Using simplification, the number is −1.
Given that, If 2 is added to a number and this sum is tripled, the result is 4 more than the number.
Let the number is x.
Therefore from given information we get
2 is added to a number.
Then it is x+2.
Sum is tripled.
So 3(x+2)
4 more than number means x+4.
So according to the given statement equation should be
3(x+2)=x+4
Simplifying the expression
3x+6=x+4
Subtract 6 on both side
3x+6−6=x+4−6
3x=x−2
Subtract x on both sie
3x−x=x−2−x
2x=−2
Divide by 2 on both side we get
x=−1
Hence, the number is −1.
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What is the
relationship among the unit rate, slope, and constant
rate of change of a proportional linear relationship?
The relation among unit rate, slope and constant rate of change of a proportional linear relationship is y = kx.
What is unit rate?
The rate of change is the ratio between the x and y (or input and output) values in a relationship. Another term for the rate of change for proportional relationships is the constant of proportionality. If the rate of change is yx, then so is the constant of proportionality.
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.
The slope is defined as y = mx +b
b =1, m=k
y =k x.
Here, k is constant rate of change.
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identify the slope. pls help asap
Answer:
Step-by-step explanation:
Slope: 6/3 = -2
since the line is going from left to right, it is a negative slope
Answer:
-7/3 or 2.3333333333333
Step-by-step explanation:
X= -1 – -4 = 3
Y= -4 – 3 = -7
y = -2.3333333333333x – 6.3333333333333
or
y = -7/3 x - 19/3
So when y= -6.33 that will mean x= -2.71
Suppose that a timer for video game has a randomly determined length of time after which an enemy appears. the timer is programmed so that the enemy is equally likely to appear any time between .25 minutes and 2.75 minutes after the timer starts.
(a) Draw a density curve model this distribution of random numbers. Be sure to include scales on both axes.
(b) About what percent of the time will an enemy appear between 0.5 minutes and 2 minutes after the timer starts?
(c) Find the 20th percentile of this distribution.
Considering the uniform distribution, we have that:
a) The density curve is given by the image at the end of the answer.
b) The percentage of time in which an enemy will appear between 0.5 minutes and 2 minutes after the timer starts is of 60%.
c) The 20th percentile for the distribution is of 0.75 minutes.
What is the uniform probability distribution?The uniform probability distribution is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
In this problem, the bounds are given as follows:
a = 0.25, b = 2.75.
The height of the density curve is of:
f(x) = 1/(b - a).
Hence:
f(x) = 1/(2.75 - 0.25) = 0.4.
As shown by the image given at the end of the answer.
The probability that a measure is between two values is given by:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence, for item b:
P(0.5 < X < 2) = (2 - 0.5)/(2.75 - 0.25) = 0.6 = 60%.
The 20th percentile is the value of X for which:
X = a + 0.2(b - a).
Hence:
X = 0.25 + 0.2(2.75 - 0.25) = 0.75 minutes.
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NO LINKS!! Use the diagram below, classify the angle pairs as corresponding, alternate interior, consecutive interior, or none
Answer:
a) Consecutive interior angles.
b) Alternate exterior angles.
c) Corresponding angles.
d) Alternate interior angles.
e) Corresponding angles.
f) None.
g) Alternate exterior angles.
h) Consecutive interior angles.
i) None.
j) Corresponding angles.
k) Corresponding angles.
l) Alternate exterior angles.
m) Alternate interior angles.
n) Consecutive interior angles.
Step-by-step explanation:
Transversal
A line that crosses two other lines in the same plane at two distinct points.
Corresponding angles
A pair of angles that are in the same position relative to both lines crossed by the transversal.
Alternate interior angles
A pair of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.
Alternate exterior angles
A pair of angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.
Consecutive interior angles
A pair of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.
a) Lines p and q are crossed by transversal line s.
Therefore, ∠4 and ∠7 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.
b) Lines r and s are crossed by transversal line p.
Therefore, ∠2 and ∠11 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal p.
c) Lines p and q are crossed by transversal line s.
Therefore, ∠12 and ∠16 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.
d) Lines r and s are crossed by transversal line q.
Therefore, ∠8 and ∠13 are alternate interior angles as they are on the inner side of lines r and s, but on opposite sides of the transversal q.
e) Lines p and q are crossed by transversal line s.
