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The solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Solve as shown below,

(a) 8 × 3 = 24

(b) –7 × 5 = -35

(c) –6 × (–9) = -(-54) = 54

(d) 8 ÷ (–2) = 8 × 1 / (-2) = - 4

(e) –24 ÷ (–3) = -24 ×  1 / (-3) = 8

(f) –36 ÷ 6 = -36 × 1 \ 6 = -6

Therefore, the solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

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Answer:

This is incorrect, the correct answer is 2

Step-by-step explanation:

3+4+(-5)

Answer:

2

Step-by-step explanation:

The scatter plot suggests that there is a relationship between the number of chinups and push-ups, but it is not a perfect relationship

What is Scatter plot ?

A scatter plot is a type of graph that is used to display the relationship between two variables. It is a visual representation of a set of data points, where each point represents the values of two variables for a single observation.

Based on the scatter plot, it appears that there is a positive correlation between the number of chin-ups and push-ups several students did. This means that as the number of chin-ups increase, the number of push-ups also tend to increase.

We can see this trend in the general upward slope of the points in the scatter plot. However, there is also a fair amount of variability in the data, as some students did more push-ups than others even when they did a similar number of chin-ups.

Therefore,  the scatter plot suggests that there is a relationship between the number of chin-ups and push-ups, but it is not a perfect relationship

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There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Answer:

$26.42

Step-by-step explanation:

P = 30 * 0.82 * 1.074 = 26.42

Answer:

=£5898.38

Step-by-step explanation:

5000×1.07×1.05^(2)

=£5898.38

The factored forms of the expressions are:

115x² + 14x - 8 = (5x - 2)(23x + 4)

32x² - 24x - 36 = 4(2x - 3)(4x + 3)

We have,

To rewrite each expression in factored form, we need to factorize the quadratic expressions.

For the expression 115x² + 14x - 8:

The factored form can be obtained by finding two binomials whose product is equal to the given expression. Factoring the quadratic expression, we have:

115x² + 14x - 8 = (5x - 2)(23x + 4)

For the expression 32x² - 24x - 36:

Similarly, we need to factorize the quadratic expression:

32x² - 24x - 36 = 4(8x² - 6x - 9) = 4(2x - 3)(4x + 3)

Therefore,

The factored forms of the expressions are:

115x² + 14x - 8 = (5x - 2)(23x + 4)

32x² - 24x - 36 = 4(2x - 3)(4x + 3)

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The value x in the formula represents the value of each observation of the data-set.

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The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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The Task objective chosen is: A Measuring Task

The Objective is: To investigate the fairness of a local athlete's track for runners starting on different lines.

To carry about the investigation, follow the steps given below.

Lastly, make a crossword puzzle that includes mathematical vocabulary in a clever manner.

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```Class IX```

*Mathematics Project work*

*Do any one*

1. *A Measuring Task*

To investigate your local athletes track to see whether it is worked fairly for runners who start on different lines.

2. *Design a crossword puzzle with mathematical terms*

To review mathematics vocabulary, to give the opportunity for creative expression in designing puzzles, to act as a means of motivating the study of a given unit and to given recreation .​

The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Answer:

  -2 ≤ x < 12

Step-by-step explanation:

-15x +4 ≤ 34

Add 15x-34 to both sides

  -30 ≤ 15x

Divide by 15

  -2 ≤ x

__

-6x +70 > -2

Add 6x +2 to both sides

  72 > 6x

Divide by 6

  12 > x

__

The two solution spaces overlap. Since the AND of the two inequalities is involved, the solution of both is just that part of the number line where there is overlap.

The solution is ...

  -2 ≤ x < 12

Answer:

The answer is -3

Step-by-step explanation:

(-6*4)+21=-3

24-21=3

Answer: x= 1

Step-by-step explanation:

The correct statement is

Option(A). The average weight of the new offensive line is 304.

Average:

The ratio of the sum of the observation and the number of observations in a particular set is the mean value or average of the data.

=> Average = [Sum of observations ]/ Number of observations

=> Sum of observation = Average × Number of observations

Here we have

The average weight for the five starting offensive linemen of the Charlotte Panthers is 300 pounds.  

The heaviest starter gets injured and his replacement weighs 20 pounds more than the injured starter.

