Express y in terms of x in the equation ax + by = c where b ≠ 0.
a). y = (a/b)x + c/b
b). y = (a/b)x - c/b
c). y = -(a/b)x + c/b
d). y = -(a/b)x - c/b

Answer:

Given triangles are similar

Step-by-step explanation:

We can tell that given triangles are similar by comparing their side lengths.

HG is proportional to KJ

GI is proportional to JL

IH is proportional to LK

we can see the proportion better if we write it like this:

25/75 = 1/3

30/90 = 1/3

19/57 = 1/3

The Volume formula of square pyramid is :

where V = volume

b = base length

h = height

From the problem,

V = 32 cubic feet

b = 4 feet

The height will be :

The answer is 6 feet

Answer:

Step-by-step explanation:

let us denote each cup of flour by f and each cup of water by w

4f + 2w =p

Answer:

5.7 metres

Step-by-step explanation:

2.5+3.2=5.7

Answer:

any line that has the same slope, so in this case any line that has -3 as its slope.

Step-by-step explanation:

an example of a line parallel would be y=-3x+2

In order for the exponential function and the tangent line to be equivalent at a certain point, their function values and their first derivatives must be equal at that point.

At a given point, if the function values of an exponential function and its tangent line are equal, it means that they have the same value and slope at that point.

This requires that their first derivatives at that point are equal. The first derivative of an exponential function is also an exponential function, so the derivative of the tangent line must also be an exponential function with the same slope as the original function.

Therefore, the two functions must have the same first derivative at that point. This condition is necessary for the two functions to be equivalent at that point.

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Answer:

joe mama

Step-by-step explanation:

Answer:

your answer is going to be :

Step-by-step explanation:

C. 3.5x + 4y ≤ 45, 0 ≤ y ≤ 11.25

Answer:

c

Step-by-step explanation:

Answer:

Given:

The distances, in yards, that a team moves on its first five plays are 2, 21, 4, 3, and 25.

Solved:

1. The greatest number is 25

2. If the moved distances are square, which one is largest?

3. The move which is greater than 4 is considered "big play"

=> 21 and 25 are big play (21 > 4, 25 > 4)

Hope this helps!

:)

The pedestrian route that runs diagonally across the park is 5√10 miles.

It states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

We have,

A rectangle:

Length = 15 miles

Wide = 5 miles

Diagonal length can be considered as the hypotenuse.

Applying the Pythagorean theorem.

Diagonal side² = length² + wide²

Diagonal side² = 15² + 5²

Diagonal side² = 225 + 25 = 250

Diagonal side = √250 = 5√10 miles.

Thus the pedestrian route that runs diagonally across the park is 5√10 miles.

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Answer:

180°

Step-by-step explanation:

Assume that

Ashan has x marbles.

Wally has two more marbles than Ashan

So, Wally has x+2 marbles.

Ashan and Wally have 88 marbles.

So,

x + (x + 2) = 88

2x + 2      = 88

2x             = 86

x               = 43

Ashan has 43 marbles.

The area of the sector of a circle  is 28π square miles

The area of a sector of a circle is equal to the area of the circle multiplied by the ratio of the central angle to the full circumference. Therefore, the area of the sector of a circle with a radius of 6 miles formed by a central angle of 2.8 radians is equal to the area of the circle multiplied by the ratio of 2.8 radians to 2π radians (or the circumference of the circle). This means that the area of the sector is equal to 6^2π * 2.8/2π = 28π square miles. In other words, the area of the sector of a circle with a radius of 6 miles formed by a central angle of 2.8 radians is equal to 28π square miles. To visualize this, imagine a pizza slice with a radius of 6 miles. The area of the pizza slice is equal to 28π square miles. The area of the sector is the same as the area of the pizza slice. Therefore, the area of the sector of a circle with radius of 6 miles formed by a central angle of 2.8 radians is equal to 28π square miles.

