The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers. x + (x + 1) + (x + 2) = 42 x + (x + 2) + (x + 4) = 42 (x minus 1) + x + (x + 1) = 42 (x minus 2) + x + (x + 2) = 42 x + 2 x + 3 x = 42

The required number of seconds would it take to travel the the length of the building is 91.

The equation for speed is basic like distance partitioned by time. You take the distance voyaged (for instance 3 meters) and gap it when (three seconds) to get the speed (one meter each second) Thus, we can characterize Speed as the pace of progress of position of an article toward any path.

We have,

length of the building = 455 meter

speed of elevator = 5 m/s

We know,

speed = distance/time

5 = 455/time

Time = 455/5

Time = 91 seconds.

Thus,time take to travel the the length of the building is 91 seconds.

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Answer: 55

Step-by-step explanation:

7x+13=9x+1

-1           -1

7x+12=9x

-7x       -7x

12=2x

12/2=6

x=6

7*6+13=55

9*6+1=55

Area will be 2[tex]r^{2}[/tex]

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form.

Given radius of circle is r

Then area of circle=π[tex]r^{2}[/tex]

The diagonal of the square is comparable to the diameter (2r) of the circle since two opposing corners of the square contact it.

Now, we will set up Pythagoras' Theorem to determine one side of the square:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

Since it is a square a=b which means all  the sides are same

∴2[tex]a^{2}[/tex] = [tex]c^{2}[/tex]

We know c, which is 2r, the diagonal.

∴2[tex]a^{2}[/tex] = [tex](2r)^{2}[/tex]

⇒[tex]a^{2}[/tex] = 2[tex]r^{2}[/tex]

We can leave it as [tex]a^{2}[/tex]

since a is one side of the square and [tex]a^{2}[/tex] would be the area of the square.

So the area of the square =2[tex]r^{2}[/tex]

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d

it's because it is 1 event

Answer:

53 if rounding to nearest 10

53.38 if not

Step-by-step explanation:

It's pretty simple actually, let's put vocabulary though

π = pie

r = radius C = circumference

ok now the formula for circumference is,

C = 2πr

because they gave you the radius, it is very simple

plug it in.

C = 2(3.14)(8.5)

3.14 x 2 = 6.28

8.5 x 6.28 = 53.38

if you're rounding to the nearest 10 it will be 53.

welcome:)

The Cp and Cpk values indicate that the process is capable of meeting the specifications for relative humidity in the greenhouse.

The amount of water vapor in the air as compared to the maximum amount that it can contain at a certain temperature is known as relative humidity. It is computed as a percentage by dividing the actual amount of water vapor in the air by the maximum amount of water vapor the air can contain at the same temperature, then multiplying the result by 100. For instance, if the air can hold 10 grams of water vapor at a certain temperature and there are only 5 grams of water vapor present, the relative humidity would be 50%. High relative humidity can be uncomfortable and promote the development of mold and other microorganisms.

How to solve?

The mean is (60+78+70+84+81+80+85+60+88+75)/10 = 76.8

The standard deviation is sqrt(((60-76.8)^2+(78-76.8)^2+(70-76.8)^2+(84-76.8)^2+(81-76.8)^2+(80-76.8)^2+(85-76.8)^2+(60-76.8)^2+(88-76.8)^2+(75-76.8)^2)/10) = 6.9

Cp = (85-65)/(66.9) = 0.56

Cpk = min((85-76.8)/(36.9), (76.8-65)/(36.9)) = min(0.86, 0.71) = 0.71

The Cp and Cpk values indicate that the process is capable of meeting the specifications for relative humidity in the greenhouse.

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The length of the other wall is 3 meters, according to the declaration made.

Pythagoras' Theorem states that within a right-angled triangle, any square on the hypotenuse side is precisely equal to the sum of something like the squares on the other two sides. The Perpendicular, Base, as well as Hypotenuse are the names of the three sides of this triangle. The hypotenuse throughout this example is the longest side since it is located across from the 90° angle.

The Pythagorean theorem, Pythagorean tuning, all five elements solids, ancient Theory and Proportions, understanding sphericity of the Earth, as well as the identification of the morning and evening luminaries and Venus are only a few of the the mathematical and scientific discoveries that Pythagoras gets attributed with in antiquity.