Therefore, ∠11 and ∠15 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.
f) ∠7 and ∠10 have no relationship.
g) Lines p and q are crossed by transversal line r.
Therefore, ∠1 and ∠14 are alternate exterior angles as they are on the outer side of lines p and q, but on opposite sides of the transversal r.
h) Lines p and q are crossed by transversal line s.
Therefore, ∠12 and ∠15 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.
i) ∠6 and ∠7 have no relationship
j) Lines r and s are crossed by transversal line p.
Therefore, ∠1 and ∠3 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal p.
k) Lines r and s are crossed by transversal line q.
Therefore, ∠14 and ∠16 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal q.
l) Lines r and s are crossed by transversal line q.
Therefore, ∠6 and ∠15 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal q.
m) Lines p and q are crossed by transversal line r
Therefore, ∠5 and ∠10 are alternate interior angles as they are on the inner side of lines p and q, but on opposite sides of the transversal r.
n) Lines r and s are crossed by transversal line q.
Therefore, ∠8 and ∠14 are consecutive interior angles as they are on the inner side of lines r and s, and are on the same side of the transversal q.
-(4x-5)+16x>-31
I need the work shown please :))
The solutions of the inequality are given by:
x > -3
How to solve the inequality?
Here we have the following inequality:
-(4x - 5) + 16x > -31
To solve this, we need to isolate the variable x in one of the sides of the inequality, so let's do that.
-(4x - 5) + 16x > -31
-4x + 5 + 16x > -31
(-4 + 16)*x + 5 > -31
12x + 5 > -31
12x > -31 - 5
12x> -36
x > -36/12
x > -3
So all the values of x that are larger than -3 are solutions of the inequality.
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which expressions are equivalent to 3^4/9/3^2/9? select all that apply
Answer:
first and third expressions
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex]
then
[tex]\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }[/tex]
= [tex]3^{\frac{4}{9}-\frac{2}{9} }[/tex] ← first expression
= [tex]3^{\frac{2}{9} }[/tex] ← third expression
The sum of three numbers is -3. If the second number is subtracted from the sum of the first and third numbers, the result is -3. If the third number is subtracted from the sum of the first and second numbers, the result is -5. Find the three numbers.
Answer:
The three numbers are -4, 0, and 1.
The sum of three numbers is -3: -4 + 0 + 1 = -3
If the second number is subtracted from the sum of the first and third numbers, the result is -3: (-4 + 1) - 0 = -3
If the third number is subtracted from the sum of the first and second numbers, the result is -5: (-4 + 0) - 1 = -5
Step-by-step explanation:
x --> first number
y --> second number
z --> third number
x + y + z = -3
(x + z) - y = -3
(x + y) - z = -5
x = -3 - y - z
(-3 - y - z + z) - y = -3
-3 - y - y = -3
-2y = 0
y = 0
(-3 - y - z + y) - z = -5
-3 - z - z = -5
-3 - 2z = -5
-2z = -2
z = 1
x = -3 - 0 - 1
x = -4
I need some help with this problem please
Answer:
1st = 2 sin (x)
2nd = cos^2 (x)
3rd = sin^2 (x)
To qualify to compete in the high jump finals, athletes must jump a certain height in the
semi-finals. Jon jumped 1 inches below the qualifying height, but his friend Anthony
made it to 2 inches above the qualifying height. How much lower was Jon's semi-final
jump compared with Anthony's?
Jon's semi-final jump compared with Anthony's was 3 inches lower. This was based on the heights given.
How to find the value?Given that Jon jumped 1 inches below the qualifying height, but his friend Anthony
made it to 2 inches above the qualifying height.
In this case, the difference in the jump will be gotten by subtracting the values. This will be illustrated as:
= Anthony's jump - Jon's jump
= 2 - (-1)
= 2 + 1
= 3
Therefore, Jon was 3 inches lower.
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Mary borrowed $12,000.00 for starting a bakery shop at $11.5% per year at simple interest. What is the amount of money that she yas to pay at the end of 3 yesrs to clear her debt ?
The amount of money that she yas to pay at the end of 3 yesrs to clear her debt is: $16,140.
