The solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.
What do math inequalities mean?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols <, >, ≤, ≥ and ≠.Given inequality is given as:
|x-1| ≤ 5
Simplifying this inequality we get,
-5 ≤ x-1 ≤ 5
Adding 1 on both sides, we get,
-5+1 ≤ x-1 ≤ 5+1
-4 ≤ x ≤ 6
Therefore, the solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.
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NOTE: The given question is incomplete on the portal. Here is the complete question.
QUESTION: What is the solution set of the inequality |x-1| ≤ 5?
How many time greater i the value of the digit 2 in 23. 876 than the value of the digit 2 in 3. 254?
The value of the digit 2 in 23,876 is 100 times greater than value of digit 2 in 3,254. This result is obtained by paying attention to the place value of the number in the number.
How to determine the value of the digit 2These are the specified parameters:
Numbers 23,876 and 3,254.
The value of the digit 2 in 23,876 is 20,000
The value of the digit 2 in 3,254 is 200
Magnification the value of the digit 2
= 20,000 ÷ 200
= 100
So the value of the number 2 at 23,876 is 100 times greater than the value of the number 2 at 3,254.
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Tickets to a baseball game are $11 for adults and $6 for children. If twenty more children’s tickets are sold than adult tickets, how many of each type of ticket is sold if a total of $9,300 is taken in?
Answer:
560 children tickets
540 adult
Step-by-step explanation:
560x6=3360
540x11=5940
3360+5940 = 9300
find the smallest two-digit prime number such that reversing the digits of the number produces a composite number.
Answer: The smallest two-digit prime number such that reversing the digits of the number produces a composite number is 19
Step-by-step explanation:
11, which is the smallest two-digit prime number, 11 remains the same number when the digits are reversed, and it is a prime number, of course.
The next two-digit prime number is 13. 13 becomes the prime number 31 when the digits are reversed.
17 is the following two-digit prime number. The result of flipping the digits of 17 is 71, a prime number.
19 is the following two-digit prime number. Reversing the digits of 19 results in 91, which is composite because 7*13= 91
Thus, 19 is the answer.
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PLS HELP, 50 POINTS + BRAINLY FOR CORRECT ANSWER!!!
Answer: No, only Alex's solution is correct.
Step-by-step explanation:
Morgan's solution is incorrect because he subtracted 3 from the parentheses, which is illegal (in math, of course). This means that his answer is incorrect.
Answer: Alex is correct.
Step-by-step explanation:
Alex's steps are correct and are used properly, unlike Morgan, which did steps that aren't allowed and don't make sense. Alex's answer is correct.
The guidance department has reported that of the senior class, 2. 3% are members of key club, k, 8. 6% are enrolled in ap physics, p, and 1. 9% are in both. What is the probability of p given k?.
the probablilty of p and k is 82.6%.
Given:
key club P(k) = 2.3%
physics P(p) = 8.6%
(p∩k) = 1.9%
formula:
P(p/k) = P(p∩k)/P(k)
putting the value,
P(p/k) = 1,9%/2.3%
= 0.019/0.023
= 0.826 = 82.6%
hence the probability of p given k is 82.6%.
#123
The probability of P given K is 0.826.
Given information;
The guidance department has stated that of the senior class, 2.3% are members of key club, K, 8.6% are enrolled in AP physics, P, and 1.9% are enrolled in both. This information is supplied in the question.
To get the probability of P given K [P(A)];
P(K) = 2.3
P(P) = 8.6
P(P ∩ K) = 1.9
P(A) = P(P ∩ K) / P(K)
= 1.9/2.3
= 0.826
Hence, the probability of P given K is 0.826.
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A reseller has a budget of $800 to purchase desks. Each desk costs an
equal amount and is available at a fixed discounted percent. The expression
800 (48d-0.18.48d) represents the amount of the budget, in dollars, left
after buying d desks.
The expression that represents the total amount of discount in dollars is; (48d - 0.18 x 48d)
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by the mathematical symbol; which can b used to indicate the logical syntax's order of operations and other features.
We are given that the reseller has a budget of $800 to purchase desks. Each desk costs an equal amount and is available at a fixed discounted percent.
