The absolute value equation representingnumbers all x whose distance from is 11 units is
|1 - x| = 11 What is absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to write the absolute value equationThe equation is written in the form below
|1 - x| = 11
removing the absolute value sign
1 - x = ± 11
solving for x for positive value
1 - x = 11
1 - 11 = x
x = -10
solving for x for negative value
1 - x = -11
1 + 11 = x
12 = x
The absolute value equation as required is |1 - x| = 11 the values of is 12 or -10
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according to a recent study, the mean number of hours college students spent playing video games per month was 43 hours with a population standard deviation of 2 hours. two weeks before final exams were scheduled to begin, 100 college students were randomly selected. what is the probability that the mean number of hours spent playing video games is less than 42.8 hours? use the z-table below. round your answer to three decimal places if necessary.
The probability that the mean number of hours spent playing video games is less than 42.8 hours is 0.15866
we are given the mean of ( m )= 43 hours and the standard deviations (s) of 2 hours, where the sample size (n) = 100.
Obtain the Zscore ;
Z = (x - m) ÷s/sqrt(n)
Z = (42.8 - 43) ÷ 2/sqrt(100)
Z = - 0. 2 ÷ 0.2
Z = - 1
so we need the probability of P(Z < - 1), from the table of z-score the probability of a z-score of -1 is 0.15866.Hence, the probability that the mean number of hours spent playing video games is less than 42.8 hours is 0.15866
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A scale on a map is 1 200 000. Work out the distance on the map, in cm, if the real distance is 10 km 15 km 4 km
The distance on the map, in cm, given the real distances, and the scale of the map are:
10 km = 5 cm15 km = 7.5 cm4 km = 2 cmHow to find the distance on the map?A scale of 1 : 200, 000 means that every 1 cm on the map is 200, 000 cm on the ground.
To find the distance on the map of 10 km, first convert it to cm:
= 10 km x 100, 000 cm per km
= 1, 000, 000 cm
The distance on the map is therefore:
= 1, 000, 000 / 200, 000 cm scale
= 5 cm on map
The distance of 15 km on the map is:
= (15 km x 100, 000) / 200, 000
= 7.5 cm
The distance of 4 km is:
= (4 x 100, 000) / 200, 000
= 2 cm
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A recipe for stir fry calls for 6 cups of rice for every 4 cups of veggies. Suppose a restaurant is making a large batch of stir fry using 15 cups of veggies. How much rice would they need? Start by labeling the double number line with the cups of veggies and cups of rice that the recipe calls for. Veggies (cups) 0 4 Rice (cups) 0 6 Great job! To find how many cups of rice they’d need for 15 cups of veggies, it can be helpful to first find the unit rate, or the amount of rice needed for 1 cup of veggies. Partition the number line to find the number of cups of rice needed for every 1 cup of veggies. Veggies (cups) 0 4 Rice (cups) 0 6 Good work! Label the bottom number line to find the number of cups of rice the restaurant would need for 1 cup of veggies.
Answer:
(i)15v=10r
Step-by-step explanation:
let no. of rice=r
let stir fry=s
let no. of veggies=v
6r=4v
then if, v=15, r=?
if 6r=4v, then v=6/4r
v=2/3r,
1X v= 1X2/3 r
15 X v= 15X2/3r
25v=5X2r=10r
BASEBALL A scale drawing of a baseball field is shown on the coordinate plane, where home plate is at (3, 3) , first base is at (13, 3) , second base is at (13, 13) , and third base is at (3, 13) . Suppose the baseball field is rotated 270° counterclockwise about second base, what are the coordinates of each base?
The coordinates of each base is listed below
preimage image
1 (3, 3) 1. (3, -3)
2 (13, 3) 2' (3, -13)
3 (3, 13) 3' (13, -3)
How to write a the new coordinates after transformationRotation is one of the numerous types of transformation. it involves circular movement about an axis
The transformation rule for 270° counterclockwise rotation
(x, y) → (y, -x)
The preimage coordinates of the base field and the image coordinates
Applying the transformation rule rule gives
preimage image
1 (3, 3) → 1. (3, -3)
2 (13, 3) → 2' (3, -13)
3 (3, 13) → 3' (13, -3)
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At the beginning of a marble game, Abby, Brea, and Cleo were each given some marbles. Then, Abby gave Brea and Cleo some of her marbles, which doubles the number of marbles Brea and Cleo each had. Finally, Brea gave Abby and Cleo some of her marbles, which doubles the number of marbles Abby and Cleo each had. If Brea had 10 marbles at the beginning and 0 marbles at the end, what is the total number of marbles that were given to the three of them at the beginning of the game?
