Dominic fills some jars with chutney that
he has made.
Each jar weighs 230 g when it is empty
and can contain 300 cm³ of chutney.
8 full jars of chutney weigh a total of
5.68 kg.
Calculate the density of the chutney, in
g/cm³.
If your answer is a decimal, give it to
1 d.p.

Answer:

x(8 + 3x)

Step-by-step explanation:

8x + 3x^2

Find what is common between the two coefficients, which is x.

So place x as the multiplier:

x(8 + 3x) = will give you the same result (8x + 3x^2).

Hope you understood :)

The sum of numbers 4 and - 9 is, - 5.

And, A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The numbers are,

⇒ 4 and - 9

Now, Sum of the numbers 4 and - 9 as;

⇒ 4 + (-9)

⇒ 4 - 9

⇒ - 5

Thus, The sum of numbers 4 and - 9 is, - 5.

And,  A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.

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The denominator of the fraction at point Y is equal to 24.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Let the variable d represent the denominator of the fraction at point Y and since point Y is the same distance from 0 as point X, which is at 2/3 on a number line, this can be modeled by this mathematical expression:

8/d = 1 - 2/3

8/d = 1/3

Cross-multiplying, we have:

d = 8 × 3

d = 24.

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Answer:

Sophia's airplane flew 8.6 + 2.2 = 10.8 yards.

Franco threw his airplane 1.5 times as far as Sophia's airplane, which means that Franco's airplane flew 1.5 * 10.8 = 16.2 yards.

Therefore, Franco's paper airplane flew 16.2 yards.

Answer:

Franco went 16.2 yards

Step-by-step explanation:

8.6 + 2.2 = 10.8

10.8 x 1.5 = 16.2

The given expression (3p)³ without exponents is 27×p×p×p.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given exponential expression is (3p)³.

Here, (3p)³=3p×3p×3p

= 27×p×p×p

Therefore, the given expression (3p)³ without exponents is 27×p×p×p.

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Answer: 4

Step-by-step explanation: Amplitude has to do with how high and low the function goes according to the midline. The midline for this function is at -3. The maximum point is 1, and the minimum point is -7. The function goes up 4 units and down 4 units

Answer:

Amplitude = 4

Step-by-step explanation:

The amplitude of a sinusoidal function is the height (vertical distance) from the midline to the peak (or trough).

To calculate the amplitude, simply divide the vertical distance between the maximum and minimum y-values by 2.

From inspection of the given graph:

Therefore:

[tex]\implies \sf Amplitude = \dfrac{1-(-7)}{2}=\dfrac{8}{2}=4[/tex]

Answer: 5/8 "=" 10/16

Step-by-step explanation: To compare the fractions 5/8 and 10/16, we need to find a common denominator. In this case, the least common multiple of 8 and 16 is 16.

So, we can write the fractions as:

5/8 = (52)/(82) = 10/16

So the fractions are equal, therefore, the symbol that correctly compares them is = (the equal sign).

Answer: =

Step-by-step explanation:

In order to compare the fractions, we must make sure that the fractions have common denominators. Because 8 is a factor of 16, we will convert 5/8 into a fraction that has a denominator of 16. To do this, we need to multiply the numerator and denominator by the same number, in this case, 2 since that is what multiplies by 8 to get 16. (5/8) * (2/2) = 10/16 (you can just multiply across the top and bottom to solve). Now, we can compare. 10/16 is the same as 10/16, so an = would be the appropriate symbol. Hope this helps!

Answer:

1:3 5/9

18/18=1 64/18=3 5/9

Answer:

Step-by-step explanation:

To calculate how long it will take John to recover his investment, we need to divide the cost of the degree by the difference in income between the two options.

$10,000 / ($35,000 - $20,000) = $10,000 / $15,000 = 0.67 years or 0.67*12 = 8 months.

So, it will take John 8 months to recover his investment if he goes to school.

Please note that this is a simplified calculation as it does not take into account the cost of living, taxes, and other expenses.

