Which postulate or theorem can be used to prove that angle abc is congruent to angle def?

Answer:

32.64%

Step-by-step explanation:

Let's define the random variable X in the following way:

X: the volume of a soda in a quart soda bottle. We know that X is normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces, i.e.,

[tex]\mu[/tex] = 32 ounces

[tex]\sigma[/tex] = 1.2 ounces

The normal density function for a random variable with a mean of 32 and a standard deviation of 1.2 is given by

[tex]f(x)=\frac{1}{\sqrt{2\pi }1.2} \exp[-\frac{(x-32)^{2} }{2(1.2)^2} ][/tex]

and we need to calculate the following probability

[tex]P(X\leq 31.46)[/tex], this probability is given by

[tex]P(X\leq 31.46) =\int\limits^{31.46}_{-\infty} {\frac{1}{\sqrt{2\pi }1.2} \exp[-\frac{(x-32)^{2} }{2(1.2)^2} ]} \, dx[/tex] = 0.3263552

you can use a computer to calculate this probability or a table from a book. You can use the following instruction in the R statistical programming language for example

pnorm(31.46, mean = 32, sd = 1.2)  with give us 0.3263552, then,

the percentage we are looking for is (0.3263552)(100)=32.64.

Answer:

9

Step-by-step explanation:

2w+2L=42

2(12)+2L=42

24+2L=42

-24 on both sides

2L=18

divide by two

L=9

the speed of jack = 190m/25s = 7.6 m/s
the speed of jill = 200m/25s = 8 m/s 

the distance travelled by jack in 2nd race= 200m 
the distance travelled by jill in 2nd race= 210m 

the time taken by jack in 2nd race = 200m/(7.6 m/s) = 26.3158 s
the time taken by jill in 2nd race = 210m/(8 m/s) = 26.25 s

therefore jill will still win and lead by 26.3158s – 26.25s = 0.0658 seconds

The pilot must compute the bearing as an angle from the north clockwise using the arctangent of the absolute value of the westward distance divided by the northward distance, then subtract this angle from 360 degrees. Wind from the north would require additional eastward adjustment to this bearing, varying with wind speed and the plane's speed.

The student is inquiring about navigation in the context of a trigonometry problem. The pilot must determine the bearing to fly directly to the airport from a point 48 miles west and 49 miles north of it. To solve this, we view the problem as a right-angle triangle where the plane is at the point (x, y) = (-48, 49) relative to the airport at an origin (0, 0). The bearing needed is calculated by finding the angle from the north in a clockwise direction, which constitutes the direction in which the pilot must fly.

The bearing θ can be found using the arctangent function: θ = arctan(|-48| / 49). Once this is computed, the bearing is 360 - θ degrees (because bearings are measured clockwise from the north). This is because the plane is to the west of the airport, so we calculate the angle relative to the western axis and subtract it from 360 to get the eastern bearing required.

If there were a wind blowing from the north, the pilot would have to adjust this bearing further east to compensate for the westward push of the wind. This would also depend on the speed of the plane relative to the air mass and the speed of the wind itself. A stronger wind or a slower plane would require a greater adjustment.

Answer:

135.6°

Step-by-step explanation:

tan Θ = opp/adj

tan Θ = 48/49

Θ = tan^-1 48/49

Θ = 44.4°

180° - 44.4° = 135.6°

Answer:

Substitution Property of Equality

Step-by-step explanation:

I just took this test, that was the answer

A proof is a mathematical statement that shows that a postulate is true. The statement that should appear in the box is:

Substitution Property of Equality

Given that:

[tex]\angle PQR = 17^o[/tex]

[tex]\angle RQS = 13^o[/tex]

Then, we have:

[tex]\angle PQS = \angle PQR + \angle RQS[/tex]

Substitute the values of PQR and RQS

[tex]\angle PQS = 17^o + 13^o[/tex]

Because the values of PQR and RQS are substituted to get: [tex]\angle PQS = 17^o + 13^o[/tex]