The expression 800 (48d - 0.18 x 48d) represents the amount of the budget, left after buying d desks.
Therefore, the expression that represents the total amount of discount in dollars are;
(48d - 0.18 x 48d)
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During lockdown Dr Jack reckoned that the number of people getting sick in his town was decreasing by 40% every week. If 3000 people were sick in the first week and 1800 in the second week (3000 x 0.60 = 1800) then how many people would have become sick in total over an indefinite period of time?
The number of people that would have become sick in total over an indefinite period of time is of:
7500.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, meaning that each term is obtained by the multiplication of the previous term by the common ratio q.
The nth term of a geometric sequence is given by the rule presented as follows:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of an infinite sequence, as long as |q| < 1, is given by:
[tex]S = \frac{a_1}{1 - q}[/tex]
The first term and the common ratio in this problem are given as follows:
[tex]a_1 = 3000[/tex], as 3000 people got sick during the first week.q = 0.6, as the number decayed by 40% each week, that is, it was multiplied by 0.6 each week.Hence the total number of people who got sick is obtained as follows:
S = 3000/0.4 = 7500.
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Find the absolute oof each integer 7
three friends said their heights were 5 13/30 feet, 5 1/6 feet, and 5 68/90 feet. put the heights of the friends in order from least greatest.
Answer:
convert the fractions to a common denominator of 90
5 1/6 , 5 13/30 , 5 68/90
. A quilt is 72 inches wide and 88 inches long. If the quilt has no border or sashing and the
blocks have 4 inch sides, how many blocks does the quilt have?
[A] 396
[B] 160
[C] 6336
[D] 320
[E] 469
4. A quilt is 42 inches wide and 69 inches long, including a border of 3 inches all the way around.
The quilt’s square blocks have 9-inch sides. If you don’t count the border, how many blocks
does the quilt have?
[A] 27
[B] 39
[C] 18
[D] 28
[E] 42
Answer:
[A] 396,[D] 28.Step-by-step explanation:
Question 1The area of the quilt is:
A(q) = 72*88 = 6336 in²The area of each block:
A(b) = 4*4 = 16 in²Number of blocks:
n = A(q) / A(b) = 6336/16 = 396 in²Correct choice is [A]
Question 2Dimensions of the quilt excluding borders on each side:
Width = 42 - 3*2 = 42 - 6 = 36 in,Length = 69 - 3*2 = 69 - 6 = 63 in.Area of the quilt:
A(q) = 36*63 = 2268 in²Area of each block with side 9 in:
A(b) = 9*9 = 81 in²Number of blocks:
n = A(q) / A(b) = 2268/81 = 28Correct choice is [D]
The composition of transformations Ry=-5 r (90,A) maps ABC to XYZ if the perimeter of XYZ is 26 what is the possible set of values of AB, BC, and AC? Explain.
If the perimeter of XYZ is 26 then the answer will be 6.5.
What is composition of transformation?
A composition of transformations combines two or more transformations that were separately applied to the prior image. The result of a composition of reflections along parallel lines is identical to that of a translation (twice the distance between the parallel lines).
What is Perimeter?
The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given;
The composition of transformations Ry=-5 r (90,A) maps ABC to XYZ .
the perimeter of XYZ is 26
ΔABC is the reflection of ΔXYZ which is transformed with angle 90°.
So,the answer will be [tex]26\div 4 = 6.5[/tex].
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If triangle ABC ~ AVW find the values of x and y
The values of x and y are 44.8 & 19.2 respectively.
What is the similarity theorem of the triangle?
According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.
We have,
ΔABC ~ ΔAVW
We know the similarity theorem of triangle,
[tex]\frac{AC}{AW} = \frac{CB}{VW}[/tex]
28/ x = 16/10
x = 1.6 * 28
x = 44.8
[tex]\frac{AB}{AV} = \frac{CB}{VW}[/tex]
y/12 = 16/10
y = 1.6 * 12
y = 19.2
The values of x and y are 44.8 & 19.2 respectively.
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PLEASE HELP IM BEING TIMED
If M(31, –5) is the midpoint of the line segment whose endpoints are A and B(2, –19), what are the coordinates of endpoint A?
