Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?
f(x)=-3x-6
f(x)=-3x-4
f(x)=-3x + 16
f(x) = -3x + 14

Weight of a large box = 15.5 kg and weight of a small box is = 6.5 kg

Here two types of boxes; large and small.

What is linear equation in two variables?

An equation is said to be linear equation in two variables if it can be written in the form of ax + by + c = 0

where, a, b, c are real numbers.

Let weight of a large box = x kg

And weight of a small box is = y kg

Formation of linear equations according to questions

5x + 3y = 97 …(i)

2x + 12y = 109 …(ii)

Now solving (i) and (ii) by 2(i) – 5(ii):

\(10x + 6y = 194 \\ 10x + 60y = 545 \\ -54y = -351\)

\(y=6.5\)

⇒y = 6.5 kg

Substituting the value of y into equation (i) we get

5x + 3(6.5) = 97

X = 15.5 kg

Thus, weight of a large box = 15.5 kg and weight of a small box is = 6.5 kg.

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At scores of 13 and 14, the two piles correspond to the two frequency local maxima.

Here's the frequency distribution table:

Score Frequency

9 1

10 1

11 3

12 4

13 5

14 5

15 2

The distribution has two piles of scores and is roughly symmetrical. This is due to the fact that the frequencies are concentrated in the center of the distribution and become less frequent as you move away from it.

The two piles correspond to the two frequency local maxima at scores of 13 and 14.

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That´s q I am sure I hope this helps

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.

The means are the same and the standard deviations are different.

There are two lists given for which the means and the standard deviations need to be compared. So we first find the mean and standard deviation of each list one-by-one using the formulas,

Mean = (1/n)∑x

Variance = [(1/n)∑x²]- mean²

Standard deviation = √variance

List A  

x:  1      2     3      4     5      6

x²: 1      4     9    16    25     36

n = 6

Mean = (1/6)[1+2+3+4+5+6] = 21/6 = 3.5

Variance = 1/6[1+4+9+16+25+36] - 3.5² = 15.167-12.25 = 2.917

Standard deviation = √2.917 = 1.71

List B

x:  2    3    3     4     4    5

x²: 4    9    9    16   16   25

Mean = 1/6(2+3+3+4+4+5) = 21/6 = 3.5

Variance = 1/6(4+9+9+16+16+25)-3.5² = 13.167 - 12.25 = 0.917

Standard deviation = √0.917 = 0.9576

Hence the means are the same and the standard deviations are different.

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Answer:

Step-by-step explanation:

1) 2y + 6x

2) 2y + 8x +2

Answer:

the y to 0 is -2, and the y to 3 is 1

the ordered pairs in order go (-3,-5), (-2,-4), (-1,-3),(0,-2),(1,-1),(2,0),(3,1)

the rule is y=x-2

Step-by-step explanation:

For given  regression model, the number 59.89 in the table tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

In this question we have been given a summary of regression model.

We need to explain the meaning of the number 59.89 in the table.

For given regression model, to view the results of the model, we can use the summary() function in R programming.

In given summary consider the 'Coefficients' table.

The first row gives the estimates of the y-intercept, and the second row gives the regression coefficient of the model.

The 'Estimate' column is the estimated effect, also called the regression coefficient or r² value.

The number 59.89 in the table is coefficient for IsSandwich.

This number tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Therefore, the meaning of the number 59.89 in the table: for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

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The complete question is as shown in the following image

Answer:

• Elevation is the difference between original length and final length

\( = 285 - 140 \\ \\ = { \underline{ \: \: 145 \: \: feet \: \: }}\)

Answer:

Step-by-step explanation:

Change in elevation:

Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

7/10

Step-by-step explanation:

3/10 (blue) +4/10 (red) = 7/10  or 1- 3/10 (green) = 7/10

hope it helps

see the attachment

Answer:

the answer is A. Remainder: 50 Not a factor

Step-by-step explanation:

\( \: \: \: \: \large\bf\implies \: 4.32\)

\( \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32\)

First of all we know that to do this type of question that is ↓

5 weeks do Newton and Descartes spend at home. This can be solved using the concept of fractions.

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Given that,

Newton and Descartes have a 70-day summer vacation

They go to camp for 23/70 of their vacation

= 70 × (23/70)

= 23

Next, they travel for 6/35 of their vacation

= 70 × (6/35)

= 12

So, they stay home the rest of their vacation

= 70 - 23 - 12

= 35

Now, they stay home (35 ÷ 7) = 5 weeks.