This means that the reason that should appear in the box is: Substitution Property of Equality

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Let

s-------> is the distance in Kilometer

V-----> the speed of the bicyclist in Km/h

t------> is the time in hours

we know that

[tex]V=s/t[/tex]

in this problem we have

[tex]V=12\frac{Km}{h}[/tex]

Part a) Find s for [tex]t=3.5\ h[/tex]

we know that

[tex]V=s/t[/tex]

solve for s

[tex]s=Vt[/tex]

substitute the values

[tex]s=12*3.5=42\ Km[/tex]

therefore

the answer Part a) is

[tex]42\ Km[/tex]

Part b) Find t for [tex]s=30\ Km[/tex]

we know that

[tex]V=s/t[/tex]

solve for t

[tex]t=s/V[/tex]

substitute the values

[tex]t=30/12=2.5\ h[/tex]

therefore

the answer Part b) is

[tex]2.5\ h[/tex]

Answer:

Part A) 18 km           Part B) 2.5 hours

Step-by-step explanation:

Part A:

Formula: s = 60 - 12t

Substitute numbers:

s = 60 - 12(3.5) = 60 - 42 = 18 km

Part B:

Formula: s = 60 - 12t

Substitute numbers:

30 = 60 - 12t

30 - 60 = -12t

-30 = -12t

t = 2.5 hours

The congruence statement that does not prove that two triangles are congruent is SSA (Side-Side-Angle).

The SSA congruence is not a valid congruence criterion for triangles because it may not necessarily guarantee congruence.

Having two sides and a non-included angle equal in two triangles does not ensure that all corresponding angles and sides are equal.

In some cases, two triangles with SSA congruence may not be congruent.

The other three congruence criteria (ASA, SAS, SSS) are valid and sufficient to prove congruence between two triangles.

ASA (Angle-Side-Angle):

This criterion states that if two triangles have two corresponding angles and the included side between those angles equal, then the triangles are congruent.

ASA is a valid criterion because it guarantees that all corresponding angles and sides are equal, leading to congruence.

SAS (Side-Angle-Side):

This criterion states that if two triangles have two pairs of corresponding sides and the included angle equal,

then the triangles are congruent. SAS is also a valid criterion because it ensures that the corresponding sides and angles are equal, thus establishing congruence.

SSA (Side-Side-Angle): This criterion states that if two triangles have two pairs of corresponding sides equal and a non-included angle equal,

then the triangles are congruent. SSA is NOT a valid criterion for proving triangle congruence. It is also known as the "ambiguous case" or "the one and only case."

This is because, in some situations, two triangles with SSA congruence may not actually be congruent.

There can be more than one possible triangle that satisfies the given conditions, leading to ambiguity.

SSS (Side-Side-Side): This criterion states that if two triangles have all three pairs of corresponding sides equal,

then the triangles are congruent. SSS is a valid criterion for proving congruence as it guarantees that all corresponding sides are equal, resulting in congruent triangles.

Therefore, ASA, SAS, and SSS are valid congruence criteria that ensure congruence between triangles. However, SSA is not a reliable criterion for proving triangle congruence, as it may lead to multiple possible triangles.

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Answer:

Place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc.

Step-by-step explanation:

She is constructing an equilateral triangle.  This means that all 3 sides must be congruent.  She has drawn an arc by placing her compass on point P and setting it to the width of segment PQ.  This arc passes through point Q.

In order to ensure that the sides are congruent, she must keep her compass the same width.  She will now go to the opposite end of the segment, point Q, and construct an arc that runs through point P.  The goal is to intersect her first arc at a point that will serve as the third vertex of the triangle.

The next step in constructing an equilateral triangle after drawing the line segment and the first arc is;

Option B; Place the point of the compass on point Q and draw an arc that intersects the first arc using the same width for the opening of the compass as the first arc.

To answer this question, we will enumerate all the steps required to construct an equilateral triangle.