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

im assuming its b because the quality for the pic is bad and i cant really see it

Step-by-step explanation:

Answer:

the answer is c i believe

Answer:less than

Step-by-step explanation:304 is a smaller number than 340

The most effective type of graph to compare the shoe size of 4th grade students with their heights would be a scatter plot because it allows for the visualization of individual data points and the examination of their relationship.

A scatter plot is a type of graph where individual data points are plotted along two axes. In this case, the shoe size of 4th grade students can be represented on one axis (e.g., x-axis) and their heights on the other axis (e.g., y-axis). Each data point corresponds to a specific student and includes both their shoe size and height.

By plotting the data points on a scatter plot, we can observe the distribution and pattern of the relationship between shoe size and height. If there is a correlation between the two variables, it can be visually identified on the scatter plot. For example, if taller students tend to have larger shoe sizes, we would expect to see a general trend of data points sloping upwards from left to right.

The scatter plot allows the teacher to examine the individual data points and identify any outliers or patterns within the dataset. It provides a visual representation that facilitates a comprehensive understanding of the relationship between shoe size and height among the 4th grade students.

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One example of a phenomenon that is commonly modeled as normally distributed is the heights of adult individuals in a population. The distribution of heights in a given population tends to follow a normal or Gaussian distribution.

The normal distribution is often observed in naturally occurring phenomena due to the central limit theorem. This theorem states that when independent random variables are added, their sum tends to be approximately normally distributed, regardless of the distribution of the original variables. Many biological characteristics, including height, tend to be influenced by multiple genetic and environmental factors that can be considered as a combination of various independent variables. Consequently, when these factors combine, the resulting distribution of heights approximates a normal distribution.

Estimating the mean and standard deviation of heights:

To estimate the mean and standard deviation of heights in a population, a representative sample of individuals can be measured. This sample should ideally be randomly selected to ensure it is representative of the entire population. The mean height of the sample would provide an estimate of the population mean, while the sample standard deviation would provide an estimate of the population standard deviation.

For example, if we measure the heights of 500 individuals in a population and calculate the sample mean as 170 cm and the sample standard deviation as 10 cm, these values can be considered estimates for the population mean and standard deviation, respectively. These estimates are based on the assumption that the sample is representative of the entire population.

It's important to note that the mean and standard deviation can vary among different populations or demographic groups, such as males and females or different age ranges. Thus, specific estimates for mean and standard deviation should be obtained based on the relevant population or subgroup of interest.

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Answer:

60 cm

Step-by-step explanation:

60 cm

add the all together

Answer:

182

Step-by-step explanation:

starting from TU witch is 109 you keep adding so you get the eqation

109+158+199+262=728

then it's 728 divied by (/) 4 becase that is how many you added and you get 182 cars

\(y= (\frac{8}{2} )\times x\) is the equation for the relationship between x and y.

Let's assume that x represents the number of square feet in her garden, and y represents the number of carrots she can grow at a time.

According to the information provided, when the garden size is 2 square feet, she can grow 8 carrots.

We can establish a relationship between x and y using this data.

To determine the equation, we can infer that as the garden size increases, the number of carrots she can grow also increases.

We can assume a linear relationship between x and y, where the number of carrots grows proportionally with the garden size.

Based on this, we can write the equation as follows:

\(y= (\frac{8}{2} )\times x\)

In this equation, (8/2) represents the growth rate of carrots per square foot of the garden.

By multiplying the growth rate by the garden size (x), we can determine the number of carrots she can grow (y) at any given garden size.

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The y-intercept of the given exponential function would be represents the initial value of the investment is $500 which is the correct option (B).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

The given exponential function f(x) = 500(1.03)ˣ

Here x would be represented growth of the savings plan per year

To determine the y-intercept of the function

We have to substitute the value of x = 0 in the given function,

⇒ f(x) = 500(1.03)⁰

⇒ f(x) = 500(1)

⇒ f(x) = 500

Therefore, the y-intercept of the given exponential function would be represents the initial value of the investment is $500.