(–27, –33)
(16.5, –12)
(45, 24)
(60, 9)
The coordinates of the endpoint A = (A, B) is (60, 9)
What is the midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
Midpoint = (31, -5) = (x, y)
Endpoints:
A = (a, b) and B = (2, -19) = (c, d)
The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Now,
31 = (a + 2)/2
31 x 2 = a + 2
62 = a + 2
a = 62 - 2
a = 60
-5 = (b - 19)/2
-5 x 2 = b - 19
-10 = b - 19
-10 + 19 = b
b = 9
Thus,
The coordinates of the endpoint A = (A, B) is (60, 9)
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A survey by the national retail federation found that women spend on average r146. 21 on a saturday lunch. Assume the standard deviation is r29. 44. Find the percentage of women who spend less than r160. 00 on a saturday lunch. Assume the variable is normally distributed.
0.68 is the variable is normally distributed when standard deviation is r29. 44.
What is standard deviation in math?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. A low standard deviation means that values are clustered close to the mean, whereas a high standard deviation means that values are typically far from the mean.μ = 146.21 σ = 23.44 x ~ n
P{ x < 160 } = ρ{ x - μ/σ < 160 - 146.21/29.44 }
= ρ{ z < 0.47 }
= 0.6808
≈ 0.68
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Help me Understand how 12 + 5 = 169 = 13 Using the Pythagorean Theorem
Using the Pythagorean Theorem, 12² + 5² = 169 = ✓169 = 13
What is Pythagoras theorem?This is simply the way that one can find the missing length of a right angled triangle.
In this case, it should be noted that the theorem is in the form of:
a² + b² = c²
c = hypothenuse
a and b are the other sides
Based on the information given, this will be:
5² + 12²
= 25 + 144
= 169
Now the square root of 169 is ✓169 = 13.
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John has $23.65 to spend on a book and magazines. The book costs $5.95. the magazine cost 2.95 each
Make let statements and equation than solve the equation you made
Unit-Solving equations
Answer:
Let x = # of magazines , $23.65=$5.95+$2.95x , x = 6
Step-by-step explanation:
$23.65=$5.95+$2.95x
this is equation for this one because we know that 23.65 is the total money they have total and 5.95 cost for book and 2.95 dollar what each magazine. however, this equation needs to be solved to find x
23.65=5.65+2.95x
23.65-5.95=-5.95+2.95x
17.70=2.95x
17.70/2.95=
6=x
He can buy 6 magazines with his money.
If the area of AABC is 288in², and if DB = 15in, and CD = 9in, what is the length of AD
The length of the side AD is 24 inches
Consider the triangle ABC
The area of the triangle = 288 square inches
The length of the side CD = 9 inches
The length of the side DB = 15 inches
The length of the the base = The length of the side CD + The length of the side DB
Substitute the values in the equation
The length of the the base = 9 + 15
= 24 inches
The area of the triangle = (1/2) × Base × Height
Substitute the values in the equation
288 = (1/2) × 24 × AD
288 = 12 × AD
AD = 288 / 12
AD = 24 inches
Hence, the length of the side AD is 24 inches
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Write the point-slope form of the equation of the line that passes through the origin and has a slope of 2
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.
SHOW ALL WORK!!!!!
Answer:
Point Slope Form: y - 0=2 (x - 0)
Simplified Form: y=2x
Step-by-step explanation:
The point-slope form of line is given by:
y - y1=m(x - x1)
Where
m is the slope
is the first x-coordinate
is the first y-coordinate
Given slope is 2, thus we can say:
m = 2
Also, it says the line goes through the point (0,0), so:
and
Now, substituting, we get the point slope form to be:
y-y1=m(x - x1)
y-0=2(r-0)
y=2(x)
y=2x
The equation of line will be y = 2x
The slope of the equation m = 2 and the point P ( x₁ , y₁ ) = P ( 0 , 0 )
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Let the point be represented as P
The value of P = P ( 0 , 0 )
The slope of the equation m = 2
Slope m = 2
Now , the equation of line in the slope intercept form is
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 0 = 2 ( x - 0 )
On simplifying the equation , we get
y = 2x
Therefore , the value of A is y = 2x
Hence , the equation of line is y = 2x
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Part A Giulio is looking to take out a loan of $5,000 that he plans to pay back over the next 3 years. He has two options: • The first option includes a simple interest rate of 2.8%. • The second option includes an interest rate of 2.7% compounded monthly. Find the balance that Giulio would pay for each loan option. Type the correct answer in each box. Use numerals instead of words. If necessary, round to the nearest hundredt If Giulio chooses the first option with simple interest, he will pay a total of $ If he chooses the second option with the lower rate and compound interest, he will pay a total of $
Answer:If Giulio chooses the first option he will pay about 4,500
If he chooses the second option with the lower rate and compound interest, he will pay a total of about 3,000.