Step 1; Construct a line segment PQ to serve as the length of the side of the equilateral triangle and label the 2 endpoints P and Q.

Step 2; Place one leg of the compass at point P and with the other leg at point Q, swing an arc above line PQ

Step 3; Without Changing the width of the compass, place the first leg at point Q and with the second leg now at point P, swing another arc to intersect the first arc.

Step 4; Label the point of intersection R and draw a straight line from P to R and from Q to R to complete the equilateral triangle.

Looking at the given options, the one that tallies with step 3 which is the next step for the question is Option B.

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Answer:

Number of neutrons=5

Step-by-step explanation:

We are given that

Number of protons in lithium=Z=3

Mass number of lithium=A=8

We have to find the neutrons in the isotope lithium-8.

We know that

Number of neutrons=A-Z

Where A= Mass number

Z= Number of protons=Atomic number

Substitute the values then we get

Number of neutrons=8-3=5

Answer : 5

The number of the neutrons that we have in the  isotope lithium-8 is 5 neutrons.

The quantity of protons in an element's nucleus is indicated by the element's atomic number. Lithium has three protons on average because it has an atomic number of three.

You deduct the atomic number from the mass number (the sum of the protons and neutrons in the nucleus) to get the number of neutrons in an isotope. In this instance, the isotope lithium-8, which has a mass number of 8, is present.

Mass number - Atomic number = Number of neutrons

8 - 3 = 5

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The sum of the measures of the complementary, supplementary, and vertical angles for angle a of 33° is 237°.

The question asks for the sum of the measures of the complementary angle, supplementary angle, and vertical angle for angle a, given that angle a is 33°.

The complementary angle to angle a would be one that adds up to 90° with angle a. Since angle a is 33°, the complementary angle would be 90° - 33° = 57°.

The supplementary angle to angle a is one that adds up to 180° with angle a. The supplementary angle would thus be 180° - 33° = 147°.

The vertical angle to angle a shares the same measure as angle a, because vertical angles are equal. So, the vertical angle measure is 33°.

To find the total sum of these angles, you would add 57° + 147° + 33° = 237°.

The number of ways 5 suspects can be selected from 9 by the police is 126.

The number of ways the police can select 5 suspects from 9 is calculated using combinations. In this case, it is a combination problem because the order in which the suspects are selected does not matter. The formula for combinations is:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of suspects and k is the number of suspects to be selected.

Therefore, substituting n = 9 and k = 5 into the formula:
C(9, 5) = 9! / (5! * (9 - 5)!)
C(9, 5) = 126 ways

Answer:

inequalities are x + y ≤ 13 and 4x + 7y ≥ 65

Step-by-step explanation:

Given: Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She wants to make at least $65 dollars. She is only allowed to work 13 hours per week.

We have to write and graph the system of inequalities to represent this situation.

Let she babysits for x hours per week

and she works as a tutor for y hours per week

Then given she is allowed to work for 13 hours per week.

this inequality is stated as x + y ≤ 13

Mary babysits for $4 per hour if she babysits for x hours then she get 4x

She also works as a tutor for $7 per hour if she teach for y hours then she get 7y

also, she wants to make at least $65 dollars.

Then, this inequality is represented as 4x + 7y ≥ 65

Plotting of this two inequality is represented as graph shown below.

There will be two values for the absolute value of |b-12|=15, that are -3 and 27

Absolute value describes the distance from zero that a number is on the number line, without considering direction. Absolute value describes the distance from zero that a number is on the number line, without considering direction.

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign,  its magnitude of the number irrespective of the sign of the number.

For example :- the absolute value of 5 is 5, and the absolute value of −5 is also 5.

Given that, find the absolute value of |b-12| = 15,

Solving for b,

|b-12| = 15

Removing the mod, it will give two values in negative and positive,

b-12 = 15 or b-12 = -15

b = 15+12 or b = -15+12

b = 27 or b = -3

Hence, there will be two values for the absolute value of |b-12|=15, -3 and 27

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