5x+3 is greater than or equal to x-9
The solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3
How to determine the inequality solution?The statement is given as:
5x+3 is greater than or equal to x-9
Express as an inequality
5x + 3 >= x - 9
Collect the like terms
5x - x >= -9 - 3
Evaluate the like terms
4x > = -12
Divide both sides by 4
x >= -3
Hence, the solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3
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a national survey conducted among a simple random sample of 1,507 adults shows that 56% of americans think the civil war is still relevant to american politics and political life.
a)
[tex]z=4.658\\p_v=P(z > 4.65)=1-P(z < 4.65)=1.581x*10^{-6}[/tex]
b) By assuming a significance level of α = 0.05 and observing that [tex]p_v[/tex] > α, we can reject the null hypothesis at this level of significance. And in this instance, it makes sense that more than 50% of Americans believe that the Civil War still has an impact on American politics and political life.
c) The confidence interval at 90% would be shown (0.527;0.593).
About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.
What is a survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.
a)
1) The presented data and the notation "n=1507" refer to the random sample of Americans, "X" denoting the proportion of those Americans in the sample who believe that the Civil War is still significant to American politics and political life, and "p cap" denoting the estimated number of those Americans.
Since the problem specifies that majority α=0.05 represents the significance threshold, [tex]p_0[/tex] is the number that we wish to test (no given, but is assumed)
Z would stand for the statistic (interesting variable), and [tex]p_v[/tex] for the p value (variable of interest)
P is the percentage of the public that believes that the Civil War still has an impact on American politics and political life.
2) Useful concepts and formulas
The allegation that more Americans than 50% believe the Civil War is still significant to American politics and political life needs to be tested through a hypothesis (Majority). :
Alternative Hypothesis: p[tex]\geq[/tex] 0.5
Null Hypothesis: p[tex]\leq[/tex] 0.5
The proportion is thought to have a normal distribution.
This test for the percentage of union membership has one tail higher.
Verify whether the sample conforms to the presumptions required for the test to be applied.
a) The random sample must be representative; in this situation, there is no mention of this issue, but it is safe to presume that it exists.
b) The sample size must be sufficient.
[tex]np_0=1507*0.5=753.5 > 10\\n(1-p_0)=1507*(1-0.5)=753.5 > 10[/tex]
3. Determine the statistic.
The formula used to calculate the statistic is as follows:
[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }= \frac{0.56-0.5}{\sqrt{\frac{0.5(1-0.5)}{1507} } }=4.658[/tex]
P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]
According to the alternative hypothesis, the following would be the p value:
P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]
Using this formula, the confidence interval would be determined.
p ± [tex]z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n} }[/tex]
With the value of [tex]\alpha[/tex] and [tex]\alpha _2[/tex], we can get the quantile necessary for the interval in the normal standard distribution for the 90% confidence interval.
[tex]z_{\frac{\alpha }{2} }=2.58[/tex]
adding the following to the formula for the confidence interval:
[tex]0.56-2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.527\\0.56+2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.593[/tex]
Also provided would be the 90% confidence interval (0.527;0.593).
About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.
And because the interval does not contain the value of 0.5, we can conclude that, at a 90% level of confidence, the percentage of Americans who believe that the Civil War is still relevant to American politics and political life is higher than 0.5. This result is consistent with the result of part b.
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Which additional fact is needed to prove by Side-Angle-Side (SAS)?
The information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.
How to Apply the Side-Angle-Side (SAS)?The Side-Angle-Side (SAS) is a triangle congruence theorem that is used to prove that two triangles are congruent to each other if they have two pairs of corresponding congruent sides and a pair of included congruent angles.
The diagram given gives us the following information:
A pair of congruent sides - BD ≅ BD
A pair of congruent angles - <ADB ≅ CDB.
Thus, the information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.
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I need help with this question.
The question is (if you cant see the picture well) :
ANALYZE Determine whether the statement is sometimes, always, or never true. Justify your argument using a counterexample or proof.
In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex.
The statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true
How to determine whether the statement is sometimes, always, or never true?The statement is given as:
In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex.
As a general rule;
If any two angles are congruent in a triangle, then it means that the sides that opposite the two congruent angles are congruent sides.
The above is an illustration of the base angle theorem
The base angle theorem goes hand-in-hand with the isosceles triangle theorem which is illustrated by the given statement
Hence, the statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true
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the sum of four numbers is 1,764. oneof the numbers, n, is 40% more than the sum of the other three numbers. what is the value of n?
Four numbers has a sum of 1764 and the value of one of those numbers is 1029.
Use algebraic expressions to solve for the value of n.
Algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc).
One of the four numbers is already denoted as variable n. Let m be the sum of the three other numbers.
If the sum of the four numbers is 1,764, then:
n + m = 1764
If n is 40% more than the sum of the other three numbers, then:
n = 40% m + m
n = 1.4 m
Substitute n from the 2nd equation to the 1st equation.
n + m = 1764
1.4 m + m = 1764
2.4 m = 1764
m = 735
Recall that n = 1.4 m.
n = 1.4 (735)
n = 1029
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Please help soon!!