Step-by-step explanation: I dont have an explanation but I think I'm right
gaby can tun at a speed of 12 mph how many miles can she cover in 12 minutes
A. 0.42 miles
B. 60 miles
C. 144 miles
D. 2.4 miles
The distance covered by gaby at a speed of 12 mph in 12 minutes is
2.4 miles.
Given,
Speed at which gaby is walking = 12 mph
we are asked to determine the distance covered by gaby at a given speed in 12 minutes = ?
We know, Distance = Speed × Time
speed = 12 mph
time = 12 minutes
= 12/60 hr
Distance = 12 × 12/60
= 5/2
= 2.4 miles
Hence gaby can cover 2.4 miles in 12 minutes.
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Find the area of the triangle if the perimeter of the triangle is 50 ft.
Answer:
120 ft²
Step-by-step explanation:
The length of each of the congruent sides is (50-16)/2 = 17 ft.
So, using the Pythagorean theorem, the altitude drawn from the vertex angle to the base has a length of 15 ft.
Thus, the area is (1/2)(15)(16) = 120 ft².
1/2x + 3/4x + 1/4x + 4
1/2x + 3/4x + 1/4x + 4
2/4 x + 3/4x + 1/4x + 4
1.5x + 4 or 3/2x + 4
(Both are the same, depends on if you need decimal or fractional answer)
The vertices of a triangle are A(-4, 6), B(6.4), and C(6. - 2). Draw the image after a dilation with a scale factor of 1/2.
Step-by-step explanation:
we have to mark the angles in the point denoted in the graph and connect it
The illustration of the dilated triangle has been shown.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
The vertices of a triangle are A(-4, 6), B(6.4), and C(6. - 2).
The scale factor of 1/2.,
Coordinates of the vertices of the triangle with scale factor,
A' = (-4 × 1/2 , 6 × 1/ 2)
A' = (-2, 3)
Similarly,
B' = (3, 2)
C' = (3, -1)
Thus, the illustration of the dilated triangle has been shown.
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a pack of 6 batteries of the same type costs £2.79.By calculating the price per battery,determine if this is better value. You must show your working
The required price of one battery from the pack is £0.465.
How we calculate the price of a battery when have a price of collection of the batteries?When we given a pack of objects with some cost, then to calculate the price of one object, divide the amount of pack by number of objects in the pack.
According to given information:we have, price of 6 battery = £2.79
Then, the price of one battery = £2.79/6 = £0.465
Thus, the the price per battery is £0.465.
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plsssss helppppp meeeeeee
The solution of the system of equations y = -x + 6 and y = (1/2)x - 6 be
(8 , -2)
Given, two linear equations
y = -x + 6
y = (1/2)x - 6
Now, to plot the first equation i.e. y = -x + 6
first plot two points
(0 , 6) and (6 , 0)
Now, pass a straight line through these two points and we get the graph of the given equation.
Now, to plot the second equation i.e. y = (1/2)x - 6
first plot two points
(0 , -6) and (12 , 0)
Now, pass a straight line through these two points and we get the graph of the given equation.
Now, to get the solution Plot the point of intersection of these two lines i.e. (8 , -2)
Hence, the solution of the system of equations be (8 , -2).
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This table shows some values of function
| x | 0 | 3 | 5 |
| f(x) | 13 | 104 | 416 |
Which of the following equations models f(x)?
