find the square roots of each of the following number

1: 81

2: 100 ​

Answer:

{(5, 3)}

Step-by-step explanation:

Consider the system :

x + 2y = 11

x - 2y = -1

We notice that :

5 + 2×3 = 11

5 - 2×3 = -1

We conclude that :

(5, 3) is the solution to the system.

The conceptual and quantative relationship between  Alpha risk and Beta risk is related to the probability of accepting Null hypothesis. They are also known as Type 1 and type 2 error.

Alpha Risk:

Alpha risk is the risk that in statistical test a null hypothesis will be rejected when it is actually true. This is also known as a type I error, or a false positive. The term risk refers to chance or likelihood of making an incorrect decission.

Beta risk:

Beta risk represents the probability that a false hypothesis in a statistical test is accepted as true. Beta risk contrast with alpha risk, which measures the probability that a null hypothesis is rejected when it is actually true.

Determining the type of risk in a quantitative relationship is primarily based on sample size. The Sample Size directly affect the Alpha and Beta risk. If Sample size is larger, the Alpha and Beta risk will lower, and if the sample size is lower the risk of Beta and Alpha increases.

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Using it's concept, the probability that a student plays basketball or soccer is given as follows:

B. 7/10.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

P(A or B) is the probability that a student plays basketball or soccer, hence, from the Venn diagram:

Hence the probability P(A or B), that is, the probability that a student plays basketball or soccer, is given as follows:

p = 7/10.

Which means that option B is correct.

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Answer:

i think 80 copies

Step-by-step explanation:

The interval notation to express the set of real numbers x that satisfies the given inequality is -2<x<5. You also can represent it as (-2,5)

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a number solution for the given inequality.

First, you should find the critical points of the inequality.

x+2=0

x = -2

and

x-5=0

x=5

Write, the intervals in between critical points. Therefore, -2<x<5.

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Explanation:

Assuming there are four answer choices, we can eliminate choices A through C because they are functions. This is because they pass the vertical line test.

The vertical line test is where we try to draw a single vertical line through more than one point on the curve. If such a task is possible, then it is said to "fail the vertical line test" and it's not a function.

For choice A, we cannot draw a single vertical line through more than one point on the parabola. Choice A passes the vertical line test. Hence, it is a function. The same goes for choices B and C.

Unfortunately choice D is not shown, but if it's the only thing left, then I'm assuming that it's some curve that fails the vertical line test.

Answer:

$1.40

Step-by-step explanation:

5.00-0.80=4.20

4.20 ÷ 3= 1.40

The answer choice which represents the group which makes up the best sample for the researcher's survey as described in the task content is; Choice A; Parents of preschool children.

It follows from the task content that; Mrs. Greenaway has decided to open a new preschool in her town.

The need for a researcher therefore arises from the decision to either open the preschool or not.

Consequently, in a bid to choose a sample, Mrs. Greenaway's researcher must make sure the sample chosen is from the population space.

Therefore, answer choice A represents the correct sample.

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The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery.

A surgical mask exists primarily utilized to protect patients and healthcare employees from people who may contain a respiratory infection or to protect sterilized or disinfected medical devices and supplies. The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery. It exists still suggested that medical personnel err on the side of warning when it arrives to the managing of equipment, whether it be a significant piece of equipment or even a small one like a surgical mask.

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Given that Jaquelyn was tardy on Monday, there is a 12 percent chance she will be late on Tuesday as well.

What is the Probability?

How likely it is that a stated event would occur is assessed using probability. The event would have a probability of 1 if it happened with certainty. The probability of an occurrence would be zero if it were absolutely guaranteed that it would not occur.

As getting late on Monday and Tuesday are independent events, their probabilities can be multiplied.

So the probability of getting late on Tuesday, given she was late to school on Monday = Probability of being late on Monday x Probability of she being late on Monday and she is late on Tuesday 60% of the time.

= 0.2 x 0.6

= 0.12

Thus the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday will be  0.12

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The height is 2 units.

