TERM 1 ASSIGNMENT GRADE 7 Question 3 3.1. Calculate the following WITHOUT using a calculator; 3.1.1 6234 ×32​

Answer: The total number of ways the photography student can choose 4 photos out of 21 is given by the combination formula:

Step-by-step explanation: C(21, 4) = (21!)/((4!)(21-4)!) = 5985

Out of the 21 photos, 9 were photos of babies. The number of ways the student can choose 4 baby photos out of 9 is given by:

C(9, 4) = (9!)/((4!)(9-4)!) = 126

Therefore, the probability that all 4 photos chosen are of babies is:

P = (number of ways to choose 4 baby photos)/(total number of ways to choose 4 photos)

P = C(9, 4)/C(21, 4)

P = 126/5985

P ≈ 0.021

So, the probability that all 4 photos chosen are of babies is approximately 0.021 or 2.1%.

The graph's function limit at x=4 is 6.

In mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.

The formal definition of the limit of a function f(x) as x approaches a value a is as follows:

For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.

Limit f(x) at x tend to 4⁺ =6.

Limit f(x) at x tend to 4⁻ =6

Hence, the graph's function limit at x=4 is 6.

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As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.

given

AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.

We can apply the Pythagorean theorem to segment AB as follows:

[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]

AB² = 50

AB = √50 = 5√2

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

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The width of the top of the bookcase should be approximately 12.2 inches to give Bria's soap carving collection an area of 300 square inches.

Simply multiply the length and width measurements to get the area of your square or rectangular area in square inches.

Assume the bookcase's top is rectangular, with length "L" and width "b". Because the area of a rectangle is the product of its length and width, we get:

L * b = 300

To find "b," we can rearrange the equation as follows:

b = 300 / L

We don't have enough information to directly solve for "L," but we can make an educated guess based on the figure provided. Based on the illustration, the bookcase appears to be roughly twice as long as it is wide. So let us suppose:

L ≈ 2b

When we plug this into the equation above, we get:

b = 300 / (2b) (2b)

To simplify, we have:

b^2 = 150

When we take the square root of both sides, we get:

b ≈ 12.2

We have, rounded to the nearest tenth of an inch:

b ≈ 12.2 inches

As a result, the width of the top of the bookcase should be approximately 12.2 inches in order to give Bria's soap carving collection a 300-square-inch area.

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The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.

A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.

The intervals of the piecewise function are;

f(x) = √(x + 5) if x < -2

f(x) = |x + 1| -2 ≤ x ≤ 2

f(x) = (x - 2)² if x > 2

The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²

The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2

The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.

The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.

The correct option for the graph of the piecewise function is therefore the third option.

Please find the attached the graph of the piecewise function created with MS Excel

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Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).

By determining the value of a single unit or quantity and then scaling that value up or down to determine the value of another quantity, the unitary method is a mathematical strategy used to solve problems. According to the unitary method's guiding concept, if one quantity or unit has a certain value, then a predetermined number of those same quantities or units will have a proportionate value. For instance, 5 apples would cost $5 if 1 fruit cost $1.

given

We can use the person's weight and body fat proportion to determine how many pounds of body fat they have. We can commence by calculating the decimal weight of the body fat:

weight of body fat Equals body fat percentage * weight

= 0.163% * 163 lbs.

= 26.509 lbs.

Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).

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Answer:

Difference=£2.4

Step-by-step explanation:

Here in shop A

130 cm=£1.82

1 cm=£1.82/130

1 cm=0.014

Now

400 cm=0.014*400

=£5.6

Again, In shop B

235cm=£1.88

1 cm=£1.88/235

1 cm=£0.008

Now

400cm=0.008*400

=£3.2

Now,

Difference=£5.6-£3.2

=£2.4

The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.

To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:

[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]

[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]

[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]

The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.

Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.

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The resultant force is equal to F1, which is {-300i + 170j + 190k}N, and the couple moment acting at point 0 is  (-0.19i - 0.34j + 0.15k) N.m.

To determine the resultant force acting at point O, we can add all the forces acting at point O. In this case, we have only one force F1 = {-300i + 170j + 190k}N. Therefore, the resultant force acting at point O is F1 itself.

To determine the couple moment acting at point O, we can use the formula:

M = r x F

where r is the position vector from point O to any point on the line of action of force F.

Since we don’t know the position vector r, we can choose any arbitrary point on the line of action of force F. Let’s say we choose point A which lies on the line of action of force F and is perpendicular to it.

Therefore, r = OA where OA is the position vector from point O to point A. We can find OA by subtracting position vectors of points O and A i.e., OA = A - O.

