If it takes 3 days for 10 workers to finish building one house, how many days will it take 15 workers to finish 4 houses?

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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Answer:

m∠J = 100° is the answer.

Step-by-step explanation:

Given : ΔABC ≅ ΔJKL,

            m∠B = 55°

            m∠L = 25°

To find : ∠J

Since in both the triangles ABC and JKL

m∠A ≅ m∠J

m∠B ≅ m∠K = 55°

m∠C ≅ m∠L = 25°

Since measure of ∠K and ∠L are known then we can calculate the third angle j

m∠J + m∠K + m∠L = 180°

55° + 25° + m∠J = 180°

80° + m∠J = 180°

m∠J = 180 - 80

        = 100°

Therefore, m∠J = 100° is the answer.

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.

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°

A rational function with the required characteristics is f(x) = 8(x + 6)(x - 5) / (x + 4)(x - 4), considering vertical asymptotes, x-intercepts, and a horizontal asymptote.

To write an equation for a rational function with given characteristics, we need to incorporate the vertical asymptotes, x-intercepts, and horizontal asymptote into our function.

Firstly, vertical asymptotes at x = -4 and x = 4 suggest that the denominator of our function will be in the form (x + 4)(x - 4), as setting x to -4 or 4 will make the denominator zero, which creates the asymptotes.

Secondly, x-intercepts at x = -6 and x = 5 indicate that the numerator will have factors that become zero at these x-values. Hence, the numerator should be(x + 6)(x - 5).

Finally, for the function to have a horizontal asymptote at y = 8, the degree of the numerator and denominator must be the same, and the leading coefficients of the numerator and denominator must have a ratio that equals 8. To achieve the horizontal asymptote, we multiply the numerator by 8, thus the leading coefficients of the numerator and denominator are in the ratio 8:1.

Combining all these elements gives us our rational function: f(x) = 8(x + 6)(x - 5) / (x + 4)(x - 4)

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.

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

Kristaps Porzingis was born on August 2, 1995. As of the knowledge cutoff in 2023, he is 27 years old. For the latest information, current sources should be consulted as his age changes annually.

The age of Kristaps Porzingis, a professional basketball player, can be determined by knowing his date of birth. Kristaps Porzingis was born on August 2, 1995. As of the knowledge cutoff in 2023, he would be 27 years old. It is always advised to check current sources for the most up-to-date information as the age of a living person changes every year.

As of my last knowledge update in January 2022, Kristaps Porzingis was born on August 2, 1995. To determine his current age, you can subtract his birth year from the current year. However, please note that I do not have real-time information, and his age might have changed since my last update. I recommend checking the latest sources, such as news articles, the official NBA website, or Porzingis' official social media accounts, for the most up-to-date information on his age.

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:

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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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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Final answer:

The first airplane travels at 110 miles per hour, and the second airplane travels at 135 miles per hour.

Explanation:

The question deals with two airplanes leaving Chicago's Midway Airport at the same time and heading in opposite directions.

One travels at a speed that is 25 miles per hour faster than the other.

After 2 hours, they are 490 miles apart, and we need to find the speed of each airplane.

Let's define the speed of the slower airplane as x miles per hour.

Then, the faster airplane's speed would be x + 25 miles per hour.

Since they are traveling in opposite directions for 2 hours, we can set up the equation:

2x + 2(x + 25) = 490

Solving for x will give us the speed of the slower airplane, and x + 25 will give us the speed of the faster airplane.

2x + 2x + 50 = 490
4x + 50 = 490
4x = 440
x = 110

Thus, the speed of the slower airplane is 110 mph, and the faster airplane is 135 mph (110 mph + 25 mph).