Two equal sides of a triangle are each 4m less than three times the third side. Write down the dimensions of the triangle, if its perimeter is 55m

A linear system that has more variables than equations has infinitely many solutions.

A linear equation in n variables has an (n - 1)-dimensional solution space, meaning that there is a subspace in which all solutions to the equation lie.

If a linear system has more variables than equations, then it is likely that there is more than one subspace that satisfies all the equations in the system, resulting in infinitely many solutions.

It is not possible for the system to have no solutions or only one solution because the system is underdetermined, meaning that there are not enough equations to fully determine the values of all the variables.

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The populations of interest are the 30 patients in the treatment group and the 30 patients in the control group. The parameter of interest is the pulse rate at a critical point during the operation

a. Identify the populations and parameters of interest. Then state hypotheses.

The populations of interest are the 30 patients in the treatment group and the 30 patients in the control group. The parameter of interest is the pulse rate at a critical point during the operation. The null hypothesis is that beta-blockers do not reduce the pulse rate, while the alternative hypothesis is that beta-blockers do reduce the pulse rate.

b. State and verify conditions for carrying out a significance test.

The conditions for carrying out a significance test are that the data must be sampled randomly, the samples must be independent, the data must be normally distributed, and the sample sizes must be equal. The data in this study was randomly sampled, the samples are independent, and the sample sizes are both 30. However, we cannot assume that the data is normally distributed without testing.

c. Calculate the test statistic and the P-value.

The test statistic is calculated using the formula t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2), where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes. In this case, t = (65.2 - 70.3) / sqrt(7.8^2/30 + 8.3^2/30) = -5.45. The P-value is calculated by finding the probability of obtaining a result at least as extreme as the observed one if the null hypothesis is true. In this case, the P-value is 0.000003.

The populations of interest are the 30 patients in the treatment group and the 30 patients in the control group. The parameter of interest is the pulse rate at a critical point during the operation

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I can only draw the conclusion that if a triangle is equilateral, then it is describing various based on the previous statement, "If a triangle is isosceles, it is then equilateral."

Equilateral describes a triangle that has three equal sides. A triangle is referred to as isosceles if two of its sides are equal.

An equilateral triangle in geometry is a triangle whose sides are all of the same length. Since the three sides are equal, the three angles that are opposite the equal sides are also equal. As a result, it is also known as an equiangular triangle because each angle is 60 degrees.

The length of each side is the same. Two sides of an isosceles triangle are of equal length. Scalene triangle: Each side measures a different distance.

A triangle with two equal sides is called an isosceles triangle. Additionally, the two angles that face the two equal sides are also equal. To put it another way, "An isosceles triangle is a triangle with two congruent sides."

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The age of first boy is 15 and age of second boy is 3.

Now, According to the question:

The x and y-axis are two important lines of the coordinate plane. The x-axis is a horizontal number line and the y-axis is a vertical number line. These two axes intersect perpendicularly to form the coordinate plane. The x-axis is also called the abscissa and the y-axis is called the ordinate.

"Information available from the question"

The sum of ages of two boys are 18.

Let x be the first boy

and, y be the second boy.

x +y = 18

(x +3) = 3(y+3)

Calculate the product or quotient

x + 3 = 3y + 9

x = 3y + 9 - 3

x = 3y + 6

Now,

3y + 6 + y = 18

Calculate the sum or difference:

4y + 6 = 18

4y = 18 - 6

4y = 12

y = 12/4

y = 3

So, For the value of x:

x + 3 = 18

x = 18 - 3

x = 15

Hence, The age of first boy is 15 and age of second boy is 3.

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Answer: a number alexa has a number

Step-by-step explanation:

Answer: The number they are thinking of is 4.

Step-by-step explanation: The greatest common factor of 4 is 4 and 4 goes into 40.

The sum of the arithmetic series 5, 9, 13, 17, ..., (4n + 1) will be n(2n + 3) which is true.

