Math Kangaroo Brazil 2020 Grade 7-8 Question. Please Solve both question 25 and 26

Answer:

10

Step-by-step explanation:

[tex] \sqrt{26 {}^{2} - 24 {}^{2} }[/tex]

[tex] = \sqrt{676 - 576} [/tex]

[tex] = \sqrt{100} [/tex]

[tex] = 10[/tex]

Answer: 10

Step-by-step explanation: You can use the Pythagorean theorem which is a^2+b^2=c^2. Plug in the numbers that you already have and square them to find the answer, which is 10. Hope this helps! If you need more of an explanation pls let me know ;)

Answer:

-2[tex]t^{3}[/tex] + 5t - 1

Step-by-step explanation:

(7[tex]t^{3}[/tex] + 3t - 1) + (-9[tex]t^{3}[/tex] + 2t)

7[tex]t^{3}[/tex] - 9[tex]t^{3}[/tex] + 3t + 2t - 1  Combine like terms

-2[tex]t^{3}[/tex] + 5t - 1

Like terms have to have the same variable and the same exponents to be like terms.

Carmen and her dog, Duke walked at a slower rate at 0.625 blocks/min

Carmen and her dog, Duke would take 19.2 minutes to work 12 blocks.

In math, a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.

Carmen/Duke walks 5/8 = 0.625

Terell/Lady walks 8/12 = 0.677

Therefore, from the average time, Carmen and Duke walk slower.

Carmen and Duke will walk 12 blocks in;

= 12/0.625

= 19.2 minutes

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Answer:

GCF of 12 and 100 by Prime Factorization

Prime factorization of 12 and 100 is (2 × 2 × 3) and (2 × 2 × 5 × 5) respectively. As visible, 12 and 100 have common prime factors. Hence, the GCF of 12 and 100 is 2 × 2 = 4.

GCF of 12 and 100 by Listing Common FactorsFactors of 12: 1, 2, 3, 4, 6, 12Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 12 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 100 is 4.

Answer: 8 x + 5 y + 1

8x+5y+1

so that would be B)

Hello there!

Answer:

14

Step-by-step explanation:

Let the smaller side is x. Then the largest side is x * 7/5.

Perimeter is equal to 2 * (x + 7/5 * x) or 48.

2 * (x + 7/5 * x) = 48

5/5 * x + 7/5 * x = 24

12/5 * x = 24

12/5 * 5/12 * x = 24 * 5/12

x = 10.

Tha larger side is 10 * 7/5 = 14.

Step-by-step explanation:

Given ,

To Find : Which side is longer

We know the formula to find the perimeter of a parallelogram is,

[tex]P = 2(a+b)[/tex]

We take 'x' to find out which side is longer

[tex]48 = 2(7x+5x)\\48 = 2(12x)\\48 = 24x\\\frac{48}{24} = x[/tex]

[tex]2 = x[/tex]

Side a = 7x = 7 x 2 = 14

Side b = 5x = 5 x 2 = 10

Side a [tex]\geq[/tex] Side b

Hence,  side a is longer

The central theme of Arachne is human limitation and hubris.The center of the ellipse is located midway between the foci .

The center of the ellipse is located midway between the foci. The minor axis is the line segment going through the center and perpendicular to the major axis, with both endpoints on the ellipse. The length of the ellipse's major axis is equal to the bigger of 2a or 2b, while the length of its minor axis is equal to the smaller. The major axis, which is the largest distance between any two points on the ellipse, is the line that connects both foci and runs from one end to the other. The minor axis, which is the shortest path between two points on the ellipse, is the line that passes through the center of the major axis in a perpendicular direction.

given

The central theme of Arachne is human limitation and hubris. Arachne, a young girl who is a remarkably gifted weaver, thrives on the adulation of her customers.

As a result of her youth and inexperience as well as her awareness of her exceptional talents, Arachne eventually boasts that her weaving is even greater than Athena's.

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Explanation:

The zeros in 0.00798516 are not considered significant because they are not between nonzero values.

If we had something like 1.207, then that zero would be considered significant.

The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.

Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.

Answer: 0.00799

0.00798516 rounded off to three significant figures is 0.00799

hope that helps...

The modifications and their effects on the ecosystem include:

With the construction of the Los Angeles aqueduct, water was transported to the west such that many desert regions there became lush urban areas and farmlands.

Large high ways and the damming of the Colorado River did not have such a good impact however, as they both led to runoff and to water bodies in the Owen valley drying up.

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All of the clients of the insurance company are the population, and the parameter is the annual average cost of health care for all of the clients of the insurance company.