By the given formulas

Total weight of the 5 linemen = 5 × 300 = 1500

Given that the heaviest starter was replaced with a stater who weighs 20 pounds more than the injured starter

After replacement, the total weight of 5 linemen = 1500 + 20 = 1520  

The average weight of the 5 line men = [1520]/5 = 304  

Therefore,

The correct statement is

Option(A). The average weight of the new offensive line is 304.

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The set of points that could represent the dilation is J' (15, 35), K' (70, 35), L' (50, 5), M' (-5, 5)

The coordinates are given as:

J (3, 7), K (14, 7), L (10, 1), and M (-1, 1).

When dilated across the origin, the points become

(x,y) => k(x,y)

Where k represents the scale factor

Assume that k = 5.

So, we have:

J (3, 7), K (14, 7), L (10, 1), and M (-1, 1).

J' (15, 35), K' (70, 35), L' (50, 5), M' (-5, 5)

Hence, the set of points that could represent the dilation is J' (15, 35), K' (70, 35), L' (50, 5), M' (-5, 5)

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Parallelogram JKLM has the coordinates J (3, 7), K (14, 7), L (10, 1), and M (-1, 1). Which of the following sets of points represents a dilation from the origin of parallelogram JKLM?

A.

J' (8, 12), K' (19, 12), L' (15, 6), M' (4, 6)

B.

J' (3, 35), K' (70, 7), L' (50, 1), M' (-1, 5)

C.

J' (15, 7), K' (70, 7), L' (50, 1), M' (-5, 1)

D.

J' (15, 35), K' (70, 35), L' (50, 5), M' (-5, 5)

Answer:

answer is 3.8 inches per year

A box indicates a 90° angle.

So to find m<a, we can setup the equation 41 + a = 90.

Now subtract 41 from both sides to get a = 49.

Hello!

45% of x = 7.2

45x/100 = 7.2

45x = 7.2 * 100

45x = 720

x = 720/45

x = 16

the number = 16

Answer:

(6,3), (10,5),(14,7)

Step-by-step explanation:

6/3 = 2

10/5 = 2

14/7 = 2

Answer:

\(2l + 2w = 48\)

if garden is 15' long

\(2(15) + 2w = 48 \\ 30 + 2w = 48 \\ 30 - 30 + 2w = 48 - 30 \\ 2w = 18 \\ \frac{2w}{2} = \frac{18}{2} \\ w = 9 \: feet \: wide\)

given that for all numbers of p and q,

q = 5/3p + 46

lets find p when q is 21

so lets substitute the value of q into the given equation

q = 5/3p + 46

21 = 5/3p + 46

lets collect like terms

21 - 46 = 5/3p

-25 = 5/3p

lets cross multiply

3 X -25 = 5p

-75 = 5p

5p = -75

divide both sides by 5

5p/5 = -75/5

p = -15

therefore for all values of p and q, q = 5/3p + 46,

the value of p is -15 when q is 21

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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a. Scatter plot: we can use the Years as the x-axis and Damage as the y-axis.

b. Regression line equation: y = -2.2909 + 1.3636x.

c. Scatter plot with regression line: [Insert scatter plot with regression line here].

d. Correlation coefficient: r ≈ 0.949.

e. Sum of squared deviations (SSD): SSD ≈ 170.94.

Prediction for a person who has smoked for 30 years: Predicted percentage of lung damage ≈ 38.963%.

a. To create a scatter plot, we can use the Years as the x-axis and Damage as the y-axis. Below is the resulting scatter plot.

b. To determine the equation of the best-fit regression line, we can use the formula y = a + bx, where a is the y-intercept and b is the slope. The values of a and b can be calculated using the following formulas:

b = (n∑xy - ∑x∑y) / (n∑x^2 - (∑x)^2)

a = (∑y - b∑x) / n

Here, n represents the sample size, ∑x, and ∑y are the sums of the x and y values, and ∑xy and ∑x^2 are the sums of the products and squares of the x and y values, respectively.

After performing the necessary calculations, we find:

b = (7(1924) - (173)(262)) / (7(642) - (173)^2) ≈ 1.3636

a = (176/7) - (1.3636/7)(118) ≈ -2.2909

Therefore, the equation of the regression line is y = -2.2909 + 1.3636x.

c. We can plot the regression line on the scatter plot. Here is the updated scatter plot with the regression line:

d. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.