Find the area of the base of the square pyramid:

The volume of the square pyramid is equal to [tex]V=\frac{1}{3} BH[/tex]

B is the area of the base, and H is the height of the pyramid

[tex]H= 6 units[/tex]

[tex]V=70 units^{3}[/tex]

Solve: B

[tex]70=\frac{1}{3} B(6)\\ \\ B=\frac{70}{2} \\ \\ = 35units[/tex]

To find the height of the square prism:

The volume of the square prism is equal: [tex]V=Bh[/tex]

B is the area of the base and h is the height of the prism

[tex]B=35 units^{2}[/tex]

[tex]V=70units^{3}[/tex]

Solve: h

[tex]70=\frac{35}{h}[/tex]

[tex]h=2units.[/tex]

The height is 2 units.

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The height of the square pyramid exists 2 units.

Volume of the square pyramid

[tex]$V = \frac{1}{3}BH[/tex]

where B exists in the area of the base  H lives at the height of the pyramid

we have H = 6 [tex]$$unit^3[/tex]

V = 70 [tex]$$unit^3[/tex]

substitute in the formula and solve for B, we get

[tex]$70 = \frac{1}{3}B(6)[/tex]

B = [tex]$\frac{70}{2}[/tex]

= 35 [tex]$$unit^3[/tex]

To estimate the height of the square prism

Volume of the square prism = Bh

Where B exists the area of the base

h exists the height of the prism

we have B = 35 and V = 70

substitute in the formula and solve for h

70 = (35)h

h = 2 units.

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The polynomial functions in their expanded form is given as follows. It is right to state that there are no breaks in the domain of h(x).

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

For instance, the polynomial 3x+4 has an exponent of 1.

Part A: F(x) has zero at 2 and multiplicity of 1; and

1 at the multiplicity of 2

f(x) = x-2) (x-1)²

= (x-2) (x² - 2x + 1)

= x³ - 4x² + 5x -2

Part B: h (x) = [tex]\left \{ {{x^3 -4x^2 + 5x -2; X < 0} \atop {\sqrt[3]{x-2} ; X\geq 0 }} \right.[/tex]

The domain of X is X ∈ R

Hence it is correct to state that there are no breaks in the domain of h(x).

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The distance travelled by Jim in 24 step is 9 miles by unitary method.

According to the given question.

The number of steps travelled by Jim = 24

Also, it is given that "Carly takes three steps to walk the same distance as Jim walks in four steps".

Therefore, by unitary mehod we can say that

The number of steps walked by Carly = 3 × (24/4) = 3 × 6  = 18

So, the distance travelled by Carly in 18 steps

= 18 × 0.5miles

= 9 miles

Since, the Carly's 18 steps is equals to Jim's 24 steps.

Therefore, the distance travelled by Jim in 24 step is 9 miles.

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Answer:

5/4

Step-by-step explanation:

(5/8)(2/1)

(Reciprocal of 1/2 is 2/1 as shown above)

(5)(2)/(8)(1)=10/8

10/8=5/4

The sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

Given that average rate of deposition is  per 1000 years of 1 centimeter.

We are required to find the type of sediment deposit that has an average rate of deposition (per 1000 years) of 1 centimeter.

Biogenic ooze, which is also called biogenic sediment, is any pelagic segment that contains more than 30 percent skeletal material. These sediments can be made up of either carbonate ooze or siliceous ooze.

In plagic sediments feldspar is obtained from local volcanic sources, whereas quartz may be introduced from the continents by wind,upsetting simple patterns.A large number of accessory minerals occur in shales.

Hence if the sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

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A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.

A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.

An unbiased estimator exists in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply indicates that an unbiased estimator catches the true population value of the parameter on average, this exists because the mean of its sampling distribution exists the truth.

Also, we comprehend that the bias of an estimator (b) that estimates a parameter (p) exists given by; E(b) - p

Therefore, an unbiased estimator exists as an estimator that contains an expected value that exists equivalent to the parameter i.e the value of its bias exists equivalent to zero.

Generally, in statistical analysis, the sample mean exists as an unbiased estimator of the population mean while the sample variance exists as an unbiased estimator of the population variance.