How to find the interest rate?First step is to find the interest
Interest = ( Principal × Interest rate × time)
Interest = $12,000 × 11.5% × 3
Interest = $4,140
Now let find the amount she use to clear the debt
Amount = Principal + Interest
Amount = $12,000 + $4,140
Amount = $16,140
Therefore she will use $16,140 to clear the debt.
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40 POINTS AND BRAINLIEST!! <3
can someone help please
Answer: 2%
Step-by-step explanation:
First, we know that the experimental value is 13.3, and the true value 13.6. After plugging in, we get |13.3 - 13.6| = -0.3 which is just 0.3 as it is the absolute value. Then, we divide it by 13.6 which brings us the equation 0.3/1.36 which rounds to 0.022. Continuing, we multiply it by 100 which gets our answer of 2.2. The nearest percent is 2, so our answer is 2 percent.
Now that you have converted a terminating decimal number into a fraction, try converting a repeating decimal number into a fraction. Repeating decimal numbers are more difficult to convert into fractions. The first step is to assign the given decimal number to be equal to a variable x, For the decimal number 0.3 that means x=0.3 if x=0.3 what does 10x equal?
If a decimal number, x = 0.3 then 10x is 10 multiplying 0.3 the result is 3
What is a decimal ?A decimal is a number that is divided into two parts: a whole and a fraction.
Between integers and fractions, decimal numbers reflect the numerical value of whole
How to find 10x0.3 is x which is a decimal
10 multiplies 0.3 the result is 3
The process involve converting a fraction to a whole number as the result of multiplication changed the number system from decimal to a whole number
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Kyle starts a fundraiser with 43 pennies. He recruits all of the players on his baseball team to participate. His goal is to triple the number of pennies each day. Assume Kyle meets his daily goal.
Use x to represent the number of days and y to represent the total number of pennies.
Enter an equation in the box that represents this scenario.
The equation to represent this scenario is y = 43*(3)ˣ , the correct option is (a) .
In the question ,
it is given that ,
Number of pennies that Kyle starts the fundraiser = 43 pennies
goal is to triple the number of pennies each day .
let "x" to represent the number of days .
let the total number of pennies be "y" .
this situation is represented by an exponential increase ,
that can be represented as
y = 3ˣ * 43
y = 43*3ˣ
Therefore , The equation to represent this scenario is y = y = 43*3ˣ .
The given question is incomplete , the complete question is
Kyle starts a fundraiser with 43 pennies. He recruits all of the players on his baseball team to participate. His goal is to triple the number of pennies each day. Assume Kyle meets his daily goal. Use x to represent the number of days and y to represent the total number of pennies .
Select the Equation that represents the this scenario ?
(a) y = 43(3)ˣ
(b) y = 3(43)ˣ
(c) y = [(43)(3)]ˣ
(d) y = 43(x)³
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a group of climbers are at an altitude of at most 17,500 feet. They are on their way to the top of mount everest, which is at an altitude of 29,035 feet. How many more feet do they have left to climb?
PLEASE AASSAAPP
Answer: They have to climb 11,535 ft.
Step-by-step explanation:
To solve this equation, we need to do this equation:
29,035 ft - 17,500 ft.
29,035 ft - 17,500 ft = 11,535 ft.
The area of a children's rectangular playground is 1189 square meters. The length
is 12 meters longer than the width. Determine the length and width of the
playground.
Answer:
[tex]1+\sqrt{1190}[/tex] and [tex]\sqrt{1190}-11[/tex]
Step-by-step explanation:
Let the length in meters be [tex]l[/tex]. Then, the width is [tex]l-12[/tex].
[tex]l(l-12)=1189 \\ \\ l^2-12l=1189 \\ \\ l^2-2l-1189=0 \\ \\ l=\frac{2 +\sqrt{(-2)^2-4(1)(-1189)}}{2(1)} \text{ } (l>0) \\ \\ l=1+\sqrt{1190} \\ \\ \implies l-12=\sqrt{1190}-11[/tex]
7/15 + 9/15 + 4/15!!!!!!
Answer:
4/3 or 1.333333
Step-by-step explanation:
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0. How confident can you be that your predicted value will be reasonably close to the actual value?
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
I can be certain that my predicted value will match the actual value exactly.