Let a₁ be the first term, L be the last term, n be the number of terms, and d be a common difference.

Then the sum of the arithmetic sequence will be

Sₙ = (n / 2)[a₁ + L]

From the sequence, the first term is 5 and the last term is (4n + 1). Then the sum of the sequence is given as,

Sₙ = (n/2)(5 + 4n + 1)

Sₙ = (n/2)(4n + 6)

Sₙ = n (2n + 3)

The sum of the arithmetic series 5, 9, 13, 17, ..., (4n + 1) will be n(2n + 3) which is true.

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The measurement of angle FWU is given as follows:

< FWU = 14.65º.

The measure is obtained using the two secant theorem, which states that the angle measure is half the difference between the angle measures of the two arcs.

The angle measures for each arc are given as follows:

The difference between these two measures is obtained as follows:

67.4 - 38.1 = 29.3.

The angle measure is half of this, hence it is obtained as follows:

< FWU = 0.5 x 29.3

< FWU = 14.65º.

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1600 + 30m is the expression indicates the amount of water, in gallons, in the swimming pool after m minutes.

An expression is combination of variables, numbers and operators.

Given that there are already 1,600 gallons of water in a swimming pool.

water is filling the pool at a rate of 30 gallons per minute,

We need to find the expression indicates the amount of water, in gallons, in the swimming pool after m minutes

Let m = number of minutes

The expression will be:

1600 + (30 × m)

1600 + 30m

Hence, 1600 + 30m is the expression indicates the amount of water, in gallons, in the swimming pool after m minutes.

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Answer:

6 1/5= 31/5

Step-by-step explanation:

1)  The number of gallons of soapy water that are in Elianni's bucket are; 1.5 gallons

2) The number of more quarts that it can hold is; 14 more quarts

Elianni puts 12 pints of soapy water in the bucket to wash her blue Hondi. From conversion factors, we know that;

1 pint = 1/8 gallon

Thus;

12 pints = 12 * (1/8)

12 pints =  (12/8) gallons

= 3/2 = 1.5 gallons.

Due to the fact that the bucket is 5 gallon capacity, It can hold:

5 - 1.5 = 3.5 gallons more.

But from conversion factors, we know that;

1 gallon = 4 quarts.

Thus;

3.5 gallons = 3.5 * 4

= 14 quarts more.

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The solution to the compound inequality in interval notation

( -∞, -6] or (1, ∞). So option D is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

Two expressions,

⇒ 3(2x+1) > 9

x+2 ≤ −4

Further, solving both the expressions

3(2x+1) > 9

2x+1 > 9/3

2x  >  3 - 1

 x  >   2/2

 x  >  1

⇒ x+2 ≤ −4

    x ≤  -4 -2  

    x ≤   -6

( -∞, -6] or (1, ∞)

Hence, the interval is ( -∞, -6] or (1, ∞)

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The measure of each angles are 80 , 35 and 122 degrees.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given in the figure,

in triangle which contains angles 70 and 30.

let another angle be x .

70 + 30 + x  = 180

x +100 = 180

x = 180 - 100

x = 80

And 80 , 65 and another angle be y in another triangle lies on same line

so

80 + 65 + y = 180

y = 180 - 145

y = 35

let another angle be z .

so

z + y + 23 = 180

z = 180 - 58

z = 122

Therefore, The measure of each angles are 80 , 35 and 122 degrees.

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The 11th bee collected 2047 grams of pollen.

This can be determined by using a simple arithmetic progression. If the first bee collected 100 grams of pollen, the second bee collected more than twice that amount, or 1002 = 200 grams.

Then, the third bee collected more than twice the amount collected by the second bee, or 2002 = 400 grams. This pattern can be continued, and the 11th bee would have collected 1002^(10) = 1001024 = 104800 grams, or 104.8 kg of pollen.

