The inequalities are solved below
What are inequalities?
A connection in mathematics that compares two numbers or other mathematical functions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. To indicate various sorts of inequalities, a variety of notations are employed. The following characteristics control inequalities. Any of these characteristics are also true if monotonic functions are restricted to strictly monotonic functions and all non-strict inequalities ( and ) are replaced by their equivalent strict inequalities ( and >). On each side of an inequality, a common constant c can be added to or removed from.
The inequalities are solved below
-2x-7>1 x-2≥-1
or, -2x>1+7 or, x≥-1+2
or, -x>8/2 or, x≥1
or, x<-4
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If the first term of gp is 1 and 4th is 27 find the ratio term and the 9th term
The ratio term of given geometric progression is 3 and the 9th term of the GP is 6561.
What is Geometric Progression?
A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54,_ _ _ _ has a common ratio of 3.
Given in question,
first term of the GP is 1,
4th term of the GP is 27,
[tex]4^{th} term = ar^3[/tex]
[tex]ar^3 = 27[/tex]
Therefore, the ratio term of geometric progression, r = 3
We know that, [tex]a_n = ar^{n-1}[/tex]
[tex]a_9 = ar^8[/tex]
[tex]a_9 = 3^8[/tex]
a9 = 6561
Therefore, the 9th term of given geometric progression is 6561.
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Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.
In linear equation, R = 4c is an equation to represent the amount R Natalia and her friends raised after selling c cakes.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as .
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like
R = mc + b
We need to find the value of m and b, to get an equation to represent the situation.
The first point we have from the information given is (15, 60) => 15 cakes sold for $60.
The second point is (22, 88) => 22 cakes sold for $88.
Slope(m) = 88 - 60/22 - 15 = 28/7 = 4
To find b, substitute c = 15, R = 60 and m = 4, into R = mc + b
60 = 4(15) + b
60 = 60 + b
b = 0
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into R = mc + b to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
R = 4c + 0
R = 4c
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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. tan 26° = ___
Answer:
0.49
Explanation:
Given the expression:
tan 26°
Evaluating using calculator
tan 26° = 0.4877
Hence the decimal rounded to the nearest hundredth is 0.49
Answer:
0.49 to nearest hundredth
Step-by-step explanation:
tan 26⁰ = 0.48773
PLEASE HELP I NEED THIS ASAP PLEASE!!!!
Answer: Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04in²
Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04 in²
Radius (r) 0.999493 in
Diameter 1.998986 in
Circumference (c) 6.28 in
Area 3.13841 in²
Radius (r) 8.49569 in
Diameter 16.99138 in
Circumference (c) 53.38 in
Area 226.75 in²
Radius (r) 2.5 cm
Diameter 5 cm
Circumference (c) 15.70796 cm
Area 19.63495 cm²
Radius (r) 1.1 yd
Diameter 2.2 yd
Circumference (c) 6.9115 yd
Area 3.80133 yd²
Radius (r) 2 in
Diameter 4 in
Circumference (c) 12.56637 in
Area 12.56637 in²
Step-by-step explanation: I hope this helps.
Mandrel has 15 electronic books and 24 education CDs. He gives 5 books and 12 CDs to his nephew. What
ratio of each did he give to his nephew? Are the ratios proportional?
Answer:
10:12
Step-by-step explanation:
15-5=10
24-12=12
og ratio is 15:24
new ratio is 10:12
ABCD is a rectangle. Find angles a and b to the nearest degree
Solution
Given, ABCD is a rectangle AC is diagonal
Then AD=BC and AB=CD
And ∠ABC=∠BCA=∠CDA=∠DAB=90
0
In ΔABC and ΔADC
∠ABC=∠ADC (Angle of rectangle)
AB=DC (Opposite side of rectangle )
AC=AC (Common side)
∴ΔABC≅ΔADC
∴∠ACD=∠ACB
∵∠ACD+∠ACB=90
0
..........[Angle ACB is the angle of rectangle]
∴2∠ACD=90
0
⇒∠ACD=45
0
Which of the following is NOT a misuse of statistics?Choose the correct answer below.A. Utilizing valid statistical methods and correct sampling techniquesB. Making conclusions about a population based on a voluntary response sampleC. Concluding that a variable causes another variable because they have some correlationD. Misleading graphs
Required:
We need to find the statement which is NOT a misuse of statistics.