With a correlation coefficient of 0, A. I can’t be confident at all; this is about as close to a random guess as you can get.
What is a correlation coefficient?A correlation coefficient measures the strength of the linear relationship between two variables.
Correlation coefficients usually range between -1 to 1, and they show how one variable moves in relation to another.
A positive correlation coefficient indicates that the two variables move uniformly in the same direction, while a negative correlation coefficient shows the opposite.
A zero correlation coefficient shows no linear relationship between the two variables.
Thus, if the correlation coefficient is 0, then Option A is correct.
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7. How can you use square roots to write the solution to x² = 25?
Answer:
Step-by-step explanation:
Take the square root of both sides
[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{25}[/tex]
x=±5
what is the answer to b
B.
The age of a person's systolic pressure is 130 mm Hg is 45.98 years.
P = 0.004[tex]y^{2}[/tex] - 0.01y + 122
substitute p = 130 mm
130 = 4/1000 [tex]y^{2}[/tex] - 1/100 y + 122
8 = 4[tex]y^{2}[/tex] - 10y / 1000
8000 = 4[tex]y^{2}[/tex] - 10 y
[tex]2y^{2} -5y -4000=0[/tex]
y = 45.98 years
Therefore the age of a person's systolic pressure is 130 mm Hg is 45.98 years.
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This is a safe space please answer how you are feeling today and why!!
Answer:
feeling good
Step-by-step explanation:
I am just happy
Mrs. Gallas is playing with her class. She picks one of the points on the graph and gives three clues. If the class can correctly guess the point, they win.
Clue #1: y = 0
Clue #2: The distance from the origin is greater than 3 units.
Clue #3: The distance from the origin is greater than 3 units.
Which point did Mrs. Gallas choose?
Answer: It could be (3, -3) (3,3) or (-3,-3)
Step-by-step explanation:
they are all 3 away.
A motorboat travels 74 kilometers in 2 hours going upstream. It travels 110 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
The rate of the boat in still water is 45.5 km/hr and the rate of the current is 100.5 km/hr.
How to find speed?A motorboat travels 74 km in 2 hours going upstream.
Rate = Distance/time
Rate = 74 /2
Rate = 36 km/hr
It travels 110 km going downstream
Rate = Distance/time = 110/2
Rate = 55 km/hr
Equations:
Upstream: b-c = 36 km/hr
Downstrm: b+c = 55 km/hr
Add and solve for b
2b = 36 km/hr + 55 km/hr
2b = 91 km/hr
Divide both side by 2b
b = 91 km/hr /2
b = 45.5 km/hr (speed of the boat)
Solve for c
b+c = 55
45.5+ c = 55
c = 55 + 45.5
c = 100.5 km/hr (speed of the current)
Therefore 45.5 km/hr and 100.5 km/hr are the speed.
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BIG IDEAS MATH
# 30 i
A coordinate plane is superimposed on a property map. Each unit in the coordinate plane represents 1 foot. The
location of a wellhead on the property is given by the point (12, 6). How close is the wellhead to a property line
modeled by the line y = x - 14? If necessary, round your answer to the nearest tenth place.
feet
The distance between point (12,6) and the line y = x - 14 is given as follows:
5.6 feet.
How to obtain the distance of a point to a line?The standard equation of a line is given by the rule presented as follows:
ax + by + c = 0.
The coordinates of the point which we want to find the distance from the line are given as follows:
(x0,y0).
The equation that obtains the shortest distance of the point (x0, y0) to the line ax + by + c = 0 is presented as follows:
[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]
The line for this problem is given by the rule presented as follows:
y = x - 14.
In standard notation, it is defined by the rule presented as follows:
x - y - 14 = 0.
Hence the coefficients are presented as follows:
a = 1, b = -1, c = -14.
The point has the coordinates given as follows:
(12,6).
Hence:
x0 = 12, y0 = 6.
Thus the distance from the point to the line is obtained as follows:
[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]
D = |1(12) -1(6) - 14|/sqrt(1²+(-1)).
D = 8/sqrt(2)
D = 5.6 feet.