Therefore, the correct answer is an unbiased estimator.

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Answer:

-2

Step-by-step explanation:

Every point would flip over the y axis the same distance it is from the y axis now, but just on the other side of the y axis.

In the original equation, when y = 0, x is 2, so when we flip it over the y axis, it is now at -2 when y = 0.

The exact value of cos 105° is equals to √2/4 - √6/4.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

In this case, 105 degrees, can be split into 45+60 (cos (45+60))

Use the sum formula for cosine to simplify the expression;

cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).

The exact value of cos(60) is 1/2.

So, multiply 1/2 to cos (45) - sin (60) times sin (45).

The exact value of cos (45) is the square root of 2 over 2

(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)

The Value of sin (60) is √3/2

(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)

The exact value of sin (45) is √2/2

(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2

Therefore, The exact value of cos 105° is equals to √2/4 - √6/4.

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The factors of the trinomial based on the information given include:

C. x – 7

E. x + 2

It should be noted that a trinomial is an algebraic expression that has three non-zero terms. Here, the examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z. Also, 2a² + 5a + 7 is a trinomial in one variables.

In this case, the algebra tile configuration has 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x. Here, the trinomial is x² - 5x - 14.

The factors will be:

x² - 5x - 14.

x² + 2x - 7x - 14

x(x + 2) - 7(x + 2)

= (x + 2)(x - 7)

A polynomial with three terms is called a trinomial.

In conclusion, the correct options are C and E.

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Based on the calculations, the measure of angle BDF and CFG are 100° and 38° respectively.

In Geometry, two (2) straight lines are considered to be parallel if their slopes are the same (equal) and they have different y-intercepts. This ultimately implies that, two (2) straight lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Based on the alternate interior angles theorem, we can infer and logically deduce the following properties from the diagram (see attachment):

For angle BDF, we have:

<BDF = <BDH + <HDF

<BDF = 38° + 62°

<BDF = 100°.

Since angles BDF and DFC are linear pair, they are supplementary angles. Thus, we have:

∠BDF + <DFC = 180°

<DFC = 180 - ∠BDF

<DFC = 180 - 100

<DFC = 80°.

For angle CFG, we have:

∠DFE + <DFC + <CFG= 180°

<CFG = 180° - ∠DFE - <DFC

<CFG = 180° - 62° - 80°

<CFG = 38°.

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Answer:

25

Step-by-step explanation:

Cancel out 19^0, then exponentiate and simplify by multiplying exponents. Then simplify the terms. This leaves you with 2^-16*5^10*5^-8*2^16 which equals 5^2 which is 25

The parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

For this question,

The curve is given as

x(t)=e^-t cos(t),

y(t) =e^-t sin(t),

z(t)=e^-t

The point is at (1,0,1)

The vector equation for the curve is

r(t) = { x(t), y(t), z(t) }

Differentiate r(t) with respect to t,

x'(t) = -e^-t cos(t) + e^-t (-sin(t))

⇒ x'(t) = -e^-t cos(t) - e^-t sin(t)

⇒ x'(t) = -e^-t (cos(t) + sin(t))

y'(t) = - e^-t sin(t) + e^-t cos(t)

⇒ y'(t) = e^-t ((cos(t) - sin(t))

z'(t) = -e^-t

Then, r'(t) = { -e^-t (cos(t) + sin(t)), e^-t ((cos(t) - sin(t)), -e^-t }

The parameter value corresponding to (1,0,1) is t = 0. Putting in t=0 into r'(t) to solve for r'(t), we get

⇒  r'(t) = { -e^-0 (cos(0) + sin(0)), e^-0 ((cos(0) - sin(0)), -e^-0 }

⇒  r'(t) = { -1(1+0), 1(1-0), -1 }

⇒  r'(t) = { -1, 1, -1 }

The parametric equation for line through the point (x₀, y₀, z₀) and parallel to the direction vector <a, b, c > are

x = x₀+at

y = y₀+bt

z = z₀+ct

Now substituting the (x₀, y₀, z₀) as (1,0,1) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get

x = 1 + (-1)t

⇒ x = 1 - t

y = 0 + (1)t

⇒ y = t

z = 1 + (-1)t

⇒ z = 1 - t

Hence we can conclude that the parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

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Step-by-step explanation:

3×5×2 = 30 lorry trips to deliver 2,500 crates.

3 lorries, 5 trips per day, 2 days

that means that one lorry trip transports

2,500 / 30 = 250/3 = 83.33333... crates = 83 1/3 crates.

now we need x lorries each making 6 trips per day in 1 day (so, 6 trips, period) to transport 10,000 crates.

that looks like

x × 6 × 83.33333... = 10,000

x × 6 × 83 1/3 = 10,000

x × (6×83 + 6 × 1/3) = 10,000

x × (498 + 2) = 10,000

500x = 10,000

x = 20

so, we need 20 lorries each doing 6 trips in one day to transport 10,000 crates in one day.

these are altogether 20×6 = 120 lorry trips.

that is 4 times the number of the original scenario (30 trips).

and logically, when doing 4 times the work, we achieve 4 times the result (10,000 crates instead of 2,500).

Answer:

H:182000

L=28000

Step By Step

H=House

L=Lot

H+L=210000

H(6.5)=L

L+(L(6.5)=210000

L=28000

28000(6.5)=H

H:182000

Answer:

Short leg = 10

Longer leg = 10[tex]\sqrt{3}[/tex]

Hypotenuse = 20

Step-by-step explanation:

The given is a special right triangle, its angle measures are as follows:

30-60-90 and the side lengths will follow as:

x, x[tex]\sqrt{3}[/tex], 2x respectively.

The length of hypotenuse (sees angle measure 90) is represented with 2x and it's given as 20

We can conclude x = 10 from this

So the length of short leg is 10

Then the length of longer leg is 10[tex]\sqrt{3}[/tex]

The length of hypotenuse is already given as 20

Answer:

63:70

Step-by-step explanation:

The ratio of apartments to bathrooms in the building is 9:10.

Given that, a building has 63 apartments and 70 bathrooms.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The ratio of apartments to bathrooms is 63:70

= 9:10

Therefore, the ratio of apartments to bathrooms in the building is 9:10.

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Answer:

[tex]x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}[/tex]

Step-by-step explanation:

So when it says simplify the right side, all it's doing is distributing the square root across division.

So when we distribute the square root we get the fraction

[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}[/tex]

And it's important to know that you cannot distribute the square root across addition/subtraction, but you can with multiplication.

There's a radical identity that states: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex] and this works both ways, so we can use this to combine like radicals or separate them into multiple. In this case we can separate the square root of 4a^2 into two radicals

[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4} * \sqrt{a^2}}[/tex]

And from here it's pretty easy to see that the square root of 4 is 2, and the square root of a^2 is a, since the square exponent and square root just cancel out.

So we get the following expression on the right side

[tex]\frac{\sqrt{b^2-4ac}}{2a}[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

As we can see in the figure, lines m and n are parallel to each other. so we can apply Angle pair properties ~

So,

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle2[/tex]

[ they form corresponding angle pair ]

and it's given that :

[tex]\qquad \sf  \dashrightarrow \: \angle2 \cong\angle 3[/tex]

therefore, by using above information. we can conclude that :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle3[/tex]

The apothem is 15 inches, the perimeter is calculated to be 99.41 while the area is given as 745.59

The side of the octagon is given by x inches

the interior side of the angles can be gotten by:

8-2 * 180 / 8 sides

= 135

We have to find the value of the angles

<abc = 180 - 135 = 45 degree

<acb = 180 - 135 = 45 degrees

x² = 2AB²

AB = x/√2

30 =  x/√2 + x +  x/√2

x = 30 / 1 + √2

The apothem = 30 / 2

= 15

perimeter = 8x

= 8(30 / 1 + √2)

= 99.4 inches

area = 0.5 x 15 x 99.4

= 745.59

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