A variable in mathematics is a word or an alphabet that stands in for an unknowable quantity, value, or number. In the context of algebra or algebraic expression, the variables are employed specifically. Consider the linear equation x+9=4, which has 9 and 4 as constants and uses x as a variable.  There are many variables, including height, age, wealth, province of birth, academic standing, and kind of dwelling. The independent variable is often plotted on the x-axis whereas the dependent variable is typically plotted on the y-axis. The independent variable's value also determines

given

Information: The 400 clients' annual health care costs that the insurance provider included in the analysis.

-Variable: The expense of health care per year

400 clients were used as a sample in this study by the insurance business.

The insurance provider included 400 consumers in this survey, providing statistics on the average annual cost of health care for each of them.

-Parameter: The annual average cost of health care for all customers of the insurance provider.

All of the clients of the insurance company are the population, and the parameter is the annual average cost of health care for all of the clients of the insurance company.

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Answer:

B. 1/6

D. 3/12

F. 4 3/11

PLEASE MARK BRAINLIEST

The probabilities of the number of people told that they have hypertension, using the binomial distribution, are given as follows:

a) Zero: 0.2536 = 25.36%.

b) More than 1: 0.3461 = 34.61%.

c) Between one and three: 0.7331 = 73.31%.

d) Two or fewer: 0.9068 = 90.68%.

e) Five: 0.0008 = 0.08%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of these parameters for this problem are given as follows:

p = 0.24, n = 5.

Hence the probability for each outcome in the distribution is given as follows:

Hence the missing probabilities are given as follows:

b) More than 1: 1 - (0.2536 + 0.4003) = 0.3461 = 34.61%.

c) Between one and three: 0.4003 + 0.2529 + 0.0799 = 0.7331 = 73.31%.

d) Two or fewer: 0.2536 + 0.4003 + 0.2529 = 0.9068 = 90.68%.

The probability that a person has hypertension is given as follows:

p = 0.24.

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52s is the maximum time that she can take on her last lap and still make the team.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).

The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

We need to find the maximum time (in seconds) that she can take on her last lap and still make the team

Let x be the maximum time (in seconds) that she can take on her last lap

60=(63+62+65+58+x)/5

300=63+62+65+58+x

300=248+x

Subtract 248 on both sides

300-248=x

x=52s

Hence, 52s is the maximum time that she can take on her last lap and still make the team.

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On solving the problem we got that, 17yds and 11yds are its length and width​

The circumference of an item is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet.

length =L

width = W

length is 6 yd longer than its width,

L  =  6 + W

perimeter is 56yds:    

[tex]56= 2(L + W) \\ = > 68 = 2(6 + W) + 2W\\= > 12+ 2W + 2W = 56\\= > 4W = 44\\= > W = 11 yds\\= > L = 11+6 = 17 yds[/tex]

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Answer: 12x^3 y^3 (x − 4y)

(GCF is: 12x^3 y^3)

Step-by-step explanation:

This is the best I can do, sorry that I don't have an explanation.

By working a full year, you may expect to earn a total of $19,646.25 in earrings.

This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

An expression, also known as an algebraic expression, is any mathematical statement that consists of numbers, variables, and an arithmetic operation between them. For example, the mathematical sign + separates the phrases 4m and 5 from the variable m in the phrase 4m + 5.

Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.

= Total overtime pay of $2,193.75 (first 6 months)

Add the regular and overtime pay after that:

= $7,312.50 + $2,193.75

= $9,506,25 in total income (first 6 months)

$7,800.00totalregularpay(last6months)

Overtime pay:(26weeks in a half year) \=$8\times

7.57.5\times1.51.5\times

$ 26

= Total overtime pay of $2,340.00 (last 6 months)

Add the regular and overtime pay after that:

= $7,800.00 + $2,340.00

= $10,140.00 in total income (last 6 months)

In the end, add the combined earnings from the two half years:

= $9,506.25 + $10,140.00

= Total annual profits of $19,646.25 (expected)

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Rami's glass is fuller than Will's glass by 1/8

From the question, we have the following parameters that can be used in our computation:

Rami's glass is 1/2 full. Will's glass is 3/8 full.

Convert the fractions to decimal

This gives

Rami's glass is 0.5 full. Will's glass is 0.375 full.

0.5 is greater than 0.375

So, Rami's glass is fuller

To do this, we calculate the difference

So, we have

Difference = 0.5 - 0.375

Evaluate

Difference = 0.125

Rewrite as

Difference = 1/8

Hence, it is 1/8 fuller

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On solving the provided question, we can say that - here the value of exponential equation is 648/1296 = 0.5

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

So, the equation is

[tex]3(2x^3y^5)^3/ (2x^6y^3)^4[/tex]

and x=y=1

so, 648/1296 = 0.5

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The value of the fourth power of the expression is 1679616.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression: 6/d -10c - c, where c = -3 and d= 2

Solving the expression, we get,

6/2-10(-3)-(-3)

= 3+30+3

= 36

We are asked to find the fourth value of 36,

(36)⁴ = 36 × 36 × 36 × 36 = 1679616

Hence, the value of the expression is 1679616.