Asap!
Answer: FIRST ONE IS -1/7
The second one is 1
Step-by-step explanation:
Find the value of x.
S
34°
X =
W
U
S
V
(x + 6)°
(3x - 2)°
How is FE₂ different from FE2O3?
Please someone help me, anyone?!!
Answer:
Fe2 is elemental iron and Fe2O3 is a compound
Answer:
Step-by-step explanation:
Fe2 is elemental iron and Fe2O3 is a compound of iron and oxygen.
find the ordered pairs marked on the graph
The ordered pairs of the given graph are;
(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)
What are the Ordered Pairs?An ordered pair is defined as a composition of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses.
Ordered Pair = (x, y)
Where;
x = abscissa, the distance measure of a point from the primary axis “x”
y = ordinate, the distance measure of a point from the secondary axis “y”
Thus the ordered pairs of the given graph are;
(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)
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7 Complete each statement about multiplying positive
and negative integers using the word positive or
negative. For each statement, provide an example.
positive positive = positive
positive negative =
negative negative =
PLS HELP
a sequence is determined by f (n) = -4 +2n for n > 1. which of the following statements is the recursive definition of f?
f(1)=-2, f(n)=f(n-1)+2 for n>2
f(1)=-4, f(n)=f(n-1)++2n for n>2
f(1)=-2, f(n)=f(n-1)+(-4) for n>2
f(1)=-4, f(n)=f(n-1)+2 for n >2
The statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2 for n > 2
How to determine which of the following statements is the recursive definition of f?The function definition is given as
f(n) = -4 +2n for n > 1
Start by calculating f(2), f(3) and f(4)
So, we have
f(2) = -4 +2(2)
f(2) = 0
f(3) = -4 +2(3)
f(3) = 2
f(4) = -4 +2(4)
f(4) = 4
In the above computation, we can see that the sequence is an arithmetic sequence with a common difference of 2
So, we have
f(n) = f(n - 1) + 2
Also, we have
f(1) = -4 +2(1)
f(1) = -2
Hence, the statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2 for n > 2
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ason works on commission and earns $30 for each computer he sells. The store's manager, Sandra, earns a base salary of $1200 a
month plus $15 for each computer she sells. Let J represent Jason's earnings and let S represent Sandra's earnings for selling c
number of computers. Which system best represents this situation?
Answer:
30J + 15S = $1,200
Step-by-step explanation:
Since Jason earns $30 per computer and Sandra earns $15 per computer therefore the equation will be written as $30J + $15S = base salary per month.
30J + 15S = $1,200
the area of a rectangle is (x3 – 5x2 3x – 15), and the width of the rectangle is (x2 3). if area
The length of rectangle is (x - 5).
We are given-
Area of rectangle = [tex]x^{3} - 5x^{2} + 3x - 15[/tex]
Width of rectangle = [tex]x^{2} + 3[/tex]
Using the formula, the length will be calculated by rewriting the formula as -
Length = Area/width
Keep the values in formula to find the length of rectangle.
Length = [tex]\frac{x^{3} - 5x^{2} + 3x - 15}{x^{2} + 3}[/tex]
In numerator, separating the common values and rewriting the equation -
Length = [tex]\frac{x^{2} (x - 5) +3 (x - 5)}{x^{2} + 3}[/tex]
Rewriting the equation to for ease of solving to find the length of rectangle -
Length = [tex]\frac{(x^{2} +3)(x - 5)}{(x^{2} +3)}[/tex]
Cancelling [tex](x^{2} + 3)[/tex] as it is common in both numerator and denominator. Now, we will get the value of length of rectangle.
Length = (x - 5)
Hence, the length of rectangle is (x - 5).
The complete question is -
The area of a rectangle is [tex]x^{3} - 5x^{2} + 3x - 15[/tex], and the width of the rectangle is [tex]x^{2} + 3[/tex]. If area = length × width, what is the length of the rectangle? x + 5 x – 15 x + 15 x – 5
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On the double number line, 3 minutes corresponds to 180 beats.
0 ? 120 180 240 300
Beats:
Minutes:
0 1
2
3
4
5
How many beats are there in 3 minutes? Type your answer as a number.
what equation is equivalent to 4^x+3=64
Answer:
Step-by-step explanation:
Answer: x=64/7 Step-by-step explanation: 4x+3=64 7x=64
4x=−64
Divide both sides by 4.
x=
4
−64
Divide −64 by 4 to get −16.
x=−16
Calculate the volume of this regular solid.
Intro
8 cm
What is the volume of
TL
Round at the end to the nearest tenth.
cm³
Done
The volume of the sphere is 2144.7cm³.
Given that a sphere with radius 8 cm.
As we all know that the volume of sphere is 4/3πr³.
We will find the volume of sphere by substituting the value of radius in the formula, we get
Volume=4/3 πr³
Now, we will substitute r=8 cm in above formula, we get
V=(4/3)π(8 cm)³
V=(4/3)π(512)cm³
Now, we will simplify this by multiply by 4, we get
V=(2048/3)πcm³
Now, we will simplify it by dividing it with 3, we get
V=682.66π cm³.