Therefore, 5 weeks do Newton and Descartes spend at home.

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There are a total of 50 + 10 + 8 + 10 + 10 + 7 = 95 customers who were older than 32

A stem-and-leaf plot is a method of data representation that aids in the visualisation of statistical data. It is a convenient and simple method of recording, analysing, and understanding data with a numerical range. The stem-and-leaf plot displays data in a way that shows how often specific data values occurred.
In the given stem-and-leaf plot, each number is broken into two parts: the stem, which is the left-side digit(s), and the leaf, which is the right-side digit(s).The digits on the left side of the stem are known as the stems, and the digits on the right side of the stem are known as the leaves. The stem represents the tens digit, and the leaves represent the units digit.```
3 | 1 3 5 6 7
4 | 2 2 4 6 6 7 7
5 | 0 1 2 5 6 8 9
6 | 1 2 3 4 6 6 7 7 8 8
7 | 0 2 3 3 4 5 5 7 9 9
8 | 0 1 3 4 6 6 7
```To calculate the number of customers who were older than 32, we must first determine the values in the stem-and-leaf plot that are greater than 3. The stem is 3, and the values in the leaves are greater than 2, which indicates that they are all greater than 32. So we can count the values in the stem-and-leaf plot to find out the number of customers older than 32.
- 5 values in the stem 3 (31, 33, 35, 36, 37)
- 10 values in the stem 4 (42, 42, 44, 46, 46, 47, 47, 52, 56, 57)
- 8 values in the stem 5 (50, 51, 52, 55, 56, 58, 59, 59)
- 10 values in the stem 6 (61, 62, 63, 64, 66, 66, 67, 67, 68, 68)
- 10 values in the stem 7 (70, 72, 73, 73, 74, 75, 75, 77, 79, 79)
- 7 values in the stem 8 (80, 81, 83, 84, 86, 86, 87)

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0.105 is equivalent to the fraction 21/200 in lowest terms.

What is fraction?

A fraction is a number that represents a part of a whole. Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x.

To convert a decimal to a fraction, we need to write the digits after the decimal point as the numerator and the place value of the last digit as the denominator. In this case, the last digit is 5, which is in the hundredths place (two places to the right of the decimal point).

Therefore, we can write:

0.105 = 105/1000

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5:

105/1000 = (105 ÷ 5)/(1000 ÷ 5) = 21/200

Therefore, 0.105 is equivalent to the fraction 21/200 in lowest terms.

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Answer:

46666

Step-by-step explanation:

We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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The answer is A. 245 words  can he type in 7 minutes.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Milo types 35 words per minute.

words can he type in 7 minutes is 35*7

                                                      =245

because I have to multiple the amount of words he can type in one minute by 7.

hence, The answer is A. 245 words  can he type in 7 minutes.

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The angle that the ramp makes with the ground is approximately 28.07 degrees.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):

Sin(θ) = 8/17

We can use a calculator to find the inverse sin of this ratio to get the angle θ:

θ = sin⁻¹(8/17)

θ ≈ 28.07 degrees

Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.

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The number of street lights that will be needed is 3 street lights.

From the information, it was stated that the city places street lights at equal intervals along a city street beginning 3/8 mile from one end of the street. If the street is 7/8 mile long,

The number of street lights needed will be:

= 7/8 ÷ 3/8

= 7/8 × 8/3

= 7/3

= 3 street lights.

Therefore, the number of street lights that will be needed is 3 street lights.

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\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Step-by-step explanation:

0.09w + 1.8 = 0

0.09w = 0 - 1.8

0.09w = - 1.8

0.09w ÷ 0.09 = - 1.8/ 0.09

w = - 20

The probability that a student taken at random from Dr. Adam's class completes a term paper in more than 13 hours is 0.0436 or 4.36%.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We know that the length of time it takes a student to write a term paper, x, has a normal distribution with mean μ = 8.2 hours and standard deviation σ = 2.8 hours.

Let Z be the standard normal random variable, then we can standardize x as follows:

Z = (x - μ) / σ

Substituting the given values, we get:

Z = (13 - 8.2) / 2.8 = 1.714

we can find that the probability of a standard normal random variable being greater than 1.714 is 0.0436.

Therefore, the probability that a student taken at random from Dr. Adam's class completes a term paper in more than 13 hours is 0.0436 or 4.36%.

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Answer:

6.2

Step-by-step explanation:

hope it helpes you in the long run