According to Pythagoras theorem

[tex]c^2=a^2+b^2[/tex]

diagonal (c)= 5 m

length of one wall (a) = 4m

length of other wall (b)= ?

[tex]5^2=4^2+b^2\\25=16+b^2\\b^2=25-16\\b^2=9\\b=3[/tex]

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Axillary is 3 skulls.The remainder goes to the appendix.

The bones could potentially represent up to 22 different people.This is due to the possibility that each bone comes from a different person.

There were only 3 skulls, leading some to first believe there would only be 3 persons. However, there were 4 right femurs, indicating that there is a missing skull to correspond with one of the right femurs.

In light of this, you can only conclude, until further proof, that each bone belongs to a different person.

Axillary =3 skulls.

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The probability of randomly selected student who plays sport  given that student is senior is 0.04

P(A) denotes probability of occurring of  an event A

P(B) denotes probability of occurring of an event B

P(B/A)  is known as condition probability.

The dependent events are the only ones that give rise to the conditional probability P(B/A). The conditional probability of B given that A has happened is provided.

According to this question A denotes as student is senior

B denotes student plays sport.

What is the probability that a randomly selected  student plays a sport

given that the student is senior is same as conditional probability.

P(B/A) ->Condition probability of B given that A has happened.

Student is senior given we have to tell about student plays a sport.

P(B/A) = P(A∩B) / P(A)

Given that P(A∩B) = 0.10

P(A) = 0.25

P(B/A) = 0.10/0.25 = 0.4

Given Question is incomplete Complete Question here.

At a high school, the probability that a student is a senior is 0.25. The probability that a student plays a sport is 0.15. The probability that a student is a senior and plays a sport is 0.10. What is the probability that a randomly selected student plays a sport, given that the student is senior?

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The total jewels that are inside the box will be 14160.

It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since one diamond in the safe deposit box is worth 12,000 if each of the other jewels are worth 2,160. The total jewels that are inside the box will be:

= 12000 + 2160

= 14160

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The values of the variables x, y, z in the parallelogram are x=31, y=153, z=96.

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides. Both the congruence of opposite sides and the congruence of opposite angles require the Euclidean parallel postulate, or one of its equivalent formulations, and neither condition can be proved without it.

The values of the three supplied variables x, y, and z in the parallelogram are given to us.

Let's abbreviate the parallelogram, which is depicted in the attached image, ABCD.

Here,

m∠CAB = 31°,  m∠ABC =96°.

Since CD and AB are parallel, AC is a transversal now. So,

m∠CAB =m∠ACD

m∠ACD=31°

x=31

From the ΔABC we have,

m∠ABC +m∠ACB+m∠BAC=180°

96°+Y+31°=180°

y+127°=180°

y=153°

y=153

And also we know that the measure of opposite angles in a parallelogram are always equal.

So, m∠ADC=m∠ABC

z=96°

z=96

Therefore, the required values of x, y, z are 31, 153, 96.

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The temperature of this object in degrees Celsius is equal to -270.65°C.

Temperature can be defined as a measure of either the degree of hotness or coldness of a physical body (object).

In Science and Mathematics, temperature is measured by using a thermometer and its units include the following:

In this exercise, you're required to convert the value of temperature in degree Fahrenheit (°F) to Celsius (°C). Therefore, we would use the following mathematical expression (formula) to perform the conversion:

C = K - 273.15

When t = 2.5 K, we have:

C = K - 273.15

C = 2.5 - 273.15

C = -270.65°C.

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|20 - 25| • 2  and 33 - |6 + 17| are the following absolute value expressions are equal to 10.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think of a number's absolute value is as its distance from zero on the real number line. A more general form of the equation is y=a| xh |+k for an absolute value function.

Here,

|20 - 25| • 2,

=5*2

=10

33 - |6 + 17|

=33-23

=10

The absolute value expressions |20 - 25| • 2 and 33 - |6 + 17| are both equal to 10.

