A farmer has sixty three goats and twenty times as many sheeps. if the number of sheep he has is thirty times the number of his chickens , find the number of legs of the animals​

The equation that shows the relationship b/w x and y is

y= 3x

Generally, An equation is a mathematical statement that demonstrates that two mathematical expressions have the same value. This is the most basic version of the definition of an equation in algebra. For example, the phrase "3x + 5" = 14 is an equation, in which the two expressions "3x + 5" and "14" are separated by the symbol for "equal."

A mathematical expression is considered to be an equation if it includes the equals sign (=). Equations often use algebraic notation. Mathematicians turn to algebra when they are unsure about the value of a certain number in a computation.

In mathematics, an equation is represented by the conjunction "=", which is placed between two expressions. The "left-hand side" and "right-hand side" of an equation refer to the expressions that are located on the left and right sides of the equals sign, respectively.

Since Sipho’s mum will double the amount saved

let the amount saved be x

Therefore the equation for the total amount will be

y=x+2x

simplfing

y=x(1+2)

Therefore

y = x + 2x

y= 3x

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The rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.

This can be interpreted as follows:

In each stage, the number of black triangles is determined by the number of triangles that were present in the previous stage. This suggests that the sequence may be formed by repeatedly adding a certain number of triangles to the previous stage, with the number of added triangles equal to the number of triangles present in that stage.

Therefore, the rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.

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Answer: 3 times

Step-by-step explanation:

edge 2023

25x -15y -40z +45 =0 is the equation of the plane that passes through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1).

Let the given points be P(2 , 1 , 2) ,Q(3 , -8 , 6) and R(-2 , -3 ,1)

PQ = (3-2 , -8-1, 6-2)

     =(1 , -9, 4)

PR = (-2 -2,-3-1 ,1-2)

     =( -4 ,-4 ,-1 )

→PQ * →PR = [tex]\left[\begin{array}{ccc}i&j&k\\1&-9&4\\-4&-4&-1\end{array}\right][/tex]

             =(9+16)i + (-16+1)j + (-4 -36)k

              =  25i - 15j - 40k

Therefore , the normal vector to the plane is

→n = (25 , -15 ,-40)

Since , the plane passes through all the three points we can choose any point to find its equation .So,the equation of the plane through the point P(2,1,2) with normal vector

→n = (25,-15,-40) is

25(x-2) - 15(y-1) -40(z-2) =0

⇒25x - 50 -15y + 15-40z+80=0

⇒25x -15y -40z +45 =0

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Answer:

log10 195 = 2.29

Answer:

I found this

To solve for the value of log10 19.5, we can use the property of logarithms that states:

loga(b^c) = c * loga(b)

In this case, we can express 19.5 as 10^2.29:

19.5 = 10^2.29

So, we can find the logarithm of 19.5 by solving for c:

log10(19.5) = log10(10^2.29)

By using the property of logarithms mentioned above, we can simplify the equation to:

log10(19.5) = 2.29 * log10(10)

Since log10(10) = 1, we can further simplify the equation to:

log10(19.5) = 2.29

Therefore, the value of log10 19.5 is 2.29.

The probability of success is 0.2. The result is obtained by adding the probability of getting 9 and the probability of getting 10.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

The probability of A or B can be calculated by

P(A or B) = P(A + P(B)

A 10-sided die is rolled. Each side of the die is labeled with a number from 1 to 10. A number of 9 or 10 should be rolled to make a player succeed. Find the probability of success!

The number of each side of die are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

The probability of success is the probability of getting 9 or 10.

P(9) = 1/10

P(10) = 1/10

P(9 or 10) = P(9) + P(10)

P(9 or 10) = 1/10 + 1/10

P(9 or 10) = 2/10

P(9 or 10) = 1/5

P(9 or 10) = 0.2

Hence, the probability that a player would succeed is 0.2.

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The frequency shown in the given sinusoidal graph is:

f = 1/T (s⁻¹).

Frequency means the rate at which something occurs or is repeated over a particular period of time or in a given sample.

A sinusoidal function is a periodic function because the basic shape repeats indefinitely in both the positive and negative directions. The frequency of a sine wave is defined as the number of cycles it completes in a given interval and is the reciprocal of the period.

In a mathematical language, this is written as:

f = 1/T

Where,

f = frequency,

T = Period

To get the period, just subtract the x-coordinates of two consecutive peaks, so:

T = п - 0

T = п (s)

Therefore, the frequency is:

f = 1/T (s⁻¹).

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Answer:First we need to simplify the left side of the equation:

12,5(3x-1)+132,4 = 12,5*3x - 12,5 + 132,4 = 37,5x + 120,9

Now we need to simplify the right side of the equation:

2,8-4x = 2,8 - 4x

Now we have to set the two sides equal:

37,5x + 120,9 = 2,8 - 4x

Now we have to move all the x terms to one side of the equation:

37,5x - 4x + 120,9 = 2,8

Next step is to combine like terms:

33,5x + 120,9 = 2,8

Subtracting 120.9 from both sides of the equation:

33,5x = -118.1

Dividing both sides by 33,5

x = -3,54

So the solution of the equation is x = -3,54

Step-by-step explanation:

The first number will be 8 and the second number will be 7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The sum of the two numbers is 15. The difference between five times the first number and Three times the second number is 19.

Let the first number be 'x' and the second number be 'y'. Then the equations are given as,

x + y = 15                 ...1

5x - 3y = 19             ...2

From equations 1 and 2, then we have

5x - 3(15 - x) = 19

5x - 45 + 3x = 19

8x = 64

x = 8

Then the value of the variable 'y' is given as,

8 + y = 15

y = 15 - 8

y = 7

The first number will be 8 and the second number will be 7.

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Answer:

x = 13

Step-by-step explanation:

to solve this question you must know that angles in a triangle add up to 180 degrees

therefor 180 = 43 + 62 + (7x-16)

solve for x

180 = 43 + 62 + (7x-16)

180 = 105 + (7x-16)

Now, we can subtract 105 from both sides to get

75 = 7x-16

Next, we can add 16 to both sides to get

91 = 7x

Finally, we can divide both sides by 7 to get

x = 91/7

x = 13

So the value of x that satisfies the equation is 13

Answer:

x = 13

Step-by-step explanation:

Interior angles of a triangle sum to 180°.  Therefore:

[tex]\implies 62^{\circ}+43^{\circ}+(7x-16)^{\circ}=180^{\circ}[/tex]

[tex]\implies 62+43+(7x-16)=180[/tex]

[tex]\implies 105+7x-16=180[/tex]

[tex]\implies 7x+89=180[/tex]

[tex]\implies 7x+89-89=180-89[/tex]

[tex]\implies 7x=91[/tex]

[tex]\implies 7x \div 7=91 \div 7[/tex]

[tex]\implies x=13[/tex]

Depending on how many shots you add, a single mixed drink can be equivalent to more than one or two regular drinks. Keep in mind that a 1.25 oz. shot is equivalent to one normal drink.

What is a standard drink?

Approximately 14 grams of pure alcohol are present in one "normal" drink in the United States (or one alcoholic drink's equivalent).

                           This amount can be found in: 12 ounces of standard beer, which typically contains 5% alcohol. 12% alcohol in 5 ounces of wine is the normal amount. Approximately 40% alcohol is present in 1.5 ounces of distilled spirits.

What makes it a regular drink?

The amount of pure alcohol in various alcoholic beverages varies. Any alcoholic beverage with 10 grams of pure alcohol is referred to as a STANDARD DRINK. There are varying percentages of pure alcohol in various alcoholic beverages.

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Answer:

5x + 190 = 300

[tex]\frac{300-190}{5}[/tex]

Step-by-step explanation:

The equation

5x + 190 = 300 helps us to figure out how many minutes it will take for the tank to be empty.

5x + 190 = 300  Subtract 190 from both sides

5x + 190 - 190 = 300 - 190

5x = 110   Divide both sides by 5

[tex]\frac{5x}{5}[/tex] = [tex]\frac{110}{5}[/tex]

x = 22

It will take 22 minutes for the tank to be empty.

It is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.

To determine this:

A 95% confidence interval for a proportion gives us an estimate of the range of values where the true proportion is likely to fall. The interval (0.751, 0.863) means that we are 95% confident that the true proportion of math students who prefer to use a handheld calculator versus computer software for computations falls between 0.751 and 0.863.

Given this information, it is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.

In other words, based on the sample data and the construction of the confidence interval, there is strong evidence that the true proportion of math students who prefer to use a handheld calculator is above 75%.

It's important to note that the confidence interval is only an estimate of the true proportion, and it's possible that the true proportion is not exactly within this interval. However, the 95% confidence level means that if we were to repeat the study many times, in about 95% of the cases, the interval would contain the true proportion.

