The two equations that can represent the relationship is
i. x +( x+1) + (x+2) = 42 and
Ii. (x-1) +x + (x+1) = 42 ( option A and C)
What are consecutive integers?Consecutive integers are those numbers that follow each other. They follow in a sequence or in order. For example, a set of natural numbers are consecutive integers.
For example, 4,5,6,7 are consecutive integers. This means that the difference between two consecutive numbers is 1.
If the first number is x, then the second number is (x+1 ) and the third number is (x+3)
The sum of the three number is x +( x+1) + (x+2) = 42
if the second number is x, then the first number is (x-1) and the third number is x+1
Therefore the sum of the three numbers can also be written as (x-1) +x + (x+1) = 42
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PLS HELP!!!
I attached the question in the picture below
how much is 1kg of corn plus 1 cup of precooked corn ??
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.
He John Hancock Building in Chicago i 455 meter tall, which i about 1,400 feet, or about a quarter of a mile high. It ha one of the fatet elevator in the world, traveling at 20. 5 mile per hour, or about 5 meter per econd. How many econd woud it take to travel the the length of the building?
The required number of seconds would it take to travel the the length of the building is 91.
What is speed and its formula?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.
According to question: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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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.20 and the cost of a large greeting card is $4.25. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
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.
Find the circumference of a circular wimming pool with a radiu of 8. 5 yard. Ue 3. 14 a an approximation for pie
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:)
5 4/8 + 1 3/8 =
1. 33/8
2. 55/8
3. 6 7/16
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
which statement best explains why 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?
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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Please help and explain how to get the answer
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
Find the values of the variable in the parallogram . please!
The values of the variables x, y, z in the parallelogram are x=31, y=153, z=96.
What is a parallelogram?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 formula K=5/9(F-32)+273.15
converts temperatures from degrees Fahrenheit F to Kelvin K. An object in a laboratory is cooled to 2.5 Kelvin. What is the temperature of the object in degrees Celsius?
The temperature of this object in degrees Celsius is equal to -270.65°C.
What is temperature?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:
Kelvin (K) Fahrenheit (°F)Celsius (°C)How to convert the value of temperature from Fahrenheit (°F) to Celsius (°C)?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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Chloe's bedroom is rectangular. The length of one wall of Chloe's bedroom is 4 meters. The length from one corner of the bedroom to the diagonally opposite corner is 5 meters. What is the length of the other wall?
The length of the other wall is 3 meters, according to the declaration made.
What is the Pythagorean principle?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.
Pythagoras discovered what, exactly?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.
Briefing: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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Last month, Cho opened a checking account. Since then, he withdrew 21 dollars, which was 84% of the balance. How much did
Cho have in the account last month?
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
One diamond in the safe deposit box is worth 12,000 if each of the other jewels are worth 2,160 how many total jewels are inside the box (including the diamond)
The total jewels that are inside the box will be 14160.
How to illustrate the expression?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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Write an equation of the line in point-slope form that passes through the given points.
(3,5) and (4,7)
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
The probability of winning a three-person game of rock paper scissors is 1/3. If you just
won the last 2 rounds, what is the probability you will win the next round?
a. 1/27
b. 1/9
c. 2/3
d. 1/3
e. 1/18
d
it's because it is 1 event
0.85x18340 how do I solve this explain please
Answer:
Answer down below!
Step-by-step explanation:
Once you multiply 0.85 * 18340 you get
15589
1. The relative humidity in a greenhouse is expected to be between 65 and 85 %. Random samples taken over a span of one week yield the following values: 60,78,70,84,81,80,85, 60, 88, and 75. Find and interpret the process capability index Cp and Cpk
The Cp and Cpk values indicate that the process is capable of meeting the specifications for relative humidity in the greenhouse.
What is relative humidity?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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Solve this1
HURRY pleasee
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
A square is inscribed in a circle. Write the area of the square as a function of the radius.
Area will be 2[tex]r^{2}[/tex]
What is area?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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Work out the lowest integer value that m can take if 7m+5>49-3m
The lowest integer value m can take in the inequality 7m + 5 > 49 - 3m is 5.
How to solve inequality?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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14. the absolute value of a correlation coefficient is:14. the absolute value of a correlation coefficient is:
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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Select the correct answer from each drop-down menu.
Consider the equation below.
x^3 - 3x^2 - 4 = 1/x-1 +5
The solutions to the equation are approximately x =
0.91 and x= *blank*
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.
What is the graphical solution of a system of equations?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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Which of the following absolute value expressions are equal to 10. (More than 1)
-8 + |-17 - 1|
120 ➗ |-2 • 3|
|-15 ➗ 5| • (-5)
|20 - 25| • 2
33 - |6 + 17|
|20 - 25| • 2 and 33 - |6 + 17| are the following absolute value expressions are equal to 10.
What is absolute value expressions?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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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. 20. The probability that a student is a senior and plays a sport is 0. 8. What is the probability that a randomly selected student plays a sport, given that the student is senior?
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 additive inverse of 9/11 is __________
A blimp is flying to cover a football game. The pilot sights the stadium at a 7° angle of depression. The blimp is flying at an altitude of 400 m. How many kilometers is the blimp from the point 400 m above the stadium?
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.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
A. x2 + (y – 3)2 = 36
B. x2 + (y – 5)2 = 6
C. (x – 4)² + y² = 36
D. (x + 6)² + y² = 144
E. x2 + (y + 8)2 = 36
The equation represents a circle that has a diameter of 12 units will be x² + (y - 3)² = 36. Hence, option A is correct.
What is an equation?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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5 scapulae (3 right and 2 left)
Axillary is 3 skulls.The remainder goes to the appendix.
Which of the bones in the collection belong to the axial skeleton?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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Determine the value of x.
3
6
3√2
3√3
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
Fill in the table using this function rule y=-3x-3
After solving the equation using the function rule the values of y are [tex]9,3,-3,-9[/tex].
What is function rule?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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