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No, the data does not have any extreme outliers. The histogram does not show any outliers because all of the data is grouped within the same range of values.

For example, if there were an outlier present, it would show up as a spike outside of the normal range of the data in the histogram.

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The average (mean) height of the four students is 155.5 cm.

To calculate the average height, we sum up all the individual heights and then divide by the total number of students. In this case, the sum of the heights is 159 cm + 145 cm + 161 cm + 157 cm = 622 cm. Since there are four students, we divide the sum by 4: 622 cm ÷ 4 = 155.5 cm. Therefore, the average height of the four students is 155.5 cm.

The concept of calculating the average is a fundamental statistical measure used to summarize a group of values. It provides a central tendency or typical value of the data set. In this case, the average height gives us an idea of the typical height of the four students.

It's important to note that the average height is affected by extreme values. If there were extreme outliers in the measurements, such as a significantly higher or lower height compared to the rest, it would impact the average and might not be representative of the majority of the students. However, in this scenario, we do not have any indication of outliers or extreme values, so the average height of 155.5 cm can be considered a reasonable representation of the group's heights.

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The area of each of the missing faces is 40 m².

The length of each of the missing faces is 10 m.

The missing dimension is 10 m by 4 m.

Area is the region bounded by a plane shape.

To calculate the area of each missing face, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

And the length of each of the missing edge can be calculated using the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute into equation 2

Hence, the length is 10 m.

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The age to which a person in a particular cohort is statistically likely to live on the basis of average longevity of a population is known as life expectancy.

Life expectancy is a measure of how long individuals from a specific population are expected to live, on average.

It is influenced by various factors such as healthcare access, lifestyle choices, socioeconomic status, and genetic predispositions.

Life expectancy is typically calculated using statistical models based on mortality rates and population data.

It is an important indicator used by policymakers, healthcare professionals, and researchers to assess the overall health and well-being of a population.

In conclusion, life expectancy provides insights into the expected lifespan of individuals in a population, helping to inform decisions related to public health and social policy.

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The 95% confidence interval for the mean internet speed is approximately (34.986 Mbps, 37.414 Mbps).

To determine if the claim is supported by the data, we can perform a hypothesis test. We'll set up the following hypotheses:

Null hypothesis (H0): The mean speed of the internet connection is 35 Mbps.

Alternative hypothesis (H1): The mean speed of the internet connection is greater than 35 Mbps.

Since we have a sample mean and standard deviation, we can use a one-sample t-test. Assuming a significance level (α) of 0.05, we can calculate the t-value and compare it to the critical value from the t-distribution.

The t-value can be calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / √(sample size))

t = (36.2 - 35) / (4.32 / √(30))

t ≈ 1.653

For a one-tailed test at a 95% confidence level, the critical value (t-critical) with (n-1) degrees of freedom is approximately 1.699. Since the calculated t-value is less than the critical value, we fail to reject the null hypothesis. Therefore, the data does not provide sufficient evidence to support the claim that the mean speed of your internet connection is more than 35 Mbps.

What is the margin of error for the estimate of the mean internet speed?

The margin of error can be calculated using the formula:

Margin of Error = t-critical ×(sample standard deviation / √(sample size))

Using the t-critical value from the previous question (1.699) and the sample standard deviation (4.32) and sample size (30) provided in the information:

Margin of Error = 1.699× (4.32 / √(30))

Margin of Error ≈ 1.214 Mbps

Therefore, the margin of error for the estimate of the mean internet speed is approximately 1.214 Mbps.

What is the 95% confidence interval for the mean internet speed?

To calculate the confidence interval, we use the formula:

Confidence Interval = sample mean ± (margin of error)

Using the sample mean (36.2) and the margin of error (1.214) calculated in the previous questions:

Confidence Interval = 36.2 ± 1.214

Confidence Interval ≈ (34.986, 37.414)

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Answer:

x=1

Step-by-step explanation:

Look at the bottom of the triangle you will see that 1 = x