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Answer:

$45 would be the savings of option b

Step-by-step explanation:

A. $70*4=$280

B. $40*4=$160 + $0.25*300=$75

a-b =$45

Please see attached photo for better explanation

Answer:

88% of the coins are quarters.

To find out, you can convert the fraction 44/50 to a percentage by multiplying it by 100.

(44/50) * 100 = 88%.

The company made 42 candles from 5040 cm³ of wax.

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

Given the dimensions of the candle, which is in the shape of rectangular prisms

let l be the length, b be width and h be the height,

length = 5 cm

width = 2 cm

height = 12 cm

total wax needed for 1 candle is calculated by the volume of candle,

V = l x b x h

V = 5 x 2 x 12

V = 120 cm³

number of candles made by 5040 cm³ wax

number of candles = 5040/120

number of candles = 42

Hence, 42 candles are made.

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The complete question is,

A company makes wax candles shaped like rectangular prisms. Each candle is 5cm long, 2cm wide, and 12cm tall. If the company used 5040cm3 of wax, how many candles did they make?

The standard deviation of the mean was 1.256.

Now, in response to the question: We have given that, some stores print many coupons and advertisements on business receipts, resulting in exceptionally long receipts.

A curious customer makes the identical purchase at ten different stores and counts the length of the each receipt (in inches).

Here are the results,

8.25, 7.5, 5, 9.5, 12, 5.5, 9, 14, 11.5, 18.

Therefore, The value of the standard error of the mean is 1.256.

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The area of the triangle APB is 6.75 square inches.

We know that PA=PB=PC and that PC is perpendicular to FD. Thus C will be the midpoint of FD.

Draw a perpendicular from P to AB, let the point of intersection be Q.

We know that CQ = DB = 6 inches

That is PC + PQ = 6 inches

PQ = (6 - PC) inches

Consider triangle APQ, it is a right angled triangle, right angled at Q. So using Pythagorean theorem

PA² = PQ² + AQ²

PA² = (6 - PC)² + (AB/2)²

PA² = (6 - PA)² + (6/2)²

PA² = 36 - 12PA + PA² + 9

12PA = 45

PA = 3.75

So PA = PB = PC = 3.75 inches

Also PQ = 6 - PC = 2.25 inches

The area of a triangle can be found by using the formula:

area = (base * height) / 2.

In this case, the base, AB is equal to the length of the side of the square, which is 6 inches, and the height is equal to PQ. So the area of triangle APB is

= (6*2.25)/2

= 6.75 square inches.

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Answer:

Step-by-step explanation:

if 1 = 2 than 3 is 4

Answer:

5 4/9

Step-by-step explanation:

7/9 of 7

= 7/9 × 7

= 7/9 × 7/1

Multiply top×top and bottom×bottom

= 49/9

means 49÷9

9 goes into 49, 5 times. And 9 × 5 is 45. 49 - 45 is 4. So

49÷9 is 5 and 4 leftover.

49 ÷ 9

= 5 4/9

The slope intercept from of equation exists y = -0.25x -19.5.

The relationship between how a line's y coordinate and x coordinate change determines the slope of that line. The net modifications to the y and x coordinates, respectively, are denoted by y and x. In light of this, it is possible to express the change in y coordinate in relation to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given: A line that passes through points  (8, 13) and(-12, 18)

substituting the values, we get

m = ( 18 - 13)/ ( -12 - 8)

simplifying the above equation, we get

m = -0.25

Now, using slope intercept form

y - a = -0.25( x- b)

substitute the values in the above equation, we get

y - (13)= -0.25(x-(18))

y - 15= -0.25x-(-0.25 × 18))

simplifying the equation, we get

y = -0.25x - 4.5 -15

y = -0.25x -19.5

Therefore, the slope intercept from of equation exists y = -0.25x -19.5.

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The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.

What is null hypothesis ?

The null hypothesis is a statement that there is no statistical significance between the results of an experiment and a certain theoretical prediction or postulate. It is usually denoted by H0 and it is a statement of "no effect" or "no difference".

The null hypothesis is that the mean mpg of the vans is equal to the manufacturer's rating of 28.228.2 mpg, and the alternative hypothesis is that the mean mpg of the vans is less than the manufacturer's rating.

We can use the t-test statistic to determine the probability of observing a sample mean as extreme or more extreme than the one computed from the data, assuming that the null hypothesis is true.

The t-test statistic is: (sample mean - population mean) / (standard deviation/sqrt(sample size)) = (28.028.0 - 28.228.2) / (2.62.6 / sqrt(2727)) = -3.34

The p-value is the probability of observing a t-value as extreme or more extreme than -3.34, assuming that the null hypothesis is true. With a sample size of 2727, we can use a t-distribution table to find that the p-value is less than 0.01.

The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.

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It depends on the specific context and the nature of the graph. Without more information about the domain restriction and the graph, it is difficult to say exactly what effect changing the 2 to a 5 would have. However, in general, changing a value in a domain restriction would affect the range of possible input values for the graph and could potentially change the overall shape or behavior of the graph.

Scientists use math in experiments when they make measurements, analyze quantitative data, and make predictions based on this data.

This is known because Math is an integral part of Science which is why both subjects ( Science and Math ) are considered STEM subjects.

Scientists use math in an experiment to make measurements, analyze data, and make predictions.

For example, scientists use math to make precise measurements of physical quantities such as length, weight, and temperature. They also use math to perform calculations such as determining the concentration of a substance in a solution or the rate of a chemical reaction.

Scientists also use mathematical models and statistical analysis to analyze data and make predictions about the outcome of an experiment. They use mathematical equations to describe the relationships between different variables and to test hypotheses. They also use statistical techniques to determine the significance of their results and to make inferences about a larger population from a smaller sample of data.

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As per the given divisor and product, the value of e is 5.

The term divisor in math is defined as a number which divides another number and it is a part of the division process.

Here we have given that let us consider that s denote the set of all positive divisors of 60⁵

Here we also know that the product of all the numbers in s equals 60ⁿ for some integer n.

As per the given condition, the terms are written as,

=> s =  60⁵

=> s = 60ⁿ

Here we have to compare the given values then we the expression like the following,

=> 60⁵ = 60ⁿ

As per the rule of exponent, the value of e = 5.

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If a study concluded that among people with a certain​ virus, 99.2​% of tests conducted were​ (correctly) positive, while for people without the​ virus, 98.1​% of the tests were​ (correctly) negative.  the probability that a patient testing negative is truly free of the​ virus is 0.9967.

Probability (testing negative is truly free of the​ virus) =  (1- 0.29) (0.981) / (0.29) (1- 0.992) + (1- 0.29) (0.981)

Probability (testing negative is truly free of the​ virus) =  (0.71) (0.981) / (0.29) (0.008) + (0.71) (0.981)

Probability (testing negative is truly free of the​ virus) = 0.69651 / 0.00232 + 0.69651

Probability (testing negative is truly free of the​ virus) = 0.69651/ 0.69883

Probability (testing negative is truly free of the​ virus) =0.9967

Therefore we can conclude that the probability (testing negative is truly free of the​ virus) is 0.9967.

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The inequality that correctly compares the elevations is given as follows:

-7 and 7/10 > -10 and 9/10.

The four inequality symbols are given as follows:

The elevations are given as follows:

Those two elevations are given by mixed numbers, which are composed by both an integer part and a fractional part.

To compare which elevation is greater, we look at which one has the greater integer part. An integer part of -7 is greater than an integer part of -10, hence the inequality is given as follows:

-7 and 7/10 > -10 and 9/10.

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The z-score for the value 93, when the mean is 100 and the standard deviation is 3 is solved to be

Z scores is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of the parameters

mean, μ  = 100

standard deviation, σ = 3

sample score, X = 93

z score for the score of 93

z = (X - μ) / σ

substituting into the formula

z = (93 - 100) / 3

= -7 / 3

= -2.333

Hence we can say that the z score is 2.333

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Answer:2

Step-by-step explanation:

Therefore , the solution of the given problem of PMI comes out to be

6 ⁿ -1  is always divisible by 5.

A mathematical method known as mathematical induction is used to demonstrate that a claim, formula, or theorem holds true for every natural number. Step 1 (Base Step) demonstrates the truth of a statement for the starting value.

Here,

Given :  6 ⁿ -1  is divisible by 5

Let,

=> 6 ⁿ -1  

=> 6 ¹ - 1

=>5

P(k) is divisible by 5

P(k+1)=6

k+1−1=6.6k−1

=(5+1).6k−1

=5×6 k+6k−1

=5×6k+5m

=5(6k+m)

P(k+1) is divisible by 5

Therefore , the solution of the given problem of PMI comes out to be

6 ⁿ -1  is always divisible by 5.

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