The information in the word problem indicates that the initial total number of marbles that were given to the three of them at the beginning of the game was 40 marbles
What is a word problem in mathematics?A word problem consists of describing a situation as well as providing the necessary information to a question verbally that is to be solved by by calculations mathematically.
The initial number of marbles Brea had = 10
The number of marbles Brea had at the end = 0
Let A represent the number of marbles given to Abby, let B represent the number of marbles given to Brea and let C represent the number of marbles given to Cleo, we get;
The number of marbles Abby gave Brea and Cleo = B + C
The number of marbles Brea gave Abby and Cleo = (A - (B + C)) + 2·C
B = 10The number of marbles Brea gave Abby and Cleo = All her marbles = 2·B
2·B = 2 × 10 = 20Therefore;
20 = (A - (B + C)) + 2·C = (A - (10 + C)) + 2·C
20 = A - 10 + C
A + C = 20 + 10 = 30
A + B + C = A + 10 + C = A + C + 10 = 30 + 10 = 40
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Which of the following measures examine the spread of different values around the measures of central tendency? A. Measures of central tendency B. Measures of variability C. Measures of frequency D. Measures of percentile
Measures which examine the spread of different values around the measures of central tendency is measures of variability.
Define central tendency.A central tendency in statistics is a typical or characteristic value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most popular ways to measure central tendency. The number used to represent the center or middle of a set of data values is known as the central tendency measure.
Given,
Measures which examine the spread of different values around the measures of central tendency:
B. Measures of variability
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How do I solve this problem?
josh scored x marks in this math exam. he scored 8 more marks in english than math, and 3 more marks in geography than in math. if he received a total of 200 marks for the 3 subjects, find how many marks he scored in math.
Answer:
Math = 63
Step-by-step explanation:
Math = x
Eng = Math + 8
Geo = Math + 3
Math + Eng + Geo = 200
Substitute Eng and Geo with information above
Math + (Math + 8) + (Math + 3) = 200
3Math + 8 + 3 = 200
3Math + 11 = 200
3Math = 200 - 11
3Math = 189
Math = 189 ÷ 3
Math = 63
Samuel has a collection of toy cars. His favorites are the 27 red ones, which make up 60, percent of his collection.
The total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.
What is percentageIt's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Samuel has a collection of toy cars. His favorites are the 27 red ones.
Let Samuel has x number of toys:
From the equation:
60% of x = 27
(60/100)x = 27
0.6x = 27
x = 27/0.6
x = 45
Thus, the total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.
The complete question is:
Samuel has a collection of toy cars. His favorites are the 27 red ones which make up 60% of his collection. How many toy cars does Samuel have?
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DESIGN Marco is making two rectangular table tops. The dimensions of both are shown. If both designs have the same area, what is the value
of x?
X+4
X
2x + 3
X-2
That would be x+4=2x+3, so we must use substitution. Making x=1, hope that helps.
If 2% of a number equals 4, find 10% of that number.
Answer:20%
Step-by-step explanation: Since 2% of x = 4, that would mean 1% would equal 2. So 2 times 100 equals 200, making 20 10% of 200
PLEASE HURRY
I am having trouble
You got to set it up to boys to girls
Answer:
0,1
Step-by-step explanation:
simplest form
CAN SOMEONE DO THIS RQ? THIS IS THE LAST QUESTION I NEED TO COMPLETE THIS ASSIGNMENT.
Directions: write an expression for the sentence below.
decrease the product of 7 and 6 by a number.
Let's set "a number" to "x":
7*6 - x
This can be simplified to:
42 - x
The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27 /125 of a volt and has been reduced 3 times.
Write the voltage in exponential form.
What was the original voltage in the circuit?
Answer:
The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27 /125 of a volt and has been reduced 3 times.
Write the voltage in exponential form.
What was the original voltage in the circuit?
Step-by-step explanation:
voltage = v
v³ - exponential form
v³ = 27/125
make v³ a fraction so v³/1 then cross multiply
so... 125v³ = 27 then v³ = 27/125 or v³ = 0.216 if you like decimals better then to get v by it self you cube root mean v = ∛27/125
original voltage in circuit - v = ∛27/125
I need an awnser for this on my math hw.
The Y-intercept, or b is -3 because it is where the line touches the Y-axis. The slope, or m is 1/2 because from -3, the line goes up one, and right two. Therefore, the equation is y=1/2-3.