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bro please help. Im depressed because nobody will help me(true or false questions)
$1.50; + 5%
Please show work :>
Answer:
0.075%
Step-by-step explanation:
Answer:
1.57500 US$
Step-by-step explanation:
You equation looked like this:
$1.50; + 5% so guugle thought something else it should be:
$1.50 + 5% without the " ; "
The ammount of 5% = 0.075
Since your adding the 5% or 0.075 it would be =
1.50 + 0.075 = 1.57500
y'all get it now?
A Mazda traveled 326 miles in 7 hours and a Ford Explorer traveled 230 miles in 5
hours. Which car was traveling faster? Justify your work.
Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.
We know that the relation between distance, speed, and time is given by:
distance = speed * time
speed = distance / time
We are given;
A Mazda traveled 326 miles in 7 hours.
A Ford Explorer traveled 230 miles in 5 hours.
Let us find the rate or speed one by one:
For Mazda;
Distance = 326 miles
Time = 7 hours
Rate = distance / time = 326 / 7 mile per hour = 46.57 mile per hour
For Ford Explorer;
Distance = 230 miles
Time = 5 hours
Rate = distance / time = 230 / 5 mile per hour = 46 mile per hour
We can analyze that Mazda was traveling faster than Ford Explorer.
Thus, Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.
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E
Solving a word problem using a system of linear equations of th...
QUESTION
ODD 03
Zachary
A store is having a sale on walnuts and chocolate chips. For 4 pounds of walnuts and 8 pounds of chocolate chips, the total cost is $25. For 2 pounds of walnuts
and 3 pounds of chocolate chips, the total cost is $11. Find the cost for each pound of walnuts and each pound of chocolate chips.
As per the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.
As given in the question,
Let us consider the cost of each pound of walnuts is equal to $x.
And cost of each pound of chocolate chips is equal to $y.
Now as per the given condition system of equation is given by,
4x + 8y = 25 __(1)
2x + 3y = 11 __-(2)
Multiply (2) by 2 and subtract it from (1) we get,
4x + 8y = 25
4x + 6y = 22
0x + 2y = 3
⇒y = $(3/2)
Substitute value of y in (1) to get the value of x,
4x + 8(3/2) = 25
⇒4x = 25-12
⇒x = $(13/4)
Therefore, for the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.
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Binomial Distribution Assignment
A manufacturer of halogen bulbs knows that 3% of the production of their 100 W bulbs will be defective. A carton
contains 12 bulbs.
-What is the probability that exactly 5 bulbs in a carton of 144 bulbs will be defective?
-What is the probability that at most 2 bulbs will be defective?
-What is the probability that at least 1 bulb will be defective?
-What is the probability that between 3 and 6 bulbs will be defective?
7
The binomial distribution is a parametric probability distribution with two parameters, X and B. For a large number of trials, n, binomial probability tends to follow a continuous normal probability distribution.
What is meant by binomial distribution?The binomial distribution is a type of probability distribution that models the likelihood of one of two outcomes given a set of parameters. It sums up the number of trials when each trial has the same chance of achieving a single outcome.
Therefore,
The following is the definition of the Binomial distribution's probability mass function:
P (X = x) = (n x)p x(1p)n x, where x = 0, 1, 2, 3,..., n
Given,
Probability of defective, p = 0.03
Number of bulbs, n = 144
(i) The required probability is P(X = 5).
P(X = 5) = (1445) 0.035(1 − 0.03)144 − 5
= 144151 × (144 − 5) 1 × 0.035(1 − 0.03)144 − 5 ≈ 0.169
Within a carton of 144 bulbs, there is a 0.169 percent chance that 5 of them will be defective.
(ii) The required probability is P(X>2).
P(X>2) = 1 − P(X≤2)
= 1 − P(X = 0) − P(X = 1) − P(X = 2)
= 1 − 144101 × (144 − 0)10.030
Then simplifying,
(1 − 0.03)144 − 0 − 14411 × (144 − 1) 10.031 (1 − 0.03)144 − 1 − 14412 × (144 − 2)10.032 (1 − 0.03)144 − 2
= 1 − 0.01245 − 0.0554 − 0.1226
= 0.810
There is a 0.810 percent chance that there will be more than two faulty bulbs in a carton of 144 bulbs.
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What is -5 (x-2) + 6x = -7 +4
Answer:
Step-by-step explanation:
x=7/11