Now, let’s calculate M using M = r x F.

M = (OA) x F1

M = (A - O) x {-300i + 170j + 190k}N M

= (-0.19i - 0.34j + 0.15k) N.m

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Complete question is:

Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N

Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas.

Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas.

√9+25 = 28

π-4 = -0.8571

³√-27 = -3

2 / 3 = 0.6667

18÷2 = 9

√-27​ = 5.196

In mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).

We have √9+25 = 28

find the square root of 9 = 3

3 + 25 = 28

π-4 = 3.14 - 4

= -0.8571

³√-27 = ³√3³

= 3

2÷3 = 0.6667

18÷2 = 9

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question:

given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27​

find the value of the terms

The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.

To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.

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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.

138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.

Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.

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The slope of this linear function is equal to: B. -2/9.

The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.

The value of each expression is: C. a) 2, b) 1/2, c) 2/9.

In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (8 - 10)/(6 - (-3))

Slope (m) = (8 - 10)/(6 + 3)

Slope (m) =

Slope (m) = -2/9.

In Mathematics, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given parameters, we have:

Volume of cylinder, V = 3.14 × 5² × 10

Volume of cylinder, V = 785 m³

(√2)² = 2

(1/√2)² = 1/2

(√2/3)² = 2/9

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Answer:

To find the probability of getting someone who tested positive given that he or she had the disease, we need to use the formula for conditional probability:

P(positive|disease) = P(positive and disease) / P(disease)

From the given data, we can see that there are 136 individuals who tested positive and actually had the disease. Therefore, P(positive and disease) = 136.

We can also see that there are a total of 136 + 8 = 144 individuals who actually had the disease. Therefore, P(disease) = 144.

Substituting these values into the formula, we get:

Simplifying, we get:

Rounding to three decimal places, we get:

Therefore, the probability of getting someone who tested positive given that he or she had the disease is approximately 0.944.

The set of all n×n invertible matrices with the standard operations of matrix addition and scalar multiplication is (b) not a subspace.

A Subspace is defined as a subset of a vector space that is itself a vector space under the same operations of addition and scalar multiplication defined on the original vector space.

To be a subspace of Mₙ,ₙ, a subset of Mₙ,ₙ must satisfy three conditions:

(i) The subset must contain the zero matrix,

(ii) The subset must be closed under matrix addition, meaning that if A and B are in the subset, then (A + B) is also in the subset.

(iii) The subset must be closed under scalar multiplication, meaning that if A is in the subset and c is any scalar, then cA is also in the subset.

The set of all n×n invertible matrices does not contain the zero matrix, as the zero matrix is not invertible.

Therefore, it fails to meet the first condition and cannot be a subspace, the correct option is (b).

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The given question is incomplete, the complete question is

Determine whether the subset of Mₙ,ₙ is a subspace of Mₙ,ₙ with the standard operations of matrix addition and scalar multiplication.

The set of all n×n invertible matrices is

(a) Subspace

(b) Not a subspace.

The rate of change (or slope) of this linear function is -1/2.

A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.

The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.

Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.

The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:

slope = (change in y) / (change in x)

Let's use the points (0, -3) and (2, -4) to calculate the slope:

slope = (-4 - (-3)) / (2 - 0)

slope = -1 / 2

Therefore, the rate of change (or slope) of this linear function is -1/2.

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The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.

a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.

(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:

Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.

Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.

(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:

Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50

Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.

(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.

Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the

average monthly rent is at least $1,300. As a result, the answer is "No."

(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.

A 92% confidence interval has a z-score of 1.75. (to two decimal places).

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Answer:

(15+x)÷4 = 80-x

by criss cross we'll get:

15+x = 4(80-x)

15+x = 320-4x

x+4x=320-15

5x = 305

x = 61

Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50

What is linear regression?

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:

The mean of x is 3.5 and the mean of y is 150.

The variance of x is 2.5 and the variance of y is 2203.5.

The covariance of x and y is 607.5.

Using these values, we can calculate the slope of the regression line:

m = covariance of x and y / variance of x = 607.5 / 2.5 = 243

We can also calculate the y-intercept of the regression line:

b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5

Therefore, the equation for the linear function that best fits the given data is:

y = 243x - 16.5

Rounding both numbers to two decimal places, we get:

y = 243x - 16.50

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Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50

What is linear regression?

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:

The mean of x is 3.5 and the mean of y is 150.

The variance of x is 2.5 and the variance of y is 2203.5.

The covariance of x and y is 607.5.