The perimeter of an isosceles triangle is 380 cm and it’s unequal side is 150 find the area of triangle (by Heron’s formula)
Answer:
A ≈ 6538.35 cm²
Step-by-step explanation:
Calculating the area (A) using Heron's formula
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s is the semi perimeter and a, b, c the 3 sides
here
s = 380 ÷ 2 = 190
given perimeter = 380 and unequal side is 150 , then
equal sides = (380 - 150) ÷ 2 = 230 ÷ 2 = 115 cm
then a = 150, b = 115 , c = 115
A = [tex]\sqrt{190(190-150)(190-115)(190-115)}[/tex]
= [tex]\sqrt{190(40)(75)(75)}[/tex]
= [tex]\sqrt{42750000}[/tex]
≈ 6538.35 cm² ( to 2 dec. places )
Please help asap, this is my last question I’m quite stuck. Would highly appreciate any help in under 24 hours.
The two triangles ΔABC and ΔDEC are similar as the triangles follow the angle-angle axiom of similarity .
In the given triangles ΔABC and ΔDEC
In ΔABC
∠ABC = 21°
∠BAC = 36°
∠ACB = 180° - (36+21)°
or, ∠ACB = 180° - (57)° = 123°
In ΔDEC
∠CDE = 36°
∠DCE = 123°
∠CED = 21°
Therefore we can see that the two triangles are similar as all the angles are equal.
Hence the ΔABC and ΔDEC has 3 congruent angles by the angle sum property and the triangles are similar by angle-angle-angle axiom of similarity.
Two triangles are considered to be similar if their corresponding sides and angles match. Alternatively, comparable triangles may have the same shape but vary in size. The triangles are also congruent if the lengths of their respective sides are the same.
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Draw the Image of the following triangle after a dilation centered at the origin with a scale factor of 5/3
The graph of the image of the triangle in the question following the dilation by a scale factor of (5/3) with vertices (10, 15), (10, 10), (15, 10) created with MS Excel is attached.
What is a dilation transformation?In a dilation transformation, the dimensions of the original figure is changed by multiplying the lengths by a scale factor.
The coordinates of the vertices of the triangle in the are (6, 9), (6, 6), and (9, 6)
The coordinate of a point (x, y) following a dilation by a scale factor of k, centered at the origin is the point (k·x, k·y)
The coordinates of the vertices of the image of the triangle in the question following a dilation of 5/3 centered at the origin, are therefore;
(6, 9) [tex]\overset{R_{5/3}}\longrightarrow[/tex] ((5/3)×6, (5/3)×9) = (10, 15)
(6, 6) [tex]\overset{R_{5/3}}\longrightarrow[/tex] ((5/3)×6, (5/3)×6) = (10, 10)
6(9, 6) [tex]\overset{R_{5/3}}\longrightarrow[/tex] ((5/3)×9, (5/3)×6) = (15, 10)
The graph of the image of the triangle following a dilation by a scale factor of 5/3) can therefore be plotted using points (10, 15), (10, 10), and (15, 10) and the plot function on MS Excel
Please find attached the graph of the image of the triangle following a dilation by a scale factor of (5/3) about the origin.
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P(4.-7) is reflected across the x-axis, what is the
coordinate of P?
Answer:
9
Step-by-step explanation:
guess
i am struggling with these questions
A student skipped the step (1 minute / 60 seconds).
What is second to hours conversion?The time in seconds divided by 3,600 results in the time in hours.
Given:
A student skipped a step when he tried to convert 720 seconds into hours, and he got the following incorrect result;
720 seconds (1 hour / 60 minutes) = 12 hours.
In order to convert the seconds to hours:
First, we should convert the seconds to minutes.
And the rate of conversion is 1 minute per 60 seconds.
720 / 60 = 12 minutes.
Now, converting minutes to hours.
And the rate of conversion is 60 minutes per hour.
12/60 = 1/5 hours.
Therefore, student skipped the step where rate of conversion is (1 minute / 60 seconds).
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The real roots of the quadratic x^2 + 5x = 6 are:
Answer:
-6, 1
Step-by-step explanation:
You want the real roots of the quadratic x^2 + 5x = 6.
FactorizationThe roots are easily identified from the factored form of the equation. The factors will involve the constants that have a sum of +5 and a product of -6.
-6 = 6·(-1) = 3·(-2)
Sums of the factor pairs are 5 and 1. We will use the constants that have a sum of 5.
x^2 +5x = 6 . . . . . . given
x^2 +5x -6 = 0 . . . . . standard form
(x +6)(x -1) = 0 . . . . . . . factored form
Zero product ruleThe zero product rule tells us that a product will be zero if and only if at least one of the factors is zero. To find the values of x, we set the factors equal to zero and solve for x.
(x +6) = 0 ⇒ x = -6
(x -1) = 0 ⇒ x = 1
x = -6, or x = 1 . . . . . . . . roots of the quadratic
Which is equivalent to
[tex] \sqrt[3]{8} ^{x} [/tex]
Hair grows about 1.27 centimeters each month. How much does hair grow
in 4 months?