Based on the graph of this quadratic function with vertex (-1, -4), the domain and the range are as follows;

Domain = {-3, 0.5}.

Range = {-4, ∞}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: The vertex of any quadratic function represents the minimum of the given function.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:

Domain = -3 < x < 0.5 or [-3, 0.5].

Range = -4 < y < ∞ or [-4, ∞].

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Jonathan deposited $847 in his saving account.

This bank deposit slip is the record of the total amount that a person is depositing into a bank account. It includes the details of the items being deposited, that is, the number of checks and notes or coins of each type in the form of cash.

Given,

Amount in checks = $40 + $50 + $35 = $125

8 fifty-dollar bills = 8 × $50 =$400

12 twenty-dollar bills = 12 × $20 = $240

12 ten-dollar bills = 12 × $10 = $120

8 five- dollar bills = 8 × $5 = $40

22 1-dollar bills = 22 × $1 = $22

Subtotal = $125 + $400 + $240 + $120 + $40 + $22 = $947

Less cash = $100

Total = $947 - $100

Total = $847

Hence, $847 is the total deposited amount by Jonathan.

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Answer:

c.

Step-by-step explanation:

that is easy.

a matrix multiplied by a constant is multiplying every element in the matrix by that constant.

and subtracting a matrix from another is subtracting the elements on each position.

it is a simile as that.

for that reason I only need to look at the first, top left element to determine the correct answer :

-1×2 - 4×7 = -2 - 28 = -30

so, c. is the right answer.

the calculation in full :

2A =

-2 18 4

20 -20 4

-10 12 -10

4B =

28 -4 -4

24 -16 -12

-40 40 -28

so, 2A - 4B =

-30 22 8

-4 -4 16

30 -28 18

Answer: 3 x y (2 x + 5 y)

Step-by-step explanation:

im not really sure but i gave it a try

The number of seniors that are on academic watch than freshman will be 868.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, since there are there are 2435 seniors and 1567 freshmen on academic watch. The number of seniors that are on academic watch than freshman will be:

= 2435 - 1567

= 868

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Complete question

In a school, there are 2435 seniors and 12567 freshmen on academic watch. How many more seniors are on academic watch than freshman

Since George can build a laptop twice as fast as Kurt and working together takes them 3 hours, an equation which you would use to determine how long it will take Kurt working alone is: D. 1/t + 1/2t = 1/3.

In order to determine the amount of time it would take Kurt working alone, we would have to assign variables to the amount of time taken by George to build a laptop and the amount of time taken by Kurt to build a laptop, and then translate the word problem into an algebraic equation (expression) as follows;

Since George can build a laptop twice as fast as Kurt, an equation which models this situation is given by;

g = 2t     .....equation 1.

Next, we would write an algebraic equation (expression) that models the combined work rate;

1/c = 1/t + 1/g     .....equation 2.

Substituting equation 1 into equation 2, we have the following:

1/3 = 1/t + 1/2t

1/t + 1/2t = 1/3.

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The correction of the three capitalization that where wrongly written in the given statement are

The capitalization of a word is defined as the use of capital letters for the first word of a sentence and for all proper nouns.

The sentence, ' Darnell is Writing an Article about an early Period of art history' contains proper nouns such as art and history which should be in capital letters.

The word 'written' should be in a small letter because it didn't start the sentence.

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Answer: We can use the Squeeze theorem to find the limit.

We know that:

x^2 + y^2 >= 0 for all (x, y)

Also,

|3xy| <= 3|x||y| <= 3x^2 + 3y^2

So,

|3xy/(x^2 + y^2)| <= 3(x^2 + y^2)/(x^2 + y^2) = 3

As we approach (x, y) = (0, 0), x^2 + y^2 becomes arbitrarily close to 0, so the right-hand side of the inequality becomes arbitrarily close to 3, and the left-hand side becomes arbitrarily close to 0.

Therefore,

lim[(x,y)->(0,0)] (3xy/(x^2+y^2)) = 0

Hence, by the sandwich theorem, we can say that the limit of the function is 0.