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Answer:

The equation that explains the relationship between AB and A”B” is AB = 2A”B”. This equation is based on the transformation of a triangle ABC into a triangle A”B”C” using the translation (x+2, y+0) and the dilation by a scale factor of 2 from the origin. The translation does not affect the length of AB, but the dilation doubles it, so AB = 2A”B”.

The quantitative data is the value of data in the form of counts or numbers where each data set has a unique numerical value.

Data in math is a collection of facts and figures that can be in any form numerical or non-numerical. Numerical data is the one you can calculate, and it is always collected in number form, such as scores of students in class, wages of workers in an organization or height of players on a football team, etc.

Quantitative data is the value of data in the form of counts or numbers where each data set has a unique numerical value. This data is any quantifiable information that researchers can use for mathematical calculations and statistical analysis to make real-life decisions based on these mathematical derivations.

Therefore, the quantitative data is the value of data in the form of counts or numbers where each data set has a unique numerical value.

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Answer: The answer is 1.7 or 1 7/10.

Step-by-step explanation:

The entered points belong to an increasing, linear function.Equation: y = 1.7x + 75.1.

d = √(Δy2 + Δx2) = √(-342 + -202) = √1556 = 39.44617

The probability of drawing a total of 3 orange balls and 2 green balls = 5/2(0.6)sqaure*(1-0.6)cube

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

here we will use binomial distribution formuale

p(x)= (n/x) px.qn-x

where , p = probability of success in a single trail

q = 1-p probability of failure in one trail

n = total number of trail or number of total sample

x= number of success desired

now total number of ball contain =5

and let define probability of success is drawing 2 green ball

so probability of drawing a green ball (p) =3/5

=0.6

and we need this favouable results 2 times

so x = 2

and q = 1- p = (1-0.6)

so putting value of p, q ,x,m,n above formula we get

(n/x) px.qn-x

5/2(0.6)sqaure*(1-0.6)cube

The possibility of getting all three orange balls and two green balls in a row

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Answer:

w = -2

Step-by-step explanation:

Distribute the -9 on the left side of the equation:

-9w + 36 = 54

Add 9w to both sides of the equation:

36 = 54 + 9w

Subtract 54 from both sides of the equation:

-18 = 9w

Divide both sides of the equation by 9:

w = -2

Three division expressions that are equivalent to 35.78 ÷ 6 without using the dividing power of 10 are 357.8 ÷ 60, 17.89 ÷ 3, and 14.908 ÷ 2.5.

Three division expressions that are equivalent to 35.78 ÷ 6 without using the dividing power of 10 can be written as follows:

357.8 ÷ 60

In this expression, we multiply both 35.78 and 6 by a factor of 10 so that the decimal is removed, making the division much easier. The expression becomes 357.8 ÷ 60, which can be calculated easily. The answer can be written back in decimal form by dividing 357.8 by 60 and then multiplying by 0.1 (which is the reciprocal of 10).

17.89 ÷ 3

In this expression, we divide both 35.78 and 6 by 2, which gives us 17.89 and 3. The expression becomes 17.89 ÷ 3, which can be calculated easily. The answer can be written back in decimal form by dividing 17.79 by 3 and then multiplying by 2.

14.908 ÷ 2.5

In this expression, we divide both 35.78 and 6 by 2.4, which gives us 14.908 and 2.5. The expression becomes 14.908 ÷ 2.5, which can be calculated easily. The answer can be written back in decimal form by dividing 14.908 by 2.5 and then multiplying by 2.4.

In each of these three expressions, the result is equivalent to 35.78 ÷ 6 without using the dividing power of 10. The dividing power of 10 is a helpful tool in mathematics, but it is not always necessary to use it in order to solve a division problem.

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Answer:

The equation that describes the relationship between the distance below ground and the time for the drone's descent is: Distance = -250m - 500m(Time-1).

The probability is  [tex]\frac{17}{27}[/tex] that one or more of the children is a carrier is the same as the sum of all probabilities minus the probability that none of the children is a carrier.