Explanation:
Recall that misuse of statistics occurs when a statistical argument asserts a falsehood.
Utilizing valid statistical methods and correct sampling techniques is not a misuse of statistics.
Final answer:
A. Utilizing valid statistical methods and correct sampling techniques
Solve each equation.
4/7 v = -8 2/3
[tex] \frac{4}{7} v = - \frac{26}{3} \\ - 26(7) = 4v(3) \\ - 182 = 12v \\ \frac{ - 182}{12} = \frac{12v}{12} \\ v = - 15 \frac{2}{12} \\ v = - 15 \frac{1}{6} [/tex]
BE AWARE I USED CROSS MULTIPLICATION.
What is the
intermediate step in the form
(x + a)² = b as a result of completing
the square for the following equation?
-3x² - 35x - 189 = 13x
Using completing the square method (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.
What is completing the square method?A quadratic problem can be solved using the Completing the Square method. In order to do this, the equation's form must be altered so that the left side is a perfect square trinomial. Finding the roots or zeros of a quadratic polynomial or a quadratic equation is the most frequent use of the completing the square method, which also covers factoring quadratic equations.Get the intermediate step:
-3x² - 35x - 189 = 13x-3x² - 35x -13x- 189 = 0-3x² - 48x- 189 =0Divide the equation by 3 into both sides:
-x² - 16x- 63 = 0x² + 16x +63 = 0Adding 1 on both sides to complete the square:
x² + 16x +63 +1 = 1x² + 16x +64 = 1(x + 8)² = +1Therefore, (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.
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nancy had 209 dollars to spend on 6 of the most mundane books.after buying them she had 17 dollars. on average, how much did each book cost
The average cost of each book that Nancy got is $32
What is cost?Cost refer to the amount or value of a product. cost is usually valued in money hence one has to pay some money to h]]get the commodity of choice
In the question, the commodity is mundane books
How to solve how much each book costgiven that
Nancy had 209 dollars to spend
number of books = 6
amount remaining after buying = $17
The question can be represented mathematically as
6x + 17 = 209
where x is the cost of the each book
6x + 17 = 209
6x = 209 - 17
6x = 192
dividing through by 6
6x / 6 = 192 / 6
x = 32
hence each book costs $32
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What coordinates point can I plot in the graph? It can't be a decimals point, It has to be whole numbers because the graph doesn't let me put for example 4.86 or a fraction
First, we can start input small whole numbers in the function to see if we get a whole number. Let's try with 0, 1 and 2:
[tex]\begin{gathered} y=(\frac{1}{2})^{0+1}-9=\frac{1}{2}-9=-8.5 \\ . \\ y=(\frac{1}{2})^{1+1}-9=\frac{1}{4}-9=-8.75 \\ . \\ y=(\frac{1}{2})^{2+1}-9=\frac{1}{8}-9=-8.875 \end{gathered}[/tex]None of those values worked. Let's try negative integers, such as -1 and -2:
[tex]\begin{gathered} y=(\frac{1}{2})^{-1+1}-9=(\frac{1}{2})^0-9=1-9=-8 \\ . \\ y=(\frac{1}{2})^{-2+1}-9=(\frac{1}{2})^{-1}-9=2-9=-7 \end{gathered}[/tex]We get integer coordinates if we use negative integers. Then, we need at least 5 points. Let's use x = -1, -2, -3, -4, -5
[tex]\begin{gathered} y=(\frac{1}{2})^{-3+1}-9=(\frac{1}{2})^{-2}-9=2^2-9=4-9=-5 \\ . \\ y=(\frac{1}{2})^{-4+1}-9=(\frac{1}{2})^{-3}-9=2^3-9=8-9=-1 \\ . \\ y=(\frac{1}{2})^{-5+1}-9=(\frac{1}{2})^{-4}-9=2^4-9=16-9=7 \end{gathered}[/tex]We have the points:
(-1, -8), (-2, -7), (-3, -5), (-4, -1) and (-5, 7)
If we locate them in the cartesian plane:
And now, we can estimate the graph. An exponential function where the base is smaller than 1, describes an exponential decay, and the term "-9" is applying a shift 9 units down, and also y = -9 is a horizontal asymptote. With all this and the points we just found:
Factor completely.x^2−10x−24 Enter your answer in the box.
Given:
[tex]x^2-10x-24[/tex]To factorize:
It can be written as,
[tex]\begin{gathered} x^2-10x-24=x^2-12x+2x-24 \\ =x(x-12)+2(x-12) \\ =(x-12)(x+2) \end{gathered}[/tex]Therefore, the factorized form is,
[tex](x-12)(x+2)[/tex]how many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
The number of ways to plan her schedule of menus for the 20 school days is 10^20.
How to many number of ways to plan her schedule?To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.
For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.
The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.
How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
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The ratio of 1.4 to 26 is the same as the ratio of 2.8 to ____.
Marcus runs triathlons (races that involve running, biking, and swimming). To prepare for these triathlons, he follows a strategy of running twice as far as he swims and biking fours times as far as he runs. If he swims for 3 miles this week, what is the total distanch of his swimming, running and biking this week?
1) Gathering the data
Strategy:
Running : 2x As he swims
Biking: 4x Runs
Runs = 3 miles
Then
2) Runs = 3 miles Swims = 6 miles Biking = 12 miles
The Total distance will be the sum of those activities:
3+6+12=21 miles
a grocery store wonders if their sales will be better if they play ambient music or no music at all. each day for 222 months, the manager flips a coin to determine whether or not the store will play music that day. at the end of the 222 months, the manager finds that, on average, sales were significantly better on days where music was playing. what conclusion can they draw from this study?
Answer:
They should play music
Step-by-step explanation:
They should play music obviously because the sales were higher
Which linear inequality is represented by the graph?1. y>2/3x-22. y<2/3x+23. y
To identify the inequality of the given graph:
1. Identify the equation of the borderline in slope-intercept form (y=mx+b)
- Find the slope (m): Use two points in the line in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ Points\colon(-3,-3)and(3,1) \\ \\ m=\frac{1-(-3)}{3-(-3)}=\frac{1+3}{3+3}=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]- Identify the y-intercept (b): the value of y where the line cross the y-axis (when x is 0)
b= -1
Equation of the border line:
[tex]y=\frac{2}{3}x-1[/tex]2, Identifify the inequality sing:
-When the inequality is < or > the borderline is a dotted line
-When the inequality is ≥ or ≤ the border line is a full line
-When the inequality is < or ≤ the shaded area is under the borderline
-When the inequality is > or ≥ the shaded are is over the borderline
In this case you have a dotted borderline and a shaded area under the borderline, then, the inequality is:
[tex]y<\frac{2}{3}x-1[/tex]Use the given endpoint R and midpoint M of RS¯ to find the coordinates of the other endpoint S.
R(3, 0), M(0, 5)
Step-by-step explanation:
the midpoint coordinates between 2 points A and B are
((xa + xb)/2, (ya + yb)/2)
xa = 3
ya = 0
and so we get
(3 + xb)/2 = 0
3 + xb = 0
xb = -3
(0 + yb)/2 = 5
yb = 10
therefore, S = (-3, 10)
composite functions 65 points helpppppp
Answer:
[tex]4\sqrt{x+2} - 6[/tex]
Step-by-step explanation:
f(g(7)) = f(sqrt(x+2))
=4(sqrtx+2) - 6)
= [tex]4\sqrt{x+2} - 6[/tex]
Answer:
[tex](f \circ g)(7)=6[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=4x-6\\g(x)=\sqrt{x+2}\end{cases}[/tex]
(f o g)(x) is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function (f o g)(7) means to substitute the function g(x) when x=7 in place of the x in function f(x).
[tex]\begin{aligned}\implies (f \circ g)(7)&=f[g(7)]\\& = f(\sqrt{7+2})\\&=f(\sqrt{9})\\&=f(3)\\&=4(3)-6\\&=12-6\\&=6\end{aligned}[/tex]
A class consists of 10 boys and 20 girls. Exactly half of the boys and half of the girls have brown eyes. Determine the probability that a randomly selected student will be a boy or a student with brown eyes.
Answer:
Step-by-step explanation:
30 students 15 have brown eyes 5 of the 15 are boys
1/3 chance a boy with brown eyes will be chosen.
1/2 a chance a student with brown eyes will be chosen
A state agency recorded the number of each type of flood that occurred in the state from 2016–2020. The results are as follows. If similar proportions of flood types are predicted for the following year, what is the estimated probability that a flood in 2021 in that state will be a river flood? Round your answer to the nearest percent. A. 7%B. 60%C. 20%
The table shows different flood types and their frequencies.
Total frequency of all flood types = 18 + 6 + 4 + 2 = 30
frequency of river flood = 6
Recall, probability is expressed as
number of favorable outcomes/number of total outcomes
Thus, the estimated probability that a flood in 2021 in that state will be a river flood is
6/30 = 0.2
By changing 0.2 to percentage, we have
0.2 x 100 = 20%
The correct option is C. 20%
Please help *100 POINTS*
New Orleans is 2 feet under seas level.
Salton City has a elevation lower than New Orleans.
What is a possible elevation, in feet of Salton City
With explanation please
The given elevation of New Orleans of 2 feet below sea level gives the possible elevation of Salton City by using a number line, as 3 feet below sea level.
What is a number line?A number line pictorially presents the set of real numbers, showing their position in order of their magnitude, such that the numbers increases positively as we move from left to right with negative numbers increasing from the zero mark as we move further left.
The given elevation of New Orleans with reference to the sea level = 2 feet below (lower than) sea level
The elevation of Salton City = Lower than the elevation of New Orleans
Required; The possible elevation of Salton City
The elevation of Salton City can be found by presenting the given information on a number line as follows;
Let SL represent the sea level, let N represent New Orleans and let S represent Salton City, we have;
<___|-3______|-2____|0______>
' S. N. SL
A level higher than the elevation of New Orleans is given by a point to the right of the -2 mark on the above number line, while an elevation lower than that of New Orleans is given by a point to the left of -2 on the number line. The location of Salton City should therefore be to the left of -2, which is a point, x < -2 feet
The elevation of Salton City is less than 2 feet below sea level, which is given by the set x < -2 feet
-3 feet is less than -2 feet, therefore, a possible elevation in feet of Salton City is x = 3 feet below sea level, which is less than (<) 2 feet below sea level
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need help on this, thanks
The value of question are 65+[tex]\underline{115}[/tex]=180, [tex]11x+\underline{48}=180^o[/tex], [tex]11x=\underline{132}[/tex] and [tex]x=\underline{12}[/tex].
In the given question we have to find the value of missing term.
(1) 65+......=180
(2) 11x+.......=180
(3) 11x=.........
(4) x=........
To solve this question we have to use some theorem.
Firstly solving the first question.
As we know that the angle of straight line is 180[tex]^o.[/tex]
So from the diagram
[tex]65+z=180^o[/tex]
Subtract 65 on both side
[tex]65+z-65=180^o-65[/tex]
[tex]z=115[/tex]
Hence, 65+[tex]\underline{115}[/tex]=180.
Now finding the value of second question.
Using Alternate Exterior Angles Theorem
According to theorem the angle beside 11x - 17 is 65.
As we know that the angle of straight line is 180[tex]^o.[/tex]
So 11x-17+65=180[tex]^o.[/tex]
Simplifying
So [tex]11x+\underline{48}=180^o[/tex]
Now finding the value of third question.
From the second question answer we get [tex]11x+{48}=180^o[/tex]
Now solving this equation to find the value of 11x
Subtract 48 on both side
[tex]11x+{48}-48=180^o-48[/tex]
[tex]11x=132[/tex]
Hence, [tex]11x=\underline{132}[/tex]
Now solving the fourth question.
To find the value of fourth question we further simplify the answer of third question.
