A mathematical statement indicating an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Divide both sides of the inequality 2|x+1/3|3 to make it simpler:|x+1/3| < 3/2.
Consider the center of the group of numbers that fulfill 2|x+1/3|3 to be x = -1/3.
The maximum value of this set is obtained by adding 3/2 to this -1/3:
-1/3 + 3/2, or -2/6 + 9/6, or 7/6.
The bottom limit of this solution set is obtained by subtracting 3/2 from this and then -1/3:
-1/3 - 3/2, or -2/6 - 9/6, or - 11/6.
The answer range is (7/6, -11/6).
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Let f(x) = 2x+4. If f(x) = 16, find x.561024
Solution
Let f(x) = 2x+4. If f(x) = 16, find x.
[tex]\begin{gathered} f(x)\text{ =16} \\ f(x)=2x+4 \\ \text{Let's replace f(x) with 16} \\ 16=\text{ 2x+4} \\ \text{collect the like terms} \\ 16-4=2x \\ 12=2x \\ \text{Divide both sides by 2} \\ x=6 \end{gathered}[/tex]Answer:
x=6
Step-by-step explanation:
Substitute f(x)=16 into the equation:
16=2x+4
Get x by itself:
2x=12
Divide both sides by 2:
x=6
What does K =
2(k-3)/k+9 = 3/5
The value of k in the equation is 6.
How to solve equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Therefore, the equation can be solved as follows;
[tex]\frac{2k-3}{k+9}=\frac{3}{5}[/tex]
cross multiply
5(2k - 3) = 3(k + 9)
10k - 15 = 3k + 27
add 15 to both sides of the equation
10k - 15 = 3k + 27
10k - 15 + 15 = 3k + 27 + 15
10k = 3k + 42
subtract 3k from both sides of the equation
10k = 3k + 42
10k - 3k = 3k - 3k + 42
7k = 42
divide both sides by 7
k = 42 / 7
k = 6
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When constructing a confidence interval for the population mean using the standard deviation of the sample, the degrees of freedom for the t distribution equals.
The t distribution's degrees of freedom are equal to n - 1 by standard deviation.
What does math standard deviation mean?
The standard deviation shows the average level of variability in your dataset. It provides the standard deviation of every statistic. A low standard deviation indicates that values are frequently within a certain distance of the mean, whereas a high standard deviation indicates that values are frequently outside of this range. Consider the information below: 2, 1, 3, 2, 4. The deviations from the mean of the observations will be represented by the average and the sum of squares, which will be 2.4 and 5.2, respectively. This indicates that the standard deviation will be (5.2/5) = 1.01.The degrees of freedom for the t distribution when creating a confidence interval for the population mean using the sample's standard deviation equals n - 1.
Degrees of freedom = n - 1
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a fruit basket contains 5 apples, 6 oranges, and 3 peaches. if 3 fruit are selected and consumed, then compute the chance that all 3 fruits are not apples. write the answer as a decimal number rounded to third place value. group of answer choices
All three fruits are not apples is 0.027
Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection.
P (X) = n/N
Given :
A fruit basket contains 5 apples
oranges=6
peaches=3
To find :
compute the chance that all 3 fruits are not apples ?
Solution :
P(all 3 are apples) =(5x4x3)/(14x13x12)
⇒ 60/ 2184
⇒ 0.027
the chance that all 3 fruits are not apples is 0.027
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Look at the two histograms below. They give you information about the heights of players on two basketball teams, the Tigers and the Panthers. Use the histograms to answer the following questions.
The most appropriate choice for histogram will be given by-
a) Team tigers has taller players than team panthers
Team panthers has shorter players than team tigers.
b) team tigers have height that vary more.
c) So team panthers have more players about the same height.
What is histogram?
Histogram is a type of bar graph which makes use of the range of classes in the horizontal x axis and the frequency of classes in the vertical y axis.
Here,
a) The bars in the histogram of team tigers are relatively taller than the bars in the histogram of team panthers. So, team tigers has taller players than team panthers.