A. f(x) = 2x + 13
B. f(x)= 13(2)ˣ
C. f(x)= 8x + 80
D. f(x)= 91(2)ˣ⁻1
Please show your work and/or explain how you got your answer:
PLEASE HELP!!!!
For the given ordered pairs, function f(x)= 13(2)ˣ models f(x). Therefore, option B is the correct answer.
From the given table, the ordered pairs are (0, 13), (3, 104) and (5, 416).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Substitute (0, 13), (3, 104) and (5, 416) in the given functions and simplify
A) f(x)=2x+13
With x=0, we get f(x)=13
With x=3, we get f(x)=19
With x=5, we get f(x)=23
B) f(x)= 13(2)ˣ
With x=0, we get f(x)=13
With x=3, we get f(x)=104
With x=5, we get f(x)=416
For the given ordered pairs, function f(x)= 13(2)ˣ models f(x). Therefore, option B is the correct answer.
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List all subsets for the following set: {-2,1}
The subsets of the given set are {-2}, {1}, {-2, 1}, and ∅.
Determining the subsets of a given setFrom the question, we are to list all the subsets of the given set.
Given two sets A and B; set A is a subset of set B if all elements of A are also elements of B.
Therefore, we will find all possible sets that have the element(s) of the given set.
The given set is {-2, 1}
The subsets of this set are {-2}, {1}, {-2, 1}, and ∅
Hence,
The subsets are {-2}, {1}, {-2, 1}, and ∅
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You can convert gallons to liters by using a factor of 3.79. That is, 1 gallon is about 3.79 liters. About how many liters are in 37 gallons? Is your answer an underestimate or overestimate? Explain.
140.23 liters are in 37 gallons
We have been given you can convert gallons to liters by using a factor of 3.79
That is, 1 gallon = 3.79 liters.
We need to find the amount of liters in 37 gallons.
Let 37 gallons = x liters
As we know 1 gallon = 3.79 liters.
So, by Unitary method,
x = 37 * 3.79
x = 140.23 liters
Therefore, 140.23 liters are in 37 gallons
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2) Select all of the statements that are true concerning the measures of a circle.
a. The circumference of a circle with a radius of 1 unit is equal to pi square units.
b. The area of a circle with a diameter of 1 unit is equal to pi square units.
c. The circumference of a circle with a radius of 1 unit is equal to pi units.
d. The circumference of a circle with a diameter of 1 unit is equal to pi units.
e. The value pi represents the constant of proportionality that gives the circumference of a
circle, if you know its diameter.
f. The value pi represents the constant of proportionality that gives the area of a circle, if
you know its diameter.
The statements (b) and (d) are true concerning the measurements of a circle.
What is a circle?
A circle is a reconstructed by all elements in a plane that lie at a particular separation from the center. It is the curve sketched out by a point moving in a surface so that its radius from a particular point remains constant. The radius describes the distance either between two points on a circle and the center. Ordinarily, the radius must be a greater than 0. A circle, in particular, is a basic closed curve that splits the plane into two regions: inner and exterior. A circle can alternatively be described as a kind of ellipse with two coincident foci, zero eccentricity, and equal semi-major and semi-minor axes.
The statements:
(b) The area of a circle with a diameter of 1 unit is equal to pi square units and
(d) The circumference of a circle with a diameter of 1 unit is equal to pi units are true concerning the measurements of a circle.
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Can someone show the work for this please
The value of x in the given equation is 1 or 8.
First, let us understand the equation:
An equation is a mathematical expression that includes the equals sign. Algebra is frequently used in equations.
We are given;
x / (x + 8) + 1 / (x - 8) = 2x / (x^2 - 64)
x (x - 8) + 1 (x + 8) / (x^2 - 64) = 2x / (x^2 - 64)
x^2 - 8x + x + 8 = 2x
x^2 - 8x - 2x + x + 8 = 0
x^2 - 9x + 8 = 0
x^2 - 8x - x + 8 = 0
x(x - 8) - 1 (x - 8) = 0
(x - 1) (x - 8) = 0
(x - 1) = 0 or (x - 8) = 0
x = 1 or x = 8
So, the value of x = 1 or 8.
Thus, the value of x in the given equation is 1 or 8.
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