Mato is making a leather belt inlaid with beads. On the first day there were b beads on the belt. On
the fourth day, there were b³ beads on the same belt. There were 216 beads on the belt on the
fourth day.
How many beads were on the belt on the first day?

Answer:

the answer is 39 and 14.

The solution is, the numbers are 20 and 29.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Here, we have,

given that,

The sum of two numbers is 49

and the difference between these two numbers is 9.

let, the numbers are x & y

so, we get,

according to question:

x+y = 49 ...1

x-y = 9 ....2

so, simplifying we get,

2x = 58

or, x = 29

so, we get,

y = 20

Hence, The solution is, the numbers are 20 and 29.

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The correct reason for the statements below by dragging and dropping the correct reason from the bank are mentioned below:

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Statements

Reasons

1.  ∠2 and ∠4 are vertical angles  -  Given

2. ∠2 and ∠3 are a linear pair

   ∠3 and ∠4 are a linear pair          - Definition of a linear pair

3. ∠2 and ∠3 are supplementary     - Definition of supplementary

   ∠3 and ∠4 are supplementary

4. m∠2 + m∠3 = 180°

   m∠3 + m∠4 = 180°         -  Linear Pair Theorom

5. m∠2 + m∠3 = m∠3 + m∠4  - Substitution property of equality

6. m∠2 = m∠4  - Subtraction property of equality

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Kevin's kick can be considered the best among the four.

To determine the most impressive kick, we can compare the distances and heights achieved by each player.

Andre's kick reached a maximum height of 17 yards and landed 48 yards away from the goal.

Juana's kick followed the path y = -x + 14 - 24, where y represents the height of the ball in yards and x represents the horizontal distance from the goal line. From the graph, we can estimate that her kick landed about 38 yards from the goal and reached a maximum height of 14 yards.

Kevin's kick is shown in the graph, indicating that it landed approximately 19 yards from the goal and had a peak height of 20 yards.

Emiko's kick reached a maximum height of 18 yards and landed approximately 20 yards from the goal.

Considering these measurements, Kevin's kick stands out. It traveled the farthest, landing closest to the goal line, and it achieved the highest height, reaching 20 yards. Consequently, Kevin's kick can be considered the best among the four.

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Answer:

a

Step-by-step explanation:

The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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The first, second, third, and fourth consecutive even integers must be greater than 10, 12, 14, and 16 respectively.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let the four consecutive even integers be n, (n + 2), (n + 4) and (n + 6).

Such that twice the sum of the second and third exceeds 3 times the first by 32.

2{(n + 2) + (n + 4)} > 3(n) + 32.

2n + 4 + 2n + 8 > 3n + 32.

4n - 3n > 32 - 12.

n > 10.

So, the consecutive even numbers must all be greater than 10.

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Answer

6 is the correct answer.

Step-by-step explanation:

You need to know sin(60) = root(3)/2 = a/(4root(3)), then you can solve for 'a', get a = 6.

Answer:

23 measure

Step-by-step explanation:

because 56/7 = 8

so 104/8=23

Answer:

13 measures

Step-by-step explanation:

for every 7 measures, there is 56 beats. and if you want to find out how many beats there are per measure, you would do 56 ÷ 7 = 8.

Now that you've found thay there are 8 beats per measure, you would divide 104 by 8 to find out how many measurs there are.

104 ÷ 8 = 13

Answer:

A= \(\pi\)r²

Step-by-step explanation:

the area of a circle

Answer:

18m

Step-by-step explanation:

Width= 432m2 ÷ 24m

= 18m

Answer:

Step-by-step explanation:

432m^2 / 24m = 18 m is the width of the garden plot

Given: 2(4x - 3) = 2(x + 2) + 8

Required: The value of x

Explanation:

Opening the brackets

Further

So

Final Answer: Option A is correct.

Value of x = 3 that is option A

Here we are given with the equation as,

2(4x-3) =2(x+2) +8

Now solving both left hand side and right-hand side

taking left hand side,

2(4x-3)

2 X 4x + 2 X (-3)

8x - 6

Now solving right hand side,

2(x+2) +8

2x + 4 +8

2x+ 12

Now according to question equating both left hand side and right-hand side,

8x - 6 = 2x + 12

Now transposing variables and constants on left hand side and right-hand side respectively,

8x - 2x = 6 + 12

6x = 18

x= 12 / 6

x = 3

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Answer:

see below

Step-by-step explanation:

519 sold

studnets = x

non students = y

so x+y =519, so x = 519-y

3x+5y =1909

so 3(519-y) +5y = 1557 +2y =1909

2y = 352

y=176 non students

x = 519-176 = 343 students

Answer:

The answer is -5. To do this you first draw your number line and label it from +7 to -10. You then count from from seven till the 11th number which in this case it's -5

By solving the linear equation it can be obtained that

The value of x is 2

What is a linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

0.3 = 0.5x - 0.7

0.5x = 0.3 + 0.7

0.5x = 1

x = \(\frac{1}{0.5}\)

x = 2

The solution of this linear equation is x = 2

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9514 1404 393

Answer:

  (c)  1/(36·a^4·b^10)

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

  a^-1 = 1/a

__

  \(\left(\dfrac{(2a^{-3}b^4)^2}{(3a^5b)^{-2}}\right)^{-1}=\dfrac{(3a^5b)^{-2}}{(2a^{-3}b^4)^2}=\dfrac{3^{-2}a^{-10}b^{-2}}{2^2a^{-6}b^8}=\dfrac{1}{3^22^2}a^{-10-(-6)}b^{-2-8}\\\\=\boxed{\dfrac{1}{36a^4b^{10}}}\)

Answer:

30 centimeters

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The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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Answer:

Step-by-step explanation:

Answer:

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Answer:

2

Step-by-step explanation:

This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.

Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

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Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

The value of the given functions are:

(i) f + g = x² + x - 6

(ii) f - g = -x² + x - 4

(iii) f . g = x³ - 5x² - x + 5

(iv) f/g = ( x - 5)/(x +1)(x - 1)

(v) g(f(x)) = x² - 10x + 24

The two functions are given that

f(x) = x - 5

g(x) = x² - 1

We have to find

(i) f + g

f(x) + g(x) = ( x-5)  + (x² - 1)

                = x² + x -5 -1

               = x² + x -6

(ii) f - g

f(x) - g(x) = (x-5)- (x² - 1)

              = -x² + x -5 +1

              = -x² + x -4

(iii) f . g

f(x) . g(x) = (x-5)(x²-1)

              =x(x² - 1) -5(x² - 1)

              = x³ - x - 5x² + 5

              = x³ - 5x² - x + 5

(iv) f/g

f(x) / g(x) = (x-5) / ( x² - 1)

              = (x - 5) / (x+1)(x-1)

(v) g(f(x)) = - 1 + ( -5 + x )²

              = -1 + 25 + x² - 10x

              = x² - 10x + 24

Therefore we get the value of the function, (i) f + g = x² + x - 6, (ii) f - g = -x² + x - 4,(iii) f . g = x³ - 5x² - x + 5, (iv)f/g = ( x - 5)/(x +1)(x - 1), (v) g(f(x)) = x² - 10x + 24.

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The complete question is:

F(x)=x-5 and g(x)=x2 - 1 find (i) f + g , (ii) f-g, (iii) f. g (iv) f/g (v) g(f(x)).

All 3 angles add up to 180 degrees.

so 40 + 2x + 3x = 180

40 + 5x = 180

5x = 140

x = 28

So angle A = 2x = 2(28) = 56 degrees.

Answer: 56°

Step-by-step explanation:

We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.

     Given:

           2x + 3x + 40 = 180

     Combine like terms:

           5x + 40 = 180

     Subtract 40 from both sides of the equation:

           5x = 140

     Divide both sides of the equation by 5:

           x = 28

Next, we will substitute this value of x into the expression for ∠A.

     ∠A = 2x = 2(28) = 56°

a) This is not a binomial random variable, since the number of dots on the top face of a die can take more than two possible values.

b) The second part is also not a binomial random variable, since the probability of success (drawing a heart) changes with each trial (drawing a card without replacement).

c) X is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which 0.02% of all parts are defective.

This is a binomial random variable, since it satisfies all five conditions of a binomial random variable.

d) X is the number of times the number of dots on the top face of a fair die is even in six rolls of the die.

This is a binomial random variable, since it satisfies all five conditions of a binomial random variable.

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The probability of getting exactly 9 of them major in STEM is 0.139 or 13.9%.

The probability of getting at most 11 of them major in STEM is approximately 0.898 or 89.8%.

The probability of getting at least 11 of them major in STEM is approximately 0.318 or 31.8%.

a. Exactly 9 of them major in STEM.

In this case, the probability of success (a student majoring in STEM) is 0.27, and the number of trials is 35. The probability of exactly 9 students majoring in STEM is then given by the formula:

P(X = 9) = (35 choose 9) x (0.27)⁹ x (0.73)²⁶

where (35 choose 9) is the number of ways to choose 9 students out of 35, and (0.27)⁹ x (0.73)²⁶ is the probability of 9 successes and 26 failures. Evaluating this expression gives a probability of approximately 0.139 or 13.9%.

b. At most 11 of them major in STEM.

To calculate the probability that at most 11 students out of 35 major in STEM, we can use the cumulative binomial probability distribution. This distribution calculates the probability of at most X successes, where X is any number from 0 to the total number of trials.

The probability of at most 11 students majoring in STEM can be calculated as follows:

P(X <= 11) = P(X = 0) + P(X = 1) + ... + P(X = 11) = 0.898 or 89.8%.

c. At least 11 of them major in STEM.

The probability of less than 11 students majoring in STEM can be calculated using the cumulative binomial probability distribution, as in part (b). Specifically:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

Subtracting this probability from 1 gives the probability of at least 11 students majoring in STEM:

P(X >= 11) = 1 - P(X < 11) = 31.8%

Again, we can use the binomial distribution formula from part (a), or a binomial probability calculator or statistical software package to calculate this probability.

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Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193