Step-by-step explanation:

3y = 4x + 2 is a linear equation that satisfies the graph.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given, Few coordinates of a linear function to make the equation of line we need only two coordinates.

general formula for linear equation is y = mx + c

where, m = slope

c = constant

General formula for slope m = (y₂ - y₁)/(x₂ -x₁)

Since graph passes through the points(3, 6) and (0, 2)

Slope m = (2 - 6)/ (0 - 3)

m = -4/-3 = 4/3

Thus, equation of line will be

y = 4/3x + c

Since the Line passes through (0, ,2 ) these point will satisfy the above equation

2 = 4/3 * 0 + c

=> c = 2

substitute the values

y = 4/3x + 2

3y = 4x +6

Therefore, equation of line that relates with the graph is 3y = 4x + 6.

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Answer:

-----------------------------------------

To find the remaining credit plug in the value of x = 30 into equation and calculate:

The 1st table is proportional and the 2nd table is not proportional.

The equation y = 3x is proportional and the equation y = 2x + 1 is not proportional.

The 1st graph is not proportional and the 2nd graph is proportional.

A proportional relationship is a type of mathematical relationship in which two variables are directly proportional to each other. This means that as one variable increases, the other also increases in a consistent ratio.

The equation for a proportional relationship is typically written as y = kx, where y and x are the variables and k is a constant ratio of proportionality. In other words, y is always k times x.

From the 1st table, let's the ratios of pencils to students (k). That:

k = 3/1 = 3

k = 6/2 = 3

k = 9/3 = 3

12/4 = 3

Thus, this is proportional.

From the 2nd table, the ratios y to x are not the same. Thus, this is not proportional.

The equation y = 3x is proportional.

The equation y = 2x + 1 is not proportional.

The 1st graph is not proportional because it does not start from the origin.
The 2nd graph is proportional because it starts from the origin.

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Answer:13/5

Step-by-step explanation:The answer would be 13/5 because that is the trigonometric ratio.

Answer: An obstacle course is a series of challenging physical obstacles that must be completed in order to finish the course. To find out how many kilometers long the obstacle course is, you need to add up the distance that Caleb runs, jumps crawls, and dribbles.

First, we need to convert the 500 meters to kilometers by dividing it by 1000.

500 meters / 1000 = 0.5 kilometers

Then, we need to add the distance that Caleb crawls through the tunnel, which is 20 meters.

20 meters = 0.02 kilometers

Finally, we need to add the distance that Caleb dribbles the soccer ball, which is 100 meters.

100 meters = 0.1 kilometers

To find the total distance of the obstacle course, we need to add the distance that Caleb runs, jumps, crawls, and dribbles:

0.5 + 0.02 + 0.1 = 0.62 kilometers

So the obstacle course is 0.62 kilometers long.

Step-by-step explanation:

The inequality that we can write is:

x - 2.45 ≥ 4.6

And the solution is x ≥ 7.05

Here we want to write in mathematic form the following sentence:

"2.45 less than a number x is greater than or equal to 4.6 "

First, "2.45 less than a number x...."

Is written as the difference:

x - 2.45

And that is greater or equal to 4.6, then we will have an inequality, and it will be:

x - 2.45 ≥ 4.6

We can solve that for x by adding 2.45 in both sides, so we will get:

x ≥ 4.6 + 2.45

x ≥ 7.05

That is the inequality solved.

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The inequality 2.45 less than a number x is greater than or equal to 4.6 as an equation is

[tex] x \: \geqslant 6.95[/tex]

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

The question can be expressed mathematically as:

x - 2.4

[tex] \geqslant [/tex]

4.5

By solving the above inequality,

We have x

[tex] \geqslant [/tex]

4.5 + 2.5

Hence, the inequality gives us

[tex]x \: \geqslant 6.95[/tex]

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Quotient of x⁴ - 13x² + 36 ÷ x-3 = x³+3x²-4x-12

Factored form of x⁴ - 13x² + 36 = (x+3)(x+2)(x-2)(x-3)