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Zeros of the given equation are {-2, 3, (-1±i√3)/2}

As the last term is -6 then, ± 2 , ±3 are possible zeroes.

Try 2:-

[tex]2^4-6*(2)^2-7*2-6=-28[/tex] so  2 is not a zero.

Try 3:-

[tex]3^4-6*(3)^2-7*3-6=0[/tex]  so 3 is a zero.

[tex](-2)^4-6*(-2)^2-7*(-2)-6=0[/tex]  so -2 is also a zero.

Divide the function by (x +2)(x - 3),  that is  [tex]x^2 - x - 6[/tex]

gives  [tex]x^2 + x + 1[/tex]

[tex]x^2 + x + 1[/tex]

So we have [tex]x^2 + x + 1 = 0[/tex]

[tex]x = [-1 +\sqrt{1^1 - 4*1*1}] / 2[/tex]

= -1 + √(-3) / 2 , - 1 - √(-3)  / 2.

= -0.5 + 0.866i, -0.5 - 0.866i

In mathematics, the number that results in the original number when multiplied by itself is called the root.

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In response to the above problem, we may state that the triangle's - 5/13 measurements correspond to sin and cos.

The first six essential trigonometric functions are used in trigonometry. These functions are trigonometric ratios. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six basic trigonometric functions. The side ratio of a right-angled triangle is equivalent to the identities and functions of trigonometry. Trigonometric formulas are applied to the perpendicular side, hypotenuse, and base of a right triangle in order to calculate the sine, cosine, tangent, secant, and cotangent values.

as base/hypotenuse = cos x

and sin x = hypotenuse/perpendicular

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Answer: The equation Y-5 = -7/3(X-3) in standard form is:

3Y - 15 = -7X + 21

Step-by-step explanation:

The 3 year simple interest at 4% will be $38,192.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

The principal amount = $34,100

Interest rate = 4%

Time = 3 years Now,

Since, We know that;

Where, A is final amount.

P is principal amount.

r is interest rate.

t is time.

Substitute all the values, we get;

A = $34,100 (1 + 4/100)³

A = $34,000 (104/100)³

A = $34,000 × 104/100 × 104/100 × 104/100

A = $38,192

Thus, The Simple interest will be $38,192.

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Answer:

Its 1 because you are moving the digits 1 place to the right

Step-by-step explanation:

Answer:

  y < 1/2x +6

Step-by-step explanation:

You want the inequality graphed in the given figure.

The line is dashed, and the shading is below it, so the inequality will have the form ...

  y < ...

This is because the boundary line is not included, and the y-values in the solution are less than those on the boundary line.

The y-intercept is at +6, where the line crosses the y-axis.

The line goes 2 units to the right for each 1 unit up, so its slope is ...

  m = rise/run = 1/2

The slope-intercept equation for the boundary line is ...

  y = mx +b . . . . . . slope m; y-intercept b

  y = 1/2x +6 . . . . . equation of the boundary line in the graph

Putting the boundary line expression into the inequality form gives the inequality that describes the graph:

  y < 1/2x +6

Answer:

There could be 12 red pens and 21 black pens

Step-by-step explanation:

The slope of the line, given the point on the line and the y - intercept, is - 5. 33

The slope of a line tells us the relationship between the dependent variable and the independent variable. In other words, it tells us what a change in the independent variable leads to in the dependent variable.

The slope can be found in the slope - intercept formula form of :

y = mx + b

m is the slope

b is the y - intercept

We have the y - intercept and a y and x value in ( -3, 6 ) so the slope is:

6 = - 3 ( m ) + ( - 10 )

6 = - 3m - 10

- 3m = 6 + 10

- 3 m = 16

m = 16 / - 3

m = - 5. 33

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Triangles ABC and DEC are similar.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Here, we have,

Given the triangles ABC and DEC

For the triangle ABC:

m∠A = 36, m∠B = 21

So, the m∠C = 180 - (m∠A + m∠B ) = 180 - (36 + 21) = 123

Similarly, the angles of DEC are,

m∠D=36 , m∠C=123 & we get,  m∠E =21

So, comparing the measurements of the angles of both triangles:

m∠A=m∠D.

m∠C=m∠C

m∠B=m∠E

So, the triangles are similar using the AAA postulate.

Hence, triangles ABC and DEC are similar.

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Answer: solve the same variables

Step-by-step explanation:

1. 3y + 4.1

2. 4x +

3. 5x + 22½

4. 4y²

5. + 25

6. 0