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Answer: 2. 55/8

Step-by-step explanation: Add the whole numbers first (5+1 = 6), then add the fractions (4/8 + 3/8 = 7/8). Now we have 6 7/8 and since they want the answer in fraction form we will multiply the 6 and the 8 (6x8=48) and then add the 7 to the 48 (7+48 =55) and we leave our answer over the denominator which is 8. This leaves us with the final answer of 55/8

The lowest integer value m can take in the inequality 7m + 5 > 49 - 3m is 5.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

In other words, Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequality for the lowest integer value of m

7m + 5 > 49 - 3m

add 3m to both sides of the inequality

7m + 5 > 49 - 3m

7m + 3m + 5 > 49 - 3m + 3m

10m + 5 > 49

subtract 5 from both sides of the inequality

10m + 5 > 49

10m + 5 - 5 > 49 - 5

10m > 44

m > 44 / 10

m > 4.4

Hence,

lowest integer = 5

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Answer:

Part a
[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]

[tex]y = \boxed{70}x[/tex]

Part b.
The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute

Step-by-step explanation:

Q6

Part a

The slope-intercept form of an equation is y = mx + b

where m is the slope and b the y-intercept ie the value of y when x is 0

Here we see when x = 0, y = 0 so the value of b is 0 and the equation is simply

y = mx

To compute m, all we have to do is take 2 points on the graph, find the difference in y values(called rise) and divide by the difference in x values(called run)

This would be [tex]\dfrac{y2-y1}{x2-x1}[/tex]

We are given y2 as 280(on the numerator). The corresponding x2 value from the graph is 4

We are given x1(on the denominator) as 2. The corresponding y1 value is 140 from the graph

So just fill in the missing values to get

[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]

The above simplifies to 70

So the equation is

[tex]y = \boxed{70}x[/tex]

Part b
The interpretation is:

The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute

Answer:

Answer down below!

Step-by-step explanation:

Once you multiply 0.85 * 18340 you get

15589

From all the given statements, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.

What is an area of a triangle?

The area of a  triangle is half the product of the base of the triangle and the height of the triangle.

Area = 1/2 * base * height

As given the Area of both the big squares of figure 1 and figure 2 are equal because the side of both the squares is equal, therefore, (a+b).

figure 1,

Big square = (a+b)²,

figure 2,

Big square = (a+b)²,

Also, the sides of the 4 triangles are also the same giving the same area for all 8 triangles from Figures 1 and 2.

Figure 1,

area for 1 triangle = ab/2

area for 4 triangle =  4*(ab/2)

area for white square = big square area - 4 triangles area

                                    = (a+b)² - 4*(ab/2)

Figure 2,

area for 1 triangle = ab/2

area for 4 triangle =  4*(ab/2)

area for white square = big square area - 4 triangles area

                                    = (a+b)² - 4*(ab/2)

Hence, the given statement, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.

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Answer:

Q: How much are 5 small greeting cards?

A: $6

Q: How much are 4 large greeting cards?

A:$17

How much is it altogether? $23.

Step-by-step explanation:

Small greeting card cost: $1.20

Large greeting card cost: $4.25

Let's solve how much it would cost to get 5 small greeting cards.

5 (1.20)=6

So $6 for 5 small greeting cards

Let's solve how much it would cost for 4 large greeting cards

4 (4.25)= 17

So $17 for 4 large greeting cards.

I hope this helps!!! I didn't understand the question completely, so hopefully I added everything that you needed.

After solving the equation using the function rule the values of y are [tex]9,3,-3,-9[/tex].

A function rule is an equation that describes a relationship between two variables, where one is a dependent variable, and the other is an independent variable. Function rules are used to determine the value of the dependent variable for any given value of the independent variable. Function rules can be written as a formula, a graph, or a table of values. Function rules are often used in mathematics, physics, and other sciences to describe the behavior of a system or process.

Given: Function  [tex]y=-3x-3[/tex]

When we have a function, we just have to replace the x by the numbers on the table, in this case [tex]-4,-2,0,2[/tex].

Substituting the values of x we get,

y = -3 (-4) - 3 ⇒ 12 - 3 = 9

y = -3 (-2) - 3 ⇒ 6 - 3 = 3

y = -3 (0) - 3 ⇒ 0 - 3 = -3

y = -3 (2) - 3 ⇒ -6 - 3 = -9

Hence, the values of y are [tex]9,3,-3,-9[/tex].

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The absolute value of a correlation coefficient is the strength of the relationship between two variables.

Hence, the answer is (a) the strength of the relationship between two variables.

Correlation coefficients helps to determine the degree of  the relationship between two variables. It lies in a range of -1 to 1.

A positive correlation coefficient implies a positive relationship between the variables and a negative correlation coefficient implies an inverse relationship between the two variables. There is no linear link between the two variables if the correlation coefficient is zero.

--The question is incomplete, the correct question is as follows--

"14. The absolute value of a correlation coefficient is: a. The strength of the relationship between two variables. b. The direction of the relationship between two variables. c. The reliability of the relationship between two variables. d. The validity of the relationship between two variables."

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Answer:

Step-by-step explanation:

It is not possible to accurately compare the weight of 1 kilogram of corn to 1 cup of precooked corn because the weight of the corn will change after it is cooked. Corn is composed of water, starch, and other nutrients, and the weight of the corn will change depending on how much water is retained in the kernels.

For example, 1 cup of uncooked corn kernels (about 168 grams) will yield about 1 1/4 cups of cooked corn (about 210 grams), while 1 cup of precooked corn (about 160 grams) will yield about 1 cup of cooked corn (about 160 grams).

Therefore, the weight of 1 kilogram of corn (about 1000 grams) is significantly greater than the weight of 1 cup of precooked corn (about 160 grams). It is not possible to accurately compare the weight of these two quantities because they are in different states (raw versus cooked) and have different densities.

To find the distance from the blimp to the stadium, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of depression to the stadium, the altitude of the blimp, and the distance from the blimp to the stadium to form a right triangle.

We can then use the tangent function to find the distance from the blimp to the stadium as follows:

tan(7°) = opposite/adjacent

opposite = tan(7°) * adjacent

opposite = tan(7°) * 400 m

opposite = 0.1214 * 400 m

opposite = 48.56 m

To convert this distance from meters to kilometers, we can divide the distance in meters by 1000, as follows:

Distance in kilometers = 48.56 m / 1000

Distance in kilometers = 0.0486 km

Therefore, the distance from the blimp to the stadium is approximately 0.0486 km.

Answer:

6

Step-by-step explanation:

the hypotenuse of this special right triangle is twice the value of the leg near to the angle of 60°

x = 3 · 2 = 6

Answer: y=2x - 1

Step-by-step explanation:

The point slope form equation is y=mx + b

m is the slope, to find slope we need to find the rise/run

We see that the y increase by 2 and x increase by 1, so the slope is 2.

The y-intercept is at (0,-1), so the b is -1

So we have the equation y=2x - 1

Graphing this equation x³ - 3x² - 4 = 1/(x - 1) + 5 we get one solution of approximately x = 0.91 and another one x = 3.689.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, An equation of degree 3 which is,

x³ - 3x² - 4 = 1/(x - 1) + 5.

Now by graphing this equation we get one solution of approximately x =

0.91 and another one x = 3.689.

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Answer:25$

Step-by-step explanation: 21$ is 84% of how much money Cho had last month. So we need to find 100%. You can use a proportion which makes it easier to solve in my opinion. The proportion is 21 over x = 84/100. x is the amount of money Cho had last month which we don't know. 84/100 is 84% out of 100% since any percent is always out of 100. If we cross-multiply and make the proportion into an equation. The equation: 84*x=21*100 which simplifies into 84x=2100. If you do 2100/84, you would get 25 which is x which is the amount of money Cho had last month.

Answer:

25

Step-by-step explanation:

x= 21 * 100/84

The equation represents a circle that has a diameter of 12 units will be x² + (y - 3)² = 36. Hence, option A is correct.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the provided information in the question,

Use the equation of a circle,

(x -a)² + (y - b)² = r²

Here, a and b represent the center of the circle and r is the radius of the circle.

A center can be anywhere along the y-axis if it is (0, 3).

(x -0)² + (y - 3)² = 6²

x² + (y - 3)² = 36

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