As we know, the value of π is 3.14.
So, we will substitute this value and simplify it, we get
V=682.66×3.14
V=2144.66 cm³
Hence, the volume of the sphere when the radius is 8cm is 2144.7 cm³.
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6) the circular base of a hemisphere of radius 2 rests on the base of a square pyramid of height 6. the hemisphere is tangent to the other four faces of the pyram
The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A
What is hemisphere?
Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.
EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.
Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.
OM/2 = 6/EP
OM = 6/EP x 2
OM = [tex]6\sqrt{6^2 - 2^2} x 2 = 3\sqrt{2}/2}[/tex]
The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A
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show that cos 30 + 2 tan 60 can be written in the form k where k is an integer
Answer:
k = 4.33
Step-by-step explanation:
Cos 30 = 0.8660
Tan 60 = 1.732
2 Tan 60 = 2 (Tan 60)
2 Tan 60 = 2 (1.732)
2 Tan 60 = 3.464
Cos 30 + Tan 60 = 0.8660 + 3.464 = 4.33
k = 4.33
consider an infinite set of pairwise independent random variables which are uniformly distributed between 0 and 1. what's the expected number that you need to add to get a number that exceeds 1.
When two random variables X and Y are considered to be independent, it means that neither X's distribution nor Y's values have any bearing on the other.
What do you mean by independent random variable?A random variable is a variable used in an experiment, such as the number of coin tosses or card draws. An independent random variable is a random variable in your experiment that doesn't affect the other random variables. In other words, it has no impact on the likelihood that another event will occur. For illustration, suppose you randomly selected 50 bags of sugar from various grocery stores in order to determine the average weight of a bag of sugar. The factors are independent since you wouldn't anticipate the weight of one bag having an impact on another. A dependent random variable, on the other hand, does have an impact on the probability of other random variables.
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What is the value of x in this figure? Enter your answer in the box. hexagon
Draw this Venn diagram. Classify the following numbers. 45, 24, 52, 30, 66, 15, 85, 90, 72, 60, 20, 38 What can you tell about the numbers in the intersection?
PLEASE HELP I NEED ANSWER PLSS I OFFER 45 POINTS
Answer:
put 244 add 7e8ue
Step-by-step explanation:
i53838 divede 73838
I'm really confused by this; can someone help me?
Write the biconditional statement using the information given in the statement below.
"If a shape is an octagon, then it has 8 sides"
(01.06 mc) craig has 72 feet of material to build a fence around a rectangular flower bed on his property. if the width of the fence must be 3 feet, w
The fence is 33 feet long when measured in yards.
Here,
In order to erect a fence around a rectangular flower garden on his property, Craig has 72 feet of material.
If the fence must be 3 feet in width, then, assuming he uses the entire 72 feet of material, we must determine the fence's length in yards.
What is the rectangle's perimeter?
The rectangle's perimeter is 2 (l + b). l being the length. b=breadth (width).
Now,
A rectangular flower bed should be x feet long.
(Length + Width)2 = the perimeter of a rectangular flowerbed.
72 = 2 (x + 3)
36 = x + 3
x = 33 feet
Hence, The fence is 33 feet long when measured in yards.
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Find the principal (positivt) square root of 16. If necessary, round the answer
to the nearest hundredth (two decimal places).
Question 3 (3 points) Determine the smallest integer that makes 4x - 9 - 2x < 5x + 1 true
a 4
b 3
c 2
d 1
Answer:
d:1
Step-by-step explanation:
the answers will always be negative and the other side will always be positive
let f left parenthesis x right parenthesis equals x cubed minus x squared minus 1and x subscript 0 equals 1. to the nearest three decimal places, find x subscript 5using newton's method of approximation.
x(5) is approximately equal to 1.466.
Newton's method, additionally referred to as the Newton-Raphson method, is enormous due to the fact it's far an iterative approach which could appropriately estimate answers to equations. And it's a way for estimating numerical answers (inclusive of x-intercepts, zeros, or roots) to equations which can be too difficult to solve by means of hand.The aim is initially an preliminary guess this is extraordinarily near the real root (answer) after which utilise the tangent line to locate any other x-intercept that is even better than our first wager.An approximation is anything this is supposed to be comparable but not precisely equal to anything else.To learn more about approximation, visit :
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write an equivalent expression for 2*14 / 2*2
Answer:
Step-by-step explanation:
if * means multiplication
the equivalent expression will be :
[tex]\frac{2.14}{2.2} = \frac{7}{7} = 7[/tex]
If the * means power :
then equivalent expression will be
[tex]\frac{2^{14} }{2^{2} } = 2^{(14-2)} =2^{12}[/tex]
2x + 3x = -25
Ingrese su respuesta
Step-by-step explanation:
2x + 3x = -25
5x = -25
x = -25 / 5
x = -5
Joshua moved 5 lawns in 4 hours fill out a table if equivalent ratios
Answer:
(25,20) , (45,36)
Step-by-step explanation:
I THINK??
PLEASE HELP
find the value of x
Answer: an acute angle so it bout 55
Step-by-step explanation: