11. John is building a wall. When he uses 750 bricks, the wall is 6 metres long and 1.25m high.
John wants the finished wall to be 10 metres long and 1.25 metres high.
How many more bricks does John need to finish the wall?
(Total 3 marks)

Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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Answer:

multiply 3 to the second eqn

Answer:

c the answer is c

Step-by-step explanation:

Answer:

C

I hope this helps

Answer:

517x

Step-by-step explanation:

the product of a number and 517 is 517x

517 × x = 517x

Answer:

More than happy to help with your homework:

500 miles = 50 gallons

(Divide both sides of the EQ by 50)

10 miles = 1 gallon

(Divide both sides by gallon)

10 miles per gallon

Answer:

\(l\leq 46.75\)

Step-by-step explanation:

Put the closed endpoint at 46.75 with the arrow pointing left.

Answer:  \(\ell \le 46.75\)  (fourth choice)

Graph has a closed endpoint at 46.75 and the ray pointing to the left (i.e. shading is to the left).

Check out the diagram below.

==================================================

Explanation:

The phrasing "at most" means that's the highest ceiling possible. The longest the cape can be is 46.75 inches. So it could be this length or shorter.

If \(\ell\) is this length, then either \(\ell = 46.75\) or \(\ell < 46.75\)

We can combine those two statements into the final answer of \(\ell \le 46.75\)

The graph involves a closed point at this marker to include the endpoint (in contrast an open hole would leave the endpoint out). The shading is to the left to include every value smaller than 46.75

Realistically the smallest \(\ell\) can get is \(\ell = 0\), but we don't have to worry too much about this. This is because zero isn't anywhere near these shown values on the number line.

Answer:

a) The probability is 0.5557 = 55.57%.

b) The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.

c) Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean weight of 0.8616g and a standard deviation of 0.0518

This means that \(\mu = 0.8616, \sigma = 0.0518\)

a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.

This is 1 subtracted by the pvalue of Z when X = 0.8542. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{0.8542 - 0.8616}{0.0518}\)

\(Z = -0.14\)

\(Z = -0.14\) has a pvalue of 0.4443

1 - 0.4443 = 0.5557

The probability is 0.5557 = 55.57%.

b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.

Sample of 447 means that \(n = 447, s = \frac{0.0518}{\sqrt{447}} = 0.00245\)

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.8542 - 0.8616}{0.0245}\)

\(Z = -3.02\)

\(Z = -3.02\) has a pvalue of 0.0013

1 - 0.0013 = 0.9987

The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.

c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?

Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.

Answer:

undetermined  or most likely Tasmania

Step-by-step explanation:

Based on the choices of experts in the first round of the Australian netball competition, we can conclude that Victoria played against WA. This is because, out of the common tips, WA was tipped by an expert who also tipped Victoria and didn't tip Queensland. Therefore, WA is the likely team that Victoria played against.

To identify which team Victoria played in the Australian netball competition we can reason through our experts' tips. The experts' tips overlap at Queensland and WA as indicated by Expert A and Expert B. However, Expert C tipped Victoria, and they did not tip Queensland which tells us that Victoria did not play against Queensland, leaving us with WA. Hence Victoria must've played against WA.

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Answer:

120 different words

Step-by-step explanation:

The max longest word has 4 letters

So the word can consist of 1 letter. The number of such wordds is 3 (A,O or M)

The word can consist also of 2 letters ( letters can be repeated in the word-

the word like AA or MM are possible). The number of such words is 3*3=9

The word can consist also of 3 letters ( letters can be repeated in the word-

the word like AMA or MMM are possible). The number of such words is 3*3*3=27

The word can consist also of 4 letters ( letters can be repeated in the word-

the word like AAAA or MAOM are possible). The number of such words is 3*3*3*3=81

So total number of words is 3+9+27+81=120

When proving the properties of logarithms when exponents must be used, the property that is used in all of these is D. \(log_{b} (b^y) = y\)

When proving any property of logarithms that have to do with exponents, one property that should always be used is  \(log_{b} (b^y) = y\).

Expressing y as a product of \(log_{b} (b^y)\) is the most basic property of using exponents on logs because it has both product, quotient, and power rules of logarithms.

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Answer:

4t*4t*4t*4t*4t

Step-by-step explanation:

Therefore ,the value of a given fraction is equal to 10/12, which equals 5/6, after resolving the given problem.

To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the excess to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the fraction or reduction of a complex fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces.

Here,

Given : 5/8 X 4/3

=> 5/8 X 4/3 = 20/24

on condensing,

10/12 = 5/6

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There are 120 different ways to create a path to 3 different roller coasters at Six Flags.

There are a total of 10 choose 3 ways (120) to choose 3 roller coasters out of the 10 available at Six Flags. To calculate this, we can use the combination formula.

The combination formula is:

In this case, n is 10 and r is 3, so the total number of possible combinations is

To calculate the number of combinations without using a formula, we can use the following method: Start with the first roller coaster, then add a second roller coaster, then a third. There are 10 choices for the first roller coaster, then 9 for the second, and 8 for the third. This results in:

which is 6 times more than the 120 calculated by the combination formula. This is because the combinations ABC and CBA are the same, and so are other combinations that are just permutations of each other.

Therefore, there are 120 different ways to create a path to 3 different roller coasters at Six Flags.

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Answer:

  8m^21/y^3

Step-by-step explanation:

The relevant rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

__

There is nothing here to solve. The expression can be simplified as follows:

  \(\left(\dfrac{4m^3y}{2m^{-4}y^3}\right)^3=\left(2\dfrac{m^{3-(-4)}}{y^{3-1}}\right)^3=\left(\dfrac{2m^7}{y^2}\right)^3 =\boxed{ \dfrac{8m^{21}}{y^6}}\)

__

Additional comment

We cannot tell if your variable is v or y. We have assumed y. If it is v, you can make the necessary replacement.

Answer:

3,2 °C

Step-by-step explanation:

40,2 °C - 37 °C = 3,2 °C

Answer:

First option, (4, -6)

Step-by-step explanation:

Scaled by 2. Multiply each coordinate of point C by 2.

(2*2, -3*2) = (4, -6)

Circle 1 has center at (0, 0)

The tangent passes through the center and point (1, -2).

Equation of tangent at (1, -2):

If the same line is tangent to circle 2 then they have one common point.

Solve the system:

Substitute x:

We see only one point of contact, (3, -1), this proves the line is tangent to circle 2 as well.

Given circle:

Rewrite the equation of the circle as:

The center is (7/6, 1) the radius is √229/36

The length of the tangent t is the leg of the right triangle with another leg r being the radius and the hypotenuse d being the distance between the center and the external point:

Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:75 ithink

Step-by-step explanation:

Answer:

Your answer would be $376.88

Step-by-step explanation:

Easiest way to explain would be to take 5.25 and divide it by 12. That gives you 0.4375

Take 0.4375 and multiply by 3 for 1.3125

1.3125% of 372 = 4.8825

4.8825 + 372 = 376.8825 or $376.88

Hope this helped! - Zac

The graph represents a functional relationship between two variables X and Y. We get y=3 for the value x=2

Domain is defined as the set of values of independent variables.

In the question, all x coordinates are domain.

In a function, for each domain we get a possible output from the dependent variables which is termed as range. In this graph, the y coordinates are range because y value is dependent on x value.

The graph shows five points are plotted on XY coordinate system that represents a relationship between independent variable X and dependent variable Y.

hence, this graph is plotted from a function.

from the graph we get the domain as {-4, -2, 0, 2, 4}

the ranges are = {-3, -2, -1, 1, 3}

we get, y=3 for the value of x= 2  

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Answer:

1/17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

17

To take the reciprocal of the number, we simply take its fraction form and flip it:

17 = 17/1

Flip

1/17

Answer:

The calf raiser uses 960 oz of milk replacer for 15 calves, so each calf gets 960 oz / 15 = 64 oz of milk replacer.

To convert this to quarts, we need to divide by 32 (since there are 32 oz in a quart)

64 oz / 32 oz/quart = 2 quarts

Each calf gets 2 quarts of milk replacer and the calf raiser needs to add 34 as much water as milk replacer

So the total amount of water she needs is 2*34 = 68 quarts

To convert the quarts of water to ounces we need to multiply by 32 (since there are 32 oz in a quart)

68 quarts * 32 oz/quart = 2176 oz of water.

So the calf raiser needs 2176 ounces of water to mix with the milk replacer for 15 calves.

Answer:

30% of the sodas were regular sodas

Step-by-step explanation:

Add 21 and 49 to get the total number of sodas and 21+49=70. To get the percentage, divide 21 by 70 (21÷70) is 0.3 or 30%.

To check, do 30% (or 0.3) • 70 and you will get 21.

Answer:

Yes

Step-by-step explanation:

7:14=1:2

3:6=1:2