Two parents who are each known to be carriers of an autosomal recessive allele have four children. None of the children has the recessive condition.

Parents : Aa × Aa

Gametes:   A a

A               AA     Aa

a               Aa aa (affected)

Probability of normal carriers = [tex]\frac{2}{3}[/tex]

Probability of normal non carriers = [tex]\frac{1}{3}[/tex]

(Because 3 individuals are normal)

Probability that one or more children are carriers =

(One is carrier × 3 are non carriers) + (2 carriers × 2 non carriers) + (3 carriers × 1 non carrier) + (4 carriers)

= ([tex]\frac{2}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex]) + ([tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{3}[/tex]) + ([tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] × 1/3) + ([tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex])

[tex]=\frac{2}{81}+\frac{4}{81}+\frac{8}{81}+\frac{16}{81} =\frac{10}{27}[/tex]

[tex]=1-\frac{10}{27} \\[/tex]

[tex]=\frac{27-10}{27} =\frac{17}{27}[/tex]

Therefore, the probability is [tex]\frac{17}{27}[/tex]

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The relative frequency of class D is 0.35.

The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments.

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.

Consider the given partial relative frequency distribution.

  Class            Relative frequency

    A                         0.22

    B                         0.18

    C                         0.43

    D                            

Then,

We need to find the relative frequency of class D

We know that,

Sum of relative frequency is equal to one.

that is.

[tex]$0.22+0.18+0.25+$[/tex] relative frequency of class D=1

0.65 + relative frequency of class [tex]$\mathrm{D}=1$[/tex]

relative frequency of class D=1-0.65

=0.35

We get,

Relative frequency of class D Is 0.35

Therefore, the relative frequency of class D is 0.35

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Answer: 56.52mm

Step-by-step explanation:

The circumference of the wheel is:

C = 2 * pi * r

C = 2 * 3.14 * 225

C = 1413 mm

And the arc length between each spoke would then be:

Arc Length = C / 25

Arc Length = 1413 / 25

Arc Length = 56.52 mm

Rounding to the nearest hundredth, the approximate arc length between each spoke is 56.52 mm.

In a certain isoceles triangle, the sum of the measures of the base angles is 88 degrees less than the measure of the remaining angle. Then the measure of each angle is 44° and 92°.

Determine the measure of each angle

These are the specified parameters:

The sum of the measures of the base angles is 88° less than the measure of the remaining angle.

Large pedestal angle

a + a = 88

2a = 88

 a = 88/2

 a = 44°

Peak angle

a + a + b = 180

88 + b = 180

       b = 180 - 88

       b = 92°

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Answer:(192/9.6)÷7=20/7

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

You need to use the Pythagorean Theorem for this problem since you're solving for the lengths of a right triangle:

A right triangle is a triangle that has a 90-degree angle.

Let's say the side lengths are a, b, and c.

According to the Pythagorean Theorem, the way to relate a, b, and c is:

a^2 + b^2 = c^2   ==> c is the hypotenuse (the diagonal line on the triangle)

We already know a and b since they're given:

a=6 and b=8

Just apply these known values to the Pythagorean theorem:

6^2 + 8^2 = c^2  ==> solve for c

36 + 64 = c^2  ==> simplify

100 = c^2

c = 10  ==> take the square root on both sides

Answer: 10

By using the binominal model, the people in the sample are pessimistic about the future of marriage and family is 0.039.

A Binomial model is a mathematical model used to calculate the probability of a specific number of successful outcomes in a set number of trials

The normal model is used to compute the probability of a certain outcome occurring when the population size is much larger.

With a sample of 700 American adults, the probability of 25% or fewer of the people in the sample being pessimistic about the future of marriage and the family would be 0.039.

These answers demonstrate the importance of verifying that np and nq  are both at least 10.

If either one is below 10, the binomial model would not be an accurate representation of the probability.

On the other hand, the normal model does not have this limitation and can be used to calculate the probability even when np or nq is below 10.

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