Explanation:
In 1 month, 1.27cm grows.
So, multiply 1.27cm by 4 months to get 5.08cm
I need help again please.:)
Answer:
D
Step-by-step explanation:
D) 1755 yards is the closest amount to 1760 yards, which is how much is in a mile
The students at Gotham Elementary want to raise $500 for charity. They have raised $337 so far. How much more money do the students need to raise?
Responses
A ? + 337 = 500 or ? − 500 = 337? + 337 = 500 or ? − 500 = 337
B 337 + ? = 500 or 500 – 337 = ?337 + ? = 500 or 500 – 337 = ?
C ? − 337 = 500 or 500 + 337 = ?? − 337 = 500 or 500 + 337 = ?
D 337 + 500 = ? or 500 − ? = 337
Answer: 163$
Step-by-step explanation:
In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and four shirts cost $55, while four sweaters and five shirts costs $110, find the price of one sweater and the price of one shirt.
The price of one sweater is $15 and the price of one shirt is $10.
What is the price of one sweater and one shirt?The first step is to form a set of linear equations using the information provided in the question:
s + 4p = $55 equation 1
4s + 5p = $110 equation 2
Where:
s = price of one sweater p = price of one shirtIn order to determine the value of p, take the following steps:
Multiply equation 1 by 4
4s + 16p = 220 equation 3
Subtract equation 2 from equation 3:
11p = 110
Divide both sides of the equation by 11
p = 110 / 11
p = 10
In order to determine the value of s, substitute for p in equation 1:
s + 4(10) = $55
s + 40 = 55
s = 55 - 40
s = 15
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The diameter of the sun is about 1.4 x 10 to the power of 6 km. The diameter of the earth is about 13,000 km. What is the approximate ratio of the diameter of the sun to the diameter of the earth ?
Answer:108x10 to the 2nd power
Step-by-step explanation: Given, the diameter of the Sun is 1.4 × 10⁹ m. The diameter of the Earth is 1.2756 × 10⁷ m. We have to compare the diameters by division. Therefore, the diameter of the Sun is nearly 110 times the diameter of the Earth, So i would say 108x10 squared
1/4=[tex]2^{x}[/tex] find x
Answer:
x = 1/8
Step-by-step explanation:
divide the two from both both sides
1/4 = 2x
(1/4)/2 = x/2
1/8 = x
Answer: x = -2
Step-by-step explanation:
X is -2 because whenever you get a negative exponent you gotta make it into a fraction which is [tex]\frac{1}{4}[/tex] because I ignored the negative sign for a second and did it normally so 2 to the power of 2 is 4 put it as a fraction 1 over 4.
Normally it doesn’t happen to every problem you get. Most of the time you gotta divide the numerator by the denominator which will give you .25 in this case scenario, .25 converted to a fraction would be 1/4.
- Your Welcome.
To generate the overall equation a → 2c, which two equations should be added together?.
To generate the overall equation A → 2C, should be B → 2C added to
A → B gives the equation A + B → B + 2C.
In mathematics, an equation is a method that expresses the equality of two expressions, by using connecting them with the equals signal =. The phrase equation and its cognates in other languages may also have subtly exclusive meanings; for example, in French, an equation is described as containing one or more variables, at the same time as in English, any nicely shaped formula together with expressions associated with an equal’s signal is an equation.
Solving an equation containing variables includes determining which values of the variables make the equality actual. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that satisfy the equality are referred to as solutions of the equation. Equations come in two varieties: identities and conditional equations. An identification is actual for all values of the variables. A conditional equation is handiest genuine for unique values of the variables.
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Which one is the function here and why
The fourth option D is a function of the form of f(x) = ax(x-2)(x+2) where a is a constant.
We know that any function of the form y = f(x) will pass through the x axis at points such that there is only 1 value of x for a value of y.
Of all the options given the option D is in the form of polynomial expression which crosses the x-axis at points (-2,0 ) , (0,0) and (0,2).
The graph of the function at D will be of the form:
f(x) = ax(x-2)(x+2) a is a constant.
At y = 0 , x =-2 ,0 and 2.
Therefore for one value of y there are 3 values of x. but every value of x is mapped into one single value of y only.
For option A at x = 2 , y ahs two values -2 and 2 so it is not a function of x.
For option B the graph is not differentiable at certain points, hence it is not a function.
For option C again y has 2 values for a single x.
The values of x are used to denote the roots and zeros of the expression, which are also on the left side of the equation, and to satisfy the equation. A quadratic problem should only have two possible solutions. One contends that if there is just one solution, the problem has numerous causes.
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