r=15/75=3/15=1/3

explicit formula: a(n)=75*(1/3)^(n-1)

hope this helps

Answer:

75(1/5)^n-1

Step-by-step explanation:

I just did it.

In linear equation, $56.65are  the value of the coins in dollars .

What is a linear equation example?

We need to find how many of the 206 coins are nickels, dimes, or quarters.

We know the quantities of each coin in relation to one another.

From that relationship we can set up a ratio.

Let Q = number of quarters

Let D = number of dimes

Let N = number of nickels

Then Q:D:N = 1:1:2

this tells us if the girl had 4 coins, she would have 1 quarter, 1 dime, and 2 nickels.

We want to keep this same ratio but we want the total number of coins to be 206.

If we divide 206 by 4, we get the number that we use to multiply our ratio.

206/4 = 51.5

So she has 51.5 quarters, 51.5 dimes, and 103 nickels.

the value of the coins in dollars = 51.5(0.10) + 51.5(0.05) + 103(.25) = $56.65

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The mean, variance, and standard deviation for n = 295 and p = 0.21 by using binomial distribution are

61.95, 48.8125, and 6.988, respectively.

The binomial distribution, which is a type of probability distribution, is used to calculate the probability of a certain number of successes (or failures) in a given number of trials. The mean, variance, and standard deviation of a binomial distribution can be calculated using the following formulas:
Mean (μ) = np
Variance (σ²) = npq
Standard deviation (σ) = √(npq)
Where n is the number of trials, p is the probability of success in a single trial, and q is the probability of failure in a single trial (q = 1 - p).

Part 1 out of 4: n = 295, p = 0.21
Using the formulas above, we can calculate the mean, variance, and standard deviation for this binomial distribution.
Mean (μ) = np

= 295 × 0.21 ⇒61.95
Variance (σ²) = npq

= 295 × 0.21 × 0.79 ⇒ 48.8125
Standard deviation (σ) = √(npq)

⇒ √(48.8125) = 6.988

Therefore, the mean, variance, and standard deviation for n = 295 and p = 0.21 are 61.95, 48.8125, and 6.988, respectively.

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Answer:17 x 7= y x 2

Step-by-step explanation:

\((\stackrel{x_1}{5}~,~\stackrel{y_1}{9})~\hfill \stackrel{slope}{m}\implies 2 ~\hfill \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{2}(x-\stackrel{x_1}{5})\)

Answer:

7y+r+8x+94

Explanation

Given the algebraic expression 7(y+2) + (8+r) + 8(x + 9)

Given A, B and C. According to distributive law;

A(B+C) = AB + AC

A is distributed over C. In the same vein

On expanding the expression;

7(y+2) + (8+r) + 8(x + 9)

7y+7(2) + 8 + r + 8(x)+ 8(9)

7y+14+8+r+8x+72

Bringing the variables and constants together

7y+r+8x+14+8+72

7y+r+8x+94

a). The number of ways which the company can choose 4 workers from the list of employees is; 2,730 ways.

b). The number of ways the company can choose the workers if 2 labourers and 3 joiners are on holiday is; 700 ways.

It follows from the task content that the number of ways the company can choose 4 workers in each scenario be determined.

a). Since there are 3 labourers, 13 joiners, 10 electricians, and 7 plumbers.

The number of possible ways to choose 4 workers is; ³C₁ × ¹³C₁ × ¹⁰C₁ × ⁷C₁

= 3 × 13 × 10 × 7

= 2,730 ways.

b). Also, when 2 labourers and 3 joiners are absent, it follows that the selection space is now; 1 labourer, 10 joiners, 10 electricians and 7 plumbers.

The number of possible ways is therefore; ¹C₁ × ¹⁰C₁ × ¹⁰C₁ × ⁷C₁

= 1 × 10 × 10 × 7

= 700 ways.

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The density of this certain material is 37.2 pounds per liter.

In Science and Mathematics, the density of a chemical or physical substance such as a material can be calculated by using the following formula:

Density = M/V

Where:

Conversion:

1 kg equals 2.20462 pounds

1 cup of volume equals 0.237 liter.

Density, d = (4 × 2.20462)/0.237

Density, d = 37.15 ≈ 37.2 pounds per liter.

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Answer:

Here is the ans ..hope it helps

Inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process.

Inverse distance weighting is a method used in geostatistics to estimate values at unsampled locations based on values at surrounding sample locations. It works by assigning weights to the sample points based on their proximity to the unsampled point. The closer a sample point is to the unsampled point, the higher its weight. The weights are then used to calculate a weighted average of the sample values, which is used as the estimate for the unsampled location.
The benefit of inverse distance weighting over a simple average is that it takes into account the spatial variability of the data. A simple average treats all sample points equally, regardless of their distance from the unsampled point. This can lead to inaccurate estimates if there is a high degree of spatial variability in the data. In contrast, inverse distance weighting gives more weight to sample points that are closer to the unsampled point, which is likely to provide a more accurate estimate.
Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process. For example, if there are two variables of interest (e.g., temperature and precipitation), inverse distance weighting can be used to estimate values for both variables simultaneously. This is not possible with a simple average.
Overall, inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Its ability to account for spatial variability and incorporate multiple variables makes it a powerful technique for analyzing spatial data.

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