Zeros of  x⁴ - 13x² + 36 = -3, -2, 2, 3

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

Given,

f(x) = x⁴ - 13x² + 36 and its factor (x-3)

Using synthetic division

x⁴ - 13x² + 36 ÷ (x-3) = x³+3x²-4x-12

Quotient = x³+3x²-4x-12

= (x³+3x²)-(4x-12)

= x²(x + 3) - 4 (x + 3)

= (x+3)(x² - 4)

= (x+3)(x+2)(x-2)

x⁴ - 13x² + 36 = (x³+3x²-4x-12) (x-3)

Factored form

x⁴ - 13x² + 36 = (x+3)(x+2)(x-2)(x-3)

By factors, zeros are:

x+3 ⇒ x = -3

x+2 ⇒ x = -2

x-2 ⇒ x = 2

x-3 ⇒ x = 3

Hence, x³+3x²-4x-12 is the quotient of x⁴ - 13x² + 36 ÷ x-3 .

(x+3)(x+2)(x-2)(x-3) is the factored form of x⁴ - 13x² + 36.

x⁴ - 13x² + 36 has zeros = -3, -2, 2, 3

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The slope of this line is equal to 8/3.

The two additional points on the line are (-1, 13/3) and (1, 29/3).

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope of the data points as follows;

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

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (7 - (-1))/(0 - (-3))

Slope, m = 8/3

At point (0, 7), an equation of this line can be calculated in slope-intercept form as follows:

Note: The y-intercept is equal to 7.

y = mx + c

y = 8x/3 + 7

For the additional points, when x = 1 we have:

y = 8(1)/3 + 7

y = 8/3 + 7

y = 29/3

When x = -1, the value of y is given by;

y = 8(-1)/3 + 7

y = -8/3 + 7

y = 13/3

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The algebraic fraction which is equivalent to the given expression in which case, the denominator is 24a³b² as required is; 15b³ / 24a³b².

As evident in the task content; the given algebraic expression whose equivalent is to be determined is; 5b / 8a³.

However, to determine an equivalent expression whose denominator is; 24a³b²; one must determine the quotient of 24a³b² and 8a³.

= 24a³b² / 8a³.

= 3b²

On this note, it follows that the numerator and denominator of the given algebraic fraction can each be multiplied by 3b² in order to determine the equivalent expression.

= ( 5b • 3b² ) / ( 8a³ • 3b² )

= 15b³ / 24a³b².

Ultimately, thee required equivalent algebraic fraction is; 15b³ / 24a³b².

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Answer:

4. So Adrian can buy 3 more cd's at the sale price.

5. 36 km every week.

Step-by-step explanation:

Adrian has enough money to buy 3 cd's at $16 each. If the cd's are on a sale and are sold at a discount price of $12, he can buy more cd's because the price is cheaper. To find out how many more cd's he can buy, you can subtract the original cost of the cd's from the sale price of the cd's and then divide that amount by the sale price of the cd's.

3 cd's x $16 = $48

$48 - $12 = $36

$36 / $12 = 3

Rehman and his father jog to the park 3 km away from their house and back every evening except Sundays, so they jog a total of 6 km per day. To find out how many kilometres they jog per week, you need to multiply the distance they jog per day by the number of days they jog in a week (7 days - 1 Sunday).

6 km/day x 6 days/week = 36 km/week

So Rehman and his father jog 36 km every week.

Answer:

16pi =2pi r

pi are cancelled

r=16/2

r=8m

area of circle =pi r²

22/7×64

area=201.15m²

Step-by-step explanation:

circumference of circle is 2pie radius

area of circle is pi r²

Answer:

Step-by-step explanation:

Yes, Monica is correct. When dealing with simple interest, the amount of interest earned is determined by the principal amount, the interest rate, and the time the money is invested. Since Monica and Paul both have different principal amounts and interest rates, the amount of interest each of them earns in one year will be different. Monica's account has a higher interest rate of 3.4%, so she will earn more interest in one year compared to Paul's account, which has a lower interest rate of 2.6%.