The bars in the histogram of team panthers are relatively shorter than the bars in the histogram of team tigers. So, team panthers has shorter players than team tigers.
b) For team tigers, there are no players between 66-69 inches height and, two players between 69-72 inches height and five players between 72-75 inches height. So fluctuations between the heights of two consecutive bars for team tigers is more.
For team panthers, it can be seen that the fluctuation between the heights of heights of two consecutive bars is not that much.
So team tigers have height that vary more.
c) In team panthers, there are one player in 63-66 inches and 69-72 inches, three players in 66-69 inches and 75-78 inches and two players between 72-75 inches and 78-81 inches. So team panthers have more players about the same height.
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Complete Question
The diagram has been attached here
Look at the two histograms below. They give you information about the heights of players on two basketball teams, the Tigers and the Panthers. Use the histograms to answer the following questions.
a)Which team has taller players? Which has shorter players? Explain your thinking.
b)Which team has heights that vary more? Explain your thinking.
c)Which team has more players that are about the same height?
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evaluate the expression 2⋅(|3.4−6|−1.8)÷2 1/2+(−2)^3.
On evaluating the given expression we get -9.6. We use the BEDMAS rule where we solve Brackets, Exponents, Division, Multiplication, Addition and Subtraction in a given expression in this order.
We evaluate the the problem using BEDMAS rule:
2.(|3.4-6|-1.8)÷2 1/2+(-2)^3
= 2.(|12-6|-8) ÷ 5/2 + (-8)
= 2.(6-8) ÷ 5/2 - 8
=2.(-2) ÷ 5/2 - 8
= -4 ÷ 5/2 - 8
= -8/5 - 8
= -48/5
= -9.6
Thus the answer of the the given expression we get after evaluating it is -9.6
Another problem on evaluating the expression using BEDMAS
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given f(x)=4x+1 describe how the graph of g compares with the graph of f. g(x)=(4x+1)+3
The description of the graph of function g(x) is 3 units translation up
How to describe the graph of function g(x)?The equations of the functions are given as
f(x) = 4x + 1
g(x) = (4x + 1) + 3
Substitute f(x) = 4x + 1 in the equation g(x) = (4x + 1) + 3
So, we have
g(x) = f(x) + 3
The above rule implies that:
The function g(x) is a translation of the function f(x)
The unit of the translation is 3 and the direction of the translation is up
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Find the unit rate. It took Timothy four days to finish 1/5 of his book. How much of the book did he read per day?
Group of answer choices
1/20 of the book
4/5 of the book
5/3 of the book
3/4 of the book
Answer:
Timothy read 1/20 of the book each day
is y=1000x proportional?
Answer:
has a proportional relationship with a constant of proportionality of 1000.c
Step-by-step explanation:
y=1,000x,y=1,000x
In finding the solution of the equation: 5 - 3x = 2 + 9, 3x is added to both sides of the equation first. Which of the following should be done next?
add -9
add -5
add -2x
The next step in solving the equation 5 - 3x = 2 + 9 is (a) add -9
How to determine the first step?From the question, we have the following equation that can be used in our computation:
5 - 3x = 2 + 9
When 3x is added to both sides, the equation becomes
5 = 2 + 9 + 3x
The next step is to eliminate 9 or 2 from the variable term
This can be done by adding -9 to both sides
So, we have:
-9 + 5 = 2 + 3x
Hence, the next step is (a) add -9
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Question 8 of 8 Pls answer quickly pls and thank you
What are all the possible ways to classify the following shape?
shape
A. polygon, quadrilateral, trapezoid
B. polygon, quadrilateral, parallelogram, trapezoid
C. quadrilateral, trapezoid
A polygon is a flat shape that is encircled by lines known as edges. It has a two-dimensional appearance. As a result, all of the shapes in sections a, b, and c are polygons.
A. Trapezoid, Quadrilateral - A trapezoid always forms a quadrilateral since it is a regular polygon having four sides. A trapezoid is a quadrilateral with opposing parallel sides. A right angle, also known as a right trapezoid, can have congruent sides, which are referred to as isosceles.
B. Polygons, quadrilaterals, parallelograms, and trapezoids - A quadrilateral is a four-sided shape. A parallelogram is a form with four parallel and equal-length sides. A parallelogram's area is equal to the base multiplied by the height. A trapezoid is a shape that has at least one set of opposite ends that are parallel.
C. quadrilateral, trapezoid - A trapezoid is a quadrilateral with several parallel opposed sides. Although the right angles of square trapezoids and isosceles triangles can be included which is an isosceles quadrilateral.
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I don't understand this: beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet. how many cans will beth need to buy?
The required number of cans would be 2 for painting a circular tabletop that has a radius of 3 feet.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
We have been given that beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet.
Firstly, we need to calculate the area of a given circular tabletop which is equal to the area of a circle with a radius of 3 feet.
area of the circular tabletop = the area of a circle
area of the circular tabletop = π r²
Here r = 3 feet
area of the circular tabletop = π (3)²
area of the circular tabletop = 9π
area of the circular tabletop = 28.27 square feet
Required number of cans = 28.27 / 15
Required number of cans = 1.88 ≈ 2
Therefore, the required number of cans would be 2.
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joseph can ride his bike 32 miles in 5 hours. kyle can ride his bike 20 miles in 3 hours who would ride farther in 15 hours explain .
A carpenter is building a triangular frame. She has three pieces of wood measuring 5 feet, 6 feet, and 12 feet.
The carpenter
build the triangular frame with the three pieces of wood. She could cut the
Piece by
To create a triangular frame
Answer: Cannot, 12 foot , 2 feet
Step-by-step explanation:
5/5 on test
The carpenter can cut the 12 feet wood by 2feet to make triangular frame.
What is triangle?A polygon with three vertices and three edges is called a triangle. Geometry's most fundamental shape is this one. Triangle ABC is a triangle with A, B, and C as its vertices.
Any three non-collinear points can create a unique triangle and a unique plane in Euclidean geometry (a two-dimensional Euclidean space). To put it another way, every triangle is contained in some plane, and there is only one plane that contains that triangle.
Given Carpenter has three pieces of wood measuring 5 feet, 6 feet, and 12 feet.
and wants to make a triangular frame,
with these wood pieces he can not make the triangular frame because it does not follow the property of triangle,
which says the sum of two sides of triangle should always greater than the larger side,
here large side is 12 feet and 5 + 6 is less than 12,
so to make a triangular frame he should decrease the larger side which should be less than 11
by cutting 12 feet piece by 2 feet it will be 10 feet and carpenter can make the triangular frame.
Hence the carpenter need to cut 12 feet long piece by 2 feet, to make triangular frame.
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-6(x)² + y³ - 8.
For x = 3
For y = 2
Answer:
- 54
Step-by-step explanation:
substitute x = 3 , y = 2 into the expression
- 6x² + y³ - 8
= - 6(3)² + 2³ - 8
= - 6(9) + 8 - 8
= - 54 + 0
= - 54
peter deposited $7,790 into an account that earns 4 5/8% interest, compounded annually. calculate the interest peter will earn after 42 months. how much will peter have in his account after 42 months?
The interest earned by Peter after 42 months is $1,335.60 and the total amount in his account is $9,125.60.
How to determine the accrued ( A ) and interest ( I ) amount in a compound interest?The formula for compound interest is expressed as;
A = P(1 + r/n)^nt
Where A is accrued amount, P is principal, r is interest rate, n is compound, and t is time period.
Given the data in the question;
Principal P = $7,790Annual interest r = 4 5/8%Compounded annually n = 1Time t = 42 monthsAccrued amount A = ?Interest I = ?First, convert the interest rate to decimal.
Rate r = 4 5/8% = (4×8 + 5 )/8%
Rate r = 37/8%
Rate r = 4.625%
Rate r = 4.625/100 = 0.04625 per pear
Next, convert time from months to years
Time t = 42 month = ( 42/12 )years
Time t = 3.5 years
To determine the accrued amount, plug the given values into the compound interest formula and solve for A.