The formula for the correlation coefficient is:

r = (n∑xy - ∑x∑y) / √[(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)]

After performing the calculations, we find:

r = (7(1924) - (173)(262)) / √[(7(642) - (173)^2)(7(2878) - (176)^2)] ≈ 0.949

Therefore, the correlation coefficient is r ≈ 0.949.

e. The sum of squared deviations (SSD) is a measure of the variation around the regression line. The formula for SSD is:

SSD = Σ(yi - yi)^2

where yi is the observed value and yi is the predicted value.

After substituting the values, we find:

SSD = (20 - 15.3)^2 + (14 - 9.1)^2 + (54 - 39.8)^2 + (63 - 59.6)^2 + (17 - 11.8)^2 + (71 - 67.1)^2 + (23 - 18.4)^2 ≈ 170.94

Therefore, the SSD is approximately 170.94.

To predict the percentage of lung damage for a person who has smoked for 30 years, we can substitute x = 30 into the regression equation:

y = -2.2909 + 1.3636(30) ≈ 38.963

Therefore, the predicted percentage of lung damage for a person who has smoked for 30 years is approximately 38.963%.

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Answer:

y = -(3/4)x + 19

Step-by-step explanation:

If you look at the line, you have the y intercept already. so there is less work to do.

The equation for a linear line is y=mx+b (or c depending on which country you are from) where m is the gradient and b is the y intercept

b = 19 from the diagram

To find the gradient, it is y2-y1/x2-x1, so pick any 2 points, let say  (16,7) and (0,19)

m = 19-7/0-16

= 12/-16

=3/-4

Sub the required numbers back into the equation

y = -(3/4)x + 19

Answer:

its D

Step-by-step explanation:

The completed square form of the given quadratic equation is\(y = (x - 3)^2 + 7.\)

To complete the square for the given quadratic equation\(y = x^2 - 6x + 16\), we can follow these steps:

Factor out the coefficient of the \(x^2\) term (which is 1, in this case) from the \(x^2\) and x terms:

\(y = 1(x^2 - 6x) + 16\)

In order to make the expression a perfect square, we must add and subtract a constant term from inside the brackets. Half of the x term's squared coefficient is the constant we must add and subtract:

\(y = 1(x^2 - 6x + 9 - 9) + 16\)

In this case, half of -6 is -3, so we add and subtract\((-3)^2 = 9\) inside the parentheses.

Now that the expression is enclosed in brackets, we may write it as a square.

\(y = 1(x - 3)^2 - 9 + 16\)

Simplify the expression by combining like terms:

\(y = (x - 3)^2 + 7\)

So the completed square form of the given quadratic equation is\(y = (x - 3)^2 + 7.\)

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Answer:

this type of sampling would be considered a multistage.

The preimage of (0, 0, 0) is the set of all solutions to the system of linear equations where all the variables are equal to 0.

To find the preimage of (0, 0, 0) for the given system of equations, we can set up an augmented matrix and use row operations to solve for the variables:

```

[1 -3 2 0]

[2 -5 5 0]

[4 -7 7 0]

```

R2 → R2 - 2R1 and R3 → R3 - 4R1:

```

[1 -3 2 0]

[0 1 1 -2]

[0 5 -1 -8]

```

R3 → R3 - 5R2 and R1 → R1 + 3R2:

```

[1 0 5 -6]

[0 1 1 -2]

[0 0 -6 2]

```

Finally, we can solve for the variables in terms of the parameter t:

x + 5z = 6t

y + z = 2t

-6z = 2t

Solving for z, we get z = -1/3t. Substituting into the second equation, we get y - 1/3t = 2t, or y = 2t + 1/3t. Substituting into the first equation, we get x + 5(-1/3t) = 6t, or x = 6t - 5/3t.

Therefore, the preimage of (0, 0, 0) is the set of all vectors of the form (6t - 5/3t, 2t + 1/3t, -1/3t) for some real number t.

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Answer:

D

Step-by-step explanation:

This is a 90 degree angle

90-35=55

X=11

35+5x=90

-35. -35

5x=55

Divide both sides by 5

X=11