The calculator shows the result that Enrique got after evaluating the expression 56 + 7 × (34 – 17) – 16 . He checked his work by rounding all of the values to the nearest ten and comparing it to the calculator result. Which is true regarding his estimate and the accuracy of his calculator result?

The statements which summarize each student's conjecture are:

Trey and Serena are both trying to find the number of stones that were in the original arch or vault. Thus, when they identify the number of stones and its main features, they would be able to determine the type of arch or vault that was built there.

The statements which summarize each student's conjecture are:

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Complete Question:

The Students' Conjectures: During an archeological dig, the students found a voussoir from a semicircular stone arch. A voussoir is a trapezoidal (wedge-shaped) stone used to build an arch or vault.

1. What are the students trying to find out? (1 point)

2. Complete the table to summarize each student's conjecture: (2 points: 1 point for each row)

Answer:

Step-by-step explanation:

1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)

2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)

3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)

4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)

5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)

6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)

7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)

8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)

The probability that the student will pass the test is 0.057

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli,[1] is the discrete probability distribution of a random variable which takes the value 1 with probability [tex]p[/tex] and the value 0 with probability [tex]{\displaystyle q=1-p}[/tex]. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q.

The student will pass if he at least answers 14 questions correctly .

This can be written as a Bernoulli distribution function [tex]P(Q=i)= 20C_{i} (\frac{1}{2} )^i(1-\frac{1}{2} )^(20-i)[/tex]

P(Q≥ 14) = P(Q=14) + P(Q=15) + P(Q=16) +P(Q=17) + P(Q=18)+ P(Q=19) +   P(Q=20)

 P(Q=14) = 20[tex]C_{14}[/tex][tex](1/2)^{20}[/tex]

 P(Q=15) = 20[tex]C_{15}[/tex][tex](1/2)^{20}[/tex]

 P(Q=16) = 20[tex]C_{16}[/tex][tex](1/2)^{20}[/tex]

 P(Q=17) = 20[tex]C_{17}[/tex][tex](1/2)^{20}[/tex]

 P(Q=18) = 20[tex]C_{18}[/tex][tex](1/2)^{20}[/tex]

 P(Q=19) = 20[tex]C_{19}[/tex][tex](1/2)^{20}[/tex]

 P(Q=20) = [tex]20C_{20}(1/2)^{20}[/tex]

On summing up all we get,

P(Q≥ 14) = (38760 + 15504 + 4845+ 1140 + 190 + 20 + 1)/2^(20)

= 15115/262144=0.057

Thus the probability that the student will pass the test is 0.057

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The area of the sector in radians is calculated as: B. 8π units squared.

The area of a sector where the central angle of the sector that is shaded in a circle is given in radians is calculated using the formula that is expressed as:

Area of sector = (1/2) × r²θ; where we have:

θ = the angle subtended at the center/central angle measure in radians

r = the radius of the circle

Given the following:

The shaded area is half of the circle. Its measure would be 180 degrees which when expressed in radians would be π.

Central angle measure in radians (θ) = π

Radius (r) = 4 units

Plug in the values into the area of sector formula

Area of sector = (1/2) × r²θ = (1/2) × (4²)(π)

Area of sector = (1/2) × (16)(π)

Area of sector = (1 × 16 × π)(2)

Area of sector = (16π)(2)

Area of sector = 8π units squared

In conclusion, the area of the shaded sector in the image given below is calculated as: B. 8π units squared.

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The bronze-casting process that depends on a modelled original form is:  lost-wax casting.

Lost-wax casting is a bronze-casting process which is also referred to as the cire-perdue. In this type of metal casting, a wax model is created when a molten metal is usually poured into a mold. The wax model is then melted and drained.

In summary, the name for this bronze-casting process that relies on this wax model is called: lost-wax casting.

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Answer:After dialation

A'=6,24

B'=12,12

C'=-12,6

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The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

Herein we have an representation of a inequality of the form y ≤ f(x), where f(x) is a linear function, that is, a first grade polynomial. By geometry we know that a equation of the line can be known from two distinct points set on Cartesian plane:

Slope

m = [- 4 - (- 2)] / [4 - (- 2)]

m = (- 2) / 6

m = - 1 / 3

Intercept (m = - 1 / 3, (x, y) = (4, - 4)

b = y - m · x

b = - 4 - (- 1 / 3) · 4

b = - 4 + 4 / 3

b = - 8 / 3

Then, we find that the inequality is:

y ≤ (- 1 / 3) · x - 8 / 3

8 / 3 ≤ (- 1 / 3) · x - y

(- 1 / 3) · x - y ≥ 8 / 3

The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

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Answer:

35449 people

Explanation:

Given equation: y = 1100.74x -1976.47

Here year '2005' represents x = 005 = 5

So, the year '2034' will represent x = 034 = 34

Insert this into equation:

y = 1100.74(34) -1976.47

y = 35448.69

y ≈ 35449 (rounded to nearest whole number)

The number the teacher gave Ross is 5127

From the question, we are to determine the number that the teacher gave Ross

From the given information,

Mr. David gave Ross a number and asked him to divide it by 15.

Let the number be x

That is,

x/15

The quotient and remainder obtained by ross are 341 and 12 respectively

That is,

x/15 = 341 + 12/15

Now, we will solve the equation for x

x/15 = 341 + 12/15

Multiply through by 15

x = 15×341 + 12

x = 5115 + 12

x = 5127

Hence, the number the teacher gave Ross is 5127

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If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.

This term is used in statistics and refers to the probability that a population parameter will fall between two set values.

it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.

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The options are :

a. It becomes wider

b. It becomes more precise

c. It does not change

d. It narrows

The function can be solved as follows:

f(x) = 3x - 5

Therefore, the function can be solved as follows:

f(6 + 4) = f(10) = 3(10) - 5 = 25

f(6) + f(4) = 3(6) - 5 + (3(4) - 5)

f(6) - f(4) = 13 + 7

f(6) - f(4) = 20

f(6 - 4) = f(2) = 3(2) - 5 = 6 - 5 = 1

f(6) - f(4) = 3(6) - 5 - (3(4) - 5)

f(6) - f(4) = 18 - 5  - (12 - 5)

f(6) - f(4) = 13 - 7

f(6) - f(4) = 6

f(6.4) = f(24) = 3(24) - 5 = 72 - 5 = 67

f(6) . f(4) = (3(6) - 5 ) (3(4) - 5)

f(6) . f(4) = (18 - 5)(12 - 5)

f(6) . f(4) = (13)(7) = 91

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Answer:

  see attached

Step-by-step explanation:

There are many vocabulary words and theorems associated with angles where a transversal crosses parallel lines. These are needed for the "explain your reasoning" part of the question.

Where one line crosses another, the angles formed are either "adjacent" (share a side and vertex), or "vertical" (share only a vertex, formed from opposite rays). In Figure 11, x° and 67° are "adjacent" angles. In Figure 12, y° and 109° are "vertical" angles.

The adjacent angles are also called a "linear pair", and their total is 180°. They are supplementary.

The vertical angles are congruent.

Two sets of four angles are formed when a transversal crosses parallel lines. The relations between angles of one of those sets and angles of the other of those sets are described using several different terms:

"Alternate" angles are on opposite sides of the transversal. "Consecutive" or "same-side" angles are on the same side of the transversal. "Exterior" angles are outside the parallel lines. "Interior" angles are between the parallel lines. "Corresponding" angles are in the same relation to the point of intersection.

Alternate exterior angles (congruent): Fig. 11, x° and y°.

Alternate interior angles (congruent): Fig. 13, y° and the one marked with the right angle symbol.

Consecutive interior angles (supplementary): Fig. 12, x° and 109°; Fig. 14, x° and y°.

Consecutive exterior angles (supplementary): none shown in these figures.

Corresponding angles (congruent): Fig 14, x° and 65°; Fig. 16, x° and 130°.

The upshot of all of these relations is this:

The attached table shows the values of x° and y° in the various figures. For the purpose here, we simply identified the angles as acute or obtuse, and matched values accordingly. The explanation can get as elaborate as you like. For example, ...

  11. x° and y° are alternate exterior angles, so congruent. x° and 67° are a linear pair, so x° = 180° -67° = 113°.

  12. x° and 109° are consecutive interior angles, so supplementary. x° = 180° -109° = 71°. y° and 109° are vertical angles, so congruent.

The additional information needed to determine that ABCD is a parallelogram is: A. AB ≅ CD.

One of the criteria for proving that a quadrilateral is a parallelogram is that one of the pairs of opposite sides are congruent and also parallel to each.

We are already given that side AB is parallel to side CD, therefore, the additional information we would need to prove that quadrilateral ABCD is a parallelogram is: A. AB ≅ CD.

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The probability value become is 2c/(N-1).

According to the statement

we have given that If P and Q are both neighbors of R, and by considering unstructured network in which each node randomly chooses c neighbors.

we have to find that the probability of neighbors that they are also neighbors of each other.

So, For this purpose to find the probability is

Consider a network of N nodes unstructured and let

If each node chooses c neighbors at random,

then the probability that P will become by choose Q, or Q chooses P is roughly 2c/(N-1).

And the probability outcomes value become is 2c/(N-1).

So, The probability value become is 2c/(N-1).

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Answer: 1. A

2. A

Step-by-step explanation:

Answer:

A 0.08

Step-by-step explanation:

Answer:

x = [tex]\frac{4}{25}[/tex]

Step-by-step explanation:

1 : x = 6 [tex]\frac{1}{4}[/tex] ← change to improper fraction

1 : x = [tex]\frac{25}{4}[/tex] , then

[tex]\frac{1}{x}[/tex] = [tex]\frac{25}{4}[/tex] ( cross- multiply )

25x = 4 ( divide both sides by 25 )

x = [tex]\frac{4}{25}[/tex]

Answer:

Step-by-step explanation:

here is a solution and verify

The given equation is equivalent to (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3). And the zero of the function are: [tex]\pm \frac{3}{2}[/tex] and [tex]\pm \frac{3}{2}i[/tex].

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: D=b²-4ac and after that use this variable in the formula: [tex]x=\frac{-b\pm\sqrt{D} }{2a}[/tex].

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

The question gives: [tex]16x^4-81=0[/tex], you can factor this equation. See below.

(4x²+9)*(4x²-9)

(4x²+9)*(2x-3)*(2x+3)

Therefore, you should choose one of options: (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3).

Next step is to solve the given equation. Solving for  (4x²+9)*(2x-3)*(2x+3)=0, then:

For 2x-3=0

      x=3/2

For 2x+3=0

      x= -3/2

For 4x²+9=0

      4x²=-9

       x²= -9/4

      x = [tex]\pm \sqrt{\frac{-9}{4} }[/tex]

      x   =[tex]\pm \frac{3}{2}*\sqrt{-1 }\\ \\ \pm \frac{3}{2}*i[/tex]

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The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression:

(3x³ + 5x² - 11x + 3)/(x + 3)

= (x + 3)(x - 1/3)(x - 1) / (x + 3)

= (x - 1/3)(x - 1)

The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)

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Answer:

Step-by-step explanation:

125 I think

FALSE

To calculate the perimeter of a triangle, add the length of its sides. For example, if the sides of a triangle are a, b, and c, the perimeter of the triangle is P = a + b + c.

Since all three sides of the triangle are the same length, you can multiply the length of each side by 3 to get the perimeter.

To find the circumference of a circle, multiply the diameter of the circle by π (pi). The circumference can also be calculated by multiplying 2 x radius by pi (π = 3.14).

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1 tablet weekly reduction in his consumption of tablets.

Algebraic expression is a set of variable, constant and algebraic operations like addition, subtraction, multiplication and division. for example 3x^2+2x+3=0

Tablet after 10 week of doctor visit = 40 tablet

Tablet after 20 week of doctor visit= 30

In 10 week there is a difference of (40-30) 10 tablets.

in 10 week there is reduction of 10 tablets its mean there is reduction of 1 tablet per week

so, the weekly reduction of 1 tablet per week.

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Answer:

x/2 = 19-11

x/2 = 8

x = 8×2

x= 16

Answer:

x=16

Step-by-step explanation:

x/2 + 11 = 19

*2     *2    *2    Multiply 2 on both sides to make x stand by itself

x+22 = 38

  -22   -22

x=16

Check

Plug in 16 instead of x.

16/2 + 11 = 19

8+11=19

19=19

Hope it helps:)

The angle that the ramp makes with the ground is 16 degrees.

We can see that the ramp is and its support now constitutes a right angled triangle.

Thus, the hypotenuse of the triangle is 40feet while the opposite of the angle is 11 feet.

The angle made with the ground is;

sin x = 11/40

x = sin-1(11/40)

x = 16 degrees

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The total earnings in commission is $93.50

The given parameters are:

Commission = $5.50

Items = 17

The total commission is:

Total = $5.5 0 * 17

Evaluate

Total = $93.50

Hence, the total earnings in commission is $93.50

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Using the binomial distribution, the probabilities are given as follows:

The formula is:

[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:

The values of the parameters for this problem are:

n = 10, p = 0.4.

The probability that more than 4 weigh more than 20 pounds is:

[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]

In which:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then:

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

[tex]P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0061[/tex]

[tex]P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403[/tex]

[tex]P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209[/tex]

[tex]P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150[/tex]

[tex]P(X = 4) = C_{10,4}.(0.4)^{4}.(0.6)^{6} = 0.2502[/tex]

Hence:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0061 + 0.0403 + 0.1209 + 0.2150 + 0.2502 = 0.6325[/tex]

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.6325 = 0.3675[/tex]

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

The probability that fewer than 3 weigh more than 20 pounds is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

For more than 7, the probability is:

[tex]P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

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

[tex]P(X = 8) = C_{10,8}.(0.4)^{8}.(0.6)^{2} = 0.0106[/tex]

[tex]P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016[/tex]

[tex]P(X = 10) = C_{10,10}.(0.4)^{10}.(0.6)^{0} = 0.0001[/tex]

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

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Due to length restriction we kindly invite to check the explanation for further details about the analysis of three quadratic equations and inherent rigid transformations.

Herein we find the graph of the parent quadratic equation f(x) = x² and two proposed resulting functions, whose difference with the former one have to be explained in terms of the kind of rigid transformations they have.

By comparing them, we find that both functions g(x) and h(x) are the result of a rigid transformation of the form f'(x) = k · f(x), where the transformation is a simple vertical dilation for k > 1, simple vertical contraction for 0 < k < 1, vertical contraction and reflection around the x-axis for - 1 < k < 0 and vertical dilation and reflection around the x-axis for k < - 1.

Function g(x) is the result of dilating f(x) by a factor of 3 and function h(x) is the result of dilating and reflecting f(x) around the x-axis by a factor of - 3.

The tables for each quadratic function are summarized below:

g(x):

 x             - 2             - 1               0             1                2

g(x)            12               3              0             3               12

f(x):

 x             - 2             - 1               0             1                2

g(x)          - 12            - 3               0           - 3            - 12

Lastly, we prepare the graph with the three functions in the image attached below.

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Answer:

72

Step-by-step explanation:

This shape is a prism; it's a 3-D shape with 6 sides. Basically, it's a box.

All 6 sides are rectangles.

Surface area means that we'll find the area of all 6 rectangles and add them up.

There's a front and back, left and right, and a top and bottom.

The area of a rectangle is length×width or base×height.



The front and back are identical.

Area = length×width

Area = 6×3 = 18

Since the front and back are the same, two of the rectangles have area = 18.



The left and right are the same:

Area = 3 × 2

Area = 6

Two faces have area = 6.

The top and bottom are the same.

Area = 6 × 2

Area = 12

Again, two faces have area = 12.

To find the total surface area, add up all 6 areas.

A =18+18+6+6+12+12

A = 72