Using these values, we can calculate the slope of the regression line:

m = covariance of x and y / variance of x = 607.5 / 2.5 = 243

We can also calculate the y-intercept of the regression line:

b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5

Therefore, the equation for the linear function that best fits the given data is:

y = 243x - 16.5

Rounding both numbers to two decimal places, we get:

y = 243x - 16.50

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Answer:

The correct answer is (b+2)

Step-by-step explanation:

(3b-7) + (-2b+9)

3b-7-2b+9

3b-2b+9-7

b+2 Ans

Answer:

b+2 is the answer of this expression.

Step-by-step explanation:

(3b-7) and (-2b+9)

3b+(-2b) + (-7+9)

(3b-2b) + 2

b+2

When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is used to determine how likely or unlikely an occurrence is to occur. An event's likelihood is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of occurrence. The symbol P stands for the probability of an occurrence A. (A). It is determined by dividing the number of positive results of event A by all the potential outcomes.

given

(a) The result of rolling 3 or 6 times is 6 + 9 = 15.

Experimental chance = (Total number of rolls) / (Number of times 3 or 6 were rolled) = 15/40 = 0.375

(b) The theoretical likelihood of rolling either a 3 or a 6 on a fair number cube is equal to the total of those odds, which is 1/6 + 1/6 = 1/3 = 0.333. (rounded to three decimal places).

(c) When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

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Answer: I really don't know I'm just trying to get a quest done sorry

The sum of the distinct prime factors is 16.

There are overall 24 factors of 792 among which 792 is the most significant factor and its prime factors are 2, 3, and 11.

Hence sum = 2 + 3 + 11 = 16

Answer:

B) 33 times.

Step-by-step explanation:

The total amount of pebbles is 50. There is 22 yellow pebbles.

Note that 3/2 * 50 is 75. 3/2 * 22 = 33.

He should expect to choose a yellow pebble B) 33 times.

Answer:

x = 42.9

Step-by-step explanation:

We can let 34 represent the reference angle.  Using this angle, we see that the side measuring 24 units is the opposite side and the side measuring x is the hypotenuse.

Thus, we can use the sine trig function which is

[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]

We plug in what we have into the equation above and solve for x:

[tex]sin(34)=\frac{24}{x}\\ x*sin(34)=24\\x=\frac{24}{sin(34)}\\ x=42.9189996\\x=42.9[/tex]

Answer:

Step-by-step explanation:

The intersection of two parallel lines; x = 10 metres.

Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.

The alternate interior angles are equal because of the parallel lines characteristic.

Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.

Setting these two angles equal to each other, we can get:

x+20 = 2x+10

Simplifying this equation, we get:

x = 10.

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Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:

lwh = 600

For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:

l(3w)h = 3lwh = 3(600) = 1800 cubic feet

Therefore, the volume of the neighbor's pool is 1800 cubic feet.

Step-by-step explanation:

Answer:

This table represents a linear relationship that is also proportional:

x 0 1 2

y −4 0 4

Answer:

The second table represents a linear relationship that is also proportional.

To check if a relationship is proportional, we need to see if the ratio of y to x is constant for all values of x and y. In other words, if we divide any y value by its corresponding x value, we should get the same number for all values.

Let's check the ratio for each table:

Ratio for the first table:

-3/2 = -1.5

0/3 = 0

3/4 = 0.75

The ratio is not constant, so this relationship is not proportional.

Ratio for the second table:

-2/4 = -0.5

-1/2 = -0.5

0/0 = undefined

The ratio is constant (-0.5), so this relationship is proportional.

Ratio for the third table:

0/(-2) = 0

1/1 = 1

2/4 = 0.5

The ratio is not constant, so this relationship is not proportional.

Ratio for the fourth table:

-4/0 = undefined

0/1 = 0

4/2 = 2

The ratio is not constant, so this relationship is not proportional.

Therefore, the second table is the only one that represents a linear relationship that is also proportional.

We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Based on the sample bag of Dream Pop candy, we can calculate the probability of getting each flavor.

If all bags have equally likely flavors, then each flavor should have the same probability of being selected.

However, we can see from the sample that this is not the case.

To communicate this to the boss, we can calculate the probability of getting two different flavors and compare them.

For example:

The probability of getting a grape flavor is 16/40 or 0.4

The probability of getting a lemon flavor is 6/40 or 0.15

These probabilities are not equal, indicating that the flavors are not equally likely.

We can also compare the probabilities of getting two other flavors, such as:

The probability of getting a strawberry flavor is 12/40 or 0.3

The probability of getting a blueberry flavor is 6/40 or 0.15

Again, these probabilities are not equal, further indicating that the flavors are not equally likely.

Therefore,

We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.

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