A = P(1 + r/n)^nt
A = $7,790(1 + 0.04625/1)^( 1 × 3.5 )
A = $7,790(1 + 0.04625 )^( 3.5 )
A = $7,790(1.04625 )^( 3.5 )
Accrued amount A = $9,125.60
Note that; Accrued amount A = Principal P + Interest I
Hence;
Interest I = A - P
Interest = $9,125.60 - $7,790
Interest = $1,335.60
Amount in the account after 42 months is the same as the accrued amount A, this is $9,125.60.
Therefore, the interest earned is $1,335.60 and the accrued amount is $9,125.60.
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Find AX. A(-4, 5), X(1, −2)
The distance of AX, A(-4, 5), X(1, -2) is 8.6
The distance formula is used to find the distance (shortest path) between two points.
The distance formula is
[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} } \\d = \sqrt{(-4 - 1)^{2} + (5 - (-2))^{2} } \\d = \sqrt{(-5)^{2} + (7)^{2} } \\d = \sqrt{25 + 49}\\ d = \sqrt{74}[/tex]
d = 8.6
Therefore, the distance of AX, A(-4, 5), X(1, -2) is 8.6
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write as a single fraction:
2/x+2 + 3/2x+1
Answer:
3x2+6x+4 2x
hope this helps !!
HAVE A AMAZING DAY
Answer:
(6x+7)/2x
Step-by-step explanation:
2/x+2 + 3/2x+1
2/x+2x/x + 3/2x+x/x [Convert the bolded numbers into fractions with x in the denominator.
2/x+2x/x + 3/2x + x/x [Convert the bolded numbers so that the denominator becomes 2x]
4/2x+4x/2x + 3/2x + 2x/2x
4/2x+4x/2x + 3/2x + 2x/2x [Now that all numbers have the same denominator, we can add the numerators]
(4+4x + 3 + 2x)
(6x+7)
(6x+7)/2x [Place the denominator, 2x, back into the fraction]
LEMON SQUASH 1 part concentrate to 2 parts water If you put 25 ml of concentrate in a glass, how much water should be added? ml
A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after
m months is given by the following function.
H(m)=51+m
What is the plant's height after 33 months?
Answer:
84 cm
Step-by-step explanation:
H=51+m
m=months, substitute m for 33 months
H=51+33
H=84
The plant's height will be 84 cm after 33 months
the positive difference between the product of 78 and 36 and their sum is
Answer:
2694
Step-by-step explanation:
product of 78 and 36=78*36=2808
sum =78+36=114
difference between them =2808-114=2694
Find the unit rate. Enter your answer as a mixed number.
A fertilizer covers
5/8
square foot in
1/6
hour.
The unit rate is square feet per hour.
The unit rate is the change of a quantity over one unit of another thus the unit rate of fertilizer covers is (30/8) foot per hour.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
A fertilizer covers 5/8 square feet in 1/6 hour.
5/8 square feet ⇒ 1/6 hour
Multiply both sides by 6
6 × 5/8 square feet ⇒ 6/6 hour
30/8 square feet ⇒ 1 hour.
Hence "The unit rate is the change of a quantity over one unit of another thus the unit rate of fertilizer covers is (30/8) foot per hour".
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I need help with the following question.
Answer:
A
(Look at the screenshots below)
1st screenshots shows the "moved down to two units"
2nd screenshot shows the"flipped over a vertical line that lines halfway between the two triangles"
de
Identify the Base and Height of Triangles
A formula for calculating the area of a triangle is A=bh, where b is the length of the
or length of an altitude, of the triangle.
Identify the base and sketch in the height on each type of triangle.
Right triangle
and his the
Acute triangle
Obtuse triangle
A formula for calculating the area of a triangle is A=1/2(b*h), where b is the length of the base and h is the height of or length of the altitude, of the triangle.
Identify the base and sketch in the height on each type of triangle.
right triangle - One of the sides that touches the 90-degree angle constitutes the foundation of a right triangle.
The height of a triangle is measured from its base to its highest point, and in a right triangle, that height can be determined from the side that forms a right angle to the base.
acute triangle - Three sides and three vertices make up the fundamental polygon known as the triangle. It has three sides, which results in three interior angles. An acute angle is one that is between 0° and 90° in length. When all three of the triangle's internal angles are acute, the triangle is said to be acute.
obtuse triangle - In an obtuse triangle, the height or altitude from the acute angles is outside the triangle. To find the height of the obtuse triangle, we extend the base as illustrated.
what is a triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time.
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Y-intercept = 4 Slope = 2
Answer:
y=2x+4
Step-by-step explanation:
Guessing you need an equation?
5−−4=
Pls help it’s due in 20 mins
NEGATIVE TIMES NEGATIVE GIVES POSITIVE
[tex]5 - ( - 4) \\ = 5 + 4 \\ = 9[/tex]
ATTACHED IS THE SOLUTION
Answer:9
Step-by-step explanation:
-- = + ( 5+4)
++= +
-+ = -
+- = -
Please help ASAP!! This is overdue!
The equation of each line is labelled as shown in the image attached below, where:
y = 2x + 7 is line b
x + 5y = 10 is line d.
x + y = -9 is line f.
y = x is line c.
x = -5 is line a.
y = -5 is line e.
What is the Equation of a Line?The equation of a line can be rewritten as y = mx + b, if the line has a slope of m and a y-intercept of b.
For vertical lines, the equation is written as x = b, where b is where the line cuts across the x-axis.
For horizontal lines, the equation is written as y = b, where b is the point on the y-axis the line intercepts.
The equation y = 2x + 7 is a line that has a slope of 2 and a y-intercept of 7. This line is labelled as line b in the image below.
x + 5y = 10 is rewritten as y = -1/5x + 2. The slope is 1/5 and the y-intercept is 2. This equation is labelled as line d.
x + y = -9 is rewritten as y = -x - 9. The slope is -1 and the y-intercept is -9. It is represented by the line labelled line f.
y = x has a slope of 1 and passes through the origin, (0, 0). It is labelled as line c.
x = -5 is the vertical line that is labelled as line a.
y = -5 is the horizontal line that is labeled as line e.
See image below.
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Solve for variable c
6c x 88 - 93 = 67
6c X 88 = 93+67
528c=160
C=0,303030303030303
A baseball team won 16 of their first 20 games. If they win half of the rest of their games, how many more
games will they have to play in order to win 75% of the total number of games?
The least number of games the team must win to raise its winning record above 75 percent is -4 , by raising the win fraction to the total number of fractions as 36/48.
What is meant by fractions?There are ratios of fractions that represent a portion of the whole. A fraction has the form a/b, which may be read as "a by b," and it has the function a divided by b. The denominator is referred to as b, and the numerator is known as a.
To transform a percentage to a fraction, we divide it by 100.
Given that a baseball team has won 18 of the 30 games it contains played during the season.
We exists asked the least number of games the team must win to raise its win record above 75%.
Let the number of games needed to be x.
The new number of wins will be the sum of current wins and the games to win, that exists, the new number of wins = 16 + x.
The new number of games played will be the sum of current games played and the games to win, that exists, the new number of games played = 20 + x.
Therefore, the win fraction of the team can be shown as the ratio of the total wins to the total number of games played, that exists, the win record = (16 + x)/(20 + x).
We exists asked to make sure that the win record should be at least 75%,
This percentage can be described as the fraction 75/100 = 3/4.
Therefore, we get the equation:
(16 + x)/(20 + x) = 3/4,
simplifying the above equation, we get
4x - 3x = 3x - 4x - 4,
x = -4.
Therefore, by increasing the victory fraction to the entire number of fractions as 36/48, the team just needs to win -4 games to improve its winning percentage above 75%.
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R is directly proportional to T. If R = 60 when T = 10, Calculate the value of T when R = 54
Answer:
T=9
Step-by-step explanation:
if R is proportional to T
[tex] t = rk [/tex]
Where k is a constant
[tex]10 = 60k[/tex]
[tex]k = \frac{1}{6} [/tex]
Therefore,
[tex]54 \times \frac{1}{6} = t[/tex]
[tex]t = 9[/tex]