[tex]11x=132[/tex]
Divide by 11 on both side
[tex]\frac{11}{11}x=\frac{132}{11}[/tex]
[tex]x=12[/tex]
Hence, [tex]x=\underline{12}[/tex]
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Find the slope of the line that passes through (64, 94) and (48, -3).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the points has a value of 97/16
How to determine the slope of the points?From the question, the line passes through the following points
(64, 94) and (48, -3).
The slope of the line that passes through the points is then calculated using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are the coordinates above
Substitute the known values in the above equation
So, we have the following equation
Slope = (94 + 3)/(64 - 48)
Evaluate the difference and the sum
Slope = 97/16
Hence, the slope is 97/16
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Select the two values of x that are roots of this equation.3x² + 1 = 5xA. x =5+√13x = 5+√136☐ B. x =5-√136□ C. x=-1-√59X6D. X =-1+√596
3x^2 + 1 = 5x
3x^2 - 5x + 1 = 0
quadratic formula
[tex]x=-\frac{b\pm\sqrt{b^2-4ac}}{2a}[/tex]where ax^2 + bx + c = 0
so
[tex]x=\frac{5\pm\sqrt{-5^2-4(3)(1)}}{2(3)}[/tex][tex]x=\frac{5\pm\sqrt{25-12}}{6}[/tex]You can see that the 25 - 12 = 13 so the answers are A and B
∠A and \angle B∠B are complementary angles. If \text{m}\angle A=(6x+2)^{\circ}m∠A=(6x+2)
∘
and \text{m}\angle B=(4x+18)^{\circ}m∠B=(4x+18)
∘
, then find the measure of \angle A∠A.
The measure of ∠ A is 44 degrees.
Given that:-
∠ A and ∠ B are complementary angles.
∠ A = (6x +2) degrees
∠ B = (4x + 18) degrees
We have to find the measure of ∠ A.
We know that the sum of two complementary angles is 90 degrees.
Hence, we can write,
(6x + 2) + (4x + 18) = 90
(6x + 4x) + (2 + 18) = 90
10x + 20 = 90
10x = 90 - 20
10x = 70
x = 70/10
x = 7 degrees
Hence,
∠ A = 6*7 + 2 = 42 +2 = 44 degrees.
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PLEASE HELP ASAP!!!!!!!!!!!!! WITH STEPS PLEASEEEEEE!!!!!!!!!!!!!
Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
Step-by-step explanation:
This should be the right solution.
A construction crew has just built a new road. They built the road at a rate of 18.75 kilometers per week. They worked for 3 weeks. How many kilometers of road did they build?
Answer:
6.25 weeks
Step-by-step explanation:
Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.
Which lines are perpendicular to 3x – y = 10? Select all that apply. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
What is the equation of a perpendicular line?Let the equation of the line be y = ma + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx +c is given as y = -(1/m)x + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
3x – y = 10
y = 3x – 10
Then the equation of the perpendicular line is given as,
y = –(1/3)x + d
The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
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The latest crime statistics in the united states suggest that eighteen-to-twenty-four-year-olds make up about – percent of the population but account for – percent of criminal arrests, while people sixty-five and older make up more than – percent of the population but account for less than – percent of arrests
Using concepts of statistics, we got 7% people are from age 18-24,and 15% for criminal arrests,65 and older are in 13% population and cover less than 1% crime rate.
The topic of crime in the United States is very large, technically covering any action that is punishable under a state or federal law. Any analysis of the topic requires division into further sub-categories. One common way to do this is by limiting analysis to crimes involving jail time (i.e. misdemeanors and felonies, which generally differ via the length of jail time involved), then differentiate between violent crimes or property crimes. Violent crimes are described as offenses which involve force or the threat of force, while property crime majorly includes offences involving the taking of money or property, but where there is not any force or threat of force against the victims. Property crimes are outnumbering violent crimes in the U.S. in 2020, numbering 6.45 million and 1.31 million respectively. Larceny was the actually most common property crime with 4.6 million incidents, while the aggravated assaults accounted for around two thirds of violent crimes.
Hence, percentage of people whose age is in between 18-24 is 7%,
people from age 18-24 engaged in illegal work=15%,
percentage of people whose age is 65 or more than =13%,
people involved in crime having age more than or equal to 65=1%
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